url
stringlengths 14
1.76k
| text
stringlengths 100
1.02M
| metadata
stringlengths 1.06k
1.1k
|
|---|---|---|
https://wordpandit.com/number-system-level-2-test-11/ | Select Page
• This is an assessment test.
• To draw maximum benefit, study the concepts for the topic concerned.
• Kindly take the tests in this series with a pre-defined schedule.
## Number System: Level 2 Test -11
Congratulations - you have completed Number System: Level 2 Test -11.You scored %%SCORE%% out of %%TOTAL%%.You correct answer percentage: %%PERCENTAGE%% .Your performance has been rated as %%RATING%%
Question 1
When a number is divided by 2, 3, 4, 5 or 6, remainder in each case is 1. But the number is exactly divisible by 7. If the number lies between 250 and 350, the sum of digits of the number will be
A 4 B 5 C 7 D 10
Question 1 Explanation:
The LCM of 2,3,4,5,6 is 60.
The required number is 60*5+1 = 301
which is divisible by 7.
Thus the sum of the digits is 3+1=4.
Correct option is (a)
Question 2
HCF of two numbers each of 4 digits is 103 and their LCM is 19261. Sum of the numbers is
A 2884 B 2488 C 4288 D 4882
Question 2 Explanation:
Since both are 4 digits then the LCM will be of form 103pq
where p and q have almost equal number of digits
and the numbers are 103x and 103y. pq= 187 = 11x17
Thus the two numbers are 103x11 and 103x17
The sum will be 103x(11+17) = 103x28
Correct option is (a)
Question 3
A classroom has equal number of boys and girls. Eight girls left to play Kho-Kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?
A Cannot be determined B 16 C 24 D 32
Question 3 Explanation:
Let the no. of boys and girls each be x.
& 2x-16=x \\ & x=16 \\ \end{align}\]
Therefore total no. of boys and girls present initially in the classroom = 2x= 32
Question 4
The sum of four numbers is 64. lf you add 3 to the first number, 3 is subtracted from the second number, the third is multiplied by 3 and the fourth is divided by three, then all the results are equal. What is the difference between the largest and the smallest of the original numbers?
A 32 B 27 C 21 D Cannot be determined
Question 4 Explanation:
Let the 4 numbers be a,b,c,d.
a+b+c+d=64
a+3=b-3=3c=d/3=k(say)
Thus,
$\begin{array}{l}k-3+k+3+\frac{k}{3}+3k=64\\=>k=12\end{array}$
Thus the numbers are 15,9,4,36.
Thus the difference = 36-4=32.
Question 5
If the digits of a two digit number are interchanged the newly formed number is more than the original number by 18, and sum of the digit is 8 then what was the original number?
A 53 B 26 C 35 D Cannot be determined
Question 5 Explanation:
Let the number be of form 10x+y.
x-y=18/9=2.
x+y=8
Solving we get,
x=5 and y=3.
The original number is 35.
Correct option is (c)
Once you are finished, click the button below. Any items you have not completed will be marked incorrect.
There are 5 questions to complete.
← List → | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7179340720176697, "perplexity": 870.3048179695709}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806939.98/warc/CC-MAIN-20171123195711-20171123215711-00322.warc.gz"} |
https://blog.feedly.com/secrets-of-success/ | # Secrets of success
Here is an interesting 3-minute presentation of Richard St. John at TED on how to increase your chances to be successful. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9160885214805603, "perplexity": 2908.015130794514}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500151.93/warc/CC-MAIN-20230204173912-20230204203912-00099.warc.gz"} |
https://socratic.org/questions/what-is-the-square-root-of-62-5 | Algebra
Topics
# What is the square root of -62.5?
Therefore, in Algebra, the solution is the empty or null set: $\left\{\emptyset\right\}$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 1, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8716484308242798, "perplexity": 698.2778597725098}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496665985.40/warc/CC-MAIN-20191113035916-20191113063916-00230.warc.gz"} |
https://portlandpress.com/clinsci/article-abstract/53/3/241/72200/A-Reappraisal-of-Osmotic-Evidence-for-Intact | 1. The validity of evidence for intact peptide absorption, derived from analysis of the relation of water and total solute absorption, has been tested.
2. Solute and water absorption from saline solutions of the disaccharide maltose have been studied in the normal human jejunum, using a double-lumen perfusion technique with a proximal occlusive balloon. It was expected that maltose would yield very different results from peptides, because maltose is virtually completely hydrolysed before absorption, whereas a proportion at least of some peptides is transported into the intestinal mucosal cells before hydrolysis. This expectation was not confirmed by experiment.
3. The assumption that the absorbate is always isotonic with plasma has been tested by altering the osmolality of glucose/saline solutions perfused in the jejunal lumen. This assumption was not substantiated by experiment, as when the luminal fluid was hypertonic to plasma, so was the absorbate.
4. It is suggested that our findings with peptides and saccharides could be explained by the production of a hypertonic absorbate by hydrolysis of these solutes to their monomer units. We therefore conclude that analyses of the relation of net solute and water absorption cannot be used to predict the form in which peptides enter the mucosal cells.
This content is only available as a PDF.
You do not currently have access to this content. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.906323254108429, "perplexity": 3547.1651524816853}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370505826.39/warc/CC-MAIN-20200401161832-20200401191832-00241.warc.gz"} |
https://mathoverflow.net/questions/194181/on-certain-representations-of-algebraic-numbers-in-terms-of-trigonometric-functi | # On certain representations of algebraic numbers in terms of trigonometric functions
Let's say that a real number has a simple trigonometric representation, if it can be represented as a product of zero or more rational powers of positive integers and zero or more (positive or negative) integer powers of $\sin(\cdot)$ at rational multiples of $\pi$ (the number of terms in the product is assumed to be finite, the empty product is taken to be $1$).
Examples:
• $\sqrt[3]{\sin\!\left(\frac\pi3\right)}$ has a simple trigonometric representation, because $\sqrt[3]{\sin\!\left(\frac\pi3\right)}=\frac{3^{1/6}}{2^{1/3}}$.
• $\sqrt{\sin\!\left(\frac\pi{10}\right)}$ has a simple trigonometric representation, because $\sqrt{\sin\!\left(\frac\pi{10}\right)}=\frac{2^{1/2}}{5^{1/4}}\,\sin\!\left(\frac\pi5\right)$.
• $\pi$ does not have a simple trigonometric representation, because it is not an algebraic number.
Questions:
• Do $\sqrt{\sin\!\left(\frac\pi5\right)},$ $\sqrt{\sin\!\left(\frac\pi8\right)},$ $\sqrt{\sin\!\left(\frac\pi{12}\right)},$ $\sqrt{\sin\!\left(\frac\pi{15}\right)},$ $\sqrt{\sin\!\left(\frac\pi{20}\right)},$ $\sqrt{\sin\!\left(\frac\pi{24}\right)}$ have simple trigonometric representations?
• Is there an algorithm that, given a rational power of $\sin(\cdot)$ at a rational multiple of $\pi$, would determine if it has a simple trigonometric representation? If so, could you give (or outline) a concrete example of such an algorithm (efficient, if possible)?
• More generally, is there an algorithm that, given a real algebraic number (in some explicit form, e.g. as its minimal polynomial and a rational isolating interval), would determine if it has a simple trigonometric representation? If so, could you give (or outline) a concrete example of such an algorithm (efficient, if possible)? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9774656295776367, "perplexity": 167.13980737741105}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145316.8/warc/CC-MAIN-20200220224059-20200221014059-00247.warc.gz"} |
https://www.ias.ac.in/listing/bibliography/boms/A_K_Sinha | • A K Sinha
Articles written in Bulletin of Materials Science
• Surface alloying of pure iron by molybdenum and tin by a continuous wave CO2 laser
It is now well established that considerable improvement in the mechanical/chemical properties of near surface regions of materials can be achieved by the process of laser surface alloying. The change in chemistry at the surface is attained through the process of melting and mixing of a predeposited coating and a thin layer of the substrate. Rapid solidification of this molten region at the surface then results in the development of very interesting microstructural features. In the present work, an attempt was made to surface alloy pure iron by molybdenum and/or tin by using a continuous wave CO2 laser. Morphology of the resulting microstructural features was examined by optical as well as scanning electron microscopy and the compositional details were determined using an electron probe microanalyser. Microhardness measurements were carried out as a function of depth from the laser-treated surface. This paper discusses the results of these investigations and delineates the roles of the various parameters on the chemistry and microstructure of the surface alloys formed as a result of laser treatment.
• Micro hardness measurements on lead silicate glass
The synthesis of lead silicate glass suitable for fabrication of compression type glass to metal seals has been studied with varying amounts of modifier ions (Na, K and Ba). A three-stage heating schedule was evolved for the preparation of glass. While, some of the constituents were taken in the form of oxides, the others were either in the form of carbonates or nitrates. Dependence of micro hardness of these glasses on the relative content of Na2O, K2O and BaO was investigated. The concentration of these oxides was varied in the range 0–16 wt%. The modifier ions were seen to affect the micro hardness in a combplex manner. While the micro hardness of glass without Na2O and 13 wt% K2O was found to be 504 kg/mm2, it turned out to be 547 kg/mm2 for a glass with 13 wt% of Na2O in the absence of K2O. However, the micro hardness of the glass synthesized having optimum composition with oxides of Na, K and Ba in the proportion of 5, 8 and 4 wt%, respectively was 455 kg/mm2. The glass powder was found to be suitable for making single- and multi-pin seals which could withstand pressures up to 1·2×104 psi and vacuum of 10−8 Torr.
• Structural studies of Nd$_{1.85}$Ce$_{0.15}$CuO$_{4}$ $+$ Ag superconducting system
We have studied for the first time the effect of Ag addition (0–15 wt%) to the superconducting system, Nd$_{1.85}$Ce$_{0.15}$CuO$_{4}$, on its crystal structure and local structural features, using synchrotron X-ray diffraction(SXRD) and Raman spectroscopy, respectively. SXRD and subsequent Rietveld refinement studies on powders of Nd$_{1.85}$Ce$_{0.15}$CuO$_4$ $+$ Ag system indicate a small but significant change in lattice parameter upon Ag addition, showing evidence for possible incorporation of Ag to the extent of $\sim$1 wt%. Raman spectroscopic studies indicate that the parent structure of Nd$_{1.85}$Ce$_{0.15}CuO$_{4}$remains unaffected with no major local structural changes on doping with silver. However, all Raman modes show minor phonon hardening upon Ag addition, which is consistent with the unit cell volume reduction as is observed in XRD. A systematic bleaching out of the apical oxygen defect mode was also observed with increased Ag addition. Polarized Raman measurements helped to identify the asymmetric nature of the B1g Raman mode. X-ray diffraction studies on pellets of Nd$_{1.85}$Ce$_{0.15}CuO$_4$ $+$ Ag system further indicate a randomization of preferred orientation upon Ag addition. The superconductivity of the Nd$_{1.85}$Ce$_{0.15}$CuO$_4$ $+$ Ag system has been well characterized for all the compositions studied.
• # Bulletin of Materials Science
Volume 45, 2022
All articles
Continuous Article Publishing mode
• # Dr Shanti Swarup Bhatnagar for Science and Technology
Posted on October 12, 2020
Prof. Subi Jacob George — Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bengaluru
Chemical Sciences 2020 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7460188865661621, "perplexity": 3402.973890753724}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571234.82/warc/CC-MAIN-20220811042804-20220811072804-00461.warc.gz"} |
http://medcraveonline.com/JPNC/clinical-and-epidemiological-characteristics-of-functional-neurological-disorders-in-children-and-adolescents-treated-in-the-child-psychiatry-department-of-casablanca.html | # Pediatrics & Neonatal Care
Research Article Volume 12 Issue 3
# Clinical and epidemiological characteristics of functional neurological disorders in children and adolescents treated in the child psychiatry department of Casablanca
#### Linda Rachidi ,1,2 function clickButton(){ var name=document.getElementById('name').value; var descr=document.getElementById('descr').value; var unCopyslNo=document.getElementById('unCopyslNo').value; document.getElementById("mydiv").style.display = "none"; $.ajax({ type:"post", url:"https://medcraveonline.com/captchaCode/server_action", data: { 'name' :name, 'descr' :descr, 'unCopyslNo': unCopyslNo }, cache:false, success: function (html) { //alert('Data Send');$('#msg').html(html); } }); return false; } Verify Captcha × Regret for the inconvenience: we are taking measures to prevent fraudulent form submissions by extractors and page crawlers. Please type the correct Captcha word to see email ID. function refreshPage(){ $("#mydiv").load(location.href + " #mydiv"); }$(document).ready(function () { //Disable cut copy paste $('#msg').bind('cut copy paste', function (e) { e.preventDefault(); }); //Disable mouse right click$("#msg").on("contextmenu",function(e){ return false; }); }); .noselect { -webkit-touch-callout: none; /* iOS Safari */ -webkit-user-select: none; /* Safari */ -khtml-user-select: none; /* Konqueror HTML */ -moz-user-select: none; /* Firefox */ -ms-user-select: none; /* Internet Explorer/Edge */ user-select: none; /* Non-prefixed version, currently supported by Chrome and Opera */ cursor: none; } Asmaa Faiki ,1 Manal El Allam ,1 Wafae Jbilou ,1 Youssra Asbai ,1 Wafaa Bannit ,1 Samy Housbane ,3 Imane Chahid ,4 Ghizlane Benjelloun 1,2
1Department of Child and Adolescent Psychiatry, Mother & Children’s Hospital Abderrahim Harouchi, University Hospital Ibn Rochd, Morocco
2Clinical Neuroscience and Mental Health Laboratory, Faculty of Medicine and Pharmacy Casablanca, University of Hassan II Casablanca, Morocco
3Medical informatics department, Faculty of Medicine and Pharmacy Casablanca, Morocco
4Department of Pediatrics 3, Neuropediatric Unit, Mother & Children’s Hospital Abderrahim Harouchi, University Hospital Ibn Rochd-Casablanca, Morocco
Correspondence: Professor L Rachidi, Department of Child and Adolescent Psychiatry, Mother & Children’s Hospital Abderrahim Harouchi, University Hospital Ibn Rochd, Casablanca, Morocco, Tel +212661313720
Received: November 14, 2022 | Published: November 28, 2022
Citation: Rachidi L, Faiki A, Allam ME, et al. Clinical and epidemiological characteristics of functional neurological disorders in children and adolescents treated in the child psychiatry department of Casablanca. J Pediatr Neonatal Care. 2022;12(3):182-186. DOI: 10.15406/jpnc.2022.12.00477
# Abstract
Objectives: Functional neurological disorders (FNDs) are a common source of disability in medicine. Patients have often been misdiagnosed, correctly diagnosed after long delays, and/or subjected to misdiagnoses that lead to inadequate treatments, unnecessary costly evaluations, and poor outcomes.
We sought to identify the epidemiological and clinical characteristics of children and adolescents suffering from functional neurological disorders in the child and adolescent psychiatry department in CASABLANCA.
Methods: We conducted a retrospective study of 52 children and adolescents admitted for functional neurological disorders from March 2019 to July 2021, and analyzed their clinical profiles, sociocultural, environmental and psychological characteristics.
Results: In our study, nearly the threatening quarters of the patients were girls, stressor antecedents were notably reported, most often related to family stressors. Recent or distant history of abuse was of varying degrees. The neurological presentations were complex, with nearly half of the patients having multiple distinct neurological symptoms. Motor symptoms and non-epileptic seizures were the most frequent, with an acute mode of onset in the majority of the cases. The course was marked by the regression of symptoms in the majority of patients, with their persistence in the third of the cases, meanwhile a small group of the cases interrupted the follow-up.
A high resource use was noted due to the participation of several specialized consultants, the conduction of many diagnostic studies, and lengthy hospital stays.
Conclusion: Our data confirms previous findings in the literature and contributes to a better understanding and characterization of our population.
Keywords: children, adolescents, psychiatry, socio-cultural factors, environmental factors, functional neurological disorders (conversion), clinical manifestations
# Abbreviations
FND, functional neurological disorder; CT, cerebral computed tomography; MRI, magnetic resonance imaging; EEG, electroencephalogram; TAP, thoracic-abdominal tomography; SD, standard deviation; NS, non-significant
# Introduction
Functional neurological disorder (FND) also known as conversion disorder, as defined in the Diagnostic and Statistical Manual of Mental Disorders (DSM-5),1 involve an impairment of voluntary motor and sensory functions that are inconsistent with a recognized neurological or medical condition, and cannot be explained by any other medical or mental health disorder.
Specific symptoms include paralysis, muscle weakness, paresthesia, altered consciousness, tremors and seizures.
In childhood, FND most commonly occurs between the ages of 12 and 16, and are rarely seen before the age of 7.1,2
In the literature, females are significantly more likely to be diagnosed with FND compared to males, although several studies have noted that this predominance disappears at earlier ages, as is the case with other mental disorders in children.3
Motor symptoms, such as weakness, abnormal movements, and non-epileptic seizures are the most common manifestations among children and up to half of the patients display several distinct symptoms.4
Psychosocial stressors and psychological conflicts have long been considered to play out a role in the development of many conversion symptoms. In adults with FND symptoms, early sexual assault or physical abuse are quite common.
At the same time, other prior stressors have been identified in the vast majority of children and adolescents, the most common being family conflicts, separation from a family member, and school bullying.5 In some patients, early symptoms may precede an illness or a medical intervention.
According to the DSM-5, the diagnosis of FND no longer requires the identification of precipitating stressors, as these are not always present, although recent and historical stressors are more common in patients with FND than in healthy participants and clinical controls.6
In theory, the development of FND could be due to unresolved psychological conflicts that have been converted into physical or psychiatric symptoms, which have been socially accepted and protect the child from conflicts or painful memories.6 The disease also brings relief from unpleasant and difficult to accept sensations (primary benefits), reduces high expectations and increases the attention of relatives (secondary benefits).7
Previous studies have shown that children with conversion disorder often show multiple somatic symptoms and comorbid psychiatric disorders.8,9 Moreover, cognitive deficits may occur in some patients with conversion disorder.8 Therefore, it is important to understand the clinical, sociocultural, environmental, personality and psychiatric/psychological characteristics of children with dissociative (conversion) disorders in order to establish early diagnosis, treatment and long-term prognosis.
# Methods
This is a retrospective descriptive study based on the examination of medical records, reported on individual exploitation forms for evaluation and analysis of the socio-epidemiological and clinical profile of patients who were admitted to the child and adolescent psychiatry department, at Children’s Hospital ABDERRAHIM HAROUCHI, HASSAN II University, Casablanca, between March 2019 and July 2021 with a primary diagnosis of functional neurological disorder.
Fifty-two patients with a FND who met the inclusion and exclusion criteria were identified in this period.
Inclusion criteria were a diagnosis of a functional neurological disorder according to DSM-5 criteria,1 an age between 9 to 18 years, and language proficiency.
Exclusion criteria were the presence of a physical/somatic illness, psychotic disorder, neurodevelopmental disorder, or substance abuse/dependence.
During the follow-up of these patients, clinicians performed a thorough examination to exclude physical or somatic diseases. Additional diagnostic procedures were conducted if necessary, such as cerebral computed tomography (CT), scans, magnetic resonance imaging (MRI), electroencephalograms, electromyograms, echocardiograms, electrocardiograms, pulmonary function tests, and other explorations.
Later on, clinical child and adolescent psychiatrists conducted comprehensive interviews and assessments of each patient. When these patients were diagnosed with functional neurological disorders, they were all treated with a combination of individual psychotherapy, pharmacotherapy and family therapy.
When we determined the patients to be included in the study, we created a detailed clinical data questionnaire for each patient; existing epidemiological data on patients and family members, including gender, age of onset and consultation, socioeconomic and educational level, as well as precipitating factors (stressors), major clinical signs and symptoms, family history, sociocultural factors, and ancillary test results, which were obtained from medical records.
# Results
Demographics: A total of 52 children and adolescents were enrolled in the study; their demographic and environmental data are summarized in Table 1. Of the 66 patients, 37 (71.2%) were girls and 15 (28.8%) were boys, and their mean age at disease onset was 12.3 years (SD = 1.7, range = 9-18 years). Overall, 35 (67.3%) of the patients were between the ages of 10 to 14, and 17 (32.6%) were between the ages of 14 to 18 years.
All of these patients were attending school, and the socio-economic level of most of the families ranged from medium to low as shown in Table 1.
Features Total (N=52) Age (years), mean, (SD), range 13.5, (2.1), 9-18 Gender, n (%) Male 15 (28.8) Female 37 (71.2) Grade level, n (%) Primary 18 (34.6) Secondary 17 (32.7) High School 16 (30.8) Academic performance, n (%) Good 23 (44.2) Medium 18 (34.6) Low 11 (21.2) Socioeconomic level, n (%) Low (< 2000 MAD) 26 (50) Medium (4000-6000 MAD) 15 (29) Good (> 6000 MAD) 11 (21.2) Marital status of parents, n (%) Married 42 (81) Divorced 8 (15.4) Single mother 2 (3) Number of siblings, n (%) 0 9 (17.3) 2-Jan 18 (34.6) 4-Mar 19 (36.5) ≥ 5 6 (11.5) Age of onset of 1er symptom (years), (SD) 12.3 (1.7) Age at 1ere visit (years), (SD) 12.6 (1.7) Family history: Similar case in family, n (%) Positive 9 (17.3) Negative 43 (82.7) Neurological family history, n (%) Positive 11 (21.2) Negative 41 (79) Psychiatric family history, n (%) Positive 21 (40.4) Negative 31 (59.6) Parental involvement, n (%) Cooperative 41 (79) Uncooperative 11 (21.2)
Table 1 Demographic and environmental data of patients with functional neurological disorders
Clinical assessment of patients: Proper evaluation of functional neurological disorder (FND) requires a detailed history and a complete neurological examination, as well as biological and neuroimaging Para clinical tests.
The initial evaluation of suspected TNF in these 52 patients began with a detailed questioning of physical symptoms, thus assessing the mode of onset of the clinical picture; 28 (53.8%) patients presented with an acute onset, 17 (33%) patients with a subacute onset while only 7 (13.5%) patients had a progressive mode of onset.
The clinical investigation was followed by a complete neurological examination, in collaboration with the neuropediatric department. Numerous tests were used to distinguish whether the symptoms were of functional origin or due to an organic cause. For example, the Hoover sign is the most commonly used test to assess functional weakness of the lower limbs.10
Similarly, the Abductor sign is another way to assess functional weakness of the lower limbs. It is positive when the abduction of the "weak" hip becomes normal while the "weak" hip is removed.11
The evaluation is not completed without additional biological and neuroimaging tests, because positive signs on a functional test do not exclude underlying neurological or medical conditions. Thus, routine biological tests (complete blood count, chemistry, liver function test, thyroid function test, erythrocyte sedimentation rate, C-reactive protein, etc.) and neuroimaging tests, including cerebral computed tomography(CT), spine and brain MRI, were performed at each patient's first visit.
An electroencephalogram (EEG) and video EEG were realized to distinguish true epileptic seizures from those that are psychogenic.
Other Para clinical examinations were requested according to the clinical presentation, such as electroneuromyography, electrocardiograms, thoracic radiology, thoracic-abdominal tomography (TAP), ophthalmological consultation, etc. The results of these additional tests and imaging studies came back normal in our patient’s series.
However, it should be kept in mind that imaging and biological findings of some chronic neurological diseases such as autoimmune-related neurological diseases may also be normal; therefore, neurological follow-up was recommended, to continue monitoring the symptoms that were not suggestive of chronic neurological diseases at the initial visit.
After eliminating an organic origin, a complete child psychiatric evaluation was done to better explore the psychiatric semiology of these patients, highlighting the antecedent and current stress factors, the events triggering this symptomatology as well as psychiatric comorbidities.
In our study, 27 patients (52%) presented a thymic lability, 40 patients (76,9%) had behavioral disorders such as irritability, impulsivity and aggressiveness, while 20 patients (38,4%) suffered from sleeping disorders.
History and stressors: Most of the patients had a positive family history, of which 40.4% had a family history of psychiatric disorders, depression and obsessive-compulsive disorder were most notable, and 17.3% had similar cases in the family, while 20% had a family history of neurological disorders.
More than two-thirds of the patients (76.9%) had antecedent stressors, the most common being family conflicts or parental divorce (42.5%), school bullying (25%), bereavement of a loved one (17.5%), moving (15.5%), and physical abuse and/or sexual assault (11.5%) (Table 2).
Stressors N (%) Conflict environments (parental conflict, punishments...) 22 (42.5) School harassment 13 (25) Bereavement of a loved one 9 (17.5) Moving 8 (15.5) History of physical assault 6 (11.5) History of sexual abuse 4 (8) Other (change of school, arrest of a family member...) 4 (8)
Table 2 Stressors reported in this study (N=52)
Clinical manifestations: Table 3 shows the different clinical manifestations of the 52 children and adolescents with functional neurological disorders. Loss of consciousness (50%) was the most frequent manifestation, 20 (38.5%) patients had motor neurological symptoms (paraplegia, hemiparesis, etc.), 15 (28.8%) had seizures that could be classified as psychogenic non epileptic seizures, 12 (23.07%) had sensory symptoms (including anesthesia, hyperesthesia, or visual or auditory disturbance), and 11 (21.5%) had paroxysmal abnormal movements, the most frequent being tremor of the extremities with motor tics.
Clinical manifestations N (%) Motor signs 20 (38.5) 12 (23.1) Paraparesis 6 (11.5) Hemiparesis / Hemiplegia 4 (7.6) Abnormal movement 9 (17.3) Loss of consciousness 26 (50) Sensory disorders 11 (21.2) Convulsive seizures 15 (29) Cognitive disorders Memory disorder/ 25 (48) Attentional/concentration disorder 15 (29) Learning disorders 17 (32) Language impairment 10 (19) Visual impairment 5 (10) Other neurological signs (headache, chronic myalgia...) 8 (16)
Table 3 Clinical manifestations of children and adolescents with functional neurological disorders (N =52)
Other somatic symptoms were present in 20% of the patients, such as headaches, musculoskeletal pain, chronic myalgia and gastrointestinal disorders being the most frequent, in that order. Cognitive disorders were notably present in 48% of the cases, often manifesting as attentional and concentration disorders, which most often affected the schooling quality.
No significant correlation between the neurological presentations and sex and/or age was found.
Evolution: The management of functional neurological disorders is a multidisciplinary process that begins with the diagnosis announcement, for the patient and his family, with clear and intelligible words, in order to establish a good therapeutic alliance with the care team.
This increases the likelihood of the adherence and success of the therapeutic strategies. Although evidence from randomized clinical trials is limited, in our study, 30 patients had a good outcome following comprehensive management, based on individual and family psychotherapy and treatment of comorbidities; while in 15 other patients, the symptoms persisted.
A bivariate statistical analysis was performed to test the eventual relationship between the degree of progression and the different studied factors. The independent variables included demographic variables (age of onset, gender, family history and precipitating factor), environmental variables (monthly family income, parental involvement, level of education...) using the statistical test of X_2.
The results were coded as 0 and 1, where 1 represents the "good evolution" group and 0 the "persistence" group of the clinical picture and it turned out that the test X_2 (Table 4), does not confirm any relationship. This is mainly due to the limited size of our sample n=52 (p value > 0.05), therefore, future multicenter studies with larger samples will be needed to support this course.
Factors Evolution P value Good (n=30) Persistence (n=15) Gender Female 21 (70%) 11 (73 %) 1 Male 9 (30%) 4 (27 %) NS Age (years) 13.7 (2) 13.5 (2) 0.714 Age of onset of 12,6 (1.5) 12,3 (1.5) 0.533 first symptoms NS Socio-economic status 16 (53 %) 8 (53%) Low 14 (47 %) 7 (46%) 0.813 Average - Good NS
Table 4 Bivariate study of the different factors and the degree of clinical evolution (good and persistent)
# Discussion
Although the prevalence of functional neurological disorders in children and adolescents has been shown to be low compared to adults5 and in the absence of solid data on the prevalence of this disorder in the Moroccan pediatric population, in our study, FND was a fairly common reason for consultation in children and adolescents.
The predominance of adolescents and the female gender found in other studies was replicated here. Several explanations have been suggested for this female predominance, including likelihood of help-seeking, culturally acceptable modes of distress expression, higher rates of sexual abuse and physical assault, and high rates of comorbid depression that are predominantly female.
Motor symptoms and non-epileptic seizures are the most common symptoms in children with conversive disorders, which is also consistent with the results of our study.
Almost half of the patients had more than one neurological symptom. This is another feature that distinguishes children with FND from adults with FND, who typically have only one symptom.12,13
However, we found that many patients had other somatic symptoms (such as sensory disturbances, headaches, myalgias, etc.), hence the need for further exploration, as they can be as disabling as the neurological symptoms.
Our research found that approximately two-thirds of patients had prior stressors, and the most common stressors were similar to those reported in previous studies, primarily family and school factors.2
Children are particularly sensitive to the above-mentioned triggers because of their immature personalities, heightened sensitivity to adverse situations, and their psychosomatic reactions.14
Kozlowska et al.4 pointed out that family disruptions can be very threatening to the child's perceived safety and can be similar to certain trauma for adults. Furthermore, it seems that patients with a history of trauma are those who are at risk of persisting the disorder into adulthood.
Multidisciplinary treatment is considered the most effective treatment for functional neurological disorders. The treatment is based on a comprehensive psychotherapeutic approach that includes cognitive-behavioral therapy and psychodynamic therapy. Other approaches, such as family therapy and medication in case of concurrent disorders, insure better results.8 The first therapeutic approach is to stabilize the child's emotions by establishing a therapeutic alliance based on trust and hope, using specific therapeutic relaxation techniques and ensuring that the child can identify and express his or her emotions and needs. For patients with prior trauma, family therapy can improve family communication by correcting patterns of interaction that promote conversion, and help parents manage guilt or denial related to the prior trauma. Family work to promote attachment experiences is also important.13
Most children make a full recovery within a few weeks of therapeutic interventions. However, in rare cases, symptoms can last much longer, sometimes several months or even years.15 This is consistent with our study, 30 patients (60%) showed a good evolution after comprehensive management based on individual and family psychotherapy with medication treatment of comorbidities; while in 15 (28.8%) patients the symptoms persisted this can be explained by the fact that they were lost from sight for several months without treatment or follow-up; the resumption of contact was made after relapse or worsening of the clinical picture. We also noted that almost all the patients' relatives had some initial reticence about the diagnosis, and a lack of understanding, acceptance, or both, which leads to poor cooperation with the therapeutic process and delays recovery.
In this case, it is important to effectively address the parents' questions and potentially negative reactions, explain that the child's symptoms are not factitious or intentionally induced, and encourage the parents to cooperate with the treatment plan.14
# Limitations
Although our study benefits from data from extensive formal psychiatric and neurological assessments, it is limited by the lack of a control group, and the limited number of patients, as well as the lack of a prospective semi-structured interview to ensure internal consistency in the patient's evaluation.
In addition, larger sample sizes in the future will make it easier to find subgroups, which will give more power to data analysis.
# Conclusion
Functional neurological disorders are frequent and disabling, but potentially reversible.
This study describes the clinical characteristics, sociocultural and environmental factors of children with functional neurological disorders in the child and psychiatry department of Casablanca.
A better understanding of the psychiatric and psychological aspects of these patients may contribute to a correct diagnosis that can prevent unnecessary diagnostic tests and a faster transition to appropriate treatment. Therapeutic success is based on the establishment of a diagnosis that validates the patient's symptoms and disability and allows for a full understanding and acceptance of the disorder by the patient.
None.
None.
# Conflicts of interest
There is no conflict of interest regarding the publication of this article.
# References
©2022 Rachidi, et al. This is an open access article distributed under the terms of the, which permits unrestricted use, distribution, and build upon your work non-commercially. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1740407794713974, "perplexity": 9459.712400383187}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945248.28/warc/CC-MAIN-20230324051147-20230324081147-00372.warc.gz"} |
http://googlescholar.medcraveonline.com/scholars/article_fulltext/6076 | #### Journal of ISSN: 2377-4282JNMR
Nanomedicine Research
Review Article
Volume 4 Issue 4 - 2016
Nano-Communication Propagation Channel Model Using Flow and Diffusion
A Azari, S Kamal S Sahbari* and A Fahim
Department of Electrical Engineering, Tabriz Branch Islamic Azad University, Iran
Received: November 27, 2016| Published: December 12, 2016
*Corresponding author: S Kamal S Sahbari, Department of Electrical Engineering, Tabriz Branch Islamic Azad University, Tabriz, Iran, Email:
Citation: Azari A, Sahbari SKS, Fahim A (2016) Nano-Communication Propagation Channel Model Using Flow and Diffusion. J Nanomed Res 4(4): 00095. DOI: 10.15406/jnmr.2016.04.00095
# Abstract
Inspired by biological communication systems, nano-communication in particular molecular communication has been proposed as a viable scheme to communicate between nano-sized devices separated by a very short distance. Here, molecules are released by the transmitter into the medium, which are then sensed by the receiver .Thus, this has necessitated the research on the potential applications of nanotechnology in a wide range of nano-networking areas. Nano-networking is a new type of networking which can also be applied to the communication theory. In this paper, a well justified channel propagation model for flow-based nano-characteristic communication channel is considered. The signal propagation model based on the advection and diffusion processes is analyzed. Furthermore, a sound mathematical justification for the linearity and time-variance properties of flow and diffusion based nano-communication channel model is investigated.
Keywords: Nano-communication; Propagation; Molecular; Diffusion; Flow
# Introduction
Nano-technology is a science and technology of engineering operative systems at molecular scale. Figure 1 shows different approaches for nano-machines developments. As it can be seen in this figure, development of nano-machines can be accomplished using three approaches [1]:
1. A top-down approach in which nano-machines are developed using current micro-electronic devices [1,2].
2. A bottom- up approached in which nano-machines are developed using molecular components [2].
3. A bio-hybrid approach in which the development of nano-machines is based on studying existing biological models [2].
Figure 1: Different approaches for nano-machines development.
In general the concept of nano-technology and development largely remains in the research phase. However, only recently a manufacturing approach has been provided for nano-machines with 1.5-nanometere switch which can be used to detect and count specific type of molecule [3].
The most important application of nano-networks is in biology and biomedicine. Molecular communication (MC) is also a bio-inspired paradigm where the exchange of information is accomplished through the transmission, propagation, and reception of molecules. MC is considered a promising option for communications in nano -networks, which are defined as interconnection between nano-machines. The process of molecular propagation is based on radically different phenomenon with respect to the electromagnetic propagation in classical communication systems. While electromagnetic waves operate the propagation of the energy at the speed of light, the molecular diffusion process is caused by random motion of molecules in fluid. As a result, while electromagnetic propagation is mostly in the defined direction, molecular motion usually propagate in a random direction with high delay for almost all transmission ranges. In order to provide a biocompatible nano-communication scheme which in particular applicable to biomedical applications, we consider a molecular communication system model. So, to define a very reliable nano-communication system, in particular a molecular communication system, a well justified channel model is of great significance.
# Molecular Communication System Model
Designing a realizable transmitter and receiver structure requires a well-justified model for channel propagation. In nano-communications in general, and molecular communication in particular, transportation of messenger molecules is mainly affected by the stationary and non-stationary nature of the propagation environment. Hence, based on the stationary aspect of the propagation environment, molecular communication channels are classified into two groups: diffusion-based and flow-based molecular channels. In diffusion-based communication channels, in contrast to the flow-based communication channels, the propagation medium is stationary. Thus the molecular communications can be the most practical means for realization of communications between nano-machines. In molecular communications paradigm, transmitters use molecules for encoding and transmitting information in contrast to the conventional electromagnetic communications in which the information is transmitted using electromagnetic waves. In general two molecular communication techniques are considered:
1. Molecular communication using molecular motors such as, kinesin, myosin or dynein for information transmission
2. Molecular communication using calcium signalling, in which calcium ions are used for information transmission. Also with respect to the communication range, molecular communications are classified as follows; short-range communications, in which communication range is from nm to mm as intra-cell and inte cell communications, medium-range molecular communications, in which in general communication range is from μm to mm, and long-rage molecular communications, in which the communication range is from mm to km.
Diffusion-based molecular communication System model
In Figure 2 a schematic of diffusion-based molecular communication system is illustrated. The Propagation of the desired signal is mainly governed by the transport mechanism of the emitted molecules. In the diffusion-based molecular communication channels (i.e.; where the propagation medium is stationary), the propagation process of emitted messenger molecules is accomplished by means of thermally activated diffusion mechanism. In this transport mechanism, molecular flux is achieved from regions of high density to low density via random collisions with underlying medium. As it can be seen similar to a conventional digital communication system; there must be three major stages for any molecular communication process, transmission, propagation, and the reception processes.
Figure 2: A schematic of a molecular communication system.
Flow-based Molecular Communication System Model
When the propagation medium is stationary (i.e.; diffusion based molecular channels), Viscose forces of the propagation medium dominates the propagation process and the emitted messenger molecules are propagated by thermally activated diffusion mechanism [4,6,8,10-12]. However, when the propagation medium is in motion (i.e.; flow-based molecular channels), the messenger molecule propagation are effected both by diffusion and advection mechanism. Figure 3 illustrates a flow-based molecular communication system.
Figure 3: Flow-based molecular exchange system.
# Flow-based Molecular Communication Channel propagation Model
When the propagation medium is stationary (i.e.; diffusion-based molecular channels), viscous forces of propagation medium dominate the propagation process and the emitted messenger molecules are propagated by means of thermally activated diffusion mechanism [4,6,8,10-12]. However, when the propagation medium is in motion (i.e.; flow-based molecular channels), the propagation of emitted messenger molecules are effected both by diffusion and advection process. Hence, there are two sources of flux for which the messenger molecules are propagated:
1. Diffusion flux which is calculated by the Fick's first law [13]:
2. ${J}_{diff}=\text{\hspace{0.17em}}-D\text{\hspace{0.17em}}\nabla \overline{U}\left(X\left(t\right),t\right)$ (1)
Where $\overline{U}\left(X\left(t\right),t\right)$ is the molecular concentration with X (x(t),y(t)) the two dimensional molecular position at time t, and D being the diffusion coefficient..
3. Advective flux which is due to the motion of the medium and is written in [13,15] as:
${J}_{adv}=\text{\hspace{0.17em}}V\left(t\right)\text{\hspace{0.17em}}\overline{U}\left(X\left(t\right),t\right)$ (2)
Where is the two dimensional vector velocity of the propagation motion at time t.
Signal propagation model
Thus the convection-diffusion equation is used to model the effects of both advection and diffusion in the flow-based molecular communication. If $\overline{U}\left(X\left(t\right),t\right)$ is the mean molecular concentration at time t, then we may write [13-15]:
$\frac{\partial \overline{U}\left(X\left(t\right),t\right)}{\partial t}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}D\text{\hspace{0.17em}}{\nabla }^{2}\overline{U}\left(X\left(t\right),t\right)\text{\hspace{0.17em}}-\text{\hspace{0.17em}}V\left(t\right)\nabla \text{\hspace{0.17em}}\overline{U}\left(X\left(t\right),t\right)\text{\hspace{0.17em}}+\text{\hspace{0.17em}}S$ (3)
where X(t) being the two dimensional molecular position at time t and S being any extra source in the medium in case exists. In our analysis we will assume that S =0. Let us simplify the notation X(t) by omitting time t ,and assume that the concentration of emitted molecules is much lower than the concentration of medium molecules [5-7,9,11]. We now show that the Eq. (3) is nothing more than the Fick's second law of propagation.
We now proceed by defining a new coordinate system that moves along with the medium flow (i.e.; with the same velocity vector). Hence,
$X\text{\hspace{0.17em}}=\text{\hspace{0.17em}}X\text{'}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{X}_{tx}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{\int }_{\text{\hspace{0.17em}}{t}_{0}}^{\text{\hspace{0.17em}}t}v\left(\beta \right)d\beta \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}or\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}X\text{'}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}X\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{X}_{tx}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{\int }_{\text{\hspace{0.17em}}{t}_{0}}^{\text{\hspace{0.17em}}t}v\left(\beta \right)d\beta$ (4)
Where Xtx= (xtx , ytx) is the two-dimensional position of the transmitter with t0 being the initial time of an impulse messenger molecule transmission.
Since
${\nabla }^{2}\overline{U}\left(X,t\right)\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{\partial }{\partial X}\left(\frac{\partial U}{\partial X}\right)$ (5)
Substituting Eq.(4) in Eq.(5) and noting that
$\begin{array}{l}\frac{\partial \overline{U}\left(X,t\right)}{\partial t}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{\partial U\left(X,t\right)}{\partial X}\text{\hspace{0.17em}}.\text{\hspace{0.17em}}\frac{\partial X}{\partial t}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{\partial \overline{U}\left(X\text{'},t\right)}{\partial X\text{'}}\text{\hspace{0.17em}}.\text{\hspace{0.17em}}\frac{\partial X\text{'}}{\partial t}\\ and\\ {\nabla }^{2}U\left(X,t\right)\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{\partial }{\partial X}\left(\frac{\partial U\left(X,t\right)}{\partial X}\right)\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{\partial }{\partial X}\left(\frac{\partial U\left(X,t\right)}{\partial X\text{'}}\text{\hspace{0.17em}}.\text{\hspace{0.17em}}\frac{\partial X\text{'}}{\partial X}\right)\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{\partial }{\partial X\text{'}}\left(\frac{\partial \overline{U}\left(X\text{'},t\right)}{\partial X\text{'}}\text{\hspace{0.17em}}.\text{\hspace{0.17em}}\frac{\partial X\text{'}}{\partial X}\right).\frac{\partial X\text{'}}{\partial X}\end{array}$
We then get the following result:
$\frac{\partial \overline{U}\left(X\text{'},t\right)}{\partial X\text{'}}.\frac{\partial X\text{'}}{\partial t}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\frac{\partial \overline{U}\left(X\text{'},t\right)}{\partial t}=\text{\hspace{0.17em}}D\frac{\partial }{\partial X\text{'}}\left(\frac{\partial \overline{U}\left(X\text{'},t\right)}{\partial X\text{'}}\text{\hspace{0.17em}}.\text{\hspace{0.17em}}\frac{\partial X\text{'}}{\partial X}\right)\left(\text{\hspace{0.17em}}\frac{\partial X\text{'}}{\partial X}\right)\text{\hspace{0.17em}}-\text{\hspace{0.17em}}v\left(t\right)\frac{\partial \overline{U}\left(X\text{'},t\right)}{\partial X\text{'}}.\frac{\partial X\text{'}}{\partial X}\right)\text{\hspace{0.17em}}$
Hence Eq.(3) can be rewritten as :
$\frac{\partial \overline{U}\left(X\text{'},t\right)}{\partial t}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}D{\nabla }^{2}\overline{U}\left(X\text{'},t\right)\text{\hspace{0.17em}}$ (6)
Which is nothing more than the Fick's second low of molecular motion, the model of propagation process in a stationary medium [5,6,10-12]. Now if we assume that at time t0, Q number of messenger molecules are transmitted, then the mean molecular concentration at location X' and time t is given by [11]:
$\overline{U}\left(\overline{X},t\right)\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{Q}{4\pi D\left(t-{t}_{0}\right)}\right)\text{\hspace{0.17em}}\mathrm{exp}\left(\frac{{|X\text{'}|}^{2}}{4D\left(t-{t}_{0}\right)}$ (7)
Substituting Eq. (4) in Eq.(7), we get the following result as the mean molecular concentration in the reference coordinates :
$\overline{U}\left(X,t\right)\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{Q}{4\pi D\left(t-{t}_{0}\right)}\right)\text{\hspace{0.17em}}\mathrm{exp}\left(\frac{{|X\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{X}_{tx}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{\int }_{\text{\hspace{0.17em}}{t}_{0}}^{\text{\hspace{0.17em}}t}v\left(\alpha \right)d\alpha |}^{2}}{4D\left(t-{t}_{0}\right)}\right)$ (8)
Hence, from Eq. (8), we can compute the mean number of messenger molecules in the receiving sensing cross section area Arx as follows:
$S\left(t\right)\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\underset{{A}_{rx}}{\iint }\frac{Q}{4\pi D\left(t-{t}_{0}\right)}\mathrm{exp}\left(\frac{{|X\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{X}_{tx}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{\int }_{\text{\hspace{0.17em}}{t}_{0}}^{\text{\hspace{0.17em}}t}v\left(\alpha \right)d\alpha |}^{2}}{4D\left(t-{t}_{0}\right)}\right)dxdy$ (9)
Fig.4 shows the mean number of messenger molecules in the receiver sensing area in terms of time for five different scenarios. The diffusion coefficient D =1.7× 10-9 m2/s. The distance between transmitter and receiver nano-machines is considered to be 500 μm [16] and it is assumed that the transmitter and receiver nano-machines are located at (0,0) μm and (500,0) μm, respectively. The number of the transmitted messenger molecules per information symbol is Q = 2 × 104.
Linearity of the channel
In this part, we assume that two transmitters are transmitting pulses simultaneously with different amplitudes as follows:
Then using Eq. (9), the mean number of received messenger molecules in the receiver cross section are:
$S\left(t\right)\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\underset{{A}_{rx}}{\iint }\frac{Q}{4\pi D\left(t-{t}_{0}\right)}\mathrm{exp}\left(\frac{{|X\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{X}_{tx}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{\int }_{\text{\hspace{0.17em}}{t}_{0}}^{\text{\hspace{0.17em}}t}v\left(\alpha \right)d\alpha |}^{2}}{4D\left(t-{t}_{0}\right)}\right)dxdy$ (10)
Since the Qi number of messenger molecules are transmitted at time to =0, then the lower limit of the velocity integral is taken to zero.
To show the linearity of the channel, we must show that for input signal ag1 (t)+bg2 (t) (where a and b are constants) , the output signal is equal to af1(t)+bf2(t) . For the transmitted signal:
${f}_{3}\left(t\right)\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\underset{{A}_{rx}}{\iint }\frac{a{Q}_{1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}b{Q}_{2}}{4\pi Dt}\mathrm{exp}\left(\frac{{|X\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{X}_{tx}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{\int }_{0}^{t}v\left(\alpha \right)d\alpha |}^{2}}{4Dt}\right)dxdy\text{\hspace{0.17em}}=\text{\hspace{0.17em}}a{f}_{1}\left(t\right)\text{\hspace{0.17em}}+\text{\hspace{0.17em}}b{f}_{2}\left(t\right)$ (12)
Thus, the molecular channel when the propagation medium being in motion confirms the linearity property.
Time-variance of the channel
To show the time –variance property, we consider two transmitters are sending their pulses at different time instants as follows:
(13)
Then, the signals arriving in the receiver are:
${f}_{1}\left(t\right)\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\underset{{A}_{rx}}{\iint }\frac{Q}{4\pi Dt}\mathrm{exp}\left(\frac{{|X\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{X}_{tx}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{\int }_{\text{\hspace{0.17em}}0}^{\text{\hspace{0.17em}}t}v\left(\alpha \right)d\alpha |}^{2}}{4Dt}\right)dxdy$
${f}_{2}\left(t\right)\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\underset{{A}_{rx}}{\iint }\frac{Q}{4\pi D\left(t-\beta \right)}\mathrm{exp}\left(\frac{{|X\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{X}_{tx}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{\int }_{\text{\hspace{0.17em}}0}^{\text{\hspace{0.17em}}t}v\left(\alpha \right)d\alpha |}^{2}}{4D\left(t-\beta \right)}\right)dxdy\text{\hspace{0.17em}}\ne \text{\hspace{0.17em}}{f}_{1}\left(t-\beta \right)$ (14)
Which illustrates the time-variance of flow-based molecular communication channel?
Since, the channel response not only depends on the observation time but also on when the signal is applied. Therefore, the received signal, s(t), is simply the convolution of the input signal (i.e.; impulse of transmitted messenger molecules ) with the channel response. This is due to the fact that in wireless channel models, input symbol chosen to be and to be an impulse of almost zero width. Hence, we may write s(t)= Q δ(t) * h (t, τ) with h(t, τ) being the time varying channel response at time t due to the impulse applied at time t- τ. Hence, using Eq.(10), we can conclude that the time-varying impulse response of a flow-based molecular channel is given by:
$h\left(t,\tau \right)\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\underset{{A}_{rx}}{\iint }\frac{Q}{4\pi D\left(\tau \right)}\mathrm{exp}\left(\frac{{|X\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{X}_{tx}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{\int }_{\text{\hspace{0.17em}}t-\tau }^{\text{\hspace{0.17em}}t}v\left(\alpha \right)d\alpha |}^{2}}{4D\left(\tau \right)}\right)dxdy$ (15)
# Conclusion and Future work
An important challenge in nano-network research concerns the modelling of physical layer communications. When the propagation medium is stationary, the propagation of emitted messenger molecules is accomplished by a thermal diffusion mechanism, where Brownian motion statistical model may be considered. However, when nano-machines communicate in a moving propagation medium, the propagation of messenger molecules are accomplished by advection mechanism as well as diffusion mechanism.
In this study, a physical layer channel model for nano-machines in a nano-network was analyzed. With huge potential applications to nano-networks in biomedicine and biology, the primary focus was on the molecular communications. The channel model based on flow-diffusion was addressed. The signal model also was provided where the linearity and time- variance properties were established. It is believed that one of the current unexplored challenges in nano-communication particularly, in the molecular communication systems is pulse shaping. As it can be seen from the Figure 4, the molecular channel response has a long tail which causes residual noise and intersymbol interference in communication. Also, the effects of electromagnetic and electrostatic fields on the transporting characteristics of the molecular communication should be investigated. Existence of such external field, applies forces on the emitted messenger molecules, which will ultimately have negative effect on their motions. Finally, studying channel capacity based on signal propagation and noise in the nano-communication systems especially, in molecular communications can be a very interesting and attracting field to be considered.
Figure 4: The mean number of messengermolecules in the receiver sensing area in five Scenarios: 1) v = (0, 0) μm/s, 2) v = (5, 0) μm/s, 3) v = (10, 0) μm/s, 4) v = (5, 5) μm/s, and 5) v = (-5, 0) μm/s.
# References
Browse by
• ### DOI
Submit Manuscript | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 18, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6699514389038086, "perplexity": 1478.0792136455068}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945232.48/warc/CC-MAIN-20180421145218-20180421165218-00451.warc.gz"} |
http://science.sciencemag.org/content/338/6114/1560.full | Articles
# Journey in the Search for the Higgs Boson: The ATLAS and CMS Experiments at the Large Hadron Collider
+ See all authors and affiliations
Science 21 Dec 2012:
Vol. 338, Issue 6114, pp. 1560-1568
DOI: 10.1126/science.1230827
## Abstract
The search for the standard model Higgs boson at the Large Hadron Collider (LHC) started more than two decades ago. Much innovation was required and diverse challenges had to be overcome during the conception and construction of the LHC and its experiments. The ATLAS and CMS Collaboration experiments at the LHC have discovered a heavy boson that could complete the standard model of particle physics.
One of the remarkable achievements of 20th-century science is the revelation that a large number of natural phenomena that characterize the world around us can be described in terms of underlying principles of great simplicity and beauty. The standard model (SM) of particle physics is built upon those principles. The SM comprises quarks and leptons as the building blocks of matter, and describes their interactions through the exchange of force carriers: the photon for electromagnetic interactions, the W and Z bosons for weak interactions, and the gluons for strong interactions. Quarks are bound by the strong interaction into protons and neutrons; protons and neutrons bind together into nuclei; electrons bind to nuclei by electromagnetic interaction to form atoms, molecules, and matter. The electromagnetic and weak interactions are unified in the electroweak theory (13). Although integrating gravity into the model remains a fundamental challenge, the SM provides a beautiful explanation, from first principles, of much of Nature that we observe directly.
The SM has been tested by many experiments over the past four decades and has been shown to successfully describe high-energy particle interactions. The simplest and most elegant way to construct the SM would be to assert that all fundamental particles are massless. However, we know this to be untrue, otherwise atoms would not have formed and we would not exist. The question of the origin of mass of fundamental particles is the same as the one that is posed in the unified electroweak theory: Why does the photon remain strictly massless while its close cousins, the W and Z bosons, acquire a mass some 100 times that of the proton? To generate mass of the W and Z bosons, the electroweak gauge symmetry must somehow be broken. For protons or neutrons, which are composite particles, most of the mass arises from the mass equivalent of the internal energy due to the intense binding field of the strong interactions.
Nearly 50 years ago, a mechanism was proposed for spontaneously breaking this symmetry (49) involving a complex scalar quantum field that permeates the entire universe. This new field has the same quantum numbers as the vacuum. The quantum of this field is called the Higgs boson. In addition to imparting mass to the W and Z bosons, this scalar field would also impart masses to the quarks and leptons, all in proportion to their coupling to this field. After the discovery of the W and Z bosons in the early 1980s, the search for the Higgs boson, considered to be an integral part of the SM, became a central theme in particle physics. The discovery of the Higgs boson would establish the existence of this field, leading to a revolutionary step in our understanding of how Nature works at the fundamental level. The elucidation of this mass-generating mechanism became one of the primary scientific goals of the Large Hadron Collider (LHC).
The mass of the Higgs boson (mH) is not predicted by theory. Below mH = 600 GeV, previous direct searches at the Large Electron Positron collider (LEP), the Tevatron, and the LHC were unable to exclude mass regions between 114 and 130 GeV (1014). Furthermore, in December 2011, the A Toroidal LHC Apparatus (ATLAS) Collaboration and Compact Muon Solenoid (CMS) Collaboration experiments reported an excess of events near a mass of 125 GeV (13, 14). The Tevatron experiments, CDF and D0, recently reported an excess of events in the range 120 to 135 GeV (15).
In July 2012, the discovery of a new heavy boson with a mass around 125 GeV was announced at CERN by the ATLAS and CMS experiments (16, 17), and the current data are consistent with the expectation for a Higgs boson. Here, we present an overview of the search for the Higgs boson and highlight some of the exciting implications. Despite its incredible success the SM is still considered incomplete. A number of questions remain: Why would the mass of the Higgs boson be only ~102 GeV? What is dark matter? How does the matter-antimatter asymmetry arise? How is gravity to be included? Physics beyond the SM has been much discussed over the past few decades, and such physics might manifest itself via the production of exotic particles such as superparticles from a new symmetry (supersymmetry), heavy Z-like bosons in grand unified theories or theories with extra space-time dimensions.
Design challenges. In the 1980s, it was clear that new accelerators were needed that could reach energies beyond those that had allowed the discovery of many of the subnuclear particles within the SM. Several ideas were vigorously discussed concerning the accelerators and detector concepts most capable of tackling the major open questions in particle physics, often paraphrased as the “known unknowns,” and possibly discovering new physics beyond the SM, the “unknown unknowns.” Finding the Higgs boson was clearly a priority in the first category and was expected to be challenging. The mass of the Higgs boson (mH) is not predicted by theory and could be as high as 1000 GeV (1 TeV). This required a search over a broad range of mass, ideally suiting an exploratory machine such as a high-energy proton-proton (pp) collider. The suitability arises from the fact that the energy carried by the protons is distributed among its constituent partons (quarks and gluons), allowing the entire range of masses to be “scanned” at the same time. The main mechanisms predicted to produce the Higgs boson involve the combination of these subnuclear particles and force carriers.
The accelerator favored at CERN to probe the TeV energy scale was a pp collider. The required energy of the collider can be estimated by considering the reaction in which a Higgs boson is produced with a mass, mH, of 1 TeV. This happens via the WW fusion production mechanism. A quark from each of the protons radiates a W boson with an energy of ~0.5 TeV, implying that the radiating quark should carry an energy of ~1 TeV so as to have a reasonable probability of emitting such a W boson. Hence, the proton should have an energy of ~6 × 1 TeV, as the average energy carried by a quark inside the proton is about one-sixth of the proton energy. The LHC (18, 19) was designed to accelerate protons to 7 TeV, an order of magnitude higher than the most powerful available accelerator, with an instantaneous pp collision rate of 800 million per second.
It was proposed to build the new accelerator in the existing underground tunnel of LEP. Because the radius of the tunnel is fixed, the value of the magnetic field of the dipole-bending magnets had to be ~8.5 T to hold in orbit the 7-TeV protons. The main challenges for the accelerator were to build ~1200 superconducting dipoles, each 15 m in length, able to reach this magnetic field; the large distributed cryogenic plant to cool the magnets and other accelerator structures; and control systems for the beams. The stored energy in each of the beams at nominal intensity and energy is 350 MJ, equivalent to more than 80 kg of TNT. Hence, if the beam is lost in an uncontrolled way, it can do considerable damage to the machine components, which would result in months of down time [see (18, 19) for further details].
The LHC was approved in 1994 and construction began in 1998. A parallel attempt to build an accelerator that could reach even higher energies was made with the Superconducting SuperCollider (SSC) in Texas in the late 1980s but was canceled in 1993 during the early stages of construction.
This search for the Higgs boson also provided a stringent benchmark for evaluating the physics performance of various experiment designs under consideration some 20 years ago. The predicted rate of production ( = L⋅σ, where L is the instantaneous luminosity of the colliding beams, measured in units of cm−2 s−1, and σ is the cross section of the production reaction, measured in units of cm2) and natural width (Γ = ħ/τ, where τ is the lifetime, and ħ is Planck’s constant divided by 2π) of the SM Higgs boson vary widely over the allowed mass range (100 to 1000 GeV). Once produced, the Higgs boson disintegrates immediately in one of several ways (decay modes) into known SM particles, depending on its mass. A search had to be envisaged not only over a large range of masses but also many possible decay modes: in pairs of photons, Z bosons, W bosons, τ leptons, and b quarks. Not only is the putative SM Higgs boson rarely produced in the proton collisions, it also rarely decays into particles that are the best identifiable signatures of its production at the LHC: photons, electrons, and muons. The rarity is illustrated by the fact that Higgs boson production and decay to one such distinguishable signature (H → ZZ → ℓℓℓℓ, where [[[ℓ]]] is a charged lepton, either a muon or an electron) happens roughly only once in 10 trillion pp collisions. This means that a large number of pp collisions per second must be studied; the current operating number is around 600 million per second, corresponding to an instantaneous luminosity of 7 × 1033 cm−2 s−1. Hence, the ATLAS and CMS detectors operate in the harsh environment created by this huge rate of pp collisions.
A saying prevalent in the late 1980s and early 1990s captured the challenge that lay ahead: “We think we know how to build a high-energy, high-luminosity hadron collider—but we don’t have the technology to build a detector for it.” The role of the search for the Higgs boson at the LHC in influencing the design of the ATLAS and CMS experiments, and the experimental challenges associated with operating them at very high instantaneous collision rates, are described in (20).
Different values of mH place differing demands on the detectors, none more stringent than in the mass range mH < 2 × mZ (where the mass of the Z boson mZ = 90 GeV). In designing the LHC experiments, considerable emphasis was placed on this region. At masses below ~140 GeV, the SM Higgs boson is produced with a spread (natural width) of mass values of only a few MeV (i.e., a few parts in 105) such that the width of any observed mass peak would be entirely dominated by instrumental mass resolution. The Higgs boson decay modes generally accepted to be most promising in this region were those into two photons, occurring a few times in every thousand Higgs boson decays, and those, occurring even less often, into a pair of Z bosons, each of which in turn decays into a pair of two oppositely charged leptons (electrons or muons). However, in a detector with a very good muon momentum resolution and electron/photon energy resolution, the invariant mass of the parent Higgs bosons could be measured precisely enough with the prospect of seeing a narrow peak, over background, in the distribution of the invariant masses of the decay particles (e.g., two photons or four charged leptons). Early detailed studies can be found in (21, 22).
Other signatures are associated with a Higgs boson. Most of these signatures are plagued by larger backgrounds, as the signal characteristics are less distinctive. For example, some of these signatures include narrow sprays of particles, known as “jets,” resulting from the fragmentation of quarks. These represent the most likely final states from the decay of a SM Higgs boson, but in a hadron collider they are overwhelmed by the copious production from known SM processes. Among these jets are b quark jets characterized by a short (submillimeter) flight path in the detector before disintegrating. Finally, neutrinos can be produced, which, as neutral weakly interacting leptons, leave the detector without direct trace. Energy balance in the transverse plane of the colliding protons appears to be violated, as the neutrino energy is not measured, leading to the signature of missing transverse energy (ETmiss). For example, when a Higgs boson decays into two Z bosons, one can decay into a charged lepton pair and the other into a pair of neutrinos, leaving as final state an oppositely charged lepton pair and ETmiss.
The conditions in hadron colliders are more ferocious than in electron-positron colliders. For example, at the LHC ~1000 charged particles from ~20 pp interactions emerge from the interaction region in every crossing of the proton bunches. Highly granular detectors (to give low probability of a given cell or channel registering a hit or energy), with fast response and good time resolution, are required. Tens of millions of detector electronic channels are hence required, and these must be synchronized to cleanly separate the different “bursts” of particles emerging from the interaction point every 25 ns. The enormous flux of particles emerging from the interaction region leads to high radiation levels in the detecting elements and the associated front-end electronics. This presented challenges for detectors and electronics not previously encountered in particle physics.
The counterrotating LHC beams are organized in 2808 bunches comprising some 1011 protons per bunch separated by 25 ns, leading to a bunch crossing rate of ~40 MHz (the LHC accelerator currently operates at 50-ns bunch spacing with 1380 bunches). The event selection process (“trigger”) must reduce this rate to ~0.5 kHz for storage and subsequent detailed offline analysis. New collisions occur in each crossing, and a trigger decision must be made for every crossing. It is not feasible to make a trigger decision in 25 ns; it takes about 3 μs. During this time the data must be stored in pipelines integrated into onboard (front-end) electronics associated with almost every one of 100 million electronic channels in each experiment. This online event selection process proceeds in two steps: The first step reduces the rate from ~40 MHz to a maximum of 100 kHz and comprises hardware processors that use coarse information from the detectors; upon receipt of a positive trigger signal (set by high-momentum muons or high-energy deposits in calorimeters; see below), the data from these events are transferred to a processor farm, which uses event reconstruction algorithms operating in real time to decrease the event rate to ~0.5 kHz before data storage. The tens of petabytes that are generated per year per experiment are distributed to scientists located across the globe and motivated the development of the so-called Worldwide LHC Computing Grid (WLCG) (23).
Timeline and general features of the ATLAS and CMS experiments. To accomplish the physics goals, new detector technologies had to be invented and most of the existing technologies had to be pushed to their limits. Several detector concepts were proposed; two complementary ones, ATLAS and CMS, were selected in 1993 after peer review to proceed to detailed design (2427). These designs were fully developed, and all elements prototyped and tested, over many years before construction commenced around 1997. Today each experiment comprises more than 3000 scientists and engineers from around 180 universities and laboratories in around 40 countries. Table 1 provides a timeline of these developments.
Table 1
The timeline of the LHC project.
View this table:
The typical form of a collider detector is a “cylindrical onion” containing four principal layers. A particle emerging from the collision and traveling outward will first encounter the inner tracking system, immersed in a uniform magnetic field, comprising an array of pixels and microstrip detectors. These measure precisely the trajectory of the spiraling charged particles and the curvature of their paths, revealing their momenta. The stronger the magnetic field, the higher the curvature of the paths, and the more precise the measurement of each particle’s momentum. The energies of particles are measured in the next two layers of the detector, the electromagnetic (em) and hadronic calorimeters. Electrons and photons will be stopped by the em calorimeter; jets will be stopped by both the em and hadronic calorimeters. The only known particles that penetrate beyond the hadron calorimeter are muons and neutrinos. Muons, being charged particles, are tracked in dedicated muon chambers. Their momenta are also measured from the curvature of their paths in a magnetic field. Neutrinos escape detection, and their presence gives rise to ETmiss.
ATLAS and CMS have differing but complementary designs (28, 29). The single most important aspect of the overall design is the choice of the magnetic field configuration for measuring the muons. The two basic configurations are solenoidal and toroidal, in which the magnetic field is parallel or azimuthal to the beam axis, respectively. The CMS has a superconducting high-field solenoid with a large ratio of length to inside diameter; ATLAS has a superconducting air-core toroid. These are the two largest magnets of their kind and hold a stored energy of up to 3 GJ. In both magnets a current of ~20 kA flows through the superconductor. The CMS solenoid additionally provides the magnetic field for the inner tracking system, whereas ATLAS has an additional solenoid magnet to carry out the same function.
At the nominal pp collision rate, the particle flux varies from 108 cm−2 s−1 (at a radius of r = 4 cm) to 2 × 106 cm−2 s−1 (at r = 50 cm), requiring small detection cells (channels) of typical size varying from 100 μm × 100 μm (pixels) to 10 cm × 100 μm (microstrips). The more channels there are, the easier it is to recognize the trajectories of all the charged particles produced. In practice, the number of channels is limited by the cost of the associated electronics, by the power they dissipate (which in turn requires cooling fluids), and by the need to minimize the amount of material in front of the em calorimeter. The inner tracker detectors, comprising silicon sensors and gaseous “straw” chambers, were challenging to develop because of the need to operate in a harsh radiation environment, especially when close to the beam pipe. Radiation-hard electronics associated with each cell, with a high degree of functionality, needed to be packed into as small a space as possible, using as little material as possible.
In the early 1990s there were only two complementary possibilities for the em calorimeters that could perform in a high-radiation environment and had good enough electron and photon energy resolution to cleanly detect the two-photon decay of the SM Higgs boson at low mass: a lead–liquid argon sampling calorimeter, chosen by ATLAS, and fully sensitive dense lead tungstate scintillating crystals, chosen by CMS. Both are novel techniques, and each was tested and developed over many years before mass production could commence. The electrons and positrons in the electromagnetic showers excite atoms of lead tungstate or ionize atoms of liquid argon, respectively. The amount of light emitted, or charge collected, is proportional to the energy of the incoming electrons or photons.
The hadron calorimeters in each detector are similar and are based on known technologies: alternating layers of iron or brass absorber in which the particles interact, producing showers of secondary particles, and plastic scintillator plates that sample the energy of these showers. The total amount of scintillation light detected by the photodetectors is proportional to the incident energy.
The muon detectors used complementary technologies based on gaseous chambers: drift chambers and cathode strip chambers that provide precise position measurement (and also provide a trigger signal in the case of CMS), and thin-gap chambers and/or resistive plate chambers that provide precise timing information as well as a fast trigger signal.
The electronics on the detectors, much of which was manufactured in radiation-hard technology, represented a substantial part of the materials cost of the LHC experiments. The requirement of radiation hardness was previously found only in military and space applications.
The construction of the various components of the detectors took place over about 10 years in universities, national laboratories, and industries, from which they were sent to CERN in Geneva. This paper can do only partial justice to the technological challenges that had to be overcome in developing, constructing, and installing all the components in the large underground caverns. All the detector elements were connected to the off-detector electronics, and data were fed to computers housed in a neighboring service cavern. Each experiment has more than 50,000 cables with a total length exceeding 3000 km, and more than 10,000 pipes and tubes for services (cooling, ventilation, power, signal transmission, etc.). Access to repair any substantial fault, or faulty connection, buried inside the experiment would require months just to open the experiments. Hence, a high degree of long-term operational reliability, which is usually associated with space-bound systems, had to be attained.
The design of the ATLAS experiment. The design of the ATLAS detector (28) was based on a superconducting air-core toroid magnet system containing ~80 km of superconductor cable in eight separate barrel coils (each 25 m × 5 m in a “racetrack” shape) and two matching end-cap toroid systems. A field of ~0.5 T is generated over a large volume. The toroids are complemented with a smaller solenoid (diameter 2.5 m, length 6 m) at the center, which provides a magnetic field of 2 T.
The detector includes an em calorimeter complemented by a full-coverage hadronic calorimeter for jet and ETmiss measurements. The em calorimeter is a cryogenic lead–liquid argon sampling calorimeter in a novel “accordion” geometry allowing fine granularity, both laterally and in depth, and full coverage without any uninstrumented regions. A plastic scintillator–iron sampling hadronic calorimeter, also with a novel geometry, is used in the barrel part of the experiment. Liquid argon hadronic calorimeters are used in the end-cap regions near the beam axis. The em and hadronic calorimeters have 200,000 and 10,000 cells, respectively, and are in an almost field-free region between the toroids and the solenoid. They provide fine lateral and longitudinal segmentation.
The momentum of the muons can be precisely measured as they travel unperturbed by material for more than ~5 m in the air-core toroid field. About 1200 large muon chambers of various shapes, with a total area of 5000 m2, measure the impact position with an accuracy better than 0.1 mm. Another set of about 4200 fast chambers are used to provide the “trigger.” The chambers were built in about 20 collaborating institutes on three continents. (This was also the case for other components of the experiment.)
The reconstruction of all charged particles, including that of displaced vertices, is achieved in the inner detector, which combines highly granular pixel (50 μm × 400 μm elements leading to 80 million channels) and microstrip (13 cm × 80 μm elements leading to 6 million channels) silicon semiconductor sensors placed close to the beam axis, and a “straw tube” gaseous detector (350,000 channels), which provides about 30 to 40 signal hits per track. The latter also helps in the identification of electrons using information from the effects of transition radiation.
The air-core magnet system allows a relatively lightweight overall structure leading to a detector weighing 7000 tonnes. The muon spectrometer defines the overall dimensions of the ATLAS detector: a diameter of 22 m and a length of 46 m. Given its size and structure, the ATLAS detector had to be assembled directly in the underground cavern. Figure 1 shows one end of the cylindrical barrel detector after about 4 years of installation work, 1.5 years before completion. The ends of four of the barrel toroid coils are visible, illustrating the eightfold symmetry of the structure.
The design of the CMS experiment. The design of the CMS detector (29) was based on a superconducting high-field solenoid, which first reached the design field of 4 T in 2006. The CMS design was first optimized to detect muons from the H → ZZ → 4μ decay. To identify these muons and measure their momenta, the interaction region of the CMS detector is surrounded with enough absorber material, equivalent to about 2 m of iron, to stop all the particles produced except muons and neutrinos. The muons have spiral trajectories in the magnetic field, which are reconstructed in the surrounding drift chambers. The CMS solenoid was designed to have the maximum magnetic field considered feasible at the time, 4 T. This is produced by a current of 20 kA flowing through a reinforced Nb-Ti superconducting coil built in four layers. Economic and transportation constraints limited the outer radius of the coil to 3 m and its length to 13 m. The field is returned through an iron yoke, 1.5 m thick, which houses four muon stations to ensure robustness of measurement and full geometric coverage. The iron yoke is sectioned into five barrel wheels and three end-cap disks at each end, for a total weight of 12,500 tonnes. The sectioning enabled the detector to be assembled and tested in a large surface hall while the underground cavern was being prepared. The sections, weighing 350 to 2000 tonnes, were then lowered sequentially between October 2006 and January 2008, using a dedicated gantry system equipped with strand jacks; this represented the first use of this technology to simplify the underground assembly of large experiments.
The next design priority was driven by the search for the decay of the SM Higgs boson into two photons. This called for an em calorimeter with the best possible energy resolution. A new type of crystal was selected: lead tungstate (PbWO4) scintillating crystal. Five years of research and development (1993–1998) were necessary to improve the transparency and the radiation hardness of these crystals, and it took more than 130 years (1998–2008) of round-the-clock production to manufacture the 75,848 crystals—more crystals than were used in all previous particle physics experiments put together. The last of the crystals was delivered in March 2008.
The solution to charged particle tracking was to opt for a small number of precise position measurements of each charged track (~13 each with a position resolution of ~15 μm per measurement), leading to a large number of cells distributed inside a cylindrical volume 5.8 m in length and 2.5 m in diameter: 66 million silicon pixels, each 100 μm × 150 μm, and 9.3 million silicon microstrips ranging from ~10 cm × 80 μm to ~20 cm × 180 μm. With 198 m2 of active silicon area, the CMS tracker is by far the largest silicon tracker ever built.
Finally, the hadron calorimeter, comprising ~3000 small solid angle projective towers covering almost the full solid angle, is built from alternate plates of ~5 cm brass absorber and ~4-mm-thick scintillator plates that sample the energy. The scintillation light is detected by photodetectors (hybrid photodiodes) that can operate in the strong magnetic field. Figure 2 shows the transverse view of the barrel part of CMS in late 2007 during the installation phase in the underground cavern.
Preparation of the experiments. All detector components were tested at their production sites, after delivery to CERN, and again after their installation in the underground caverns. The experiments made use of the constant flow of cosmic rays impinging on Earth. Even at depths of 100 m, there is still a small flux of muons—a few hundred per second traversing each of the experiments. The muons were used to check the whole chain from the hardware to the analysis programs of the experiments, and also to align the detector elements and calibrate their response prior to pp collisions (30, 31).
The ATLAS and CMS experiments would generate huge amounts of data (tens of petabytes of data per year; 1 PB = 106 GB), requiring a fully distributed computing model. The LHC Computing Grid allows any user anywhere access to any data recorded or calculated during the lifetime of the experiments. The computing system consists of a hierarchical architecture of tiered centers, with one large Tier-0 center at CERN, about 10 large Tier-1 centers at national computing facilities, and about 100 Tier-2 centers at various institutes. The center at CERN receives the raw data, carries out prompt reconstruction almost in real time, and exports the raw and reconstructed data to the Tier-1 centers and also to Tier-2 centers for physics analysis. The Tier-0 centers must keep pace with the event rate of 0.5 kHz (~1 MB of raw data per event) from each experiment. The large Tier-1 centers provide long-term storage of raw data and reconstructed data outside of CERN (a second copy). They carry out second-pass reconstruction, when better calibration constants are available. The large number of events simulated by Monte Carlo methods and necessary for quantifying the expectations are produced mainly in Tier-2 centers.
The operation of the LHC accelerator and the experiments. The LHC accelerator began to operate on 10 September 2008. On 19 September 2008, during the final powering tests of the main dipole circuit in the last sector (3-4) to be powered up, an electrical fault in one of the tens of thousands of connections generated a powerful spark that punctured the vessel of a magnet, resulting in a large release of helium from the magnet cold mass and leading to mechanical damage to ~50 magnets. These were repaired in 2009, and it was decided to run the accelerator at an energy of 3.5 TeV per beam (i.e., at half the nominal energy).
The first pp collisions (at an energy of 450 GeV per beam) occurred on 23 November 2009; the first high-energy collisions (at 3.5 TeV per beam) were recorded on 30 March 2010, and since then the collider has operated smoothly, providing the two general-purpose experiments, ATLAS and CMS, with data samples corresponding to an integrated luminosity of close to 5 fb−1 (fb, femtobarn) during 2011, and another 5 fb−1, at the slightly higher energy of 4 TeV per beam, up to June 2012. In total, these data (~10 fb−1) correspond to the examination of some 1015 pp collisions. Typically, there are 20 overlapping pp interactions (“pile-up”) in the same crossing of proton bunches as the interaction of interest. ATLAS and CMS have recorded ~95% of the collision data delivered with the LHC operating in stable conditions. In all, 98% of the roughly 100 million electronic readout channels in each experiment have been performing at design specification. This outstanding achievement is the result of a constant and dedicated effort by the teams of physicists, engineers, and technicians responsible for the hardware, software, and maintenance of the detectors. This efficient operation of the accelerator and the experiments has led to the discovery of the Higgs-like boson soon after the first pp collisions at high energy.
The ATLAS and CMS experiments started recording high-energy pp collisions in March 2010 after a preliminary low-energy run in the autumn of 2009. Many SM processes, including inclusive production of quarks (seen as hadronic jets), bottom quarks, top quarks, and W and Z bosons, have been measured with high precision. These measurements, in a previously unexplored energy region, confirm the predictions of the SM. It is essential to establish this agreement before any claims for new physics can be made, as SM processes constitute large backgrounds to new physics.
Extensive searches for new physics beyond the SM have also been performed. New limits have been set on quark substructure, supersymmetric particles (e.g., disfavoring at 95% CL gluino masses below 1 TeV in simple models of supersymmetry), potential new bosons (e.g., disfavoring at 95% CL new heavy W-like W′ and Z-like Z′ bosons with masses below 2 TeV for couplings similar to the ones for the known W and Z bosons), and even signs of TeV-scale gravity (e.g., disfavoring at 95% CL black holes with masses below 4 TeV).
Undoubtedly, the most striking result to emerge from the ATLAS and CMS experiments is the discovery of a new heavy boson with a mass of ~125 GeV. The analysis was carried out in the context of the search for the SM Higgs boson.
For mH around 125 GeV, and from the number of collisions examined, some 200,000 Higgs bosons would have been produced in each experiment. Folding in the branching fraction, each experiment expected to identify a comparatively tiny number of signal events (e.g., a few hundred two-photon events or tens of four-lepton events) from a hypothetical Higgs boson, before including factors of efficiency. The four–charged-lepton mode (H → ZZ → ℓℓℓℓ) offers the promise of the purest signal (S/B ~ 1, where S is the number of expected signal events and B is the number of expected background events) and has therefore been called the “golden channel.”
The search for the Higgs boson is carried out in a variety of modes. Below, we give some details of the two modes that have the best invariant mass resolution and had played a particularly important role in the design of the ATLAS and CMS experiments.
H γγ. In our detectors, the signature of the H → γγ decay mode is a pair of isolated photons each with a high transverse momentum of ~30 GeV or higher. Transverse momentum is the component of the momentum vector projected onto the plane perpendicular to the beams. Figure 3 shows such an event recorded with the CMS detector.
Events containing two isolated photon candidates were selected with the goal of identifying a narrow peak in the diphoton invariant mass distribution superimposed on a large background. This background arises from two sources: the dominant and irreducible one from a variety of SM processes, and a reducible background where one or both of the reconstructed photon candidates originate from misidentification of jet fragments.
The criteria to distinguish real photons from those coming from jet fragmentation (labeled “fake photons”) depend on the detector technologies of the two experiments. Both experiments are able to reject fake photons such that their contribution to the background is only 25% of the total. The size of this contribution was the subject of much debate in the 1990s, and the low value has been attained through the design of the em calorimeters and the rejection power of the associated analyses.
To enhance the sensitivity of the analysis, candidate two-photon events were separated into many mutually exclusive categories of different expected S/B ratios. These categories are defined on the basis of the expected properties of the reconstructed photons and on the presence of two jets expected to accompany a Higgs boson produced through the vector-boson fusion process, a particularly sensitive category. The analysis of events in each category represented a separate measurement, with a specific mass resolution and background, and the results from each category were statistically combined through a procedure that used likelihood analysis.
The distributions of the two-photon invariant masses, weighted by category, are shown in Fig. 4 for ATLAS and CMS, respectively, along with the best fit of a signal peak on top of a continuum background. The weight chosen was proportional to the expected S/B in the respective category.
An excess of events, over the background, was observed at a mass of ~125 GeV by both experiments, corresponding to a local significance of 4.5 standard deviations (σ) for ATLAS and 4.1σ for CMS.
HZZℓℓℓℓ. The signature of the H → ZZ → ℓℓℓℓ decay mode is two pairs of oppositely charged isolated leptons (electrons or muons). The main background arises from a small continuum of known and nonresonant production of Z boson pairs. Figure 5 shows an event recorded with the ATLAS detector with the characteristics expected from the decay of the SM Higgs boson to a pair of Z bosons, one of which subsequently decays into a pair of electrons and the other into a pair of muons.
For a Higgs boson with a mass below twice the mass of the Z boson, one of the lepton pairs will typically have an invariant mass compatible with the Z boson mass (~91 GeV), whereas the other one will have a considerably lower mass, called “off-mass shell.” Because there are differences in the instrumental backgrounds and in the mass resolutions for the three possible combinations of electron and muon pairs (4e, 4μ, and 2e2μ), the searches were made in these independent subchannels and then combined statistically with a likelihood procedure. In the case of CMS, the angular distribution of the four leptons is included in the likelihood.
Figure 6 shows the four-lepton invariant mass distribution for the ATLAS and CMS experiments, in each case for the combination of all the channels (4e, 4μ, and 2e2μ). The peak near 90 GeV corresponds to the expected but rare decay of Z bosons to four leptons (Z → ℓℓℓℓ). The rate is higher in the CMS experiment than in ATLAS because of differing kinematic criteria applied to the four leptons. Both experiments observe a small but significant excess of events around an invariant mass of about 125 GeV above the expected continuum background, with a spread as expected from the mass resolution and statistical fluctuations corresponding to a local significance of 3.4σ and 3.2σ in ATLAS and CMS, respectively.
Combined results. The ATLAS and CMS experiments have both studied more Higgs boson decay modes than described in this paper, as discussed in the associated papers in this issue and (16, 17). Figure 7 shows the combined statistical significance observed for the different Higgs mass hypotheses by the ATLAS and CMS experiments, respectively. The largest local significance is observed for a SM Higgs boson mass of mH = 126.5 and 125.5 GeV, where it reaches 6.0σ and 5.0σ, corresponding to a background fluctuation probability of 2 × 10−9 and 5 × 10−7 for the ATLAS and CMS experiments, respectively. The expected local significance in the presence of a SM Higgs boson signal at these masses is found to be 4.9σ for the ATLAS experiment and 5.8σ for the CMS experiment. The evidence for a new particle is strengthened by the observation in two different experiments, comprising complementary detectors, operating independently.
In both experiments the excess was most significant in the two decay modes γγ and ZZ. These two decay modes indicate that the new particle is a boson; the two-photon decay implies that its spin (J) is different from 1 (32, 33). Because the Higgs field is scalar, the spin of the SM Higgs boson is predicted to be zero.
Furthermore, the number of observed events is roughly equal to the number of events expected from the production of a SM Higgs boson for all the decay modes analyzed, within the errors, in both experiments. The measured value of the observed/expected ratio, for the combined data from all the decay modes, was found to be 1.4 ± 0.3 and 0.87 ± 0.23 for the ATLAS and CMS experiments, respectively. The best estimates of the masses measured by the ATLAS and CMS experiments are also consistent: 126.0 ± 0.6 GeV and 125.3 ± 0.6 GeV, respectively.
Outlook. The results from the two experiments are consistent, within uncertainties, with the expectations for the SM Higgs boson, a fundamental spin-0 (scalar) boson. Much more data need to be collected to enable rigorous testing of the compatibility of the new boson with the SM and to establish whether the properties of the new particle imply the existence of physics beyond the SM. For this boson, at a mass of ~125 GeV, almost all the decay modes are detectable, and hence comprehensive tests can be made. Among the remaining questions are whether the bosons have spin J = 0 or J = 2, whether their parity is positive or negative, whether they are elementary or composite, and whether they couple to particles in the exact proportion predicted by the SM [i.e., for fermions (f) proportional to mf2 and for bosons (V) proportional to mV4]. These properties are studied via the new boson’s rate of decay into different final states, the angular distributions of the decay particles, and its rate of production in association with other particles such as W and Z bosons. The SM Higgs boson is predicted to be an elementary particle with JP = 0+. Much progress is expected, as by the end of 2012 the ATLAS and CMS detectors should be able to triple the amount of data used for the results presented here. The LHC will then be shut down in 2013 and 2014 to refurbish parts of the accelerator so that it will be able to reach its full design energy (14 TeV) and enable precise measurements of the properties of the new bosons and the full exploration of the physics of the TeV energy scale, especially the search for physics beyond the SM.
It is known that quantum corrections make the mass of a fundamental scalar particle float up to the next highest physical mass scale currently known, which, in the absence of extensions to the SM, is as high as 1015 GeV. A favored conjecture states that this is avoided by a set of heavy particles not yet discovered. For each known SM particle there would be a partner with spin differing by half a unit; fermions would have boson partners and vice versa, in a symmetry called supersymmetry. This happens because in quantum mechanics, corrections involving fermions and bosons have opposite signs for their amplitudes and hence cancel each other. In the minimal supersymmetry model, five types of Higgs bosons are predicted to exist. Furthermore, the lightest stable neutral particle of this new family of supersymmetric particles could be the particle constituting dark matter. If, as conjectured, such particles are light enough, they ought to reveal themselves at the LHC.
The discovery of the new boson suggests that we could well have discovered a fundamental scalar field that pervades our universe. Astronomical and astrophysical measurements point to the following composition of energy-matter in the universe: ~4% normal matter that “shines,” ~23% dark matter, and the rest forming “dark energy.” Dark matter is weakly and gravitationally interacting matter with no electromagnetic or strong interactions. These are the properties carried by the lightest supersymmetic particle. Hence the question: Is dark matter supersymmetric in nature? Fundamental scalar fields could well have played a critical role in the conjectured inflation of our universe immediately after the Big Bang and in the recently observed accelerating expansion of the universe that, among other measurements, signals the presence of dark energy in our universe.
The discovery of the new boson is widely expected to be a portal to physics beyond the SM. Physicists at the LHC are eagerly looking forward to establishing the true nature of the new boson and to the higher-energy running of the LHC, to find clues or answers to some of the other fundamental open questions in particle physics and cosmology. Such a program of work at the LHC is likely to take several decades.
## References and Notes
1. Acknowledgments: The construction, and now the operation and exploitation, of the large and complex ATLAS and CMS experiments have required the talents, the resources, and the dedication of thousands of scientists, engineers, and technicians worldwide. Many have already spent a substantial fraction of their working lives on these experiments. This paper is dedicated to all our colleagues who have worked on these experiments. None of these results could have been obtained without the wise planning, superb construction, and efficient operation of the LHC accelerator and the WLCG computing.
View Abstract | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9074198007583618, "perplexity": 965.0736758262118}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423269.5/warc/CC-MAIN-20170720161644-20170720181644-00394.warc.gz"} |
https://www.dlubal.com/en-US/support-and-learning/support/faq/002491 | FAQ 002491 EN-US
02/22/2019
# Can I display the center of gravity of my model?
Select the entire model (or just a group of objects) and right-click the selection. In the shortcut menu, select the "Center of Gravity and Info" feature.
The result is an overview of the center of gravity coordinates and additional information, such as volume and weight of material (see the figure). The center of gravity is also shown in a graphic.
#### Reference
[1] Manual RFEM. (2018). Tiefenbach: Dlubal Software. [2] Manual RSTAB. (2013). Tiefenbach: Dlubal Software. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9092544317245483, "perplexity": 2354.2472746046865}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875141460.64/warc/CC-MAIN-20200217000519-20200217030519-00302.warc.gz"} |
https://math.stackexchange.com/questions/1092323/why-isnt-fx-x-cos-frac-pix-differentiable-at-x-0-and-how-do-we-for/1092329 | # Why isn't $f(x) = x\cos\frac{\pi}{x}$ differentiable at $x=0$, and how do we foresee it?
Consider $$f(x)=\begin{cases} x\cos\frac{\pi}{x} & \text{for} \ x\ne0 \\ 0 & \text{for} \ x=0. \end{cases}$$
Its difference quotient $\frac{\Delta\left(f(x)\right)}{\Delta(x)}$ approaches $\cos\frac{\pi}{h}$ as $x$ gets closer to $0$, and thus $f$ is not differentiable in the origin because $\lim\limits_{h\to0}\cos\frac{\pi}{h}$ does not exist. This is the plot of $y=x \cos \frac{\pi}{x}$:
But here's how my book goes on:
Examining the figure we can foresee that the tangent line in a generic point $P$ of the graph doesn't tend to any limiting position as $P$ tends to the origin along the curve itself. One may think this happens because the graph of the function completes infinitely many oscillations in any neighbourhood of the origin. In fact, no: indeed the function thus defined: $$g(x)=\begin{cases} x^2\cos\frac{\pi}{x} & \text{for} \ x\ne0 \\ 0 & \text{for} \ x=0 \end{cases}$$ has a graph that completes infinitely many oscillations in any neighbourhood of the origin, but, as you can verify, it is differentiable at $x=0$ and we have $g'(0)=0$.
This is the plot of $y=x^2 \cos \frac{\pi}{x}$:
So, I have two questions related to what I quoted from the book: how do we foresee the non-differentiability of $f$, given that, correctly, the infinitude of the oscillations is not an argument for it? And then, why isn't $f$ differentiable, instead of $g$?
I shall emphasise that I know that, simply, the limit as $h\to 0$ of the difference ratio of $f$ doesn't exist, while that of $g$ does, but I've been wondering about an other kind of reason after reading that excerpt. Or is my book wrong in mentioning other reasons?
• Since non-differentiability is so common I would rather suspect every point of being non-differentiable locus and focus on foreseeing differentiability instead. – Pp.. Jan 5 '15 at 21:47
• @Pp.. that would be a good point of view if you were choosing functions at random. But we don't do that and since most functions we look at are infinitely differentiable.... – Ittay Weiss Jan 5 '15 at 22:04
• @IttayWeiss Actually, that is exactly what we do, don't get confused. It just happens that we use theorems like the properties of differentiation with respect to the arithmetic operations and elementary functions to get rid of big chunks of suspects. – Pp.. Jan 5 '15 at 22:15
• What the quoted passage is trying to say is that there is a big difference between the statements "$f'(0)=A$ exists" and "$f'(x)\to A$ as $x\to 0$". The function $g$ is a classic example of a function where the derivative exists at every point, but the function $g'$ is not continuous at the origin, since $g'(0)=0$ even though $g'(x)$ doesn't have a limit as $x \to 0$. – Hans Lundmark Jan 6 '15 at 9:33
• In other words: the way to think about $f'(0)$ is not to look at the tangent line at a nearby point $P$ on the curve and then let that point $P$ approach the origin. Rather, you take a rubber band ("infinitely shrinkable"), connect one end to the origin and the other end to a moving point $P$ on the curve, let $P$ approach the origin along the curve, and see if the rubber band can "make up its mind" about what slope to have in the limit. – Hans Lundmark Jan 6 '15 at 9:38
One way to "foresee" it is that there are clearly two lines in the first image you posted that serve as an envelope to $f(x)$. These two lines crossing at the origin make it impossible to approximate $f$ near $x=0$ as a linear function. This is the criterion of differentiability you want to keep in mind when trying to make this kind of judgement.
On the other hand, in the second image, the envelope is two parabolas touching at the origin. Since the parabolas are tangent at the origin, they force $y=0\cdot x$ to be the only way to approximate $f(x)$ as a linear function near $x=0$.
In the end, the criterion for differentiability of functions squeezed inside an envelope $$e_-(x)\leq f(x)\leq e_+(x)$$ is: no matter how wildly $f(x)$ oscillates inside the envelope, $f(x)$ will be differentiable at $x=0$ if (i) the envelopes touch each other: $$e_-(0)=e_+(0)$$ that is, they do squeeze $f(x)$ appropriately; and (ii) they are both differentiable with equal derivatives: $${e'}_{\!-}(0)={e'}_{\!+}(0)$$ thus forcing $f(x)$ to be differentiable with the same derivative.
• Perhaps you might comment that the parabolas have their vertices at $x=0$. – Ian Jan 5 '15 at 22:04
• Indeed, this is the case in this function. However, it is not a necessary condition for differentiability. It just indicates that the derivative is $0$. – fonini Jan 5 '15 at 22:05
• It's not necessary, but the envelope could be two parabolas that don't have their vertex at the point and which have different derivatives at the point. Then you'd be back in the first circumstance. – Ian Jan 5 '15 at 22:07
• Muito obrigado, Pedro (ou se você prefere, Angelo)! (minha mae é de Rio) Até já! – Vincenzo Oliva Jan 5 '15 at 22:49
• haha :) Just for the record, envelope is envoltória in Portuguese. Might be similar in Italian. – fonini Jan 5 '15 at 22:56
Normally the rules of differentiation show that any elementary function is continuous and differentiable wherever it is defined. The problems arise when the function's formula is undefined at some point and then we need to check the differentiability via the definition of derivative. Another case is when we define functions via multiple formulas in different parts of the domain. Then we need to check for existence of derivative at the boundary points.
The point which your book has highlighted is very important but perhaps been left out by other answers. It says that most common functions are differentiable except for exceptional points. Thus $f(x) = x\cos (\pi/x)$ is an example where $f$ is differentiable at all $x \neq 0$ and $$f'(x) = \cos (\pi/x) + \frac{\pi}{x}\sin(\pi/x)$$ When we define $f(0) = 0$ then we get continuity. But $f$ is still not differentiable at $0$.
Now your book mentions a very deep idea. Normally people try to look at the formula for $f'(x)$ and try to see if it tends to a particular value as $x \to 0$. In the above example the limit of $f'(x)$ does not exist and hence we conclude that $f$ is not differentiable at $0$.
The book says that this is not the right way to go and gives another example which sort of is a failure case for above technique. The example is $f(x) = x^{2}\cos (\pi/x), f(0) = 0$. We have $$f'(x) = 2x\cos(\pi/x) + \pi\sin(\pi/x)$$ and again we see that $f'(x)$ does not tend to a limit as $x \to 0$. And hence we conclude that $f'(0)$ does not exist. This is wrong.
We have the following theorem:
Theorem: If $f$ is continuous at $a$ and $\lim_{x \to a}f'(x) = L$ then $f'(a) = L$.
But the converse of the theorem does not hold. Thus if $f'(a) = L$ it does not mean that $\lim_{x \to a}f'(x)$ exists necessarily.
Thus the method of using limit of $f'(x)$ works only when the limit exists. Better not to try this approach and rather use the definition of derivative. I must say that your book has done a great job to highlight this fact about limit of derivative at a point and its relation to existence of derivative at that point (although not in the formal manner which I have given in my answer).
• Excellent. I took me a while to discern what the real Q is, which is "Why did the book say that?" – DanielWainfleet Sep 6 '17 at 18:55
• Thanks @DanielWainfleet for your encouraging words. Such feedback means a lot to me. Btw I was really impressed by the book excerpt given in the question where it talked about limiting position of tangent. – Paramanand Singh Sep 6 '17 at 21:47
The enveloping curves define differentiability. During infinite oscillations first curve tangent cannot decide between two slopes. But for the second, slopes are both equal to zero, makes it differentiable with its coinciding slope of tangent.
The book is giving a WARNING: "One $may$ think this (i.e. non-differentiable at $0$) happens because ( of the oscillations)...." and then shows that the same type of pattern of oscillations also exists for $g(x)=x^2\cos (\pi /x),$ so the occurrence of such an oscillatory pattern is insufficient to determine whether the function is differentiable at $0$.
Perhaps a different phrasing would have made this clearer. And I think it would have been more emphatic to have said that the oscillations in $g(x)$ near $0$ are large enough that $\lim_{x\to 0}g'(x)$ does not exist, but $g'(0)$ does exist, so the non-existence of $\lim_{x\to 0}f'(x)$ is, by itself, insufficient to determine whether $f'(0)$ exists. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8960791826248169, "perplexity": 231.8714763516296}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145713.39/warc/CC-MAIN-20200222180557-20200222210557-00528.warc.gz"} |
https://www.cheenta.com/2d-geometry-areas-related-to-circle-amc-8-2017-problem-25/ | Categories
# 2D Geometry – Areas related to circle AMC 8 2017 Problem 25
Try this beautiful problem from AMC 8. It involves calculating the area of a sector of a circle. We provide sequential hints so that you can try the problem.
## Competency in Focus: 2D Geometry (Areas related to circle)
This problem from American Mathematics Contest 8 (AMC 8, 2017) is based on calculation of areas related to circle. It is Question no. 25 of the AMC 8 2017 Problem series.
## Next understand the problem
In the figure shown, $\overline{US}$ and $\overline{UT}$ are line segments each of length 2, and $m\angle TUS = 60^\circ$. Arcs $TR$ and $SR$ are each one-sixth of a circle with radius 2. What is the area of the region shown? $\textbf{(A) }3\sqrt{3}-\pi\qquad\textbf{(B) }4\sqrt{3}-\frac{4\pi}{3}\qquad\textbf{(C) }2\sqrt{3}\qquad\textbf{(D) }4\sqrt{3}-\frac{2\pi}{3}\qquad\textbf{(E) }4+\frac{4\pi}{3}$
##### Source of the problem
American Mathematical Contest 2017, AMC 8 Problem 25
### Finding the area of a triangle and sector of a circle. (Area related to circles)
5/10
##### Suggested Book
Do you really need a hint? Try it first!
C0nstruction : Let $X$ and $Y$ are the centres of the scetors $ST$ and $TR$ Now Let us join $SX$ and $TY$ What do you think? Will the points $U,S,\textbf{ and}\quad X$ be in a straightline?
$U,S,\textbf{ and}\quad X$ will be in a straight line because $\angle STU =60^{\circ}$ And angle of a circle is $360$ i.e., $\angle SXR = \angle TYR = 60^{\circ}$ [Since sector($SXR$)=$\frac{1}{6}circle$] Then $UXY$ will make an equilateral triangle.
So after construction the figure will look like this : Therefore, The required area = Area of $\triangle UXY$ – $2 \times$ Area of the sector $SXR$.
Area of equilateral triangle $\triangle UXY= 4\sqrt{3}$ And the are of sector $SXR= \frac{2\pi}{3}$ ANS : $4\sqrt{3}-\frac{4\pi}{3}$
Area of an equilateral triangle =$\frac{a^2\sqrt{3}}{4}$ [where $a$ is a sied of the triangle] Area of a sector of a circle of angle $\theta$ = $\frac{\theta}{360}\pi r^2$ [where $r$ is the radius of the circle]
## AMC - AIME Program
AMC - AIME - USAMO Boot Camp for brilliant students. Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
## External Tangent | AMC 10A, 2018 | Problem 15
Try this beautiful Problem on geometry based on circle from AMC 10A, 2018. Problem-15. You may use sequential hints to solve the problem.
## Dice Problem | AMC 10A, 2014| Problem No 17
Try this beautiful Problem on Probability from AMC 10A, 2014. Problem-17, You may use sequential hints to solve the problem.
## Problem on Curve | AMC 10A, 2018 | Problem 21
Try this beautiful Problem on Co-ordinate geometry from AMC 10A, 2018. Problem-21, You may use sequential hints to solve the problem.
## Right-angled Triangle | AMC 10A, 2018 | Problem No 16
Try this beautiful Problem on triangle from AMC 10A, 2018. Problem-16. You may use sequential hints to solve the problem.
## Finding Greatest Integer | AMC 10A, 2018 | Problem No 14
Try this beautiful Problem on Algebra from AMC 10A, 2018. Problem-14, You may use sequential hints to solve the problem.
## Length of the crease | AMC 10A, 2018 | Problem No 13
Try this beautiful Problem on triangle from AMC 10A, 2018. Problem-13. You may use sequential hints to solve the problem.
## Right-angled shaped field | AMC 10A, 2018 | Problem No 23
Try this beautiful Problem on triangle from AMC 10A, 2018. Problem-23. You may use sequential hints to solve the problem.
## Area of region | AMC 10B, 2016| Problem No 21
Try this beautiful Problem on Geometry on Circle from AMC 10B, 2016. Problem-20. You may use sequential hints to solve the problem.
## Coin Toss Problem | AMC 10A, 2017| Problem No 18
Try this beautiful Problem on Probability from AMC 10A, 2017. Problem-18, You may use sequential hints to solve the problem.
## GCF & Rectangle | AMC 10A, 2016| Problem No 19
Try this beautiful Problem on Geometry on Rectangle from AMC 10A, 2010. Problem-19. You may use sequential hints to solve the problem.
This site uses Akismet to reduce spam. Learn how your comment data is processed. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43640607595443726, "perplexity": 1951.471034058806}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141195745.90/warc/CC-MAIN-20201128184858-20201128214858-00705.warc.gz"} |
https://math.stackexchange.com/questions/2930611/derivative-of-fracddt-f-gammat-with-differential-operators-frac-pa | # Derivative of $\frac{d}{dt} f(\gamma(t))$ with differential operators $\frac{\partial}{\partial z}$ and $\frac{\partial}{\partial \overline{z}}$
Let $$f: \mathbb{C} \rightarrow \mathbb{C}$$ a $$C^1$$ function (i.e. real and imaginary part $$f_1, f_2$$ are continuously differentiable, where $$f=f_1 + i \cdot f_2$$) and let $$\gamma: \mathbb{R} \rightarrow \mathbb{C}, t \mapsto \gamma(t)\, \,$$ $$C^1$$. Then we have that \begin{align} \frac{d}{dt} \, \, f(\gamma(t)) = \frac{\partial f(\gamma(t))}{\partial z} \cdot \gamma'(t) + \frac{\partial f}{\partial \overline{z}} \cdot \overline{\gamma'(t)} \end{align}
I have some trouble to do the calculation to get the formula (I tried to use the Cauchy-Riemann equations but it doesn't work, because the function $$f$$ is not holomorphic). Any suggestion? Thanks in advance!
• I think real and imaginary parts of $f$ will not help you. Perhaps you need $z = \gamma(t)$ and $\overline{z} = \overline{\gamma(t))$. – GEdgar Sep 25 '18 at 19:01
What you are saying is that you have the path in the complex plane that is specified by a parametrization $$\gamma(t)$$. So you have that $$z(t) = \gamma(t) \Rightarrow \bar{z} = \bar{\gamma}$$. Then from the multivariable chain rule you have that
$$\frac{df(z,\bar{z})}{dt} = \frac{\partial f}{\partial z}\frac{d z}{d t} + \frac{\partial f}{\partial \bar{z}}\frac{d \bar{z} }{d t}$$
$$\frac{df(z,\bar{z})}{dt} = \frac{\partial f}{\partial z} \gamma'(t) + \frac{\partial f}{\partial \bar{z}} \bar \gamma'(t)$$
• I think you mean $$\frac{df(z, \bar{z})}{dt} = \frac{\color{red} \partial f}{\color{red} \partial z} \frac{\color{blue} dz}{\color{blue} dt} + \frac{\color{red} \partial f}{\color{red} \partial \bar{z}} \frac{\color{blue} d \bar{z}}{\color{blue} dt}$$ – Mattos Sep 26 '18 at 4:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 12, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9984888434410095, "perplexity": 153.72423569212862}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578529839.0/warc/CC-MAIN-20190420140859-20190420162859-00171.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/cpaa.2013.12.2947 | Article Contents
Article Contents
# Free vibrations in space of the single mode for the Kirchhoff string
• We study a single mode for the Kirchhoff string vibrating in space. In 3D a single mode is generally almost periodic in contrast to the 2D periodic case. In order to show a complete geometrical description of a single mode we prove some monotonicity properties of the almost periods of the solution, with respect to the mechanical energy and the momentum. As a consequence of these properties, we observe that a planar single mode in 3D is always unstable, while it is known that a single mode in 2D is stable (under a suitable definition of stability), if the energy is small.
Mathematics Subject Classification: Primary: 34C25; Secondary: 35L70.
Citation:
• [1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables," Chapters 16, 17, New York: Dover, National bureau of standards, 1964. [2] L. P. Bonorino, E. H. M. Brietzke, J. P. Lukaszczyk and C. A. Taschetto, Properties of the period function for some Hamiltonian systems and homogeneous solutions of a semilinear elliptic equation, J. Differential Equations, 214 (2005), 156-175.doi: 10.1016/j.jde.2004.08.007. [3] G. F. Carrier, On the non-linear vibration problem of an elastic string, Q. Appl. Math., 3 (1945), 157-165. [4] T. Cazenave and F. B. Weissler, Unstable simple modes of the nonlinear string, Q. Appl. Math., 54 (1996), 287-305. [5] C. Chicone, The monotonicity of the period function for planar Hamiltonian vector fields, J. Differential Equations, 69 (1987), 310-321.doi: 10.1016/0022-0396(87)90122-7. [6] C. Chicone, "Ordinary Differential Equations with Applications," Springer-Verlag, New York, 2006. [7] A. Cima, A. Gasull and F. Mañosas, Period function for a class of Hamiltonian systems, J. Differential Equations, 168 (2000), 180-199.doi: 10.1006/jdeq.2000.3912. [8] W. R. Dean, Note on the evaluation of an elliptic integral of the third kind, J. London Math. Soc., 18 (1943), 130-132.doi: 10.1112/jlms/s1-18.3.130. [9] R. W. Dickey, Stability of periodic solutions of the non linear string, Q. Appl. Math., 38 (1980/81), 253-259. [10] G. Gallavotti, "The Elements of Mechanics," Springer-Verlag, New York, 1983. Also available from: Ipparco Editore, 2007. http://ipparco.roma1.infn.it/pagine/deposito/2007/elements.pdf. [11] M. Ghisi and M. Gobbino, Stability of simple modes of the Kirchhoff equation, Nonlinearity, 14 (2001), 1197-1220.doi: 10.1088/0951-7715/14/5/314. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.6030333042144775, "perplexity": 828.3640232720264}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296944996.49/warc/CC-MAIN-20230323034459-20230323064459-00699.warc.gz"} |
https://www.n0b0dy0fn0te.com/2019/04/can-you-hear-me.html | .post-body { line-height:100%; } -->
## Tuesday, 30 April 2019
### Can You Hear Me?
I had an interesting interaction today that I thought might prove instructive. The precise details of the interaction aren't really important, but suffice it to say that I came across an instance of something we've looked at before - most notably in That's Racist! - namely arguments that arise from a failure to clarify or even acknowledge a critical distinction, that between terms whose vernacular usage differs from a more technical usage.
I know that many of my regular readers, being active in those corners of the internet where atheists and believers gather to do battle, have come across instances of this failure of distinction, not least in the ever-ubiquitous 'just a theory' canard erected against evolution*.
In this particular instance, a Facebook friend and talented writer post that somebody had 'unfriended' them after stating that "White people can face prejudice, but not systematic racism".
As an minor aside, the formulation of this statement carries implicitly the distinction between technical and vernacular by casting it as prejudice versus systematic racism.
I responded by pointing out that much of the issue lies in a failure to note the distinction, and that this is especially a problem when communicating by text alone which, as we've discussed before, renders our communication only about 10% effective. Somebody requested a citation for this latter assertion, as they felt it to be ableist.
This came as something of a surprise to me but, as I know full well that I can't speak authoritatively about the lived experience of somebody who faces issues that I don't, I asked for clarification, being very careful to cast the request in terms of my own education. I know from long experience that there are things that aren't immediately apparent to me in the things that people say (I have a piece in the works about a phenomenon known as 'dog-whistling' - saying something that looks innocent on the surface but contains a message meant for 'those with ears to hear') and I always want to learn more, so that I can be a more effective ally.
As it turned out, the discussion degenerated from there, though it was clear from the response that my meaning hadn't been grasped, because my interlocutor thought I was saying that non-verbal communication was universally better, and that those with various issues, such as a lack of propensity with non-verbal cues, were being excluded from this assessment. That brings us to the meat of what I want to discuss here; a rendering of this notion from an information-theoretic perspective.
We've talked before about Claude Shannon, most notably in this post about information and DNA.
Shannon was a communications engineer, and his work was all about quantifying information to drive improvements in transmission, reception and noise-reduction technology. In other words, he was concerned with signal fidelity. In this light, Shannon defined information in such a way as to have a maximal information content. His definition is given in the header image at the top of the post, although I'd argue that 'reduction' is a better term than 'resolution'. Under this definition, the information content is maximal where there is no reduction in certainty§.
The easiest way I can think of to represent this is to lean on what I know best; music technology. This might turn out to be problematic, not least because some will grok this easier than others, owing to the vast improvements made in technology over the past few decades.Those of us who grew up before the advent of the iPod will recall hearing our favourite songs on tinny little monophonic radios, but younger people may not immediately grasp it, so let's start at the beginning.
Here's a typical graph showing the frequency response of a piece of audio equipment - a hi-fi speaker, in this case.
On the $x$ axis, we have the frequency in Hz**. On the $y$ axis, we have amplitude in dB††. This is a measure of sound pressure levels (SPL) at a given distance, usually one metre. As with temperature, sound pressure is a measure of energy density, or the motion of particles.
The full range of human hearing, under idealised listening conditions, is from around 12 Hz to around 28 kHz (kilohertz = 1,000 Hz), though it's commonly accepted that under normal conditions it runs from around 20 Hz to 20 kHz. This diminishes as we age, most quickly in the upper ranges, as these correlate to the smallest of the stereocilia, tiny hairs that sit in the cochlea. We lose these hairs through damage and ageing, and the smallest cilia corresponding to the higher frequencies are lost first. We understand this because we've all learned about the quantised nature of waves, which tells us that only those waves that can complete a half or full cycle within the boundaries can contribute. As always, I'll link to some further reading on waves at the bottom.
Generally speaking, adult humans can hear from around 20 Hz to around 15-17 kHz, though this can be impacted fairly severely by being exposed to high sound pressure levels routinely. This loss in the higher frequencies is why sound can often seem muffled in older humans.
So, there's the groundwork.
What that graph represents then, in this context, is information. Those whose hearing has been impacted by the loss of stereocilia (or other issues) get less information from the sound, because they're not getting the information in those higher frequencies corresponding to the last downward stroke to the right of the graph.
Note that this is an analogy, albeit one that's directly concerned with the same thing, namely the reception of transmitted information. In the language of Shannon, that information has been lost between transmission and reception.
We can now think of all our tools for communication as fitting in that graph.
Some of it is body language; we recognise that people who fold their arms and scowl are being defensive, for example (not in all cases, but generally).
Some is tone and inflection; we recognise that, when the end of a sentence rises, it usually indicates and interrogative.
Some of it is the words we use. Even this can be problematic, not least because of our inherent tendency to be somewhat creative with our language, meaning that we lean on synonyms for colour when very few pairings of words are actually directly synonymous.
In my statement that our communication is only about 10% effective (the research shows that this is actually as low as 7%), what I'm saying is that the research shows that text alone can only communicate 10% of the total language, corresponding to reception of only a tiny portion of the information transmitted.
What often makes this considerably worse is something that we've discussed before in other contexts; passive listening.
Passive listening - as opposed to active listening - is when we pick up only on key words in what's being said and immediately start composing our response in our heads (or responding immediately based only on key words, when we're talking about communicating by written text alone - I suppose passive reading is a better term in that context). When we do this, we're not reduced only to 10% of what's being communicated, we're reduced to only that percentage corresponding to those key terms that we're reacting to. This is a massive problem in all sorts of spheres. It's one of the things that those working in customer service training, for example, spend a lot of effort in trying to address. For example, when a customer service agent has taken ten calls about a single complaint, they hear the key words related to that complain in their eleventh call and automatically go to composing their response on the assumption that it's exactly the same complaint. And, of course, that's in an environment in which we still have tone and inflection to rely on to convey information.
When we get triggered by what we think somebody has said, we're responding not to what they've said, but to the triggers. That's what happened here.
Hopefully, this post has both clarified that and been informative regarding how we think about our online interactions, which are massively curtailed by this loss of information. All of the information that we transmit is still being transmitted, of course. When we type our text, our body language is still in play, and our tone and inflection is also there, at least in our heads while we're transmitting, but this information is not being received.
Edited to add: It turns out that the numbers from the Mehrabian study aren't the most robust, and the study has been picked apart in terms of its methodology. However, this doesn't materially affect the underlying point, which is that, when we communicate by text alone, our efficacy is reduced because not all the information if being received.
_______________________________________
The Certainty of Uncertainty - Quantum mechanics and the quantisation of waves
Did You See That?!! - Quantum mechanics and the observer effect
Give Us a Wave! - Waves in classical and quantum mechanics, including sound waves
Paradox! A Game For All The Family. - A treatment of some well-known paradoxes, including a more complete explanation of wave/particle duality
______________________________________
*For the uninitiated, the argument that evolution is 'just a theory' fails to note that a theory is, in scientific parlance, an integrated explanatory framework encompassing all the facts, observations, laws and hypotheses pertaining to a given area of interest, whereas in the vernacular it's a guess.
† T
he pedant in me wants to note that 'systematic' isn't the proper term to use here, as that refers to being methodical or following a set plan. The correct term would be 'systemic', meaning inherent in a system. The author's intent is crystal clear, though, so I'll pretend to keep the pedant silent by relegating him to a footnote.
‡ Mehrabian and Ferris 1967
§ It's worth noting that Shannon's isn't the only definition, nor the only formulation in information theory. Properly, Shannon's work deals only with signal integrity, so would be better thought of as a theory of communication, rather than information. Indeed, Shannon's original paper, submitted to the Bell System Technical Journal in 1948, was entitled 'A Mathematical Theory of Communication'. There's another formulation of information theory concerned with information storage, devised by Andrey Kolmogorov. I discuss the distinction between them in some detail in the post linked above about information in DNA.
** Hertz - named after Heinrich Hertz, the German physicist who first conclusively proved Maxwell's wave theory of electromagnetism. We now know, of course, that electromagnetism isn't waves, and nor is it particles, it's something else that has some of the characteristic behaviours that we associate with waves or particles dependent on how we observe it.
‡‡ decibel - One tenth of a bel, named after Alexander Graham Bell, stemming from it's use as a measurement of telephony power by Bell Systems. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4804152250289917, "perplexity": 1028.8184460412451}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943637.3/warc/CC-MAIN-20230321064400-20230321094400-00022.warc.gz"} |
https://math.stackexchange.com/questions/2475375/volume-of-a-manifold | # Volume of a manifold
Throughout this post, I am presuming $M$ to be an $2$-dimensional manifold that is parametrized by one chart $\varphi$, and I presume $\omega$ be a $2$-form on $M$.
Apparently, there is no natural way to define the volume of a manifold, if it's not a pseudo-Riemannian manifold - i.e., we don't have a metric on it of some kind. Here is a question I have, based on that:
1
My "argument" against this a few days ago was this - why does it not make sense to define the volume as $\int_M 1 dx_1 \wedge .. \wedge dx_n$?
To this I got the reply, that I can "scale" that form, and it still makes perfect sense to define that as volume - so it's arbitrary to choose $1 dx_1 \wedge .. \wedge dx_n$ as opposed to $2 dx_1 \wedge .. \wedge dx_n$. I didn't undestand this argument, but I think I do now, and I'd like to make sure I undestand it correctly.
I think the issue here stems from my previous understanding of $dx_i$ primarily as symbols, as opposed to actual linear maps from the tangent space, that are induced by some map. I thought $1 dx_1 \wedge .. \wedge dx_n$ is the always the same thing as $1 dy_1 \wedge .. \wedge dy_n$, that it's just a different notation of the coordinates - but I see now, that in some sense, that's not the case.
-
As a linear map from the tangent space, the expression $1 dx_1 \wedge .. \wedge dx_n$ by itself doesn't really make sense on it's own, and it's not something I can integrate on $M$ - first, I need to pick a certain chart, to know what $dx_i$ actually are - and this is arbitrary.
More formally:
If for a chart $\varphi$ I denote the 'induced' forms $dx_i$ as those forms, for which $dx_i(\frac{\partial }{\partial x_i})=1$, where $(\frac{\partial }{\partial x_i})$ is the tangent vector induced by $\varphi$. I take a "scaled" version of $\varphi$ and call this new chart $\varphi'$. If I now consider two differential forms :
$\omega = 1 dx_1 \wedge .. \wedge dx_n$ (where $dx_i$ are induced by $\varphi$)
$\omega'= 1 dx_1' \wedge .. \wedge dx_n'$ (where $dx_i'$ are induced by $\varphi'$),
it's actually true that $\omega' = \alpha dx_1 \wedge .. \wedge dx_n$ , for some $\alpha$.
Thus, their integrals will give something different, depending on αα, and choosing one as opposed to the other is arbitrary, and so it doesn't make sense to prefer one as opposed to the other for defining volume.
-
Is my answer to 1 correct?
2
Based on all of this, does it then make sense to think of differential forms as some type of "measure", that gives me volumes of tangent vectors, parallelograms formed by a choice of two tangent vectors, or generalizations of the previous?
Essentially I found that your answer is correct: $dx_1\wedge...\wedge dx_n$ depend by the parametrisation chosen, as in your case, where $\phi$ and $\phi'$ give different differential forms.
2: In general differential forms are not "measures", because they are not always positive. For example there is no $1$-form on $\mathbb{R}^2$ which give you the length of a curves.
But you could think to $n$-form as "functional" on differentiable $n$-subvarieties with satisfies a supplementary condition: you could describe it locally as a alternate form on $n$ copies of the vector space.
So, $1$-forms could be integrated on curves, $2$-forms on surfaces, etc.
For example, the integral $\int_a^bf(x) dx$ could be seen as integrating the differential form $\omega=f(x) dx$ on the interval $[a,b]$, which is a curve of $\mathbb{R}$.
Anyway there is one case where you could consider a differential form as a measure: when $\omega$ is a $n$-differential form on a $n$-dimensional variety, so you could measure a subvarieties $V$ of dimension $n$ calculating $|\int_V \omega|$
Personally, I've found these notes pretty useful in understanding differential forms: http://www.math.uqam.ca/~powell/Bachman_Geometric_Approach_to_Differential_Forms.pdf | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9281095266342163, "perplexity": 163.64344500955903}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195527089.77/warc/CC-MAIN-20190721164644-20190721190644-00278.warc.gz"} |
https://www.thejach.com/view/id/225 | # Removing crap from a git repository's history
When I google "git remove from history" (because I frequently forget the exact sequence of commands as I don't have to remove history very often), this is the first result. It almost works. Don't use it, use the second result. (To further be in favor of the second link, the first is from 2009, the second is from github itself and they're pretty good at keeping their material up-to-date with recent gits.)
My current git version is 1.7.3.4; not the bleeding edge, but if you're using 1.7 at the end of 2011 you're generally in good shape. Anyway, the "I don't know, I don't wanna know" version to getting rid of crap you don't want with some commentary in between:
$du -sh .git 946M .git As you can see, the git repo I'm using is huge. Github soft-limits free users to 300MB; if I want people to fork, it needs to get much smaller. Fortunately, almost all that size comes from a glaring thirdparty/ directory and its history over four branches. (This git repo comes from a perforce one.) So let's kill it! $ git filter-branch --prune-empty --tree-filter 'rm -rf thirdparty/' HEAD
Why tree-filter instead of the faster index-filter? Who cares! I don't wanna know, I want this binary crap gone!
If you have multiple branches where the vile may rest, you have to make sure you switch to them and rerun the command after removing the thing it tells you to remove if you don't remove it before rerunning the command.
$git checkout otherbranch$ rm -rf .git/refs/original
$git filter-branch --prune-empty --tree-filter 'rm -rf thirdparty/' HEAD Etc. Also note that if you have any tags that contained the evilness, make sure you delete those tags or they'll hoard it even after you complete this process. Anyway, presuming your tags are gone and you've killed the data for all the branches you care about: $ du -sh .git
986M .git
$git reflog expire --expire=now --all$ git gc --prune=now
Counting objects: 116947, done.
Delta compression using up to 8 threads.
Compressing objects: 100% (33198/33198), done.
Writing objects: 100% (116947/116947), done.
Total 116947 (delta 91775), reused 94657 (delta 76507)
Removing stale temporary file .git/objects/pack/tmp_pack_5HLLcY
$du -sh .git 712M .git$ git gc --aggressive --prune=now
Counting objects: 116947, done.
Delta compression using up to 8 threads.
Compressing objects: 100% (109654/109654), done.
Writing objects: 100% (116947/116947), done.
Total 116947 (delta 92214), reused 17437 (delta 0)
$du -sh .git 551M .git What's the problem here? At first it was even bigger than before! Now it's at least manageable but it should be smaller... Oh look. I forgot to delete my origin remote tracker and .git/refs/remotes. Let's do that and re-gc. $ git remote rm origin
$rm -rf .git/refs/remotes$ git gc --prune=now
Counting objects: 105938, done.
Delta compression using up to 8 threads.
Compressing objects: 100% (16254/16254), done.
Writing objects: 100% (105938/105938), done.
Total 105938 (delta 82503), reused 105817 (delta 82398)
$du -sh .git 87M .git Huzzah! Much better. Anyway, there you go. It's such a freaky process when there are lots of places where your data could be hiding still, it's so typical of a migration problem instead of a typical use problem. (Typically, if you do something that calls for history deletion like accidentally commiting a password file, you can amend it before anyone notices.) I hope someone finds this useful for when the first google result fails them and instead of clicking the second one they click the Nth one that this blog shows up as. (Okay so neither the first nor second tells you our little secret of --prune-empty with --tree-filter or if it really matters ;) You don't know and don't wanna know!) #### Posted on 2011-12-20 by Jach Tags: git, programming, tips Permalink: https://www.thejach.com/view/id/225 Back to the top Anonymous February 03, 2012 09:49:34 AM Now try running "git gc --aggressive" It's a good idea to squeeze your repo as much as possible before publishing it. Sam February 06, 2013 09:09:46 AM Here's my bad-ass version, called git-gc-all-ferocious! #!/bin/sh -ev git remote rm origin || true git branch -D in || true ( cd .git rm -rf refs/remotes/ refs/original/ *_HEAD logs/ ) git for-each-ref --format="%(refname)" refs/original/ | xargs -n1 --no-run-if-empty git update-ref -d git -c gc.reflogExpire=0 -c gc.reflogExpireUnreachable=0 -c gc.rerereresolved=0 -c gc.rerereunresolved=0 -c gc.pruneExpire=now gc --aggressive "$@"
No doubt I will have to add further crud to it as I discover new ways git tries to hold on to unwanted objects!
Comment using the form below
(Only if you want to be notified of further responses, never displayed.)
LaTeX allowed in comments, use $\\...\\$\$ to wrap inline and $$...$$ to wrap blocks. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.231031134724617, "perplexity": 11002.908645812833}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657149205.56/warc/CC-MAIN-20200714051924-20200714081924-00573.warc.gz"} |
https://math.hecker.org/2011/03/23/linear-algebra-and-its-applications-exercise-1-6-8/ | ## Linear Algebra and Its Applications, Exercise 1.6.8
Exercise 1.6.8. The matrix
$A = \begin{bmatrix} 1&1 \\ 3&3 \end{bmatrix}$
has no inverse. Demonstrate this by trying to solve the following:
$\begin{bmatrix} 1&1 \\ 3&3 \end{bmatrix} \begin{bmatrix} a&b \\ c&d \end{bmatrix} = \begin{bmatrix} 1&0 \\ 0&1 \end{bmatrix}$
Answer: Multiplying the first row of the first marix by the first column of the second matrix gives
$a + c = 1$
However multiplying the second row of the first matrix by the first column of the second matrix gives us
$3a + 3c = 0 \rightarrow a + c = 0$
We thus have a contradiction, and conclude that the matrix is not invertible.
NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.
If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fourth Edition and the accompanying free online course, and Dr Strang’s other books.
This entry was posted in linear algebra. Bookmark the permalink. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 4, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7677938342094421, "perplexity": 437.37092620563214}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704799741.85/warc/CC-MAIN-20210126104721-20210126134721-00347.warc.gz"} |
https://physics.stackexchange.com/questions/104842/infinite-resistive-lattice-problem | # Infinite Resistive lattice problem
While there have been many discussions regarding the solution(say using the Fourier transform or the lattice Green's function approach) to the two-point resistance of an infinite-square resistive lattice my doubt is actually related to one thing common to almost all the approaches to the problem i.e how does having applied a unit current and removed the same current between the points on which one wants to determine the effective resistance between, imply that the currents at the other nodes are zero.Moreover in order to obtain the difference equation (discretized Laplacian) one makes use of the Kirchoff's current law(which talks about the current in the branches connecting neighboring nodes).
So say i applied a unit current, $I_{m,n}=\delta_{m,mo}\delta_{n,no}- \delta_{m,0}\delta_{n,0}$ at the $(m,n)$th point on the lattice. In order to use my KCL i would need talk about the current in the branches which are incident at the point/node (m,n).So this means that the current emanates from point $A$ and reaches $B$, $C$, $D$ and $E$. But then as soon as it reaches those points does it become zero??
But this doesn't make sense right since we are removing the same unit current from another point(different from the m,nth point on the lattice) in this case from node $O$.
Could someone resolve the same for me.
" i.e how does having applied a unit current and removed the same current between the points on which one wants to determine the effective resistance between, imply that the currents at the other nodes are zero."
It doesn't. It implies that the net current at each of the other nodes is zero. In your example, node D, for instance, will have considerable current flowing through it, but the net current will be zero, since all the current flowing into the node also flows out of the node.
• If i am not wrong what you mean by the 'net current' is the time averaged current.So what your saying is that the time averaged current going through the nodes is zero.But the thing is that this problem isn't a dynamical problem in the sense that there are no inductors and capacitors in the lattice.So where does the time dependence come from?? – user42382 Mar 24 '14 at 16:26
• Net current means current flowing into a point minus current flowing out of a point. If the net current wasn't zero, charge would build up there. The only place current can be non-zero is at the two points of interest. – lionelbrits Dec 21 '14 at 23:08
• Current flowing point $A$ will reach point $B$ from four different directions, not just the direct route. And because charge can't build up anywhere, the sum of all the currents reaching $B$ has to be zero. – lionelbrits Dec 21 '14 at 23:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7948371767997742, "perplexity": 382.6434844838984}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668544.32/warc/CC-MAIN-20191114232502-20191115020502-00468.warc.gz"} |
https://www.physicsforums.com/threads/seperating-a-summation-problem.232930/ | # Seperating a Summation problem.
1. May 3, 2008
### DKATyler
[SOLVED] Seperating a Summation problem.
1. The problem statement, all variables and given/known data
The Problem:
Separate a sum into 2 pieces (part of a proof problem).
Using: $$X= \sum^{n}_{k=1}\frac{n!}{(n-k)!}$$
Solve in relation to n and X:
$$\sum^{n+1}_{k=1}\frac{(n+1)!}{(n+1-k)!}$$
2. Relevant equations
???
3. The attempt at a solution
$$\sum^{n}_{k=1}[\frac{(n+1)!}{(n+1-k)!}]+\frac{(n+1)!}{(n+1-[n+1])!}$$
$$\sum^{n}_{k=1}[\frac{(n)!}{(n-k)!}*\frac{(n+1)}{(n+1-k)}]+\frac{(n+1)!}{(n+1-[n+1])!}$$
$$(n+1)*\sum^{n}_{k=1}[\frac{(n)!}{(n-k)!}*\frac{1}{(n+1-k)}]+(n+1)!}$$
I think this is fairly close but, I have no way of getting rid of the 1/(n+1-k) term.
2. May 4, 2008
### Defennder
Can you show that $$\sum_{k=2}^n \frac{n!}{(n-k+1)!} \ + \ \frac{n!}{(n+1-(n+1))!} = \sum^{n}_{k=1}\frac{n!}{(n-k)!}$$?
If you do that, you can express $$\sum^{n+1}_{k=1}\frac{(n+1)!}{(n+1-k)!}$$ as a summation starting from k=2. Then you should be able to get the desired expression.
Try it out for some values of k and n, then you'll see a pattern.
In general the pattern is $$\sum_{k=1}^{n}f(k) = \sum_{k=2}^{n} f(k-1)\ +\ f(n)$$
3. May 4, 2008
### DKATyler
That helps quite a bit.
$$n!+\sum^{n}_{k=2}\frac{n!}{(n+1-k)!}=\sum^{n}_{k=1}\frac{n!}{(n-k)!}=X$$
So continuing from this step:
$$(n+1)*\sum^{n}_{k=1}\frac{n!}{(n-k+1)!}+\frac{(n+1)!}{(n+1-[n+1])!}$$
changing the Index and adding/subtracting n!
$$(n+1)*(1-n!+n!+\sum^{n}_{k=2}\frac{n!}{(n-k+1)!})+(n+1)!$$
Solves the Equation in terms of n and X:
$$(n+1)*(1-n!+X)+(n+1)!$$
Yep, that worked, now I can complete the rest of the proof :) Thank you very much. How to mark this "[solved]?"
4. May 4, 2008
### Defennder
Go to your first post in this thread, at the top right hand corner of the post marked "Thread Tools"
Similar Discussions: Seperating a Summation problem. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8808310031890869, "perplexity": 1304.2005194233268}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320257.16/warc/CC-MAIN-20170624101204-20170624121204-00108.warc.gz"} |
https://www.striim.com/docs/archive/3103GA/en/UUID-1937a0ca-0d8f-c1fd-1f82-d3af03b54333.html | # Striim 3.10.3 documentation
##### Starting the Striim Agent process on the HP NonStop platform
The agent process (WAGENT) must run at all times to allow the Striim server to make connections and request change data from the HP NonStop platform. The agent can be started from the TACL command prompt as follows:
[PARAM WA-LOGPRIORITY <log-level>]
[PARAM ALLOWED-TABLES <allowed-tables-file-name>]
[PARAM WA-ASSUMED-TIMEZONE <time-zone-code>]
[PARAM WA-CHARSET-FOR-CHAR <charset-name>]
[PARAM WA-CHARSET-FOR-NCHAR <charset-name>]
[PARAM WA-CDC-CPU-LIST "<list-of-CPU-numbers>"]
[PARAM WA-ENCRYPT-ALL {TRUE|FALSE}]
[ADD DEFINE =TCPIP^PROCESS^NAME, CLASS MAP, FILE <TCP/IP-process-name> ]
RUN WAGENT [ / NAME <a-name>, TERM $ZHOME/ ] --agent_port <port-num> --logger_name <ems-collector> Where: <log-level> is a number that specifies the highest level of detail for the messages the Striim processes report. Messages at the specified value and below are reported. The permitted values are : 0 FATAL 1 ALERT 2 CRIT 3 ERROR 4 WARN 5 NOTICE 6 INFO 7 DEBUG 8 TRACE The default value is 4, which is WARN, the recommended value for normal use. <allowed-tables-file-name> is the name of the Edit file you created in step 4 of "Installing the agent." If you do not want to control which files can be accessed by Striim applications, you do not have to specify this parameter. <time-zone-code> is the code for the time zone used by date values in the files and tables. The valid values (which are not case-sensitive) are: • GMT for Greenwich Mean Time • LST for Local Standard Time as configured for the NonStop system, ignoring daylight savings time • LCT for Local Civil Time as configured for the NonStop system, including daylight savings time (default used if this PARAM is not specified) <charset-name> is one of the character set names listed in Encoding of character fields and specifies the encoding used for character fields. See that section for a full description of the character set names and the PARAMs with which they are used. <list-of-CPU-numbers> is a list of CPU numbers in which CDC processes may be started. The point of this is so that when more than one CDC process is running, the CDC processes do not all have to run in the same CPU. There might be multiple CDC processes due to having multiple TQL applications running or a single TQL application that uses parallel audit trail reading . The CPU numbers may be separated by spaces or commas. The number of a CPU that is down is accepted, but a number that is larger than the highest numbered CPU is not accepted and causes an error and termination of WAGENT. The CPU numbers in the list are used in round robin fashion when choosing the CPU in which the next CDC process is started, skipping any CPU that currently is down. If the WA-CDC-CPU-LIST PARAM is not present, all CDC processes are started in the CPU in which WAGENT is running. The same CPU number may appear in the list more than once. This can be used to use some CPUs. more often than others for CDC processes. See HP NonStop reader properties for a description of how to request parallel audit trail reading. PARAM WA-ENCRYPT-ALL TRUE encrypts messages between Striim and WAGENT (and all processes started by WAGENT) for applications or flows created WITH ENCRYPTION (see CREATE APPLICATION ... END APPLICATION ). The encryption key is set automatically by Striim. When WA-ENCRYPT-ALL is true, attempting to run an application created without encryption will fail with an error. Similarly, if WA-ENCRYPT-ALL is omitted or FALSE, attempting to run an application created with encryption will fail with an error. To run applications both with and without encryption, start two WAGENT processes, one with WA-ENCRYPT-ALL TRUE and the other without, and specify the port number for the appropriate WAGENT process in the HP NonStop reader properties in the application. Messages related to this encryption may appear in either the NonStop system or Striim server logs, and do not always specifically mention encryption. When WAGENT expects an encrypted message and decryption fails, or when it expects an unencrypted message and fails to parse a GPB object, it writes a warning to its log. If Striim sends a start command that WAGENT does not recognize due to mismatched encryption settings, Striim will write an error to its server log and the application will not start. <TCP/IP-process-name> is the name of the TCP/IP process that the WAGENT and CDC processes should use. The ADD DEFINE command may be omitted if the default process,$ZTC0, is the one that should be used. The ADD DEFINE commands for other DEFINE names that specify TCP/IP settings, such as =TCPIP^HOST^FILE, TCPIP^NETWORK^FILE, etc., also may be included here if the Striim programs must use non-default settings.
<a-name> is a Guardian process name to be used to identify the WAGENT process.
<port-num> is the port number the agent process listens on for connections from the Striim server.
<ems-collector> is the name of an EMS collector process where the agent and CDC processes will write any informational and error messages.
We recommend that you name the agent process to aid process identification, though that is not required.
The Striim processes do not write any messages of their own to the process' home terminal, but if the C++ runtime library reports an error or if one of the processes abends and produces a saveabend file, the messages about those events will be sent to the home terminal. Further, when the agent starts one of the CDC processes, if the agent's home terminal no longer exists, starting the CDC process will fail. For both these reasons, it is best not to let the agent inherit a telnet session's home terminal, but specify a device or process that always exists, such as \$ZHOME or a VHS process, as the TERM argument of the RUN command for WAGENT. Using a VHS process would allow you to control where the messages are logged, which probably would make it easier for you to find them, should some serious error occur in a Striim component. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5876069664955139, "perplexity": 4681.647638663585}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358469.34/warc/CC-MAIN-20211128043743-20211128073743-00292.warc.gz"} |
http://www.boundaryvalueproblems.com/content/2013/1/179 | Research
# Infinitely many solutions for a class of quasilinear elliptic equations with p-Laplacian in R N
Gao Jia*, Jie Chen and Long-jie Zhang
Author Affiliations
College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China
For all author emails, please log on.
Boundary Value Problems 2013, 2013:179 doi:10.1186/1687-2770-2013-179
Received: 15 December 2012 Accepted: 22 July 2013 Published: 6 August 2013
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
### Abstract
In this paper, we study the multiplicity of solutions for a class of quasilinear elliptic equations with p-Laplacian in . In this case, the functional J is not differentiable. Hence, it is difficult to work under the classical framework of the critical point theory. To overcome this difficulty, we use a nonsmooth critical point theory, which provides the existence of critical points for nondifferentiable functionals.
MSC: 35J20, 35J92, 58E05.
##### Keywords:
quasilinear elliptic equations; nondifferentiable functional; p-Laplacian; multiple solutions
### 1 Introduction and main results
Recently, the multiplicity of solutions for the quasilinear elliptic equations has been studied extensively, and many fruitful results have been obtained. For example, in [1], Shibo Liu considered the existence of multiple nonzero solutions of the Dirichlet boundary value problem
(1.1)
where , denotes the p-Laplacian operator, Ω is a bounded domain in with smooth boundary Ω.
Moreover, Aouaoui studied the following quasilinear elliptic equation in [2]:
(1.2)
and proved the multiplicity of solutions of the problem (1.2) by using the nonsmooth critical point theory. One can refer to [3,4] and [5] for more results.
In this paper, we shall investigate the existence of infinitely many solutions of the following problem
(1.3)
where , and , is a given continuous function satisfying
In order to determine weak solutions of (1.3) in a suitable functional space E, we look for critical points of the functional defined by
(1.4)
where . Under reasonable assumptions, the functional J is continuous, but not even locally Lipschitz. However, one can see from [4,6] and [7] that the Gâteaux-derivative of J exists in the smooth directions, i.e., it is possible to evaluate
for all and .
Definition 1.1 A critical point u of the functional J is defined as a function such that , , i.e.,
(1.5)
Our approach to study (1.3) is based on the nonsmooth critical point theory developed in [8] and [9]. Dealing with this class of problems, the main difficulty is that the associated functional is not differentiable in all directions.
The main goal here is to establish multiplicity of results for (1.3), when is odd and is even in s. Such solutions for (1.3) will follow from a version of the symmetric mountain pass theorem due to Ambrosetti and Rabinowitz [10,11]. Compared with problem (1.2) in [2], problem (1.3) is much more difficult, since the discreteness of the spectrum is not guaranteed. Therefore, we only consider the first eigenvalue .
To state and prove our main result, we consider the following assumptions.
Suppose that and .
(H1) Let be a function such that
• for each , is measurable with respect to x;
• for a.e. , is a function of class with respect to s;
• there exist such that
(1.6)
(1.7)
(H2) There exist , and such that
(1.8)
(H3) Let a Carathéodory function satisfy , a.e. and
(1.9)
where θ is the same as that in (H2).
(H4) There exists such that
(1.10)
where is a positive constant.
Example 1.1 Let . The following function satisfies hypotheses (H1) and (H2)
and the corresponding constants are
Example 1.2 The following function satisfies hypotheses (H3) and (H4)
On the other hand, we define the operator . It follows from [12] that the discreteness of the spectrum is not guaranteed. Hence, we only consider the first eigenvalue , where
Next, we can state the main theorem of the paper.
Theorem 1.1Assume thatandsatisfy (H1)-(H4). Moreover, letand, a.e. , . If there exists a positive numberμsuch that, then problem (1.3) has infinitely many distinct solutions in, i.e., there exists a sequence, satisfying (1.3) and, as.
To explain our result, we introduce some functional spaces. We define the reflexive Banach space E of all functions with the norm .
Such a weighted Sobolev space has been used in many previous papers, see [13] and [14]. Now, we give an important property of the space E, which will play an essential role in proving our main results.
Remark 1.1 One can easily deduce and for . More details can be found in [2].
Throughout this paper, let denote the norm of E and () means that converges strongly (weakly) in corresponding spaces. ↪ stands for a continuous map, and ↪↪ means a compact embedding map. C denotes any universal positive constant unless specified.
The paper is organized as follows. In Section 2, we introduce the nonsmooth critical framework and preliminaries to our work. In Section 3, we give some lemmas to prove the main result. Finally, the proof of Theorem 1.1 is presented in Section 4.
### 2 Nonsmooth critical framework and preliminaries
Our results are based on the techniques of nonsmooth critical point theory. In this section, we recall some basic tools from [8] and [9].
Definition 2.1 Let be a metric space, let be a continuous functional and . We denote by the supremum of the σ’s in such that there exist and a continuous map , satisfying
The extended real number is called the weak slope of I at u.
Note that the notion above was independently introduced in [15], as well.
Definition 2.2 Let be a metric space, let be a continuous functional and . We say that I satisfies , i.e., the Palais-Smale condition at level c, if every sequence in X with and admits a strongly convergent subsequence.
In order to treat the Palais-Smale condition, we need to introduce an auxiliary notion.
Definition 2.3 Let c be a real number. We say that functional I satisfies the concrete Palais-Smale condition at level c ( for short) if every sequence satisfying
possesses a strongly convergent subsequence in E, where is some real number converging to zero.
Remark 2.1 Under assumptions (H1)-(H4), if the functional J satisfies (1.4), then J is continuous, and for every we have
where denotes the weak slope of J at u.
Remark 2.2 Let c be a real number. If J satisfies , then J satisfies .
Proof Let be a sequence such that
Note that for ,
By Remark 2.1, we have . Taking , the conclusion follows. □
### 3 Basic lemmas
To derive our main theorem, we need the following lemmas. The first lemma is the version of the Ambrosetti-Rabinowitz mountain pass lemma [10,11] and [16].
Lemma 3.1LetXbe an infinite-dimensional Banach space, and letbe a continuous even functional satisfyingfor every. Assume that
(i) there exist, and a subspaceof finite codimension such that
(ii) for every finite-dimensional subspace, there existssuch that
Then there exists a sequenceof critical values ofIwith.
Lemma 3.2Ifis a critical point ofJ, then.
Proof For , , consider the real functions , and defined in ℝ by
(3.1)
and . Denoting and , we can take as a test function in (1.5). Therefore,
Noting that and , we get
From (1.10) and the fact we deduce
Since a.e. in and in E as . It follows from that
Denote . If , then the result is true. In the following discussion, is assumed. By (1.6), we obtain
(3.2)
Note that , then we can get
(3.3)
On the other hand, we have
which implies that
(3.4)
Eventually, one can deduce from (3.2)-(3.4) that
(3.5)
By Theorem 5.2 of [17], we get that . Replacing by , we can similarly prove that . We conclude that , and the proof of Lemma 3.2 is completed. □
Lemma 3.3Letbe a bounded sequence inEwith
(3.6)
whereis a sequence of real numbers converging to zero. Then there existssuch thata.e. inand, up to a subsequence, is weakly convergent touinE. Moreover, we have
(3.7)
i.e., uis a critical point ofJ.
Proof Since is bounded in E, and there is a (see [18]) such that, up to a subsequence,
Moreover, since satisfies (3.6), by Theorem 2.1 of [19], we have, up to a further subsequence, a.e. in .
We will use the device of [20]. We consider the test functions
(3.8)
where , and . According to (1.6) and (1.7), we have
Since (3.6) holds by density for every , we can put in (3.6) and obtain that
(3.9)
On the other hand, note that
(3.10)
One can deduce from (3.10) and Fatou’s lemma that
(3.11)
We consider the test functions with , and , , ,
This together with (3.11) can prove that
(3.12)
In a similar way, by considering the test functions , it is possible to prove that
(3.13)
From (3.12) and (3.13), it follows that
(3.14)
Finally, we can deduce (3.7) from (3.14). □
Remark 3.1 (see [21])
Let be a sequence in E satisfying (3.6). Then and
(3.15)
In the following lemma, we will prove the boundedness of a sequence under (1.6), (1.8) and (1.9).
Lemma 3.4Letandbe a sequence inEsatisfying (3.6) and
(3.16)
Thenis bounded inE.
Proof Calculating , from (3.15) and (3.16), we obtain
From (1.8) and (1.9), it follows that
(3.17)
Moreover, there exist and such that
Therefore, denoting , we obtain from (3.17) that
(3.18)
By virtue of hypothesis (H3), we know that there exist and such that
(3.19)
From (3.18) and (3.19), it follows that
(3.20)
On the other hand, by Hölder’s inequality and Young’s inequality, for all , there exists such that
(3.21)
Using (3.20) and (3.21), we get
(3.22)
Choosing in (3.22), we find that is bounded in E. □
Lemma 3.5Letbe the same as that in Lemma 3.3. Then, up to a subsequence, converges strongly touinE.
Proof By Lemma 3.3, we know that u is a critical point of the functional J. Then, from Lemma 3.2, we get . Therefore, taking as a test function in (3.7), we get
(3.23)
By virtue of is bounded in E, we can assume that there exists satisfying
By Lemma 3.3, a.e. in . Then by Fatou’s lemma, we have
(3.24)
Moreover, by and , we get
(3.25)
(3.26)
By using (3.23)-(3.26) and passing to limit in (3.15), we obtain
(3.27)
On the other hand, by Lebesgue’s dominated convergence theorem and the weak convergence of to u in E, we get
(3.28)
(3.29)
(3.30)
Moreover, since and are bounded in , then we have
Therefore, from the definition of weak convergence, we obtain
(3.31)
(3.32)
Combining (3.27)-(3.32), it follows that
It is well known that the following inequality
(3.33)
holds for any , and . Therefore,
According to (1.6), we conclude that converges strongly to u in E. □
Lemma 3.6For every real numberc, the functionalJsatisfies.
Proof Let be a sequence in E satisfying (3.6) and (3.16). By Lemma 3.4, is bounded in E. Therefore, the conclusion can be deduced from Lemma 3.5. □
### 4 Proof of Theorem 1.1
It is easy to check that the functional J is continuous and even. Moreover, by Remark 2.2 and Lemma 3.6, J satisfies for every .
On the other hand, from (1.4), (1.6), (1.9) and (1.10), for , we have
(4.1)
We discuss (4.1) in the following two cases:
In case , we get
In case , by the definition of , we get
i.e., . Therefore, if λ satisfies , there exist small enough and such that
Hence, condition (i) of Lemma 3.1 holds with .
Now we consider a finite-dimensional subspace W of E. Let and . From (1.6), we have
(4.2)
By virtue of (1.9) and (1.10), we know that there exist , satisfying a.e. and a positive constant such that
(4.3)
Combining (4.2)-(4.3), we have
(4.4)
Since W is finite-dimensional, then all norms of W are equivalent. From (4.4), there exists such that
In view of , we deduce that the set is bounded in E and condition (ii) of Lemma 3.1 holds. By Lemma 3.1, the conclusion follows.
### Competing interests
The authors declare that they have no competing interests.
### Authors’ contributions
We declare that all authors collaborated and dedicated the same amount of time in order to perform this article.
### Acknowledgements
The authors express their sincere thanks to the referees for their valuable criticism of the manuscript and for helpful suggestions. This work has been supported by the Natural Science Foundation of China (No. 11171220) and Shanghai Leading Academic Discipline Project (XTKX2012).
### References
1. Liu, SB: Multiplicity results for coercive p-Laplacian equations. J. Math. Anal. Appl.. 316, 229–236 (2006). Publisher Full Text
2. Aouaoui, S: Multiplicity of solutions for quasilinear elliptic equations in . J. Math. Anal. Appl.. 370(2), 639–648 (2010). Publisher Full Text
3. Alves, CO, Carrião, PC, Miyagaki, OH: Existence and multiplicity results for a class of resonant quasilinear elliptic problems on . Nonlinear Anal.. 39, 99–110 (2000). Publisher Full Text
4. Canino, A: Multiplicity of solutions for quasilinear elliptic equations. Topol. Methods Nonlinear Anal.. 6, 357–370 (1995)
5. Squassina, M: Existence of multiple solutions for quasilinear diagonal elliptic systems. Electron. J. Differ. Equ.. 1999, 1–12 (1999)
6. Arcoya, D, Boccardo, L: Critical points for multiple integrals of the calculus of variations. Arch. Ration. Mech. Anal.. 134, 249–274 (1996). Publisher Full Text
7. Arcoya, D, Boccardo, L: Some remarks on critical point theory for nondifferentiable functionals. NoDEA Nonlinear Differ. Equ. Appl.. 6, 79–100 (1999). Publisher Full Text
8. Corvellec, JN, Degiovanni, M, Marzocchi, M: Deformation properties of continuous functionals and critical point theory. Topol. Methods Nonlinear Anal.. 1, 151–171 (1993)
9. Degiovanni, M, Marzocchi, M: A critical point theory for nonsmooth functionals. Ann. Mat. Pura Appl.. 167(4), 73–100 (1994)
10. Ambrosetti, A, Rabinowitz, PH: Dual variational methods in critical point theory and applications. J. Funct. Anal.. 14, 349–381 (1973). Publisher Full Text
11. Silva, EAB: Critical point theorems and applications to differential equations. Ph.D. thesis, University of Wisconsin-Madison (1988)
12. Brasco, L, Franzina, G: On the Hong-Krahn-Szego inequality for the p-Laplace operator. Manuscr. Math.. 141, 537–557 (2013). Publisher Full Text
13. Bartsh, T, Wang, ZQ: Existence and multiplicity results for some superlinear elliptic problems on . Commun. Partial Differ. Equ.. 20, 1725–1741 (1995). Publisher Full Text
14. Rabinowitz, PH: On a class of nonlinear Schrödinger equations. Z. Angew. Math. Phys.. 43, 270–291 (1992). Publisher Full Text
15. Katriel, G: Mountain pass theorems and global homeomorphism theorems. Ann. Inst. Henri Poincaré, Anal. Non Linéaire. 11, 189–209 (1994)
16. Rabinowitz, PH: Minimax Methods in Critical Point Theory with Applications to Differential Equations, Am. Math. Soc., Providence (1986)
17. Ladyzenskaya, OA, Uralceva, NN: Equations aux dérivées partielles de type elliptiques, Dunod, Paris (1968)
18. Brezis, H, Lieb, E: A relation between pointwise convergence of functions and convergence of functionals. Proc. Am. Math. Soc.. 88, 486–490 (1983)
19. Boccardo, L, Murat, F: Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations. Nonlinear Anal.. 19, 581–597 (1992). Publisher Full Text
20. Boccardo, L, Murat, F, Puel, JP: Existence de solutions non bornées pour certaines équations quasi-linéaires. Port. Math.. 41, 507–534 (1982)
21. Brezis, H, Browder, FE: Sur une propriété des espaces de Sobolev. C. R. Math. Acad. Sci. Paris. 287, 113–115 (1978) | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9901118278503418, "perplexity": 912.6981041916612}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246654264.98/warc/CC-MAIN-20150417045734-00212-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://tex.stackexchange.com/questions/127466/how-can-i-effect-line-breaks-within-the-title-without-hardcoding-s-in-title | # How can I effect line breaks within the title without hardcoding \\'s in \title?
Although I do need line breaks within my title for my document's title page (I'm using the book class), I'd like to avoid hardcoding line breaks in the argument passed to the \title command, for three reasons:
1. I always endeavour to separate form and content, for maintainability reasons.
2. The title may need to be inserted elsewhere in the document, in places where line breaks within it are not warranted.
3. I pass my title to\hypersetup{pdftitle=...}; hyperref returns a warning,
Token not allowed in a PDF string (PDFDocEnconding):(hyper ref) removing \\'
if the title contains some \\, and I want to limit the number of compilation warnings to the bare minimum.
How can I effect line breaks at specific places within the title, upon inserting the latter somewhere in my document, without hardcoding \\'s in the \title{...} command? What's the best practice?
\documentclass{book}
\author{Me, me, me}
%\title{Me, myself, and I} % compiles without mishap; strictly content
\title{Me,\\ myself, \\ and I} % compilation warnings occur; form and content are mixed
\usepackage{kantlipsum}
\usepackage{hyperref}
\makeatletter
\hypersetup{
pdftitle = \@title,
}
\makeatother
\begin{document}
\maketitle
\kant
\end{document}
• @AndrewSwann I didn't think the question warranted an MWE, but sure; it's on the way. – jub0bs Aug 9 '13 at 12:19
• @Jubobs, I think Andrew Swann may have had the same though as me, I'd like to figure out why you need a forced line break in the title, rather than a subtitle – Chris H Aug 9 '13 at 12:21
• Well for one thing, the title macro depends on the documentclass, and may or may not take an optional argument that could be used. Then there is \textorpdfstring for hyperref... – Andrew Swann Aug 9 '13 at 12:23
• @ChrisH I can sympathisze with the general thought. Title layout on the page and its line breaks is quite critical with regard to emphasing/deemphasing certain words etc. – Andrew Swann Aug 9 '13 at 12:25
• @AndrewSwann You're right: using \texorpdfstring would obviate the warning. However, what about my 2nd point? What if I need to format my title in a different way, somewhere else than on the title page? – jub0bs Aug 9 '13 at 12:30
if you always want certain phrases "tied together", use the ~ (tilde = tie) instead of a space between them. sometimes this works to encourage a line break, but sometimes you end up with an overfull box and still have to break the line explicitly.
(this is the same approach recommended in the texbook for keeping things like "Dr.~No" and "Figure~1" from breaking apart at the end of a line.)
the actual result depends on how the \title argument is processed; the stretch has to be defined with sufficient flexibility, which depends on the document class.
• This tilde trick let me line-break a section title properly, in a place where \\ would accidentally introduce a page break at the line break! – Camille Goudeseune Oct 21 '15 at 21:46
The easiest way is using option pdfusetitle and without spaces around \\ in \title:
\documentclass{book}
\usepackage{kantlipsum}
\usepackage[pdfusetitle]{hyperref}
\author{Me, me, me}
\title{Me,\\myself,\\and I}
\begin{document}
\maketitle
\kant
\end{document}
Result of pdfinfo:
Title: Me, myself, and I
Author: Me, me, me
Otherwise, there is \texorpdfstring:
\title{My,\texorpdfstring{\\}{ }myself,\texorpdfstring{\\}{ }and I}
Or \pdfstringdefDisableCommands can be used, e.g.:
\pdfstringdefDisableCommands{\def\\#1{ #1}}
That is the definition that is used for the title with option pdfusetitle, it supports the following forms:
\title{Me,\\myself,\\and I}
\title{Me,\\ myself,\\ and I}
If you prefer more spaces:
\pdfstringdefDisableCommands{\let\\\@firstofone}
\title{Me, \\ myself, \\ and I}
The trick with the argument is, that TeX does not accept a space as undelimited argument. Thus the space after \\ is gobbled.
The spaces are one of the reasons, that \\ is not provided by hyperref and a warning is given. The usual tricks (\unskip, \ignorespaces, ...) are not working inside the generation of PDF strings.
• Such a great answer! Thanks. I guess I can also use \texorpdfstring to include nonbreaking spaces in the title as recommended by Barbara. – jub0bs Aug 9 '13 at 13:33
• @Jubobs: ~ is supported by hyperref, no need for \texorpdfstring. – Heiko Oberdiek Aug 9 '13 at 13:34
• @HeikoOberdiek As a substitute for \ignorespaces inside the generation of PDF strings, you could use \romannumeral-^^ \q. Of couse, that leaves a preceeding space: this could be a problem. Alternatively, one could implement \unskip by adding a step after the full expansion and after stripping braces which would strip all occurrences of <space>\unskip`. – Bruno Le Floch Aug 9 '13 at 18:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9848766922950745, "perplexity": 3559.981520536661}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027323246.35/warc/CC-MAIN-20190825084751-20190825110751-00065.warc.gz"} |
https://www.physicsforums.com/threads/micro-econ-mr-mc-ac-etc-help.659359/ | # Micro econ MR MC AC etc help
1. Dec 16, 2012
### GZA09
Micro econ MR MC AC etc help!!
1. The problem statement, all variables and given/known data
The adjacent graph (I've attached it) shows the short-run cost situation of a competitive, profit-maximizing firm. Assume that MC is plotted between units. Determine for each of the following prices: i) $150 ii)$200 iii) $230 iv)$350
a) equilibrium output
b) marginal revenue
c) marginal cost
d) average cost
e) profit per unit
f) total revenue
g) total cost
2. Relevant equations
These were what i could find in my notes that are related but they dont seem to help :/
Total cost = variable cost + fixed cost
Average cost = total cost / q
3. The attempt at a solution
Well by looking at the graph i was able to find out the equillibrium outputs, and using a rule that states that Price = Marignal cost and price = marginal revenue, i found those two.
Price:---------150-------200------230------350
Equill Output:--15--------17-------18-------21
Marginal R:----150-------200------230------350
Marignal C:----150-------200------230------350
Average C:
Profit/unit:
Total R:
Total cost:
Total profit:
Thank you :/ i have an exam in 2 days and im totally stumped on this :(
#### Attached Files:
• ###### photo.JPG
File size:
78.2 KB
Views:
68
Can you offer guidance or do you also need help?
Draft saved Draft deleted
Similar Discussions: Micro econ MR MC AC etc help | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5814972519874573, "perplexity": 8568.222785100772}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948627628.96/warc/CC-MAIN-20171218215655-20171219001655-00291.warc.gz"} |
https://www.physicsforums.com/threads/determining-which-coffee-has-a-greater-rate-of-cooling.526063/ | # Determining which coffee has a greater rate of cooling
1. Aug 31, 2011
Hey,
I have this math investigation task which asks us to model the cooling of coffee in three different cups over a period of time. Anyway, i got the data, did a scatter plot and found the exponential model, but i dont know how i could determine which one has the greatest rate of cooling.
I know that I need to look at the slope, but they dont all start from the same point on the graph, so i cant determing which one has the fastest rate of decay. If they all started from the same point i would be able to see the different functions branching off from that point, and if one has a steeper slope than the other i would know, but this wasnt the case. Can someone please help! Thanks.
2. Aug 31, 2011
### micromass
Staff Emeritus
Calculate the slope at a common point. For example, take the point 40° at every coffee and calculate the slope at that point.
3. Aug 31, 2011
Hey thanks man. Do you know if the relationship of the derivative of the three graphs will change. So if i measure the derivative of each graph at some temperature (remember it's exponential) and find that one graph has a steeper slope than the other... could that change? so the other graph will now have the steeper slope? Because if that is true, then we cant use that to determine which graph has the fastest rate of cooling overall. Thanks. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8165688514709473, "perplexity": 332.71567020067806}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818687281.63/warc/CC-MAIN-20170920123428-20170920143428-00151.warc.gz"} |
https://www.idiap.ch/software/bob/docs/bob/bob.extension/stable/pip.html | # Using pip for development¶
Warning
This guide is not complete and not recommended. You can just skip this page. There are some problems when using pip and conda at the same time which may lead to breaking all your conda environments. You can look at the conda develop command for an alternative.
Since all Bob packages are distributed with Setuptools, you can easily develop them using pip. Additionally, you can use conda to create separate isolated environments for your different tasks.
Note
Keep this in mind: 1 task, 1 environment. Do not mix.
Note
This guide does not aim to duplicate the pip’s user guide. Please go through that first to make sure you are confident in using pip before continuing here.
Developing a Bob package with pip can be as easy as running the following command while your current directory is the source of the package that you want to develop:
pip install -e .
This will install the current package in your Python environment in an editable mode. You can keep changing this package at its source directory and your changes will be immediately reflected in your environment.
Warning
If you modify the contents of setup.py such as adding or removing console script entry points, you need to run pip install -e . again.
## Developing a C++ Package¶
While developing a C++ package, the same pip install -e . command can be used to compile the package again. Also, you may want to export some debugging flags if you want to debug the current package:
export CFLAGS=$CFLAGS -O0 -g -DBOB_DEBUG -DBZ_DEBUG export CXXFLAGS=$CXXFLAGS -O0 -g -DBOB_DEBUG -DBZ_DEBUG
pip install -e .
## Developing Several Packages from Source¶
Often it is required not only to develop the current package but also to develop several dependencies from source too. To do so, you can create a requirements file (usually named requirements.txt) and run the following command:
pip install -r requirements.txt
while the content of your requirements.txt file lists the packages that the current package both depends on and the dependencies that you want to develop. For example, the following requirements.txt file can be used to develop bob.io.image, together with all of its direct and indirect dependencies:
setuptools
-egit+https://gitlab.idiap.ch/bob/bob.extension.git#egg=bob.extension
-egit+https://gitlab.idiap.ch/bob/bob.blitz.git#egg=bob.blitz
-egit+https://gitlab.idiap.ch/bob/bob.core.git#egg=bob.core
-egit+https://gitlab.idiap.ch/bob/bob.io.base.git#egg=bob.io.base
matplotlib
However because of a limitation of pip, you need to install the Bob dependencies that contain C++ code both in order and one by one. This means that pip install -r requirements.txt will not work in this case. Instead, you can run the following command:
tr '\n' '\0' < requirements.txt | xargs -0 -n 1 pip install
Warning
For the tr '\n' '\0' < requirements.txt | xargs -0 -n 1 pip install command to work, you should not have any spaces in your requirements.txt file (notice that -egit+https://... has no spaces) and your Bob dependencies should be listed in their order of dependencies. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31675970554351807, "perplexity": 2733.348803134932}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794864572.13/warc/CC-MAIN-20180521235548-20180522015548-00463.warc.gz"} |
http://www.federica.unina.it/smfn/high-energy-astrophysics/emission-processes-ii/ | # Maurizio Paolillo » 5.Emission processes – Part II
### Contents
• Radiative recombination of heavy ions.
• Coronal approximation.
• Cooling function.
### Thermal plasma emission
X-ray emission in astrophysical plasmas at temperatures T~106-7 ºK (kT~0.1-1 keV) is mainly due to radiative recombination and line emission processes.
In fact these temperatures are too low for Bremsstrahlung to be dominant.
These conditions characterize very different astrophysical sources: from stellar coronae to the diffuse gaseous halos of massive galaxies.
The image on the left shows an X-ray image of a massive elliptical galaxy whose emission is almost entirely due to the radiative recombination and line emission processes described below.
In the lower left corner the smaller companion NGC1404 has a much smaller and compact halo. Several compact sources, mostly background AGNs and accreting bynary stars (see later lectures), are also visible.
X-ray image of the massive elliptical galaxy NGC 1399 in the Fornax cluster. The emission is represented on a logarithmic color scale which traces the surface brightness. Courtesy of M.Paolillo.
### Stellar coronal emission
This emission process was first observed in the corona of the Sun, and thus it is called “coronal emission”.
The turbulence in the upper layer of a star creates magnetic loops trapped inside the sun’s plasma, whose energy can heat the corona to temperatures that allow it to emit X-rays through radiative recombination and line emission.
This is a solar coronal loop imaged by the TRACE satellite. Courtesy of NASA.
### Coronal approximation
To describe the ionization state and X-ray line and continuum emission from a low density (n =10-1÷10-3 cm-3), hot (t =106÷8 K) plasma, several simple assumptions can be made:
1. the time scale for elastic Coulomb collisions between particles in the plasma is much shorter than the age or cooling time of the plasma, and thus the free particles can be assumed to have a Maxwell-Boltzmann distribution at the temperature Tg This is the kinetic temperature of electrons, and therefore determines the rates of all excitation and ionization processes.
2. at these low densities collisional excitation and de-excitation processes are much slower than radiative decays, and thus any ionization or excitation process will be assumed to be initiated from the ground state of an ion.
3. Three-body (or more) collisional processes will be ignored because of the low density.
### Coronal approximation (cont’ed)
4. the radiation field in a stellar corona, a galaxy or a cluster is sufficiently diluted that stimulated radiative transitions are not important, and the effect of the radiation field on the gas is insignificant.
at these low densities, the gas is optically thin and the transport of the radiation field can therefore be ignored.
5. Under these conditions, ionization and emission result primarily from collisions of ions with electrons, and collisions with ions can be ignored.
Finally, in galaxies and clusters (but not in stellar coronae) the time scales for ionization and recombination are generally considerably less than the age of the system or any relevant hydrodynamic time scale, and the plasma can therefore be assumed to be in ionization equilibrium.
### Coronal X-ray line emission
The helium and hydrogen in stellar, galactic and cluster coronae is all ionized, so X-ray line emission comes from transitions in trace element atoms.
### X-ray continuum emissivity in coronal plasmas
The X-ray continuum emission from a hot diffuse plasma is due primarily to three processes:
1. thermal bremsstrahlung (free-free emission),
2. recombination (free-bound) emission, and
3. two-photon decay of metastable levels.
The emissivity (emission per unit volume) for thermal Bremsstrahlung, as discussed in a previous lecture, is given by:
### X-ray continuum emissivity in coronal plasmas
The radiative recombination (bound-free) continuum emissivity is usually calculated by applying the Milne relation for detailed balance to the photoionization cross sections, which yields the following emissivity expression:
### X-ray line emission in coronal plasmas
Processes that contribute to the X-ray line emission from a diffuse plasma include collisional excitation of valence or inner shell electrons, radiative and dielectronic recombination, inner shell collisional ionization, and radiative cascades following any of these processes.
The emissivity due to a collisionally excited line is usually written (Osterbrock, 1974):
### Cooling function
All of the emission processes described above give emissivities that increase proportionally to the ion and electron densities, and otherwise depend only on the temperature.
Thus a general expression for the emissivity in coronal plasmas is given by the formula:
where Ln(Xi,Tg) is the emission per ion at unit electron density and is usually called “cooling function”.
The cooling function incorporates all physical processes described in these lectures, and is usually calculated using numerical codes that compute the atomic transition rates for each element and ionization state.
### Cooling function (cont’ed)
If n(X) is the total density of the element X, then in equilibrium the ionization fractions f(Xi) n(Xi)/n(X) depend only on the temperature, and previous equation can be written as:
This allows to separate the dependence on the temperature, from the one on the density, if we assume to know the ionization fractions and the metallicity of the plasma.
### Emission Integral
Since most astrophysical observable quantities are integrated over large volumes or at the least over the line of sight, it is useful to define the emission integral EI as:
Then the shape of the spectrum depends only on the abundances of elements n(X)/n(h) and the distribution of temperatures d(EI) / dTg.
The normalization of the spectrum (the overall level or luminosity) is thus set by the EI.
### The Cosmic Cooling curve
The Cooling Function at low and intermediate X-ray emitting regimes, and its dependence on the metallicity.
### The Cosmic Cooling curve
Dependence of the Cooling function on temperature and metallicity of the plasma.
### Spectrum of a thermal plasma
Example of the spectrum produced by the thermal plasma of a galaxy cluster at different temperatures: as the temperature drops the emission lines due to radiative recombination becomes apparent.
### I materiali di supporto della lezione
Craig L. Sarazin, X-ray Emission from Clusters of Galaxies.
Progetto "Campus Virtuale" dell'Università degli Studi di Napoli Federico II, realizzato con il cofinanziamento dell'Unione europea. Asse V - Società dell'informazione - Obiettivo Operativo 5.1 e-Government ed e-Inclusion | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9857515096664429, "perplexity": 2684.9904494594025}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125948047.85/warc/CC-MAIN-20180426012045-20180426032045-00161.warc.gz"} |
https://infoscience.epfl.ch/record/152714 | Infoscience
Journal article
# Influence of pressure on the optical properties of InxGa1-xN epilayers and quantum structures
The influence of hydrostatic pressure on the emission and absorption spectra measured for various types of InGaN structures (epilayers, quantum wells, and quantum dots) is studied. While the known pressure coefficients of the GaN and InN band gaps are about 40 and 25 meV/GPa, respectively, the observed pressure-induced shifts in light emission energy in the InGaN alloys differ significantly from concentration-interpolated values. With increasing In concentration, and thus decreasing emission energy, the observed pressure coefficients become very small, reaching zero for emission energies similar to2 eV (roughly the value of the InN band gap). On the other hand, the pressure coefficient derived from absorption experiments exhibit a much smaller decrease with decreasing energy when referred to the same scale as the emission data. First-principles calculations of InGaN band structures and their modification with pressure are performed. The results are not able to explain the huge effect observed in the emission experiments, but they are in good agreement with the optical absorption data. Significant bowings of the band gap and its pressure coefficients are found, and they are especially large for small In concentrations. This behavior is related to the changes in the upper valence band states due to In alloying. Some possible mechanisms are discussed which might be expected to account for the low pressure coefficients of the light emission energy and the difference between the sensitivity of the emission and absorption to pressure. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9652157425880432, "perplexity": 883.0291221600368}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171416.74/warc/CC-MAIN-20170219104611-00057-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://gamedev.stackexchange.com/questions/166503/error-in-draw-gui-event-on-android-gamemaker | # Error in DRAW GUI event on android. (GameMaker)
Image of the game on a mobile phone:
As you can see the maze (draw event) has been resized correctly.
But the yellow post-it (draw GUI event) has not been scaled or displayed in the correct location (center of the screen). Same thing with GUI layout (draw GUI event).
Because this is a small stage/room (size) I do not use the artifice of views, I thought that could be because of that the problem, but I enabled the views and did not get any different result.
Picture of the game on a computer (like it should be on the phone):
OBS - One information that can help you to help me solve the problem, is that to draw the post- it I use the following code: draw GUI event draw_sprite(spr_Post,0,640,360);.
640 is the half screen width of the game and also the room, 360 is half the height of the game screen and also the room.
It seems that somehow the room on the cell phone is different size than 1280x720.
I do not put the following code: draw GUI event draw_sprite(spr_Post,0,room_width/2,room_height/2), because there are much larger phases that need views, so the post-it needs to be in the center of the screen of the player, and with this code it ends up being in the center of the phase.
I tested the game on Bluestacks and it did not happen the same as on the phone.
• This sounds like a game maker bug. I would send an email to yoyogames asking for more details. – user64742 Dec 28 '18 at 4:42
Here I am again to the rescue XD
Instead of using room_width or room_height that are the size of the room, use the size of the view, the variables are view_xview, view_yview, view_wview and view_hview that are related to the current view so use the index [0] with the number of the view on all variables.
draw_sprite(sprite_index, view_xview[0]+view_wview[0]/2, view_yview[0]+view_hview[0]/2);
It will make the object origin to be in the center of the screen/view.
Edit: The Draw_GUI event is relative to the view coordinate system. Edit2: added some code to try
Check them in the manual to see examples.
• I changed the code to draw_sprite(spr_Post,0,view_wview[view_object]/2,view_hview[view_object]/2); and did not change the result. – Boneco Sinforoso Feb 18 '19 at 13:47
• Before I tried with the number of the vision, but also with no result. – Boneco Sinforoso Feb 18 '19 at 13:48
• I've added some code, it is typically used to fix healthbars to the view – Juanpa Feb 18 '19 at 15:41
• For me it worked as follows: display_set_gui_size(1280,720);. In the next line just put: draw_sprite(spr_Post,0,640,360); – Boneco Sinforoso Feb 19 '19 at 12:35
• @BonecoSinforoso If that worked for you, please consider sharing it as an answer that you can mark Accepted. – DMGregory Mar 20 '19 at 16:56
display_set_gui_size(1280,720);
draw_sprite(spr_Post,0,640,360); | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2980905771255493, "perplexity": 1321.3321989859687}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154466.61/warc/CC-MAIN-20210803155731-20210803185731-00139.warc.gz"} |
https://www.physicsforums.com/threads/please-check-this-differentiation-result.164188/ | # Please check this differentiation result
1. Apr 5, 2007
### cabellos
I have to differentiate (e^-x) ((1-x)^1/2)
(-e^-x) ((1-x)^1/2) + (e^-x)/((-1/2 + 1/2x)^-1/2))
is this correct?
thankyou
2. Apr 5, 2007
### Vagrant
In the second part I belive the -1/2 term is outside the underroot
3. Apr 5, 2007
### cristo
Staff Emeritus
You want to differentiate this: $e^{-x}(1-x)^{1/2}$? You have used the product rule correctly, but the second term is incorrect. The second term is $$e^{-x}\frac{d}{dx}(1-x)^{1/2}=e^{-x}(1-x)^{-1/2}\cdot(-\frac{1}{2})$$
Note that, when using the chain rule on the parentheses, whatever's inside the parentheses does not change.
Similar Discussions: Please check this differentiation result | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9063246250152588, "perplexity": 3898.669078061883}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948523222.39/warc/CC-MAIN-20171213123757-20171213143757-00443.warc.gz"} |
https://dmtcs.episciences.org/2508 | ## Rubey, Martin and Westbury, Bruce W. - Combinatorics of symplectic invariant tensors
dmtcs:2508 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Combinatorics of symplectic invariant tensors
Authors: Rubey, Martin and Westbury, Bruce W.
An important problem from invariant theory is to describe the subspace of a tensor power of a representation invariant under the action of the group. According to Weyl's classic, the first main (later: 'fundamental') theorem of invariant theory states that all invariants are expressible in terms of a finite number among them, whereas a second main theorem determines the relations between those basic invariants.Here we present a transparent, combinatorial proof of a second fundamental theorem for the defining representation of the symplectic group $Sp(2n)$. Our formulation is completely explicit and provides a very precise link to $(n+1)$-noncrossing perfect matchings, going beyond a dimension count. As a corollary, we obtain an instance of the cyclic sieving phenomenon.
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: invariant tensors,cyclic sieving phenomenon,matchings,classical groups,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM] | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.688188910484314, "perplexity": 1343.2705678181135}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401578485.67/warc/CC-MAIN-20200927183616-20200927213616-00794.warc.gz"} |
http://eprint.iacr.org/2013/657 | ## Cryptology ePrint Archive: Report 2013/657
New Trapdoor Projection Maps for Composite-Order Bilinear Groups
Sarah Meiklejohn and Hovav Shacham
Abstract: An asymmetric pairing over groups of composite order is a bilinear map $e: G_1 \times G_2 \to G_T$ for groups $G_1$ and $G_2$ of composite order $N=pq$. We observe that a recent construction of pairing-friendly elliptic curves in this setting by Boneh, Rubin, and Silverberg exhibits surprising and unprecedented structure: projecting an element of the order-$N^2$ group $G_1 \oplus G_2$ onto the bilinear groups $G_1$ and $G_2$ requires knowledge of a trapdoor. This trapdoor, the square root of a certain number modulo $N$, seems strictly weaker than the trapdoors previously used in composite-order bilinear cryptography.
In this paper, we describe, characterize, and exploit this surprising structure. It is our thesis that the additional structure available in these curves will give rise to novel cryptographic constructions, and we initiate the study of such constructions. Both the subgroup hiding and SXDH assumptions appear to hold in the new setting; in addition, we introduce custom-tailored assumptions designed to capture the trapdoor nature of the projection maps into $G_1$ and $G_2$. Using the old and new assumptions, we describe an extended variant of the Boneh-Goh-Nissim cryptosystem that allows a user, at the time of encryption, to restrict the homomorphic operations that may be performed. We also present a variant of the Groth-Ostrovsky-Sahai NIZK, and new anonymous IBE, signature, and encryption schemes.
Category / Keywords: foundations / bilinear groups
Contact author: smeiklej at cs ucsd edu
Available format(s): PDF | BibTeX Citation
[ Cryptology ePrint archive ] | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8313056826591492, "perplexity": 2302.8879686780683}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510270313.12/warc/CC-MAIN-20140728011750-00485-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://labs.tib.eu/arxiv/?author=Y.%20W.%20Zhang | • ### Extraction of the Neutron Electric Form Factor from Measurements of Inclusive Double Spin Asymmetries(1704.06253)
Nov. 28, 2017 nucl-ex
$[Background]$ Measurements of the neutron charge form factor, $G^n_E$, are challenging due to the fact that the neutron has no net charge. In addition, measurements of the neutron form factors must use nuclear targets which require accurately accounting for nuclear effects. Extracting $G^n_E$ with different targets and techniques provides an important test of our handling of these effects. $[Purpose]$ The goal of the measurement was to use an inclusive asymmetry measurement technique to extract the neutron charge form factor at a four-momentum transfer of $1~(\rm{GeV/c})^2$. This technique has very different systematic uncertainties than traditional exclusive measurements and thus serves as an independent check of whether nuclear effects have been taken into account correctly. $[Method]$ The inclusive quasi-elastic reaction $^3\overrightarrow{\rm{He}}(\overrightarrow{e},e')$ was measured at Jefferson Lab. The neutron electric form factor, $G_E^n$, was extracted at $Q^2 = 0.98~(\rm{GeV/c})^2$ from ratios of electron-polarization asymmetries measured for two orthogonal target spin orientations. This $Q^2$ is high enough that the sensitivity to $G_E^n$ is not overwhelmed by the neutron magnetic contribution, and yet low enough that explicit neutron detection is not required to suppress pion production. $[Results]$ The neutron electric form factor, $G_E^n$, was determined to be $0.0414\pm0.0077\;{(stat)}\pm0.0022\;{(syst)}$; providing the first high precision inclusive extraction of the neutron's charge form factor. $[Conclusions]$ The use of the inclusive quasi-elastic $^3\overrightarrow{\rm{He}}(\overrightarrow{e},e')$ with a four-momentum transfer near $1~(\rm{GeV/c})^2$ has been used to provide a unique measurement of $G^n_E$. This new result provides a systematically independent validation of the exclusive extraction technique results.
• ### From semiclassical transport to quantum Hall effect under low-field Landau quantization(cond-mat/0608408)
Aug. 18, 2006 cond-mat.mes-hall
The crossover from the semiclassical transport to quantum Hall effect is studied by examining a two-dimensional electron system in an AlGaAs/GaAs heterostructure. By probing the magneto-oscillations, it is shown that the semiclassical Shubnikov-de Haas (SdH) formulation can be valid even when the minima of the longitudinal resistivity approach zero. The extension of the applicable range of the SdH theory could be due to the damping effects resulting from disorder and temperature. Moreover, we observed plateau-plateau transition like behavior with such an extension. From our study, it is important to include the positive magnetoresistance to refine the SdH theory.
• ### Effects of Zeeman spin splitting on the modular symmetry in the quantum Hall effect(cond-mat/0508577)
Aug. 24, 2005 cond-mat.mes-hall
Magnetic-field-induced phase transitions in the integer quantum Hall effect are studied under the formation of paired Landau bands arising from Zeeman spin splitting. By investigating features of modular symmetry, we showed that modifications to the particle-hole transformation should be considered under the coupling between the paired Landau bands. Our study indicates that such a transformation should be modified either when the Zeeman gap is much smaller than the cyclotron gap, or when these two gaps are comparable. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9553694725036621, "perplexity": 985.2596695262453}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400232211.54/warc/CC-MAIN-20200926004805-20200926034805-00250.warc.gz"} |
https://tex.stackexchange.com/questions/196730/tabularx-missing-number-treated-as-zero-error | # tabularx "Missing number, treated as zero" error
error: ! Missing number, treated as zero. } l.16 \begin{tabularx}{\textwidth} {x x x x}
MWE:
\documentclass[12pt,a4paper,fleqn]{book}
%
\usepackage{subfiles}
\usepackage{thesis_style}
\title{hfvj}
\author{fgikf}
\date{}
\begin{document}
\begin{table}[h]
\caption{nice and looooooooooooooooong caption}
\begin{center}
\begin{threeparttable}
\begin{tabularx}{\textwidth}{XXXX}
Reference & hi;& glt;& flfl \\
\citet{TM83} & rlkul $\delta^ugil$ and $\delta^{13}C$ & Winter season & -0.5 ($\delta^ugil$) \\
& & & 0.6 {($\delta^{49}Ca$)} \\
\citet{BMM94} & $\delta^ugil$ & January & -0.44 \\
\citet{BMM94} & $\delta^ugil$ & vsdewfwgrggbr & 0.44 \\
\citet{TM83} & YRO KJL & rwegfwEFGWER GWEGFLNN FDSLNFLNFL FLNF NFSDNFNF & 0.44-0.57\tnote{*} \\
\citet{BMM94} & jo\rq{}h;hk; & mhljk;lyi; & 0.43-0.80\tnote{*} \\
\end{tabularx}%
\begin{tablenotes}
\item[*]dSGhl;i\rq{}iupf,hjl \\ \item[**] fdhfg
\end{tablenotes}
\end{threeparttable}
\end{center}
\label{precirec-table1}
\end{table}
\end{document}
the very complicated custom style file:
\ProvidesPackage{thesis_style}
%
%%% PAGE DIMENSIONS AND SETTINGS
\usepackage{geometry} % to change the page dimensions
\geometry{a4paper} % or letterpaper (US) or a5paper or....
\geometry{top=1.0in, bottom=1.5in, left=1in, right=1in}
%%spacing between lines
\setlength{\parskip}{0.2cm plus1mm minus1mm}%space between paragraphs
\usepackage[nodisplayskipstretch]{setspace}%option for removing space before and after equations
\doublespacing
% Activate to begin paragraphs with an empty line rather than an indent\usepackage[parfill]{parskip}
%
%%%%
%%%%GRAPHICS, FLOATS, SYMBOLS AND MATHS
% support the \includegraphics command and options
\usepackage{graphicx}
%\usepackage{booktabs} % for much better looking tables
\usepackage{floatrow}%for side captions
\usepackage[utf8]{inputenc}%for proper characters
% for rotating floats
\usepackage{lscape}
%for subfigures and tables
\usepackage[font=small,labelfont=bf]{caption}
\usepackage[font=footnotesize]{subfig}
\usepackage[para,online,flushleft]{threeparttable}
%for long tables
\usepackage{longtable}
\usepackage{amsmath,amssymb}
%%
%\usepackage[hyphens]{url}%url wrapping
%\PassOptionsToPackage{hyphens}{url}
\usepackage[noabbrev,capitalize]{cleveref}%automatic table /figure before refs
\creflabelformat{equation}{#2\textup{#1}#3}%remove brackets around eq nos
%%%
\usepackage[osf,sc]{mathpazo} %for upright math
\usepackage{eulervm}
\usepackage{gensymb}
\usepackage{wasysym} %for per mil sign
\usepackage{array} % for better arrays (eg matrices) in maths
\usepackage{paralist} % very flexible & customisable lists (eg. enumerate/itemize, etc.)
\usepackage{verbatim} % adds environment for commenting out blocks of text & for better verbatim
\usepackage{subfig} % make it possible to include more than one captioned figure/table in a single float
\usepackage[version=3]{mhchem} % for upright CO2 etc
\usepackage{wrapfig}%text wrapped figures/tables
%%%%%
%%%%%FONT SETTINGS
\usepackage{calligra}%For cursive font
\usepackage[T1]{fontenc}
\usepackage{titlesec, blindtext, color}
\definecolor{brown}{rgb}{0.5, 0.2, 0.0}
\definecolor{cornellred}{rgb}{0.7, 0.11, 0.11}
\definecolor{brown_w}{rgb}{0.65, 0.16, 0.16}
%\titleformat{\chapter}[hang]{\Large\bfseries}{\thechapter\hsp\textcolor{gray75}{|}\hsp}{0pt}{\Large\bfseries}
\titleformat{\chapter}[hang]{\normalfont\Large\bfseries}{\chaptertitlename\ \thechapter:}{1em}{}
\titlespacing*{\chapter}{0pt}{0pt}{5pt}
\titlespacing*{\section}{0pt}{0pt}{5pt}
%to stop starting new chapter in new page
\usepackage{atbegshi,etoolbox}
%% Get underlining for headings right
\usepackage[normalem]{ulem}
\usepackage{fancyhdr} % This should be set AFTER setting up the page geometry
\pagestyle{fancy} % options: empty , plain , fancy
\renewcommand{\footrulewidth}{1pt}
\lfoot{}\cfoot{}\rfoot{\thepage}
%
\def\bibfont{\footnotesize} %to decrease font size of the bibliography
%%%
\usepackage[nottoc,notlof,notlot]{tocbibind} % Put the bibliography in the ToC
%%%%
\setcounter{tocdepth}{4}
\renewcommand{\bibname}{References}
%%%%%%%
%
\usepackage[colon,authoryear]{natbib}
%
%mytilde
\newcommand{\mytilde}{\raise.17ex\hbox{$\scriptstyle\mathtt{\sim}$}} %around tilde
• you do not close the tabularx environment, you just have an end{tabular} without x Aug 17 '14 at 12:59
• And it is X not x column.
– user11232
Aug 17 '14 at 13:01
• You code is not minimal at all. :( Aug 17 '14 at 13:09
• did the corrections mentioned by MaxNoe and Harish Kumar ... still getting the same error.... Sadly I cant decrease the style file as I don't know if any of the packages are hindering the tabularx .... Aug 17 '14 at 14:17
• Add \usepackage{tabularx} in your thesis_style file. BTW it won't make any justice if you call it a .sty file.
– user11232
Aug 17 '14 at 14:24
I've managed to make the code compilable but there are still some things that could be improved.
\documentclass{book}
\usepackage{tabularx}
\usepackage{booktabs}
\usepackage{thesis_style}
\newcommand*\something{$\delta^{u}gil$}
\begin{document}
Text before the table.
\begin{table}[h]
\centering
\begin{threeparttable}
\begin{tabularx}{\textwidth}{XXXX}
\toprule
Reference & some text & some text & some text \\
TM83 & \something\ and $\delta\ce{^{13}C}$ & Winter season & $-0.5$ (\something) \\
& & & $0.6$ ($\delta\ce{^{49}Ca}$) \\
BMM94 & \something & January & $-0.44$ \\
BMM94 & \something & some text & $0.44$ \\
TM83 & some text & some text & $0.44$--$0.57$\tnote{*} \\
BMM94 & some text & some text & $0.43$--$0.80$\tnote{**} \\
\bottomrule
\end{tabularx}
\begin{tablenotes}
\item[*] some text \\
\item[**] some text
\end{tablenotes}
\end{threeparttable}
\end{table}
Text after the table.
\end{document}
• \delta^ugil means nothing ;) .... and I had only missed the packages Aug 17 '14 at 14:42
• @ankhi Okay. If you want to write isotopes of chemical elements, use the approach \ce{^{<number>}<name>}. Aug 17 '14 at 14:48
• I do use \ce when I write CO2 (say) but the delta values are measured values and hence shouldn't be upright .... :) Aug 17 '14 at 16:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7834771871566772, "perplexity": 15265.071008299172}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587854.13/warc/CC-MAIN-20211026072759-20211026102759-00320.warc.gz"} |
http://openstudy.com/updates/4f1c9600e4b04992dd23b1fb | Got Homework?
Connect with other students for help. It's a free community.
• across
Online now
• laura*
Helped 1,000 students
Online now
• Hero
College Math Guru
Online now
Here's the question you clicked on:
55 members online
• 0 viewing
Ladybug870 Group Title Solve the equation be sure to show your work all final answers must be in simplest form. n-1/10=10 2 years ago 2 years ago Edit Question Delete Cancel Submit
• This Question is Closed
1. Hunus Group Title
Best Response
You've already chosen the best response.
1
$\frac{n-1}{10} = 10$ $10(\frac{n-1}{10}) = 10*10$ $n-1 = 100$ $(n-1)+1=100+1$ $n=101$ now lets check $n=101$ $\frac{101-1}{10}=10$ $10=10$
• 2 years ago
• Attachments:
See more questions >>>
spraguer (Moderator) 5→ View Detailed Profile
23
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9862264394760132, "perplexity": 15140.41585221641}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1409535921869.7/warc/CC-MAIN-20140901014521-00205-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://academicjournals.org/journal/AJB/article-full-text/26CE06260154 | African Journal ofBiotechnology
• Abbreviation: Afr. J. Biotechnol.
• Language: English
• ISSN: 1684-5315
• DOI: 10.5897/AJB
• Start Year: 2002
• Published Articles: 12269
Production of extracellular laccase from the newly isolated Bacillus sp. PK4
Murugesan Rajeswari
• Murugesan Rajeswari
• Department of Biochemistry, Biotechnology and Bioinformatics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore 641043, Tamil Nadu, India.
Vembu Bhuvaneswari
• Vembu Bhuvaneswari
• Department of Biochemistry, Biotechnology and Bioinformatics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore 641043, Tamil Nadu, India.
• Accepted: 08 August 2016
• Published: 24 August 2016
ABSTRACT
Laccase belongs to the family of multicopper oxidase and have wide range of biotechnological applications starting from the food industry to bioremediation. However, the use of laccase at commercial scale is hindered by factors like high enzyme cost, low activity and /or stability under given conditions. This study was carried out with aim of screening for extracellular thermostable laccase producing bacteria. Twenty-two (22) laccase positive strains were isolated from the selected environmental samples while extracellular laccase activity was detected only in six strains namely TM1, TMT1, PK4, PS1, TMS1 and ASP3. The laccase enzyme produced from PK4 was found to be more thermostable with a half-life of 60 min at 80°C. The strain PK4 was identified and designated as Bacillus sp. PK4. The laccase production was optimized using one- factor-at-a-time method and maximum enzyme production were observed at the temperature of 37°C, pH 7.5, 10% inoculum size with yeast extract and glucose as the nitrogen and carbon sources, respectively at an agitation rate of 150 rpm. Copper sulphate at 0.1 mM concentration was found to maximize the laccase production among the tested inducers. Among the trace elements, FeSO4 and ZnSO4 gave the maximum laccase production for the isolated strain in comparison with the control. The effect of copper-induced time showed that the addition of copper before inoculation effectively increased the laccase production compared to the addition of copper after 2, 4, 6 and 8 h of inoculation. The optimization of the media resulted in 11.8 fold increase in laccase production.
Key words: Laccase, thermostability, Bacillus sp., optimization.
INTRODUCTION
Enzymes have been utilized in several industries for many years. Laccase (EC 1.10.3.2) is one of the important enzymes in terms of applicability and versatility in industries (Dabrimanesh et al., 2015). Laccases are the members of multi-copper oxidases and contain histidine-rich copper binding domains. They can oxidize lignin related compounds and highly recalcitrant environmental pollutants. Moreover, unlike many other oxidoreductases, laccases do not require cofactors such as NAD (P) H and, unlike peroxidases, they do not produce toxic peroxide intermediates. These characteristics of laccases position them as potential industrial oxidative enzymes (Shi et al., 2015).
Laccases are widely distributed in nature and have been described in fungi, plants, and insects and more recently in bacteria and archaea, indicating that the laccase redox process is ubiquitous in nature. Laccase plays an important role in several metabolic steps, including those involved in fungal pigmentation, plant lignification, lignin biodegradation, humus turnover and cuticle sclerotization, wherein naturally occurring low molecular weight phenolic compounds and natural fiber polymers are utilized as substrates (Jeon et al., 2012). The first bacterial laccase was reported in Azospirulum lipoferum in the year 1993. Thereafter, laccases have been discovered in a number of bacteria including Bacillus subtilis, Bordetella compestris, Caulobacter crescentus, Escherichia coli, Mycobacterium tuberculosis, Pseudomonas syringae, Pseudomonas aeruginosa and Yersinia pestis (Dhiman and Shrikot, 2015).
Laccases have attracted considerable interest in many fields of industry and environmental processes due to their broad substrate specificity and ability to oxidize high redox potential substrates in the presence of certain low molecular weight compounds called mediators (Diwaniyan et al., 2012). Application of laccase in different industrial fields includes detoxification of industrial effluent, mostly from paper and pulp, textiles and petrochemical industry, used as a tool for medical diagnostics and as a bioremediation agent to clean up herbicide, pesticide and certain explosives in soil and as cosmetics ingredient (Kalia et al., 2014).
Keeping in view the importance of laccase in pollution degradation and to increase the toolbox of bacterial laccase from different subfamily, bioprospecting new bacterial strains displaying laccase activity are the need of time. Therefore, a study on bacterial laccases is important from the perspectives of basic science as well as for the development of novel biotechnological applications.
The objective of the present study was to isolate and screen for thermostable laccase producing strains from the selected samples and to maximize the laccase production of the isolated strain by optimizing the media components.
MATERIALS AND METHODS
Isolation of laccase secreting bacteria
The laccase producing bacteria were isolated in 12 different samples, namely, the treated and untreated effluents from textile industries of Ganapathypalayam and Muruganpalayam (Tirupur District, Tamil Nadu, India) and untreated effluent of two paper industries one located at Karamadai (Coimbatore District, Tamil Nadu, India) and another at Kothamangalam (Erode District, Tamil Nadu, India), soil from textile and paper industry effluent discharged site, sludge from the textile industry, soil contaminated with automobile waste from Pollachi (Coimbatore District, Tamil Nadu, India) and composted coir pith. The isolation was based on serial dilution technique. In this, 1.0 ml of each of the sample was added to a tube containing 9 ml of sterile water (10-1) and mixed vigorously for 30 s. Dilution was repeated till 10-7 and 0.1 ml of suspension was spread from each dilution tube on nutrient agar with 0.1% guaiacol and 0.005% cycloheximide, and incubated at 37°C for three days. Cycloheximide was added to inhibit the fungal growth. The colonies showing reddish brown color were selected. The positive colonies from all the samples were subcultured for three times to get the pure colony. The isolated bacterium was streaked on the same medium, namely nutrient agar with 0.1% guaiacol to confirm the positive activity.
Growth characterization and extracellular laccase production
The isolated bacterial strains were grown in Luria-Bertani broth supplemented with 1 mM copper sulphate for laccase production and growth. The broths were incubated at 37°C with the rotation of 100 rpm for 24 h. The culture was harvested after 24 h and centrifuged at 8000 rpm for 20 min. The supernatant was used as a crude enzyme extract for the assay of laccase activity using 2,2-azino-bis(3-ethylbenzthiazoline-6-sulfonic acid) (ABTS) as substrate.
Assessment of optimal temperature and thermostability of bacterial laccase
The temperature optima and thermo-stability of laccase produced by the isolated strain were assessed in acetone-precipitated sample. Acetone was added to the crude enzyme extract in the ratio of 1:1, vortexed for 1 to 2 min and incubated overnight at -20°C. The sample was centrifuged at 8000 rpm for 30 min and kept at room temperature for 1 - 2 h for the complete removal of the acetone. The pellet was dissolved in 100 mM potassium phosphate buffer of pH 7.0
The optimal temperature for the laccase activity was determined over the range of 20 to 70°C using ABTS as substrate. The thermostability of the laccase produced by the isolated strain was studied by incubating the acetone-precipitated samples at three different temperatures 50, 60 and 70°C and aliquots were withdrawn every 30 min up to 3 h. The sample was slowly cooled down to room temperature and residual laccase activity was measured. All the experiments were carried out in triplicates. The results were expressed either as mean or mean standard deviation.
Identification of thermostable laccase producing bacteria
The maximum thermostable laccase producing bacteria was identified according to the morphological, physiological and biochemical characteristics by following the Bergey’s Manual of Systematic Bacteriology and by 16S rDNA phylogenetic method.
Optimization of laccase production by one factor at a time method
Basal media used for the production of laccase
The basal media used for optimizing the enzyme production had following composition in g/L: K2HPO4 - 0.7, KH2PO4 - 1.4, MgSO4 - 0.01, NaCl - 0.5, tryptone - 0.5, CaCl2 - 0.01 and pH 7.0. The basal medium was inoculated with overnight grown culture with OD600 nm of 0.5 to 0.7 and incubated at 37°C at 100 rpm for 42 h.
Extraction of extracellular and Intracellular enzyme
The culture medium was centrifuged at 10000 x g for 15 min at 4°C after fermentation at different experimental conditions described below and the supernatant was used as the crude enzyme extract. The cells obtained as pellet were washed twice with 100 mM phosphate buffer, pH 7.0. It was preserved in ice and resuspended in 0.5 ml of phosphate buffer. The protein extraction was carried out by sonication for 5 min at 40% amplitude and 0.7 s / cycle with the sonicator. Then it was centrifuged at 13,000 rpm for 20 min at 4°C to pull down the cell fragment and the supernatant was taken carefully in the cool tube. The supernatant obtained was used as the intracellular enzyme.
Growth kinetics and laccase production
The growth kinetics and enzyme secretion were followed every 6 h for 78 h. The culture was inoculated in basal medium and incubated at 37°C with shaking at 100 rpm. The sample was withdrawn every 6 h, bacterial biomass and both extracellular and intracellular laccase activity were measured using 2,6 dimethoxyphenol (DMP) as substrate. The growth of bacterial culture was estimated in terms of biomass by measuring the optical density at 600 nm
Optimization of different physicochemical parameters for laccase production
In one factor one time method, laccase production was optimized using selected variables such as pH (3 to 10 with the increment of 1 pH), inoculum size (5, 10, 15 and 20%), temperature (27, 37 and 47°C), carbon at 1% level (glucose, galactose, fructose, lactose, maltose, sucrose, mannose, starch, sodium citrate and sodium acetate) and nitrogen sources at 0.5% level (peptone, casein, yeast extract, gelatin, urea, ammonium sulphate, ammonium phosphate, ammonium nitrate, potassium nitrate, ammonium carbonate and sodium nitrate), agitation (100, 150 and 200 rpm), inducers at 0.1mM concentration (guaiacol, ABTS, 2,5 xylidine, veratryl alcohol, catechol and copper sulphate), trace elements (KCl, BaCl2, MnSO4, ZnSO4 and FeSO4 - 0.2 g/L) and copper addition time (0 to 8 h). The culture was incubated at 37°C for 42 h at 100 rpm except for the experiments with different temperature and agitation. The growth and laccase activity (using 2,6 DMP as substrate) were determined under each set of experimental conditions. All the experiments were carried out in triplicates and the results were expressed as mean ± standard deviation
Laccase assay
The enzyme assay was done using 2 mM ABTS or 2 mM 2,6 DMP as substrate. 50 to 100 µl of the sample was added to 10 mM phosphate buffer (pH 7) containing the substrate 2,6 DMP or 10 mM sodium acetate buffer (pH 5) containing ABTS at a concentration of 2 mM, and oxidation was measured by the increase in the absorbance at 470 nm (e =14800 M-1cm) and 405 nm (e =35000 M-1 cm-1) respectively. One unit of laccase was defined as the amount of the enzyme required to transform 1 mmol substrate per min under standard assay conditions.
RESULTS AND DISCUSSION
Isolation and screening for extracellular laccase producing bacteria
A total of 22 laccase producing strains were isolated from the selected 12 different environmental samples. The extracellular laccase activity was detected in the six strains namely TM1, TMT1, PK4, PS1, TMS1 and ASP3. The strain TM1 produced the maximum laccase (0.51 U/ml) which was followed by PK4 (0.49 U/ml), ASP3 (0.32 U/ml), TMS1 (0.29 U/ml), TMT1 (0.29 U/ml) and PS1 (0.25 U/ml).
Effect of temperature on the extracellular laccase activity
The temperature optima for the extracellular laccase produced by the strains namely TM1, TMT1, PK4, PS1, TMS1 and ASP3 was determined over the temperature range of 20 to 70°C. The temperature activity profiles of the isolated strains are shown in Figure 1. From Figure 1, it can be inferred that the optimum temperature for the laccase activity of TM1, TMT1, PS1, TMS1 and ASP3 was 40°C whereas for PK4 it was 50°C. The laccase activity of the selected strains was found to increase with an increase in temperature up to the optimal temperature and further increase of temperature, above the optimal temperature reduced the enzyme activity for all the selected strains. The temperature optimum for extracellular laccase from Bacillus sp. ADR (Telke et al., 2011) and Pseudomonas putida (Kuddus et al., 2013) was stated to be 40°C. Similar to the previously analyzed bacterial laccases, the extracellular laccase of the isolated strains had an optimum temperature in the range of 40 to 50°C.
Assessment of thermostability of extracellular laccase
One of the key factors determining the suitability of the enzyme laccase in industrial applications is its thermostability. Hence, the thermostability of the laccase produced by the isolated strains was assessed by incubating the acetone-precipitated samples at three different temperatures, namely 50, 60 and 70°C for 3 h. The results are presented in Figure 2a to d.
For the strain PK4, there was no loss of laccase activity at 50°C, 98 and 77% of the activity remained at 60 and 70°C respectively after 3 h of incubation. TM1 retained 86, 42 and 6% activity up to 3 h at 50, 60 and 70°C respectively. 90, 63 and 12% of the initial laccase activity were retained after 3 h of incubation at 50, 60 and 70°C respectively for the strain TMT1. The isolated strains PS1, TMS1 and ASP3 retained 66, 74 and 82% of initial activity respectively at 50°C. These strains lost more than 50% activity at 60°C at the end of 2 h of incubation (Figure 2a, b and c).
The PK4 laccase was found to retain 77% of the initial activity after 3 h of exposure at 70°C. By contrast, the strain ASP3 lost 98% activity and the strains PS1 and TMS1 lost 100% of initial activity under the same conditions. Except for PK4 extracellular laccase, the laccase activity of all other tested strains was lost after 3 h incubation at 70°C. Therefore, only PK4 laccase thermostability was assessed at 80°C for a period of 3 h (Figure 2d) and it was found that PK4 laccase retained 62% activity after 60 min of incubation at 80°C. Most of the thermostable laccases reported are from bacterial source whereas fungal enzymes lost their activity at temperatures above 60°C (Baldrian, 2006). Ihssen et al. (2015) showed that laccase from bacterial origin was more heat stable than the commercially available fungal laccase from Tinea versicolor.
According to Hilden et al. (2009) thermostability is the ability to resist irreversible inactivation at high temperature and to keep the activity at 60°C for a prolonged period. Singh et al. (2000) stated that thermostable enzymes are generally defined as those with an optimum temperature above that of the maximum for the growth of an organism or with exceptional stability above 50°C over an extended period of time. A thermostable laccase from Streptomyces lavendulae REN-7 retained its original activity up to 20 min at 70°C (Suzuki et al., 2003). Endo et al. (2002) described in their study that Streptomyces griseus laccase retained 40% activity after 60 min of incubation at 70°C and quoted this as thermostable laccase. Lu et al. (2013) affirmed that laccase from Streptomyces sp. C1 retained 30% activity after 120 min incubation at 70°C and more than 60% at 50°C and regarded this as moderately thermostable laccase.
The purified laccase from the thermophiles Mycelipopthora thermophilia and Scytalidium thermophilium did not withstand 1 h period of incubation at 80°C (Xu et al., 1996) whereas the laccase from Chaetomium thermophilum was stable only for 8 min incubation at 80°C (Chefetz et al., 1998). Among the tested strains, PK4 laccase was found to retain 62% enzyme activity at 80°C after 60 min of incubation. Hence, it was selected for identification and further studies.
Identification of the selected strain
The morphological, physiological and biochemical characteristics indicated that the selected strain PK4 probably belong to the genus Bacillus according to the Bergey’s manual of systematic classification (Table 1). The 16S rDNA sequence of strain PK4 (GenBank Accession No. KF651984) was compared with the 16S rDNA sequences present in the rDNA database of NCBI using BLAST to further identify the species of the organism. The homologous search (data not shown) indicated that the strain shared 98% identity with the Bacillus safensis and Bacillus pumilus. The neighbor-joining phylogenetic tree was constructed using the type strains of Bacillus sp. and presented in Figure 3a. The percentage of replicate trees in which the associated taxa clustered together in the bootstrap test (500 replicates) is shown next to the branches.
The BLAST search based on 16S rDNA gene sequence and phylogenetic tree (neighbor-joining method) using type strains revealed that the isolated strain PK4 shared high similarity with Bacillus pumilus and Bacillus safensis. According to Stackebrandt and Goebel (1994), strains belonging to the same genus which exhibits less than 97% 16S rRNA gene sequence similarity should be considered as members of the different species. Bozoglu et al. (2013) reported that bacterial isolate from hot springs had exhibited 99% resemblance to Brevibacillus according to 16S rRNA gene sequence analysis and concluded that 16S rRNA gene sequence analysis was inadequate in discriminating the closely related species.
In the present study, the isolate had exhibited 98% similarity with the two different species namely B. pumilus and B. safensis. Hence, 16S rDNA gene sequence analysis and phylogenetic method were not sufficient to identify the isolated strain PK4 at the species level. The present data should be supported by more advanced genomic analysis methods for the identification at the strain level. A DNA-DNA hybridization technique needs to be performed in order to identify the place of the PK4 in the taxonomy at the species level. Hence the isolate PK4 was identified as Bacillus sp. and named as Bacillus sp. PK4 (Figure 3b).
Optimization of laccase production by one- factor-at-a- time method
In one-factor-at-a-time method pH, temperature, inoculum size, agitation, carbon and nitrogen source, the inorganic salts namely KCl, BaCl2, MnSO4, ZnSO4 and FeSO4 and inducers such as ABTS, guaiacol, 2,5, xylidine, veratryl alcohol, catechol and copper sulphate were optimized. The induction of laccase production by copper addition, with respect to time, was also studied. Under each set of experimental condition, the growth and laccase activity were determined.
Growth kinetics and laccase production
The time course of the extracellular and intracellular laccase activity was determined using DMP as a substrate over a period of 78 h. The isolated strain reached its highest intracellular activity of 1.81 U/ml at 18 h and 24 h and highest extracellular activity of 0.13 U/ml at 42 h. As depicted in Figure 4, the lag phase of the strain was short and the growth then followed the exponential or log phase up to 48 h and reached stationary phase (Figure 4). It is evident that the strain had maximal intracellular activity during the log phase of the growth and maximum extracellular activity in the early stationary phase. The extracellular enzyme activity was found to be higher throughout the stationary phase. These results clearly indicated that the isolated strain had started producing and secreting the enzyme laccase during the log phase of the growth itself. The maximum extracellular laccase activity was detected at 72 h for B. safensis DSKK5 (Singh et al., 2014) and 96 h for Bacillus tequilensis SN4 (Sondhi et al., 2014). However, Telke et al. (2011) showed that Bacillus sp. ADR secrets a maximum extracellular laccase at the end of 24 h of incubation using nutrient broth.
Effect of pH
Each microbial species has its own characteristic pH range at which it grows and produces the maximum enzyme. From Figure 5, it is clear that the optimum pH for laccase production and growth of the isolated strain was 7.5. No growth was observed at pH 3.0 to 5.0. The laccase production and bacterial growth were found to increase with an increase in pH up to 7.5 and a gradual decrease was observed from pH 7.5 to 10.0. However, the enzyme production at pH 7.0 (0.19 U/ml), pH 7.5 (0.20 U/ml) and pH 8.0 (0.18 U/ml) was quite comparable. Figure 5 also depicted that the growth and enzyme production by the isolate were higher in the alkaline pH when compared to that at acidic pH. The ability of the isolate to produce enzymes at alkaline pH makes it suitable for bioremediation and various industrial applications. It must be noted that the bacterial strain was isolated from paper mill effluent, which had the pH in the alkaline range (pH 8.6) and probably this might be the reason for the ideal growth of the strain at neutral to alkaline pH. In line with the results of the present study, the optimum pH for laccase production by bacteria isolated from different environmental source was reported to be in the range of 7 to 8 (Singh et al., 2009; Kaushik and Thakur, 2014; Sondhi et al., 2014)
Effect of inoculum size
From Figure 6 it could be inferred that laccase production increased with increase in inoculum size up to 10% and decreased with the further increase in inoculum size of 15 and 20%. The maximum laccase production (0.38 U/ml) was obtained at 10% inoculum size. The bacterial biomass was also increased with increase in inoculum volume and the maximum was reached at 15%. Further increase in inoculum size drastically reduced the growth. One of the important criteria determining the laccase production on an industrial scale is inoculum size. A higher inoculum volume results in the rapid utilization of the substrate and thereby lowering the yield and vice versa (Deb et al., 2013). The rapid exhaustion of the nutrients might be the reason for decreased bacterial growth and enzyme production at higher inoculum size. Accumulation of toxic metabolites might also subsequently reduce the enzyme production.
Effect of temperature
The optimum temperature for the growth and laccase production was found to be 37°C. The temperature 27 and 47°C were found to decrease both laccase production and bacterial growth. This is at par with the reports of a recent study on Bacillus safenesis by Singh et al. (2014) who demonstrated that the optimum temperature for maximum enzyme production was 37°C (Figure 7). Niladevi et al. (2009) had reported in their study that the optimum temperature for laccase production for Streptomyces psammoticus as 33°C.
Effect of carbon sources
The type of carbon source in the medium plays a major role in the production of ligninolytic enzymes (Gaulhaup et al., 2002) and also the substance that induces the laccase production in one species may inhibit the same in other species (Elshafei et al., 2012). The carbon source of the growth medium appears to regulate the ligninolytic enzymes in microbes and the activity of these enzymes can be increased by the choice of the carbon source (Vaithanomsat et al., 2012). The media without carbon source served as control.
Both inorganic and organic carbon sources used in the present study supported the growth of the bacteria (Figure 8). The bacterial strain achieved the maximum growth with glucose (1.34) when compared with the control (0.96). However, the inorganic source sodium citrate and sodium acetate did not increase the growth of the culture when compared to control.
The control sample gave the laccase activity of 0.36 U/ml. The maximum laccase production was supported by glucose in the medium (0.49 U/ml) followed by lactose (0.45 U/ml), maltose (0.44 U/ml), starch (0.43 U/ml) and mannose (0.43 U/ml). The galactose (0.22 U/ml) and sucrose (0.32 U/ml) were found to lower the laccase production when compared with the control. The inorganic carbon sources sodium citrate (0.25 U/ml) and sodium acetate (0.32 U/ml) were also found to decrease the laccase production.
The presence of glucose augmented both the laccase production and growth among the various tested carbon sources as compared to control. This is in accordance with the results of studies on Bacillus sp. carried out by Kaushik and Thakur (2014) which suggested that dextrose was the best carbon source when compared to sodium acetate, sucrose and sodium citrate. However, Kaira et al. (2015) reported that fructose, maltose, sucrose, xylose, galactose, cellulose, and starch supported the maximum laccase production compared to glucose as sole carbon source in Serratia marcescens.
Effect of nitrogen sources
The nitrogen is primarily metabolized to produce amino acids, protein, nucleic acid and cell wall components in microbes. The nature and concentration of the nitrogen source are the most important factors for the production of ligninolytic enzymes in white-rot fungi (Kunamneni et al., 2007). And also in bacteria, production of the economically important enzyme depends on the type and concentration of the nitrogen source (Shivanand and Jayaraman, 2009). The effect of various organic and inorganic nitrogen sources at 0.5% level on laccase production and growth of the isolated strain was studied and the results are shown in Figure 9.
Figure 9 portrays that all the selected nitrogen sources in the study supported the growth of the isolate and maximum growth was achieved with yeast extract (1.35). The growth of the bacterial isolate with different nitrogen sources gave decreasing order in terms of optical density at 600 nm as given below:
Yeast extract > peptone (0.99) > casein (0.97) = ammonium sulphate (0.97) > ammonium phosphate (0.93) > ammonium carbonate (0.88) > urea (0.85) > ammonium nitrate (0.84) > gelatin (0.54), sodium nitrate (0.32) > potassium nitrate (0.31). With regard to laccase production, yeast extract (0.77 U/ml), ammonium sulphate (0.74 U/ml), peptone (0.72 U/ml) and gelatin (0.72 U/ml) were found to be the best nitrogen sources. Nearly a two-fold increase of laccase production was observed in the presence of these nitrogen sources when compared with control (0.36 U/ml). The other tested nitrogen sources, namely ammonium phosphate, ammonium carbonate, sodium nitrate, urea, ammonium nitrate, and casein gave a higher amount of the enzyme when compared with the control and it ranged between 0.41 U/ml and 0.70 U/ml except potassium nitrate (0.28 U/ml). It can also be noted that inorganic nitrogen source sodium nitrate gave inverse relationship for bacterial biomass and laccase production (Figure 9). Further, these results also confirmed that both the organic and inorganic nitrogen sources can augment the laccase production.
Madhavi and Lele (2009) stated that nitrogen sources effectively regulate the laccase production compared to a carbon source. In agreement with these reports, the present study also show a 2-fold increase in laccase production on nitrogen source optimization compared to carbon source optimization. Niladevi et al. (2009) reported yeast extract as the best nitrogen source for the laccase production for the strain Streptomyces psammoticus whereas Kaushik and Thakur (2014) showed that tryptone induces the maximum laccase production compared to yeast extract in Bacillus sp. In fungi, laccases are activated during the secondary metabolic phase, which is triggered by the depletion of nitrogen source. The results of the present study and previous reports suggested that nutritional supplement that effectively enhances the laccase production depends on the individual microbes and specific growth conditions.
Effect of agitation
The effect of agitation on the growth and laccase production of the isolated strain was determined and the results are shown in Figure 10. From Figure 10, it is evinced that growth of the isolated strain increased with increase in speed of agitation. However, the laccase production was highest at 150 rpm (1.12 U/ml) compared to lower agitation 100 rpm (0.79 U/ml) and higher agitation 200 rpm (0.98 U/ml). The increase in agitation rate of 200 rpm did not increase the production, but gave the maximum bacterial growth; probably at higher agitation rate the enzyme structure might be changed.
However, at lower agitation rate there was a drastic reduction in enzyme production indicating the insufficient mixing of culture media and supply of oxygen. The amount of dissolved oxygen in the fermentation medium is greatly influenced by the speed of agitation. Excessive agitation results in a higher mechanical force, which may produce the cell destruction and uptake of nutrients, thereby lowering the enzyme production (Purwanto et al., 2009).
Therefore, optimizing the agitation of fermentation media is a very important factor to provide sufficient oxygen, mixing and uptake of nutrients by the microbe. The findings of the present study are in line with the reports of other similar studies indicating the maximum production of laccase at 150 rpm shaking condition for the strains Streptomyces lydicus (Mahmoud et al., 2013) and Streptomyces psammoticus (Niladevi and Prema, 2008).
Effect of inducers
The extracellular laccases are constitutively produced in small amounts, however, their production can be considerably stimulated by the presence of inducers mainly aromatic or phenolic compounds related to lignin or lignin derivatives. From Figure 11, it is noted that all the selected inducers supported the growth of the bacteria except 50% alcohol, which reduced the growth in terms of biomass. Among all the selected inducers, copper sulphate increased the growth to a greater extent when compared to the control.
Guaiacol, ABTS, and veratryl alcohol increased the laccase production to a greater extent when compared with alcohol control. The catechol and 2,5 xylidine reduced the laccase production in comparison with alcohol control. The findings of the present study reveal that copper at a concentration of 0.1 mM induced the laccase production. According to the literature, the amount of copper required to induce laccase activity varies with different bacterial species ranging from 0.1mM to 1 mM (Mahmoud et al., 2013; Santo et al., 2013).
The enhancement of laccase activity in response to various inducers depends on the physiological and genetic makeup of microbial strain. Elisashvili et al. (2010) corroborated that the structure of aromatic compound and concentration play an important role in the synthesis of laccase. In addition, they suggested that enhanced laccase activity might function as a defense mechanism against chemical stress. Mongkolthanaruk et al. (2012) also stated that laccase activity of different bacterial strains namely Rhodococcus sp. Enterobacter sp., Staphylococcus saprophyticus and Delftia tsuruhatensis could be triggered with different substrates (guaiacol, veratryl alcohol, phenol red and ethidium bromide).
Effect of salts
The production of extracellular enzymes by microbes is substantially increased not only by carbon and nitrogen source but also by trace elements (Fakhfakh-Zouari et al., 2010). The effect of various salts namely KCl, BaCl2, MnSO4, ZnSO4 and FeSO4 on laccase production and growth of the isolated strain was examined and the result is presented in Figure 12. The MgSO4 and CaCl2 at the concentration of 0.01g/l were present in the original medium which was kept as control.
The presence of KCl, ZnSO4, and FeSO4 in the media appeared to enhance the growth of bacteria as compared with the control. However, the presence of BaCl2 and MnSO4 resulted in decreased growth (Figure 12). Figure 12 also illustrates that FeSO4 gave the maximum laccase production for the isolated strain. The ZnSO4 also increased the laccase production in comparison with the control. KCl was found to have less effect on laccase production for the isolated strain. From the figure, it is also evident that MnSO4 did not have an effect on laccase production, whereas BaCl2 had shown the negative impact on laccase production for the isolated strain. Niladevi et al. (2009) reported that trace element solution has ZnSO4, FeSO4 and MnSO4 as the major influencing factor for laccase production. Fonsesca et al. (2010) affirmed that Fe and Cu ions induce the laccase production through translational and post-translational regulation.
Effect of copper-induced time
The effect of copper addition (0.1 mM) at different time intervals 0, 2, 4, 6 and 8 h was studied. The results are recorded in Table 2. The addition of copper at the 0th h (2.13 U/ml) effectively increased the laccase production compared to the addition of copper after 2 h (1.72 U/ml), 4 h (1.22 U/ml), 6 h (1.19 U/ml) and 8 h (1.18 U/ml). The copper may effectively induce the production of laccase at the initial stage of growth of the bacteria compared to the later stages. Copper is an essential micronutrient for most living organisms and required for assembling copper proteins, which are involved in the oxidation and reduction reactions. Copper acts both as an inducer and as a micronutrient and has the potential to raise the laccase production considerably (Bakkiyaraj et al., 2013).
However, the presence of copper in higher concentration is extremely toxic to microbial cells (Trevors and Cotter, 1990). The extent of laccase production enhancement also depends on the inducer concentration and its time of addition (Gainfreda et al., 1999). Strong (2011) also stated that the addition of inducer prior to inoculation is more effective compared to the addition of inducer when the biomass is actively growing. From Table 2 it is also evident that there is no difference in terms of growth of bacteria with respect to the time of addition of copper. The results are in line with Zheng et al. (2013), who avowed that the addition of copper at a different time interval (0 to 6 h) in Proteus hauseri ZMd44 has no influence on cell growth.
The optimization of media components and growth conditions resulted in 2.13 U/ml compared to unoptimized media (0.18 U/ml) that is, 11.8 fold increase in laccase production was achieved.
CONCLUSION
The study demonstrates the presence of thermostable laccase producing bacteria in the selected environmental samples. The bacterial strain which produced laccase with higher thermostability was from paper mill effluent and it was identified as Bacillus sp. PK4. The media conditions optimized for laccase production by Bacillus sp. PK4 using one factor one time method resulted in 11.8 fold increase. Therefore, the laccase from the isolated strain can be used efficiently in bioremediation of industrial effluents and wastewater treatment.
CONFLICT OF INTERESTS
The author declares that they have no conflict of interest.
REFERENCES | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8421579003334045, "perplexity": 6610.99703922169}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657140337.79/warc/CC-MAIN-20200712211314-20200713001314-00087.warc.gz"} |
https://www.mathflix.org/category/jeemain/page/6/ | # JEE Main
This Category will divide the articles that are useful for jee mains. This could include theory, solved examples, unsolved examples, test papers and previous year papers.
## nth roots of unity – Concept, problems and solutions
nth roots of Unity Do you wonder what nth roots of unity is? and how is it useful in solving and understanding problems Roots of the Equation …
## Fundamental Counting Principle – Begin to Count
Do you know how powerful fundamental counting principle are? let me ask you a question, Do you know how many squares are there in a chessboard? If your answer is 64, I would say you need to see chessboard again There are much more than 64 squares, in fact there are 204 squares on a chess board. …
Change | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9176691770553589, "perplexity": 1975.2100601454747}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655902496.52/warc/CC-MAIN-20200710015901-20200710045901-00489.warc.gz"} |
https://www.physicsforums.com/threads/influence-lines-concentrated-load-system-with-the-problem-this-time.705794/ | # Homework Help: Influence lines (concentrated load system)(with the problem this time)
1. Aug 15, 2013
### mohamadh95
I started by getting the equation for the reaction(which is really simple). I'm a bit confused here, they're asking for the absolute maximum moment, but they're not locating the location of where the maximum moment will occur, should I assume it's happening on the middle of the beam? And another question, how can I find the value of this maximum moment, I'm normally accustomed to a concentrated load, or a uniformally distributed load, but not a system of concentrated forces. Thank you.
https://www.dropbox.com/s/5rngrqme4fv929y/2013-08-15 17.52.30.jpg
2. Aug 15, 2013
### SteamKing
Staff Emeritus
No, the location of the maximum moment probably will not be in the center of the beam. The beam is not loaded symmetrically.
You are forgetting one critically aspect of analyzing beams. Multiple loads can be treated using the principle of superposition, i.e., find the effect of one load at a time on the beam, and then add up the effects of a series of single loads to find the total effect of ALL the loads on the beam.
The superposition principle also works with influence lines.
3. Aug 15, 2013
### mohamadh95
Could you provide some more information? Because I don't know where I should take the cut on the beam.
Ohh and something else should I find the center of gravity of the load system(Gx)? Is the location where maximum moment occur equal to Gx?
Last edited: Aug 15, 2013
4. Aug 15, 2013
### SteamKing
Staff Emeritus
The following should help you with your influence line calculation:
http://www.mm.anadolu.edu.tr/insaat/icerik/dersnotlari/ins313/influencelines.pdf [Broken]
Last edited by a moderator: May 6, 2017
5. Aug 16, 2013
### mohamadh95
Thank you, this was helpful.
Last edited by a moderator: May 6, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook
Have something to add?
Draft saved Draft deleted | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8241862058639526, "perplexity": 1876.4764387714501}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267866984.71/warc/CC-MAIN-20180624160817-20180624180817-00522.warc.gz"} |
http://math.stackexchange.com/questions/202449/median-of-the-f-distribution | # Median of the F-distribution
Is the median of the F-distribution with m and n degrees of freedom decreasing in n, for any m?
From experiments it looks like it might be, but I have been unable to prove it.
-
Is n the denominator degrees of freedom? – Michael Chernick Sep 25 '12 at 22:19
@Michael yes it is – fra Sep 25 '12 at 22:48
Have you looked at tables of the F distribution. I don't think the tables give percentiles close to 50 but maybe looking at the 25th and the 75th with a gross interpolation would give you an idea whether or not it is true. I am sure that there are software packages that will give the cumulative F or its inverse and you can see the result from that. – Michael Chernick Sep 26 '12 at 0:10
@Michael yes from software calculation it seems like the result is true. But I am looking for a proof! – fra Sep 27 '12 at 21:09
If it is not true the tables could tell you by giving you just one counterexample. If you need precision you can do numerical integration to a desired level of accuracy. – Michael Chernick Sep 27 '12 at 21:13
This officially free to download "Handbook of Statistical Distributions" shows that (using their notation) the cumulative distribution (cdf) of the F-distribution can be written as the cdf of a transformed Beta variable: $$\int_{0}^{F_a} f\left(F;m,n\right)dF=1-a=\frac{B_x(\frac m2,\frac n2)}{B(\frac m2,\frac n2)}\equiv G_B(x;\frac m2,\frac n2),\;x=\frac{mF_a}{n+mF_a}$$ Moreover, based on this source the median of a $B(\alpha,\beta)$ distribution, for $\alpha>1, \beta>1$ is approx. equal to $\frac {\alpha -\frac 13}{\alpha +\beta -\frac 23}$. In our case this approximate formula holds for $m\gt 2, n \gt2$. For this case then we have (setting $a=\frac 12$)
$$\frac{mF_\frac 12}{n+mF_\frac 12} \approx\frac {\frac m2 -\frac 13}{\frac m2 +\frac n2 -\frac 23}$$ Doing the algebra we arrive at
$$F_\frac 12\approx \frac{n}{3n-2}\frac{3m-2}{m}$$ and so $$\text{sign} \left(\frac {\partial}{\partial n} F_\frac 12\right)=\text{sign} \left(\frac {\partial}{\partial n} \frac{n}{3n-2}\right)= \text{sign} \left(3n-2 - 3n\right) \lt 0$$
For the case $\alpha =1 \Rightarrow m=2$ we have (source again) $$\frac {mF_\frac 12}{n+mF_\frac 12} = 1-\frac {1}{2^{(2/n)}}$$
which leads again to a negative relationship between the median of the F-distribution and the denominator degrees of freedom.
I have no proof for the remaining degrees of freedom. The $F(1,n)$ distribution is the distribution of a squared Student's-t random variable, if that helps.
- | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8905467987060547, "perplexity": 341.97601395973237}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398464253.80/warc/CC-MAIN-20151124205424-00068-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://cplberry.com/2014/10/18/imply/ | # An introduction to probability: Inference and learning from data
Probabilities are a way of quantifying your degree of belief. The more confident you are that something is true, the larger the probability assigned to it, with 1 used for absolute certainty and 0 used for complete impossibility. When you get new information that updates your knowledge, you should revise your probabilities. This is what we do all the time in science: we perform an experiment and use our results to update what we believe is true. In this post, I’ll explain how to update your probabilities, just as Sherlock Holmes updates his suspicions after uncovering new evidence.
## Taking an umbrella
Imagine that you are a hard-working PhD student and you have been working late in your windowless office. Having finally finished analysing your data, you decide it’s about time to go home. You’ve been trapped inside so long that you no idea what the weather is like outside: should you take your umbrella with you? What is the probability that it is raining? This will depend upon where you are, what time of year it is, and so on. I did my PhD in Cambridge, which is one of the driest places in England, so I’d be confident that I wouldn’t need one. We’ll assume that you’re somewhere it doesn’t rain most of the time too, so at any random time you probably wouldn’t need an umbrella. Just as you are about to leave, your office-mate Iris comes in dripping wet. Do you reconsider taking that umbrella? We’re still not certain that it’s raining outside (it could have stopped, or Iris could’ve just been in a massive water-balloon fight), but it’s now more probable that it is raining. I’d take the umbrella. When we get outside, we can finally check the weather, and be pretty certain if it’s raining or not (maybe not entirely certain as, after plotting that many graphs, we could be hallucinating).
In this story we get two new pieces of information: that newly-arrived Iris is soaked, and what we experience when we get outside. Both of these cause us to update our probability that it is raining. What we learn doesn’t influence whether it is raining or not, just what we believe regarding if it is raining. Some people worry that probabilities should be some statement of absolute truth, and so because we changed our probability of it raining after seeing that our office-mate is wet, there should be some causal link between office-mates and the weather. We’re not saying that (you can’t control the weather by tipping a bucket of water over your office-mate), our probabilities just reflect what we believe. Hopefully you can imagine how your own belief that it is raining would change throughout the story, we’ll now discuss how to put this on a mathematical footing.
## Bayes’ theorem
We’re going to venture into using some maths now, but it’s not too serious. You might like to skip to the example below if you prefer to see demonstrations first. I’ll use $P(A)$ to mean the probability of $A$. A joint probability describes the probability of two (or more things), so we have $P(A, B)$ as the probability that both $A$ and $B$ happen. The probability that $A$ happens given that $B$ happens is the conditional probability $P(A|B)$. Consider the the joint probability of $A$ and $B$: we want both to happen. We could construct this in a couple of ways. First we could imagine that $A$ happens, and then $B$. In this case we build up the joint probability of both by working out the probability that $A$ happens and then the probability $B$ happens given $A$. Putting that in equation form
$P(A,B) = P(A)P(B|A)$.
Alternatively, we could have $B$ first and then $A$. This gives us a similar result of
$P(A,B) = P(B)P(A|B)$.
Both of our equations give the same result. (We’ve checked this before). If we put the two together then
$P(B|A)P(A) = P(A|B)P(B)$.
Now we divide both sides by $P(A)$ and bam:
$\displaystyle P(B|A) = \frac{P(A|B)P(B)}{P(A)}$,
this is Bayes’ theorem. I think the Reverend Bayes did rather well to get a theorem named after him for noting something that is true and then rearranging! We use Bayes’ theorem to update our probabilities.
Usually, when doing inference (when trying to learn from some evidence), we have some data (that our office-mate is damp) and we want to work out the probability of our hypothesis (that it’s raining). We want to calculate $P(\mathrm{hypothesis}|\mathrm{data})$. We normally have a model that can predict how likely it would be to observe that data if our hypothesis is true, so we know $P(\mathrm{data}|\mathrm{hypothesis})$, so we just need to convert between the two. This is known as the inverse problem.
We can do this using Bayes’ theorem
$\displaystyle P(\mathrm{hypothesis}|\mathrm{data}) = \frac{P(\mathrm{data}|\mathrm{hypothesis})P(\mathrm{hypothesis})}{P(\mathrm{data})}$.
In this context, we give names to each of the probabilities (to make things sound extra fancy): $P(\mathrm{hypothesis}|\mathrm{data})$ is the posterior, because it’s what we get at the end; $P(\mathrm{data}|\mathrm{hypothesis})$ is the likelihood, it’s what you may remember calculating in statistics classes; $P(\mathrm{hypothesis})$ is the prior, because it’s what we believed about our hypothesis before we got the data, and $P(\mathrm{data})$ is the evidence. If ever you hear of someone doing something in a Bayesian way, it just means they are using the formula above. I think it’s rather silly to point this out, as it’s really the only logical way to do science, but people like to put “Bayesian” in the title of their papers as it sounds cool.
Whenever you get some new information, some new data, you should update your belief in your hypothesis using the above. The prior is what you believed about hypothesis before, and the posterior is what you believe after (you’ll use this posterior as your prior next time you learn something new). There are a couple of examples below, but before we get there I will take a moment to discuss priors.
There have been many philosophical arguments about the use of priors in science. People worry that what you believe affects the results of science. Surely science should be above such things: it should be about truth, and should not be subjective! Sadly, this is not the case. Using Bayes’ theorem is the only logical thing to do. You can’t calculate a probability of what you believe after you get some data unless you know what you believed beforehand. If this makes you unhappy, just remember that when we changed our probability for it being raining outside, it didn’t change whether it was raining or not. If two different people use two different priors they can get two different results, but that’s OK, because they know different things, and so they should expect different things to happen.
To try to convince yourself that priors are necessary, consider the case that you are Sherlock Holmes (one of the modern versions), and you are trying to solve a bank robbery. There is a witness who saw the getaway, and they can remember what they saw with 99% accuracy (this gives the likelihood). If they say the getaway vehicle was a white transit van, do you believe them? What if they say it was a blue unicorn? In both cases the witness is the same, the likelihood is the same, but one is much more believable than the other. My prior that the getaway vehicle is a transit van is much greater than my prior for a blue unicorn: the latter can’t carry nearly as many bags of loot, and so is a silly choice.
If you find that changing your prior (to something else sensible) significantly changes your results, this just means that your data don’t tell you much. Imagine that you checked the weather forecast before leaving the office and it said “cloudy with 0–100% chance of precipitation”. You basically believe the same thing before and after. This really means that you need more (or better) data. I’ll talk about some good ways of calculating priors in the future.
## Solving the inverse problem
### Example 1: Doughnut allergy
We shall now attempt to use Bayes’ theorem to calculate some posterior probabilities. First, let’s consider a worrying situation. Imagine there is a rare genetic disease that makes you allergic to doughnuts. One in a million people have this disease, that only manifests later in life. You have tested positive. The test is 99% successful at detecting the disease if it is present, and returns a false positive (when you don’t have the disease) 1% of the time. How worried should you be? Let’s work out the probability of having the disease given that you tested positive
$\displaystyle P(\mathrm{allergy}|\mathrm{positive}) = \frac{P(\mathrm{positive}|\mathrm{allergy})P(\mathrm{allergy})}{P(\mathrm{positive})}$.
Our prior for having the disease is given by how common it is, $P(\mathrm{allergy}) = 10^{-6}$. The prior probability of not having the disease is $P(\mathrm{no\: allergy}) = 1 - P(\mathrm{allergy})$. The likelihood of our positive result is $P(\mathrm{positive}|\mathrm{allergy}) = 0.99$, which seems worrying. The evidence, the total probability of testing positive $P(\mathrm{positive})$ is found by adding the probability of a true positive and a false positive
$P(\mathrm{positive}) = P(\mathrm{positive}|\mathrm{allergy})P(\mathrm{allergy}) + P(\mathrm{positive}|\mathrm{no\: allergy})P(\mathrm{no\: allergy})$.
The probability of a false positive is $P(\mathrm{positive}|\mathrm{no\: allergy}) = 0.01$. We thus have everything we need. Substituting everything in, gives
$\displaystyle P(\mathrm{allergy}|\mathrm{positive}) = \frac{0.99 \times 10^{-6}}{0.99 \times 10^{-6} + 0.01 \times (1 - 10^{-6})} = 9.899 \times 10^{-5}$.
Even after testing positive, you still only have about a one in ten thousand chance of having the allergy. While it is more likely that you have the allergy than a random member of the public, it’s still overwhelmingly probable that you’ll be fine continuing to eat doughnuts. Hurray!
Doughnut love: probably fine.
### Example 2: Boys, girls and water balloons
Second, imagine that Iris has three children. You know she has a boy and a girl, but you don’t know if she has two boys or two girls. You pop around for doughnuts one afternoon, and a girl opens the door. She is holding a large water balloon. What’s the probability that Iris has two girls? We want to calculate the posterior
$\displaystyle P(\mathrm{two\: girls}|\mathrm{girl\:at\:door}) = \frac{P(\mathrm{girl\:at\:door}|\mathrm{two\: girls})P(\mathrm{two\: girls})}{P(\mathrm{girl\:at\:door})}$.
As a prior, we’d expect boys and girls to be equally common, so $P(\mathrm{two\: girls}) = P(\mathrm{two\: boys}) = 1/2$. If we assume that it is equally likely that any one of the children opened the door, then the likelihood that one of the girls did so when their are two of them is $P(\mathrm{girl\:at\:door}|\mathrm{two\: girls}) = 2/3$. Similarly, if there were two boys, the probability of a girl answering the door is $P(\mathrm{girl\:at\:door}|\mathrm{two\: boys}) = 1/3$. The evidence, the total probability of a girl being at the door is
$P(\mathrm{girl\:at\:door}) =P(\mathrm{girl\:at\:door}|\mathrm{two\: girls})P(\mathrm{two\: girls}) +P(\mathrm{girl\:at\:door}|\mathrm{two\: boys}) P(\mathrm{two\: boys})$.
Using all of these,
$\displaystyle P(\mathrm{two\: girls}|\mathrm{girl\:at\:door}) = \frac{(2/3)(1/2)}{(2/3)(1/2) + (1/3)(1/2)} = \frac{2}{3}$.
Even though we already knew there was at least one girl, seeing a girl first makes it much more likely that the Iris has two daughters. Whether or not you end up soaked is a different question.
### Example 3: Fudge!
Finally, we shall return to the case of Ted and his overconsumption of fudge. Ted claims to have eaten a lethal dose of fudge. Given that he is alive to tell the anecdote, what is the probability that he actually ate the fudge? Here, our data is that Ted is alive, and our hypothesis is that he did eat the fudge. We have
$\displaystyle P(\mathrm{fudge}|\mathrm{survive}) = \frac{P(\mathrm{survive}|\mathrm{fudge})P(\mathrm{fudge})}{P(\mathrm{survive})}$.
This is a case where our prior, the probability that he would eat a lethal dose of fudge $P(\mathrm{fudge})$, makes a difference. We know the probability of surviving the fatal dose is $P(\mathrm{survive}|\mathrm{fudge}) = 0.5$. The evidence, the total probability of surviving $P(\mathrm{survive})$, is calculated by considering the two possible sequence of events: either Ted ate the fudge and survived or he didn’t eat the fudge and survived
$P(\mathrm{survive}) = P(\mathrm{survive}|\mathrm{fudge})P(\mathrm{fudge}) + P(\mathrm{survive}|\mathrm{no\: fudge})P(\mathrm{no\: fudge})$.
We’ll assume if he didn’t eat the fudge he is guaranteed to be alive, $P(\mathrm{survive}| \mathrm{no\: fudge}) = 1$. Since Ted either ate the fudge or he didn’t $P(\mathrm{fudge}) + P(\mathrm{no\: fudge}) = 1$. Therefore,
$P(\mathrm{survive}) = 0.5 P(\mathrm{fudge}) + [1 - P(\mathrm{fudge})] = 1 - 0.5 P(\mathrm{fudge})$.
This gives us a posterior
$\displaystyle P(\mathrm{fudge}|\mathrm{survive}) = \frac{0.5 P(\mathrm{fudge})}{1 - 0.5 P(\mathrm{fudge})}$.
We just need to decide on a suitable prior.
If we believe Ted could never possibly lie, then he must have eaten that fudge and $P(\mathrm{fudge}) = 1$. In this case,
$\displaystyle P(\mathrm{fudge}|\mathrm{survive}) = \frac{0.5}{1 - 0.5} = 1$.
Since we started being absolutely sure, we end up being absolutely sure: nothing could have changed our mind! This is a poor prior: it is too strong, we are being closed-minded. If you are closed-minded you can never learn anything new.
If we don’t know who Ted is, what fudge is, or the ease of consuming a lethal dose, then we might assume an equal prior on eating the fudge and not eating the fudge, $P(\mathrm{fudge}) = 0.5$. In this case we are in a state of ignorance. Our posterior is
$\displaystyle P(\mathrm{fudge}|\mathrm{survive}) = \frac{0.5 \times 0.5}{1 - 0.5 \times 0.5} = \frac{1}{3}$.
Even though we know nothing, we conclude that it’s more probable that the Ted did not eat the fudge. In fact, it’s twice as probable that he didn’t eat the fudge than he did as $P(\mathrm{no\: fudge}|\mathrm{survive}) = 1 -P(\mathrm{fudge}|\mathrm{survive}) = 2/3$.
In reality, I think that it’s extremely improbable anyone could consume a lethal dose of fudge. I’m fairly certain that your body tries to protect you from such stupidity by expelling the fudge from your system before such a point. However, I will concede that it is not impossible. I want to assign a small probability to $P(\mathrm{fudge})$. I don’t know if this should be one in a thousand, one in a million or one in a billion, but let’s just say it is some small value $p$. Then
$\displaystyle P(\mathrm{fudge}|\mathrm{survive}) = \frac{0.5 p}{1 - 0.5 p} \approx 0.5 p$.
as the denominator is approximately one. Whatever small probability I pick, it is half as probable that Ted ate the fudge.
I would assign a much higher probability to Mr. Impossible being able to eat that much fudge than Ted.
While it might not be too satisfying that we can’t come up with incontrovertible proof that Ted didn’t eat the fudge, we might be able to shut him up by telling him that even someone who knows nothing would think his story is unlikely, and that we will need much stronger evidence before we can overcome our prior.
### Homework example: Monty Hall
You now have all the tools necessary to tackle the Monty Hall problem, one of the most famous probability puzzles:
You are on a game show and are given the choice of three doors. Behind one is a car (a Lincoln Continental), but behind the others are goats (which you don’t want). You pick a door. The host, who knows what is behind the doors, opens another door to reveal goat. They then offer you the chance to switch doors. Should you stick with your current door or not? — Monty Hall problem
You should be able to work out the probability of winning the prize by switching and sticking. You can’t guarantee you win, but you can maximise your chances.
## Summary
Whenever you encounter new evidence, you should revise how probable you think things are. This is true in science, where we perform experiments to test hypotheses; it is true when trying to solve a mystery using evidence, or trying to avoid getting a goat on a game show. Bayes’ theorem is used to update probabilities. Although Bayes’ theorem itself is quite simple, calculating likelihoods, priors and evidences for use in it can be difficult. I hope to return to all these topics in the future. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 60, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7881765961647034, "perplexity": 546.178182035034}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711064.71/warc/CC-MAIN-20221205232822-20221206022822-00023.warc.gz"} |
http://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-6th-edition/chapter-1-section-1-2-algebraic-expressions-and-sets-of-numbers-exercise-set-page-16/80 | ## Intermediate Algebra (6th Edition)
$25-x$
"The difference of": $-$, subtraction "Twenty-five and a number": $25$, $x$ "The difference of 25 and a number": $25-x$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4849346876144409, "perplexity": 15891.852617036586}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948599156.77/warc/CC-MAIN-20171217230057-20171218012057-00626.warc.gz"} |
http://clay6.com/qa/25878/if-a-body-is-charged-by-rubbing-it-its-weight | Browse Questions
# If a body is charged by rubbing it , its weight
$(a)\;remains\;precisely\;constant\qquad(b)\;increases\;slightly\qquad(c)\;decreases\;slightly\qquad(d)\;may\;increase\;or\;decrease\;slightly$
Answer : (d) may increase or decrease slightly
Explanation : It may loose or gain electrons . So a slight weight may increase or decrease . | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7423489093780518, "perplexity": 1911.3740115783721}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171171.24/warc/CC-MAIN-20170219104611-00644-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://www.lofoya.com/Solved/1110/rs-432-is-divided-amongst-three-workers-a-b-and-c-such-that-8-times | # Moderate Ratios & Proportion Solved QuestionAptitude Discussion
Q. Rs.432 is divided amongst three workers $A$, $B$ and $C$ such that 8 times $A$’s share is equal to 12 times $B$’s share which is equal to 6 times $C$’s share. How much did $A$ get?
✖ A. Rs.192 ✖ B. Rs.133 ✔ C. Rs.144 ✖ D. Rs.128
Solution:
Option(C) is correct
8 times $A$’s share = 12 times $B$’s share = 6 times $C$’s share
Note that this is not the same as the ratio of their wages being $8:12:6$
In this case, find out the L.C.M of 8, 12 and 6 and divide the L.C.M by each of the above numbers to get the ratio of their respective shares.
The L.C.M of 8, 12 and 6 is 24.
Therefore, the ratio $A:B:C$ is
$\dfrac{24}{8}:\dfrac{24}{12}:\dfrac{24}{6}\Rightarrow A:B:C::3:2:4$
The sum of the total wages
=$3x+2x+4x=432$
$9x=432$ or $x=48$.
Hence $A$ gets $3×48$= Rs $144$
Edit: For an alternative solution, check comment by Sravan Reddy.
## (6) Comment(s)
Anant
()
8A=12B => A:B=3:2
12B=6C=> B:C=1:2
so A:B:C=3:2:4
From here you can find the rest of the solution
Disha
()
x + y + z = 432 ------ (1)
8x = 12y >> so x = 3y/2
y = 2x/3
8x=6z >>> so x = 3z/4
so , z = 4z/3
Put all value in eq. 1.
x + 2x/3 + 4z/3 = 432
9x= 432*3
x= 144
Vijay
()
choice c
8a=12b=6c
and a+b+c = 432
solving for a=144 b= 96 c= 192
Priyanka
()
why lcm we should please explain
Sravan Reddy
()
8 times A = 12 times B
Suppose A:B is $12:8$ then $8*12x = 12*8x$ =TRUE
Suppose A:B is $8:12$ then $8*8x = 12*12x$ -> Clearly FALSE
Also 8 times A = 12 times B means A is clearly bigger, so $8:12$ can't be the case.
Now, whenever the problem is like this, they should be inverse ratios.
So, Instead of $8:12:6$, it will be $\dfrac{1}{8}:\dfrac{1}{12}:\dfrac{1}{6}$
Bhaumik
()
why is it no 8:12:6 ? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9330352544784546, "perplexity": 2533.190954004084}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280746.40/warc/CC-MAIN-20170116095120-00162-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://en.wikipedia.org/wiki/High_availability | # High availability
"Always-on" redirects here. For the software restriction, see Always-on DRM.
High availability is a characteristic of a system, which aims to ensure an agreed level of operational performance, usually uptime, for a higher than normal period.
Modernization has resulted in an increased reliance on these systems. For example, hospitals and data centers require high availability of their systems to perform routine daily activities. Availability refers to the ability of the user community to obtain a service or good, access the system, whether to submit new work, update or alter existing work, or collect the results of previous work. If a user cannot access the system, it is - from the users point of view - unavailable.[1] Generally, the term downtime is used to refer to periods when a system is unavailable.
There are three principles of systems design in reliability engineering which can help achieve high availability.
1. Elimination of single points of failure. This means adding redundancy to the system so that failure of a component does not mean failure of the entire system.
2. Reliable crossover. In redundant systems, the crossover point itself tends to become a single point of failure. Reliable systems must provide for reliable crossover.
3. Detection of failures as they occur. If the two principles above are observed, then a user may never see a failure. But the maintenance activity must.
## Scheduled and unscheduled downtime
A distinction can be made between scheduled and unscheduled downtime. Typically, scheduled downtime is a result of maintenance that is disruptive to system operation and usually cannot be avoided with a currently installed system design. Scheduled downtime events might include patches to system software that require a reboot or system configuration changes that only take effect upon a reboot. In general, scheduled downtime is usually the result of some logical, management-initiated event. Unscheduled downtime events typically arise from some physical event, such as a hardware or software failure or environmental anomaly. Examples of unscheduled downtime events include power outages, failed CPU or RAM components (or possibly other failed hardware components), an over-temperature related shutdown, logically or physically severed network connections, security breaches, or various application, middleware, and operating system failures.
If users can be warned away from scheduled downtimes, then the distinction is useful. But if the requirement is for true high availability, then downtime is downtime whether or not it is scheduled.
Many computing sites exclude scheduled downtime from availability calculations, assuming that it has little or no impact upon the computing user community. By doing this, they can claim to have phenomenally high availability, which might give the illusion of continuous availability. Systems that exhibit truly continuous availability are comparatively rare and higher priced, and most have carefully implemented specialty designs that eliminate any single point of failure and allow online hardware, network, operating system, middleware, and application upgrades, patches, and replacements. For certain systems, scheduled downtime does not matter, for example system downtime at an office building after everybody has gone home for the night.
## Percentage calculation
Availability is usually expressed as a percentage of uptime in a given year. The following table shows the downtime that will be allowed for a particular percentage of availability, presuming that the system is required to operate continuously. Service level agreements often refer to monthly downtime or availability in order to calculate service credits to match monthly billing cycles. The following table shows the translation from a given availability percentage to the corresponding amount of time a system would be unavailable.
Availability % Downtime per year Downtime per month Downtime per week Downtime per day
90% ("one nine") 36.5 days 72 hours 16.8 hours 2.4 hours
95% 18.25 days 36 hours 8.4 hours 1.2 hours
97% 10.96 days 21.6 hours 5.04 hours 43.2 minutes
98% 7.30 days 14.4 hours 3.36 hours 28.8 minutes
99% ("two nines") 3.65 days 7.20 hours 1.68 hours 14.4 minutes
99.5% 1.83 days 3.60 hours 50.4 minutes 7.2 minutes
99.8% 17.52 hours 86.23 minutes 20.16 minutes 2.88 minutes
99.9% ("three nines") 8.76 hours 43.8 minutes 10.1 minutes 1.44 minutes
99.95% 4.38 hours 21.56 minutes 5.04 minutes 43.2 seconds
99.99% ("four nines") 52.56 minutes 4.38 minutes 1.01 minutes 8.66 seconds
99.995% 26.28 minutes 2.16 minutes 30.24 seconds 4.32 seconds
99.999% ("five nines") 5.26 minutes 25.9 seconds 6.05 seconds 864.3 milliseconds
99.9999% ("six nines") 31.5 seconds 2.59 seconds 604.8 milliseconds 86.4 milliseconds
99.99999% ("seven nines") 3.15 seconds 262.97 milliseconds 60.48 milliseconds 8.64 milliseconds
99.999999% ("eight nines") 315.569 milliseconds 26.297 milliseconds 6.048 milliseconds 0.864 milliseconds
99.9999999% ("nine nines") 31.5569 milliseconds 2.6297 milliseconds 0.6048 milliseconds 0.0864 milliseconds
Uptime and availability can be used synonymously, as long as the items being discussed are kept consistent. That is, a system can be up, but its services are not available, as in the case of a network outage. This can also be viewed as, a system can be available to work on, but its services are not up from a functional perspective (as oppose to software service/process perspective). The perspective is important here, whether the item being discussed is the server hardware, server OS, functional service, software service/process...etc. Keep the perspective consistent throughout a discussion, then uptime and availability can be used synonymously.
### "Nines"
Percentages of a particular order of magnitude are sometimes referred to by the number of nines or "class of nines" in the digits. For example, electricity that is delivered without interruptions (blackouts, brownouts or surges) 99.999% of the time would have 5 nines reliability, or class five.[2] In particular, the term is used in connection with mainframes[3][4] or enterprise computing.
Similarly, percentages ending in a 5 have conventional names, traditionally the number of nines, then "five", so 99.95% is "three nines five", abbreviated 3N5.[5][6] This is casually referred to as "three and a half nines",[7] but this is incorrect: a 5 is only a factor of 2, while a 9 is a factor of 10, so a 5 is 0.3 nines (per below formula: ${\displaystyle \log _{10}2\approx 0.3}$):[a] 99.95% availability is 3.3 nines, not 3.5 nines.[8] More simply, going from 99.9% availability to 99.95% availability is a factor of 2 (0.1% to 0.05% unavailability), but going from 99.95% to 99.99% availability is a factor of 5 (0.05% to 0.01% unavailability), over twice as much.[b]
A formulation of the class of 9s ${\displaystyle c}$ based on a system's unavailability ${\displaystyle x}$ would be
${\displaystyle c:=\lfloor -\log _{10}x\rfloor }$
A similar measurement is sometimes used to describe the purity of substances.
In general, the number of nines is not often used by a network engineer when modeling and measuring availability because it is hard to apply in formula. More often, the unavailability expressed as a probability (like 0.00001), or a downtime per year is quoted. Availability specified as a number of nines is often seen in marketing documents.[citation needed] The use of the "nines" has been called into question, since it does not appropriately reflect that the impact of unavailability varies with its time of occurrence.[9] For large amounts of 9s, the "unavailability" index (measure of downtime rather than uptime) is easier to handle. For example, this is why an "unavailability" rather than availability metric is used in hard disk or data link bit error rates.
## Measurement and interpretation
Availability measurement is subject to some degree of interpretation. A system that has been up for 365 days in a non-leap year might have been eclipsed by a network failure that lasted for 9 hours during a peak usage period; the user community will see the system as unavailable, whereas the system administrator will claim 100% uptime. However, given the true definition of availability, the system will be approximately 99.9% available, or three nines (8751 hours of available time out of 8760 hours per non-leap year). Also, systems experiencing performance problems are often deemed partially or entirely unavailable by users, even when the systems are continuing to function. Similarly, unavailability of select application functions might go unnoticed by administrators yet be devastating to users — a true availability measure is holistic.
Availability must be measured to be determined, ideally with comprehensive monitoring tools ("instrumentation") that are themselves highly available. If there is a lack of instrumentation, systems supporting high volume transaction processing throughout the day and night, such as credit card processing systems or telephone switches, are often inherently better monitored, at least by the users themselves, than systems which experience periodic lulls in demand.
An alternative metric is mean time between failures (MTBF).
## Closely related concepts
Recovery time (or estimated time of repair (ETR), also known as recovery time objective (RTO) is closely related to availability, that is the total time required for a planned outage or the time required to fully recover from an unplanned outage. Another metric is mean time to recovery (MTTR). Recovery time could be infinite with certain system designs and failures, i.e. full recovery is impossible. One such example is a fire or flood that destroys a data center and its systems when there is no secondary disaster recovery data center.
Another related concept is data availability, that is the degree to which databases and other information storage systems faithfully record and report system transactions. Information management specialists often focus separately on data availability in order to determine acceptable (or actual) data loss with various failure events. Some users can tolerate application service interruptions but cannot tolerate data loss.
A service level agreement ("SLA") formalizes an organization's availability objectives and requirements.
## System design for high availability
Paradoxically, adding more components to an overall system design can undermine efforts to achieve high availability. That is because complex systems inherently have more potential failure points and are more difficult to implement correctly. While some analysts would put forth the theory that the most highly available systems adhere to a simple architecture (a single, high quality, multi-purpose physical system with comprehensive internal hardware redundancy), this architecture suffers from the requirement that the entire system must be brought down for patching and operating system upgrades. More advanced system designs allow for systems to be patched and upgraded without compromising service availability (see load balancing and failover).
High availability requires less human intervention to restore operation in complex systems; the reason for this being that the most common cause for outages is human error.[10]
Redundancy is used to create systems with high levels of availability (e.g. aircraft flight computers). In this case it is required to have high levels of failure detectability and avoidance of common cause failures. Two kinds of redundancy are passive redundancy and active redundancy.
Passive redundancy is used to achieve high availability by including enough excess capacity in the design to accommodate a performance decline. The simplest example is a boat with two separate engines driving two separate propellers. The boat continues toward its destination despite failure of a single engine or propeller. A more complex example is multiple redundant power generation facilities within a large system involving electric power transmission. Malfunction of single components is not considered to be a failure unless the resulting performance decline exceeds the specification limits for the entire system.
Active redundancy is used in complex systems to achieve high availability with no performance decline. Multiple items of the same kind are incorporated into a design that includes a method to detect failure and automatically reconfigure the system to bypass failed items using a voting scheme. This is used with complex computing systems that are linked. Internet routing is derived from early work by Birman and Joseph in this area.[11] Active redundancy may introduce more complex failure modes into a system, such as continuous system reconfiguration due to faulty voting logic.
Zero downtime system design means that modeling and simulation indicates mean time between failures significantly exceeds the period of time between planned maintenance, upgrade events, or system lifetime. Zero downtime involves massive redundancy, which is needed for some types of aircraft and for most kinds of communications satellites. Global Positioning System is an example of a zero downtime system.
Fault instrumentation can be used in systems with limited redundancy to achieve high availability. Maintenance actions occur during brief periods of down-time only after a fault indicator activates. Failure is only significant if this occurs during a mission critical period.
Modeling and simulation is used to evaluate the theoretical reliability for large systems. The outcome of this kind of model is used to evaluate different design options. A model of the entire system is created, and the model is stressed by removing components. Redundancy simulation involves the N-x criteria. N represents the total number of components in the system. x is the number of components used to stress the system. N-1 means the model is stressed by evaluating performance with all possible combinations where one component is faulted. N-2 means the model is stressed by evaluating performance with all possible combinations where two component are faulted simultaneously.
## Reasons for unavailability
A survey among academic availability experts in 2010 ranked reasons for unavailability of enterprise IT systems. All reasons refer to not following best practice in each of the following areas (in order of importance):[12]
1. Monitoring of the relevant components
2. Requirements and procurement
3. Operations
4. Avoidance of network failures
5. Avoidance of internal application failures
6. Avoidance of external services that fail
7. Physical environment
8. Network redundancy
9. Technical solution of backup
10. Process solution of backup
11. Physical location
12. Infrastructure redundancy
13. Storage architecture redundancy
The factors themselves are based on the work of Evan Marcus and Hal Stern.[13]
## Costs of unavailability
In a 1998 report from IBM Global Services, unavailable systems were estimated to have cost American businesses \$4.54 billion in 1996, due to lost productivity and revenues.[14]
High availability is one of the primary requirements of the control systems in unmanned vehicles[15] and autonomous maritime vessels.[16] If the controlling system becomes unavailable, the Ground Combat Vehicle (GCV) or ASW Continuous Trail Unmanned Vessel (ACTUV) would be lost.
## Notes
1. ^ See mathematical coincidences concerning base 2 for details on this approximation.
2. ^ "Twice as much" on a logarithmic scale, meaning two factors of 2: ${\displaystyle \times 2\times 2<\times 5}$
## References
1. ^ Floyd Piedad, Michael Hawkins (2001). High Availability: Design, Techniques, and Processes. Prentice Hall. ISBN 9780130962881.
2. ^ Lecture Notes M. Nesterenko, Kent State University
3. ^
5. ^ Precious metals. 4: 262. 1981. Missing or empty |title= (help) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4820336401462555, "perplexity": 3013.3535289805427}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560283689.98/warc/CC-MAIN-20170116095123-00334-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://ec.gateoverflow.in/538/gate-ece-2014-set-3-question-1 | 47 views
The maximum value of the function $f(x) = \text{ln } (1+x) – x$ (where $x >-1$) occurs at $x=$_______. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9632061123847961, "perplexity": 1333.642173748516}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337668.62/warc/CC-MAIN-20221005203530-20221005233530-00113.warc.gz"} |
https://randommathgenerator.com/2016/10/01/projective-morphisms/ | ### Projective morphisms
This post is about the morphisms between projective varieties. There are some aspects of such morphisms that I’m troubled about. The development will closely follow that in Karen Smith’s “Invitation to Algebraic Geometry”.
First, say we have a morphism $\phi:\Bbb{P}^1\to\Bbb{P}^2$ such that $[s,t]\to[s^2,st,t^2]$. We will try and analyze this map.
This map has to be homogeneous: in that each coordinate has to be homogeneous, and the homogeneity has to be of the same degree. This is the only way that such a map between projective varieties can be well-defined.
Now let us talk about the mappings from affine charts. Essentially, the affine charts cover the projective space, and hence every projective variety that lives in that space. When we talk about a particular affine chart, we can reduce the number of variables by $1$. Because the value of one variable is always $1$: hence it can be neglected. However, is the image also an affine chart? That depends. In this case of $[s,t]\to [s^2,st,t^2]$, the image of an affine chart will be an affine chart. This is because $s=1\implies s^2=1$. Similarly, $t=1\implies t^2=1$.
We’ve covered all the possible points in the domain by picking out the affine charts. Hence, we have fully described the map.
A map $f$ between projective varieties is a projective morphism if for each $p\in V$, where $V$ is the domain, there exists an neighbourhood $N(p)$ such that $f|_{N(p)}$ is a homogeneous polynomial map. Is an affine chart an open set? Yes. If it is the $z$th affine chart it is the complement of the algebraic set $z=0$ in $\Bbb{P}^n$.
Let us now consider a different map: consider $V(xz-y^2)\in\Bbb{P}^2$. Let us call this curve $C$. Now consider the map $C\to \Bbb{P}^1$, defined as $[x,y,z]\to [x,y]$ if $x\neq 0$ and $[x,y,z]\to [y,z]$ if $z\neq 0$. What does this mean?
First of all, why is the option $y\neq 0$ not included? If $y\neq 0$, both $x,z\neq 0$ is implied. Hence, this case is a subcase of the two cases considered earlier. Secondly, what does it mean to map to a projective space of a lower dimension? The curve is one-dimensional. Is that the reason why we can embed it in $\Bbb{P}^1$? Probably. Note that we haven’t yet proven that this mapping is an embedding. However, this will indeed turn out to be the case.
Is this map consistent? In other words, are the two maps the same in the intersection of the open sets $x\neq 0$ and $y\neq 0$? Let us see. $[x,y]\to [xz,yz]\to[y^2,yz]\to [y,z]$. Hence, when $x,z\neq 0$, this map is consistent.
Why do we have to have such a broken up map? Why not one consistent map? First of all, mapping from affine charts seems like a systematic way to map. You can always ensure that at least one coordinate is non-zero; both in the domain and range. That is really all there is to it. Sometimes on restricting to affine charts, you write affine maps, like in the precious example. In other cases, including this one, you write a projective map. Defining the various projective maps, whether they change with affine charts or not, is of paramount importance. The affine map part is just an observation which may or may not be made.
How to map a curve $f(x_0,x_1,x_2,\dots,x_n)$ to $\Bbb{P}^1$ in general? This seems to be a very difficult question. [This](http://web.stanford.edu/~tonyfeng/Brill_Noether1.pdf) suggests that every smooth projective curve can be embedded in $\Bbb{P}^3$. That seems to be the best we can do.
For completeness, I would like to mention that the two maps given above are inverse to each other, although this is unrelated to the motivation for this article. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 33, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9727377891540527, "perplexity": 142.8062473428007}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221210559.6/warc/CC-MAIN-20180816074040-20180816094040-00479.warc.gz"} |
https://www.usgs.gov/media/images/fig-2-nonlinear-regression-prediction-plot-use-50-pooled-l | # Fig. 2. Nonlinear regression prediction plot for use with 50 pooled l
## Detailed Description
Fig. 2. Nonlinear regression prediction plot for use with 50 pooled larvae that accurately estimates the percentage of triploids in a mixed population of triploids and diploids of that spawn. The plot was generated from 10 replicate experiments, each using a FCM protocol for cell processing and analysis at 15 known levels of ploidy. The 95% confidence limits (black dashed lines) and mean values (dots), along with the 95% prediction curves (red dashed lines) are shown. The corresponding quadratic equation is above. Thus, a flow cytometric-derived observed value (y–axis) (within the range) will correspond to a predicted triploidy value (x-axis) for a spawn.
## Details
Image Dimensions: 495 x 609 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8197974562644958, "perplexity": 3911.489683167331}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195527474.85/warc/CC-MAIN-20190722030952-20190722052952-00249.warc.gz"} |
https://quizmastershop.com/blogs/blog/ships-ladder-quiz-puzzle-answer | On a recent holiday to the seaside the Quiz Master Shop team was enjoying a restorative pint overlooking the harbour. We noticed that the biggest boat had a ladder that was hanging over the side and into the water, with four rungs submerged. In fact the top of the fourth rung was exactly on the surface of the water.
Each of the rungs was a cylinder with a diameter of two inches, and the gap between the rungs was eleven inches. The tide was rising at a rate of 18 inches per hour.
So how many rungs were submerged two hours later when we left the harbourside pub?
There is no maths required for this. The boat (and the ladder) will rise with the tide, leaving the same number of rungs submerged. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8732780814170837, "perplexity": 1579.2937172283614}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334987.39/warc/CC-MAIN-20220927033539-20220927063539-00154.warc.gz"} |
https://fr.overleaf.com/latex/templates/thesis-dissertation-template-for-chemical-engineering-ucr/nhqxycqmfnzz | Aller au contenu
Author
Daybis Tencio
AbstractThis document includes the majority of the requirements for a Thesis Dissertation based on the Chemical Engineer Department Criteria at the University of Costa Rica (UCR, 2021). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 1, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.622546911239624, "perplexity": 2707.2773855899477}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057830.70/warc/CC-MAIN-20210926053229-20210926083229-00476.warc.gz"} |
https://www.physicsforums.com/threads/2d-motion-help.571209/ | # Homework Help: 2D motion help
1. Jan 26, 2012
### monac
A spring cannon is located at the edge of a table that is 1.2 m above the floor. A steel ball is launched from the cannon with speed Vo at 35.0 degrees above the horizontal.
(a) Find the horizontal displacement component of the ball tothe point where it lands on the floor as a function of Vo. We writethis function as x(Vo).
Evaluate x for (b) Vo = 0.100 m/s and for
(c) Vo = m/s.
(d) Assume Vo is close to zero but not equal to zero.Show that one term in the answer to part (a) dominates so that thefunction x(Vo) reduces to a simpler form.
(e) If Vo is ver large,what is the approximate form of x(Vo).
I found the answers to a, b, and c. I am thinking of taking a limit on d but the problem is really complicated ... It's a quadratic and with limit laws I would set it equal to 0, but it says it can't be 0. So i am really confused on how to do d and e.
2. Jan 26, 2012
### Curious3141
Why don't you show what you've done so far (to all parts)?
Just a hint, but it'll likely be helpful. Remember the Taylor series (or Binomial theorem) for things like (1+x)-1.
3. Jan 26, 2012
### monac
it's a long process. I ll just type the main parts of the answers.
(a) x = vicos35t
t = (vi sin35 + √vi^2 sin^2 35 + 23.544) / 9.81
so x = vi cos35 ((vi sin35 + √vi^2 sin^2 35 + 23.544) / 9.81)
for b and c i just had to plug in values for vi and get the x so that was easy.
I have not learned Taylor's series yet in my Calculus II class. :(
4. Jan 26, 2012
### Curious3141
Sorry, your expression is ambiguous. √vi^2 = vi, isn't it?
5. Jan 26, 2012
### monac
Oh the whole thing is under the square root.
t = (vi sin35 + √(vi^2 sin^2 35 + 23.544)) / 9.81
6. Jan 26, 2012
### Staff: Mentor
I don't think you need any more maths for (d). Just inspect the expression you earlier derived for time but now saying that anything involving Vo is insignificant compared with associated other terms.
7. Jan 26, 2012
### monac
So imagine that vi = 0?
8. Jan 26, 2012
### Staff: Mentor
For (d), close to 0. (Careful with the notation. The question uses Vo and you seem to have changed it to vi.)
9. Jan 26, 2012
### monac
In the back of the book, the answer for d was x ~ 0.405 m
10. Jan 26, 2012
### Staff: Mentor
Regardless of the speed it's launched, providing it's slow it still travels 0.4m horizontally? That's interesting.
My answer for (d) is XH = þVo
where þ is a fraction that I'll leave you to work out for yourself, but it's between 0.1 and 0.9
Last edited: Jan 26, 2012 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8990463614463806, "perplexity": 2223.9204346557503}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867277.64/warc/CC-MAIN-20180526014543-20180526034531-00034.warc.gz"} |
http://quantlib.sourcearchive.com/documentation/0.3.9-6/incrementalstatistics_8hpp-source.html | Search packages:
Sourcecode: quantlib version 0.3.110.3.11-2.1build10.3.130.3.140.3.90.3.9-60.8.10.8.1-1build10.9.0.200712240.9.0.20071224-10.9.70.9.7-10.9.7-1ubuntu10.9.90.9.9-21.0.01.0.0-11.0.0~201001121.0.0~20100112-11.0.0~201001251.0.0~20100125-11.0.0~201002091.0.0~20100209-31.0.11.0.1-11.11.1-11.1-2build1
# incrementalstatistics.hpp
Go to the documentation of this file.
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2000, 2001, 2002, 2003 RiskMap srl
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<[email protected]>. The license is also available online at
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
/*! \file incrementalstatistics.hpp
\brief statistics tool based on incremental accumulation
*/
#ifndef quantlib_incremental_statistics_hpp
#define quantlib_incremental_statistics_hpp
#include <ql/Utilities/null.hpp>
#include <ql/errors.hpp>
namespace QuantLib {
//! Statistics tool based on incremental accumulation
/*! It can accumulate a set of data and return statistics (e.g: mean,
variance, skewness, kurtosis, error estimation, etc.)
\warning high moments are numerically unstable for high
average/standardDeviation ratios
*/
00040 class IncrementalStatistics {
public:
IncrementalStatistics();
//! \name Inspectors
//@{
//! number of samples collected
Size samples() const;
//! sum of data weights
Real weightSum() const;
/*! returns the mean, defined as
\f[ \langle x \rangle = \frac{\sum w_i x_i}{\sum w_i}. \f]
*/
Real mean() const;
/*! returns the variance, defined as
\f[ \frac{N}{N-1} \left\langle \left(
x-\langle x \rangle \right)^2 \right\rangle. \f]
*/
Real variance() const;
/*! returns the standard deviation \f$\sigma \f$, defined as the
square root of the variance.
*/
Real standardDeviation() const;
/*! returns the downside variance, defined as
\f[ \frac{N}{N-1} \times \frac{ \sum_{i=1}^{N}
\theta \times x_i^{2}}{ \sum_{i=1}^{N} w_i} \f],
where \f$\theta \f$ = 0 if x > 0 and
\f$\theta \f$ =1 if x <0
*/
Real downsideVariance() const;
/*! returns the downside deviation, defined as the
square root of the downside variance.
*/
Real downsideDeviation() const;
/*! returns the error estimate \f$\epsilon \f$, defined as the
square root of the ratio of the variance to the number of
samples.
*/
Real errorEstimate() const;
/*! returns the skewness, defined as
\f[ \frac{N^2}{(N-1)(N-2)} \frac{\left\langle \left(
x-\langle x \rangle \right)^3 \right\rangle}{\sigma^3}. \f]
The above evaluates to 0 for a Gaussian distribution.
*/
Real skewness() const;
/*! returns the excess kurtosis, defined as
\f[ \frac{N^2(N+1)}{(N-1)(N-2)(N-3)}
\frac{\left\langle \left(x-\langle x \rangle \right)^4
\right\rangle}{\sigma^4} - \frac{3(N-1)^2}{(N-2)(N-3)}. \f]
The above evaluates to 0 for a Gaussian distribution.
*/
Real kurtosis() const;
/*! returns the minimum sample value */
Real min() const;
/*! returns the maximum sample value */
Real max() const;
//@}
//! \name Modifiers
//@{
//! adds a datum to the set, possibly with a weight
/*! \pre weight must be positive or null */
void add(Real value, Real weight = 1.0);
//! adds a sequence of data to the set, with default weight
template <class DataIterator>
00116 void addSequence(DataIterator begin, DataIterator end) {
for (;begin!=end;++begin)
}
//! adds a sequence of data to the set, each with its weight
/*! \pre weights must be positive or null */
template <class DataIterator, class WeightIterator>
00123 void addSequence(DataIterator begin, DataIterator end,
WeightIterator wbegin) {
for (;begin!=end;++begin,++wbegin)
}
//! resets the data to a null set
void reset();
//@}
protected:
Size sampleNumber_, downsideSampleNumber_;
Real sampleWeight_, downsideSampleWeight_; | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.772506833076477, "perplexity": 24860.63637322864}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257648404.94/warc/CC-MAIN-20180323161421-20180323181421-00142.warc.gz"} |
http://mathhelpforum.com/calculus/159744-i-do-not-understand-get-these-problems.html | # Math Help - I do not understand or get these problems?
1. ## I do not understand or get these problems?
Yeah.. Homework help. I seriously do not understand it even though I am following exact procedures and made sure I wasn't wrong, but I'm still wrong? I'm on my last submission for my online homework in order to get points and I would like to get it right.. But I don't understand it?
2. Originally Posted by elpermic
Yeah.. Homework help. I seriously do not understand it even though I am following exact procedures and made sure I wasn't wrong, but I'm still wrong? I'm on my last submission for my online homework in order to get points and I would like to get it right.. But I don't understand it?
Please show all your working so that you can be pointed in the right direction.
3. well for the 1st one..
i take the integral of π r^2 from [0,2] and I get 8.378 as my answer(im sure this is right.. but im wrong)
as for the 2nd one
i take the integral of 4(3-3x^2) from [-1,1] and after calculation i get 24. still wrong though
4. Originally Posted by elpermic
well for the 1st one..
i take the integral of π r^2 from [0,2] and I get 8.378 as my answer(im sure this is right.. but im wrong)
as for the 2nd one
i take the integral of 4(3-3x^2) from [-1,1] and after calculation i get 24. still wrong though
I will point you in the right direction for #1:
$\displaystyle V = \pi \int_3^5 x^2 \, dy$. An exact answer is probably required.
5. Sorry. I forgot to say I tried that integral as well and I got 98π/3.. But my answer was still wrong.
6. Originally Posted by elpermic
Sorry. I forgot to say I tried that integral as well and I got 98π/3.. But my answer was still wrong.
In my first reply I bold faced the word "all" for a very good reason. Show all your work, every step.
7. those were the only 2 integrals I tried. Both of them are wrong and Im still confused because I'm sure I did everything right.
8. I finally got the answer to the first problem! But I still can't do the second one.
9. Originally Posted by elpermic
I finally got the answer to the first problem! But I still can't do the second one.
I will point you in the right direction: $\displaystyle V = \int_0^3 (2x)^2 \, dy$.
Your job is to understand where this has come from and what to do with it. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9349547028541565, "perplexity": 574.8218504094466}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1404776438940.80/warc/CC-MAIN-20140707234038-00058-ip-10-180-212-248.ec2.internal.warc.gz"} |
https://brilliant.org/discussions/thread/daniel-lius-messageboard/ | # Daniel Liu's Messageboard
I've seen some other people do this, so why not, I'll jump on the bandwagon.
First a few things: I am a 8th grader who is taking Geometry in class, but is working on advanced Pre-calculus concepts and a little Calculus for fun.
You can ask me on advice, whether it be doing math competitions or how to write good problems. Any question is encouraged, as long as I deem it fit for me to answer (no privacy-infringing questions please). Or you can just talk about whatever you want to talk about with me :3
Note by Daniel Liu
4 years, 7 months ago
MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2
paragraph 1
paragraph 2
[example link](https://brilliant.org)example link
> This is a quote
This is a quote
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$
Sort by:
How Make Good Problems ?
I Have To Feeling that my Problems are Much Easy !
- 4 years, 7 months ago
Making a good problem all starts with an idea. Surf the internet for ideas to start from. Wikipedia is a good source, if you do not have other resources like AoPS books and the whatnot.
Once you have a basic idea, play around with it. Explore, and question what will happen if you do something. Once you happen upon a particularly good idea, you can expand upon that idea. Make it more complex, add "bells and whistles", if you may. You can do this by trying to find a relation to some other part of math: the problems that use ideas from multiple categories of math are often the best. If you are out of ideas on how to relate to other categories, just try to make it harder to solve. For example, replace $$10$$ with $$100$$. Combine the idea multiple times onto each other. In the case of Algebra, randomly do algebraic maneuvers in hopes of making it more complicated. The only thing to avoid is to make it a "relay" problem, where you take the answer of a solved problem and use it for the next part of the problem.
Once you make your problem more sophisticated (without making it a drag) you have to solve it yourself. Yep you have to actually solve the problem yourself first. Fortunately, you already have your idea in mind, so you already know how to proceed. Make sure not to mess up the math.
Once you have done that, you're done! You have successfully made a new problem.
I hope this helped a little. If you have any questions or problems, feel free to ask. If you are in the process of creating a problem and really don't have any idea how to make it more complicated than a simple idea, you can also ask me for help.
- 4 years, 7 months ago
- 4 years, 7 months ago
I really don't get why you guys are arguing over such petty things. :?
- 4 years, 7 months ago
Create Problems is a New Tool To Me!
I Always Resolved Problems, But Never Did My Own Problems!
I'll try to work harder!
Thank You , All the Best !
- 4 years, 7 months ago
Hi Daniel, I like your problem very much! It is awesome! I wonder if you can make your own tag like #DanielLiu or something? It would be more convenient for me :D
- 4 years, 6 months ago
If you look in my profile, there's an unshared set called "Daniel's problems". All (or almost all) my problems are contained there back to a certain point.
- 4 years, 2 months ago
What sources do you refer to?? I mean I'm 17 and I just know basics of calculus. I'm very interested in maths and would like to learn advanced stuff but I never stumble upon good sources.(Except brilliant of course.)
- 4 years, 7 months ago
I use AoPS for competition problems. You can find competition problems here and here
I also have many of the AoPS books. You can find them here.
I have used Khan Academy for learning Calculus.
Participating in various local and national math competitions has also helped a lot.
Is this enough for your purposes?
- 4 years, 7 months ago
Yep.Thanks a lot. Will ask for further help if needed.
- 4 years, 7 months ago
Do you have anyone/thing who has inspired you to be who you are now or will be in the future? ~_~
- 4 years, 7 months ago
I want to help other people learn math and other things when I grow up, so people like Calvin Lin, Richard Rusczyk, Salman Khan, etc.
- 4 years, 7 months ago
How many hours do you study maths ?
- 3 years, 5 months ago
Hi, bob! :P
- 4 years, 7 months ago
I doubt using my AoPS nickname is convenient on Brilliant.org :P
- 4 years, 7 months ago
It's not your AoPS nickname, its my nickname for YOU! :D
- 4 years, 7 months ago
You're still in Year 8? I'm in Year 8.
- 3 years, 5 months ago
- 3 years, 5 months ago
Hi Daniel,It is nice to talk to a* MathWiz* Like you.Have you ever been to India?
- 3 years, 5 months ago
Sorry, I haven't.
- 3 years, 5 months ago
Will you Please add me on facebook,I will be really very happy to have a friend like you.
- 3 years, 5 months ago
Done.
- 3 years, 5 months ago
If you accept my friend request, then we could have some talks related to maths.
- 2 years, 11 months ago
Some weeks ago , I noticed that your status stated' 150 problems with 300 solutions' . Have you uploaded them on brilliant? I am eager to solve them. Thanks!
- 3 years, 8 months ago
Yes, they are on brilliant. You can check my profile and search a bit to find them.
- 3 years, 8 months ago
Thanks a lot! Nice set!
- 3 years, 8 months ago
@Daniel Liu I'm on AoPs too (Shabashbeta147) How do I see my documents I've saved using TeXer?I know they give the link but when I click on it it just takes me back to the same page of TeXer.Please please please please please please please tell me how.
- 3 years, 9 months ago
As it's quite obvious, you're really good at math and I myself aspire to become better like geniuses such as you. Unfortunately, i only started doing real math (aka math outside of school) labout a year ago (9th grade, I'm actually 15 ignore my profile age). So over the past year I have taught myself trig, alg 2, advanced geom, and half of pre-calc. I've heard of some kids who started at age 2 and they're unbelievably smart at math. So when did you start?
- 4 years, 3 months ago
I wonder who this is :P
- 4 years, 6 months ago
@Daniel Liu I just looked on your profile for a certain problem when I noticed that solving a Rubik's cube is one of your interests. Can you talk about that? How fast can you solve it, and with what method? Have you been to any competitions?
Personally, I can do it in about 20-30 seconds with a method I came up with on my own that is quite similar to CFOP. No competitions, though. They don't have those in Florida anymore.
Also, you said somewhere else that I got you hooked on Homestuck. How far have you gotten (what act), and who are your favorite characters?
- 4 years, 7 months ago
I'm not very good at Rubik's cubes. My best is about 40 seconds. I have also not gone to any competitions.
As for Homestuck, I am currently up to date. Waiting for the final update now... :D
- 4 years, 7 months ago
What cube do you use? With a standard Rubik's brand I can do it in a minute at the expense of an aching hand, but is generally use my modified Zhanchi (made by the Chinese company Dayan).
Wow, you read that fast. I got it in 7 weeks, 5 days (6 weeks 12 days!) Who are your favorite characters? In addition to Eridan, I like Terezi, Dave, and Jade.
- 4 years, 7 months ago
Teenager Meenah, Sollux, Dave, Jane, Mayor (omg such a cute mayor XD), Roxy...
Yea they're all pretty cool. I don't really not like any of the characters in particular.
- 4 years, 7 months ago
Yes, there is no one cuter than the Mayor!
- 4 years, 7 months ago
I thought message boards were a private non-re-shareable thing; at least according to the description of Peter's set right here.
Umm... could you post your solution to Classic Climbing Problem 2? I'd really love that!
- 4 years, 7 months ago
The main difference is whether you want your messageboard to be sharable.
If you post it as a note to a set, it will not be sharable, and others will not see it in their newsfeed. If they have a link (or are @mentioned), they will be able to access it. This leads to conversations that are initiated by you, and you have slightly greater control over it.
Posting it as a note directly would allow your messageboard to be sharable, and hence much more public. You tend to end up with broader discussions, sometimes initiated by others who are interested in getting to know you. Of course, you could have both versions.
I set mine up by posting to a set, as I wanted to have 'semi-private' conversations easily. The original intention was to easily drop a quick note to various people, somewhat akin to being able to comment on their problem/set.
Staff - 4 years, 7 months ago
I guess I prefer the semi-private conversations to the public ones. Maybe I'll do a public message board.
To be honest, I was somewhat overwhelmed by the number of message-boards in my feed today.
On a related note, what do you think of adding a message board feature to everyone's profile? It'd be hard to moderate though.
- 4 years, 7 months ago
Certainly possible - if lots of people seem to like them we'll think about a more elegant integration.
Staff - 4 years, 7 months ago
Hello, my name is Vish! Nice to meet you. :-0
- 4 years, 7 months ago
What's the meaning of life? Jk... x"D What do you do in your spare time? Do you know any languages other than English?
- 4 years, 7 months ago
42 :D
I do math in my spare time, for fun and for preparing for competitions. I also enjoy playing video games.
I know (Mandarin) Chinese too.
- 4 years, 7 months ago
Oh nice!
- 4 years, 7 months ago | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8773383498191833, "perplexity": 2011.1334179362188}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823872.13/warc/CC-MAIN-20181212112626-20181212134126-00573.warc.gz"} |
http://math.stackexchange.com/questions/211023/solving-a-particular-differential-equation?answertab=oldest | # Solving a particular differential equation
I have a differential equation:
$y''-\frac{3}{2(1+x)(2-x)}y'+\frac{3y}{4(1+x)(2-x)}-\frac{Kf(x)(1+x)^2y}{2x(1+x)(2-x)}=0$.
Here $K>0$ is a fixed constant and $f(x)$ is some (as yet) unknown function of $x$, which is in our hands to chose.
What I want is that I should decide $f(x)$ suitably to find a solution $y(x)$ of the above with the condition $y(0)=1$ where $y(x)$ is a rational function of $x$, i.e. a quotient of two polynomials. The solution should not be free of $K$.
I tried setting $f(x)$ so that the coefficient of $K$ becomes $1$ but the differential equation turned out to be so complicated that I could not solve it.
Can anyone offer any help or suggestions please?
-
Let $R(x)$ be any rational function such that $R(0)=1$ and define $$f(x)=\Bigl(R''-\frac{3}{2(1+x)(2-x)}R'+\frac{3R}{4(1+x)(2-x)}\Bigr)\frac{2x(1+x)(2-x)}{(1+x)^2R}.$$ The $R$ is a solution of your equation with $K=1$.
Thanks for your reply. However I am not looking for a solution which is free of $K$, or is true for a fixed value of $K$. – Shahab Oct 11 '12 at 11:34
Quite simply, I want a solution which is a rational function of $x$ but the term $K$ is present in that solution (eg $(1+Kx)/(1-x)$.) – Shahab Oct 11 '12 at 12:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9020992517471313, "perplexity": 84.72937203524616}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860112727.96/warc/CC-MAIN-20160428161512-00201-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://proglearn.neurodata.io/experiments/xor_rxor_with_unaware.html | # Gaussian XOR and Gaussian R-XOR Experiment with Task Unaware Settings¶
[1]:
# import dependencies
import numpy as np
import random
from proglearn.sims import generate_gaussian_parity
import matplotlib.pyplot as plt
import seaborn as sns
# functions to perform the experiments in this notebook
import functions.xor_rxor_with_unaware_fns as fn
## Ksample test¶
Using ksample test from hyppo we can determine at which angle rxor is significantly different enough from xor to require a new task/transformer. The following code using functions from xor_rxor_aware_unaware_fns.py to calculate p-values from k sample test dcorr from rxor angles 0 to 90 degrees for sample sizes 100, 500, and 1000.
[2]:
# number of times to run the experiment, decrease for shorter run times
mc_rep = 10
# set angle range
angle_sweep = range(0, 90, 1)
[3]:
# calculates and plots angle vs pvalue from ksample test xor vs rxor
# returns numpy array containing all p-vals from all mc_rep experiments at all angles in angle_sweep
pvals_100, pvals_500, pvals_1000 = fn.calc_ksample_pval_vs_angle(mc_rep, angle_sweep)
[4]:
# sets plotting params
sns.set_context("talk")
# plots the mean p-values of the mc_rep experiments with error bars
# dotted green line at p-value = 0.05
plt.figure(figsize=(8, 8))
fn.plot_pval_vs_angle(pvals_100, pvals_500, pvals_1000, angle_sweep)
## Task aware BTE and generalization error (XOR)¶
Next, we’ll run the progressive learner to see how different angles of rxor affect backward transfer efficiency and multitask generalization error of xor (task1). We start by defining the following hyperparameters.
[5]:
# number of times to run the experiment, decrease for shorter run times
mc_rep = 100
# samples to use for task1 (xor)
# samples to use for task2 (rxor)
# we will use the same angle_sweep as before
angle_sweep = range(0, 90, 1)
[6]:
# call the function to run the experiment
# give us arrays with mean_te and mean_error
[7]:
# plot angle vs BTE
fn.plot_bte_v_angle(mean_te)
[8]:
# plot angle vs generalization error
plt.figure(figsize=(8, 8))
plt.plot(angle_sweep, mean_error[:, 1])
plt.xlabel("Angle of Rotation")
plt.ylabel("Generalization Error (xor)")
plt.show()
## Task Unaware: K-sample testing “dcorr”¶
Instead of adding a new task for every angle of rxor, we use a k sample test to determine when rxor is different enough to warrant adding a new task. Then we plot the BTE and multitask generalization error of xor (task1). Once again, we start by definining hyperparameters. We will examine BTE and generalization error for 100, 500, and 1000 task samples.
[9]:
# number of times to run the experiment, decrease for shorter run times
mc_rep = 100
# samples to use for task1 (xor)
# samples to use for task2 (rxor)
# we will use the same angle_sweep as before
angle_sweep = range(0, 90, 1)
[10]:
# call our function to run the experiment
un_mean_te, un_mean_error = fn.unaware_bte_v_angle(
)
[11]:
# plot angle vs BTE
fn.plot_unaware_bte_v_angle(un_mean_te)
[12]:
# plot angle vs generalization error
plt.figure(figsize=(8, 8))
plt.plot(angle_sweep, un_mean_error[:, 1])
plt.xlabel("Angle of Rotation")
plt.ylabel("Generalization Error (XOR)")
plt.show()
[13]:
# number of times to run the experiment, decrease for shorter run times
mc_rep = 100
# samples to use for task1 (xor)
# samples to use for task2 (rxor)
# we will use the same angle_sweep as before
angle_sweep = range(0, 90, 1)
# call our function to run the experiment
un_mean_te, un_mean_error = fn.unaware_bte_v_angle(
)
# plot angle vs BTE
fn.plot_unaware_bte_v_angle(un_mean_te)
[14]:
# plot angle vs generalization error
plt.figure(figsize=(8, 8))
plt.plot(angle_sweep, un_mean_error[:, 1])
plt.xlabel("Angle of Rotation")
plt.ylabel("Generalization Error (XOR)")
plt.show()
[15]:
# number of times to run the experiment, decrease for shorter run times
mc_rep = 100
# samples to use for task1 (xor)
# samples to use for task2 (rxor)
# we will use the same angle_sweep as before
angle_sweep = range(0, 90, 1)
# call our function to run the experiment
un_mean_te, un_mean_error = fn.unaware_bte_v_angle(
)
# plot angle vs BTE
fn.plot_unaware_bte_v_angle(un_mean_te)
[16]:
# plot angle vs generalization error
plt.figure(figsize=(8, 8))
plt.plot(angle_sweep, un_mean_error[:, 1])
plt.xlabel("Angle of Rotation")
plt.ylabel("Generalization Error (XOR)")
plt.show() | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3268512487411499, "perplexity": 11275.885060076482}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335276.85/warc/CC-MAIN-20220928180732-20220928210732-00512.warc.gz"} |
http://www.supadamn.com/fume-food-mkhp/r-and-g-electric-20e659 | # r and g electric
Our founder, Thomas Edison, must have seen something special in the Capital District when he selected Schenectady as the original headquarters of the General Electric Company. The price was great as well. Under compression (strain in the opposite direction), the resistance of the strained section of conductor decreases. G&W Electric Acquires Italy-based company Tozzi Electrical Equipment. At R & G Auto Electrics, we take our work seriously to make sure we offer our clients the best service and quality selection of automotive electrical parts. is a fixed reference temperature (usually room temperature), and J&G Electric Co.,Inc. _ = / _ for AC circuits, just as = / for DC circuits. For the 15th consecutive year, SDG&E has received awards for outstanding electric reliability, innovation and system resiliency. Other factors and conditions are relevant as well. I would recommend him. Includes R & G Electric Reviews, maps & directions to R & G Electric … 349 likes. LATEST PRODUCTS - 2020 Yamaha YZF-R1/ R1M accessories available now - Find Out More!. Updates. For ideal resistors, Z and Y reduce to R and G respectively, but for AC networks containing capacitors and inductors, X and B are nonzero. _ State Certified Electrical and General Contractors, taking care of business since 1986. The Registered Agent on file for this company is Roger Scharp/D and … Learn More. Email Address. We work with our customers to meet their requests and find exactly the right part they need for the right price. Superconductors require cooling to temperatures near 4 K with liquid helium for most metallic superconductors like niobium–tin alloys, or cooling to temperatures near 77 K with liquid nitrogen for the expensive, brittle and delicate ceramic high temperature superconductors. Home About Pay Invoice Home About Pay InvoiceW.I.R.E.D for Excellence! G&W Electric Altea S.r.l. {\displaystyle T_{0}} Rocky (R&G Electrics) did a fantastic job and went through a lot of trouble to replace a 30 year old fuse box. For this reason it is usual to specify the temperature that {\displaystyle T_{0}} Electrical License: 476083. Because the linear approximation is only an approximation, This electrical energy is dissipated, heating the resistor in the process. They upgraded the kitchen and living lighting with a modern look recess lighting. Security. G & R electrical were established in 2002, becoming Limited in 2005 and have built a strong business model based on trust and delivery. RPG Electric's mission is to provide world-class installation and service. Hours of Operation. As electricians and electrical contractors, R and G Electrics UK undertakes a wide range of installation work, from an extra socket to complete re-wiring of the house to large scale commercial refurbishment projects. 83 likes. Fast Worldwide Delivery. Mesquite, NV 89027. Thank you, Mr. Rubalcava , for your excellent service." More details can be found in the article: Electrical resistivity and conductivity. The company is a well established, professional Electrical Company specialising in all aspects of electrical installation works. Resistivity varies with temperature. Check the complaint history, rating and reviews on this company. See the discussion on strain gauges for details about devices constructed to take advantage of this effect. G&R Electric LLC, Townsend, Delaware. We work with our customers to meet their requests and find exactly the right part they need for the right price. Although when I was there, customers were in and not … CAREERSHome About Pay Invoice Home About Pay Invoice Grand Rapids, Michigan The genesis of GR Electric,was founded in the basement of, now president, Brad Dekock in 2006. Get the r and g neck gaiter and mug. In an insulator, such as Teflon, each electron is tightly bound to a single molecule so a great force is required to pull it away. GR Electric is known for the high standard of all its Electrical Contractor services and workmanship - and value for money. To communicate or ask something with the place, the Phone number is (626) 893-7817 if you don't know how to go R & G Electric click here.You … Learn More. Therefore, these components can be used in a circuit-protection role similar to fuses, or for feedback in circuits, or for many other purposes. I wanted to finish my basement and had GR Electric do the wiring on it they drew up the prints and got the permit they were very patient with me as it took a long time for me to finish the drywall so they can finish up the outlets and switches. The parameter Recent work: Installation of a new 100 amp panel. First, they can be used as thermometers: By measuring the resistance, the temperature of the environment can be inferred. Recent work: See case 146180 for fire assessment - permit to check location **lz**. Fans were also installed in every room...best part it was well done and affordable...thank you!" G & R Electric Corp., Hialeah, Florida. We are highly knowledgeable, professional. A permanently installed Generac home backup generator protects your home automatically. But for a capacitor or inductor, the maximum current flow occurs as the voltage passes through zero and vice versa (current and voltage are oscillating 90° out of phase, see image below). Learn more. Miguel Garcia. {\displaystyle \rho =1/\sigma } Electric Inc. has been providing high-quality service and customer satisfaction since 2007. Both these effects contribute to increasing the resistance of the strained section of conductor. View Video. Electrician in Eufaula. Posted on Apr 13, 2019. In some cases, however, the effect is put to good use. The company has 1 principal on record. R G ELECTRIC is listed in the categories Electrical Contractors, Electrical Work and Electric Contractors and offers Additions, Commercial Projects, Consulting, Contracting, Design, Engineering, Industrial Projects, Add … This formula is not exact, as it assumes the current density is totally uniform in the conductor, which is not always true in practical situations. In general, self-heating can turn a resistor into a nonlinear and hysteretic circuit element. Search for news: 69 results Subscribe to our emails for the latest news on all our products, services and solutions. Near room temperature, the resistivity of metals typically increases as temperature is increased, while the resistivity of semiconductors typically decreases as temperature is increased. Strada Statale 16 – Zona Industriale Incoronata 71122 – Foggia (FG) - Italy Phone: +39 0881 811 411. In semiconductors, resistivity also changes when exposed to light. G & R Electric. Random element in games. R and G Electrics UK Ltd are London based electricians / electrical contractors providing a full range of Domestic, Commercial & Industrial electrical services. is the resistance at temperature Just as the resistance of a conductor depends upon temperature, the resistance of a conductor depends upon strain. Electric is a Maryland Tradename filed on February 6, 2007. α Second, they can be used in conjunction with Joule heating (also called self-heating): If a large current is running through the resistor, the resistor's temperature rises and therefore its resistance changes. The Registered Agent on file for this company is Roger Scharp/D and is located at 2425 E 2250 N, Layton, UT 84041. We will do everything we can to meet your expectations! Electricité générale, bâtiment, dépannage, domotique, sur tout l'île de La Réunion Opposition to the passage of an electric current, This article is about specific applications of conductivity and resistivity in electrical elements. At GR Electric, we bring with us over 50 years of electrical contracting experience and a growing understanding of the latest technologies and innovations in our industry. m). The principal is … About R & G Electric: Established in 1995, R & G Electric is located at 2110 10th Ave N in Humboldt, IA - Humboldt County and is a business listed in the categories Electrical Contractors, Electric Motor Repairing & Service, Heating Contractors & Systems, Electric Motors, Air Conditioning & Heating Repair, Heating Contractors, Electric Motor Repair, Electric Motors & … Learn More. This effect may be undesired, causing an electronic circuit to malfunction at extreme temperatures. For this reason, the geometrical cross-section is different from the effective cross-section in which current actually flows, so resistance is higher than expected. Resistance and conductance can still be defined for non-ohmic elements. is an A+ rated electrical contractor. 0 Featured News. In many cases we’ll have the exact replacement motor in stock which you can receive same day. Many electrical elements, such as diodes and batteries do not satisfy Ohm's law. R & G Electric is an Utah Corporation - Domestic - Profit filed on December 20, 1982. Via Trasvolatori Atlantici 30/A 44124 Ferrara (FE), Italy Phone: +39 0532 225 731. 1 Located in the heart of the Permian Basin, C.R.G. The company's filing status is listed as Delinquent and its File Number is 20131534582. RFG Electric is an Long Island electrician and electrical contractor that services NY and the 5 boroughs. ★ R.g. R & G Electric is rated with a F rating from Business Consumer Alliance as of 1/17/2021. Icom IC-705 10W HF/6m/2m/70cm Portable Transceiver $1299.95 Free Shipping Limit of 2 per customer. He also fixed my washing machine, ceiling lights, and smoke detectors. {\displaystyle \alpha } As another example, incandescent lamps rely on Joule heating: the filament is heated to such a high temperature that it glows "white hot" with thermal radiation (also called incandescence). Search for other Electricians in North Bend on The Real Yellow Pages®. For the term used when referring to touchscreens, see, The resistivity of copper is about 1.7×10. was measured at with a suffix, such as Report Electric Outage; Report Streetlight Outage; View Outage List; View Outage Map; Stay Informed. When temperature-dependent resistance of a component is used purposefully, the component is called a resistance thermometer or thermistor. Learn More. Similarly, if two conductors near each other carry AC current, their resistances increase due to the proximity effect. There are two types of resistance:[1][2]. Home About Pay Invoice Home About Pay InvoiceW.I.R.E.D for Excellence! Resistivity and conductivity are reciprocals: Residential and commercial Comfort. [email protected] Australia Wide, NEW & Surplus Electric Motor Supply. Repeat business is the foundation of any business and the creation of strategic partnerships with all stakeholders is crucial to any business’s continuing success. When an alternating current flows through a circuit, the relation between current and voltage across a circuit element is characterized not only by the ratio of their magnitudes, but also the difference in their phases. About Us Services. RG Électrique. Electric Inc. has been providing high-quality service and customer satisfaction since 2007. We program PLCs and HMIs to meet your custom application. R Welcome to R&G Setting the standard in crash protection and bolt-on motorcycle accessories. Beginning with nothing more than an idea for an electric company based on the principles of good customer … about Read More » 1 0 Fast Secure checkout. Find R & G Electric in Humboldt with Address, Phone number from Yahoo US Local. For other types of conductivity, see, "Resistive" redirects here. For the case of electrolyte solutions, see the article: Conductivity (electrolytic). Our electricians provide commercial & residential services in Maryland, Virginia, Washington DC 0 [9], The temperature coefficient G&R Electrical Wholesalers provide the highest level of customer care and technical support for all your electrical wholesale and service requirements. {\displaystyle \alpha } {\displaystyle R=1/G} Mission Statement. [8] One reason, mentioned above is the skin effect (and the related proximity effect). About R G ELECTRIC: R G Electric offers Health Care at 2313 12Th Ave W Williston, ND - Williams County and is a business with Contractors and Engineers on staff. Resistivity is a measure of the material's ability to oppose electric current. On the other hand, Joule heating is sometimes useful, for example in electric stoves and other electric heaters (also called resistive heaters). Message . R.G. Roma, Italy New Dehli, India Bahia, Brasil / . Amid the growing urgency to address climate change and its impacts, SDG&E has released a comprehensive sustainability strategy with specific, actionable commitments in the areas of environmental stewardship, clean transportation, grid modernization, community engagement and other company operations to help California … Find the R.G. TX. Y Name. Electric R. R.G. RG Moss Electric. 2626 RIGGAN ST CORPUS CHRISTI, TX 78404 Get Directions (361) … Opening at 8:00 AM. See who you know at R G Electric Co, leverage your professional network, and get hired. Look for more businesses with the D&B Business Directory at DandB.com. About Us & Why We are The Best For the Job. Electric CLAIM THIS BUSINESS. For your peace of mind and security R and G Electrics UK is fully insured as per the requirements of the new building regulations (Part P) in force from 1st Jan 2005. T α = Beginning with nothing more than an idea for an electric company based on the principles of good customer … about Read … We offer a wide range of experience from small residential jobs, custom homes, commercial buildings, industrial machine shops, food processing facilities & cold storage facilities. The Registered Agent on file for this company is Russell Garvin and is located at 38 Cochise Court, Gypsum, CO 81637. With competitive prices, a fast delivery service and a dedication to our clients, G&R Electrical really is the full electrical services package. R & G Electric is located in La Puente city of California state. 3 reviews of R & G Electric "He installed some new lights in my bedroom, my kitchen, and my bathrooms. These are called non-ohmic or non-linear, and their current–voltage curves are not straight lines through the origin. R and G Electrics UK also operates a genuine 24hr domestic & commercial emergency service; where we respond to callouts within one hour, day or night. CAREERSHome About Pay Invoice Home About Pay Invoice Grand Rapids, Michigan The genesis of GR Electric,was founded in the basement of, now president, Brad Dekock in 2006. Had a problem with the brake lights and turn signals and they were able to figure out the problem. Please enter what you're searching for. Pacific Gas and Electric Company provides natural gas and electric service to approximately 16 million people throughout a 70,000-square mile service area in northern and central California. Over 400 Bike Models. Special price valid Until 1/31/2021 Now In Stock! Our services include: Residential, Industrial, Commercial, Agricultural and Automation work. G&W Electric is a growing company that cultivates a team-first environment and prioritizes the success and well-being of its employees. For more details, see the, Mathematical descriptions of the electromagnetic field, Electrical resistivities of the elements (data page), Electrical resistivity and conductivity § Temperature dependence, technological applications of superconductivity, National Institute for Occupational Safety and Health, "Electron conductance models using maximal entropy random walks", https://en.wikipedia.org/w/index.php?title=Electrical_resistance_and_conductance&oldid=999079996, Creative Commons Attribution-ShareAlike License, 1 meter of copper wire with 1 mm diameter, This page was last edited on 8 January 2021, at 11:21. The company's personal approach to its clients helps maintain a friendly, workable and lasting relationship. This is called Joule heating (after James Prescott Joule), also called ohmic heating or resistive heating. _ α Vous souhaitez une nouvelle installation ou une rénovation qui nécessite l’intervention d’un professionnel qualifié garantissant votre sécurité? {\displaystyle \alpha } is typically +3×10−3 K−1 to +6×10−3 K−1 for metals near room temperature. These are a common type of light detector. RG Electric Company, Inc In addition to our construction and electrical know-how, we believe that our strong design-build capabilities set us apart from the competition. The Company Feiz Electric dba Rag Electric is a licensed electrical contracting company established in May, 1987. Je suis électricien indépendant sur … Random element in games. It is usually negative for semiconductors and insulators, with highly variable magnitude.[e]. Get the r and g neck gaiter and mug. 267 Vineyard Lane. Auto Electrical and Air Conditioning Service and Repairs In Mackay, QLD Resistors (and other elements with resistance) oppose the flow of electric current; therefore, electrical energy is required to push current through the resistance. G&W Electric Acquires Italy-based company Altea S.R.L. We’re Australia’s leading Electric Motor Distributor, supplying quality, cost effective electric motors to a wide range of industries for over 40 years. Electrical Work. Browse Small shop and parking is on the street which means it could be difficult to park if they have lots of customers at once. α {\displaystyle R_{0}} friendly, and dependable. Resistance thermometers and thermistors are generally used in two ways. Simple ohmmeters cannot measure low resistances accurately because the resistance of their measuring leads causes a voltage drop that interferes with the measurement, so more accurate devices use four-terminal sensing. RPG Electric Ltd. RPG Electric Ltd is an electrical contracting firm specializing in new builds and renovations for institutional environments, including healthcare facilities, commercial spaces, academic environments, and community structures. Get Quote Call (918) 689-7539 Get directions WhatsApp (918) 689-7539 Message (918) 689-7539 Contact Us Find Table View Menu Make Appointment Place Order. Some resistors, particularly those made from semiconductors, exhibit photoconductivity, meaning that their resistance changes when light is shining on them. where R and G are resistance and conductance respectively, X is reactance, and B is susceptance. Electric, Inc. provides electric service for customers in West Texas, New Mexico and surrounding areas. Please enter your search location. ρ On the street of Broadmoor Avenue and street number is 632. Semiconductors lie between these two extremes. Get reviews, hours, directions, coupons and more for G & R Electric at 610 E 6th St, North Bend, NE 68649. Find everything you need to know about G & R Electric on Yellowpages.ca. He was professional and took time to make sure that everything was perfect. Contact us to request electrical services. Sales Offices. With a variety of electrical service offerings to choose from, we're sure you'll be happy working with us. High voltage breaks down the skin, lowering resistance to 500 Ω. For more details see Thermistor#Self-heating effects. Complex numbers are used to keep track of both the phase and magnitude of current and voltage: The impedance and admittance may be expressed as complex numbers that can be broken into real and imaginary parts: where R and G are resistance and conductance respectively, X is reactance, and B is susceptance. Building a Better Future . G&W Electric Unveils New Website Showcasing Customized Solutions and Expertise. Multifamily. Products; Resources; My Account; Talk to a D&B Advisor 1-800-280-0780. Business Directory. R and G Electric Company in San Benito, TX | Photos | Reviews | 31 building permits. is different for different reference temperatures. 14 reviews of A&G Electric Company "A&G Electric Company was referred by a friend and did a great job with my parents home. Outage Alerts; Outage News; Be Prepared. = is called the temperature coefficient of resistance, At R+G Electrical we fit and maintain a wide range of sophisticated door entry systems, from keypad, keyless entry or pass key entry, ensuring there is no unauthorised access to your premises or property. The dissipation of electrical energy is often undesired, particularly in the case of transmission losses in power lines. . A key feature of AC circuits is that the resistance and conductance can be frequency-dependent, a phenomenon known as the universal dielectric response. As a consequence, the resistance of wires, resistors, and other components often change with temperature. for DC circuits. Electrical, Inc. specializes in OEM support for the small to midsize custom manufacturer. Find R & G Electric in Humboldt with Address, Phone number from Yahoo US Local. is an empirical parameter fitted from measurement data. The company's filing status is listed as Expired and its File Number is 819976-0142. / R.G. Electric ★ 13 Lacroix Bay Rd, Westmeath, Ontario, 6135874574 ★ electric In the history of heavy equipment development, no single man’s name is more respected or revered as that of R. G. LeTourneau. G&W Electric S.r.l. Includes R & G Electric Reviews, maps & directions to R & G Electric in Humboldt and more from Yahoo US Local However, unlike ohmic resistance, non-linear resistance is not constant but varies with the voltage or current through the device; i.e., its operating point. It runs on natural gas or liquid propane (LP) fuel, and sits outside just like a central air conditioning unit. Another situation for which this formula is not exact is with alternating current (AC), because the skin effect inhibits current flow near the center of the conductor. α Our electricians have 10+ years of experience making our work efficient and reliable. G All electrical work carried out by R and G Electrics UK conforms to, or exceeds the requirements of BS7671; and … State Electrical Contractor, Ec Electrical Contractor, Electrical, Electrician License: SEC20318, 20318, CONT2009-0881. G&C Electric offers many areas of quality services including, new construction and remodels for residential and commercial, boat dock and … α Our professional, knowledgeable and friendly electricians & plumbers are here to serve all your needs. With a team of safety oriented, professional electricians coupled with our commitment to customer satisfaction, we offer our clients the full package. Therefore, if superconductive wire is made into a closed loop, current flows around the loop forever. Another reason is that the resistivity itself may depend on frequency (see Drude model, deep-level traps, resonant frequency, Kramers–Kronig relations, etc.). Nevertheless, there are many technological applications of superconductivity, including superconducting magnets. Call us at (412) 854-0883 to learn more. For example, in an ideal resistor, the moment when the voltage reaches its maximum, the current also reaches its maximum (current and voltage are oscillating in phase). Our sister company, Robert G. Dashiell, Jr., P.E., Inc. provides professional electrical and mechanical design services for all building types. Learn about working at R G Electric Co. Join LinkedIn today for free. 12 reviews of R G Auto Electric & Batteries "This place was great. For a fresh Energizer E91 AA alkaline battery, the internal resistance varies from 0.9 Ω at −40 °C, to 0.1 Ω at +40 °C. Street, Dillwyn, VA 22193 listed as Forfeited and its File is! Phone Number from Yahoo us Local intervention D ’ un professionnel qualifié garantissant votre sécurité, Florida that everything perfect! 'S mission is to provide world-class installation and service. each other carry AC current, their resistances due! = 1 / σ { \displaystyle \alpha } is typically +3×10−3 K−1 to +6×10−3 K−1 for metals near room.. = 0 and I ≠ 0 qualifié garantissant votre sécurité our clients the full package usually. Ac circuits, just as = / for DC circuits we program PLCs HMIs... The system in crash protection and bolt-on motorcycle accessories reduce the losses by reducing the current for a given.. Is used purposefully, the resistivity of copper is about specific applications of superconductivity, including superconducting.... Grande région de Montréal et vous offre des services d'électricité résidentiel et commercial 1-800-280-0780. Business Directory at DandB.com with,. ; report Streetlight Outage ; View Outage Map ; Stay Informed neck and. 30 years of experience in Podium, Wrap, Garden and Hybrid style New... Maryland, Virginia, Washington DC R.G YZF-R1/ R1M accessories available now - find Out more! approximation is an! Yamaha r and g electric R1M accessories available now - find Out more! you 'll happy. Electric - Killarney - Phone Number, website, Address & opening hours - MB - electricians & Contractors... In stock which you can receive same day a D & B Business Directory at.... Une rénovation qui nécessite l ’ intervention D ’ un professionnel qualifié garantissant sécurité... The full package has received awards for outstanding Electric reliability, innovation and system resiliency 2020 Yamaha R1M... Electricians & plumbers are here to serve all your electrical wholesale and service. 20318 CONT2009-0881! Prioritizes the success and well-being of its employees, Albany, the of! Resources ; for Municipalities ; Critical Facilities Request ; we 're sure you 'll be happy with! And well-being of its employees superconductive wire is made of ceramic or.. High voltage transmission helps reduce the losses by reducing the current for a given.! Two ways exact replacement Motor in stock which you can receive same day rating reviews. Ceramic or polymer. ) Permian Basin, C.R.G 2250 N, Layton, UT 84041 part it was done... Power lines Dehli, India Bahia, Brasil Australia Wide, New Mexico was founded in 1962 by John Geneva... You in the heart of the strained section of conductor through the origin energy..., Dillwyn, VA 23936 ( 434 ) 983-2324 G & R,! Network, and smoke detectors personal approach to its clients helps maintain friendly! Found in the opposite direction ), also called ohmic heating or heating!, providing them with Electric material requirements Consumer Alliance as of 1/17/2021 bedroom, kitchen! Service INC is committed to providing customers with unsurpassed product support of this.!, if superconductive wire is made of metal, usually platinum, while thermistor... Behers electrical service offerings to choose from, we 're sure you be... And friendly electricians & electrical Contractors instrument for measuring resistance is called heating!, providing them with Electric material requirements YZF-R1/ R1M accessories available now - find Out!! About working at R G Auto Electric & batteries this place was great, and! Help you r and g electric on energy costs this winter Australia Wide, New Mexico and surrounding areas to! Us & Why we are the best for the latest news on our! The temperature coefficient α { \displaystyle \alpha } is different for different reference temperatures ( LP ),! Resistive heating and Automation work LP ) fuel, and get hired the universal dielectric response sister,. Above is the skin, lowering resistance to 500 Ω & opening hours - -! And surrounding areas is an empirical parameter fitted from measurement data Outage List ; View Map. This winter fitted from measurement data to French language × your Account is now active is an. The passage of an Electric current log in ; fr Passer en français / Switch to French language × Account! Llc is a well established, professional electricians coupled with our customers meet... He installed some New lights in my bedroom, my kitchen, my. Electric material requirements ( FE ), also called ohmic heating or resistive heating negative for semiconductors and insulators with... Particularly in the opposite direction ), also called ohmic heating or heating! Fr Passer en français / Switch to French language × your Account is now active exactly zero and... Electricians provide commercial & residential services in Maryland, Virginia, Washington DC R.G, Albany, the of., customers were in and not … building a Better Future Corp., Hialeah, Florida Electric S.R.L or! Loop forever this also means there is no Joule heating, or in other words dissipation... Material 's ability to oppose Electric current, this article is about specific applications of conductivity,,! An empirical parameter fitted from measurement data personal approach to its clients helps maintain a friendly workable! Location * * by reducing the current for a given power time to make sure everything! Altea r and g electric French language × your Account is now active electricians & plumbers are here to serve your! Report Electric Outage ; View Outage Map ; Stay Informed photoresistors ( or light dependent resistors.. Not satisfy Ohm 's law, Phone Number from Yahoo us Local language × your Account is active. Maintain a friendly, workable and lasting relationship G & R Electric, Inc. of,... Into a nonlinear and hysteretic circuit element 20, 1982, see, resistive. In every room... best part it was well done and affordable... thank you! Delinquent its... On strain gauges for details about devices constructed to take advantage of effect. Brake lights and turn signals and they were able to figure Out the.! State Certified electrical and General Contractors, taking care of Business since 1986 different reference temperatures Agricultural and work. Portable Transceiver$ 1299.95 free Shipping Limit of 2 per customer wire is made of,... Program PLCs and HMIs to meet their requests and find exactly the right price dielectric response these!, Mr. Rubalcava, for your excellent service. of customers at once, resistivity also when! Generally used in two ways at DandB.com you! self-heating can turn a resistor into closed... Is shining on them serving Corvallis, Albany, the temperature of the electrical controls for! Is made of metal, usually platinum, while a thermistor is made of,... ( strain in the heart of the strained section of conductor bedroom, my kitchen and. Energy costs this winter on all our products, services and solutions carry AC current this! Near room temperature the loop forever across the Southwest down the skin, lowering resistance to 500 Ω HF/6m/2m/70cm Transceiver. The entire state of Oregon for 43 years the company 's filing status is listed as Expired its... Oem support for all your electrical wholesale and service. licensed electrical company... Here to serve all your needs temperature-dependent resistance of wires, resistors, in! Professional, knowledgeable and friendly electricians & plumbers are here to serve all needs! The discussion on strain gauges for details about devices constructed to take of... That their resistance changes when light is shining on them, CA | Photos | reviews | building... High-Quality service and customer satisfaction, we offer our clients the full package city California! Just as = / for DC circuits clients the full package, heating resistor. Is located in La Puente city of California state of transmission losses in power.. Improvements, Remodels and service. resistive '' redirects here see, resistive redirects.... ) still be defined for non-ohmic elements near room temperature +3×10−3 K−1 to +6×10−3 K−1 for metals near temperature! Infinite conductance, because they can be used as thermometers: by measuring the resistance of,. Park, CA | Photos | reviews | 223 building permits is active! These are called photoresistors ( or light dependent resistors ) while a is! 71122 – Foggia ( FG ) - Italy Phone: +39 0532 731. To its clients helps maintain a friendly, workable and lasting relationship other components often change with.... Your Equipment, New & Surplus Electric Motor Supply can have V = 0 and ≠... Natural gas or liquid propane ( LP ) fuel, and my bathrooms G Setting the standard in protection! Depends upon strain resistance and conductance can be used as thermometers: by the..., including superconducting magnets and get hired for fire assessment - permit to check location * * *. ; report Streetlight Outage ; View Outage List ; View Outage List ; View Outage Map ; Stay.! Park, CA | Photos | reviews | 223 building permits program PLCs and HMIs meet. Company Feiz Electric dba Rag Electric is a Colorado Limited-Liability company filed on February 6, 2007 the.... Street Number is 20131534582 need to know about G & W Electric Italy-based.. ) infinite conductance, because they can be found in the opposite direction ), the resistance and can... Qui nécessite l ’ intervention D ’ un professionnel qualifié garantissant votre?... Via Trasvolatori Atlantici 30/A 44124 Ferrara ( FE ), Italy Phone +39. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24062015116214752, "perplexity": 5025.095485692752}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038464065.57/warc/CC-MAIN-20210417222733-20210418012733-00143.warc.gz"} |
https://math.stackexchange.com/questions/3129344/condition-when-angle-between-two-lines-is-pi-over-3 | Condition when angle between two lines is ${\pi\over 3}$
The whole question is-
Show that if the angle between the lines whose direction cosines are given $$l+m+n=0$$ and $$fmn+gnl+hlm=0$$ is $${\pi\over 3}$$ then $${1\over f}+{1\over g}+{1\over h}=0$$.
I'm trying to solve the problem in the following manner-
From the first equation $$n=-l-m$$, substituting this value of $$n$$ in the second equation we get-
$$fm(-l-m)+g(=l-m)l+hlm=0$$
$$\implies g\left({l\over m}\right)^2+(f+g+h)\left({l\over m}\right)+f=0$$
Now, the roots of this equation are $${l_1\over m_1}$$ and $${l_2\over m_2}$$. So, product of them $${l_1\over m_1}.{l_2\over m_2}={f\over g}\implies {l_1 l_2\over f}={m_1 m_2\over g}$$.
Similarly, we get $${m_1 m_2\over g}={n_1 n_2\over h}$$.
Hence, $${l_1 l_2\over f}={m_1 m_2\over g}={n_1 n_2\over h}=K$$(say)
Thus, $$\cos {\pi\over3}=l_1 l_2+m_1 m_2+n_1n_2=K(f+g+h)\implies K=\frac{\sqrt{3}}{2(f+g+h)}$$.
Now, I can't proceed further. I can't prove $${1\over f}+{1\over g}+{1\over h}=0$$.
Can anybody solve the problem? Thanks for assistance in advance.
• The direction cosines (in $3D$) are (three) numbers, not an equation, aren't they? – user Feb 28 '19 at 17:47
• Yes, I am saying that the direction cosines of the two lines $(l_1,m_1,n_1)$ and $(l_2,m_2,n_2)$ satisfy these equations. – MathBS Mar 2 '19 at 19:00
• This is still not clear. Do you mean that the direction cosines are $(l,m,n)$ and $(fmn,gnl,hlm)$, respectively? – user Mar 2 '19 at 20:03
• If $(l_1,m_1,n_1), (l_2,m_2,n_2)$ are the direction cosines of two lines respectively. Then $l_1+m_1+n_1=0, fm_1 n_1+gn_1 l_1+hl_1 m_1=0$ and $l_2+m_2+n_2=0, fm_2 n_2+gn_2 l_2+hl_2 m_2=0$ – MathBS Mar 4 '19 at 15:17
As clarified in the comments, the correct formulation of the problem is:
Show that the angle between the lines whose direction cosines $$(l_1,m_1,n_1)$$ and $$(l_2,m_2,n_2)$$ satisfy the equations $$l+m+n=0\tag1$$ and $$fmn+gnl+hlm=0\tag2$$ is $${\pi\over 3}$$ if $${1\over f}+{1\over g}+{1\over h}=0.\tag3$$
In fact as will be shown below even stronger statement with "if" replaced by "if and only if" holds. It will be additionally assumed $$(l_1,m_1,n_1)\nparallel(l_2,m_2,n_2)$$, $$(f,g,h)\ne(0,0,0)$$. Otherwise extra solutions are possible.
The entirety of the conditions implies that neither of $$l_i,m_i,n_i$$ is $$0$$. Indeed an assumption that any of the components - say $$n_1$$ - is $$0$$ results in combination with $$(1)$$ and $$(2)$$ in the equality $$(f,g,h)=(0,0,0)$$.
Observe now that equality $$(1)$$ $$(l,m,n)\cdot(1,1,1)=0$$ means that the vectors $${\bf a}_1=(l_1,m_1,n_1)$$ and $${\bf a}_2=(l_2,m_2,n_2)$$ are orthogonal to the vector $${\bf 1}=(1,1,1)$$. This implies $${\bf a}_1\times {\bf a}_2 \parallel {\bf 1}$$ or component-wise: $$m_1n_2-n_1m_2=n_1l_2-l_1n_2=l_1m_2-m_1l_2=\frac{\sin\alpha}{\sqrt3},\tag4$$ where $$\alpha$$ is the angle between $${\bf a}_1$$ and $${\bf a}_2$$ which is to be found. The last equality is due to $$\sin^2\alpha=|{\bf a}_1\times {\bf a}_2|^2=\sum_{i=x,y,z}({\bf a}_1\times {\bf a}_2)_i^2.$$
Similarly the equation $$(2)$$ $$(f,g,h)\cdot(mn,nl,lm)=0$$ means that the vectors $${\bf b}_1=(m_1n_1,n_1l_1,l_1m_1)$$ and $${\bf b}_2=(m_2n_2,n_2l_2,l_2m_2)$$ are orthogonal to the vector $${\bf c}=(f,g,h)$$. This in turn implies that the vector $${\bf c}$$ is collinear to the vector product $${\bf b}_1\times {\bf b}_2$$, which reads component-wise: \begin{align} (f,g,h)& =A\big(l_1l_2(n_1m_2-m_1n_2),m_1m_2(l_1n_2-n_1l_2),n_1n_2(m_1l_2-l_1m_2)\big)\\ &=\frac{A\sin\alpha}{\sqrt3}(l_1l_2,m_1m_2,n_1n_2)\tag5 \end{align} where $$A$$ is a non-zero constant.
We start now with the proof of the "if" part. The equations $$(3)$$ and $$(5)$$ imply: $$\frac{1}{l_1l_2}+\frac{1}{m_1m_2}+\frac{1}{n_1n_2}=0\tag6$$ or $$m_1m_2n_1n_2+n_1n_2l_1l_2+l_1l_2m_1m_2=0.\tag7$$ With help of $$(1)$$ the equation reads: \begin{align} 0&=(l_1+m_1)(l_2+m_2)(l_1l_2+m_1m_2)+l_1l_2m_1m_2\\ &=(l_1l_2+m_1m_2+l_1m_2)(l_1l_2+m_1m_2+m_1l_2).\tag8 \end{align} Now we can proceed with computation of $$\cos\alpha={\bf a}_1\cdot {\bf a}_2$$: \begin{align} \cos\alpha &=l_1l_2+m_1m_2+n_1n_2\\ &=l_1l_2+m_1m_2+(l_1+m_1)(l_2+m_2)\\ &=2(l_1l_2+m_1m_2)+l_1m_2+m_1l_2\\ &\stackrel{(8)}=\pm(l_1m_2-m_1l_2)\stackrel{(4)}=\pm\frac{\sin\alpha}{\sqrt3}.\tag9 \end{align} Squaring the equation one finally obtains: $$\cos^2\alpha=\frac13 \sin^2\alpha\implies \cos^2\alpha=\frac14 \implies \alpha=\frac\pi3.\tag{10}$$
As already mentioned the inverse implication $$\alpha={\pi\over 3}\implies {1\over f}+{1\over g}+{1\over h}=0$$ holds as well, since, provided the equality $$(1)$$, the equations $$(6)-(10)$$ are equivalence relations, so that the whole argument can be easily reversed.
In general if a, b, c and d, e, f are components of 2 vectors then the direction cosines are for the first vector : $$\frac{a}{\sqrt{a^2 + b^2 + c^2}}$$ and $$\frac{b}{\sqrt{a^2 + b^2 + c^2}}$$ and $$\frac{c}{\sqrt{a^2 + b^2 + c^2}}$$ similarly for the second vector.
Then the angle $$\theta$$ between these vectors is
$$cos\theta = \frac{ad + be + cf}{\sqrt{a^2 + b^2 + c^2}\sqrt{d^2 + e^2 + f^2}}$$
Using the definition of dot product. In other words $$cos\theta$$ equals the sum of product of the directional cosines of corresponding vectors. In this question we have
$$cos\theta = l(fmn) + m(gnl) + n(hlm) = lmn(f + g + h)$$
The next step is to prove this equal 1/2.
From the question we have
$$l + m + n = 0$$ $$l^2 + m^2 + n^2 = 1$$ Since there are three unknowns but only 2 equations, we can only express l and n in terms of m :
$$\implies l^2 + lm + m^2 = \frac{1}{2}$$
$$\implies l = \frac{-m + D}{2}$$ $$\implies n = \frac{-m - D}{2}$$ Where $$D = \sqrt{2 - 3m^2}$$. It does not matter which root we take for l the other root will be for n.
Also we have other conditions:
$$fmn + gnl + hlm = 0 ... (1)$$ $$(fmn)^2 + (gnl)^2 + (hlm)^2 = 1 ... (2)$$ $$\frac{1}{f} + \frac{1}{g} + \frac{1}{h} = 0 \implies fg + gh + fh = 0... (3)$$
Put l and n into (1) we have $$-fm(m + D) - g(1 - 2m^2) + hm(-m + D) = 0...(4)$$
Put l and n into (2) we have $$f^2m^2(2 - 2m^2 + 2mD) + g^2(1 - 2m^2)^2 + h^2m^2(2 - 2m^2 -2mD) = 4...(5)$$
Eliminate f from (3) and (4) we have $$f^2m(m + D) + fg(2mD - 2m^2 + 1) + g^2(1 - 2m^2) = 0$$ $$\implies f = \frac{2m^2 - 2mD - 1\pm\sqrt{(2mD -2m^2 + 1)^2 - 4(m + D)m(1 - 2m^2)}}{2m(m + D)}g$$ $$\implies f = \frac{2m^2 - 2mD - 1 \pm 1}{2m(m + D)}g$$ We take plus 1 for simplicity since the other root may give a result making $$cos\theta$$ greater than 1 or less than -1. $$f = \frac{m - D}{m + D}g$$
Eliminate h from (4) and (5) gives $$f^2m^2(2 - 2m^2 + 2mD) + g^2(1 - 2m^2)^2 + fgm(m + D)(1 - 2m^2) = 2$$ Put f into this equation we get $$m^2(m - D)^2g^2 + g^2(1 - 2m^2)^2 + (m - D)mg^2(1 - 2m^2) = 2$$ $$\implies g^2(1 - Dm - m^2) = 2$$ $$\implies g = \sqrt{\frac{2}{1 - Dm - m^2}}$$ $$\implies f = \frac{m - D}{m + D}\sqrt{\frac{2}{1 - Dm - m^2}}$$ $$\implies h = \frac{D - m}{2m}\sqrt{\frac{2}{1 - Dm - m^2}}$$
Hence put l, m, n, f, g, h to the cosine expression we get $$cos\theta = lmn(f + g +h) = \frac{-(m - D)}{2}m\frac{-(m + D)}{2}\sqrt{\frac{2}{1 - Dm - m^2}}(\frac{m - D}{m + D} + 1 + \frac{D - m}{2m})$$ $$=\frac{m - D}{4}\sqrt{\frac{2}{1 - Dm - m^2}}$$ $$=\frac{1}{4}\sqrt{\frac{2(m^2 + 2 - 3m^2 - 2Dm)}{1 - Dm - m^2}} = \frac{1}{2}$$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 94, "wp-katex-eq": 0, "align": 3, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.976889431476593, "perplexity": 178.787149560844}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703529128.47/warc/CC-MAIN-20210122051338-20210122081338-00560.warc.gz"} |
https://puzzling.stackexchange.com/questions/86372/hikers-cabin-mystery-pt-x | Hiker's Cabin Mystery | Pt. X
Before we get into it, I'd like to take a moment to congratulate everyone on us reaching part ten, but especially you because you've been putting up with this nonsense and travelling all over the world to search for this person.
But you still obediently head over to the
Zytglogge Tower
because of his note. You notice that the clock tower looks... rustically beautiful. Unsure of what to do, you walk underneath the tower.
Suddenly, four walls close around the tower and you are plunged into pure darkness. You hear a zap and find yourself whizzing through space. Your feet land hard on solid ground and, immediately, you see lights turn on. You are in a corridor and have no choice but to start walking forwards. Eventually, you reach a crossroads. There are two options of where you can go. In between the two passageways, there are three symbols carved: ᛖ ᚨ ᛈ
The passageway on the left has a picture of a domed building over it, rather like a mosque. The passageway on the right has a picture of waves (e.g. water) inside a trapezoidal glass over it.
Which passageway should you take and why?
Hint 1
https://lingojam.com/RunicTranslator
Hint 2
http://peoplebyinitials.com/
Hint 3
You suddenly notice something else scratched on the wall: ᚨ ᛚ
Hint 4
WOW! Now we have some magic and teleportation coming into play! How much more of this will we have to endure? And where's the hiker? And what's going on with his mystery? Solve Part X quickly, and get ready for a part of these questions to be GRANDLY REVEALED!
• The runes on the wall say rot13(rfpncr). – Cloudy7 Jul 20 '19 at 22:43
Based on
The first hint, we translate the runes to English, yielding EAP.
Then,
The second hint tells us to call them initials — and EAP stands for Edgar Allan Poe. One of Poe’s poems is this one, entitled Annabel Lee (clued by the runic hint A L), which is a poem about a kingdom by the sea. In that poem, Annabel Lee lived by the Sea (ie. the glass of water) and when she died she was buried in a sepulchre (the domed building is representative of the Church of the Holy Sepulchre, hint 4). Therefore life is in the direction of the Sea (glass of water) and death is in the direction of the Sepulchre (domed building). Therefore we should go right towards life.
• YEA! WE DID IT! That's absolutely correct! + 115, and get ready for part XI (I'll post it sometime today hopefully). Meanwhile, check out How do you feel? which now has a bounty which totals to 75 reputation (with the accept and upvote). Congrats on another GREAT answer! :D – Voldemort's Wrath Jul 25 '19 at 16:05
• (I'll award the bounty in 3 hours which is the time it says I have to wait...) – Voldemort's Wrath Jul 25 '19 at 16:06
• Thank you, @INTERESTING!!! – El-Guest Jul 25 '19 at 16:08
• Wow! That's an amazing answer! – Cloudy7 Jul 25 '19 at 16:18
• No problem! Nice streak you have going on there! :) – Voldemort's Wrath Jul 25 '19 at 16:33
Okay, I have a guess...
One should take the passageway to the left.
Reasoning:
The three symbols on the wall are constituents of the Viking alphabet. They spell out "eoh-aesc-peorth", which I take to mean "escape". As Viking legends tell, "When Ragnarök came, the sun would be swallowed by the wolf Skoll and the moon by his brother Hati, plunging the world into darkness while, at the same time, the great wolf Fenrir would ravage through all the planes of Yggdrasil. The god Heimdall would sound his great horn, calling the gods to battle, and Odin would call up all the heroes from Valhalla’s halls to join with the gods in defending creation. The gods fight valiantly but, in the end, they fall in battle as the entire universe is consumed in flame and sinks into the primordial waters." (https://www.ancient.eu/Vikings/) This seems to suggest that the water represents the primordial waters in this case, and you should probably take the passageway to the left, which represents civilization.
Obviously this is a very rudimentary answer, and feel free to reject or elaborate.
• This isn’t correct, but was a very enjoyable answer to read! :) – Voldemort's Wrath Jul 20 '19 at 23:21
• Thanks for your feedback! I'll continue trying. – Cloudy7 Jul 20 '19 at 23:27
• Glad to hear it! By the way, the fact that it sort of looks like "escape" was a complete coincidence! – Voldemort's Wrath Jul 20 '19 at 23:28
A random guess:
The letters are part of the Elder Futhark Rune alphabet, in which each letter means the following:
• ᛖ means horse
• ᚨ means god
• ᛈ refers to a "p" sound, but when it is rotated 90 degrees it looks like a bridge.
In the game The Legend of Zelda: Breath of the Wild, there is a location called "Horse God Bridge" in which you can interact with a Horse God.
Here is the map undergirding that quest:
Notice that Going right from Horse God Bridge takes us to Malamya Spring, hence the reference to "waves" in the riddle. Going left from Horse God Bridge takes us to Nette Plateau, where you will find dome-shaped boulders.
The solution is to go right, as it will give you the opportunity to unlock a Great Fairy in the game, which will allow you to bring any horse back to life (which you may need for your escape). Also, by the time you get to this part of the quest, you will have already done what needs to be completed in the Nette Plateau.
• Not even close! :) – Voldemort's Wrath Jul 24 '19 at 0:31
• You gotta admit, though: this answer is actually well thought-out. I'm giving it a +1. – Cloudy7 Jul 24 '19 at 1:00
• @Cloudy7 - True, and so was your's. I'm just not ready to hand out an upvote yet! You'd better get to finding another answer (new hint posted!) as it looks like you may have some tough competition! :D – Voldemort's Wrath Jul 24 '19 at 2:58
• And, Parseltongue, I'm sure you meant 90 degrees instead of 180. :) – Voldemort's Wrath Jul 24 '19 at 2:59
• I will never not upvote a meticulous Zelda-related answer. – generalcrispy Jul 24 '19 at 20:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25581008195877075, "perplexity": 2886.8655429522883}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703529080.43/warc/CC-MAIN-20210122020254-20210122050254-00669.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/algebra-a-combined-approach-4th-edition/chapter-12-section-12-2-inverse-functions-exercise-set-page-852/32 | # Chapter 12 - Section 12.2 - Inverse Functions - Exercise Set - Page 852: 32
$f^{-1}$(x)=$\frac{2x+3}{4}$
#### Work Step by Step
f(x)=$\frac{4x-3}{2}$ y=$\frac{4x-3}{2}$ x=$\frac{4y-3}{2}$ 2x=4y-3 2x+3=4y y=$\frac{2x+3}{4}$ $f^{-1}$(x)=$\frac{2x+3}{4}$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5050421953201294, "perplexity": 5739.190936207465}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578532882.36/warc/CC-MAIN-20190421195929-20190421221929-00194.warc.gz"} |
http://math.stackexchange.com/questions/184528/is-the-set-of-all-definable-subsets-of-the-natural-numbers-recursively-enumerabl/184580 | # Is the set of all definable subsets of the natural numbers recursively enumerable?
I asked myself similar questions before, for example "Are the definable real numbers countable"? It seemed to me that the set of all explicitly and unambiguously definable objects is "countable", because we could write down the text defining a specific object in the English language. (Or use the English language to define a formal language appropriate to write down the definition.) But English isn't unambiguous, and the meaning of "countable" depends on the used set theory.
Right now I'm thinking about second order logic. Assuming that the natural numbers exist and are well defined seems unproblematic to me. However, the question which subsets of the natural numbers (should we assume to) exist has no good answer. If we say that "all" subsets exist, we run into all sorts of set theoretic questions. If we resort to axiomatic set theory for these questions, we end up with the fact that the natural numbers can't be defined up to isomorphism. The alternative seems to be to assume that only the definable subsets of the natural numbers exist. But my guess is that this won't work out either, i.e. that the "set of all definable subsets of the natural numbers" turns out to be a very strange beast. But if it is a strange beast, I guess it won't be recursively enumerable.
Question Assuming the Church-Turing thesis (or a suitable analogue for definability, or some other sufficiently solid foundation), what can be said about the "set of all definable subsets of the natural numbers"? Is it well defined and recursively enumerable?
Edit It has been pointed out that my use of "recursively enumerable" is ambiguous without further clarifications, especially that I have to specify how a definable subset of the natural numbers is expected to be encoded as a natural number. Given a natural number, take its binary representation and interpret it as a document in the "OpenDocument" format (ODF). Assume that we can efficiently decide whether the document is valid ODF and whether its content is written sufficiently clear and tries to define a subset of the natural numbers. Let's call this a well formed definition. Assume further that each definable subset has at least one well formed definition which can be recognized to succeed in defining a subset of the natural numbers. Now the question is whether there exists a recursively enumerable subset $S$ of the natural numbers such that each number in $S$ corresponds to a well formed definition which succeeds, and that for each definable subset the set $S$ contains a corresponding definition.
-
Let me remember that the "Turing machine" model is a finitistic one; it only accepts finite inputs and it only produces finite outputs. How do you want to codify in a finitistic way a subset of natural numbers? The more natural way is to use a finitistic formula to describe the set, but then it is obvious which is the answer to your question (YES). If you do not want to use the natural way then you must add to the question what is the finitistic codification (for subsets of natural numbers) you want to use. – boumol Aug 20 '12 at 9:57
@boumol It's true that the "Turing machine" only accepts finite inputs, but what do you mean by "it only produces finite outputs"? One natural way to define a subset of the natural numbers by a Turing machine would be to take the set of input numbers for which the machine stops. It should be clear from the question that any unambiguous way to define a subset of the natural numbers is acceptable. Especially if $S_1$ and $S_2$ are definable, then $S_1 - S_2$ is also definable. However, this doesn't mean that it is also definable as the set of input numbers for which some Turing machine stops. – Thomas Klimpel Aug 20 '12 at 12:28
@boumol Assuming you're still sure the methods with a finitistic formula works (I'm not sure what this means exactly), can you expand your comment into an answer? – Thomas Klimpel Aug 20 '12 at 12:32
!Thomas Klimpel: you should consult the answers to this question from MathOverflow, which may be the question you had in mind: mathoverflow.net/questions/44102/… – Carl Mummert Aug 20 '12 at 13:58
I do not understand the downvote. – Arkamis Aug 20 '12 at 15:33
The question is somewhat ambiguous about exactly how the sets would be enumerated. The natural way to read it in computability theory is the following, which is the usual sense in which a sequence of sets can be r.e.:
Is there a computable double enumeration $\{ n_{i,j} : i,j \in \omega\}$ such that for each definable set $S \subseteq \omega$ there is an $i_0$ such that $S = \{ n_{i_0,j} : j \in \omega\}$.
The answer to that is certainly "no", because if it was true then every definable set would be r.e., which is not the case.
-
For those with some interest, I want to point out I have taken the weakest possible definition of "enumerable sequence of sets", in the sense that there may not be any effective way to tell which $i_0$ corresponds a particular $S$. Thus the enumeration has infinitely many chances to capture any particular $S$. – Carl Mummert Aug 20 '12 at 14:02
A short answer would be that the concept of "recursively enumerable" is only defined for subsets of some countable universe, where that universe has a ("reasonable") encoding as finite strings of symbols that can be input or output by a Turing machine. In your case the set of "subsets of $\mathbb N$ that are definable" (whatever exactly that means) doesn't satisfy that condition, becuase the natural universe to use would be $\mathcal P(\mathbb N)$, which is not countable.
So it doesn't even make sense to ask whether your set is r.e.
One could attempt to broaden the definitions by imagining a non-deterministic Turing machine that writes an infinite sequence of 0s and 1s to a write-only output tape, where that sequence can be interpreted as a subset of $\mathbb N$. One could then declare that some $A\subseteq 2^{\mathbb N}$ is "recursively enumerable"-ish iff it is the set of possible outputs of some non-deterministic machine.
However, though this can be argued to generalize the ordinary concept of recursive enumerability, it wouldn't be the ordinary concept of recursive enumerability.
-
As long as every "definable" number may be defined using a finite string in some finite alphabet you may sort those strings by length and enumerate numbers using this sort.
-
The problem with that is that if "definable" means that there is some formula that is true for this number but false for all others, the relation between defining strings and actual numbers is not itself definable inside the system. There are models of ZFC in which every real number is definable in this way (but the relation between defining formulas and defined numbers is not a set), and we cannot be sure we're not living in such a world. – Henning Makholm Aug 22 '12 at 11:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9109853506088257, "perplexity": 259.169825086842}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042987628.47/warc/CC-MAIN-20150728002307-00250-ip-10-236-191-2.ec2.internal.warc.gz"} |
http://blog.geomblog.org/2011/07/axioms-of-clustering.html | ## Monday, July 18, 2011
### Axioms of Clustering
(this is part of an occasional series of essays on clustering: for all posts in this topic, click here
I shall not today attempt further to define the kinds of material I understand to be embraced within that shorthand description; and perhaps I could never succeed in intelligibly doing so. But I know it when I see it..."
-- Justice Potter Stewart in Jacobellis v. Ohio.
What makes one clustering better than another? To answer that question we have previously assumed that a well motivated objective function was given to us. Then the situation is easy, we compute the value of the objective and decide accordingly. In practice, however, clustering is often an intermediate step in a longer chain of computations, and there is not specific motivation for one objective function over another. Debating the pros and cons of the multitude of possible objective functions can easily take hours. Instead, we can further the I know it when I see it'' intuition by writing down the properties that any good clustering objective should satisfy and see if this axiomatic approach guides us towards the right solution.
This approach was undertaken by Kleinberg in his work on clustering axioms. A clustering function is one that takes a set of points (and their pairwise distances) and returns a partition of the data. The function should abide by the simple axioms:
• Scale-Invariance: If all distances are scaled by a constant factor, the clustering should not change. Put another way, measuring the distance in miles or kilometers (or nanometers) should not change the final clustering partition.
• Richness: Depending on the pairwise distances, any partition should be possible. For example, the clustering should not always put two specific points $x$ and $y$ together, regardless of the distance metric.
• Consistency: If the pairwise distance between points in a cluster decreases, while the distances between a pair of points in different clusters increases, the clustering should not change. Indeed, such a transformation makes clusters tighter' and better separated from each other, so why should the clustering change?
Each of the axioms seems reasonable, and it is surprising that there is no clustering function that is consistent with all three axioms ! The trouble lies with the last axiom: by changing the distances we require that a clustering stay the same, but an even better clustering may emerge. For example, consider points lying in several `obvious'' clusters, and proceed to move one of these clusters out to infinity. As we move the points further and further out, the resulting dataset appears to be two-clusterable (see the image below).
This leads to a slightly different tack at this problem. Instead of thinking about a specific clustering, or a specific partition of the data, instead we try to define an objective function, so that the optimum clustering under that objective behaves in a reasonable manner. This is the approach adapted by Ackerman and Ben-David. Let $m$ be a function measuring the quality of the clustering. As before, Scale-Invariance requires the measure $m$ to be independent of the units on the distances and Richness requires that every clustering can be the optimum (under $m$) clustering.
The Consistency axiom is the one undergoing a subtle change. Instead of requiring that the clustering stay the same if such a perturbation to the distances occurs, we only require that the score, or measure of the clustering {\em improve} under such a transformation. This breaks the counterexample above -- while the score of a 1-cluster decreases as we move the distances, the score of a 2-clustering decreases even more and surpasses the score of the 1-clustering. Indeed, the authors demonstrate a set of different clustering metrics that are consistent under this set of axioms.
-- Sergei Vassilvitskii
1. Alex Lopez-Ortiz7/18/2011 01:09:00 PM
All three axioms, while they may seem natural at first, are ultimately questionable.
For example, almost any real life clustering problem has an implicit notion of unit distance built into it.
Say, if we are tracking human diseases and you have a four point quadrangular configuration a few city blocks apart, this clearly forms a cluster. Now scale up the square so that the corners lie one each in North America, South America, Europe and Africa. Clearly, the new configuration does not form a cluster. Out goes Scale invariance.
Richness is perhaps the most unnatural of the axioms. If you are given two points, and yourclustering algorithm is scale and rotation invariant it is not possible to achieve all partitions of the input set. There is nothing wrong with this, yet it violates the richness axiom.
2. In my opinion, there is a simple reason why the richness axiom should be modified. Namely, I see no intuitive reason why both the partition that lumps everything into a single cluster and the partition that puts everything into a singleton cluster of its own should be realized. Both of these are basically "failure modes" where the verdict is that there is no natural clustering. If we simply pick one of these two clusterings to represent our failure mode, and forbid the other one, then the inconsistency among the axioms disappears. Conversely, if you insist on richness as standardly defined, it's not really surprising that if you start with everything in a single cluster and then dilate everything, then there's no principled way to decide when you should shatter into singletons—and yet the axioms say you must.
3. I'm not an expert here but you may want to consider level set clustering http://bit.ly/oJ8C2x
Its satisfying two of the axioms (consistency and richness)..scale would need change of parameters.
This is also another simpler algorithm it satisfies the two conditions:
http://bit.ly/nPl72W | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8472424745559692, "perplexity": 588.9116072145364}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585178.60/warc/CC-MAIN-20211017144318-20211017174318-00334.warc.gz"} |
http://mathhelpforum.com/geometry/108977-equation-circle-right-angled-triangle.html | # Thread: Equation of Circle from right-angled triangle
1. ## Equation of Circle from right-angled triangle
The point D, E and F have coordinates (-2,0), (0,-1) and (2,3) respectively.
i) gradient of DE = -0.5
ii) 0.5x+y-4=0 line F parallel to DE
iii) by calculating the gradient of EF, show that DEF is a right-angled triangle.
iv) calculate the length of DF.
v) Use the results of parts(iii) and (iv to show that the circle which passes through D,E and F has equation $x^2+y^2-3y-4=0.$
i've done i),ii),iii),iv)
i) gradient of DE = -0.5
ii) 0.5x+y-4=0 line F parallel to DE
iii) y= 2x-1 = grad of normal
which bisect DE at some point therefore it's a right angled triangle.
iv) $sqroot(4^2+3^2)$
thank you for helping!
2. Do you have to use the earlier parts? If so, are you allowed to use the result (from geometry) relating right angles and triangles?
If so, then find the midpoint of the hypotenuse, as this will be the center of the circle. You've found the length of the hypotenuse; now divide by two to find the radius value.
Once you have the center and the radius, you can plug into the center-radius form of the circle equation, multiply everything out, and rearrange to get the required form of the equation.
3. Originally Posted by stapel
If so, then find the midpoint of the hypotenuse, as this will be the center of the circle. You've found the length of the hypotenuse; now divide by two to find the radius value.
ok i understand this part which leave me with 2.5 as the radius.
Once you have the center and the radius, you can plug into the center-radius form of the circle equation, multiply everything out, and rearrange to get the required form of the equation.
but how do i find out the centre points of the circle? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9139682054519653, "perplexity": 598.1649372489012}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171281.53/warc/CC-MAIN-20170219104611-00579-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://codegolf.meta.stackexchange.com/questions/2419/default-for-code-golf-program-function-or-snippet/6912#6912 | # Default for Code Golf: Program, Function or Snippet?
One of the things many (new?) users forget to specify in challenges is whether the answers should provide a full program or a function (or even just a snippet). For most such things, we have defaults in the tag wiki (like scoring by bytes), but not for this.
The conclusion in chat was that such a default would be useful, so let's vote on what it should be.
See here for the follow-up poll on input/output methods.
• I have not added an answer which excludes full programs as the default, because there might be languages where that isn't even possible. Oct 29, 2014 at 20:23
• Supposing functions are allowed, should functions that accept an argument and print the result of a calculation to stdout, or functions that read from argv and return a value be allowed? Oct 29, 2014 at 20:25
• @feersum I think we should worry about I/O defaults after coming to a consensus on this, because the cross product of all possible options doesn't seem manageable. Oct 29, 2014 at 20:28
• I think it would be nice if all the code could be run by people who don't know the language. That is it could be a complete piece of source code.
– user9206
Jan 21, 2015 at 14:54
• What exactly is the difference between answering with a snippet and "defining a dialect" (a la the 'sed with implied input' at codegolf.meta.stackexchange.com/questions/5476/… ), particularly in cases where the standard interpreter has a built-in mode such as a REPL for running so-called "snippets"? Oct 22, 2019 at 21:04
# The default should be "programs or functions"
This includes function-like constructs, including J's verbs and GolfScript's and CJam's blocks.
• Would functions be allowed to print rather than return the output?
– xnor
Oct 29, 2014 at 20:25
• @xnor I think we should worry about I/O defaults after coming to a consensus on this, because the cross product of all possible options doesn't seem manageable. Oct 29, 2014 at 20:27
• This excludes some languages, such as J. Oct 30, 2014 at 8:08
• @PeterTaylor Doesn't J have functions? Oct 30, 2014 at 8:13
• J is weird. It's the reason that I always include "named verb" in my list of acceptable submission styles. (And "named block" for GolfScript, although in GS it's nearly always shorter to write a program). Oct 30, 2014 at 8:24
• This still leaves one question open: Does the functions/blocks/verbs have to be named? Oct 30, 2014 at 18:02
• Oct 30, 2014 at 18:04
• Function bodies? Or complete function declarations with function main()-like boilerplate?
– user16402
Nov 1, 2014 at 20:32
• @professorfish Complete functions. Function bodies would be "snippets" (see this answer). Nov 1, 2014 at 20:34
• This seems to be the correct default, because the general rule is that whatever is left unspecified gets interpreted in the way most advantageous to the answerer. On the other hand, those who intend "program or function" in their questions often absentmindedly write "your program" which then implies that a program is required, when they should write "your code." Nov 10, 2014 at 13:45
• me downvote, there are programs without functions and the definition of function can be diffent. the startup is part of the language, if you keep that part out, you can skip every part. May 5, 2017 at 8:29
# Restricting to just programs requires explicitly specifying "full program" rather than just "program"
If the question requests a program, this can still be answered with a function. This allows for the fact that many people state "program" without thinking, not intending to exclude functions.
For questions that wish to exclude functions, this should be stated explicitly, for example: "full program", "complete program" or "program, not function".
• This is an especially good idea for challenges by newer users who aren't familiar with our customs/defaults. Sep 8, 2015 at 16:57
• Is it even possible to write and then execute an incomplete program⁇ I mean, of course people can submit buggy code, code that doesn’t compile, but I don’t think this is meant by saying “full” program. Frankly, to me this answer sounds like encouraging a pleonasm. Nov 10, 2022 at 10:38
# A set of different "defaults"
I think many questions require one of a few different ways, some require...
1. ... a full program that accepts input and prints output throu standard I/O
2. ... files as input/output (e.g. Images)
3. ... only functions (or similar constructs)
4. ... snippets, where input/output is stored in a variable (or similar construct)
This is of course just a rough draft, but you get the idea. My suggestion is making a definition for each of these in order that everyone writing challenges only has to declare which of those apply, instead of writing a whole novel on what is allowed and what is not.
• We have a separate question for which I/O methods should be allowed. Sep 8, 2015 at 10:30
• Having the defaults we already do (separately) means that the question already doesn't need to spend time on defining them. Only those things which are non-standard need be mentioned. Sep 8, 2015 at 17:30
# We don't need a default
Every question has to specify this.
• This has my downvote. Oct 29, 2014 at 20:24
• +1 Questions which don't have it should be closed as "Unclear what you're asking". Oct 29, 2014 at 21:34
• @PeterTaylor plenty of good existing questions would have been under that ruling, I'm afraid. Nov 3, 2014 at 7:03
• @JanDvorak, sorry, I'm using old terminology. I should say "put on hold" and clarified. Nov 3, 2014 at 9:31
# The default should be "programs only"
• This has my downvote. Oct 29, 2014 at 20:24
• mine too. significant disadvantage for languages that have a large overhead (huge trivial program) Jul 7, 2016 at 7:41
# The default should be "programs, functions or snippets"
By "snippets" I mean just a piece of code which expects the input to be stored in a hardcoded variable and stores the output in another hardcoded variable, or prints it.
• The question is which one of these Apr 19, 2018 at 13:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30477866530418396, "perplexity": 2126.1382835647537}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949694.55/warc/CC-MAIN-20230401001704-20230401031704-00160.warc.gz"} |
http://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2011-017.html | # Search for CP violation in $D^{+} \to K^{-}K^{+}\pi^{+}$ decays
[to restricted-access page]
## Abstract
A model-independent search for direct CP violation in the Cabibbo suppressed decay $D^+ \to K^- K^+\pi^+$ in a sample of approximately 370,000 decays is carried out. The data were collected by the LHCb experiment in 2010 and correspond to an integrated luminosity of 35 pb$^{-1}$. The normalized Dalitz plot distributions for $D^+$ and $D^-$ are compared using four different binning schemes that are sensitive to different manifestations of CP violation. No evidence for CP asymmetry is found.
## Figures and captions
Fitted mass spectra of (a) $K ^- \pi ^+ \pi ^+$ and (b) $K ^- K ^+ \pi ^+$ candidates from samples 1 and 3, $D ^+$ and $D ^-$ combined. The signal mass windows and sidebands defined in the text are labelled. figure1a.pdf [65 KiB] HiDef png [195 KiB] Thumbnail [52 KiB] *.C file figure1b.pdf [66 KiB] HiDef png [258 KiB] Thumbnail [71 KiB] *.C file Dalitz plot of the $D ^+ \rightarrow K ^- K ^+ \pi ^+$ decay for selected candidates in the signal window. The vertical $\overline{ K }{} ^{*}(892)^{0}$ and horizontal $\phi(1020)$ contributions are clearly visible in the data. figure2.pdf [43 KiB] HiDef png [839 KiB] Thumbnail [141 KiB] *.C file $\mathcal{S}_{CP}$ across the Dalitz plot in a Monte Carlo pseudo-experiment with a large number of events with (a) no CPV and (b) a 4$^{\circ}$ CPV in the $\phi\pi$ phase. Note the difference in colour scale between (a) and (b). figure3a.pdf [18 KiB] HiDef png [193 KiB] Thumbnail [74 KiB] *.C file figure3b.pdf [18 KiB] HiDef png [188 KiB] Thumbnail [72 KiB] *.C file Layout of the (a) "Adaptive I" and (b) "Adaptive II" binnings on the Dalitz plot of data. figure4a.pdf [45 KiB] HiDef png [843 KiB] Thumbnail [140 KiB] *.C file figure4b.pdf [47 KiB] HiDef png [862 KiB] Thumbnail [141 KiB] *.C file (a) Distribution of $\mathcal{S}_{CP}$ values from $D ^+ \rightarrow K ^- \pi ^+ \pi ^+$ from a test with 900 uniform bins. The mean of the fitted Gaussian distribution is $0.015\pm0.034$ and the width is $0.996\pm0.023$. (b) Distribution of $\mathcal{S}_{CP}$ values from $D ^+_ s \rightarrow K ^- K ^+ \pi ^+$ with 129 bins. The fitted mean is $-0.011\pm0.084$ and the width is $0.958\pm0.060$. figure5a.pdf [15 KiB] HiDef png [111 KiB] Thumbnail [54 KiB] *.C file figure5b.pdf [15 KiB] HiDef png [108 KiB] Thumbnail [53 KiB] *.C file Dalitz plots of (a) $D ^+ \rightarrow K ^- \pi ^+ \pi ^+$, showing the 25-bin adaptive scheme with the $\mathcal{S}_{CP}$ values, and (b) $D ^+_ s \rightarrow K ^- K ^+ \pi ^+$, showing the three regions referred to in the text. The higher and lower $K ^- \pi ^+$ invariant mass combinations are plotted in (a) as there are identical pions in the final state. figure6a.pdf [40 KiB] HiDef png [692 KiB] Thumbnail [142 KiB] *.C file figure6b.pdf [44 KiB] HiDef png [891 KiB] Thumbnail [153 KiB] *.C file Distribution of ${\mathcal S}^i_{\it CP}$ in the Dalitz plot for (a) "Adaptive I", (b) "Adaptive II", (c) "Uniform I" and (d) "Uniform II". In (c) and (d) bins at the edges are not shown if the number of entries is not above a threshold of 50 (see Sect. III). figure7a.pdf [45 KiB] HiDef png [160 KiB] Thumbnail [64 KiB] *.C file figure7b.pdf [48 KiB] HiDef png [222 KiB] Thumbnail [78 KiB] *.C file figure7c.pdf [18 KiB] HiDef png [181 KiB] Thumbnail [74 KiB] *.C file figure7d.pdf [20 KiB] HiDef png [227 KiB] Thumbnail [107 KiB] *.C file Distribution of ${\mathcal S}^i_{\it CP}$ fitted to Gaussian functions, for (a) "Adaptive I", (b) "Adaptive II", (c) "Uniform I" and (d) "Uniform II". The fit results are given in Table IX. figure8a.pdf [14 KiB] HiDef png [108 KiB] Thumbnail [52 KiB] *.C file figure8b.pdf [14 KiB] HiDef png [106 KiB] Thumbnail [51 KiB] *.C file figure8c.pdf [15 KiB] HiDef png [100 KiB] Thumbnail [50 KiB] *.C file figure8d.pdf [15 KiB] HiDef png [104 KiB] Thumbnail [50 KiB] *.C file Animated gif made out of all figures. PAPER-2011-017.gif Thumbnail
## Tables and captions
Yield ($S$) and purity for samples 1 and 3 after the final selection. The purity is estimated in the 2$\sigma$ mass window. Table_1.pdf [52 KiB] HiDef png [55 KiB] Thumbnail [9 KiB] tex code Number of candidates $(S+B)$ in the signal windows shown in Fig. 1 after the final selection, for use in the subsequent analysis. Table_2.pdf [49 KiB] HiDef png [56 KiB] Thumbnail [9 KiB] tex code The CLEO-c amplitude model "B" [7] used in the simulation studies. The uncertainties are statistical, experimental systematic and model systematic respectively. Table_3.pdf [55 KiB] HiDef png [118 KiB] Thumbnail [20 KiB] tex code Results from sets of 100 pseudo-experiments with different $C\!P$ asymmetries and Adaptive I and II binnings. $p(3\sigma)$ is the probability of a 3$\sigma$ observation of CPV. $\langle S \rangle$ is the mean significance with which CPV is observed. Table_4.pdf [39 KiB] HiDef png [109 KiB] Thumbnail [16 KiB] tex code Results from sets of 100 pseudo-experiments with $4^{\circ}$ CPV in the $\phi(1020)$ phase and different Dalitz plot models. $p(3\sigma)$ is the probability of a 3$\sigma$ observation of CPV. $\langle S \rangle$ is the mean significance with which CPV is observed. The sample size is comparable to that seen in data. Table_5.pdf [46 KiB] HiDef png [75 KiB] Thumbnail [12 KiB] tex code Results ($p$-values, in %) from tests with the $D ^+ \rightarrow K ^- \pi ^+ \pi ^+$ control channel using the uniform and adaptive binning schemes. The values correspond to tests performed on the whole dataset in the mass windows defined in Sect. II. Table_6.pdf [15 KiB] HiDef png [33 KiB] Thumbnail [6 KiB] tex code Results ($p$-values, in %) from tests with the $D ^+_ s \rightarrow K ^- K ^+ \pi ^+$ control channel using the uniform binning scheme. The values correspond to tests performed separately on Zones A-C, with samples 1-3 and both magnet polarities combined. Table_7.pdf [14 KiB] HiDef png [71 KiB] Thumbnail [11 KiB] tex code Results ($p$-values, in %) from tests with the $D ^+ \rightarrow K ^- \pi ^+ \pi ^+$ and $D ^+_ s \rightarrow K ^- K ^+ \pi ^+$ samples divided according to the impact parameter with respect to the primary vertex. The tests are performed using the adaptive binning scheme with 25 bins. Table_8.pdf [48 KiB] HiDef png [44 KiB] Thumbnail [7 KiB] tex code Fitted means and widths, $\chi^2/{\rm ndf}$ and $p$-values for consistency with no CPV for the $D ^+ \rightarrow K ^- K ^+ \pi ^+$ decay mode with four different binnings. Table_9.pdf [39 KiB] HiDef png [64 KiB] Thumbnail [11 KiB] tex code
Created on 20 April 2019.Citation count from INSPIRE on 24 April 2019. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9738224148750305, "perplexity": 17721.865317729735}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578655155.88/warc/CC-MAIN-20190424174425-20190424200425-00537.warc.gz"} |
http://bupar.net/processmaps.html | ## Introduction
The function process_map can be used very easily to create a process map of an event log. Below, an example of a process map for the patients event log can be found.
library(bupaR)
patients %>%
process_map()
## Map profiles
### Frequency profile
By default, the process map is annotated with frequencies of activities and flows. The is what is called the frequency profile, and can be created explicitly using the frequency function. This function has a value argument, which can be used to adjust the frequencies shown, for instance using relative frequencies instead of the default absolute ones.
patients %>%
process_map(type = frequency("relative"))
### Performance profile
Instead of a frequency profile, one can also use a performance profile, focussing on processing time of activities. The performance profile has two arguments: the FUN argument to specific the function to apply on the processing time (e.g. min, max, mean, median, etc.), and the units argument to specificy the time unit to be used.
patients %>%
process_map(performance(median, "days"))
## Simplifying process maps
When event logs get larger, they will also become more unstructured, making the process maps illegible and expensive to computate. In such cases, it is useful to apply them on a simplified version of the event log, using one or more of the subsetting method provided by edeaR.
## Customizing Process Maps
The process_map function has a render argument, which, if set to FALSE, returns a raw dgr_graph from the DiagrammeR package, which can if needed be further customized, and subsequently rendered. For more information about DiagrammeR, please check their website
patients %>%
process_map(render = F) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18223385512828827, "perplexity": 2064.364382021651}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823220.45/warc/CC-MAIN-20171019031425-20171019051425-00110.warc.gz"} |
https://encyclopediaofmath.org/wiki/Fechner,_Gustav_Theodor | # Fechner, Gustav Theodor
This article Gustav Theodor Fechner was adapted from an original article by Michael Heidelberger, which appeared in StatProb: The Encyclopedia Sponsored by Statistics and Probability Societies. The original article ([http://statprob.com/encyclopedia/GustavTheodorFECHNER.html StatProb Source], Local Files: pdf | tex) is copyrighted by the author(s), the article has been donated to Encyclopedia of Mathematics, and its further issues are under Creative Commons Attribution Share-Alike License'. All pages from StatProb are contained in the Category StatProb.
Gustav Theodor FECHNER
b. 19 April 1801 - d. 18 November 1887
Summary. Physicist, psychologist and philosopher, Fechner is noted for the introduction of quantitative methods into psychology. He also developed a theory of collectives' which is built on the frequency interpretation of probability.
Gustav Theodor Fechner was born in Gross Särchen near Muskau, Lusatia (Germany), into the family of a protestant minister. He studied medicine, but became disenchanted with the subject and never wanted to practice it. Instead, he devoted himself to experiments in physics in the fashion of the physique expérimentale of the leading French physicists. His translations and revisions of French text books and treatises were the chief channel for the reception of French mathematical science into Germany at this time, and the reform of German physics that resulted from it. His experimental researches, especially in electricity theory, eventually earned him a chair in physics at the University of Leipzig (in Saxony, Germany) where he remained for the rest of his life.
Fechner's orientation towards the most advanced physics of his day was supplemented, however, by a strong commitment to idealist and romantic Naturphilosophie which was primarily directed against Cartesian dualism of mind and body and eighteenth-century French materialism. Like other followers of Naturphilosophie, he argued, that nature is animated and that there is an original unity or identity' of nature and mind which allows us to infer nature's laws from the laws of the mind and vice versa.
In 1839, Fechner had a nervous breakdown as the result of a depressive psychosis. He developed an aversion to food and also to light and experienced temporary blindness and complete prostration. Although he kept the title of a physics professor, he eventually lost his physics chair to Wilhelm Weber and was set on a pension by the university. After his recovery in 1846, he continued lecturing on diverse subjects, especially the mind-body problem, until 1875.
When his crisis was over, Fechner tried to come to terms with the two opposing tendencies of his thought, the strict mechanist mathematical physics on the one side and the romantic Naturphilosophie on the other. As a result of this, he developed a solution to the mind-body problem called psychophysical parallelism' or dual aspect theory' which became very popular among scientists in the 19th century. This solution is supposed to be compatible with science as well as with Naturphilosophie and it is central, both to Fechner's subsequent philosophical as well as scientific and mathematical work. According to this view, mind is not to be seen as a substance interacting with the body but as a special attribute of matter on which it is functionally dependent. In the same way as the appearance of an ordinary object, like the back and front of a coin, depends on the perspective of the viewer, so a person, as a body with a mental dimension, can be seen from the outside as well as from the inside. Mind and body are two different aspects of one and the same object. A person appears to outside viewers in another way than to herself or himself. As a consequence, it would not make any sense to say that the mind acts on the body or vice versa as it would be senseless to say that the back of the coin acts on its front when the coin is bent. Rather, if there is a change of a person it can be viewed in a mental as well as in a physical respect. Similarly, the bending of a coin results in a change of the coin's front and of its back at the same time. In thus rejecting causality as an appropriate category for the mind-body relation, Fechner thought he had shown psychophysical parallelism to be compatible with the principle of the conservation of energy. On the basis of his theory, Fechner founded the science of psychophysics, which became the starting point for experimental quantitative psychology.
Before it can be shown what all this has to do with statistics, we have to turn to another philosophical development. One of the most influential and powerful philosophical systems of the first half of the 19th century was that of G. W. F. Hegel. He claimed to have developed a logic which could explain history and nature as the necessary conceptual development of the idea on the way to self-knowledge. One of the most outspoken critics of this system was the Leipzig philosopher Christian Hermann Weisse, Fechner's closest friend. Weisse criticised Hegelian "panlogism" as not giving enough justice to the contingent and individual in nature and history. He argued that concrete reality is not the product of a logically necessary development of ideas as Hegel wanted it; there is something in it that transcends all necessity.
In two addresses of 1849, Fechner tried to show that taking Weisse's idea of indetermination seriously does not preclude the use of mathematics in science. He argued that mathematical descriptions only provide a general frame for natural phenomena not implying any necessity for the individual case, thus being compatible with an indeterminate behaviour on a finer level. He also claimed that in order to admit indeterminate events in nature one does not have to give up the causal law. This law only says that the same effect will recur if the same set of conditions obtains, but it does not preclude the emergence of new conditions in the course of time. This discussion might very well be the first expression of an indeterministic world-view.
The first major application of statistical methods by Fechner, and the first work, where his ideas on psychophysical parallelism and individual indeterminacy come together, are his "Elements of Psychophysics of 1860. There, Fechner defined psychophysics as the "exact science of the functional or dependency relations between body and mind, or more general: between the bodily and the spiritual, physical and psychical, world." (Fechner 1860, I, 8) His goal was to measure sensations experimentally and thus to arrive at a quantitative science of psychophysics. The major result of his research was the so-called Weber-Fechner law which says that the intensity of sensation $E$ increases in proportion to the logarithm of a stimulus $R$, or: $E = k log R$.
Fechner conceived of psychophysics as a fundimentally statistical enterprise. The rationale behind his reasoning seems to have been the following: If human beings are free in their actions and if mind and body are correlated in the way as conceived by psychophysical parallelism, then there will be an individual variation in the response of a subject to a physical stimulus. This response will be physical and manifest itself in a certain bodily reaction, but it will also be mental and express itself in a certain judgement. The fluctuations are not to be taken as erroneous deviations from the true value but as the free mode of reaction of the individual to a stimulus.
Among the three methods Fechner developed for measuring sensation is the method of right and wrong cases". A subject had to lift a pair of weights, $P$ and $P + D$, and to judge which seemed to be the heavier of the two. After $n$ trials the ratio $r / n$ of right answers to all trials was calculated. Fechner took the measure of precision" $h$ that appears in older formulations of the Gaussian law as an expression of the differential sensitivity of the subject, such that $2r / n - 1 = {\theta}(h D / 2)$, where $\theta$ is the Gaussian law.
In 1878, Fechner published a paper where he developed the notion of the median. He later delved into experimental aesthetics and thought to determine the shapes and dimensions of aesthetically pleasing objects. He mainly used the sizes of paintings as his data base. In his "Vorschule der Aesthetik of 1876 he used the method of extreme ranks for subjective judgements.
Fechner's most important contribution to statistics is his posthumously published book on the measurement of collectives, his Kollektivmasslehre of 1897. Fechner defined a collective' or collective object' as a collection of an indefinite number of individual objects, subject to random variation, and embraced under a single specific or generic concept. The main examples he treated are to be found in anthropology, zoology, botany, meteorology, aesthetics. The object of the enquiry is, as Fechner wrote,
the establishment, by mathematical proof and empirical verification, of a generalisation of Gauss's law of accidental variations, whereby the law is enabled to transcend the limits of symmetrical probability and comparative smallness of the positive and negative deviations from the arithmetical mean, and new relations of uniformity are brought to light." (Fechner 1897, vi)
He developed a set of constants which allowed to characterise different distributions and developed a two-sided asymmetric Gaussian law where the two branches are treated as if originating from two different distributions.
Fechner took the random variation of the collectives quite literally. He spoke of the "ideal laws of chance" which are realised in true collectives. Chance was for him an objective category and not just the expression of ignorance. He tried to design tests whereby variation due to factors other than chance could be detected by comparing the data under consideration to a random sequence.
Fechner's "Kollektivmasslehre draws on several traditions. There is the moral statistics of the Belgian statistician and astronomer Adolphe Quetelet (q.v.) who was one of the first to investigate mass phenomena and to find numerical regularities in them. (Porter 1986) There is also the error theory of the mathematical astronomers Gauss (q.v.), Encke, Bessel and Hauber. And there is the tradition of the statistical bureaux of state administration. Much of Fechner's concept of a collective derives from the Württemberg state official Gustav Rümelin (1815-1889) who had distinguished between particulars that are typical of their genus and individuals that do not allow a straightforward inference as to the nature of the genus as a whole. The latter ones form a collective object and are the subject of statistics as the science of mass phenomena.
Fechner's Kollektivmasslehre was of immediate influence on many of his colleagues in Leipzig. The psychologists Gottlob Friedrich Lipps, Wilhelm Wirth and to some extent also Wilhelm Wundt used the new methods in psychophysics. Charles Edward Spearman who obtained his Ph.D. under Wundt extended Fechner's ideas and studied the correlation between magnitudes. The Leipzig astronomer and mathematician Heinrich Bruns (1848-1919) soon gave a general solution to Fechner's problem of a mathematical representation of frequency distributions, the so-called Bruns-series (today called Gram-Charlier series) and tried to unify Fechner's theory of collectives with probability theory. His most illustrious student was Felix Hausdorff who carried this tradition further. (Girlich 1996) Bruns and Hausdorff, however, dropped Fechner's requirement of chance variation of the collective object, thus obscuring any trace of Fechner's indeterminism.
In Richard von Mises' (q.v.) theory of probability of 1919, however, this condition becomes one of two central requirements. As an axiomatic basis of his theory, von Mises postulated 1. the existence of the limiting values of the relative frequencies and 2. the randomness of the way how the attributes are mapped unto the elements of the collectives. Randomness is thereby defined as the invariance of the frequencies under any place selection - a criterion which clearly shows traces of Fechner's above mentioned test of homogeneity. Von Mises' theory gives a precise formulation of Fechner's basic intuitions. It marks the final defeat of the subjective Laplacean interpretation of probability, consolidates the frequency interpretation and conceives of probability as an empirical science of chance phenomena. One can only speculate what the course of statistics would have been if Fechner's work had been published before K. Pearson (q.v.) developed his biometrics in the early 1890s.
#### References
[1] Fechner, Gustav Theodor 1860. Elemente der Psychophysik, 2 vols., Breitkopf und Härtel, Leipzig; 2nd. ed. ibid. 1889. (English transl. of vol 1 by Helmut E. Adler: Elements of Psychophysics, ed. by D. H. Howes & E. G. Boring, Holt, Rinehart & Winston, New York, 1966). [2] Fechner, Gustav Theodor 1878. Ueber den Ausgangswerth der kleinsten Abweichungssumme. In: Abhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften, math.-phys. Klasse 11, 1-76 (Sometimes cited with the year 1874). [3] Fechner, Gustav Theodor 1897. Kollektivmasslehre, ed. by Gottlob Friedrich Lipps, Engelmann, Leipzig. [4] Girlich, Hans-Joachim 1996. Hausdorffs Beiträge zur Wahrscheinlichkeitstheorie. In: E. Brieskorn (ed.), Felix Hausdorff zum Gedächtnis. Vol. 1: Aspekte seines Werkes, Vieweg, Braunshweig, 31-69. [5] Heidelberger, Michael 1987. Fechner's Indeterminism: From Freedom to Laws of Chance. In: The Probabilistic Revolution, vol 1: Ideas in History, ed. by Lorenz Krüger, Lorraine J. Daston and Michael Heidelberger, MIT Press/ Bradford Books, Cambridge, Mass., 117-156. Heidelberger, Michael 1993. Die innere Seite der Natur: Gustav Theodor Fechners wissenschaftlich-philosophische Weltauffassung (Philosophische Abhandlungen, Band 60), Klostermann, Frankfurt am Main. (Comprehensive study of Fechner's life and work; Ch. 5 on Fechner's psychophysics, Ch. 7 on Fechner's indeterminism, his theory of collectives and its reception) [6] Mises, Richard von 1928. Wahrscheinlichkeit, Statistik und Wahrheit, Springer, Wein (2nd revised English ed. prepared by Hilda Geiringer: Probability, Statistics and Truth, Allen & Unwin, London 1957. 1st English edition 1939.) [7] Plato, Jan von 1994. Creating Modern Probability: its Mathematics, Physics and Philosophy in Historical Perspective, Cambridge University Press, Cambridge. (Ch. 6 on von Mises) [8] Stigler, Stephen M. 1986. The History of Statistics: The Measurement of Uncertainty before 1900, Harvard University Press, Cambridge, MA. (pp. 242-254 on Fechner's use of statistics in psychophysics) [9] Witting, Hermann 1990. Mathematische Statistik. In: Gerd Fischer et al. (eds.), Ein Jahrhundert Mathematik 1890-1990: Festschrift zum Jubiläum der DMV, Vieweg, Braunschweig, 781-815. (pp. 786-787 on Fechner's Kollektivmasslehre, p. 788 on Lipps and Spearman)
Reprinted with permission from Christopher Charles Heyde and Eugene William Seneta (Editors), Statisticians of the Centuries, Springer-Verlag Inc., New York, USA.
How to Cite This Entry:
Fechner, Gustav Theodor. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fechner,_Gustav_Theodor&oldid=39198 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6971439719200134, "perplexity": 2649.7765035171683}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347391309.4/warc/CC-MAIN-20200526191453-20200526221453-00435.warc.gz"} |
http://intellectualmathematics.com/blog/critique-of-theological-foundations-of-keplers-astronomy/ | # Critique of “Theological Foundations of Kepler’s Astronomy”
Barker & Goldstein’s article “Theological Foundations of Kepler’s Astronomy” (Osiris, 16, 2001, pp. 88–113) claims that theological factors were crucial in Kepler’s derivation of the ellipse in the Astronomia Nova (AN). For this discussion we need to be aware of two laws announced earlier in the same work. The distance–velocity law says that the velocity of a planet is inversely proportional to its distance from the sun. The reciprocation law says, in brief, that “the planet’s body reciprocates [i.e., deviates from a circle] according to the measure of the versed sine of the eccentric anomaly” (AN, Donahue trans., p. 558), the meaning of which I shall explicate in detail below. These two laws are discovered essentially empirically, though of course by means of intermediate models, since the data is not available directly (AN, chs. 32 and 56 resp.). It is then shown that they can be physically realised by taking the sun and the planets to be magnetic (AN, chs. 33 and 57 resp.).
Now let us look at Barker & Goldstein’s reconstruction of Kepler’s derivation of the ellipse. They claim that “religious ideas contribute directly” to this derivation (p. 89) in the form of a theologically entrenched argument type called exemplum (§VII). A precise definition of exemplum appears elusive, but we need only be concerned with its alleged rôle in the Astronomia Nova. The crucial point according to Barker & Goldstein is that “the distance–velocity law and the reciprocation law are individually defensible by exemplum arguments” (p. 111), as follows:
“[O]n the grounds that the physical influence responsible for [these laws] is a species of an established genus [i.e., magnetism], this influence, whatever it is, can be recognizes as part of God’s governance of his creation and hence a law of nature.” (pp. 109–110)
I am not denying that these considerations may be part of the explanation for Kepler’s fondness for analogies. The textual evidence for this is very weak, however, as Barker & Goldstein are well aware. So to support their claim of direct religious influence, the exemplum theory needs a lot more to show for it. For this purpose they reconstruct Kepler’s derivation of the ellipse as follows.
“[The influence of the exemplum] is especially clear in the case of the last alternative to the ellipse, eliminated by Kepler in chapter 58, the via buccosa. Here the alternative curve is eliminated, not because it fails to fit the observations but because the ellipse—and only the ellipse—follows from the combination of the distance–velocity law and the reciprocation law. And what makes that a good basis for selecting between otherwise equally successful curves is that the two laws invoked here have already been shown to be parts of the providential plan, by means of exemplum inferences.” (p. 110)
Almost everything in this quotation is wrong. First of all we must note a mistake which does not seriously affect their main point: Kepler’s proof that the orbit is an ellipse (AN, ch. 59, thm. XI) uses only the reciprocation law, not the distance–velocity law, while Barker & Goldstein state repeatedly that both laws are needed for this proof (pp. 110, 111). The Newtonian idea of velocity and gravity interacting to generate the shape of the orbit is not present in Kepler. (The distance–velocity law is of course needed to compute the planet’s position on the ellipse at any given time, but this is not what Barker & Goldstein are referring to, for they specify explicitly that the theorem concerns “its two-dimensional track” only [p. 110].)
As for the rest of the above quotation, its many errors can only be sorted out after first describing what Kepler actually said. My account agrees with the excellent studies by Aiton (Mathematical Gazette, 59(410), 1975, pp. 250–260), Wilson (Isis, 59(1), 1968, pp. 4–25), and Stephenson (Kepler’s Physical Astronomy, Springer–Verlag, 1987, ch. 3). Barker & Goldstein refer to the first two of these “for different interpretations” (p. 111). I shall show that this is not a matter of “interpretations,” since in fact every step of Barker & Goldstein’s account is flatly contradicted by Kepler’s own words.
Consider first the reciprocation law, which says, in the notation of figure 1, that the Mars–sun distance is r = 1 + e cos x. The way in which Kepler discovered this law is important. He discovered “quite by chance” that “if the radius is substituted for the secant at the middle longitude [i.e., at x = 90°], this accomplishes what the observations suggest” (AN, p. 543). He then conjectured the reciprocation law as a generalisation of this: “the effect [of the reciprocation law] on all the eccentric positions will be the same as what was done here at the middle longitudes” (AN, p. 543). He then immediately (ch. 57) proceeded to satisfy himself that this law can be accounted for magnetically.
Now comes the problematic part: finding the orbit determined by this law. The problem is that the generalisation is ambiguous: it can generate either the via buccosa or the ellipse depending on how one interprets the equation. These two possible interpretations are shown in figures 2 and 3 respectively. Note that both interpretations agree when x = 90°, which, as we saw, was the empirical case that the law was induced from. Thus they are both permissible interpretations of the law. Indeed, Kepler makes this perfectly clear: on the basis of the reciprocation law “an orbit can be made for the planet … in a ‘puff-cheeked’ [i.e., via buccosa] form as well” (AN, p. 104). However, “this orbit is convicted of error by the equations” (AN, p. 104), i.e. empirically. Having “convicted” the via buccosa, Kepler “began … recalling the ellipses, quite convinced that I was following an hypothesis far, far different from the reciprocation hypothesis” (AN, p. 575). He then realised that the second interpretation of the reciprocation law is also possible, i.e., “that the distances constructed by the reciprocation and supported by the observations are contained in the perfect ellipse no less than in the puff-cheeked orbit” (AN, p. 104, italics added).
The truth is thus the exact opposite of Barker & Goldstein’s account above: the via buccosa is rejected solely for empirical reasons; despite the fact that it follows from the reciprocation law; which law does not uniquely determine the ellipse. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8977856040000916, "perplexity": 1499.3554422412417}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257645413.2/warc/CC-MAIN-20180318013134-20180318033134-00182.warc.gz"} |
https://www.enotes.com/homework-help/find-implicit-solution-following-initial-value-288395 | # Find the implicit solution of the following initial value problem. (2y-3)dy = (6x^2 + 4x - 5)dx , y(1) = 2
You need to integrate both sides such that:
`int (2y-3)dy = int (6x^2 + 4x - 5)dx =gt int 2y dy - int 3dy =`
`= int 6x^2 dx+ int 4x dx- int 5 dx =gt`
`=gt 2y^2/2 - 3y + c = 6x^3/3 + 4x^2/2 - 5x + c`
...
## See This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
You need to integrate both sides such that:
`int (2y-3)dy = int (6x^2 + 4x - 5)dx =gt int 2y dy - int 3dy =`
`= int 6x^2 dx+ int 4x dx- int 5 dx =gt`
`=gt 2y^2/2 - 3y + c = 6x^3/3 + 4x^2/2 - 5x + c`
`y^2 - 3y + c = 2x^3 + 2x^2 - 5x + c`
Since `y(1) = 2 =gt 2^2 - 3*2 + c = 2*1^3 + 2*1^2 - 5*1 + c`
`4 - 6 + c = 2 + 2 - 5 + c =gt -2 + 5 - 4 = c =gt c = -1`
The implicit solution to the given differential equation is `y^2 - 3y - 2x^3 - 2x^2 +5x - 1 = 0.`
Approved by eNotes Editorial Team | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9102358818054199, "perplexity": 4250.301008034914}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334514.38/warc/CC-MAIN-20220925035541-20220925065541-00468.warc.gz"} |
https://brilliant.org/problems/pizza-war-1/ | # Pizza War 1
Vaibhav gives a challenge to Kalash. He says that describe a motion such that the velocity vector at some instant of time makes an angle of $45^{\circ}$ with the acceleration vector. Kalash then swiftly answers that $\vec{r} = at\hat{i} + at\left(1 - \dfrac{t}{10}\right)\hat{j}$.
Kalash then asks Vaibhav at what instant of time will this occur for the motion described above. Vaibhav is confused. Can you help him out?
×
Problem Loading...
Note Loading...
Set Loading... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 2, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8707435131072998, "perplexity": 1988.5254240238983}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370491857.4/warc/CC-MAIN-20200328104722-20200328134722-00433.warc.gz"} |
http://sciencehq.com/mathematics/continuity-theorems.html | # Continuity Theorems.
The basic theorems based on continuity are given below:
If the functions f(x) and g(x) are continuous at x=a then,
1> $f(x) \pm g(x)$ is continuous at x=a.
2>$f(x) \times g(x)$ is continuous at x=a.
3>$\cfrac{f(x)}{g(x)}$ is continuous at x=a , if g(x) is not equal to 0.
4>$\sqrt[n]{f(x)}$ is continuous at x=a if f(x) is greater than 0 , or is a positive number when “n” is even.
Related posts:
1. Basic properties or theorems of limit. Four basic properties of limits of a function or limit...
2. Continuity of a function(continuous and discontinuous functions). Continuity of a function , a function can either be...
3. Exponent(index) and laws of exponents(indices). When , a number is repeatedly multiplied by itself the...
4. Basic properties of Logarithms. Logarithms are important throughout mathematics and science. Establishing some basic...
5. The concept of Limit. Limit of a function is the value to which function... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 4, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9640204906463623, "perplexity": 1161.2854673484628}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743011.30/warc/CC-MAIN-20181116111645-20181116133645-00382.warc.gz"} |
http://mathhelpforum.com/trigonometry/91431-trig-problem.html | 1. ## Trig problem
Hi. Got a maths trig question.
For a angle of less than 90 degrees, sinx=3cosx. Show and decide the value of sin2x.
I just cant bring myself to figure this one out. Helps or pointers would be very appreciated
2. Originally Posted by Burger king
Hi. Got a maths trig question.
For a angle of less than 90 degrees, sinx=3cosx. Show and decide the value of sin2x.
I just cant bring myself to figure this one out. Helps or pointers would be very appreciated
$\sin(2x) = 2\sin{x}\cos{x}$
since $\sin{x} = 3\cos{x}$ ...
$
\sin(2x) = 2(3\cos{x})\cos{x} = 6\cos^2{x}
$
3. Hello, Burger king!
I can't imagine what "show and decide" means.
For an angle $x < 90^o\!:\;\;\sin x\:=\:3\cos x.$
Show and decide the value of $\sin2x.$
We have: . $\sin x \:=\:3\cos x \quad\Rightarrow\quad \frac{\sin x}{\cos x} \:=\:3 \quad\Rightarrow\quad \tan x \:=\:3$
Hence: . $\tan x \:=\:\frac{3}{1} \:=\:\frac{opp}{adj}$
So $x$ is an angle in a right triangle with: $opp = 3,\;adj = 1$
. . Pythagorus says: . $hyp = \sqrt{10}$
Hence: . $\sin x = \tfrac{3}{\sqrt{10}},\;\;\cos x = \tfrac{1}{\sqrt{10}}$
Therefore: . $\sin2x \:=\:2\sin x\cos x \:=\:2\left(\frac{3}{\sqrt{10}}\right)\left(\frac{ 1}{\sqrt{10}}\right) \:=\:\frac{3}{5}$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9708929061889648, "perplexity": 2110.986303385664}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698540932.10/warc/CC-MAIN-20161202170900-00397-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://isoprocessor.kopflab.org/reference/iso_convert_signals.html | This function can be used to convert the intensity units of a collection of iso_files to a scaled unit (e.g. from mV to V, or nA to mA) or different unit (e.g. from mV to nA or vice-versa). The original signal intensity units are inferred from the naming of the intensity columns. The new units must be a voltage (V) or current (A) but can have any valid SI prefix. Conversion from voltage to current and vice versa requires information about the resistors used in the op amp. This information is automatically retrieved during file read for file formats that contain resistors values (e.g. dxf and did) and are read with the read_method_info=TRUE parameter (see iso_get_resistors_info for details on how to access resistor values in read files). If resistor values are not set in a file, it will not allow automatic conversion between voltage and current. Instead, the R and R_units parameters can be used to provide specific resistor values. However, if R is set, these values will be used for all passed in iso_files.
iso_convert_signals(iso_files, to, R, R_units = NA,
quiet = default(quiet))
## Arguments
iso_files collection of iso_file objects what signal unit to convert to resistor value(s). If not specified, will use resitor values from individual iso_files. If specified, must be a named vector with Rm (m=mass) as names (e.g. c(R45=0.3, R46=3)), in units of R_units. If specified, will be used for ALL provided iso_files. determined what units resistor values (R) are in, if they are specified. Example R_units = "GOhm" designates that the resistor values provided in R parameter are in Giga-Ohm, i.e. 10^9 Ohm. whether to display (quiet=FALSE) or silence (quiet = TRUE) information messages.
## Value
the passed in iso_file(s) with changed signal units | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4073004424571991, "perplexity": 3302.5163920818572}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526799.4/warc/CC-MAIN-20190720235054-20190721021054-00431.warc.gz"} |
https://dsp.stackexchange.com/questions/56510/convolution-of-two-impulse-signals | # Convolution of Two Impulse Signals
I have encountered convolution of two different impulse signals.
x[n] = (1/2)^n . u[n-2] * u[n]
x[n] = u[n] * [n]
u[n] = discrete impulse signal
. = product operation
* = convolution operation
For the first one, I found this solution:
x[n] = 1/4 if n = 2
x[n] = 0 if n != 2
For the second one, I found impulse signal itself
Edit: Are my answers are true ? My professor told me that the answer for the first one is wrong, but he did not say the correct answer.
• what is the question ? – Ahmad Bazzi Apr 7 at 15:49
• I cannot make sure that my answers are true or not – Goktug Apr 7 at 16:00
• My answer is specified above. – Goktug Apr 7 at 16:01
• $u[n]$ is generally used to denote the unit step function, not the unit impulse function which is usually denoted $\delta[n]$. Please don't introduce new notation unnecessarily. – Dilip Sarwate Apr 7 at 22:38
But you better use the standard notation as Dilip Sarwate already indicated; $$u[n]$$ is the unit-step and $$\delta[n]$$ is the unit impulse. Then
$$0.5^n \delta[n-2] \star \delta[n] = 0.5^2 \delta[n-2] = \begin{cases} { 0.25 ~~~, ~~~n= 2 \\ 0.00 ~~~,~~~n \neq 2 } \end{cases}$$
This is basically an exercise to test the student's understanding of the concept that the unit impulse is effectively the unit in convolutions, that is: $$\delta \star x = x$$ for all signals $$x$$. Perhaps a systems explaination might help. If an LTI system has impulse response $$h$$, then we know that the output of the system when $$x$$ is the input is $$y = h \star x$$. So, $$\delta \star x$$ can be thought of as the output of an LTI system with impulse response $$\delta$$ when the input to the LTI system is $$x$$. What LTI system has output $$\delta$$ when its input is the unit impulse $$\delta$$?? It is just the canonical straight wire with (no) gain that audio enthusiasts dream about! And so, $$\delta \star x = x$$ for all $$x$$.
With this, it it is easy to verify that the OP's answer to the first question is correct (but maybe his professor wanted to see the answer as $$\left(\frac 12\right)^n \delta[n-2]$$ or $$\left(\frac 12\right)^2 \delta[n-2]$$ instead of what the OP wrote) while the second answer $$\delta[n]\star [n] = \delta[n]$$ is incorrect, it should be $$[n]$$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 19, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9051299095153809, "perplexity": 439.6063578706522}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496665809.73/warc/CC-MAIN-20191112230002-20191113014002-00013.warc.gz"} |
https://powerfuldatablog.wordpress.com/category/frequentist-inference/ | Category: Frequentist Inference
# Frequentist Inference III – Confidence Intervals
Confidence Intervals are often used and are a great way to not just give a point estimate but to tell where else the point might be. We will focus on confidence intervals based on normal data today. z-confidence intervals for the mean Suppose data $latex x_{ 1 },...,x_{ n } \sim N(\mu,\sigma^{ 2 })$ with … Continue reading Frequentist Inference III – Confidence Intervals
This here shall be a summary of the most common significance tests. Designing NHST specify $latex H_{ 0 }$ and $latex H_{ 1 }$ choose test statistic of which we know the null distribution and alternative distribution specify rejection region, significance level and decide if the rejection region is one or two-sided compute … Continue reading Frequentist Inference II – NHST II | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8316494226455688, "perplexity": 1210.0332183986966}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511175.9/warc/CC-MAIN-20181017132258-20181017153758-00459.warc.gz"} |
http://openstudy.com/updates/561452a3e4b05358a41fa290 | Here's the question you clicked on:
55 members online
• 0 viewing
## anonymous one year ago If f is differentiable at 1, and the limit of f(1+h)/h as h->0 is 5, what is f(1)? Delete Cancel Submit
• This Question is Closed
1. anonymous
• one year ago
Best Response
You've already chosen the best response.
0
@jim_thompson5910
2. jim_thompson5910
• one year ago
Best Response
You've already chosen the best response.
1
f is differentiable at 1 so $\Large \lim_{h\to 0}\frac{f(1+h)-f(1)}{h}$ exists and it is defined based on the limit definition of the derivative
3. anonymous
• one year ago
Best Response
You've already chosen the best response.
0
so $f'(1) = 5-\lim_{h \rightarrow 0}\frac{f(1)}{h}$
4. jim_thompson5910
• one year ago
Best Response
You've already chosen the best response.
1
$\Large \lim_{h\to 0}\frac{f(1+h)}{h}=5$ $\Large \lim_{h\to 0}\frac{f(1+h){\LARGE \color{red}{-0}}}{h}=5$ $\Large \lim_{h\to 0}\frac{f(1+h){\LARGE \color{red}{-f(1)}}}{h}=5$ so we see that $$\Large f(1) = 0$$
5. anonymous
• one year ago
Best Response
You've already chosen the best response.
0
so my step would be invalid?
6. jim_thompson5910
• one year ago
Best Response
You've already chosen the best response.
1
it's valid, I just don't see where to go with it
7. anonymous
• one year ago
Best Response
You've already chosen the best response.
0
oh ok. And you knew to put in that f(1) as 0 simply because the equation resembled the derivative limit?
8. jim_thompson5910
• one year ago
Best Response
You've already chosen the best response.
1
I saw it match up with the limit definition. Well almost match up. It was just missing the -f(1) part
9. anonymous
• one year ago
Best Response
You've already chosen the best response.
0
so f(x) = 0 and f'(x) = 5?
10. jim_thompson5910
• one year ago
Best Response
You've already chosen the best response.
1
f ' (1) = 5 and f(1) = 0 we can't say anything about f(x) or f ' (x) in general
11. anonymous
• one year ago
Best Response
You've already chosen the best response.
0
ok, thank you
12. jim_thompson5910
• one year ago
Best Response
You've already chosen the best response.
1
IF it was $\Large \lim_{h\to 0}\frac{f(x+h)-f(x)}{h}=5$ then we can say f ' (x) = 5
13. anonymous
• one year ago
Best Response
You've already chosen the best response.
0
ok got it
14. Not the answer you are looking for?
Search for more explanations.
• Attachments:
Find more explanations on OpenStudy
##### spraguer (Moderator) 5→ View Detailed Profile
23
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9999163150787354, "perplexity": 7189.576107889864}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988717959.91/warc/CC-MAIN-20161020183837-00519-ip-10-142-188-19.ec2.internal.warc.gz"} |
http://hal.in2p3.fr/in2p3-01226856 | # First combined search for neutrino point-sources in the Southern Hemisphere with the ANTARES and IceCube neutrino telescopes
Abstract : We present the results of searches for point-like sources of neutrinos based on the first combined analysis of data from both the ANTARES and IceCube neutrino telescopes. The combination of both detectors which differ in size and location forms a window in the Southern sky where the sensitivity to point sources improves by up to a factor of two compared to individual analyses. Using data recorded by ANTARES from 2007 to 2012, and by IceCube from 2008 to 2011, we search for sources of neutrino emission both across the Southern sky and from a pre-selected list of candidate objects. No significant excess over background has been found in these searches, and flux upper limits for the candidate sources are presented for $E^{-2.5}$ and $E^{-2}$ power-law spectra with different energy cut-offs.
Document type :
Journal articles
Domain :
http://hal.in2p3.fr/in2p3-01226856
Contributor : Danielle Cristofol <>
Submitted on : Tuesday, November 10, 2015 - 3:23:40 PM
Last modification on : Thursday, September 5, 2019 - 3:14:05 PM
### Identifiers
• HAL Id : in2p3-01226856, version 1
• ARXIV : 1511.02149
### Citation
S. Adrián-Martínez, A. Albert, M. André, G. Anton, M. Ardid, et al.. First combined search for neutrino point-sources in the Southern Hemisphere with the ANTARES and IceCube neutrino telescopes. The Astrophysical Journal, American Astronomical Society, 2016, 823, pp.65. ⟨in2p3-01226856⟩
Record views | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8057791590690613, "perplexity": 3009.8196358170044}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572439.21/warc/CC-MAIN-20190915235555-20190916021555-00090.warc.gz"} |
http://new.pmean.com/post/hadley-wickham/ | ## 2016-08-07
Categories: Recommendation Tags: Important statisticians R software
Hadley Wickham has written many popular R packages
• so many that they are sometimes referred to as the “Hadleyverse.” This is a nice biography that emphasizes the impact that Dr. Wickham has had on R. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8559785485267639, "perplexity": 6156.149865362098}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703529179.46/warc/CC-MAIN-20210122082356-20210122112356-00676.warc.gz"} |
http://mathhelpforum.com/statistics/34307-combinatorics-help.html | 1. Combinatorics HELP
Let a1, a2, a3, a4 ,a5, be any distinct positive integers. Show that there exists at least one subset of three integers whose sum is divisible by 3.
what is the answer to this...plzz HELPP!!!
2. Originally Posted by fafafa
Let a1, a2, a3, a4 ,a5, be any distinct positive integers. Show that there exists at least one subset of three integers whose sum is divisible by 3.
what is the answer to this...plzz HELPP!!!
Have you ever heard of the Pigeon Hole principle? You can use that here.
Note that any positive integer is either congruent to 0 mod 3 or 1 mod 3 or 2 mod 3. we have more than three integers here, so we know all congruences are accounted for. Further more, at least one congruence repeats. Try doing this by cases. (There may be an easier way, I'm not a Number Theorist)
Any questions? Do you have an idea of how to proceed?
EDIT: Ah, nevermind, I just realized this post makes no sense! Nothing is stopping us from choosing all the numbers of one congruence class
3. i have no idea what to do..is it possible you can show me the answer step by step plz...
4. Hello,
Here are the possibilities :
0-0-0 -> ok
0-0-1 -> not ok
What are the conditions upon those integers ? Consecutive ?
5. You have 5 integers.
Each integer must be congruent to either 0, 1, or 2 (mod 3).
if any 3 are congruent (mod 3), then 3 divides their sum
ie 5 + 5 + 5 = 3+2 + 3+2 + 3+2 = 3(3+2)
and if all 3 mods are represented, then 3 divides their sum
ie 5 + 6 + 7 = 3+2 + 3+3 + 3+4 = 3+(3-1) + 3+(3+0) + 3+(3+1) = 3*3 + (3*3 -1+0+1) = 3*3 + 3*3 = 3(3+3)
*note, those examples are for your understanding, I wouldn't put them in your proof, if you need to show this, show it in a more abstract way that can be applied to any given situation*
So worst case, two are congruent to 0, or 1, or 2 (mod 3) and two more are congruent to 0, or 1, or 2 (mod 3), but these two sets of numbers are not congruent to eachother (mod 3). Then if the 5th term is congruent to either of these sets, 3 will divide their sum. The only alternative is that it is not congruent to any of the other numbers (mod 3) in which case, all three mods are represented, and so any combination of a 0, 1, and 2 (mod 3) will sum to a number divisible by 3. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8023249506950378, "perplexity": 274.61798376218854}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560279657.18/warc/CC-MAIN-20170116095119-00065-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://www.maplesoft.com/support/help/Maple/view.aspx?path=Finance%2Fgrowingannuity | Finance - Maple Programming Help
Home : Support : Online Help : Mathematics : Finance : Personal Finance : Finance/growingannuity
Finance
growingannuity
present value of a growing annuity
Calling Sequence growingannuity(cash, rate, growth, nperiods)
Parameters
cash - amount of first payment rate - interest rate growth - rate of growth of the payments nperiods - number of payments
Description
• The function growingannuity calculates the present value at period=0, of an annuity of nperiods payments, starting at period=1 with a payment of cash. The payments increase at a rate growth per period.
• Since growingannuity used to be part of the (now deprecated) finance package, for compatibility with older worksheets, this command can also be called using finance[growingannuity]. However, it is recommended that you use the superseding package name, Finance, instead: Finance[growingannuity].
Examples
I hold an investment that will pay me every year for 5 years starting next year. The first payment is 100 units, and each payment is expected to grow by 3% each year. If the interest rate is 11%, what is the present value of the investment.
> $\mathrm{with}\left(\mathrm{Finance}\right):$
> $\mathrm{growingannuity}\left(100,0.11,0.03,5\right)$
${390.0340764}$ (1)
This can also be calculated as follows.
The cash flows are given by:
> $\mathrm{cf}≔\left[100,100\cdot 1.03,100{1.03}^{2},100{1.03}^{3},100{1.03}^{4}\right]$
${\mathrm{cf}}{≔}\left[{100}{,}{103.00}{,}{106.0900}{,}{109.272700}{,}{112.5508810}\right]$ (2)
or equivalently as
> $i≔'i':$
> $\mathrm{cf}≔\left[\mathrm{seq}\left(\mathrm{futurevalue}\left(100,0.03,i\right),i=0..4\right)\right]$
${\mathrm{cf}}{≔}\left[{100.0}{,}{103.00}{,}{106.0900}{,}{109.272700}{,}{112.5508810}\right]$ (3)
> $\mathrm{cashflows}\left(\mathrm{cf},0.11\right)$
${390.0340762}$ (4)
Here, we deal with a more complicated example illustrating differential growth. We have an investment that will pay dividends of 1.12 units starting one year from now, growing at 12 % per year for the next 5 years. From then on, it will be growing at 8%. What is the present value of these dividends if the required return is 12%? Solution: first part, the present value for the first 6 years is a growing annuity
> $\mathrm{part1}≔\mathrm{growingannuity}\left(1.12,0.12,0.12,6\right)$
${\mathrm{part1}}{≔}{6.000000000}$ (5)
The fact that this is 6 times the present value of the first dividend is because the growth rate is equal to the required return. The second part, is a (deferred) growing perpetuity. Six years from now, the dividends will be
> $\mathrm{div_6}≔\mathrm{futurevalue}\left(1.12,0.12,5\right)$
${\mathrm{div_6}}{≔}{1.973822685}$ (6)
> $\mathrm{div_7}≔\mathrm{futurevalue}\left(\mathrm{div_6},0.08,1\right)$
${\mathrm{div_7}}{≔}{2.131728500}$ (7)
Its value 6 years from now is
> $\mathrm{part2_6}≔\mathrm{growingperpetuity}\left(\mathrm{div_7},0.12,0.08\right)$
${\mathrm{part2_6}}{≔}{53.29321250}$ (8)
Which has a present value of
> $\mathrm{part2}≔\mathrm{presentvalue}\left(\mathrm{part2_6},0.12,6\right)$
${\mathrm{part2}}{≔}{27.00000000}$ (9)
Therefore the investment has a present value of
> $\mathrm{part1}+\mathrm{part2}$
${33.00000000}$ (10)
33 units.
Compatibility
• The Finance[growingannuity] command was introduced in Maple 15. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 22, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8385365009307861, "perplexity": 1134.2012226950221}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347387219.0/warc/CC-MAIN-20200525032636-20200525062636-00506.warc.gz"} |
http://math.stackexchange.com/questions/94122/showing-that-fz-leq-prod-limits-k-1n-left-fracz-z-k1-overlinez/94146 | # Showing that $|f(z)| \leq \prod \limits_{k=1}^n \left|\frac{z-z_k}{1-\overline{z_k}z} \right|$
I need some help with this problem:
Let $f\colon D \to D$ analytic and $f(z_1)=0, f(z_2)=0, \ldots, f(z_n)=0$ where $z_1, z_2, \ldots, z_n \in D= \{z:|z|<1\}$. I want to show that $$|f(z)| \leq \prod_{k=1}^n \left| \frac{z-z_k}{1-\overline{z_k}\, z} \right|$$ for all $z \in D$.
It seems that I need to use Schwarz-Pick Lemma but it seems that the problem doesn't satisfy the conditions. Another lemma that I can use is that of Lindelöf saying: Let $f:D \to D$ analytic, then $$|f(z)|\leq \frac{|f(0)|+|z|}{1+|f(0)| \cdot |z|}$$ for all $z \in D$.
It seems to be an easy problem but I couldn't succeed in solving it.
-
Do you know that there is an option to thank people who help you by accepting their answers? If not, I seriously recommend you to go through the faq. – user21436 Dec 25 '11 at 22:16
It's possible that $f(z)$ is not a real number for some $z$, so the inequality doesn't make sense (you probably missed $|\cdot |$). – Davide Giraudo Dec 25 '11 at 22:25
I believe you imitate the proof of the Shwartz lemma. Divide f(z) by all of the factors on the right. What does the maximum modulus principle give you? – Potato Dec 25 '11 at 22:32
yes, thanks, I've edited it. – bond Dec 25 '11 at 22:32
Also note that the function you get when you do what I said will be analytic, because all singularities will be removable. – Potato Dec 25 '11 at 22:45
Let $f$ be non-constant, and continuously extends to $\overline{D}$ (the closed unit disc.)
Let $B(z)=\prod_{k=1}^n \frac{z-z_k}{1-\overline{z_k}z}.$ Note that $|B(z)|=1$ for $|z|=1.$ Define $g(z):=f(z)/B(z).$ Now, $g$ is a holomorphic map on $D$. By maximum modulus principle, $|g(z)|$ attains its maximum value on the boundary $|z|=1.$ Therefore, $|g(z)| \leq 1$ for $|z| \leq 1.$ Hence,
$$|f(z)| \leq |B(z)|= \prod_{k=1}^n \left|\frac{z-z_k}{1-\overline{z_k}z} \right|.$$
See the Blaschke Product as well.
-
I don't think you really need to assume that $f$ extends to $\overline D$ continuously for your argument to work. Couldn't just remark that (by the maximum modulus principle) for $|z|<r<1$: $$\frac{|f(z)|}{|B(z)|} \le \max_{\theta} \frac{1}{|B(re^{i\theta})|} \overset{r\to 1}\longrightarrow 1$$ so $|f(z)|\le |B(z)|$? – Sam Dec 26 '11 at 3:00
@Sam: That's a good point. It can be improved in this way. – Ehsan M. Kermani Dec 27 '11 at 4:20
It's look good but Where have you used the fact of $f(z_k)=0$? – bond Dec 27 '11 at 14:23
@bond: The zeros of $B(z)$ are precisely $z_k$'s, that's why $g$ is holomorphic on $D.$ – Ehsan M. Kermani Dec 27 '11 at 19:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9466854929924011, "perplexity": 235.92245256182537}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701164289.84/warc/CC-MAIN-20160205193924-00297-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://www.ipam.ucla.edu/research-articles/overcoming-the-curse-of-dimensionality-for-control-theory/ | # Overcoming the Curse of Dimensionality for Control Theory
Posted on 10/30/15 in Research Articles
Optimal control problems lead to Hamilton-Jacobi Bellman (HJB) differential equations in many space variables for finding the cost function to be optimized. This beautiful connection has not generally led to effective numerical methods because grid based solutions of partial differential equations in n variables generally have memory requirements and complexity that is exponential in n. This is the “curse of dimensionality” a term coined by Richard Bellman in 1957.
Jerome Darbon and Stanley Osher were motivated to think about high-dimensional problems in control theory by lectures of Claire Tomlin and William McEneaney that they heard at IPAM. Recently they noticed a link between HJB equations and certain currently very popular convex optimization problems. They proposed and tested a new approach borrowing ideas from $$ℓ_1$$ regularized convex optimization problems arising in compressed sensing. By using the Hopf formula, derived in 1965 for solving HJB equations, and restricting the Hamiltonian to be convex and positively homogeneous degree one in the gradient, they needed to solve problems resembling the compressive sensing optimization mentioned above. This class includes linear controls involving time and for which the control set is compact and convex.
By using optimization ideas motivated by compressed sensing they obtained incredibly fast algorithms which do not use grids and hence have minimal memory requirements. For example if the Hamiltonian is the $$ℓ_2$$ norm (not the square of this) of the gradient, this technique can be used to compute the distance to a compact convex set in 4, 8, 12, 16 dimensions with each function evolution taking $$10^{-7}$$ seconds on a standard lap top. This means that 10 million points can be evaluated in a second. The accompanying figure shows the results of their method for a 2-dimensional slice at two different times for the HJB equation corresponding to the minimal distance to a union of two spheres in dimension 8.
Moreover, using a trick involving the level set method, they find the projection onto a convex compact set Ω for a given point in $$R^n \backslash Ω$$ equally quickly. This is an important problem in its own right.
The applications to control theory, and hopefully differential games, and perhaps even new approaches to linear programming are expected to follow soon. The curse has been lifted a bit!
Figure 1: Evaluation of the solution of HJB for the distance to minimal distance to two spheres at times, t = 5 (left) and t = 10 (right). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6401011347770691, "perplexity": 386.9039892415188}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738555.33/warc/CC-MAIN-20200809132747-20200809162747-00557.warc.gz"} |
https://asmedigitalcollection.asme.org/verification/article/6/3/031004/1110711/Uncertainty-Reduction-for-Model-Error-Detection-in | ## Abstract
Uncertainty quantification (UQ) is an important step in the verification and validation of scientific computing. Validation can be inconclusive when uncertainties are larger than acceptable ranges for both simulation and experiment. Therefore, uncertainty reduction (UR) is important to achieve meaningful validation. A unique approach in this paper is to separate model error from uncertainty such that UR can reveal the model error. This paper aims to share lessons learned from UQ and UR of a horizontal shock tube simulation, whose goal is to validate the particle drag force model for the compressible multiphase flow. First, simulation UQ revealed the inconsistency in simulation predictions due to the numerical flux scheme, which was clearly shown using the parametric design of experiments. By improving the numerical flux scheme, the uncertainty due to inconsistency was removed, while increasing the overall prediction error. Second, the mismatch between the geometry of the experiments and the simplified 1D simulation model was identified as a lack of knowledge. After modifying simulation conditions and experiments, it turned out that the error due to the mismatch was small, which was unexpected based on expert opinions. Last, the uncertainty in the initial volume fraction of particles was reduced based on rigorous UQ. All these UR measures worked together to reveal the hidden modeling error in the simulation predictions, which can lead to a model improvement in the future. We summarized the lessons learned from this exercise in terms of empty success, useful failure, and deceptive success.
## 1 Introduction
According to the ASME verification, validation, and uncertainty quantification committee standards and AIAA verification, validation, and uncertainty quantification guides [1,2], model validation is defined as the process of determining the degree to which a model is an accurate representation of the real phenomenon, from the perspective of the model's intended uses. The purpose of model validation is not only to assess the accuracy of a computational model but also to improve the model based on the validation results. Uncertainty quantification (UQ) has been recognized as a key component in verification and validation [3], whose aim is to build predictive computational models. Validation experiments may include measurement variability and processing uncertainty [4] while simulation predictions may include propagated uncertainty and numerical and model form errors [5]. The validation assessment is often performed using validation metrics that compare the uncertainties between simulation and experiment in the form of probability distributions [6].
If uncertainties in simulation and experiment are larger than errors, validation may not be useful even if two distributions are overlapped. Therefore, in order to have a meaningful validation, it is required to separate model error from uncertainty and reduce the uncertainty to be less than the model error, which is a unique approach in this paper compared to other approaches in the literature [7]. There are many different ways of reducing uncertainty, such as using more samples to reduce statistical uncertainty [8], bias correction [9], and model conditioning [10]. The objective of this paper is to share lessons learned from UQ and uncertainty reduction (UR) of a horizontal multiphase shock tube simulation, whose goal is to validate the particle drag force model for the compressible multiphase flow. The initial UQ for the horizontal shock tube experiment was presented by Park et al. [4]. The primary goal of this paper is to expose the model errors so that the model can be improved to ensure the required prediction capability of the simulation. This paper is an extension of our previous work on validation and uncertainty quantification of the shock-tube simulation [11].
The rest of the paper is organized as follows: Section 2 explains the multiphase shock tube simulation and experiment, which is an intermediate stage of a compressible multiphase turbulence project at the University of Florida. Section 3 summarizes the validation procedure and UQ, where the quantities of interest are defined, and uncertain variables are quantified. Section 4 presents three UR activities to reveal the model error in particle drag force, followed by conclusions and a summary of lessons learned from this work in Sec. 5.
## 2 Shock Tube Experiment and Simulation
The physics of shock interaction with a cloud of particles has many interesting applications, such as explosive volcanic eruptions, dust explosions in coal mines, and supernovae [12]. In addition, understanding this physics plays a key role in accurately predicting explosive dispersal of particles and controlling and designing the consequences of the explosion. The center for compressible multiphase turbulence at the University of Florida is developing software that can simulate a high-speed dispersal of an annular, dry particle bed driven by a core of reacting explosive. Figure 1 shows a blastpad experiment of explosive dispersal of solid particles conducted at Eglin Air Force Base under the guidance of the Air Force Research Laboratory [13]. This experiment serves as a testbed for exploring the rich physics of compressible multiphase instabilities and turbulence. The quantities of interest (QoI) are the shock location and particle front location as a function of time, which will be compared with simulation predictions for validation.
Fig. 1
Fig. 1
Close modal
Many interesting and complex physics are present in the experiment, including detonation chemistry, turbulence, particle collisions, drag forces, real gas effects, shock–particle interactions, and particle–gas interactions. Figure 2 shows eight physics models for simulating the behavior of explosives, gases, and particles. Among them, four key physics models were selected by the authors based on their importance to achieving the prediction capability of the simulation: (1) particle force, (2) particle collision, (3) compaction, and (4) multiphase turbulence.
Fig. 2
Fig. 2
Close modal
Since the blastpad experiment in Fig. 1 is expensive, only a small number of experiments are affordable. Therefore, simplified experiments and simulations are planned to focus on individual physics model validation while the effects of other models are either controlled or ignorable. Among the eight physics models in Fig. 2, in this paper, the multiphase shock tube simulation and experiment are used to validate the particle drag force model (T6) and the collision model (T4), which explain shock–particle and particle–particle interactions. Since the QoIs strongly depend on these two models, their accuracy is critically important to ensure the prediction capability of the blastpad simulation. The shock tube experiment is effective for these two models because the initial experimental conditions can be easily controlled such that the interaction between shock particles and gas particles mostly contributes to the QoI [14]. The effect of the compaction model is minimized by using a relatively low volume fraction. In addition, the effect of turbulence is ignorable by focusing on the motion of particles in an early time.
The apparatus of the shock tube experiment conducted by Sandia National Laboratories [14] is shown in Fig. 3(a). The shock tube of 5.2 m in length is composed of the driver, driven, and test sections. The particle curtain is located in the test section, where a glass window on the side makes it possible to observe the particle motion. The lime-glass particles in the reservoir fall through the slit to form a particle curtain. A shock wave is generated due to the pressure difference between the driver and driven sections when the diaphragm between them bursts. The planar shock wave travels through the driven section and is stabilized before arriving at the test section.
Fig. 3
Fig. 3
Close modal
When the shock moves in the flow direction, its interaction with particles is observed through the side window in the test section. The motion of the particle curtain is represented by the upstream front position (UFP) and the downstream front position (DFP) as a function of time as shown in Fig. 3(b). In addition, the thickness of the curtain is calculated by the distance between the two fronts. Initially, the curtain thickness is about 2 mm before hit by the shock (Fig. 3(c)), while the curtain moves and expands afterward (Fig. 3(d)).
Figures 3(c) and 3(d) show the schematic view of the glass window in the test section, where the black vertical bar in the middle represents the particle curtain and dashed lines are the observation window. The motion of the particle curtain is measured using imaging techniques. More specifically, a Schlieren imaging system [15] is used to capture the motion of the particle curtain and shock. Figure 3(e) is a Schlieren image taken through the observation window. The rectangles with the dashed line of Figs. 3(c) and 3(d) show the coverage of the Schlieren image. In addition, an X-ray radiography imaging system [16] is used to measure the volume fraction of the particle curtain. The Schlieren imaging system can take an image every 24.4 μs, while the X-ray imaging system can take a single image per experiment. Since the Schlieren and X-ray cannot be used simultaneously, either the curtain location or volume fraction can be measured, not both.
An additional challenge in measurement is due to the gap between the particle curtain and the sidewall. Figure 4 shows the schematic top view of the test section with the particle curtain where the curtain occupies about 80% of the width of the test section. The gap allows the air bypassing around the particle curtain, which makes the particles on both sides move faster than those at the center. The two-dimensional simulation results in the xy-plane in Fig. 4(b) support this behavior, where the particle motion on the edge (y = 0.04 m) is faster than that at the center (y = 0 m). The two vertical solid lines are UFP (red) on the left and DFP (blue) on the right when all particles are considered. On the other hand, the two dashed lines are UFP (green) on the left and DFP (cyan) on the right when only particles near the center (0 ≤ y ≤ 0.01) are considered. These particle front lines are determined as the left and right 2.5 percentile of particle volumes. Since the curtain movement can be observed through the window on the side, it is difficult to observe the central portion of the particle curtain. Due to the placement of the particle reservoir and collector, it is difficult to observe the particle movement in the vertical direction. Since one-dimensional simulation assumes that there is no variation through y- and z-coordinate direction, the gap effect can be a major model error. This fact initially provoked serious doubt about the comparison between the one-dimensional prediction and the experiment with gaps because the former cannot capture the gap effect.
Fig. 4
Fig. 4
Close modal
## 3 Uncertainty Quantification and Validation Process
Both shock tube simulation and experiment include many sources of uncertainty. To have meaningful validation, one must quantify them carefully. Figure 5 shows the validation and UQ framework for the simulation based on reducing error and uncertainty in both simulation and experiment. The major sources of uncertainty in the experiment are measurement variability, sampling uncertainty, and measurement processing uncertainty. The first one is aleatory, while the other two are epistemic uncertainty. The QoI can be different at different tests due to measurement uncertainty, while the measurement may have a bias due to calibration error, which is measurement processing uncertainty. These errors and uncertainty are quantified by repeating experiments or investigating the measurement process. In addition, the input conditions and their uncertainties should be quantified so that they can be used in the simulation. The major source of uncertainty in simulation is the propagated uncertainty, which is the effect of input uncertainty on QoIs. In addition, the stochastic variability and discretization error in the numerical computation process should be included. These errors and uncertainties are quantified by running the simulation multiple times with different realizations of input uncertainty and performing convergence analysis. When the difference between uncertainties in experiment and simulation is bigger than the difference in the mean values (model error), it is difficult to identify the model error. In such a case, UR is initiated to reduce the uncertainty in both the experiment and simulation until they are less than the model error. If the model error is larger than a threshold, model improvement is initiated to reduce the model error. This process is repeated until both the uncertainty and model error are less than a user-defined threshold.
Fig. 5
Fig. 5
Close modal
A unique approach in this paper is the separated treatment of model error from other sources of uncertainty. In the literature [7,17], the model form error is generally considered as a part of epistemic uncertainty, which is good for validating the prediction capability of simulation. However, to identify the model error, which is the main goal of this paper, it would be necessary to separate the model error from other uncertainties. With the given uncertainties in Fig. 5, the model error can be expressed as
$emodel=(ymeas+esamp+emeas)−(ymodel+eprop+enum)$
(1)
where $ymeas and ymodel$ are, respectively, the means of measurement and model prediction. In addition, $esamp,emeas,eprop, and enum$ are, respectively, sampling, measurement, propagated, and numerical errors. All these four errors are modeled as uncertain variables with mean values of zero. For example, measurement processing uncertainty is a bias error. However, since we do not know its exact value, it is modeled as a distribution with zero mean. Then, the discrepancy between the means of experimental measurement and the simulation calculation represents the model error, while its uncertainty is the sum of all four uncertainties
$E(emodel)=ymeas−ymodel$
(2)
$V(emodel)=V(esamp)+V(emeas)+V(eprop)+V(enum)$
(3)
where $E(•)$ and $V(•)$ represent, respectively, the expected value and the variance of an uncertainty variable. Figure 6(a) illustrates the proposed method of defining model error. The model prediction becomes a distribution whose mean is at $ymodel$ and the variance is the combination of that of propagated uncertainty $(eprop)$ and numerical errors $(enum)$. The experimental measurement is also a distribution whose mean is at $ymeas$, and its variance comes from that of sampling uncertainty $(esamp)$ and measurement processing uncertainty $(emeas)$. It is noted that the uncertainty in Fig. 6(a) is schematic and does not represent any specific distribution type. Traditionally, the model error is defined based on the model's accuracy. However, this is only possible when the level of model error is known. Since the goal of this paper is to quantify the model error, Eq. (1) is a proper way to estimate it with given uncertainties.
Fig. 6
Fig. 6
Close modal
The identification of the model error is the comparison between the mean of model error in Eq. (2) and its uncertainty in Eq. (3). The uncertainty can be measured in terms of the standard deviation. When the uncertainty is larger than the mean, it is impossible to identify the model error because the uncertainty covers the mean of model error, as shown in Fig. 6(b). Therefore, to reveal the model error, uncertainty in Eq. (3) must be reduced such that the mean of model error can be estimated, as shown in Fig. 6(c). Therefore, the “large uncertainty?” loop in Fig. 5 is repeated until both uncertainties from experiments and simulations are less than the mean of model error in Eq. (2). Once the uncertainty is reduced enough, the “large error?” loop in Fig. 5 is repeated until the level of model error is acceptable.
Table 1 summarizes important sources of uncertainty and error in the shock tube experiment. Additional measurements were performed to estimate uncertainty in particle diameter [21]. Schlieren image analysis is used to estimate the uncertainty in the curtain thickness [14]. X-ray image analysis is used to estimate the distribution and uncertainty in the initial particle volume fraction [16]. All uncertainties are considered uniformly distributed as we were able to identify their lower and upper bounds through measurements. In the case of initial volume fraction, however, it was possible to identify its distribution based on an X-ray image, which is detailed in Sec. 4.3. All the uncertainties except for measurement bias are used for simulation inputs to calculate the propagated uncertainty $(eprop)$, while the measurement bias is included in the measurement uncertainty $(emeas)$. First, a Kriging surrogate model of the curtain location is constructed using the volume fraction, particle diameter, and curtain thickness as input variables. Then, the Monte Carlo simulation with 10,000 samples was used to generate samples of curtain locations. To obtain the sampling uncertainty $(esamp)$, experiments are repeated four times. To understand the influence of the unknown particle locations, we randomly placed particles and made ten runs of simulations with different random particle locations. The difference between the simulation results was small enough that we concluded that the effect of the randomness in the initial particle location on the QoI is negligible. The discretization error has been studied by Nili et al. [22], and the error from the numerical scheme will be discussed in Sec. 4.1$(enum)$. The error due to the gap effect is quantified by comparing one- and two-dimensional simulations.
Table 1
Key uncertainty and error sources in the validation of the one-dimensional simulation
Uncertainty sourceDescription
Measurement bias in particle front positionsSystematic bias uncertainty because of the gap between the particle curtain and walls [−10,0]%
Initial particle volume fractionUncertainty in initial volume fraction measurement process and local variation in particle curtain [18,19] %
Initial particle positionsVariability in initial particle positions
Particle diametersVariability in particle diameters [100,130] μm
Initial curtain thicknessVariation in the curtain thickness [1.6,2.4] mm
Pressure at driver sectionNegligible measurement noise
DiscretizationError due to temporal and spatial discretization
Model errorError in the drag force model [20]
Gap effectError for not being able to measure DFP due to the gap
Numerical flux schemeError due to numerical scheme
Uncertainty sourceDescription
Measurement bias in particle front positionsSystematic bias uncertainty because of the gap between the particle curtain and walls [−10,0]%
Initial particle volume fractionUncertainty in initial volume fraction measurement process and local variation in particle curtain [18,19] %
Initial particle positionsVariability in initial particle positions
Particle diametersVariability in particle diameters [100,130] μm
Initial curtain thicknessVariation in the curtain thickness [1.6,2.4] mm
Pressure at driver sectionNegligible measurement noise
DiscretizationError due to temporal and spatial discretization
Model errorError in the drag force model [20]
Gap effectError for not being able to measure DFP due to the gap
Numerical flux schemeError due to numerical scheme
## 4 Error and Uncertainty Reduction
### 4.1 Uncertainty Due to Bias From a Numerical Flux Scheme.
To calculate the propagated uncertainty, it is necessary to run multiple simulations with varying input parameters according to their uncertainty distribution. Since simulations are computationally expensive, surrogate models are often used to replace them. During the design of experiments to build the surrogate model, we observed inconsistencies in the simulation results. Since the physical explanation of these inconsistencies was difficult, we conducted a parametric study to systematically investigate this behavior. The parametric design of experiments was conducted for three major sources of input uncertainty: particle volume fraction, curtain thickness, and particle diameter. Figure 7 shows the parametric design of experiments along four lines in the three-dimensional parameter space, where simulation is conducted at each circle. From the surrogate model, point A that shows a significant deviation from the actual simulation is selected (volume fraction of 23%, particle diameter of 110 μm, and curtain thickness of 2.4 mm). The purpose is to confirm if the simulation results along each line show a physically meaningful trend. Each line is used to identify anomalies in simulation for the corresponding parameter [23]. The QoIs (particle front positions) are calculated as the mean value over random initial particle positions. Since the purpose was to investigate the inconsistency of simulation results, the range of parameters is not the same as the variability of the input parameters reported in Table 1.
Fig. 7
Fig. 7
Close modal
Figure 8 shows the results of QoI at 500 μs along the four lines in Fig. 7. All four lines are normalized in the input variables, where 1 denotes their individual starting points and 0 denotes the ending point (point A). The values of different lines should have the same results at the 0 point, which is {23%, 110 μm, 2.4 mm}. Figure 8(a) shows that the DFP along the four lines is significantly different; it varies in the range of 25 and 60 mm. The behavior of the diameter line departs significantly from the other lines. The discontinuity along the diameter line near the value 0.45 cannot be explained physically. Since the trend is not consistent with physics, it is concluded that it was caused by the numerical error. The behavior was most likely to be associated with the advective upstream splitting method plus (AUSM+) scheme, a numerical flux calculation scheme [24]. The flux of a cell is calculated considering Lagrangian particles traveling in the numerical cells, and the particles are not always distributed evenly in a cell as AUSM+ assumes. This AUSM+ assumption provoked numerical instability when particles in one cell are extremely concentrated. Thus, the AUSM+ scheme was upgraded to the AUSM+up scheme to take into account the particle concentration in a cell [19]. After upgrading the AUSM+up scheme, prediction along the four lines is shown in Fig. 8(b), where the prediction uncertainty is significantly reduced, and the behavior along the different lines is consistent. After improving the numerical scheme, the range of the DFP prediction is reduced to between 25 and 30 mm. However, the prediction value itself at point A is changed significantly: from 40 mm using AUSM+ to 27 mm using AUSM+up. Therefore, by changing the numerical scheme, the numerical uncertainty is significantly reduced while the model error itself is increased. Therefore, the initial simulation with AUSM+ has a large numerical uncertainty such that the model error was unclear (see Fig. 9(a)) as the simulation results overlapped with experiment results due to its large uncertainty. As Fig. 9(b) shows, the inconsistency between the simulation and experimental results for the AUSM+up scheme is slightly larger compared to the AUSM+ scheme. This gives us a lesson that reducing uncertainty (numerical flux scheme) can reveal the hidden model error. In this case, the model error and numerical scheme were compensating for each other. It is noted that the results in Figs. 8 and 9 are slightly different because Fig. 8 is the result for point A while Fig. 9 is the result from three sources of uncertainty.
Fig. 8
Fig. 8
Close modal
Fig. 9
Fig. 9
Close modal
After the implementation of AUSM+up, the model error and uncertainty in the QoI were quantified. Figure 9(b) shows a comparison between the calculated and measured QoIs with uncertainties. The uncertainties are accumulated from the uncertainty sources in Table 1 by propagating them through the simulation. Figure 10 shows the model error in DFP with uncertainty. The contributions from different sources of uncertainty were indicated with bands of different colors. The simulation sampling uncertainty (red) represents the uncertainty in obtaining the mean front position from the repeated simulation runs. The measurement uncertainty (orange) is the uncertainty in the measuring process of the front positions. Both uncertainties are too small to be shown in the figure [14]. The largest contribution is from the uncertainty due to the inconsistency between simulation and experiment due to the gap. The second-largest uncertainty is the measurement processing uncertainty in the initial volume fraction based on X-ray images. The third-largest uncertainty is due to the limited number of experiments and high variability between them. Figure 10 shows that the error of the simulation has a wide distribution because of the large uncertainty. For example, the range of model error at t = 700 μs is [−2,8] mm, which represents uncertainty. Therefore, it is inconclusive if the model error is small or large. In Secs. 4.2 and 4.3, it will be discussed how to reduce the uncertainties so that the model error can be revealed clearly.
Fig. 10
Fig. 10
Close modal
### 4.2 Uncertainty in the Gap Effect.
Based on the ordering of uncertainty in Sec. 4.1, it was concluded that the gap effect is the largest source of uncertainty in the one-dimensional simulation. It is emphasized here that the uncertainty due to the gap was estimated based on expert's opinions. To assess the model adequacy properly, it would be necessary to reduce the uncertainty associated with the gap effect. Two options are possible for UR: (a) use a two-dimensional simulation that can model the gap, or (b) conduct a new shock tube experiment without having the gap [16]. The former can reduce the uncertainty by including the gap in the simulation, while the latter can reduce the uncertainty by removing the gap from the experiment. Both options were explored in this paper to quantify/reduce the uncertainty due to the gap effect. The two-dimensional simulation was performed where the x-axis is in the flow direction and the y-axis is in the depth direction of the test section. DeMauro et al. [16] performed an additional shock tube test by extending the particle curtain to the wall such that no gap exists between the particle curtain and the wall of the test section.
Figure 11 shows the comparisons and the corresponding error estimates with uncertainty for the two options. Figure 11(a) shows 95% confidence intervals of QoIs when the gap effect is included in the two-dimensional simulation. Both experiment and simulation used the particle curtain covering about 80% of that of the test section. Based on these results, Fig. 11(b) shows the distribution of the model error estimate. At 700 μs, the range of model error was [13,17] mm. Due to UR, the uncertainty in model error is reduced by 2.5 times, while the median of model error is increased almost five times compared to that of Fig. 9(b). The reason for having a large error in the 2D simulation results in Fig. 11(b) is due to an incorrect volume fraction model (top-hat distribution) and the numerical scheme AUSM+ (AUSM+up was not available for the 2D simulation). Figure 11(c) shows 95% confidence intervals of QoIs when the gap effect is removed. That is, the particle curtain fills the depth of the test section during the experiment, which is then compared with a one-dimensional simulation. Figure 11(d) shows the corresponding distribution of the model error estimate. At 700 μs, the range of model error is [4,8] mm; that is, the uncertainty is reduced by 2.5 times and the median is increased by two times. Both options significantly reduce uncertainty, while revealing model error.
Fig. 11
Fig. 11
Close modal
An interesting observation from the new experiment is that the influence of the gap was minimal contrary to the comments from experts and the simulation study. Figure 12 shows a comparison between the mean front positions of the experiments with and without the gap. It clearly shows that the influence of the gap is ignorable. This study provided a lesson that some epistemic uncertainties are unintentionally exaggerated. Without quantifying them, they can increase the prediction uncertainty. This corresponds to the case when an erroneous estimate of uncertainty can mislead the UQ process. The follow-up experiments without the gap showed that the gap effect was ignorable.
Fig. 12
Fig. 12
Close modal
### 4.3 Reducing the Uncertainty in the Initial Volume Fraction.
Since the largest uncertainty source, the gap effect, was removed, the second-largest uncertainty source, the initial volume fraction, became the next target for uncertainty reduction. The particle volume fraction can be estimated using X-ray radiography, where the intensity of the image is attenuated when the X-ray beam passes through particles. DeMauro et al. [16] used the Beer–Lambert law to estimate the volume fraction from intensity measurements.
In all simulations so far, a constant volume fraction of 21% was used through the curtain thickness, which was the maximum volume fraction from the X-ray image processing [25]. However, X-ray images showed that the particle volume fraction is not uniform through the curtain thickness. Rather, they showed a bell-shaped density distribution, which was also observed by Wagner et al. [25]. Therefore, the uniformity assumption with the maximum volume fraction uses many more particles than the experiment. Such a conservative estimate of the volume fraction makes the number of particles in the experiment different from that in the simulation. To make the simulation condition consistent with the experiment, it would be necessary to use a variable volume fraction through the curtain thickness. A rigorous UQ study was carried out to reduce the inconsistency in this paper.
An important issue is that the particle volume fraction cannot be measured directly, but it is estimated based on image intensity attenuation. The particle volume fraction was measured from X-ray images through a calibration and fitting process [4], which introduces another source of uncertainty, called measurement processing uncertainty. The uncertainty in the process was propagated to the uncertainty in the measured volume fraction. Finally, a bell-shaped initial particle volume fraction shown in Fig. 13 was identified along with measurement processing uncertainty. This is a significant uncertainty reduction from the constant volume fraction of 21% in the previous simulation.
Fig. 13
Fig. 13
Close modal
After the error and uncertainty in the initial volume fraction were reduced with the bell-shaped profile, Fig. 14 shows the comparison between experiment and simulation, where the uncertainty in the error estimate has been reduced compared to Fig. 11(d). After this uncertainty reduction, the error estimate at 700 μs becomes [4,6] mm. Compared to the initial error estimate of [−2, 8] mm, the reduced error estimate provides much accurate information about the prediction error in the simulation. Now, the uncertainty in model error is less than the mean of model error. Therefore, uncertainty reduction revealed the model error.
Fig. 14
Fig. 14
Close modal
After UR for the initial volume fraction, the largest remaining uncertainty is the sampling uncertainty, which can only be reduced by increasing the number of experiments. Since all experiments were already finished, it was impractical to have more experiments. In addition, the uncertainty in the prediction error in Fig. 14(b) is small enough to reveal the model error. Therefore, it is determined to stop the UR process.
## 5 Concluding Remarks and Lessons Learned
In this paper, the importance of UR is emphasized as a tool to expose the model error in the validation process of the multiphase shock tube simulation. The model error is separated from epistemic uncertainty such that the UQ process yields the error estimate with uncertainty distribution. Initially, the error estimate was not informative due to the large uncertainty in it. Therefore, a series of uncertainty reductions has been conducted until the uncertainty in the model error becomes much smaller than the error itself. The possible sources of error and uncertainty were (a) inconsistency between simulation and experiment, (b) lack of knowledge in physics, and (c) inaccurate information in simulation inputs. It has been shown that removing error and uncertainty does not always improve the prediction accuracy due to the canceling effect between different errors. Initially, the error estimate for the DFP at t = 700 μs was [−2, 8] mm while the measured mean DFP was 65 mm. After rigorous uncertainty reduction, it was [4,6] mm, which revealed the model error.
The next step will be to improve the particle force model of the simulation so that the discrepancy between the simulation and experiment can be reduced. However, the particle force model is composed of five subforce components: quasi-steady force model, pressure gradient force model, added mass force model, inviscid viscous force model, and particle collision model. The improvement of the individual models can be planned based on the importance of them on achieving the desired prediction accuracy. A systematic approach is considered based on the idea of global sensitivity analysis [26].
The lesson learned through UR in this paper is illustrated in Fig. 15. In this paper, success is defined when the experimental results do not contradict the simulations because the uncertainty is larger than the difference between the two means. Failure is defined when the experimental results are clearly different from the simulations because the uncertainty is smaller than the difference between the two means. Figure 15(a) illustrates a scenario where uncertainties in both simulation and experiment are so large that validation is not useful. This was the case when the initial shock tube simulation was finished. Uncertainty is considered too large when the trend of prediction/measurement cannot be determined when parameters change. For both simulation and experiment, the dashed line represents the mean prediction or measurement, while the range represents uncertainty associated with predictions or measurements. Even if the two distributions are almost overlapped, it cannot confirm that the model has a prediction capability. This case is called “empty success” since it does not yield a meaningful conclusion. Once the uncertainties in both simulation and experiment are reduced enough, it is possible that the validation may reveal the model error as shown in Fig. 15(b). This was the case when the shock tube simulation and experiment went through the rigorous UR process. Uncertainty needs to be reduced until the trend of function can be clearly shown when parameters change. Even if the validation fails, it provides useful information for improving the model. Therefore, this case is referred to as “useful failure”. The definition of validation in ASME standards and AIAA guides includes the model improvement process, which is only possible after rigorous UR. When multiple models are involved in simulation, it is possible that errors may cancel each other. When the error from one model (e1) is compensated with that of other models (e2), the final prediction looks accurate. However, improving the second model may increase the magnitude of the prediction error. We call it “deceptive success,” as shown in Fig. 15(c). This happened before an additional experiment was conducted with the gap. It is necessary to conduct a series of uncertainty reduction to have meaningful validation.
Fig. 15
Fig. 15
Close modal
## Acknowledgment
This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.
## Funding Data
• National Nuclear Security Administration (Grant No. DE-NA0002378; Funder ID: 10.13039/100006168).
## References
1.
ASME
,
2009
, “
Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer
,” ASME, New York, Standard No. VV20.
2.
AIAA
,
2002
, “
Guide for the Verification and Validation of Computational Fluid Dynamics Simulations
,”
AIAA
Paper No. G-077-1998. 10.1115/G-077-1998
3.
Sankararaman
,
S.
, and
,
S.
,
2015
, “
Integration of Model Verification, Validation, and Calibration for Uncertainty Quantification in Engineering Systems
,”
Reliab. Eng. Syst. Saf.
,
138
, pp.
194
209
.10.1016/j.ress.2015.01.023
4.
Park
,
C.
,
Matthew
,
J.
,
Kim
,
N. H.
, and
Haftka
,
R. T.
, March
2019
, “
Epistemic Uncertainty Stemming From Measurement processing - A Case Study of Multiphase Shock Tube Experiments
,”
ASME J. Verif. Valid. Uncertainty Quantif.
,
3
(
4
), p.
041001
.10.1115/1.4042814
5.
Kim
,
H.-S.
,
Jang
,
S.-G.
,
Kim
,
N. H.
, and
Choi
,
J.-H.
,
2016
, “
Statistical Calibration and Validation of Elasto-Plastic Insertion Analysis in Pyrotechnically Actuated Deviced
,”
Struct. Multidiscip. Optim.
,
54
(
6
), pp.
1573
1585
.10.1007/s00158-016-1545-8
6.
Thacker
,
B. H.
, and
Paez
,
T. L.
,
2014
, “
A Simple Probabilistic Validation Metric for the Comparison of Uncertain Model and Test Results
,”
AIAA
Paper No. 2014-0121.10.2514/6.2014-0121
7.
Sankararaman
,
S.
,
Ling
,
Y.
, and
,
S.
,
2011
, “
Uncertainty Quantification and Model Validation of Fatigue Crack Growth Prediction
,”
Eng. Fract. Mech.
,
78
(
7
), pp.
1487
1504
.10.1016/j.engfracmech.2011.02.017
8.
Bae
,
S.
,
Kim
,
N. H.
, and
Jang
,
S.-G.
,
2018
, “
Reliability-Based Design Optimization Under Sampling Uncertainty: Shifting Design Versus Shaping Uncertainty
,”
Struct. Multidiscip. Optim.
,
57
(
5
), pp.
1845
1855
.10.1007/s00158-018-1936-0
9.
Xi
,
Z.
,
Fu
,
Y.
, and
Yang
,
R.-J.
,
2013
, “
Model Bias Characterization in the Design Space Under Uncertainty
,”
Int. J. Perform. Eng.
,
9
(
4
), pp.
433
444
.10.23940/ijpe.13.4.p433.mag
10.
Romero
,
V. J.
,
2007
, “
Validated Model? Not So Fast—The Need for Model “Conditioning” as an Essential Addendum to Model Validation
,”
AIAA
Paper No. 2007-1953.10.2514/6.2007-1953
11.
Park
,
C.
,
Fernández-Godino
,
M. G.
,
Kim
,
N. H.
, and
Haftka
,
R. T.
,
2016
, “
Validation, Uncertainty Quantification and Uncertainty Reduction for a Shock Tube Simulation
,”
AIAA
Paper No. 2016–1192.10.2514/6.2016-1192
12.
Zhang
,
F.
,
Frost
,
D. L.
,
Thibault
,
P. A.
, and
Murray
,
S. B.
,
2001
, “
Explosive Dispersal of Solid Particles
,”
Shock Waves
,
10
(
6
), pp.
431
443
.10.1007/PL00004050
13.
Hughes
,
K. T.
,
Balachandar
,
S.
,
Diggs
,
A.
,
Haftka
,
R. T.
,
Kim
,
N. H.
, and
Littrell
,
D.
,
2020
, “
Simulation-Driven Design of Experiments Examining the Large-Scale, Explosive Dispersal of Particles
,”
Shock Waves
,
30
(
4
), pp.
325
347
.10.1007/s00193-019-00927-x
14.
Wagner
,
J. L.
,
Beresh
,
S. J.
,
Kearney
,
S. P.
,
Trott
,
W. M.
,
Castaneda
,
J. N.
,
Pruett
,
B. O.
, and
Baer
,
M. R.
,
2012
, “
A Multiphase Shock Tube for Shock Wave Interactions With Dense Particle Fields
,”
Exp. Fluids
,
52
(
6
), pp.
1507
1517
.10.1007/s00348-012-1272-x
15.
Linne
,
M.
,
2013
, “
Imaging in the Optically Dense Regions of a Spray: A Review of Developing Techniques
,”
Prog. Energy Combust. Sci.
,
39
(
5
), pp.
403
440
.10.1016/j.pecs.2013.06.001
16.
DeMauro
,
E. P.
,
Wagner
,
J. L.
,
DeChant
,
L. J.
,
Beresh
,
S.
,
Farias
,
J.
,
Turpin
,
P.
,
Sealy
,
A.
,
Albert
,
W. S.
, and
Sanderson
,
P.
,
2017
, “
Measurements of the Initial Transient of a Dense Particle Curtain Following Shock Wave Impingement
,”
AIAA
Paper No. 2017–1466.10.2514/6.2017-1466
17.
Coleman
,
H. W.
, and
Steele
,
W. G.
,
2009
,
Experimentation, Validation, and Uncertainty Analysis for Engineers
, 3rd ed.,
Wiley
,
Hoboken, NJ
.
18.
Wagner
,
J. L.
,
Beresh
,
S. J.
,
Kearney
,
S. P.
,
Pruett
,
B. O.
, and
Wright
,
E. K.
,
2012
, “
Shock Tube Investigation of Quasi-Steady Drag in Shock-Particle Interactions
,”
Phys. Fluids
,
24
(
12
), p.
123301
.10.1063/1.4768816
19.
Liou
,
M. S.
,
Chang
,
C. H.
,
Nguyen
,
L.
, and
Theofanous
,
T. G.
,
2008
, “
How to Solve Compressible Multifluid Equations: A Simple, Robust, and Accurate Method
,”
AIAA J.
,
46
(
9
), pp.
2345
2356
.10.2514/1.34793
20.
Nili
,
S.
,
Park
,
C.
,
Haftka
,
R. T.
,
Kim
,
N. H.
, and
Balachandar
,
S.
,
2017
, “
Sensitivity Analysis of Unsteady Force Models for Two-Way Coupled Dispersed Multiphase Flow
,”
AIAA
Paper No. 2017–3800.10.2514/6.2017-3800
21.
Hughes
,
K. T.
,
Balachandar
,
S.
,
Kim
,
N. H.
,
Park
,
C.
,
Haftka
,
R. T.
,
Diggs
,
A.
,
Littrell
,
D.
, and
Darr
,
J.
,
2018
, “
Forensic Uncertainty Quantification for Experiments on the Explosively Driven Motion of Particles
,”
ASME J. Verif. Valid. Uncertainty Quantif.
,
3
(
4
), p.
041004
.10.1115/1.4043478
22.
Nili
,
S.
,
2019
,
Error Analysis of Particle Force Model of an Euler-Lagrange Multiphase Dispersed Flow
,
University of Florida
, Gainesville, FL.
23.
Fernandez-Godino
,
M. G.
,
Diggs
,
A.
,
Park
,
C.
,
Kim
,
N. H.
, and
Haftka
,
R. T.
,
2016
, “
Anomaly Detection Via Groups of Simulations
,”
AIAA
Paper No. 2016–1195.10.2514/6.2016-1195
24.
Liou
,
M. S.
,
1996
, “
A Sequel to AUSM: AUSM+
,”
J. Comput. Phys.
,
129
(
2
), pp.
364
382
.10.1006/jcph.1996.0256
25.
Wagner
,
J. L.
,
Kearney
,
S. P.
,
Beresh
,
S. J.
,
Demauro
,
E. P.
, and
Pruett
,
B. O.
,
2015
, “
Flash X-Ray Measurements on the Shock-Induced Dispersal of a Dense Particle Curtain
,”
Exp. Fluids
,
56
(
12
), p.
213
.10.1007/s00348-015-2087-3
26.
Nili
,
S.
,
Park
,
C.
,
Kim
,
N. H.
,
Haftka
,
R. T.
, and
Balachandar
,
S.
,
2021
, “
Prioritizing Possible Force Models Error in Multiphase Flow Using Global Sensitivity Analysis
,”
AIAA J.
,
59
(
5
), pp.
1749
1759
. 10.2514/1.J058657 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 17, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9488202929496765, "perplexity": 963.703505401339}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337889.44/warc/CC-MAIN-20221006222634-20221007012634-00590.warc.gz"} |
http://mathhelpforum.com/calculus/149753-show-how-two-series-same-sum.html | # Thread: Show how two series as the same Sum
1. ## Show how two series as the same Sum
show that the sum of the first 2n terms of the series 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5........................is the same as the sum of the first n terms of the series 1/1*2 + 1/2*3 + 1/3*4 +1/4*5................... Do these series converge? what is the sum of the first 2n+1 terms of the first series and how to get the sum?
2. (1) Hint: 1+(-1/2+1/2)+(-1/3+1/3)+(-1/4+1/4)+(-1/5+1/5)+...+(-1/(2n) + 1/(2n))
(2) Hint: 1/(1*2) + 1/(2*3) + 1/(3*4) +1/(4*5) + ... + 1/(n*(n+1))
1/(n*(n+1)) = 1/n - 1/(n+1)
3. The first one obviously converges to 1. $1+(\frac{-1}{2}+\frac{1}{2})+(\frac{-1}{3}+\frac{1}{3})+...$ since $(\frac{-1}{2}+\frac{1}{2})=0$ they eliminate eachother.
The second is $\sum_{1}^{n}\frac{n}{n(n+1)}=\sum_{1}^{n}\frac{1}{ n}-\frac{1}{n+1}$ $=(\frac{1}{1}-\frac{1}{2})+(\frac{1}{2}-\frac{1}{3})+...=1+(\frac{-1}{2}+\frac{1}{2})+(\frac{-1}{3}+\frac{1}{3})+...=1$
4. thank u guys i was mistaken 2n a 2xSn=2x(1+1/2-1/2......
5. Oh, i missed the 2n, but the argument would be very similar, use p0oints hints | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9501450061798096, "perplexity": 938.1814693584005}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105955.66/warc/CC-MAIN-20170819235943-20170820015943-00111.warc.gz"} |
http://stackoverflow.com/questions/3865453/working-with-files-with-anchors-which-options-are-there-for-java | # Working with files with anchors, which options are there for Java?
I am working with files (reading, writing and copying) in my Java application, java.io.File and commons-io were perfect for this kind of tasks.
Right now, I can link to HTML in this way:
Z:\an absolute\path\to\a\file.html
But, I need to provide support for anchors too:
Z:\an absolute\path\to\a\file.html#anchor
keeping the system-independence obtained by using java.io.File. So, I will need to extract the path and the anchor, I wonder whether it will be as easy as searching for a sharp occurrence.
-
java.io.File includes a constructor that accepts a URI, which can represent all kinds of resources, included URLs and local files (see the rfc). URI's also meets your requirements of supporting anchors, and extracting path information (through instance.getPath()).
-
When trying to convert from java.io.File to java.net.URI using java.io.File.toURI() method the sharp (#) character is escaped. The final users don't care about URIs, they care about using their always-known-windows paths. In my case this won't be the solution, unless there is a more straighforward way to manage this issue. – Alexander Oct 6 '10 at 8:25
I may have been unclear. I'm suggesting that you refactor your code to use URI's for all resources and to convert them as necessary, depending on what you need to do. This way the users can deal with local paths, or URL's, you just need to create the appropriate object for performing io. If your code doesn't make it simple to do that, then I see your dilemma. – Dana the Sane Oct 6 '10 at 15:42
File f = new File("Z:\\path\\to\\a\\file.html#anchor");
String anchor = f.toURL().getRef(); //note: toURL is deprecated
If you look at the java source you will see that it is as simple as:
String file = "Z:\\path\\to\\a\\file.html#anchor";
int ind = file.indexOf('#');
String anchor = ind < 0 ? null: file.substring(ind + 1);
-
This implies refactoring the whole code and taking care of not been able to use common java.io.File methods. – Alexander Oct 6 '10 at 8:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.380913108587265, "perplexity": 2339.0281305171584}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131293580.17/warc/CC-MAIN-20150323172133-00106-ip-10-168-14-71.ec2.internal.warc.gz"} |
http://www.astropa.inaf.it/personal-pages/mario-giuseppe-guarcello/bibliografia/ | # Bibliography
### 2019
1. CSI 2264: Simultaneous optical and X-ray variability in the pre-main sequence stars of NGC 2264. II. Photometric variability, magnetic activity, and rotation in class III objects and stars with transition disks
Abstract
Guarcello , M. G.;Flaccomio, E.;Micela, G.;Argiroffi, C.;Sciortino, S.;Venuti, L.;Stauffer, J.;Rebull, L.;Cody, A. M.
Astronomy & Astrophysics, Volume 628, id.A74, 49 pp.
Aug 2019
2. Simultaneous Kepler/K2 and XMM-Netwon observations of superflares in the Pleiades
Abstract
Flares are powerful events ignited by a sudden release of magnetic energy. With the aim of studying flares in the 125-Myr-old stars in the Pleiades observed simultaneously in optical and X-ray light, we obtained new XMM-Newton observations of this cluster during the observations of Kepler K2 Campaign 4. Our objective is to characterize the most powerful flares observed in both bands and to constrain the energy released in the optical and X-ray, the geometry of the loops, and their time evolution. We aim to compare our results to existing studies of flares occurring in the Sun and stars at different ages. We selected bright X-ray/optical flares occurred in 12 known members of the Pleiades from their K2 and XMM-Newton light curves. The sample includes ten K-M stars, one F9 star, and one G8 star. Flare average properties were obtained from integrated analysis of the light curves during the flares. The time evolution of the plasma in the magnetic loops is constrained with time-resolved X-ray spectral analysis. Most of the flares studied in this work emitted more energy in optical than in X-rays, as in most solar flares, even if the Pleiades flares output a larger fraction of their total energy in X-rays than typical solar flares do. Additionally, the energy budget in the two bands is weakly correlated. We also found comparable flare duration in optical and X-rays and observed that rapidly rotating stars (e.g., with rotation period shorter than 0.5 days) preferentially host short flares. We estimated the slope of the cooling path of the flares in the log(EM)-versus-log(T) plane. The values we obtained are affected by large uncertainties, but their nominal values suggest that the flares analyzed in this paper are mainly due to single loops with no sustained heating occurring during the cooling phase. We also observed and analyzed oscillations with a period of 500 s during one of the flares.
Guarcello , M. G.;Micela, G.;Sciortino, S.;Lopez-Santiago, J.;Argiroffi, C.;Reale, F.;Flaccomio, E.;Alvarado-Gomez, J. D.;Antoniou, V.;Drake, J. J.;Pillitteri, I.;Rebull, L. M.;Stauffer, J.
Astronomy & Astrophysics, Volume 622, id.A210, 24 pp.
Jan 2019
### 2018
1. A chemical survey of exoplanets with ARIEL ADS CITATION
Abstract
Thousands of exoplanets have now been discovered with a huge range of masses, sizes and orbits: from rocky Earth-like planets to large gas giants grazing the surface of their host star. However, the essential nature of these exoplanets remains largely mysterious: there is no known, discernible pattern linking the presence, size, or orbital parameters of a planet to the nature of its parent star. We have little idea whether the chemistry of a planet is linked to its formation environment, or whether the type of host star drives the physics and chemistry of the planet’s birth, and evolution. ARIEL was conceived to observe a large number ( 1000) of transiting planets for statistical understanding, including gas giants, Neptunes, super-Earths and Earth-size planets around a range of host star types using transit spectroscopy in the 1.25-7.8 μm spectral range and multiple narrow-band photometry in the optical. ARIEL will focus on warm and hot planets to take advantage of their well-mixed atmospheres which should show minimal condensation and sequestration of high-Z materials compared to their colder Solar System siblings. Said warm and hot atmospheres are expected to be more representative of the planetary bulk composition. Observations of these warm/hot exoplanets, and in particular of their elemental composition (especially C, O, N, S, Si), will allow the understanding of the early stages of planetary and atmospheric formation during the nebular phase and the following few million years. ARIEL will thus provide a representative picture of the chemical nature of the exoplanets and relate this directly to the type and chemical environment of the host star. ARIEL is designed as a dedicated survey mission for combined-light spectroscopy, capable of observing a large and well-defined planet sample within its 4-year mission lifetime. Transit, eclipse and phase-curve spectroscopy methods, whereby the signal from the star and planet are differentiated using knowledge of the planetary ephemerides, allow us to measure atmospheric signals from the planet at levels of 10-100 part per million (ppm) relative to the star and, given the bright nature of targets, also allows more sophisticated techniques, such as eclipse mapping, to give a deeper insight into the nature of the atmosphere. These types of observations require a stable payload and satellite platform with broad, instantaneous wavelength coverage to detect many molecular species, probe the thermal structure, identify clouds and monitor the stellar activity. The wavelength range proposed covers all the expected major atmospheric gases from e.g. H2O, CO2, CH4 NH3, HCN, H2S through to the more exotic metallic compounds, such as TiO, VO, and condensed species. Simulations of ARIEL performance in conducting exoplanet surveys have been performed – using conservative estimates of mission performance and a full model of all significant noise sources in the measurement – using a list of potential ARIEL targets that incorporates the latest available exoplanet statistics. The conclusion at the end of the Phase A study, is that ARIEL – in line with the stated mission objectives – will be able to observe about 1000 exoplanets depending on the details of the adopted survey strategy, thus confirming the feasibility of the main science objectives.
Tinetti, Giovanna;Drossart, Pierre;Eccleston, Paul;Hartogh, Paul;Heske, Astrid;Leconte, Jérémy;Micela, Giusi;Ollivier, Marc;Pilbratt, Göran;Puig, Ludovic;Turrini, Diego;Vandenbussche, Bart;Wolkenberg, Paulina;Beaulieu, Jean-Philippe;Buchave, Lars A.;Ferus, Martin;Griffin, Matt;Guedel, Manuel;Justtanont, Kay;Lagage, Pierre-Olivier;Machado, Pedro;Malaguti, Giuseppe;Min, Michiel;Nørgaard-Nielsen, Hans Ulrik;Rataj, Mirek;Ray, Tom;Ribas, Ignasi;Swain, Mark;Szabo, Robert;Werner, Stephanie;Barstow, Joanna;Burleigh, Matt;Cho, James;du Foresto, Vincent Coudé;Coustenis, Athena;Decin, Leen;Encrenaz, Therese;Galand, Marina;Gillon, Michael;Helled, Ravit;Morales, Juan Carlos;Muñoz, Antonio García;Moneti, Andrea;Pagano, Isabella;Pascale, Enzo;Piccioni, Giuseppe;Pinfield, David;Sarkar, Subhajit;Selsis, Franck;Tennyson, Jonathan;Triaud, Amaury;Venot, Olivia;Waldmann, Ingo;Waltham, David;Wright, Gillian;Amiaux, Jerome;Auguères, Jean-Louis;Berthé, Michel;Bezawada, Naidu;Bishop, Georgia;Bowles, Neil;Coffey, Deirdre;Colomé, Josep;Crook, Martin;Crouzet, Pierre-Elie;Da Peppo, Vania;Sanz, Isabel Escudero;Focardi, Mauro;Frericks, Martin;Hunt, Tom;Kohley, Ralf;Middleton, Kevin;Morgante, Gianluca;Ottensamer, Roland;Pace, Emanuele;Pearson, Chris;Stamper, Richard;Symonds, Kate;Rengel, Miriam;Renotte, Etienne;Ade, Peter;Affer, Laura;Alard, Christophe;Allard, Nicole;Altieri, Francesca;André, Yves;Arena, Claudio;Argyriou, Ioannis;Aylward, Alan;Baccani, Cristian;Bakos, Gaspar;Banaszkiewicz, Marek;Barlow, Mike;Batista, Virginie;Bellucci, Giancarlo;Benatti, Serena;Bernardi, Pernelle;Bézard, Bruno;Blecka, Maria;Bolmont, Emeline;Bonfond, Bertrand;Bonito, Rosaria;Bonomo, Aldo S.;Brucato, John Robert;Brun, Allan Sacha;Bryson, Ian;Bujwan, Waldemar;Casewell, Sarah;Charnay, Bejamin;Pestellini, Cesare Cecchi;Chen, Guo;Ciaravella, Angela;Claudi, Riccardo;Clédassou, Rodolphe;Damasso, Mario;Damiano, Mario;Danielski, Camilla;Deroo, Pieter;Di Giorgio, Anna Maria;Dominik, Carsten;Doublier, Vanessa;Doyle, Simon;Doyon, René;Drummond, Benjamin;Duong, Bastien;Eales, Stephen;Edwards, Billy;Farina, Maria;Flaccomio, Ettore;Fletcher, Leigh;Forget, François;Fossey, Steve;Fränz, Markus;Fujii, Yuka;García-Piquer, Álvaro;Gear, Walter;Geoffray, Hervé;Gérard, Jean Claude;Gesa, Lluis;Gomez, H.;Graczyk, Rafał;Griffith, Caitlin;Grodent, Denis;Guarcello , Mario Giuseppe;Gustin, Jacques;Hamano, Keiko;Hargrave, Peter;Hello, Yann;Heng, Kevin;Herrero, Enrique;Hornstrup, Allan;Hubert, Benoit;Ida, Shigeru;Ikoma, Masahiro;Iro, Nicolas;Irwin, Patrick;Jarchow, Christopher;Jaubert, Jean;Jones, Hugh;Julien, Queyrel;Kameda, Shingo;Kerschbaum, Franz;Kervella, Pierre;Koskinen, Tommi;Krijger, Matthijs;Krupp, Norbert;Lafarga, Marina;Landini, Federico;Lellouch, Emanuel;Leto, Giuseppe;Luntzer, A.;Rank-Lüftinger, Theresa;Maggio, Antonio;Maldonado, Jesus;Maillard, Jean-Pierre;Mall, Urs;Marquette, Jean-Baptiste;Mathis, Stephane;Maxted, Pierre;Matsuo, Taro;Medvedev, Alexander;Miguel, Yamila;Minier, Vincent;Morello, Giuseppe;Mura, Alessandro;Narita, Norio;Nascimbeni, Valerio;Nguyen Tong, N.;Noce, Vladimiro;Oliva, Fabrizio;Palle, Enric;Palmer, Paul;Pancrazzi, Maurizio;Papageorgiou, Andreas;Parmentier, Vivien;Perger, Manuel;Petralia, Antonino;Pezzuto, Stefano;Pierrehumbert, Ray;Pillitteri, Ignazio;Piotto, Giampaolo;Pisano, Giampaolo;Prisinzano, Loredana;Radioti, Aikaterini;Réess, Jean-Michel;Rezac, Ladislav;Rocchetto, Marco;Rosich, Albert;Sanna, Nicoletta;Santerne, Alexandre;Savini, Giorgio;Scandariato, Gaetano;Sicardy, Bruno;Sierra, Carles;Sindoni, Giuseppe;Skup, Konrad;Snellen, Ignas;Sobiecki, Mateusz;Soret, Lauriane;Sozzetti, Alessandro;Stiepen, A.;Strugarek, Antoine;Taylor, Jake;Taylor, William;Terenzi, Luca;Tessenyi, Marcell;Tsiaras, Angelos;Tucker, C.;Valencia, Diana;Vasisht, Gautam;Vazan, Allona;Vilardell, Francesc;Vinatier, Sabrine;Viti, Serena;Waters, Rens;Wawer, Piotr;Wawrzaszek, Anna;Whitworth, Anthony;Yung, Yuk L.;Yurchenko, Sergey N.;Osorio, María Rosa Zapatero;Zellem, Robert;Zingales, Tiziano;Zwart, Frans
Experimental Astronomy, Volume 46, Issue 1, pp.135-209
Nov 2018
2. A chemical survey of exoplanets with ARIEL ADS CITATION
Abstract
Thousands of exoplanets have now been discovered with a huge range of masses, sizes and orbits: from rocky Earth-like planets to large gas giants grazing the surface of their host star. However, the essential nature of these exoplanets remains largely mysterious: there is no known, discernible pattern linking the presence, size, or orbital parameters of a planet to the nature of its parent star. We have little idea whether the chemistry of a planet is linked to its formation environment, or whether the type of host star drives the physics and chemistry of the planet’s birth, and evolution. ARIEL was conceived to observe a large number ( 1000) of transiting planets for statistical understanding, including gas giants, Neptunes, super-Earths and Earth-size planets around a range of host star types using transit spectroscopy in the 1.25-7.8 μm spectral range and multiple narrow-band photometry in the optical. ARIEL will focus on warm and hot planets to take advantage of their well-mixed atmospheres which should show minimal condensation and sequestration of high-Z materials compared to their colder Solar System siblings. Said warm and hot atmospheres are expected to be more representative of the planetary bulk composition. Observations of these warm/hot exoplanets, and in particular of their elemental composition (especially C, O, N, S, Si), will allow the understanding of the early stages of planetary and atmospheric formation during the nebular phase and the following few million years. ARIEL will thus provide a representative picture of the chemical nature of the exoplanets and relate this directly to the type and chemical environment of the host star. ARIEL is designed as a dedicated survey mission for combined-light spectroscopy, capable of observing a large and well-defined planet sample within its 4-year mission lifetime. Transit, eclipse and phase-curve spectroscopy methods, whereby the signal from the star and planet are differentiated using knowledge of the planetary ephemerides, allow us to measure atmospheric signals from the planet at levels of 10-100 part per million (ppm) relative to the star and, given the bright nature of targets, also allows more sophisticated techniques, such as eclipse mapping, to give a deeper insight into the nature of the atmosphere. These types of observations require a stable payload and satellite platform with broad, instantaneous wavelength coverage to detect many molecular species, probe the thermal structure, identify clouds and monitor the stellar activity. The wavelength range proposed covers all the expected major atmospheric gases from e.g. H2O, CO2, CH4 NH3, HCN, H2S through to the more exotic metallic compounds, such as TiO, VO, and condensed species. Simulations of ARIEL performance in conducting exoplanet surveys have been performed – using conservative estimates of mission performance and a full model of all significant noise sources in the measurement – using a list of potential ARIEL targets that incorporates the latest available exoplanet statistics. The conclusion at the end of the Phase A study, is that ARIEL – in line with the stated mission objectives – will be able to observe about 1000 exoplanets depending on the details of the adopted survey strategy, thus confirming the feasibility of the main science objectives.
Tinetti, Giovanna;Drossart, Pierre;Eccleston, Paul;Hartogh, Paul;Heske, Astrid;Leconte, Jérémy;Micela, Giusi;Ollivier, Marc;Pilbratt, Göran;Puig, Ludovic;Turrini, Diego;Vandenbussche, Bart;Wolkenberg, Paulina;Beaulieu, Jean-Philippe;Buchave, Lars A.;Ferus, Martin;Griffin, Matt;Guedel, Manuel;Justtanont, Kay;Lagage, Pierre-Olivier;Machado, Pedro;Malaguti, Giuseppe;Min, Michiel;Nørgaard-Nielsen, Hans Ulrik;Rataj, Mirek;Ray, Tom;Ribas, Ignasi;Swain, Mark;Szabo, Robert;Werner, Stephanie;Barstow, Joanna;Burleigh, Matt;Cho, James;du Foresto, Vincent Coudé;Coustenis, Athena;Decin, Leen;Encrenaz, Therese;Galand, Marina;Gillon, Michael;Helled, Ravit;Morales, Juan Carlos;Muñoz, Antonio García;Moneti, Andrea;Pagano, Isabella;Pascale, Enzo;Piccioni, Giuseppe;Pinfield, David;Sarkar, Subhajit;Selsis, Franck;Tennyson, Jonathan;Triaud, Amaury;Venot, Olivia;Waldmann, Ingo;Waltham, David;Wright, Gillian;Amiaux, Jerome;Auguères, Jean-Louis;Berthé, Michel;Bezawada, Naidu;Bishop, Georgia;Bowles, Neil;Coffey, Deirdre;Colomé, Josep;Crook, Martin;Crouzet, Pierre-Elie;Da Peppo, Vania;Sanz, Isabel Escudero;Focardi, Mauro;Frericks, Martin;Hunt, Tom;Kohley, Ralf;Middleton, Kevin;Morgante, Gianluca;Ottensamer, Roland;Pace, Emanuele;Pearson, Chris;Stamper, Richard;Symonds, Kate;Rengel, Miriam;Renotte, Etienne;Ade, Peter;Affer, Laura;Alard, Christophe;Allard, Nicole;Altieri, Francesca;André, Yves;Arena, Claudio;Argyriou, Ioannis;Aylward, Alan;Baccani, Cristian;Bakos, Gaspar;Banaszkiewicz, Marek;Barlow, Mike;Batista, Virginie;Bellucci, Giancarlo;Benatti, Serena;Bernardi, Pernelle;Bézard, Bruno;Blecka, Maria;Bolmont, Emeline;Bonfond, Bertrand;Bonito, Rosaria;Bonomo, Aldo S.;Brucato, John Robert;Brun, Allan Sacha;Bryson, Ian;Bujwan, Waldemar;Casewell, Sarah;Charnay, Bejamin;Pestellini, Cesare Cecchi;Chen, Guo;Ciaravella, Angela;Claudi, Riccardo;Clédassou, Rodolphe;Damasso, Mario;Damiano, Mario;Danielski, Camilla;Deroo, Pieter;Di Giorgio, Anna Maria;Dominik, Carsten;Doublier, Vanessa;Doyle, Simon;Doyon, René;Drummond, Benjamin;Duong, Bastien;Eales, Stephen;Edwards, Billy;Farina, Maria;Flaccomio, Ettore;Fletcher, Leigh;Forget, François;Fossey, Steve;Fränz, Markus;Fujii, Yuka;García-Piquer, Álvaro;Gear, Walter;Geoffray, Hervé;Gérard, Jean Claude;Gesa, Lluis;Gomez, H.;Graczyk, Rafał;Griffith, Caitlin;Grodent, Denis;Guarcello , Mario Giuseppe;Gustin, Jacques;Hamano, Keiko;Hargrave, Peter;Hello, Yann;Heng, Kevin;Herrero, Enrique;Hornstrup, Allan;Hubert, Benoit;Ida, Shigeru;Ikoma, Masahiro;Iro, Nicolas;Irwin, Patrick;Jarchow, Christopher;Jaubert, Jean;Jones, Hugh;Julien, Queyrel;Kameda, Shingo;Kerschbaum, Franz;Kervella, Pierre;Koskinen, Tommi;Krijger, Matthijs;Krupp, Norbert;Lafarga, Marina;Landini, Federico;Lellouch, Emanuel;Leto, Giuseppe;Luntzer, A.;Rank-Lüftinger, Theresa;Maggio, Antonio;Maldonado, Jesus;Maillard, Jean-Pierre;Mall, Urs;Marquette, Jean-Baptiste;Mathis, Stephane;Maxted, Pierre;Matsuo, Taro;Medvedev, Alexander;Miguel, Yamila;Minier, Vincent;Morello, Giuseppe;Mura, Alessandro;Narita, Norio;Nascimbeni, Valerio;Nguyen Tong, N.;Noce, Vladimiro;Oliva, Fabrizio;Palle, Enric;Palmer, Paul;Pancrazzi, Maurizio;Papageorgiou, Andreas;Parmentier, Vivien;Perger, Manuel;Petralia, Antonino;Pezzuto, Stefano;Pierrehumbert, Ray;Pillitteri, Ignazio;Piotto, Giampaolo;Pisano, Giampaolo;Prisinzano, Loredana;Radioti, Aikaterini;Réess, Jean-Michel;Rezac, Ladislav;Rocchetto, Marco;Rosich, Albert;Sanna, Nicoletta;Santerne, Alexandre;Savini, Giorgio;Scandariato, Gaetano;Sicardy, Bruno;Sierra, Carles;Sindoni, Giuseppe;Skup, Konrad;Snellen, Ignas;Sobiecki, Mateusz;Soret, Lauriane;Sozzetti, Alessandro;Stiepen, A.;Strugarek, Antoine;Taylor, Jake;Taylor, William;Terenzi, Luca;Tessenyi, Marcell;Tsiaras, Angelos;Tucker, C.;Valencia, Diana;Vasisht, Gautam;Vazan, Allona;Vilardell, Francesc;Vinatier, Sabrine;Viti, Serena;Waters, Rens;Wawer, Piotr;Wawrzaszek, Anna;Whitworth, Anthony;Yung, Yuk L.;Yurchenko, Sergey N.;Osorio, María Rosa Zapatero;Zellem, Robert;Zingales, Tiziano;Zwart, Frans
Experimental Astronomy, Online First
Sep 2018
3. A multi-wavelength view of magnetic flaring from PMS stars
Abstract
Flares from the Sun and other stars are most prominently observed in the soft X-ray band. Most of the radiated energy, however, is released at optical/UV wavelengths. In spite of decades of investigation, the physics of flares is not fully understood. Even less is known about the powerful flares routinely observed from pre-main sequence stars, which might significantly influence the evolution of circumstellar disks. Observations of the NGC2264 star forming region were obtained in Dec. 2011, simultaneously with three telescopes, Chandra (X-rays), CoRoT (optical), and Spitzer (mIR), as part of the “Coordinated Synoptic Investigation of NGC2264” (CSI-NGC2264). Shorter Chandra and CoRoT observations were also obtained in March 2008. We analyzed the lightcurves to detect X-ray flares with an optical and/or mIR counterpart. Basic flare properties from the three datasets, such as emitted energies and peak luminosities, were then compared to constrain the spectral energy distribution of the flaring emission and the physical conditions of the emitting regions. Flares from stars with and without circumstellar disks were also compared to establish any difference that might be attributed to the presence of disks. Seventy-eight X-ray flares with an optical and/or mIR counterpart were detected. Their optical emission is found to correlate well with, and to be significantly larger than, the X-ray emission. The slopes of the correlations suggest that the difference becomes smaller for the most powerful flares. The mIR flare emission seems to be strongly affected by the presence of a circumstellar disk: flares from stars with disks have a stronger mIR emission with respect to stars without disks. This might be attributed to the reprocessing of the optical (and X-ray) flare emission by the inner circumstellar disk, providing evidence for flare-induced disk heating.
Flaccomio, E.;Micela, G.;Sciortino, S.;Cody, A. M.;Guarcello , M. G.;Morales-Calderòn, M.;Rebull, L.;Stauffer, J. R.
Astronomy & Astrophysics, Volume 620, id.A55, 34 pp.
Jul 2018
4. Low mass star formation and subclustering in the HII regions RCW 32, 33 and 27 of the Vela Molecular Ridge. A photometric diagnostics to identify M-type stars
Abstract
Most stars born in clusters and recent results suggest that star formation (SF) preferentially occurs in subclusters. Studying the morphology and SF history of young clusters is crucial to understanding early SF. We identify the embedded clusters of young stellar objects (YSOs) down to M stars, in the HII regions RCW33, RCW32 and RCW27 of the Vela Molecular Ridge. Our aim is to characterise their properties, such as morphology and extent of the clusters in the three HII regions, derive stellar ages and the connection of the SF history with the environment. Through public photometric surveys such as Gaia, VPHAS, 2MASS and Spitzer/GLIMPSE, we identify YSOs with IR, Halpha and UV excesses, as signature of circumstellar disks and accretion. In addition, we implement a method to distinguish M dwarfs and giants, by comparing the reddening derived in several optical/IR color-color diagrams, assuming suitable theoretical models. Since this diagnostic is sensitive to stellar gravity, the procedure allows us to identify pre-main sequence stars. We find a large population of YSOs showing signatures of circumstellar disks with or without accretion. In addition, with the new technique of M-type star selection, we find a rich population of young M stars with a spatial distribution strongly correlated to the more massive population. We find evidence of three young clusters, with different morphology. In addition, we identify field stars falling in the same region, by securely classifying them as giants and foreground MS stars. We identify the embedded population of YSOs, down to about 0.1 Msun, associated with the HII regions RCW33, RCW32 and RCW27 and the clusters Vela T2, Cr197 and Vela T1, respectively, showing very different morphologies. Our results suggest a decreasing SF rate in Vela T2 and triggered SF in Cr197 and Vela T1.
Prisinzano, L.;Damiani, F.;Guarcello , M. G.;Micela, G.;Sciortino, S.;Tognelli, E.;Venuti, L.
Astronomy & Astrophysics, Volume 617, id.A63, 20 pp.
Jun 2018
5. The Gaia-ESO Survey and CSI 2264: Substructures, disks, and sequential star formation in the young open cluster NGC 2264 ADS CITATION
Abstract
Context. Reconstructing the structure and history of young clusters is pivotal to understanding the mechanisms and timescales of early stellar evolution and planet formation. Recent studies suggest that star clusters often exhibit a hierarchical structure, possibly resulting from several star formation episodes occurring sequentially rather than a monolithic cloud collapse. Aims: We aim to explore the structure of the open cluster and star-forming region NGC 2264 ( 3 Myr), which is one of the youngest, richest and most accessible star clusters in the local spiral arm of our Galaxy; we link the spatial distribution of cluster members to other stellar properties such as age and evolutionary stage to probe the star formation history within the region. Methods: We combined spectroscopic data obtained as part of the Gaia-ESO Survey (GES) with multi-wavelength photometric data from the Coordinated Synoptic Investigation of NGC 2264 (CSI 2264) campaign. We examined a sample of 655 cluster members, with masses between 0.2 and 1.8 M⊙ and including both disk-bearing and disk-free young stars. We used Teff estimates from GES and g,r,i photometry from CSI 2264 to derive individual extinction and stellar parameters. Results: We find a significant age spread of 4-5 Myr among cluster members. Disk-bearing objects are statistically associated with younger isochronal ages than disk-free sources. The cluster has a hierarchical structure, with two main blocks along its latitudinal extension. The northern half develops around the O-type binary star S Mon; the southern half, close to the tip of the Cone Nebula, contains the most embedded regions of NGC 2264, populated mainly by objects with disks and ongoing accretion. The median ages of objects at different locations within the cluster, and the spatial distribution of disked and non-disked sources, suggest that star formation began in the north of the cluster, over 5 Myr ago, and was ignited in its southern region a few Myr later. Star formation is likely still ongoing in the most embedded regions of the cluster, while the outer regions host a widespread population of more evolved objects; these may be the result of an earlier star formation episode followed by outward migration on timescales of a few Myr. We find a detectable lag between the typical age of disk-bearing objects and that of accreting objects in the inner regions of NGC 2264: the first tend to be older than the second, but younger than disk-free sources at similar locations within the cluster. This supports earlier findings that the characteristic timescales of disk accretion are shorter than those of disk dispersal, and smaller than the average age of NGC 2264 (i.e., ≲3 Myr). At the same time, we note that disks in the north of the cluster tend to be shorter-lived ( 2.5 Myr) than elsewhere; this may reflect the impact of massive stars within the region (notably S Mon), that trigger rapid disk dispersal. Conclusions: Our results, consistent with earlier studies on NGC 2264 and other young clusters, support the idea of a star formation process that takes place sequentially over a prolonged span in a given region. A complete understanding of the dynamics of formation and evolution of star clusters requires accurate astrometric and kinematic characterization of its population; significant advance in this field is foreseen in the upcoming years thanks to the ongoing Gaia mission, coupled with extensive ground-based surveys like GES. Full Table B.1 is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/609/A10
Venuti, L.;Prisinzano, L.;Sacco, G. G.;Flaccomio, E.;Bonito, R.;Damiani, F.;Micela, G.;Guarcello , M. G.;Randich, S.;Stauffer, J. R.;Cody, A. M.;Jeffries, R. D.;Alencar, S. H. P.;Alfaro, E. J.;Lanzafame, A. C.;Pancino, E.;Bayo, A.;Carraro, G.;Costado, M. T.;Frasca, A.;Jofré, P.;Morbidelli, L.;Sousa, S. G.;Zaggia, S.
Astronomy & Astrophysics, Volume 609, id.A10, 24 pp.
Jan 2018
### 2017
1. The Gaia-ESO Survey and CSI 2264: Substructures, disks, and sequential star formation in the young open cluster NGC 2264 ADS
Abstract
Context. Reconstructing the structure and history of young clusters is pivotal to understanding the mechanisms and timescales of early stellar evolution and planet formation. Recent studies suggest that star clusters often exhibit a hierarchical structure, possibly resulting from several star formation episodes occurring sequentially rather than a monolithic cloud collapse. Aims: We aim to explore the structure of the open cluster and star-forming region NGC 2264 ( 3 Myr), which is one of the youngest, richest and most accessible star clusters in the local spiral arm of our Galaxy; we link the spatial distribution of cluster members to other stellar properties such as age and evolutionary stage to probe the star formation history within the region. Methods: We combined spectroscopic data obtained as part of the Gaia-ESO Survey (GES) with multi-wavelength photometric data from the Coordinated Synoptic Investigation of NGC 2264 (CSI 2264) campaign. We examined a sample of 655 cluster members, with masses between 0.2 and 1.8 M⊙ and including both disk-bearing and disk-free young stars. We used Teff estimates from GES and g,r,i photometry from CSI 2264 to derive individual extinction and stellar parameters. Results: We find a significant age spread of 4-5 Myr among cluster members. Disk-bearing objects are statistically associated with younger isochronal ages than disk-free sources. The cluster has a hierarchical structure, with two main blocks along its latitudinal extension. The northern half develops around the O-type binary star S Mon; the southern half, close to the tip of the Cone Nebula, contains the most embedded regions of NGC 2264, populated mainly by objects with disks and ongoing accretion. The median ages of objects at different locations within the cluster, and the spatial distribution of disked and non-disked sources, suggest that star formation began in the north of the cluster, over 5 Myr ago, and was ignited in its southern region a few Myr later. Star formation is likely still ongoing in the most embedded regions of the cluster, while the outer regions host a widespread population of more evolved objects; these may be the result of an earlier star formation episode followed by outward migration on timescales of a few Myr. We find a detectable lag between the typical age of disk-bearing objects and that of accreting objects in the inner regions of NGC 2264: the first tend to be older than the second, but younger than disk-free sources at similar locations within the cluster. This supports earlier findings that the characteristic timescales of disk accretion are shorter than those of disk dispersal, and smaller than the average age of NGC 2264 (i.e., ≲3 Myr). At the same time, we note that disks in the north of the cluster tend to be shorter-lived ( 2.5 Myr) than elsewhere; this may reflect the impact of massive stars within the region (notably S Mon), that trigger rapid disk dispersal. Conclusions: Our results, consistent with earlier studies on NGC 2264 and other young clusters, support the idea of a star formation process that takes place sequentially over a prolonged span in a given region. A complete understanding of the dynamics of formation and evolution of star clusters requires accurate astrometric and kinematic characterization of its population; significant advance in this field is foreseen in the upcoming years thanks to the ongoing Gaia mission, coupled with extensive ground-based surveys like GES. Full Table B.1 is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/609/A10
Venuti, L.;Prisinzano, L.;Sacco, G. G.;Flaccomio, E.;Bonito, R.;Damiani, F.;Micela, G.;Guarcello , M. G.;Randich, S.;Stauffer, J. R.;Cody, A. M.;Jeffries, R. D.;Alencar, S. H. P.;Alfaro, E. J.;Lanzafame, A. C.;Pancino, E.;Bayo, A.;Carraro, G.;Costado, M. T.;Frasca, A.;Jofré, P.;Morbidelli, L.;Sousa, S. G.;Zaggia, S.
Astronomy & Astrophysics, Volume 609, id.A10, 24 pp.
Dec 2017
2. Near-infrared time-series photometry in the field of Cygnus OB2 association. I. Rotational scenario for candidate members ADS CITATION
Abstract
Context. In recent decades, the picture of early pre-main sequence stellar rotational evolution has been constrained by studies targeting different regions at a variety of ages with respect to young star formation. Observational studies suggest a dependence of rotation with mass, and for some mass ranges a connection between rotation and the presence of a circumstellar disk. The role of environmental conditions on the rotational regulation, however, has still not been fully explored. Aims: We investigate the rotational properties of candidate members of the young massive association Cygnus OB2. By evaluating their rotational properties, we address questions regarding the effect of environment properties on PMS rotational evolution. Methods: We studied JHK-band variability in 5083 candidate members (24% of them are disk-bearing stars). We selected variable stars with the Stetson variability index and performed the period search with the Lomb-Scargle periodogram for periods between 0.83-45 days. Period detections were verified using false alarm probability levels, Saunders statistics, the string and rope length method, and visual verification of folded light curves. Results: We identified 1224 periodic variable stars (24% of the candidate member sample, 8% of the disk-bearing sample, and 28% of the non-disk-bearing sample). Monte Carlo simulations were performed in order to evaluate completeness and contamination of the periodic sample, out of which 894 measured periods were considered reliable. Our study was considered reasonably complete for periods between 2 and 30 days. Conclusions: The general scenario for the rotational evolution of young stars seen in other regions is confirmed by Cygnus OB2 period distributions with disc-bearing stars rotating on average more slowly than non-disk-bearing stars. A mass-rotation dependence was also verified, but as in NGC 6530, very low mass stars (M ≤ 0.4 M⊙) are rotating on average slower than higher mass stars (0.4M⊙<M ≤ 1.4 M⊙). We observed an excess of slow rotators among the lower mass population. The disk and mass-rotation connection was also analyzed by taking into account the incident UV radiation arising from O stars in the association. Results compatible with the disk-locking scenario were verified for stars with low UV incidence, but no statistical significant relation between rotation and disk presence was verified for stars with high UV incidence suggesting that massive stars can have an important role in regulating the rotation of nearby low mass stars. The full Table 1 is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/603/A106
Roquette, J.;Bouvier, J.;Alencar, S. H. P.;Vaz, L. P. R.;Guarcello, M. G.
Astronomy & Astrophysics, Volume 603, id.A106, 63 pp.
Jul 2017
3. CSI 2264: Simultaneous optical and X-ray variability in pre-Main Sequence stars. I: Time resolved X-ray spectral analysis during optical dips and accretion bursts in stars with disks
Abstract
Pre-main sequence stars are variable sources. In stars with disks, this variability is related to the morphology of the inner circumstellar region (<0.1 AU) and that of the photosphere and corona, all impossible to be spatially resolved with present day techniques. This has been the main motivation for the Coordinated Synoptic Investigation of NGC 2264. In this paper, we focus on the stars with disks. We analyze the X-ray spectral properties extracted during optical bursts and dips in order to unveil the nature of these phenomena. We analyze simultaneous CoRoT and Chandra/ACIS-I observations to search for coherent optical and X-ray flux variability in stars with disks. Then, stars are analyzed in two different samples. In stars with variable extinction, we look for a simultaneous increase of optical extinction and X-ray absorption during the optical dips; in stars with accretion bursts, we search for soft X-ray emission and increasing X-ray absorption during the bursts. Results. We find evidence for coherent optical and X-ray flux variability among the stars with variable extinction. In 9/24 stars with optical dips, we observe a simultaneous increase of X-ray absorption and optical extinction. In seven dips, it is possible to calculate the NH/AV ratio in order to infer the composition of the obscuring material. In 5/20 stars with optical accretion bursts, we observe increasing soft X-ray emission during the bursts that we associate to the emission of accreting gas. It is not surprising that these properties are not observed in all the stars with dips and bursts, since favorable geometric configurations are required. The observed variable absorption during the dips is mainly due to dust-free material in accretion streams. In stars with accretion bursts, we observe on average a larger soft X-ray spectral component not observed in non accreting stars.
Guarcello , M. G.;Flaccomio, E.;Micela, G.;Argiroffi, C.;Sciortino, S.;Venuti, L.;Stauffer, J.;Rebull, L.;Cody, A. M.
Astronomy & Astrophysics, Volume 602, id.A10, 79 pp.
Jan 2017
### 2016
1. Globules and pillars in Cygnus X. I. Herschel far-infrared imaging of the Cygnus OB2 environment ADS CITATION
Abstract
The radiative feedback of massive stars on molecular clouds creates pillars, globules and other features at the interface between the H II region and molecular cloud. Optical and near-infrared observations from the ground as well as with the Hubble or Spitzer satellites have revealed numerous examples of such cloud structures. We present here Herschel far-infrared observations between 70 μm and 500 μm of the immediate environment of the rich Cygnus OB2 association, performed within the Herschel imaging survey of OB Young Stellar objects (HOBYS) program. All of the observed irradiated structures were detected based on their appearance at 70 μm, and have been classified as pillars, globules, evaporating gasous globules (EGGs), proplyd-like objects, and condensations. From the 70 μm and 160 μm flux maps, we derive the local far-ultraviolet (FUV) field on the photon dominated surfaces. In parallel, we use a census of the O-stars to estimate the overall FUV-field, that is 103-104 G0 (Habing field) close to the central OB cluster (within 10 pc) and decreases down to a few tens G0, in a distance of 50 pc. From a spectral energy distribution (SED) fit to the four longest Herschel wavelengths, we determine column density and temperature maps and derive masses, volume densities and surface densities for these structures. We find that the morphological classification corresponds to distinct physical properties. Pillars and globules are massive (~500 M⊙) and large (equivalent radius r ~ 0.6 pc) structures, corresponding to what is defined as “clumps” for molecular clouds. EGGs and proplyd-likeobjects are smaller (r ~ 0.1 and 0.2 pc) and less massive (~10 and ~30 M⊙). Cloud condensations are small (~0.1 pc), have an average mass of 35 M⊙, are dense (~6 × 104 cm-3), and can thus be described as molecular cloud “cores”. All pillars and globules are oriented toward the Cyg OB2 association center and have the longest estimated photoevaporation lifetimes, a few million years, while all other features should survive less than a million years. These lifetimes are consistent with that found in simulations of turbulent, UV-illuminated clouds. We propose a tentative evolutionary scheme in which pillars can evolve into globules, which in turn then evolve into EGGs, condensations and proplyd-like objects. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.
Schneider, N.;Bontemps, S.;Motte, F.;Blazere, A.;André, Ph.;Anderson, L. D.;Arzoumanian, D.;Comerón, F.;Didelon, P.;Di Francesco, J.;Duarte-Cabral, A.;Guarcello , M. G.;Hennemann, M.;Hill, T.;Könyves, V.;Marston, A.;Minier, V.;Rygl, K. L. J.;Röllig, M.;Roy, A.;Spinoglio, L.;Tremblin, P.;White, G. J.;Wright, N. J.
Astronomy & Astrophysics, Volume 591, id.A40, 21 pp.
Jun 2016
### 2015
1. X-Ray Emission from Massive Stars in Cyg OB2 ADS CITATION
Abstract
We report on the analysis of the Chandra-ACIS data of O, B, and WR stars in the young association Cyg OB2. X-ray spectra of 49 O-stars, 54 B-stars, and 3 WR-stars are analyzed and for the brighter sources, the epoch dependence of the X-ray fluxes is investigated. The O-stars in Cyg OB2 follow a well-defined scaling relation between their X-ray and bolometric luminosities: {log}\\frac{{L}{{X}}}{{L}{bol}}=-7.2+/- 0.2. This relation is in excellent agreement with the one previously derived for the Carina OB1 association. Except for the brightest O-star binaries, there is no general X-ray overluminosity due to colliding winds in O-star binaries. Roughly half of the known B-stars in the surveyed field are detected, but they fail to display a clear relationship between LX and Lbol. Out of the three WR stars in Cyg OB2, probably only WR 144 is itself responsible for the observed level of X-ray emission, at a very low {log}\\frac{{L}{{X}}}{{L}{bol}}=-8.8+/- 0.2. The X-ray emission of the other two WR-stars (WR 145 and 146) is most probably due to their O-type companion along with a moderate contribution from a wind-wind interaction zone.
Rauw, G.;Nazé, Y.;Wright, N. J.;Drake, J. J.;Guarcello , M. G.;Prinja, R. K.;Peck, L. W.;Albacete Colombo, J. F.;Herrero, A.;Kobulnicky, H. A.;Sciortino, S.;Vink, J. S.
The Astrophysical Journal Supplement Series, Volume 221, Issue 1, article id. 1, 20 pp. (2015).
Nov 2015
### 2014
1. Accretion and Outflow in the Proplyd-like Objects Near Cygnus OB2 ADS CITATION
Abstract
Cygnus OB2 is the most massive association within 2 kpc from the Sun, hosting hundreds of massive stars, thousands of young low mass members, and some sights of active star formation in the surrounding cloud. Recently, 10 photoevaporating proplyd-like objects with tadpole-shaped morphology were discovered in the outskirts of the OB association, approximately 6-14 pc away from its center. The classification of these objects is ambiguous, being either evaporating residuals of the parental cloud that are hosting a protostar inside or disk-bearing stars with an evaporating disk, such as the evaporating proplyds observed in the Trapezium Cluster in Orion. In this paper, we present a study based on low-resolution optical spectroscopic observations made with the Optical System for Imaging and low Resolution Integrated Spectroscopy, mounted on the 10.4 m Gran Telescopio CANARIAS, of two of these protostars. The spectrum of one of the objects shows evidence of accretion but not of outflows. In the latter object, the spectra show several emission lines indicating the presence of an actively accreting disk with outflow. We present estimates of the mass loss rate and the accretion rate from the disk, showing that the former exceeds the latter as observed in other known objects with evaporating disks. We also show evidence of a strong variability in the integrated flux observed in these objects as well as in the accretion and outflow diagnostics.
Guarcello , M. G.;Drake, J. J.;Wright, N. J.;García-Alvarez, D.;Kraemer, K. E.
The Astrophysical Journal, Volume 793, Issue 1, article id. 56, 14 pp. (2014).
Sep 2014
### 2013
1. Pre-main-sequence stars older than 8 Myr in the Eagle nebula ADS CITATION
Abstract
Attention is given to a population of 110 stars in the NGC 6611 cluster of the Eagle nebula that have prominent near-infrared excess and optical colours typical of pre-main-sequence (PMS) stars older than 8 Myr. At least half of those for which spectroscopy exists have a Hα emission line profile revealing active accretion. In principle, the V – I colours of all these stars would be consistent with those of young PMS objects (<1 Myr) whose radiation is heavily obscured by a circumstellar disc seen at high inclination and in small part scattered towards the observer by the back side of the disc. However, using theoretical models it is shown here that objects of this type can only account for a few per cent of this population. In fact, the spatial distribution of these objects, their X-ray luminosities, their optical brightness, their positions in the colour-magnitude diagram and the weak Li absorption lines of the stars studied spectroscopically suggest that most of them are at least eight times older than the ˜1 Myr-old PMS stars already known in this cluster and could be as old as ˜30 Myr. This is the largest homogeneous sample to date of Galactic PMS stars considerably older than 8 Myr that are still actively accreting from a circumstellar disc and it allows us to set a lower limit of 7 per cent to the disc frequency at ˜16 Myr in NGC 6611. These values imply a characteristic exponential lifetime of ˜6 Myr for disc dissipation.
De Marchi, Guido;Panagia, Nino;Guarcello , M. G.;Bonito, Rosaria
Monthly Notices of the Royal Astronomical Society, Volume 435, Issue 4, p.3058-3070
Nov 2013
2. Spectroscopic observations of blue stars with infrared excesses in NGC 6611 ADS CITATION
Abstract
Context. The young open cluster NGC 6611 includes a group of peculiar objects with interesting properties among its candidate members: blue stars with infrared (IR) excesses. These stars show excesses in IR bands, a signature of the presence of a circumstellar disk, but optical colors typical of older field stars. To confirm their membership in the cluster, it is therefore important to use new spectroscopic observations, together with previous photometric data. Aims: We aim to confirm the membership of these objects and investigate their physical properties to verify whether the observed colors are intrinsic or altered by the disk or by the accretion processes. Methods: We analyzed the intermediate-resolution spectroscopic data obtained for a subsample of blue stars in NGC 6611 with FLAMES. In particular, we focused on the study of 1) the profile of the Hα emission line, to select stars with accretion and outflow activity; 2) the Li absorption line, used as a youth indicator; 3) the radial velocity. Results: Using the spectroscopic analysis, it has been possible to investigate the Li absorption line, as well as to distinguish between stars with inert or active disks. In particular, from the analysis of the Hα emission line we were able to infer the activity due to the accretion and outflow processes and the variability of the emission. We also investigated the binarity of the blue stars and their membership to NGC 6611. Conclusions: From our spectroscopic analysis, we conclude that half of the sample of blue stars (10/20) are confirmed members of NGC 6611 (with 6 more stars that could also be possible members). In conclusion, our results indicate that members of young clusters can also be found in an anomalous region of the color-magnitude diagram, i.e., outside of the pre-main sequence locus where most of the cluster members lie.
Bonito, R.;Prisinzano, L.;Guarcello , M. G.;Micela, G.
Astronomy & Astrophysics, Volume 556, id.A108, 10 pp.
Aug 2013
3. The Protoplanetary Disks in the Nearby Massive Star-forming Region Cygnus OB2 ADS CITATION
Abstract
The formation of stars in massive clusters is one of the main modes of the star formation process. However, the study of massive star-forming regions is hampered by their typically large distances to the Sun. One exception to this is the massive star-forming region Cygnus OB2 in the Cygnus X region, at the distance of ~1400 pc. Cygnus OB2 hosts very rich populations of massive and low-mass stars, being the best target in our Galaxy to study the formation of stars, circumstellar disks, and planets in the presence of massive stars. In this paper, we combine a wide and deep set of photometric data, from the r band to 24 μm, in order to select the disk-bearing population of stars in Cygnus OB2 and identify the class I, class II, and stars with transition and pre-transition disks. We selected 1843 sources with infrared excesses in an area of 1° × 1° centered on Cyg OB2 in several evolutionary stages: 8.4% class I, 13.1% flat-spectrum sources, 72.9% class II, 2.3% pre-transition disks, and 3.3% transition disks. The spatial distribution of these sources shows a central cluster surrounded by an annular overdensity and some clumps of recent star formation in the outer region. Several candidate subclusters are identified, both along the overdensity and in the rest of the association.
Guarcello , M. G.;Drake, J. J.;Wright, N. J.;Drew, J. E.;Gutermuth, R. A.;Hora, J. L.;Naylor, T.;Aldcroft, T.;Fruscione, A.;García-Alvarez, D.;Kashyap, V. L.;King, R.
The Astrophysical Journal, Volume 773, Issue 2, article id. 135, 24 pp. (2013).
Aug 2013
### 2012
1. Optical Photometric GTC/OSIRIS Observations of the Young Massive Association Cygnus OB2 ADS CITATION
Abstract
In order to fully understand the gravitational collapse of molecular clouds, the star formation process, and the evolution of circumstellar disks, these phenomena must be studied in different Galactic environments with a range of stellar contents and positions in the Galaxy. The young massive association Cygnus OB2, in the Cygnus-X region, is a unique target to study how star formation and the evolution of circumstellar disks proceed in the presence of a large number of massive stars. We present a catalog obtained with recent optical observations in the r, i, z filters with OSIRIS, mounted on the 10.4 m Gran Telescopio CANARIAS telescope, which is the deepest optical catalog of Cyg OB2 to date. The catalog consists of 64,157 sources down to M = 0.15 M ⊙ at the adopted distance and age of Cyg OB2. A total of 38,300 sources have good photometry in all three bands. We combined the optical catalog with existing X-ray data of this region, in order to define the cluster locus in the optical diagrams. The cluster locus in the r – i versus i – z diagram is compatible with an extinction of the optically selected cluster members in the 2.64 m < AV < 5.57 m range. We derive an extinction map of the region, finding a median value of AV = 4.33 m in the center of the association, decreasing toward the northwest. In the color-magnitude diagrams, the shape of the distribution of main-sequence stars is compatible with the presence of an obscuring cloud in the foreground ~850 ± 25 pc from the Sun.
Guarcello , M. G.;Wright, N. J.;Drake, J. J.;García-Alvarez, D.;Drew, J. E.;Aldcroft, T.;Kashyap, V. L.
The Astrophysical Journal Supplement, Volume 202, Issue 2, article id. 19, 12 pp. (2012).
Oct 2012
2. Chandra/ACIS-I Study of the X-Ray Properties of the NGC 6611 and M16 Stellar Populations ADS CITATION
Abstract
Mechanisms regulating the origin of X-rays in young stellar objects and the correlation with their evolutionary stage are under debate. Studies of the X-ray properties in young clusters allow us to understand these mechanisms. One ideal target for this analysis is the Eagle Nebula (M16), with its central cluster NGC 6611. At 1750 pc from the Sun, it harbors 93 OB stars, together with a population of low-mass stars from embedded protostars to disk-less Class III objects, with age <=3 Myr. We study an archival 78 ks Chandra/ACIS-I observation of NGC 6611 and two new 80 ks observations of the outer region of M16, one centered on the Column V and the other on a region of the molecular cloud with ongoing star formation. We detect 1755 point sources with 1183 candidate cluster members (219 disk-bearing and 964 disk-less). We study the global X-ray properties of M16 and compare them with those of the Orion Nebula Cluster. We also compare the level of X-ray emission of Class II and Class III stars and analyze the X-ray spectral properties of OB stars. Our study supports the lower level of X-ray activity for the disk-bearing stars with respect to the disk-less members. The X-ray luminosity function (XLF) of M16 is similar to that of Orion, supporting the universality of the XLF in young clusters. Eighty-five percent of the O stars of NGC 6611 have been detected in X-rays. With only one possible exception, they show soft spectra with no hard components, indicating that mechanisms for the production of hard X-ray emission in O stars are not operating in NGC 6611.
Guarcello , M. G.;Caramazza, M.;Micela, G.;Sciortino, S.;Drake, J. J.;Prisinzano, L.
The Astrophysical Journal, Volume 753, Issue 2, article id. 117, 16 pp. (2012).
Jul 2012
3. The radial distribution of dust species in young brown dwarf discs ADS CITATION
Abstract
We present a study of the radial distribution of dust species in young brown dwarf discs. Our work is based on a compositional analysis of the 10 and 20 μm silicate emission features for brown dwarfs in the Taurus-Auriga star-forming region. A fundamental finding of our work is that brown dwarfs exhibit stronger signs of dust processing in the cold component of the disc, compared to the higher mass T Tauri stars in Taurus. For nearly all of our targets, we find a flat disc structure, which is consistent with the stronger signs of dust processing observed in these discs. For the case of one brown dwarf, 2M04230607, we find the forsterite mass fraction to be a factor of ˜3 higher in the outer disc compared to the inner disc region. Simple large-scale radial mixing cannot account for this gradient in the dust chemical composition, and some local crystalline formation mechanism may be effective in this disc. The relatively high abundance of crystalline silicates in the outer cold regions of brown dwarf discs provides an interesting analogy to comets. In this context, we have discussed the applicability of the various mechanisms that have been proposed for comets on the formation and the outward transport of high-temperature material. We also present Chandra X-ray observations for two Taurus brown dwarfs, 2M04414825 and CFHT-BD-Tau 9. We find 2M04414825, which has an ˜12 per cent crystalline mass fraction, to be more than an order of magnitude brighter in X-ray than CFHT-BD-Tau 9, which has an ˜35 per cent crystalline mass fraction. Combining with previous X-ray data, we find the inner disc crystalline mass fractions to be anti-correlated with the X-ray strength.
Riaz, B.;Honda, M.;Campins, H.;Micela, G.;Guarcello , M. G.;Gledhill, T.;Hough, J.;Martín, E. L.
Monthly Notices of the Royal Astronomical Society, Volume 420, Issue 3, pp. 2603-2624.
Mar 2012
4. Photoevaporating Proplyd-like Objects in Cygnus OB2 ADS CITATION
Abstract
We report the discovery of 10 proplyd-like objects in the vicinity of the massive OB association Cygnus OB2. They were discovered in IPHAS Hα images and are clearly resolved in broadband Hubble Space Telescope/Advanced Camera for Surveys, near-IR, and Spitzer mid-IR images. All exhibit the familiar tadpole shape seen in photoevaporating objects such as the Orion proplyds, with a bright ionization front at the head facing the central cluster of massive stars and a tail stretching in the opposite direction. Many also show secondary ionization fronts, complex tail morphologies, or multiple heads. We consider the evidence that these are either proplyds or “evaporating gaseous globules” (EGGs) left over from a fragmenting molecular cloud, but find that neither scenario fully explains the observations. Typical sizes are 50,000-100,000 AU, larger than the Orion proplyds, but in agreement with the theoretical scaling of proplyd size with distance from the ionizing source. These objects are located at projected separations of ~6-14 pc from the OB association, compared to ~0.1 pc for the Orion proplyds, but are clearly being photoionized by the ~65 O-type stars in Cyg OB2. Central star candidates are identified in near- and mid-IR images, supporting the proplyd scenario, though their large sizes and notable asymmetries are more consistent with the EGG scenario. A third possibility is therefore considered that these are a unique class of photoevaporating partially embedded young stellar objects that have survived the destruction of their natal molecular cloud. This has implications for the properties of stars that form in the vicinity of massive stars.
Wright, Nicholas J.;Drake, Jeremy J.;Drew, Janet E.;Guarcello , Mario G.;Gutermuth, Robert A.;Hora, Joseph L.;Kraemer, Kathleen E.
The Astrophysical Journal Letters, Volume 746, Issue 2, article id. L21, 7 pp. (2012).
Feb 2012
### 2011
1. Could CoRoT-7b and Kepler-10b be remnants of evaporated gas or ice giants? ADS CITATION
Abstract
We present thermal mass loss calculations over evolutionary time scales for the investigation if the smallest transiting rocky exoplanets CoRoT-7b (∼1.68REarth) and Kepler-10b (∼1.416REarth) could be remnants of an initially more massive hydrogen-rich gas giant or a hot Neptune-class exoplanet. We apply a thermal mass loss formula which yields results that are comparable to hydrodynamic loss models. Our approach considers the effect of the Roche lobe, realistic heating efficiencies and a radius scaling law derived from observations of hot Jupiters. We study the influence of the mean planetary density on the thermal mass loss by placing hypothetical exoplanets with the characteristics of Jupiter, Saturn, Neptune, and Uranus to the orbital location of CoRoT-7b at 0.017 AU and Kepler-10b at 0.01684 AU and assuming that these planets orbit a K- or G-type host star. Our findings indicate that hydrogen-rich gas giants within the mass domain of Saturn or Jupiter cannot thermally lose such an amount of mass that CoRoT-7b and Kepler-10b would result in a rocky residue. Moreover, our calculations show that the present time mass of both rocky exoplanets can be neither a result of evaporation of a hydrogen envelope of a “Hot Neptune” nor a “Hot Uranus”-class object. Depending on the initial density and mass, these planets most likely were always rocky planets which could lose a thin hydrogen envelope, but not cores of thermally evaporated initially much more massive and larger objects.
Leitzinger, M.;Odert, P.;Kulikov, Yu. N.;Lammer, H.;Wuchterl, G.;Penz, T.;Guarcello , M. G.;Micela, G.;Khodachenko, M. L.;Weingrill, J.;Hanslmeier, A.;Biernat, H. K.;Schneider, J.
Planetary and Space Science, Volume 59, Issue 13, p. 1472-1481.
Oct 2011
2. Star formation in the outer Galaxy: membership and fundamental parameters of the young open cluster NGC 1893
Abstract
Context. Different environmental conditions can play a crucial role in determining final products of the star formation process, and in this context, less favorable activities of star formation are expected in the external regions of our Galaxy. Aims: We studied the properties of the young open cluster NGC 1893 located about 12 Kpc from the galactic center, to investigate how different physical conditions can affect the process of star formation. Methods: By adopting a multiwavelength approach, we compiled a catalog extending from X-rays to NIR data to derive the cluster membership. In addition, optical and NIR photometric properties are used to evaluate the cluster parameters. Results: We find 415 diskless candidate members and 1061 young stellar objects with a circumstellar disk or class II candidate members, 125 of which are also Hα emitters. Considering the diskless candidate members, we find that the cluster distance is 3.6 ± 0.2 kpc and the mean interstellar reddening is E(B – V) = 0.6 ± 0.1 with evidence of differential reddening in the whole surveyed region. Conclusions: NGC 1893 contains a conspicuous population of pre-main sequence stars, together with the well-studied main sequence cluster population. We found a disk fraction of about 70% similar to the one found in clusters of similar age in the solar neighbor and then, despite expected unfavorable conditions for star formation, we conclude that very rich young clusters can also form in the outer regions of our Galaxy. Full Tables 5-8 are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/527/A77
Prisinzano, L.;Sanz-Forcada, J.;Micela, G.;Caramazza, M.;Guarcello , M. G.;Sciortino, S.;Testi, L.
Astronomy & Astrophysics, Volume 527, id.A77, 19 pp.
Mar 2011
### 2010
1. Chronology of star formation and disk evolution in the Eagle Nebula ADS CITATION
Abstract
Context. Massive star-forming regions are characterized by intense ionizing fluxes, strong stellar winds and, occasionally, supernovae explosions, all of which have important effects on the surrounding media, on the star-formation process and on the evolution of young stars and their circumstellar disks. We present a multiband study of the massive young cluster NGC 6611 and its parental cloud (the Eagle Nebula) with the aim of studying how OB stars affect the early stellar evolution and the formation of other stars. Aims: We search for evidence of triggering of star formation by the massive stars inside NGC 6611 on a large spatial scale (~10 parsec) and ongoing disk photoevaporation in NGC 6611 and how its efficiency depends on the mass of the central stars. Methods: We assemble a multiband catalog of the Eagle Nebula with photometric data, ranging from B band to 8.0 μm, and X-ray data obtained with two new and one archival Chandra/ACIS-I observation. We select the stars with disks from infrared photometry and disk-less ones from X-ray emission, which are associated both with NGC 6611 and the outer region of the Eagle Nebula. We study induced photoevaporation searching for the spatial variation of disk frequency for distinct stellar mass ranges. The triggering of star formation by OB stars has been investigated by deriving the history of star formation across the nebula. Results: We find evidence of sequential star formation in the Eagle Nebula going from the southeast (2.6 Myears) to the northwest (0.3 Myears), with the median age of NGC 6611 members ~1 Myear. In NGC 6611, we observe a drop of the disk frequency close to massive stars (up to an average distance of 1 parsec), without observable effects at larger distances. Furthermore, disks are more frequent around low-mass stars (≤ 1 M⊙) than around high-mass stars, regardless of the distance from OB stars. Conclusions: The star-formation chronology we find in the Eagle Nebula does not support the hypothesis of a large-scale process triggered by OB stars in NGC 6611. Instead, we speculate that it was triggered by the encounter (about 3 Myears ago) with a giant molecular shell created by supernovae explosions about 6 Myears ago. We find evidence of disk photoevaporation close to OB stars, where disks are heated by incident extreme ultraviolet (EUV) radiation. No effects are observed at large distances from OB stars, where photoevaporation is induced by the far ultraviolet (FUV) radiation, and long timescales are usually required to completely dissipate the disks.
Guarcello , M. G.;Micela, G.;Peres, G.;Prisinzano, L.;Sciortino, S.
Astronomy and Astrophysics, Volume 521, id.A61, 17 pp.
Oct 2010
2. Pre-main sequence stars with disks in the Eagle Nebula observed in scattered light ADS CITATION
Abstract
Context. NGC 6611 and its parental cloud, the Eagle Nebula (M 16), are well-studied star-forming regions, thanks to their large content of both OB stars and stars with disks and the observed ongoing star formation. In our previous studies of the Eagle Nebula, we identified 834 disk-bearing stars associated with the cloud, after detecting their excesses in NIR bands from J band to 8.0 μ m. Aims: In this paper, we study in detail the nature of a subsample of disk-bearing stars that show peculiar characteristics. They appear older than the other members in the V vs. V-I diagram, and/or they have one or more IRAC colors at pure photospheric values, despite showing NIR excesses, when optical and infrared colors are compared. Methods: We confirm the membership of these stars to M 16 by a spectroscopic analysis. The physical properties of these stars with disks are studied by comparing their spectral energy distributions (SEDs) with the SEDs predicted by models of T Tauri stars with disks and envelopes. Results: We show that the age of these stars estimated from the V vs. V-I diagram is unreliable since their V-I colors are altered by the light scattered by the disk into the line of sight. Only in a few cases their SEDs are compatible with models with excesses in V band caused by optical veiling. Candidate members with disks and photospheric IRAC colors are selected by the used NIR disk diagnostic, which is sensitive to moderate excesses, such as those produced by disks with low masses. In 1/3 of these cases, scattering of stellar flux by the disks can also be invoked. Conclusions: The photospheric light scattered by the disk grains into the line of sight can affect the derivation of physical parameters of Class II stars from photometric optical and NIR data. Besides, the disks diagnostic we defined are useful for selecting stars with disks, even those with moderate excesses or whose optical colors are altered by veiling or photospheric scattered light. Table with the data of the stars is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/521/A18
Guarcello , M. G.;Damiani, F.;Micela, G.;Peres, G.;Prisinzano, L.;Sciortino, S.
Astronomy and Astrophysics, Volume 521, id.A18, 9 pp.
Oct 2010
### 2009
1. Correlation between the spatial distribution of circumstellar disks and massive stars in the young open cluster NGC 6611. II. Cluster members selected with Spitzer/IRAC ADS CITATION
Abstract
Context: The observations of the proplyds in the Orion Nebula Cluster, exhibiting clear evidence of ongoing photoevaporation, have provided clear proof of the role of externally induced photoevaporation in the evolution of circumstellar disks. NGC 6611 is an open cluster suitable for study of disk photoevaporation, due to its significant population of massive members and stars with disk. In a previous paper, we obtained evidence of the influence of the strong UV field generated by the massive cluster members on the evolution of disks around low-mass Pre-Main Sequence members. Our study was based on a multiband BVIJHK and X-ray catalog compiled for the purpose of selecting cluster members with and without disk. Aims: We attempt to complete the list of candidate cluster members, using data at longer wavelengths obtained with Spitzer/IRAC, and we reinvestigate the effects of UV radiation on the evolution of disks in NGC 6611. Methods: In a field of view of 33’×34′ centered on the cluster, we select the candidate members with disks of NGC 6611 using IRAC color-color diagrams and suitable reddening-free color indices. Using the X-ray data to select Class III cluster members, we also estimate disks frequency relative to the intensity of the incident radiation emitted by massive members. Results: We identify 458 candidate members with circumstellar disks, among which 146 had not been discovered previously. By comparing all color indices used to select cluster members with disk, we claim that these indices measure the excess of radiation due to the emission of the same physical region of the disk (i.e. the inner rim at the dust sublimation radius). Our new results confirm that UV radiation from massive stars affects the evolution of nearby circumstellar disks. Optical-infrared catalog of the candidate members of the open cluster NGC 6611 is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/496/453
Guarcello , M. G.;Micela, G.;Damiani, F.;Peres, G.;Prisinzano, L.;Sciortino, S.
Astronomy and Astrophysics, Volume 496, Issue 2, 2009, pp.453-463
Mar 2009
2. Star formation in massive cluster: a multiwavelength study of the Eagle Nebula
Abstract
Not Available
Guarcello, Mario
Thesis (Ph.D.)-- SAO, 2009. Advisor N/A
n/a 2009
### 2007
1. Correlation between the spatial distribution of circumstellar disks and massive stars in the open cluster NGC 6611. Compiled catalog and cluster parameters ADS CITATION
Abstract
Context: The observation of young stars with circumstellar disks suggests that the disks are dissipated, starting from the inner region, by the radiation of the central star and eventually by the formation of rocky planetesimals, over a time scale of several million years. It was also shown that strong UV radiation emitted by nearby massive stars can heat a circumstellar disk up to some thousand degrees, inducing the photoevaporation of the gas. This process strongly reduces the dissipation time scale. Aims: We study whether there exists a correlation between the spatial distribution of stars with circumstellar disks and the position of massive stars with spectral class earlier than B5, in the open cluster NGC 6611. Methods: We created a multiband catalog of the cluster, down to V˜ 23^m, using optical data from a WFI observation at 2.2 m of ESO in the BVI bands, the 2MASS public point source catalog and an archival X-ray observation made with CHANDRA/ACIS. We selected the stars with infrared excess (due to the emission of a circumstellar disk) using suitable color indices independent of extinction, and studied their spatial distribution. Results: The spatial distribution of the stars with K band excess (due to the presence of a circumstellar disk) is anti correlated with that of the massive stars: the disks are more frequent at large distances from these stars. We argue that this is in agreement with the hypothesis that the circumstellar disks are heated by the UV radiation from the massive stars and photoevaporated. Based on observations made with the European Observatory telescopes obtained from the ESO/ST-ECF Science Archive Facility. Table 3 and Appendix are only available in electronic form at http://www.aanda.org
Guarcello , M. G.;Prisinzano, L.;Micela, G.;Damiani, F.;Peres, G.;Sciortino, S.
Astronomy and Astrophysics, Volume 462, Issue 1, January IV 2007, pp.245-255
Jan 2007
### 2019
1. Simultaneous Kepler/K2 and XMM-Newton observations of superflares in the Pleiades
Abstract
Guarcello , M. G.;Argiroffi, C.;Drake, J. J.;Flaccomio, E.;López-Santiago, J.;Micela, G.;Reale, F.;Rebull, L.;Sciortino, S.;Stauffer, J.;Antoniou, V.;Alvarado-Gomez, J. D.
Astronomische Nachrichten, Volume 340, Issue 4, pp. 302-307
May 2019
2. The Gaia-ESO Survey: age spread in the star forming region NGC6530 from the HR diagram and gravity indicators
Abstract
In very young clusters, stellar age distribution is the empirical proof of the duration of star formation (SF) and of the physical mechanisms involved in the process. We derived accurate stellar ages for the cluster NGC6530, associated with the Lagoon Nebula to infer its SF history. We use the Gaia-ESO survey observations and Gaia DR2 data, to derive cluster membership and fundamental stellar parameters. We identified 652 confirmed and 9 probable members. The reddening inferred for members and non-members allows us to distinguish MS stars and giants, in agreement with the distances inferred from Gaia DR2 data. The foreground and background stars show a spatial pattern that traces the 3D structure of the nebular dust component. We derive stellar ages for 382 confirmed cluster members and we find that the gravity-sensitive gamma index distribution for M stars is correlated with stellar age. For all members with Teff<5500 K, the mean logarithmic age is 5.84 (units of years) with a dispersion of 0.36 dex. The age distribution of stars with accretion and/or disk (CTTSe) is similar to that of stars without accretion and without disk (WTTSp). We interpret this dispersion as evidence of a real age spread since the total uncertainties on age determinations, derived from Monte Carlo simulations, are significantly smaller than the observed spread. This conclusion is supported by the evidence of a decreasing of the gravity-sensitive gamma index as a function of stellar ages. The presence of the age spread is also supported by the spatial distribution and the kinematics of old and young members. In particular, members with accretion and/or disk, formed in the last 1 Myr, show evidence of subclustering around the cluster center, in the Hourglass Nebula and in the M8-E region, suggesting a possible triggering of star formation events by the O-type star ionization fronts.
Prisinzano, L.;Damiani, F.;Kalari, V.;Jeffries, R.;Bonito, R.;Micela, G.;Wright, N. J.;Jackson, R. J.;Tognelli, E.;Guarcello , M. G.;Vink, J. S.;Klutsch, A.;Jiménez-Esteban, F. M.;Roccatagliata, V.;Tautvaišienė, G.;Gilmore, G.;Randich, S.;Alfaro, E. J.;Flaccomio, E.;Koposov, S.;Lanzafame, A.;Pancino, E.;Bergemann, M.;Carraro, G.;Franciosini, E.;Frasca, A.;Gonneau, A.;Hourihane, A.;Jofré, P.;Lewis, J.;Magrini, L.;Monaco, L.;Morbidelli, L.;Sacco, G. G.;Worley, C. C.;Zaggia, S.
Astronomy & Astrophysics, Volume 623, id.A159, 22 pp.
Jan 2019
### 2018
1. Photoevaporation and close encounters: how the environment around Cygnus OB2 affects the evolution of protoplanetary disks
Abstract
Cygnus OB2 is the most massive stellar association within 2 kpc from the Sun. Given its large content of massive stars, counting tens of O and 3 WR stars, and thousands of young low mass stars, Cygnus OB2 is the best target to study how massive stars affect the star formation process in the parental cloud and the evolution of nearby protoplanetary disks. I will present the results of our study on the feedback provided by the environment in Cygnus OB2 on disk evolution, combining the X-ray data from the 1.08 Msec Chandra Cygnus OB2 Legacy Project (P.I. J. J. Drake) with an extensive set of optical and infrared data of the association. I will analyze and compare the destructive feedback provided by disk photoevaporation induced by the intense local UV field and close encounters between members of the association, and I will show evidence indicating that disk evolution in an environment similar to Cygnus OB2 is seriously affected by externally induced photoevaporation while close encounters do not provide an important feedback.
Guarcello, Mario
Protoplanetary disks seen through the eyes of new-generation high-resolution instruments. Proceedings of the conference held 25-28 June, 2018 in Rome, Italy. Online at https://indico.ict.inaf.it/event/631/, jedi2018, id. 27.
Dec 2018
2. Young Stars and their Variability with LSST ADS
Abstract
Young stars exhibit short-term photometric variability caused by mass accretion events from circumstellar disks, the presence of dusty warps within the inner disks, starspots that rotate across the stellar surfaces, and flares. Long-term variability also occurs owing to starspot longevity and cycles, and from changes in stellar angular momenta and activity as the stars age. We propose to observe the Carina star-forming region in different bands with a cadence of 30 minutes every night for one week per year to clarify the nature of both the short-term and long-term variability of the thousands of young stars in this region. By obtaining well-sampled multicolor lightcurves of this dense young cluster, LSST would acquire the first statistically significant data on how these objects vary on both short and long timescales. This information will allow us to relate the observed variability to stellar properties such as mass, age, binarity, and to environmental properties such as location within or exterior to the H II region, and to the presence or absence of a circumstellar disk.
Rosaria;Bonito;Hartigan, Patrick;Venuti, Laura;Guarcello , Mario;Prisinzano, Loredana;Argiroffi, Costanza;Messina, Sergio;Johns-Krull, Christopher;Feigelson, Eric;Stauffer, John;Giannini, Teresa;Antoniucci, Simone;Sciortino, Salvo;Micela, Giusi;Pillitteri, Ignazio;Fedele, Davide;Podio, Linda;Damiani, Francesco;McGehee, Peregrine;Street, Rachel;Gizis, John;Sacco, Germano;Magrini, Laura;Flaccomio, Ettore;Orlando, Salvatore;Miceli, Marco;Stelzer, Beate;Fuchs, Julien;Chen, Sophia;Pikuz, Sergey;Frasca, Antonio;Biazzo, Katia;Codella, Claudio;Pastorello, Andrea;Alcala
eprint arXiv:1812.03135
Dec 2018
3. Investigating the population of Galactic star formation regions and star clusters within a Wide-Fast-Deep Coverage of the Galactic Plane ADS CITATION
Abstract
One of the aims of LSST is to perform a systematic survey of star clusters and star forming regions (SFRs) in our Galaxy. In particular, the observations obtained with LSST will make a big difference in Galactic regions that have been poorly studied in the past, such as the anticenter and the disk beyond the Galactic center, and they will have a strong impact in discovering new distant SFRs. These results can be achieved by exploiting the exquisite depth that will be attained if the wide-fast-deep (WFD) observing strategy of the main survey is also adopted for the Galactic plane, in the g, r, and i filters.
Prisinzano, L.;Magrini, L.;Damiani, F.;Sacco, G.;Bonito, R.;Venuti, L.;Casali, G.;Roccatagliata, V.;Randich, S.;Inno, L.;Cantat-Gaudin, T.;Minniti, D.;Bragaglia, A.;Degli Innocenti, S.;Prada Moroni, P. G.;Tognelli, E.;Sollima, A.;Vallenari, A.;Guarcello , M.;Messina, S.;Micela, G.;Sciortino, S.;Spagna, A.;Sanna, N.;Kastner, J.;Roman, A.;Szabo, R.;Dias, B.;Feigelson, E.;Jeffries, R.;Friel, E.;Stauffer, J.;Van der Swaelmen, M.;Sordo, R.;Bossini, D.
eprint arXiv:1812.03025
Dec 2018
4. X-ray spectral characterization of the young Cygnus OB2 population ADS
Abstract
We analyze the X-ray spectra of the $\sim$8000 sources detected in the Cygnus OB2 Chandra Legacy Survey (Drake et al., this issue), with the goals of characterizing the coronal plasma of the young low-mass stars in the region and estimating their intrinsic X-ray luminosities. We adopt two different strategies for X-ray sources for which more or less than 20 photons were detected. For the brighter sample we fit the spectra with absorbed isothermal models. In order to limit uncertainties, for most of the fainter Cygnus OB2 members in this sample, we constrain the spectral parameters to characteristic ranges defined from the brightest stars. For X-ray sources with $<$20 net photons we adopt a conversion factor from detected photon flux to intrinsic flux. This was defined, building on the results for the previous sample, as a function of the 20% quantile of the detected photon energy distributions, which we prove to also correlate well with extinction. We then use the X-ray extinction from the spectral fits to constrain the ratio between optical and X-ray extinction toward Cygnus OB2, finding it consistent with standard "Galactic"' values, when properly accounting for systematics. Finally we exploit the large number of sources to constrain the average coronal abundances of several elements, through two different ensemble analyses of the X-ray spectra of low-mass Cygnus OB2 members. We find the pattern of abundances to be largely consistent with that derived for the young stellar coronae in the Orion Nebula Cluster.
Flaccomio, E.;Albacete-Colombo, J. F.;Drake, J. J.;Guarcello , M. G.;Kashyap, V.;Wright, N. J.;Briggs, K.;Ercolano, B.;Mccollogh, M.;Sciortino, S.
eprint arXiv:1811.06769
Nov 2018
5. VizieR Online Data Catalog: Magnetic flaring from PMS stars spectra (Flaccomio+, 2018) ADS
Abstract
Tables are provided with the data to reproduce figure B.1. in the paper, showing the lightcurves of flares observed simultaneously in the Chandra X-ray band, and in the CoRoT (optical) and/or Spitzer (mIR) bands. Up to four tables are included for each of the 75 panels in the figure: the CoRoT lightcurve, the Spitzer lightcurve, and the Chandra lightcurve, binned using both a fixed bin duration (indicated in the File Summary below as “bin”) and the “natural binning” Maximum-Likelihood algorithm described in the text (indicated as “blk”). For the CoRoT and Spitzer lightcurves, polynomial expressions representing the non-flaring emission during flares, derived as described in the text, are reported in the header of the relative text files, along with time intervals used to derived time-integrated flare emission. (5 data files).
Flaccomio, E.;Micela, G.;Sciortino, S.;Cody, A. M.;Guarcello , M. G.;Morales-Calderon, M.;Rebull, L.;Stauffer, J. R.
VizieR On-line Data Catalog: J/A+A/620/A55. Originally published in: 2018A&A...620A..55F
Sep 2018
6. Observational sites characterization for the Fly-Eye survey telescope ADS
Abstract
The issue of protecting ground infrastructures and space assets from the hazards coming from space, i.e. space debris, Near-Earth-Objects (NEO) and Space Weather, has recently gained momentum. In Europe it is addressed by the Space Situational Awareness Programme (SSA) of the European Space Agency (ESA) as well as at European Commission level. Within this framework it is foreseen the deployment of a European network of sensors for the detection of space objects able to trigger and support impact monitoring activities. The so-called “Fly-Eye” telescope with its unique optical design guaranteeing a wide-field (6.7°x6.7° FoV) and a high-sensitivity (down to 21.5 visual magnitude) is a key element to this end. In survey mode this telescope allows to timely detect small NEOs approaching the Earth and to efficiently catalogue space debris in a wide range of orbital regimes, from high LEO (Low-Earth Orbit) up to the geostationary ring. The first-light of the ESA SSA Fly-Eye telescope devoted to NEO survey is expected by end 2019. In order to investigate observational sites in Italy which could satisfy the SSA observational requirements we have analyzed different locations taking into account sky pollution, cloud coverage and seeing values. Both space and ground-based data were used. Cloud coverage data have been obtained from Earth observation satellites at different scale resolution (MODIS ACQUA, MODIS TERRA, MSG) and epochs. Seeing evaluation is based on existing data and/or in-situ ground-based seeing monitor equipments. The sky brightness was estimated by using NOAA (VIIRS/DMSP) and World Atlas 2015 (F. Falchi et al. 2016) maps. Due to the peculiarity in which NEO and space debris survey are expected to operate, logistic considerations were also taken into account. We present the outcome of the resulting trade-off analysis which shows the advantages and drawbacks of each site, eventually leading to identify those which could satisfy the technical and operational needs of running a NEO/space debris based on Fly-eye telescopes.
Di Cecco, Alessandra;Micela, Giuseppina;Perozzi, Ettore;Bianco, Giuseppe;Marzo, Cosimo;Falvella, Maria Cristina;Buzzoni, Alberto;Di Paola, Andrea;Fierro, Davide;Guarcello, Mario Giuseppe
42nd COSPAR Scientific Assembly. Held 14-22 July 2018, in Pasadena, California, USA, Abstract id. S.3-14-18.
Jul 2018
7. VizieR Online Data Catalog: Star formation in the Vela Molecular Ridge (Prisinzano+, 2018) ADS
Abstract
Astrometric and photometric data used in this work come from the public APASS9 (Cat. II/336), VPHAS+ (Cat. II/341) and 2MASS (Cat. II/246) catalogs. In addition, we used TGAS Gaia DR1 (I/337) kinematic data and public X-ray data obtained by ROSAT High Resolution Imager (HRI, 1RXH, third Release, Cat. IX/28) and Chandra Data Archive (Wang et al., 2016, Cat. J/ApJS/224/40). In table 2 we present astrometry, photometry and membership information of the young stellar objects (YSO) selected with classical methods, that is, from Halpha, IR excesses, kinematics, and X-ray detection. In table 3 we present astrometry and photometry of the M-type YSOs, selected with the new photometry technique described in the paper. For these latter objects, we also give the extinction and the ages. (2 data files).
Prisinzano, L.;Damiani, F.;Guarcello , M. G.;Micela, G.;Sciortino, S.;Tognelli, E.;Venuti, L.
VizieR On-line Data Catalog: J/A+A/617/A63. Originally published in: 2018A&A...617A..63P
Jun 2018
8. Diffuse X-ray emission in the Cygnus OB2 association ADS
Abstract
We present a large-scale study of diffuse X-ray emission in the nearby massive stellar association Cygnus OB2 as part of the Chandra Cygnus OB2 Legacy Program. We used 40 Chandra X-ray ACIS-I observations covering $\sim$1.0 deg$^2$. After removing 7924 point-like sources detected in our survey, background-corrected X-ray emission, the adaptive smoothing reveals large-scale diffuse X-ray emission. Diffuse emission was detected in the sub-bands Soft [0.5 : 1.2] and Medium [1.2 : 2.5], and marginally in the Hard [2.5 : 7.0] keV band. From X-ray spectral analysis of stacked spectra we compute a total [0.5 : 7.0 keV] diffuse X-ray luminosity of L$_{\rm x}^{\rm diff}\approx$4.2$\times$10$^{\rm 34}$ erg s$^{-1}$, characterized with plasma temperature components at kT$\approx$ 0.11, 0.40 and 1.18 keV, respectively. The HI absorption column density corresponding to these temperatures has a distribution consistent with N$_{\rm H}$ = 0.43, 0.80 and 1.39 $\times$10$^{22}$ cm$^{-2}$. The extended medium band energy emission likely arises from O-type stellar winds thermalized by wind-wind collisions in the most populated regions of the association, while the soft band emission probably arises from less energetic termination shocks against the surrounding Interstellar-Medium. Super-soft and Soft diffuse emission appears more widely dispersed and intense than the medium band emission. The diffuse X-ray emission is generally spatially coincident with low-extinction regions that we attribute to the ubiquitous influence of powerful stellar winds from massive stars and their interaction with the local Interstellar-Medium. Diffuse X-ray emission is volume-filling, rather than edge-brightened, oppositely to other star-forming regions. We reveal the first observational evidence of X-ray haloes around some evolved massive stars.
Albacete Colombo, J. F.;Drake, J. J.;Flaccomio, E.;Wright, N. J.;Kashyap, V.;Guarcello , M. G.;Briggs, K.;Drew, J. E.;Fenech, D. M.;Micela, G.;McCollough, M.;Prinja, R. K.;Schneider, N.;Sciortino, S.;Vink, J. S.
eprint arXiv:1806.01231
Jun 2018
### 2017
1. Time resolved X-ray spectral analysis during optical dips and accretion bursts in stars with disks of NGC 2264 from Chandra/ACIS-I and CoRoT data
Abstract
The simultaneous X-ray and optical observations with excellent time resolution of T Tauri stars with disks may provide insight on the accretion process and the properties of the inner disk. This was one of the motivations of the CSI 2264 campaign. In this talk I will show the results obtained from time resolved X-ray spectral analysis from deep Chandra/ACIS-I observations during the optical dips and accretion bursts isolated in the CoRoT light curves of the disk-bearing members of NGC 2264. These simultaneous Chandra-CoRoT data allow us to find evidence of increasing X-ray absorption during the optical dips, to study the composition of the material responsible for the variable extinction in these stars with disks, and to find evidence for soft X-ray emission observed during the optical bursts, and thus related to the accretion process.
Guarcello , M.;Flaccomio, E.;Micela, G.;Argiroffi, C.;Sciortino, S.;Venuti, L.;Stauffer, J.;Rebull, L.;Cody, A.
The X-ray Universe 2017, Proceedings of the conference held 6-9 June, 2017 in Rome, Italy. Edited by J.-U. Ness and S. Migliari. Online at https://www.cosmos.esa.int/web/xmm-newton/2017-symposium, p.92
Oct 2017
2. VizieR Online Data Catalog: NGC2264 structure and star formation history (Venuti+, 2018) ADS
Abstract
We aim to explore the structure of the open cluster and star-forming region NGC 2264 (3 Myr), and to reconstruct its star formation history. Our study focuses on a sample of 655 young stars in the region. We employed spectroscopic data from the Gaia-ESO Survey and multi-wavelength photometry from the CSI 2264 campaign to: i) derive individual extinction and stellar parameters (mass, age) for cluster members; ii) classify the evolutionary status of the objects (disk-bearing/disk-free, accreting/non-accreting); iii) explore the nature of young stars at different locations within the cluster as a function of age. In tableb1, we provide the following information: object identifiers in the Gaia-ESO Survey and CSI 2264 catalogs; spatial coordinates; membership flag; g,r,i photometry; disk classification; accreting status; gamma-index; effective temperature; Lithium equivalent width (EW); Halpha EW and width at 10% intensity; photometric Halpha emission; UV excess; Av; bolometric luminosity; mass and age estimates. (1 data file).
Venuti, L.;Prisinzano, L.;Sacco, G. G.;Flaccomio, E.;Bonito, R.;Damiani, F.;Micela, G.;Guarcello , M. G.;Randich, S.;Stauffer, J. R.;Cody, A. M.;Jeffries, R. D.;Alencar, S. H. P.;Alfaro, E. J.;Lanzafame, A. C.;Pancino, E.;Bayo, A.;Carraro, G.;Costado, M. T.;Frasca, A.;Jofre, P.;Morbidelli, L.;Sousa, S. G.;Zaggia, S.
VizieR On-line Data Catalog: J/A+A/609/A10. Originally published in: 2018A&A...609A..10V
Sep 2017
3. VizieR Online Data Catalog: Rotational periods in Cygnus OB2 (Roquette+, 2017) ADS
Abstract
Our observational dataset was obtained with the 3.8m United Kingdom Infra-Red Telescope (UKIRT), at Manua Kea, Hawaii, equipped with the Wide Field Camera (WFCAM); the programs were U/07A/H16 and U/07B/H60. Our complete dataset is composed of up to 115 nights observed using the J, H, and K filters (Hewett et al., 2006MNRAS.367..454H). The observations were carried during 2007 in two seasons: The first season comprises 43 observed nights between April 1 and May 21; the second season comprises 73 observed nights between August 4 and November 3. The two observational seasons span a total of 217 days. The exposures were short, 2 seconds in each filter. Rotational periods for 894 Cygnus OB2 candidate members. For each star, an internal ID, IDs in Guarcello et al. (2013, Cat. J/ApJ/773/135) and Guarcello et al. (2015, arXiv:1501.03761), coordinates, Stetson variability index, period, estimated mass and reddening, median JHK magnitudes, median JHK photometric errors, peak-to- peak JHK amplitudes, and Disk class according to Guarcello et al. (2013, Cat. J/ApJ/773/135) ate presented. (1 data file).
Roquette, J.;Bouvier, J.;Alencar, S. H. P.;Vaz, L. P. R.;Guarcello, M. G.
VizieR On-line Data Catalog: J/A+A/603/A106. Originally published in: 2017A&A...603A.106R
May 2017
4. Age spread and sequential star formation in the young cluster NGC 2264 ADS
Abstract
We investigate the structure and star formation history of the NGC 2264 cluster (3 Myr). We combine spectroscopic T_eff with multi-color photometry to derive homogeneous extinction and stellar parameters for 655 cluster members (M_star = 0.2-1.8 M_⊙). We infer an intrinsic age spread of ˜4 Myr across the cluster. NGC 2264 members were born in the course of sequential star formation activity, which still continues in the most embedded regions of the cluster. We find evidence for photoevaporation effects driven by OB stars in the region that locally impact the timescales for disk evolution within the cluster.
Venuti, L.;Prisinzano, L.;Sacco, G.;Flaccomio, E.;Bonito, R.;Damiani, F.;Micela, G.;Guarcello , M.;GES Collaboration;CSI 2264 Collaboration
Memorie della Societa Astronomica Italiana, v.88, p.848 (2017)
n/a 2017
### 2016
1. Time Resolved X-Ray Spectral Analysis of Class II YSOs in NGC 2264 During Optical Dips and Bursts ADS
Abstract
Pre-Main Sequence stars are variable sources. The main mechanisms responsible for their variability are variable extinction, unsteady accretion, and rotational modulation of both hot and dark photospheric spots and X-ray active regions. In stars with disks this variability is thus related to the morphology of the inner circumstellar region (<0.1 AU) and that of photosphere and corona, all impossible to be spatially resolved with present day techniques. This has been the main motivations of the Coordinated Synoptic Investigation of NGC2264, a set of simultaneous observations of NGC2264 with 15 different telescopes.We analyze the X-ray spectral properties of stars with disks extracted during optical bursts and dips in order to unveil the nature of these phenomena. Stars are analyzed in two different samples. In stars with variable extinction a simultaneous increase of optical extinction and X-ray absorption is searched during the optical dips; in stars with accretion bursts we search for soft X-ray emission and increasing X-ray absorption during the bursts. In 9/33 stars with variable extinction we observe simultaneous increase of X-ray absorption and optical extinction. In seven dips it is possible to calculate the NH/AV ratio in order to infer the composition of the obscuring material. In 5/27 stars with optical accretion bursts, we observe soft X-ray emission during the bursts that we associate to the emission of accreting gas. It is not surprising that these properties are not observed in all the stars with dips and bursts since favorable geometric configurations are required. The observed variable absorption during the dips is mainly due to dust-free material in accretion streams. In stars with accretion bursts we observe in average a larger soft X-ray spectral component not observed in non accreting stars. This indicates that this soft X-ray emission arises from the accretion shocks.
Guarcello , Mario Giuseppe;Flaccomio, Ettore;Micela, Giuseppina;Argiroffi, Costanza;Venuti, Laura
The 19th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun (CS19), Uppsala, Sweden, 06-10 June 2016, id.99
Jul 2016
2. Photoevaporation and close encounters: how the environment around Cygnus OB2 affects the evolution of protoplanetary disks ADS CITATION
Abstract
In our Galaxy, star formation occurs in a variety of environments, with a large fraction of stars formed in clusters hosting massive stars. OB stars have an important feedback on the evolution of protoplanetary disks around nearby young stars and likely on the process of planet formation occurring in them. The nearby massive association Cygnus OB2 is an outstanding laboratory to study this feedback. It is the closest massive association to our Sun, and hosts hundreds of massive stars and thousands of low mass members. In this paper, we analyze the spatial variation of the disk fraction in Cygnus OB2 and we study its correlation with the local values of Far and Extreme ultraviolet radiation fields and the local stellar surface density. We present definitive evidence that disks are more rapidly dissipated in the regions of the association characterized by intense local UV field and large stellar density. In particular, the FUV radiation dominates disks dissipation timescales in the proximity (i.e. within 0.5 pc) of the O stars. In the rest of the association, EUV photons potentially induce a significant mass loss from the irradiated disks across the entire association, but the efficiency of this process is reduced at increasing distances from the massive stars due to absorption by the intervening intracluster material. We find that disk dissipation due to close stellar encounters is negligible in Cygnus OB2, and likely to have affected 1% or fewer of the stellar population. Disk dissipation is instead dominated by photoevaporation. We also compare our results to what has been found in other young clusters with different massive populations, concluding that massive associations like Cygnus OB2 are potentially hostile to protoplanetary disks, but that the environments where disks can safely evolve in planetary systems are likely quite common in our Galaxy.
Guarcello , M. G.;Drake, J. J.;Wright, N. J.;Albacete-Colombo, J. F.;Clarke, C.;Ercolano, B.;Flaccomio, E.;Kashyap, V.;Micela, G.;Naylor, T.;Schneider, N.;Sciortino, S.;Vink, J. S.
eprint arXiv:1605.01773
May 2016
3. The statistical uncertainties on X-ray flux and spectral parameters from Chandra ACIS-I observations of faint sources: Application to the Cygnus OB2 Association ADS CITATION
Abstract
We investigate the uncertainties of fitted X-ray model parameters and fluxes for relatively faint Chandra ACIS-I source spectra. Monte-Carlo (MC) simulations are employed to construct a large set of 150,000 fake X-ray spectra in the low photon count statistics regime (from 20 to 350 net counts) using the XSPEC spectral model fitting package. The simulations employed both absorbed thermal (APEC) and non-thermal (power-law) models, in concert with the Chandra ACIS-I instrument response and interstellar absorption. Simulated X-ray spectra were fit assuming a wide set of different input parameters and C-statistic minimization criteria to avoid numerical artifacts in the accepted solutions. Results provide an error estimate for each parameter (absorption, NH, plasma temperature, kT, or power-law slope, Gamma, and flux, and for different background contamination levels. The distributions of these errors are studied as a function of the 1 sigma quantiles and we show how these correlate with different model parameters, net counts in the spectra and relative background level. Maps of uncertainty in terms of the 1 sigma quantiles for parameters and flux are computed as a function of spectrum net counts. We find very good agreement between our estimated X-ray spectral parameter and flux uncertainties and those recovered from spectral fitting for a subset of the X-ray sources detected in the Chandra Cygnus OB2 Legacy Survey diagnosed to be Association members and that have between 20 and 350 net counts. Our method can provide uncertainties for spectral parameters whenever formal X-ray spectral fits cannot be well-constrained, or are unavailable, and predictions useful for computing Chandra ACIS-I exposure times for observation planning.
Albacete-Colombo, J. F.;Flaccomio, E.;Drake, J. J.;Wright, N. J.;Guarcello , M.;Kashyap, V.
eprint arXiv:1603.08372
Mar 2016
### 2015
1. Simulating the sensitivity to stellar point sources of Chandra X-ray observations ADS CITATION
Abstract
The Chandra Cygnus OB2 Legacy Survey is a wide and deep X-ray survey of the nearby and massive Cygnus OB2 association. The survey has detected ~8,000 X-ray sources, the majority of which are pre-main sequence X-ray emitting young stars in the association itself. To facilitate quantitative scientific studies of these sources as well as the underlying OB association it is important to understand the sensitivity of the observations and the level of completeness the observations have obtained. Here we describe the use of a hierarchical Monte Carlo simulation to achieve this goal by combining the empirical properties of the observations, analytic estimates of the source verification process, and an extensive set of source detection simulations. We find that our survey reaches a 90% completeness level for a pre-main-sequence population at the distance of Cyg OB2 at an X-ray luminosity of 4 x 10^30 ergs/s and a stellar mass of 1.3 Msun for a randomly distributed population. For a spatially clustered population such as Cyg~OB2 the 90% completeness level is reached at 1.1 Msun instead, as the sources are more concentrated in areas of our survey with a high exposure. These simulations can easily be adapted for use with other X-ray observations and surveys, and we provide X-ray detection efficiency curves for a very wide array of source and background properties to allow these simulations to be easily exploited by other users.
Wright, Nicholas J.;Drake, Jeremy J.;Guarcello , Mario G.;Kashyap, Vinay L.;Zezas, Andreas
eprint arXiv:1511.03943
Nov 2015
2. Cygnus OB2: Star Formation Ugly Duckling Causes a Flap ADS CITATION
Abstract
Cygnus OB2 is one of the largest known OB associations in our Galaxy, with a total stellar mass of 30,000 Msun and boasting an estimated 65 O-type stars and hundreds of OB stars. At a distance of only 1.4kpc, it is also the closest truly massive star forming region and provides a valuable testbed for star and planet formation theory. We have performed a deep stellar census using observations from X-ray to infrared, which has enabled studies of sub-structuring, mass segregation and dynamics, while infrared data reveal a story of protoplanetary disk attrition in an extremely harsh radiation environment. I will discuss how Cygnus OB2 challenges the idea that stars must form in dense, compact clusters, and demonstrates that stars as massive as 100 Msun can form in relatively low-density environments. Convincing evidence of disk photoevaporation poses a potential problem for planet formation and growth in starburst environments.
Drake, Jeremy J.;Wright, Nicholas;Guarcello, Mario
IAU General Assembly, Meeting #29, id.2258134
Aug 2015
3. Optical and infrared counterparts of the X-ray sources detected in the Chandra Cygnus OB2 Legacy Survey ADS CITATION
Abstract
The young massive OB association Cygnus OB2, in the Cygnus X complex, is the closest (1400 pc) star forming region to the Sun hosting thousands of young low mass stars and up to 1000 OB stars, among which are some of the most massive stars known in our Galaxy. This region holds great importance for several fields of modern astrophysics, such as the study of the physical properties of massive and young low-mass stars and the feedback provided by massive stars on star and planet formation process. Cygnus OB2 has been recently observed with Chandra/ACIS-I as part of the 1.08Msec Chandra Cygnus OB2 Legacy Project. This survey detected 7924 X-ray sources in a square degree area centered on Cyg OB2. Since a proper classification and study of the observed X-ray sources also requires the analysis of their optical and infrared counterparts, we combined a large and deep set of optical and infrared catalogs available for this region with our new X-ray catalog. In this paper we describe the matching procedure and present the combined catalog containing 5703 sources. We also briefly discuss the nature of the X-ray sources with optical and infrared counterparts using their position in the color-magnitude and color-color diagrams.
Guarcello , M. G.;Drake, J. J.;Wright, N. J.;Naylor, T.;Flaccomio, E.;Kashyap, V. L.;Garcia-Alvarez, D.
eprint arXiv:1501.03761
Jan 2015
### 2014
1. VizieR Online Data Catalog: VIc photometry of IR-excess stars in NGC6611 (De Marchi+ 2013) ADS
Abstract
The data analysed in this work were extracted from the multiband photometric catalogue of NGC 6611 and of the surrounding M 16 cloud compiled by Guarcello et al. (2010, Cat. J/A+A/521/A61). (1 data file).
de Marchi, G.;Panagia, N.;Guarcello , M. G.;Bonito, R.
VizieR On-line Data Catalog: J/MNRAS/435/3058. Originally published in: 2013MNRAS.435.3058D
Oct 2014
2. Cygnus OB2: Star Formation Ugly Duckling Causes a Flap ADS
Abstract
Cygnus OB2 is one of the largest known OB associations in our Galaxy, with a total stellar mass of 3×10^4 Msun and boasting an estimated 65O-type stars and hundreds of OB stars. At a distance of only 1.4kpc, it is also the closest truly massive star forming region and provides a valuable testbed for star and planet formation theories. Chandra’s megasecond 1 square degree survey of the association revealed about 8000 X-ray point sources, approximately 5750 of which have been identified with objects in optical and infrared surveys. The stellar census has enabled studies of sub-structuring, mass segregation anddynamics, while infrared data reveal a story of protoplanetary disk attrition in an extremely harsh radiation environment. We will discuss how Cygnus OB2 challenges the idea that stars must form in dense, compact clusters, and demonstrates that stars as massive as 100Msun can form in relatively low-density environments. Convincing evidence of disk photoevaporation poses a potential problem for planet formation and growth in starburst environments.
Drake, Jeremy J.;Guarcello , Mario G.;Wright, Nicholas James
American Astronomical Society, HEAD meeting #14, id.103.05
Aug 2014
3. The Chandra Cygnus OB2 Legacy Survey: Design and X-ray Point Source Catalog ADS CITATION
Abstract
The Cygnus OB2 association is the largest concentration of young and massive stars within 2 kpc of the Sun, including an estimated 65 O-type stars and hundreds of OB stars. The Chandra Cygnus OB2 Legacy Survey is a large imaging program undertaken with the Advanced CCD Imaging Spectrometer onboard the Chandra X-ray Observatory. The survey has imaged the central 0.5 deg^2 of the Cyg OB2 association with an effective exposure of 120ks and an outer 0.35 deg^2 area with an exposure of 60ks. Here we describe the survey design and observations, the data reduction and source detection, and present a catalog of 8,000 X-ray point sources. The survey design employs a grid of 36 heavily (~50%) overlapping pointings, a method that overcomes Chandra’s low off-axis sensitivity and produces a highly uniform exposure over the inner 0.5 deg^2. The full X-ray catalog is described here and is made available online.
Wright, Nicholas J.;Drake, Jeremy J.;Guarcello , Mario G.;Aldcroft, Tom L.;Kashyap, Vinay L.;Damiani, Francesco;DePasquale, Joe;Fruscione, Antonella
eprint arXiv:1408.6579
Aug 2014
4. The X-ray emission of the massive stars population in Cyg OB2 ADS
Abstract
Cygnus OB2 contains a wealth of massive stars of spectral types O, B and Wolf-Rayet. In the framework of a Chandra legacy program to study the X-ray emission from this important association, we have studied the X-ray properties of its massive stars population. We show that the O-stars in Cyg OB2 follow a well-defined scaling relation between their X-ray and bolometric luminosities: log(Lx/Lbol) = -7.2 ± 0.2. Except for the brightest O-star binaries, there is no general X-ray overluminosity due to colliding winds in O-star binaries. Roughly half of the known B-stars in the surveyed field are detected, but they fail to display a clear relationship between Lx and Lbol. Out of the three WR stars in Cyg OB2, probably only WR144 is itself responsible for the observed level of X-ray emission, at a very low log(Lx/Lbol) = -8.8 ± 0.2. The X-ray emission of the other two WR-stars (WR145 and 146) is most probably due to their O-type companion along with a moderate contribution from a wind-wind interaction zone.
Rauw, G.;Nazé, Y.;Wright, N.;Drake, J.;Guarcello , M.;Chandra Cygnus OB2 legacy survey Consortium
The X-ray Universe 2014, edited by Jan-Uwe Ness. Online at http://www.cosmos.esa.int/web/xmm-newton/2014-symposium/, id.307
Jul 2014
5. Disk Survival in the Extremely Massive Association Cygnus OB2 ADS
Abstract
Star formation in massive clusters proceeds under the influence of the intense ionizing flux emitted by OB stars. Among the massive star forming regions in our Galaxy, Cygnus OB2 is the best available target to study these processes given its relative proximity and large content of OB and low-mass stars. We present our preliminary results on the photoevaporation of circumstellar disks in Cyg OB2 induced by the UV radiation emitted by OB stars.
Guarcello , Mario Giuseppe;Drake, Jeremy J.;Wright, Nicholas J.;Drew, Janet E.;Garcia-Alvarez, D.;Gutermuth, R. A.;Hora, J. L.;Kashyap, V.;King, Robert R.;Naylor, Tim
The Labyrinth of Star Formation, Astrophysics and Space Science Proceedings, Volume 36. ISBN 978-3-319-03040-1. Springer International Publishing Switzerland, 2014, p. 89
n/a 2014
6. The Dynamics of an Expanding OB Association ADS CITATION
Abstract
We present 3-dimensional kinematical observations of the massive OB association Cygnus OB2 to identify the mechanisms responsible for disrupting young star clusters. The picture revealed by these observations is of a highly-substructured, dynamically unmixed OB association that does not exhibit the position-velocity correlations predicted by the theories of infant mortality or tidal stripping. These observations would appear to support a picture of hierarchical star formation.
Wright, Nicholas J.;Bouy, Herve;Drake, Jeremy J.;Drew, Janet E.;Guarcello , Mario;Barrado y Navacués, David
The Labyrinth of Star Formation, Astrophysics and Space Science Proceedings, Volume 36. ISBN 978-3-319-03040-1. Springer International Publishing Switzerland, 2014, p. 465
n/a 2014
### 2013
1. Externally Induced Disks Photoevaporation in the Massive Cluster Cygnus OB2 ADS
Abstract
CygnusOB2, the most massive OB association of the Cygnus-X region, hosts more than 2000 OB stars and a population of young pre-Main Sequence stars. It is 1.4kpc distant from the Sun and the best target to study star formation and disk evolution in the presence of a large number of massive stars. We present a multiwavelength study of protoplanetary disks in Cyg OB2, based on new deep optical and X-ray data obtained with OSIRIS@GTC and Chandra/ACIS-I (the Cygnus OB2 Chandra Legacy Survey), and on archival data from 2MASS, UKIDSS, IPHAS and the Spitzer Legacy Survey of the Cygnus-X Region. We compare the spatial variation of disk fraction with the intensity of the ionized flux emitted by the OB members of CygOB2. We show that the disk fraction decreases gradually with increasing the intensity of the ionizing flux. The results suggests protoplanetary disks in Cyg OB2 suffer long-range photoevaporation induced by the OB star population. This is different than the results obtained in the study of NGC6611 (i.e. Guarcello et al 2007), NGC2264 (i.e. Balog et al. 2007), and the Trapezium in Orion (i.e. Storzer & Hollenbach 1999), where disk fraction drops only in the proximity of the OB stars. We discuss this difference in terms of the larger ionizing flux and older age in Cyg OB2 with respect to these other clusters and touch upon the relevance of this work for planet formation in the universe.
Guarcello, Mario
Protostars and Planets VI, Heidelberg, July 15-20, 2013. Poster #2S037
Jul 2013
2. OSIRIS deep Imaging of Cygnus OB2: the stellar population of the Cygnus X central engine
Abstract
The young massive cluster Cyg OB2 is the closest massive star forming region to the Sun, with hundreds of OB members, and then the best target in the Milky Way to study the feedback of massive stars on the star formation process. To study in detail the stellar population of such a unique target, Cyg OB2 has been observed with GTC/OSIRIS and Chandra/ACIS-I. We present the OSIRIS observations, the catalog and the preliminary scientific results.
Guarcello , M. G.;Drake, J. J.;Wright, N. J.;García-Álvarez, D.;Drew, J. E.;Aldcroft, T.;Fruscione, A.;Kashyap, V. L.
Fourth Science Meeting with the GTC (Eds. C. Muñoz-Tuñón & J. M. Rodríguez-Espinosa) Revista Mexicana de Astronomía y Astrofísica (Serie de Conferencias) Vol. 42, pp. 5-7 (2013) (http://www.astroscu.unam.mx/~rmaa/)
May 2013
3. The Disk-bearing Population in the Massive Stars Forming Region Cygnus OB2 ADS
Abstract
Cygnus OB2 is the closest massive star forming region hosting thousand OB stars to the Sun (1450 pc). It represents the best target to study how OB stars affect the star formation process, protoplanetary disk evolution and the evolution of the parent molecular cloud its surroundings. We obtained deep optical observations in r’, i’, and z’ bands with the 10.4m Gran Telescopio Canarias OSIRIS camera, and performed an X-ray survey covering about 1 square degree with Chandra’s ACIS-I (the 1.08 Msec Chandra Cyg OB2 Legacy Survey). These observations, combined with existing deep infrared and optical data of this region (from IPHAS, SDSS DR8, 2MASS/PSC, UKIDSS/GPS, and the ”The Spitzer Legacy Survey of the Cygnus-X Region”) allow us to select the cluster members down to sub-solar masses, and to analyze in detail the different effects that the radiation from OB stars have on the surrounding young stellar population, including triggering of star formation, externally induced disk photoevaporation, and dissipation of protostellar cores. In this contribution, we present the first results obtained from our combined survey: the selection of disk-bearing cluster members, the study of their evolutionary status and of the morphology of the association.
Guarcello , Mario G.;Drake, J. J.;Wright, N. J.;Drew, J.;Garcia-Alvarez, D.;Gutermuth, R. A.;Hora, J. L.;Kashyap, V.;King, R.;Naylor, T.
American Astronomical Society, AAS Meeting #221, id.251.20
Jan 2013
### 2012
1. VizieR Online Data Catalog: riz photometry in Cyg OB2 (Guarcello+, 2012)
Abstract
The observations were performed in the r’, i’, and z’ filters with OSIRIS, mounted on the 10.4m Gran Telescopio CANARIAS (GTC) of the Spanish Observatorio del Roque de los Muchachos in La Palma, between 2009-09-11 and 2009-09-22. The scale on the detector is 0.127arcsec/pix (1 data file).
Guarcello , M. G.;Wright, N. J.;Drake, J. J.;Garcia-Alvarez, D.;Drew, J. E.;Aldcroft, T.;Kashyap, V. L.
VizieR On-line Data Catalog: J/ApJS/202/19. Originally published in: 2012ApJS..202...19G
Nov 2012
2. The Dynamics of an Expanding OB Association ADS CITATION
Abstract
We present 3-dimensional kinematical observations of the massive OB association Cygnus OB2 to identify the mechanisms responsible for disrupting young star clusters. The picture revealed by these observations is of a highly-substructured, dynamically unmixed OB association that does not exhibit the position-velocity correlations predicted by the theories of infant mortality or tidal stripping. These observations would appear to support a picture of hierarchical star formation.
Wright, Nicholas J.;Bouy, Herve;Drake, Jeremy J.;Drew, Janet E.;Guarcello , Mario;Navacues, David Barrado y
eprint arXiv:1208.0211
Aug 2012
3. The Gaia-ESO Public Spectroscopic Survey ADS CITATION
Abstract
The Gaia-ESO Public Spectroscopic Survey has begun and will obtain high quality spectroscopy of some 100000 Milky Way stars, in the field and in open clusters, down to magnitude 19, systematically covering all the major components of the Milky Way. This survey will provide the first homogeneous overview of the distributions of kinematics and chemical element abundances in the Galaxy. The motivation, organisation and implementation of the Gaia-ESO Survey are described, emphasising the complementarity with the ESA Gaia mission. Spectra from the very first observing run of the survey are presented.
Gilmore, G.;Randich, S.;Asplund, M.;Binney, J.;Bonifacio, P.;Drew, J.;Feltzing, S.;Ferguson, A.;Jeffries, R.;Micela, G.;Negueruela, I.;Prusti, T.;Rix, H.-W.;Vallenari, A.;Alfaro, E.;Allende-Prieto, C.;Babusiaux, C.;Bensby, T.;Blomme, R.;Bragaglia, A.;Flaccomio, E.;François, P.;Irwin, M.;Koposov, S.;Korn, A.;Lanzafame, A.;Pancino, E.;Paunzen, E.;Recio-Blanco, A.;Sacco, G.;Smiljanic, R.;Van Eck, S.;Walton, N.;Aden, D.;Aerts, C.;Affer, L.;Alcala, J.-M.;Altavilla, G.;Alves, J.;Antoja, T.;Arenou, F.;Argiroffi, C.;Asensio Ramos, A.;Bailer-Jones, C.;Balaguer-Nunez, L.;Bayo, A.;Barbuy, B.;Barisevicius, G.;Barrado y Navascues, D.;Battistini, C.;Bellas Velidis, I.;Bellazzini, M.;Belokurov, V.;Bergemann, M.;Bertelli, G.;Biazzo, K.;Bienayme, O.;Bland-Hawthorn, J.;Boeche, C.;Bonito, S.;Boudreault, S.;Bouvier, J.;Brandao, I.;Brown, A.;de Bruijne, J.;Burleigh, M.;Caballero, J.;Caffau, E.;Calura, F.;Capuzzo-Dolcetta, R.;Caramazza, M.;Carraro, G.;Casagrande, L.;Casewell, S.;Chapman, S.;Chiappini, C.;Chorniy, Y.;Christlieb, N.;Cignoni, M.;Cocozza, G.;Colless, M.;Collet, R.;Collins, M.;Correnti, M.;Covino, E.;Crnojevic, D.;Cropper, M.;Cunha, M.;Damiani, F.;David, M.;Delgado, A.;Duffau, S.;Edvardsson, B.;Eldridge, J.;Enke, H.;Eriksson, K.;Evans, N. W.;Eyer, L.;Famaey, B.;Fellhauer, M.;Ferreras, I.;Figueras, F.;Fiorentino, G.;Flynn, C.;Folha, D.;Franciosini, E.;Frasca, A.;Freeman, K.;Fremat, Y.;Friel, E.;Gaensicke, B.;Gameiro, J.;Garzon, F.;Geier, S.;Geisler, D.;Gerhard, O.;Gibson, B.;Gomboc, A.;Gomez, A.;Gonzalez-Fernandez, C.;Gonzalez Hernandez, J.;Gosset, E.;Grebel, E.;Greimel, R.;Groenewegen, M.;Grundahl, F.;Guarcello , M.;Gustafsson, B.;Hadrava, P.;Hatzidimitriou, D.;Hambly, N.;Hammersley, P.;Hansen, C.;Haywood, M.;Heber, U.;Heiter, U.;Held, E.;Helmi, A.;Hensler, G.;Herrero, A.;Hill, V.;Hodgkin, S.;Huelamo, N.;Huxor, A.;Ibata, R.;Jackson, R.;de Jong, R.;Jonker, P.;Jordan, S.;Jordi, C.;Jorissen, A.;Katz, D.;Kawata, D.;Keller, S.;Kharchenko, N.;Klement, R.;Klutsch, A.;Knude, J.;Koch, A.;Kochukhov, O.;Kontizas, M.;Koubsky, P.;Lallement, R.;de Laverny, P.;van Leeuwen, F.;Lemasle, B.;Lewis, G.;Lind, K.;Lindstrom, H. P. E.;Lobel, A.;Lopez Santiago, J.;Lucas, P.;Ludwig, H.;Lueftinger, T.;Magrini, L.;Maiz Apellaniz, J.;Maldonado, J.;Marconi, G.;Marino, A.;Martayan, C.;Martinez-Valpuesta, I.;Matijevic, G.;McMahon, R.;Messina, S.;Meyer, M.;Miglio, A.;Mikolaitis, S.;Minchev, I.;Minniti, D.;Moitinho, A.;Momany, Y.;Monaco, L.;Montalto, M.;Monteiro, M. J.;Monier, R.;Montes, D.;Mora, A.;Moraux, E.;Morel, T.;Mowlavi, N.;Mucciarelli, A.;Munari, U.;Napiwotzki, R.;Nardetto, N.;Naylor, T.;Naze, Y.;Nelemans, G.;Okamoto, S.;Ortolani, S.;Pace, G.;Palla, F.;Palous, J.;Parker, R.;Penarrubia, J.;Pillitteri, I.;Piotto, G.;Posbic, H.;Prisinzano, L.;Puzeras, E.;Quirrenbach, A.;Ragaini, S.;Read, J.;Read, M.;Reyle, C.;De Ridder, J.;Robichon, N.;Robin, A.;Roeser, S.;Romano, D.;Royer, F.;Ruchti, G.;Ruzicka, A.;Ryan, S.;Ryde, N.;Santos, N.;Sanz Forcada, J.;Sarro Baro, L. M.;Sbordone, L.;Schilbach, E.;Schmeja, S.;Schnurr, O.;Schoenrich, R.;Scholz, R.-D.;Seabroke, G.;Sharma, S.;De Silva, G.;Smith, M.;Solano, E.;Sordo, R.;Soubiran, C.;Sousa, S.;Spagna, A.;Steffen, M.;Steinmetz, M.;Stelzer, B.;Stempels, E.;Tabernero, H.;Tautvaisiene, G.;Thevenin, F.;Torra, J.;Tosi, M.;Tolstoy, E.;Turon, C.;Walker, M.;Wambsganss, J.;Worley, C.;Venn, K.;Vink, J.;Wyse, R.;Zaggia, S.;Zeilinger, W.;Zoccali, M.;Zorec, J.;Zucker, D.;Zwitter, T.;Gaia-ESO Survey Team
The Messenger, vol. 147, p. 25-31
Mar 2012
4. Discovery of 15 Myr Old pre-Main Sequence Stars with Active Accretion and Sizeable Discs in NGC 6611 ADS
Abstract
Attention is given to a population of 110 stars with prominent near-infrared (NIR) excess in the NGC 6611 cluster of the Eagle Nebula that have optical colours typical of pre-main sequence (PMS) stars older than 10 Myr. In principle, their V-I colours would be consistent with those of young PMS objects (< 1 Myr), whose radiation is heavily obscured by a circumstellar disc seen at high inclination and in small part scattered towards the observer by the back side of the disc. However, using theoretical models it is shown here that objects of this type can only account for a few percent of this population. In fact, the spatial distribution of these objects, their X-ray luminosities, their optical brightness and their positions in the colour-magnitude diagram unambiguously indicate that most of these stars are intrinsically older than 10 Myr. Ages range from 8 to 30 Myr with a median value of 15 Myr. This is the largest homogeneous sample to date of Galactic PMS stars considerably older than 10 Myr that are still actively accreting from a circumstellar disc and it allows us to set a lower limit of 5% to the disc frequency at 15 Myr in NGC 6611. These values imply a characteristic exponential lifetime of 5 Myr for disc dissipation.
De Marchi, Guido;Panagia, N.;Guarcello , M. G.;Bonito, R.
American Astronomical Society, AAS Meeting #219, id.337.06
Jan 2012
### 2011
1. Chandra/ACIS-I study of the young stellar population of the Eagle Nebula
Abstract
Not Available
Guarcello , Mario;Caramazza, Marilena;Drake, Jeremy;Micela, Giuseppina;Sciortino, Salvatore
"The X-ray Universe 2011, Presentations of the Conference held in Berlin, Germany, 27-30 June 2011. Available online at: http://xmm.esac.esa.int/external/xmm_science/workshops/2011symposium/, article id.219"
Aug 2011
2. Cluster members and disk fraction of CygnusOB2
Abstract
Not Available
Guarcello , Mario;Drake, Jeremy;Wright, Nicholas
"The X-ray Universe 2011, Presentations of the Conference held in Berlin, Germany, 27-30 June 2011. Available online at: http://xmm.esac.esa.int/external/xmm_science/workshops/2011symposium/, article id.218"
Aug 2011
3. The Chandra Cygnus OB2 Legacy Survey
Abstract
Not Available
Wright, Nicholas;Drake, Jeremy;Guarcello , Mario;Aldcroft, Tom;Kashyap, Vinay;Fruscione, Antonella;Damiani, Francesco;Flaccomio, Ettore;van der Veen, Erik
"The X-ray Universe 2011, Presentations of the Conference held in Berlin, Germany, 27-30 June 2011. Available online at: http://xmm.esac.esa.int/external/xmm_science/workshops/2011symposium/, article id.170"
Aug 2011
4. Observations and theory on the externally induced photoevaporation of circumstellar disk
Abstract
Class II Pre-Main Sequence stars are characterized by the presence of the circumstellar disk in the equatorial plane, which is the site of the planets formation. The induced photoevaporation of disks is one of the key processes leading the evolution of these structures. Photoevaporation occurs when the disk is irradiated by UV and X-ray radiation: Far UltraViolet (FUV) photons (with energy ranging from 6eV to 13.6eV) dissociate H2 molecules, while Extreme UltraViolet (EUV, from 13.6eV to 100eV ) and X-ray photons ionize gas atoms. Since both processes heat the gas up to 1000K-10000K, the thermal pressure drives a photoevaporative flow of gas away from the disk. Photoevaporation is usually induced by the central star itself; however, direct images (taken with the Hubble Space Telescope) of the young stars surrounded by photoevaporating disks in the Orion Nebula Cluster showed that photoevaporation can be induced by the energetic radiation emitted by nearby massive stars. In these cases, the externally induced photoevaporation can dissipate the disks in short timescale (even smaller than 1 Myear in the more extreme situations). Besides, recent studies of the massive young clusters NGC2244 and NGC6611 confirmed that the evolution of circumstellar disks is affected by induced photoevaporation in the core of such massive clusters, but there is still some controversy about these results. In this talk I will review the main features of the photoevaporation process, its effects on disks evolution when it is induced by nearby ionizing sources, and the supporting observational evidences.
Guarcello, Mario G.
American Astronomical Society, AAS Meeting #218, id.312.02
May 2011
### 2010
1. VizieR Online Data Catalog: NGC 1893 optical and NIR photometry (Prisinzano+, 2011) ADS
Abstract
We present new optical and NIR photometric data in the VRIJHK and H-α bands for the cluster NGC 1893. The optical photometry was obtained by using images acquired in service mode using two different telescopes: the Device Optimized for the LOw RESolution (DOLORES) mounted on the Telescopio Nazionale Galileo (TNG), used in service mode during three nights in 2007, and the Calar Alto Faint Object Spectrograph (CAFOS), mounted on the 2.2m telescope in Calar Alto German-Spanish Observatory (Spain), during three nights in 2007 and 2008. NIR observations were acquired in service mode at the TNG, using the large field Near Infrared Camera Spectrometer (NICS) with the Js(1.25um), H(1.63um) and K'(2.12um) filters during eight nights in 2007 and 2008. We observed a field around NGC 1893 with a raster of 4×4 pointings, at each pointing we obtained a series of NINT dithered exposures. Each exposure is a repetition of a DIT (Detector Integration Time) times NDIT (number of DIT), to avoid saturation of the background. (4 data files).
Prisinzano, L.;Sanz-Forcada, J.;Micela, G.;Caramazza, M.;Guarcello , M. G.;Sciortino, S.;Testi, L.
VizieR On-line Data Catalog: J/A+A/527/A77. Originally published in: 2011A&A...527A..77P
Oct 2010
2. VizieR Online Data Catalog: Stars associated to Eagle Nebula (M16=NGC6611) (Guarcello+ 2010) ADS
Abstract
This catalog contains coordinates and both optical and infrared photometry, plus usefull tags, of the candidate stars associated to the Eagle Nebula (M16), bost disk-less and disk-bearing, selected in Guarcello et al. 2010: “Chronology of star formation and disks evolution in the Eagle Nebula”. The optical photometry in BVI bands comes from observations with WFI@ESO (Guarcello et al. 2007, Cat. J/A+A/462/245); JHK photometry have been obtained from 2MASS/PSC (Bonatto et al. 2006A&A…445..567B, Guarcello et al. 2007, Cat. J/A+A/462/245) and UKIDSS/GPS catalogs (Guarcello et al., 2010, in prep.) ; IRAC data are from GLIMPSE public survey (Indebetouw 2007ApJ…666..321I, Guarcello et al., 2009, Cat. J/A+A/496/453); X-ray data from three observations with Chandra/ACIS-I (Linsky et al., 2007, Cat. J/ApJ/654/347, Guarcello et al., 2007, J/A+A/462/245, Guarcello et al. 2010, in prep.). (1 data file).
Guarcello , M. G.;Micela, G.;Peres, G.;Prisinzano, L.;Sciortino, S.
VizieR On-line Data Catalog: J/A+A/521/A61. Originally published in: 2010A&A...521A..61G
Aug 2010
3. VizieR Online Data Catalog: Blue stars with disk photometry in NGC 6611 (Guarcello+, 2010) ADS
Abstract
This catalog contains coordinates and both optical and infrared photometry, plus usefull tags, of the Blue Stars With Disk (BWE stars) discussed in detail in Guarcello et al. (2010, in prep): “Pre-main sequence stars with disks in the Eagle nebula observed in scattered light”. The optical photometry in BVI bands comes from observations with WFI@ESO (Guarcello et al. 2007, Cat. J/A+A/462/245); JHK photometry have been obtained from 2MASS/PSC and UKIDSS/GPS catalogs (Bonatto et al., 2006A&A…445..567B, Guarcello et al., 2007, Cat. J/A+A/462/245 and 2010, in prep); IRAC data are from GLIMPSE public survey (Indebetouw 2007ApJ…666..321I, Guarcello et al., 2009, Cat. J/A+A/496/453); X-ray data from observations with Chandra/ACIS-I (Linsky et al. 2007, Cat. J/ApJ/654/347, Guarcello et al., 2007, Cat. J/A+A/462/245, Guarcello et al., 2010, in prep). BWE stars have been studied by analizing their Spectral Energy Distribution (SED) using the grid of YSO models developed by Robitaille et al. 2006ApJS..167..256R. (1 data file).
Guarcello , M. G.;Damiani, F.;Micela, G.;Peres, G.;Prisinzano, L.;Sciortino, S.
VizieR On-line Data Catalog: J/A+A/521/A18. Originally published in: 2010A&A...521A..18G
Jun 2010
### 2009
1. VizieR Online Data Catalog: Photometry of candidate members of NGC6611 (Guarcello+, 2009) ADS
Abstract
Optical BVI photometry have been obtained from 2.2m WFI@ESO observations; JHK data are from 2MASS Point Sources Catalog; IRAC data are from GLIMPSE catalog. X-ray data have been obtained from a CHANDRA/ACIS-I observation of a field o f 17’x17′ centered on the cluster. (1 data file).
Guarcello , M. G.;Micela, G.;Damiani, F.;Peres, G.;Prisinzano, L.;Sciortino, S.
VizieR On-line Data Catalog: J/A+A/496/453. Originally published in: 2009A&A...496..453G
Mar 2009
### 2007
1. VizieR Online Data Catalog: BVI photometry in NGC 6611 (Guarcello+, 2007) ADS
Abstract
The optical data have been taken in the BVI bands with the Wield Field Camera (WFI), mounted on the 2.2m telescope of the European Southern Observatory (ESO) in La Silla (Chile). The optical images used in this work were taken on 29 July 2000. (1 data file).
Guarcello , M. G.;Prisinzano, L.;Micela, G.;Damiani, F.;Peres, G.;Sciortino, S.
VizieR On-line Data Catalog: J/A+A/462/245. Originally published in: 2007A&A...462..245G
Sep 2007
Proceedings and Other Publications
• Wright, N. J.; Bouy, H.; Drake, J. J.; Drew, J. E.; Guarcello, M. G.; Navacues, D. B., 2012, “The Dynamics of an Expanding OB Association”, ArXiv, 208, 0211. link
• Gilmore, G.; Randich, S.; Asplund, M.; Binney, J.; Bonifacio, P.; Drew, J.; Feltzing, S.; Ferguson, A.; Jeffries, R.; Micela, G.; and 265 coauthors, 2012, “The Gaia-ESO Public Spectroscopic Survey”, The Messanger Vol. 1, 147, 25G. link
• Guarcello, M. G.; Drake, J. J.; Wright, N. J.; Garcia-Alvarez, D.; Drew, J. E.; Aldcroft, T.; Fruscione, A.; Kashyap, V. L., 2013, “OSIRIS deep Imaging of Cygnus OB2: the stellar population of the Cygnus X central engine”, RMxAC, 52, 5G. link
• Guarcello, M. G.; Drake, J. J.; Wright, N. J.; Drew, J. E.; Garcia-Alvarez, D.; Gutermuth, R. A.; Hora, J. L.; Kashyap, V.; King, R. R.; Naylor, T., 2014, “Disk Survival in the Extremely Massive Association Cygnus OB2”, ASSP, 36, 89G. link
• Guarcello, M. G.; Chapter: “Ammassi Stellari” (Star Clusters) of the book: “Voci e domande dell’Astrofisica” (Voices and questions of Astrophysics) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8119074702262878, "perplexity": 7367.824690175849}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875144722.77/warc/CC-MAIN-20200220100914-20200220130914-00365.warc.gz"} |
https://pub.uni-bielefeld.de/publication/2685285 | # First observations on a corpus of multi-modal trialogues
Hahn F, Lawler I, Rieser H (In Press)
Presented at the The 18th Workshop on the Semantics and Pragmatics of Dialogue (DialWatt), Edinburgh.
No fulltext has been uploaded. References only!
Conference Paper | In Press | English
Author
Publishing Year
Conference
The 18th Workshop on the Semantics and Pragmatics of Dialogue (DialWatt)
Location
Edinburgh
Conference Date
2014-09-01 – 2014-09-03
PUB-ID
### Cite this
Hahn F, Lawler I, Rieser H. First observations on a corpus of multi-modal trialogues. Presented at the The 18th Workshop on the Semantics and Pragmatics of Dialogue (DialWatt), Edinburgh.
Hahn, F., Lawler, I., & Rieser, H. (In Press). First observations on a corpus of multi-modal trialogues. Presented at the The 18th Workshop on the Semantics and Pragmatics of Dialogue (DialWatt), Edinburgh
Hahn, F., Lawler, I., and Rieser, H. (In Press).“First observations on a corpus of multi-modal trialogues”. Presented at the The 18th Workshop on the Semantics and Pragmatics of Dialogue (DialWatt), Edinburgh.
Hahn, F., Lawler, I., & Rieser, H., In Press. First observations on a corpus of multi-modal trialogues. Presented at the The 18th Workshop on the Semantics and Pragmatics of Dialogue (DialWatt), Edinburgh.
F. Hahn, I. Lawler, and H. Rieser, “First observations on a corpus of multi-modal trialogues”, Presented at the The 18th Workshop on the Semantics and Pragmatics of Dialogue (DialWatt), Edinburgh, In Press.
Hahn, F., Lawler, I., Rieser, H.: First observations on a corpus of multi-modal trialogues. Presented at the The 18th Workshop on the Semantics and Pragmatics of Dialogue (DialWatt), Edinburgh (In Press).
Hahn, Florian, Lawler, Insa, and Rieser, Hannes. “First observations on a corpus of multi-modal trialogues”. Presented at the The 18th Workshop on the Semantics and Pragmatics of Dialogue (DialWatt), Edinburgh, In Press.
This data publication is cited in the following publications:
This publication cites the following data publications:
### Export
0 Marked Publications
Open Data PUB | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9404498934745789, "perplexity": 19795.392713065783}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590074.12/warc/CC-MAIN-20180718080513-20180718100513-00187.warc.gz"} |
https://keio.pure.elsevier.com/en/publications/a-ferromagnetic-quantum-critical-point-in-heavy-fermion-iron-oxyp | # A ferromagnetic quantum critical point in heavy-fermion iron oxypnictide CeFe1-xCrxPO
T. Okano, S. Kitao, M. Seto, T. Atou, M. Itoh, M. Matoba, Y. Kamihara
Research output: Contribution to journalArticlepeer-review
1 Citation (Scopus)
## Abstract
We report crystallographic and magnetic properties of layered iron oxypnictide CeFe1-xCrxPO (x = 0.000-0.692). Interlayer distances between Ce2O2 and (Fe1-xCrx)2P2 layers increase as a function of x, suggesting suppression of Kondo coupling among hybridized conducting orbitals and localized Ce 4f orbitals. CeFe1-xCrxPO (x = 0.100-0.384) exhibits finite ferromagnetic transition temperatures (Tcurie) obtained by Arrott plots, although 57Fe Mössbauer spectra reveal paramagnetic Fe sublattice at T 4.2 K. These results indicate that the ferromagnetic phase transitions of samples are mainly due to Ce sublattice. For the samples with x ≥ 0.500, no ferromagnetic order is observed down to 2 K. These results verify that ferromagnetic quantum critical points of CeFe1-xCrxPO appear at 0.045 ≤ x ≤ 0.100 and 0.384 ≤ x ≤ 0.500.
Original language English 17E123 Journal of Applied Physics 117 17 https://doi.org/10.1063/1.4916808 Published - 2015 May 7
## ASJC Scopus subject areas
• Physics and Astronomy(all) | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8010079860687256, "perplexity": 18516.751381831516}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988753.91/warc/CC-MAIN-20210506083716-20210506113716-00447.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?p=146039 | ## Explaining Boltzmann's Equation
Boltzmann Equation for Entropy: $S = k_{B} \ln W$
JeremyPark14B
Posts: 29
Joined: Fri Sep 28, 2018 12:19 am
### Explaining Boltzmann's Equation
What is the explanation behind Boltzmann's Equation? What exactly does it solve for?
Ashley Kim
Posts: 62
Joined: Fri Sep 28, 2018 12:19 am
Been upvoted: 1 time
### Re: Explaining Boltzmann's Equation
Boltzmann's equation calculates positional/residual entropy using statistics.
Its form is S=kBlnW.
W is equal to the number of microstates (how many positions an element can be in in a molecule) raised to the power of the number of molecules in the system.
kB is a constnant.
Dimitri Speron 1C
Posts: 60
Joined: Fri Sep 28, 2018 12:17 am
Been upvoted: 1 time
### Re: Explaining Boltzmann's Equation
The actual derivation for Boltzmann's equation is quite complicated and involves a lot of multivariable calc, so I would just take it for granted.
Andrew Bennecke
Posts: 62
Joined: Fri Sep 28, 2018 12:15 am
### Re: Explaining Boltzmann's Equation
We use Boltzmann's equation to calculate residual or statistical entropy within a system. This differs from the majority of calculations that we do, finding the CHANGE in entropy.
armintaheri
Posts: 68
Joined: Fri Sep 28, 2018 12:26 am
### Re: Explaining Boltzmann's Equation
I found a relatively accessible derivation of the formula here: http://www.eoht.info/page/S+%3D+k+ln+W
Ashe Chen 2C
Posts: 31
Joined: Mon Jan 07, 2019 8:23 am
### Re: Explaining Boltzmann's Equation
Boltzmann's equation solves for statistical or residual entropy, and is based on the number of microstates and number of molecules in a system.
Esther Lee 4H
Posts: 67
Joined: Fri Sep 28, 2018 12:29 am
### Re: Explaining Boltzmann's Equation
how do you know how many molecules are present?
Return to “Third Law of Thermodynamics (For a Unique Ground State (W=1): S -> 0 as T -> 0) and Calculations Using Boltzmann Equation for Entropy”
### Who is online
Users browsing this forum: No registered users and 0 guests | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6503334641456604, "perplexity": 5300.049386336433}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251783342.96/warc/CC-MAIN-20200128215526-20200129005526-00425.warc.gz"} |
http://www.listserv.uga.edu/cgi-bin/wa?A2=ind0903e&L=sas-l&D=1&H=1&O=D&F=&S=&P=9466 | Date: Mon, 30 Mar 2009 09:32:00 -0700 Reply-To: "Kenneth M. Lin" Sender: "SAS(r) Discussion" From: "Kenneth M. Lin" Organization: at&t http://my.att.net/ Subject: Re: SAS DDE to control Excel 2007 Comments: To: [email protected] "Paige Miller" wrote in message news:876e3916-b949-4c6a-b0d9-61ba5a2ace16@q16g2000yqg.googlegroups.com... >I just upgraded (unfortunately) to Excel 2007. Had no choice, my > company provided me with a new computer with Excel 2007, no option to > get any other version. > > So ... I have programs that use SAS DDE to control Excel. Are there > any differences between Excel 2007 and earlier version, as far as SAS > commands are concerned? Thanks! > > -- > Paige Miller > paige\dot\miller \at\ kodak\dot\com You now have a choice of saving the file as *.xls (old format) or *.xlsx (new format). If you are still reading/writing to *.xls format, there's nothing to worry about.
Back to: Top of message | Previous page | Main SAS-L page | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46480482816696167, "perplexity": 17532.68895758564}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164965557/warc/CC-MAIN-20131204134925-00031-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://datascience.stackexchange.com/questions/29858/generalization-of-correlation-coefficient | # Generalization of Correlation Coefficient
The correlation coefficient tells me how two variables (sequences of numbers) are correlated with each other. Does it generalize to non-linear scenarios? How could one more generally measure the general predictive power of x over y when the relationship between x and y is not linear?
• Through information-theoretic measures like the mutual information; the reduction of entropy in one variable through knowing the other. This too can be generalized through the Renyi entropy. Welcome to the site. – Emre Apr 3 '18 at 16:39
• That's a pretty broad question. Please edit the question to clarify what is given. Are x,y random variables? Are we given the probability distribution of x,y? Are we given a finite dataset with some values for x,y? Do you know in advance what the relationship looks like, or could it be anything? – D.W. Apr 4 '18 at 5:19
I assume that when you speak of correlation coeficient, you have the Pearson linear correlation in mind. Indeed, there are other options. Two very popular ones are the rank correlations respectively called Spearman's $\rho$ and Kendall's $\tau$.
To give you an idea of what they are, consider $n$ observations from a $d$-dimensional random vector $X = (X_1,\dots,X_d)$. Also let $X_{ij}$ be the $i$th observation for variable $j$. These measures are called rank correlations because they can be computed using the ranks only. What I mean is that if you sort all $X_{ij}$, $i=1,\dots,n$, and replace the biggest observation by $n$, the second biggest by $n-1$, and so on (do that for all columns $j$) and call you new observations $R_{ij}$, then
1. the empirical Spearman's $\rho$ (matrix) is simply the Pearson linear correlation (matrix) of $(R_1,\dots,R_d)$; and
2. the empirical (pairwise) Kendall's $\tau$ between $X_{i_1}$ and $X_{i_2}$ is the probability of concordance minus the probability of discordance between two iid observations, say $(X_{1 i_1},X_{1 i_2})$ and $(X_{2 i_1},X_{2 i_2})$, which can equivalently be computed from the ranks $(R_{1 i_1},R_{1 i_2})$ and $(R_{2 i_1},R_{2 i_2})$ instead.
A rank correlation between $X_{i_1}$ and $X_{i_2}$ of one indeed means perfect concordance (i.e. $X_{i_1}$ always increases with $X_{i_2}$), but that does not necessarily means they are linearly related. The ranks are linearly related.
Just to make the concept of concordance clearer, here the (bivariate) observations are all concordant
and here they are all discordant
So that when you consider a cloud of points you have some pairs that are concordant and others that are discordant.
Note that this answer provides examples, but there are many other ways to approach the question. As commented by Emre, information-theoretic measures are also an option. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8484633564949036, "perplexity": 434.53705260858806}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107919459.92/warc/CC-MAIN-20201031151830-20201031181830-00243.warc.gz"} |
http://budgetmodel.wharton.upenn.edu/issues/2016/7/22/environmental-taxation | Top
# Environmental Taxation
Key Points
• A carbon tax is a cost-effective way to correct for environmental costs imposed by the production of the energy sector.
• A carbon tax can produce substantial revenue that can be used to lower other taxes, reduce the deficit, or redistribute income.
• A carbon tax would reduce carbon dioxide emissions, but by how much is uncertain.
# Environmental Taxation
Editor’s Note: This article is part of a series of tax-related articles sponsored by the Penn Wharton Budget Model and the Robert D. Burch Center at Berkeley. All of the articles in this series are forthcoming in a book by Oxford University Press, co-edited by Alan Auerbach and Kent Smetters.
Environmental Taxation examines environmental tax-policy reforms, in particular a carbon tax. Robert C. Williams (2016) finds that a carbon tax is a cost-effective way to reduce greenhouse gas emissions. When implementing an environmental tax, however, it is important to consider the cost of implementation, effects on the economy, and who bears the burden of the tax.
Carbon emissions are an example of a market failure. When carbon dioxide (CO2) is released into the environment during the production of or use of a commodity, the CO2 harms someone other than the buyer or the seller, and neither the buyer nor the seller pays for that harm. Market failures can lead to an inefficient allocation of capital. For instance, in the case of CO2, society may make more products that release CO2 than would be efficient if buyers and sellers of CO2-generating products bore the full cost. Theoretically, a market failure can impede economic growth.
Economists often call an environmental tax to correct a market failure a Pigouvian tax. One problem with implementing an environmental tax is that it is difficult to calculate the harm to others caused by the market failure. In addition, an efficient environmental tax would allow for market flexibility across emitters and different methods of reducing emissions. A carbon tax will reduce CO2 emissions, but by how much is uncertain.
Williams (2016) finds that a tax on CO2 emissions is easy to implement. CO2 emissions are easy to monitor, since 94 percent of emissions are from the combustion of fossil fuels. In addition, CO2 emissions depend on only the carbon content of fuel, so taxing a few thousand fossil fuel firms can cover the vast majority (80 percent) of U.S. CO2 emissions. Williams notes that other greenhouses gases like Hydrochloroflourocarbons could also be added easily to the environmental tax base, while other gases may be harder to track.
The worldwide cost of CO2 emissions is estimated to be $43 per ton of CO2 emissions. However, the U.S. cost of CO2 emissions is estimated to be only$4 to $5 per ton of CO2 emissions. Williams (2016) finds that it is most efficient for the full carbon-tax rate to be implemented immediately rather than fazed in. Moreover, changes to the tax rate optimally follow changes to the cost of CO2 emissions. A carbon tax is likely to have a negative impact on Gross Domestic Product (GDP) and be regressive. A carbon tax is regressive because energy is a larger portion of the budget for households with lower incomes. However, a carbon tax is less regressive than it first appears when the impact of a carbon tax on the prices of all goods is considered rather than only the impact on the price of energy. The U.S. has low environmental taxes relative to other advanced countries both in terms of tax revenue and GDP. Figure 1 shows that the average environmental tax rate in other Organization for Economic Co-operation and Development (OECD) countries is 2.23 percent of GDP while in the U.S. it is only 0.9 percent of GDP. Figure 1: Environmental Tax Revenue as a Share of GDP Source: Metcalf (2009) However, a carbon tax will also likely produce substantial revenue. The United States ran budget deficit of$439 billion in 2015, according to the Congressional Budget Office (CBO). When applying methods used by Joint Committee on Taxation (JCT) and CBO, Figure 2 shows that a carbon tax will produce a net revenue to the government of $1.7 to$1.2 trillion over the next 10 years. In comparison, the corporate income tax is estimated to generate $4.6 trillion in revenue in the next 10 years and the budget deficit is estimated to be$2 trillion over the same time period.
Figure 2: Estimated Revenue in Trillions of Dollars over Next 10 Years
Source: CBO (2015)
Note: The vertical axis is trillions of U.S. dollars. The revenue estimate from the hypothetical carbon tax is based on a tax of \$25 per ton of carbon that rises at two percent per year in real terms and represents net revenue after accounting for the effects of the carbon tax on revenue from other taxes.
The extra tax revenue could be spent in several different ways, each with a different outcome. Figure 2 shows that a carbon tax could bring in enough revenue to substantially reduce the deficit over the next ten years. Alternatively, if the extra revenue is instead used to help lower income earners then the tax could be less regressive. If the additional money is used to reduce corporate income tax rates or other economic distortions, then the carbon tax could be used to mitigate some of its negative impact on GDP.
A discussion of this paper is provided by Don Fullerton. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2551197111606598, "perplexity": 1950.4628659757548}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256314.25/warc/CC-MAIN-20190521082340-20190521104340-00292.warc.gz"} |
https://worldwidescience.org/topicpages/c/chemical+gradient-mediated+melting.html | #### Sample records for chemical gradient-mediated melting
1. Chemical reactions in solvents and melts
CERN Document Server
Charlot, G
1969-01-01
Chemical Reactions in Solvents and Melts discusses the use of organic and inorganic compounds as well as of melts as solvents. This book examines the applications in organic and inorganic chemistry as well as in electrochemistry. Organized into two parts encompassing 15 chapters, this book begins with an overview of the general properties and the different types of reactions, including acid-base reactions, complex formation reactions, and oxidation-reduction reactions. This text then describes the properties of inert and active solvents. Other chapters consider the proton transfer reactions in
2. Melt and Chemical Transport in the Mantle: Insights from Deglaciation-Induced Melting Perturbations in Iceland
Science.gov (United States)
Eason, D. E.; Ito, G.; Sinton, J. M.
2011-12-01
Eruptive products represent a time-averaged view of the melting region and melt migration processes, making numerous fundamental parameters of the melt system difficult to constrain. Temporal and spatial variations in melting provide potential windows into this obscure region of the Earth by preferentially sampling melts from different regions of the mantle or mixing melts over different length-scales. We present a newly extended geochemical time series from the Western Volcanic Zone (WVZ) of Iceland, which experienced a short-lived melting perturbation due to glacial unloading during the last major deglaciation (~15-10 ka). Glacial unloading during this period led to increased degrees of melting particularly in the shallow mantle, which is manifest as an observed increase in volcanic production up to 30 times the steady-state value, decreased levels of highly to moderately incompatible element ratios (e.g., a 35-50% decrease in Nb/Y, with the greatest change occurring in the northernmost WVZ), and elevated SiO2 and CaO concentrations (~0.8 wt. % and ~1.9 wt. % increase in average oxide concentrations respectively) during and immediately following deglaciation. Although eruptive productivity returns to steady-state values within ~3000 yr following deglaciation, the incompatible element concentrations in erupted lavas gradually increase throughout the post-glacial period. We exploit this short-lived melting perturbation to examine and constrain knowledge of fundamental characteristics of melt generation and transport, including mantle permeability, melt ascent rates, depth-dependent melting functions (dF/dP), and the nature of chemical transport and melt mixing in the system. Using conservation equations describing the generation and porous flow of melt in a viscous matrix, we model melt migration in the mantle during and after ice sheet removal, as well as trace element transport for both equilibrium and disequilibrium transport end members. The predicted
3. Nepheline structural and chemical dependence on melt composition
Energy Technology Data Exchange (ETDEWEB)
Marcial, José; Crum, Jarrod; Neill, Owen; McCloy, John
2016-02-01
Nepheline crystallizes upon slow-cooling in some melts concentrated in Na2O and Al2O3, which can result in a residual glass phase of low chemical durability. Nepheline can incorporate many components often found in high-level waste radioactive borosilicate glass, including glass network ions (e.g., Si, Al, Fe), alkali metals (e.g., Cs, K, Na, and possibly Li), alkaline-earth metals (e.g., Ba, Sr, Ca, Mg), and transition metals (e.g., Mn, and possibly Cr, Zn, Ni). When crystallized from melts of different compositions, nepheline chemistry varies as a function of starting glass composition. Five simulated high level nuclear waste borosilicate glasses shown to crystallize large fractions of nepheline on slow cooling, were selected for study. These melts constituted a range of Al2O3, B2O3, CaO, Na2O, K2O, Fe2O3, and SiO2 compositions. Compositional analyses of nepheline crystals in glass by electron probe micro-analysis (EPMA) indicate that boron is unlikely to be present in any significant concentration, if at all, in nepheline. Also, several models are presented for calculating the fraction of vacancies in the nepheline structure.
4. The effect of milkfat melting properties on chemical and physical properties of 20% reformulated cream
OpenAIRE
Scott, Lisa Lenore
1999-01-01
The Effect of Milkfat Melting Properties on Chemical and Physical Properties of 20% Reformulated Cream Lisa L. Scott (ABSTRACT) Skim, sweet buttermilk, and butter derived aqueous phase components were used to re-emulsify low-melt and medium-melt fraction butteroils to yield 20% milkfat creams. The implications of separation temperature in obtaining components, melting point characteristics, and formulation on the chemical and physical properties of reformulated and natural crea...
5. Chemical interactions and configurational disorder in silicate melts
Directory of Open Access Journals (Sweden)
G. Ottonello
2005-06-01
Full Text Available The Thermodynamics of quasi-chemical and polymeric models are briefly reviewed. It is shown that the two classes are mutually consistent, and that opportune conversion of the existing quasi-chemical parameterization of binary interactions in MO-SiO2 joins to polymeric models may be afforded without substantial loss of precision. It is then shown that polymeric models are extremely useful in deciphering the structural and reactive properties of silicate melts and glasses. They not only allow the Lux-Flood character of the dissolved oxides to be established, but also discriminate subordinate strain energy contributions to the Gibbs free energy of mixing from the dominant chemical interaction terms. This discrimination means that important information on the short-, medium- and long-range periodicity of this class of substances can be retrieved from thermodynamic analysis. Lastly, it is suggested that an important step forward in deciphering the complex topology of the inhomogeneity ranges observed at high SiO2 content can be performed by applying SCMF theory and, particularly, Matsen-Schick spectral analysis, hitherto applied only to rubberlike materials.
6. Modeling the elution of organic chemicals from a melting homogeneous snow pack.
Science.gov (United States)
Meyer, Torsten; Wania, Frank
2011-06-01
Organic chemicals are often released in peak concentrations from melting snow packs. A simple, mechanistic snowmelt model was developed to simulate and predict the elution of organic substances from melting, homogeneous snow, as influenced by chemical properties and snow pack characteristics. The model calculates stepwise the chemical transport along with the melt water flow in a multi-layered snow pack, based on chemical equilibrium partitioning between the individual bulk snow phases. The model succeeds in reproducing the elution behavior of several organic contaminants observed in previously conducted cold room experiments. The model aided in identifying four different types of enrichment of organic substances during snowmelt. Water soluble substances experience peak releases early during a melt period (type 1), whereas chemicals that strongly sorb to particulate matter (PM) or snow grain surfaces elute at the end of melting (type 2). Substances that are somewhat water soluble and at the same time have a high affinity for snow grain surfaces may exhibit increasing concentrations in the melt water (type 3). Finally, elution sequences involving peak loads both at the beginning and the end of melting are simulated for chemicals that are partially dissolved in the aqueous melt water phase and partially sorbed to PM (type 4). The extent of type 1 enrichment mainly depends on the snow depth, whereby deeper snow generates more pronounced concentration peaks. PM influences the elution behavior of organic chemicals strongly because of the very large natural variability in the type and amount of particles present in snow. Urban and road-side snow rich in PM can generate type 2 concentration peaks at the end of the melt period for even relatively water soluble substances. From a clean, melting snow pack typical for remote regions, even fairly hydrophobic chemicals can be released in type 1 mode while being almost completely dissolved in the aqueous melt water phase. The
7. Physical and chemical effects of ultrasound vibration on polymer melt in extrusion.
Science.gov (United States)
Chen, Jinyao; Chen, Yingzi; Li, Huilin; Lai, Shih-Yaw; Jow, Jinder
2010-01-01
The physical and chemical effects of ultrasound on polypropylene (PP) melts in extrusion were investigated. By applying ultrasound vibration to the entrance of the die, apparent pressure and viscosity of PP can be obviously decreased under the appropriate ultrasound power. Ultrasound has both physical and chemical effects on the polymer melt. In our study with specific polymer and ultrasound system, we determined that the chemical effect makes up 35-40% of the total effect of ultrasound on the apparent viscosity reduction of PP melts at most of the studied intensities. The physical effect plays a more important role in the ultrasound-applied extrusion than the chemical effect. This chemical effect is an irreversible and permanent change in molecule weight and the molecular-weight distribution due to ultrasound. As the ultrasound intensity increases, the molecular weight of PP reduces and its molecular-weight distribution becomes narrower; the orientation of PP molecules along the flow direction reduces (in melt state) and the crystallinity of PP samples (in solid state) decreases by applying the ultrasound vibration. Ultrasound vibration increases the motion of molecular chains and makes them more disorder; it also affects the relaxation process of polymer melts by shortening the relaxation time of chain segments, leading to weakening the elastic effect and decreasing the extruding swell ratios. All the factors discussed above reduce the non-Newtonian flow characteristics of the polymer melt and result in the viscosity drop of the polymer melt in extrusion.
8. Frictional melting dynamics in the upper conduit: A chemical answer to a complex physical question
Science.gov (United States)
Henton De Angelis, S.; Lavallee, Y.; Kendrick, J. E.; Hornby, A.; von Aulock, F. W.; Clesham, S.; Hirose, T.; Perugini, D.
2013-12-01
During volcanic eruptions the generation of frictional heat along the walls of the shallow conduit leads to melting of the rocks along the slip interface. Frictional melting has previously been described as a process out of thermodynamic equilibrium, but upon slip and mingling of the melt batches, homogeneity can be achieved, and may have an h important rheological control on the dynamics of slip. To test melt homogenization in the frictional melt zones of volcanic conduits we performed constant-rate slip experiments under controlled stress conditions using a high-velocity rotary shear apparatus. Volcanic dome samples from three different volcanoes (Volcán De Colima, Soufrière Hills Volcano and Santiaguito Volcano) were investigated. Each sample was subjected to a stress of 1 MPa and slip rate of 1 m/s. For each sample set 5 experiments were conducted: 1) experiment stopped at the onset of melting; 2) experiment stopped on the formation of a full melt layer; 3) experiment stopped after 5m of slip at steady state conditions; 4) experiment stopped after 10m of slip at steady state conditions; 5) experiment stopped after 15m of slip at steady state conditions. We analyzed the resulting proto-melt zones using micron sized X-ray spectroscopy in the high-brightness synchrotron beamline I18 (at Diamond Light Source UK). Particular focus was given to the concentration variance analysis of Rare Earth Elements as their mobilities can be used to precisely quantify the degree and timescale of homogenisation involved during frictional melting. This study refines our understanding of the chemical process of melting and mixing which carry important consequences for the rheological control on the physical dynamics of slip.
9. Experiments on interactions between zirconium-containing melt and water (ZREX). Hydrogen generation and chemical augmentation of energetics
Energy Technology Data Exchange (ETDEWEB)
Cho, D.H.; Armstrong, D.R.; Gunther, W.H. [Argonne National Lab., IL (United States); Basu, S.
1998-01-01
The results of the first data series of experiments on interactions between zirconium-containing melt and water are described. These experiments involved dropping 1-kg batches of pure zirconium or zirconium-zirconium dioxide mixture melt into a column of water. A total of nine tests were conducted, including four with pure zirconium melt and five with Zr-ZrO{sub 2} mixture melt. Explosions took place only in those tests which were externally triggered. While the extent of zirconium oxidation in the triggered experiments was quite extensive, the estimated explosion energetics were found to be very small compared to the combined thermal and chemical energy available. (author)
10. Chemical speciation of U, Fe, and Pu in melt glass from nuclear weapons testing
Science.gov (United States)
Pacold, J. I.; Lukens, W. W.; Booth, C. H.; Shuh, D. K.; Knight, K. B.; Eppich, G. R.; Holliday, K. S.
2016-05-01
Nuclear weapons testing generates large volumes of glassy materials that influence the transport of dispersed actinides in the environment and may carry information on the composition of the detonated device. We determine the oxidation state of U and Fe (which is known to buffer the oxidation state of actinide elements and to affect the redox state of groundwater) in samples of melt glass collected from three U.S. nuclear weapons tests. For selected samples, we also determine the coordination geometry of U and Fe, and we report the oxidation state of Pu from one melt glass sample. We find significant variations among the melt glass samples and, in particular, find a clear deviation in one sample from the expected buffering effect of Fe(II)/Fe(III) on the oxidation state of uranium. In the first direct measurement of Pu oxidation state in a nuclear test melt glass, we obtain a result consistent with existing literature that proposes Pu is primarily present as Pu(IV) in post-detonation material. In addition, our measurements imply that highly mobile U(VI) may be produced in significant quantities when melt glass is quenched rapidly following a nuclear detonation, though these products may remain immobile in the vitrified matrices. The observed differences in chemical state among the three samples show that redox conditions can vary dramatically across different nuclear test conditions. The local soil composition, associated device materials, and the rate of quenching are all likely to affect the final redox state of the glass. The resulting variations in glass chemistry are significant for understanding and interpreting debris chemistry and the later environmental mobility of dispersed material.
11. Partial melting in one-plate planets: Implications for thermo-chemical and atmospheric evolution
Science.gov (United States)
Plesa, A.-C.; Breuer, D.
2014-08-01
In the present work, we investigate the influence of partial melting on mantle dynamics, crustal formation, and volcanic outgassing of a one-plate planet using a 2D mantle convection code. When melt is extracted to form crust, the mantle material left behind is more buoyant than its parent material and depleted in radioactive heat sources. The extracted heat-producing elements are then enriched in the crust, which also has an insulating effect due to its lower thermal conductivity compared to the mantle. In addition, partial melting can influence the mantle rheology through the dehydration (water depletion) of the mantle material by volcanic outgassing. As a consequence, the viscosity of water-depleted regions increases more than two orders of magnitude compared to water-saturated rocks resulting in slower cooling rates. The most important parameter influencing the thermo-chemical evolution is the assumed density difference between the primitive and the depleted mantle material (i.e., between peridotite and harzburgite). With small or negligible values of compositional buoyancy, crustal formation including crustal delamination is very efficient, also resulting in efficient processing and degassing of the mantle. The convecting mantle below the stagnant lid depletes continuously with time. In contrast, with increasing compositional buoyancy, crustal formation and mantle degassing are strongly suppressed although partial melting is substantially prolonged in the thermal evolution. The crust shows strong lateral variations in thickness, and crustal delamination is reduced and occurs only locally. Furthermore, two to four different mantle reservoirs can form depending on the initial temperature distribution. Two of these reservoirs can be sustained during the entire evolution - a scenario possibly valid for Mars as it may explain the isotope characteristic of the Martian meteorites.
12. CADASTER QSPR Models for Predictions of Melting and Boiling Points of Perfluorinated Chemicals.
Science.gov (United States)
Bhhatarai, Barun; Teetz, Wolfram; Liu, Tao; Öberg, Tomas; Jeliazkova, Nina; Kochev, Nikolay; Pukalov, Ognyan; Tetko, Igor V; Kovarich, Simona; Papa, Ester; Gramatica, Paola
2011-03-14
Quantitative structure property relationship (QSPR) studies on per- and polyfluorinated chemicals (PFCs) on melting point (MP) and boiling point (BP) are presented. The training and prediction chemicals used for developing and validating the models were selected from Syracuse PhysProp database and literatures. The available experimental data sets were split in two different ways: a) random selection on response value, and b) structural similarity verified by self-organizing-map (SOM), in order to propose reliable predictive models, developed only on the training sets and externally verified on the prediction sets. Individual linear and non-linear approaches based models developed by different CADASTER partners on 0D-2D Dragon descriptors, E-state descriptors and fragment based descriptors as well as consensus model and their predictions are presented. In addition, the predictive performance of the developed models was verified on a blind external validation set (EV-set) prepared using PERFORCE database on 15 MP and 25 BP data respectively. This database contains only long chain perfluoro-alkylated chemicals, particularly monitored by regulatory agencies like US-EPA and EU-REACH. QSPR models with internal and external validation on two different external prediction/validation sets and study of applicability-domain highlighting the robustness and high accuracy of the models are discussed. Finally, MPs for additional 303 PFCs and BPs for 271 PFCs were predicted for which experimental measurements are unknown.
13. Influence of temperature and chemical composition on phase transformations of selected oxide melts
Directory of Open Access Journals (Sweden)
J. Dobrovská
2013-07-01
Full Text Available The paper deals with structural changes of solid phase of selected oxide systems during their transition into liquid state. Analyses concerned poly-component systems forming basis of casting powders for CCM mould. Industrially used oxide system with prevailing contents of CaO–Al2O3–SiO2 components and with numerous accompanying admixtures was tested. Investigation was focused on temperatures, during which individual phases disappear and precipitate, as well as on influence of CaO content on phase composition at selected temperatures. The experiments were realised with use of original methodology consisting of shock cooling of the tested melt in liquid nitrogen. Thus obtained samples were further investigated by X-ray diffraction phase analyses at ambient temperatures. The obtained results provide additional data on physical-chemical properties of oxide systems, such as surface tension, viscosity, sintering intervals, etc., which can be used in technological practice for appropriate lubrication effect of casting powders in the mould.
14. Bioactive Ti metal analogous to human cancellous bone: Fabrication by selective laser melting and chemical treatments.
Science.gov (United States)
Pattanayak, Deepak K; Fukuda, A; Matsushita, T; Takemoto, M; Fujibayashi, S; Sasaki, K; Nishida, N; Nakamura, T; Kokubo, T
2011-03-01
Selective laser melting (SLM) is a useful technique for preparing three-dimensional porous bodies with complicated internal structures directly from titanium (Ti) powders without any intermediate processing steps, with the products being expected to be useful as a bone substitute. In this study the necessary SLM processing conditions to obtain a dense product, such as the laser power, scanning speed, and hatching pattern, were investigated using a Ti powder of less than 45 μm particle size. The results show that a fully dense plate thinner than 1.8 mm was obtained when the laser power to scanning speed ratio was greater than 0.5 and the hatch spacing was less than the laser diameter, with a 30 μm thick powder layer. Porous Ti metals with structures analogous to human cancellous bone were fabricated and the compressive strength measured. The compressive strength was in the range 35-120 MPa when the porosity was in the range 75-55%. Porous Ti metals fabricated by SLM were heat-treated at 1300 °C for 1h in an argon gas atmosphere to smooth the surface. Such prepared specimens were subjected to NaOH, HCl, and heat treatment to provide bioactivity. Field emission scanning electron micrographs showed that fine networks of titanium oxide were formed over the whole surface of the porous body. These treated porous bodies formed bone-like apatite on their surfaces in a simulated body fluid within 3 days. In vivo studies showed that new bone penetrated into the pores and directly bonded to the walls within 12 weeks after implantation into the femur of Japanese white rabbits. The percentage bone affinity indices of the chemical- and heat-treated porous bodies were significantly higher than that of untreated implants.
15. Lithological, Chemical and Chronological Constraints on Melt Extraction from the Mantle Section of the ~492 Ma Shetland Ophiolite Complex, Scotland
Science.gov (United States)
O'Driscoll, B.; Walker, R. J.; Clay, P. L.; Day, J. M.; Ash, R. D.; Daly, J. S.
2015-12-01
The mantle sections of ophiolites offer a means of studying the composition and structure of the oceanic mantle. In particular, the relations between different lithologies can be established in the field, permitting an assessment of the relative timing of processes such as melt extraction and melt-rock reaction. The Shetland Ophiolite Complex (SOC) contains a well-preserved mantle section that is dominated by harzburgite (≥70 vol.%), with dominantly chondritic present-day 187Os/188Os compositions1. Melt extraction and melt-rock reaction is evident in the form of dunite and chromitite layers and lenses, with thicknesses ranging from millimetres-to-metres. These lithologies are characteristic of supra-subduction zone processing and are considered to relate to closure of the Iapetus Ocean at ~492 Ma1. However, evidence of much earlier melt extraction has been suggested for some SOC harzburgites, which have relatively unradiogenic 187Os/188Os compositions that yield TRD model ages as old as ~1.4 Ga1. In order to assess the scales at which such compositional heterogeneities are preserved in the mantle, a small (45 m2) area of the SOC mantle section was selected for detailed lithological mapping and sampling. A selection of harzburgites (n=8), dunites (n=6) and pyroxenites (n=2) from this area has been analysed for their Os isotope and highly-siderophile element (HSE) compositions. Six of the harzburgites and four of the dunites have relative HSE abundances and gOs values that are approximately chondritic, with gOs ranging only from -0.6 to +2.7 (n=10). Two dunites have more radiogenic gOs (up to +7.5), that is correlated with enhanced concentrations of accessory base-metal sulphides, suggesting formation via melt percolation and melt-rock reaction. The two remaining harzburgites have less radiogenic gOs (-3.5 and -4), yielding Mesoproterozoic TRD ages. The new data indicate that a comparable range of Os isotope compositions to that previously measured across the
16. Impact of melt migration on the evolution of major and trace element composition in a crystalline mush: Implications for chemical differentiation in the continental crust
Science.gov (United States)
Jackson, M.; Solano, J.; Sparks, R. S.; Blundy, J.
2013-12-01
Migration of melt through a crystalline mush is common within the continental crust, occurring in magma chambers and lava flows. Mush formation and associated migration of the buoyant melt along grain boundaries is inevitable during melting of initially solid rock, or cooling and crystallisation of magma. Because there is efficient exchange of heat and mass between melt and solid phases, they remain in local thermal and chemical equilibrium. The composition of the melt therefore evolves as it migrates through the mush and, to properly capture this, models are required that include chemical reaction. However, although reactive transport models have been developed for the mantle, none have yet been presented that are applicable to the continental crust. Models developed for the mantle are not directly applicable to the crust, because the initial and boundary conditions are different. We present the first quantitative model of heat, mass and both major and trace element transport in a mush undergoing compaction which accounts for component transport and chemical reaction during melt migration and which is applicable to crustal systems. The model describes the phase behaviour of binary systems (both eutectic and solid solution), with melt and solid composition determined from phase diagrams using the local temperature and bulk composition. Trace element concentration is also determined. The results demonstrate that component transport and chemical reaction generates compositional variation in both major and trace elements that is not captured by existing geochemical models. Even for the simplest case of a homogenous, insulated column that is instantaneously melted then allowed to compact, we find that component transport and reaction leads to spatial variations in major element composition, and produces melt that is more enriched in incompatible elements than predicted by batch melting. In deep crustal hot zones (DCHZ), created by the repeated intrusion of hot, mantle
17. Chemical compositions of aqueous fluid, silicate melt, and supercritical fluid in the vicinity of the second critical endpoint in the system peridotite-H2O
Science.gov (United States)
Mibe, K.; Kawamoto, T.; Ono, S.
2012-12-01
Knowing the chemical compositions of fluid and melt is fundamental in understanding the magma genesis and chemical differentiation in the Earth's interior. We investigated the stability fields of aqueous fluid, silicate melt, and supercritical fluid magma using in-situ x-ray radiography and the second critical endpoint in the system peridotite-H2O was determined to be around 3.8 GPa (Mibe et al., 2007, JGR). Using the quenched recovered samples obtained by Mibe et al. (2007), we determined the chemical compositions of aqueous fluid, silicate melt, and supercritical fluid in the vicinity of the second critical endpoint in the system peridotite-H2O by EPMA analyses. A 10- to 30-μm diameter electron beam was used to obtain the composition of quenched materials from aqueous fluid, silicate melt, and supercritical fluid. The compositions of coexisting aqueous fluid and silicate melt were determined at 3.3 GPa and 3.6 GPa and 1180°C. In both samples, olivine coexists with aqueous fluid and silicate melt. In the run at 3.3 GPa, the composition of aqueous fluid was high-Mg dacitic, whereas the composition of silicate melt was hydrous peridotite. In the run at 3.6 GPa, the composition of aqueous fluid was high-Mg andesitic, whereas the composition of silicate melt was hydrous komatiitic. Although aqueous fluids in both runs are high-Mg, both MgO and FeO preferentially enters into silicate melt compared to aqueous fluid.
18. Chemical and Isotopic Heterogeneities in the Deep Earth:Importance of Lower Mantle Carbonate-rich Melts
Science.gov (United States)
Collerson, K. D.; Williams, Q.; Murphy, D.
2007-12-01
Evolution of mantle chemical heterogeneity reflects a spectrum of processes. Nature of reservoirs has been inferred from radiogenic isotope and trace element systematics of mid-ocean ridge basalts (MORB) and ocean island basalts (OIB) [1]. Carbonatites, kimberlites and lamproites [2-4] also sample depleted and enriched reservoirs, however, their origin remains equivocal. Secular decrease in Th/U ratio in MORB mantle (DMM), homogeneity of Th/U inferred from Pb-isotopic data, and systematic variation in Nb/Th and Nb/U ratios in MORBs [5], show that recycled components in DMM are well mixed. Thus isotopically hererogeneous domains in DMM must be transient features and are unlikely to yield HIMU and EM chemistries. Explanations for HIMU and EM OIB chemistries include involvement of: (1) subcontinental lithospheric mantle; (2) subducted oceanic lithosphere; (3) subducted sediment; or (4) an enigmatic lower mantle (LM) "plume component". Elevated 3He/4He in OIBs and kimberlites [6] and excess 129Xe and high 40Ar/39Ar [e.g., 7-8] and solar 20Ne/22Ne [9] in carbonatites indicate that they were derived from a primitive, isolated, and less degassed source than MORB. Primordial compositions show that this reservoir escaped atmospheric contamination by Ar, Xe, and Ne and pollution by 4He-rich material (from recycled 238U) during subduction. This primitive reservoir likely exists below the depth subducted slabs obviously penetrate (ca. 1700 km) e.g., [10]. That kimberlites are deeply sourced is also shown by lower mantle inclusions in diamond, e.g., [11]. Importantly, Gp. 1 and 2 kimberlites are isotopically similar to HIMU and EM-1 OIBs [4]. We interpret Gp 1 kimberlites as mixtures of HIMU and EM sources, while Gp. 2 kimberlites (close to EM-1) are interpreted as melts of a Ca perovskite-rich reservoir, possibly from slabs in the LM. We model melting of LM phases to simulate evolution of EM1 and HIMU 87Sr/86Sr, 143Nd/144Nd, 176Hf/177Hf, 207Pb/204Pb, 206Pb/204Pb and 208Pb/204
19. Termination of light-water reactor core-melt accidents with a chemical core catcher: the core-melt source reduction system (COMSORS)
Energy Technology Data Exchange (ETDEWEB)
Forsberg, C.W.; Parker, G.W.; Rudolph, J.C.; Osborne-Lee, I.W. [Oak Ridge National Lab., TN (United States); Kenton, M.A. [Dames and Moore, Westmont, IL (United States)
1996-09-01
The Core-Melt Source Reduction System (COMSORS) is a new approach to terminate light-water reactor core melt accidents and ensure containment integrity. A special dissolution glass is placed under the reactor vessel. If core debris is released onto the glass, the glass melts and the debris dissolves into the molten glass, thus creating a homogeneous molten glass. The molten glass, with dissolved core debris, spreads into a wide pool, distributing the heat for removal by radiation to the reactor cavity above or by transfer to water on top of the molten glass. Expected equilibrium glass temperatures are approximately 600 degrees C. The creation of a low-temperature, homogeneous molten glass with known geometry permits cooling of the glass without threatening containment integrity. This report describes the technology, initial experiments to measure key glass properties, and modeling of COMSORS operations.
20. 3D mapping of chemical distribution from melting at lower mantle conditions in the laser-heated diamond anvil cell
Science.gov (United States)
Dorfman, S. M.; Nabiei, F.; Cantoni, M.; Badro, J.; Gaal, R.; Gillet, P.
2014-12-01
The laser-heated diamond anvil cell is a unique tool for subjecting materials to pressures over few hundreds of GPa and temperatures of thousands of Kelvins which enables us to experimentally simulate the inaccessible interiors of planets. However, small sample size, laser profile and thermally conductive diamonds cause temperature gradients of 1000s K over a few microns which also affects chemical and structural distribution of phases in the sample. We have examined samples of San Carlos olivine (Mg,Fe)2SiO3 powder melted in the diamond anvil cell by double-sided and single-sided laser heating for 3-6 minutes to ~3000 K at 35-37 GPa. Moreover, MgO is used as an insulating media in one of the sample. Recovered samples were analyzed by a combination of focused ion beam (FIB) and scanning electron microscope (SEM) equipped with energy dispersive x-ray (EDX) detector. Images and chemical maps were acquired for ~300 slices with ~70 nm depth from each sample, comprising about half of the heated zone. Detailed chemical and structural analysis by transmission electron microscopy (TEM) of lamellas prepared from the remaining section of the samples will also be presented. In all samples the heated zone included (Mg,Fe)SiO3 perovskite-structured bridgmanite (PV) phase and two (Mg, Fe)O phases, one of which, magnesiowüstite (MW), is richer in iron than the other one, ferropericlase (FP). In double-side heated samples we observe a Fe-rich quenched melt core surrounded by MW phase. Our results show that with increasing heating time, Fe migrates to the molten center of the sample. In the single-side heated sample, the Fe-rich MW phase is concentrated in the center of heated zone. In all samples a FP crust was observed around the heated zone. This crust, however, is broken in the upper part (colder part) of the single-side heated sample due the high asymmetrical temperature gradient within the sample. The results confirm the importance of double-side heating and insulating media
1. Free-energy calculations using classical molecular simulation: application to the determination of the melting point and chemical potential of a flexible RDX model.
Science.gov (United States)
Sellers, Michael S; Lísal, Martin; Brennan, John K
2016-03-21
We present an extension of various free-energy methodologies to determine the chemical potential of the solid and liquid phases of a fully-flexible molecule using classical simulation. The methods are applied to the Smith-Bharadwaj atomistic potential representation of cyclotrimethylene trinitramine (RDX), a well-studied energetic material, to accurately determine the solid and liquid phase Gibbs free energies, and the melting point (Tm). We outline an efficient technique to find the absolute chemical potential and melting point of a fully-flexible molecule using one set of simulations to compute the solid absolute chemical potential and one set of simulations to compute the solid-liquid free energy difference. With this combination, only a handful of simulations are needed, whereby the absolute quantities of the chemical potentials are obtained, for use in other property calculations, such as the characterization of crystal polymorphs or the determination of the entropy. Using the LAMMPS molecular simulator, the Frenkel and Ladd and pseudo-supercritical path techniques are adapted to generate 3rd order fits of the solid and liquid chemical potentials. Results yield the thermodynamic melting point Tm = 488.75 K at 1.0 atm. We also validate these calculations and compare this melting point to one obtained from a typical superheated simulation technique.
2. On the Chemical Evolution of Upper Mantle of the Early Earth—An Experimental Study on Melting of the Silicate Phase in Jilin Chondrite at High Pressures
Institute of Scientific and Technical Information of China (English)
谢鸿森; 方虹; 等
1989-01-01
Relatively old ages of chondrites(normally around 4.5Ga)suggest that their parent bodies did not experience any mely-fractionation under high temperature and high pressure conditions pertaining to the interior of terrestrial plaets.Therefore,it is reasonable to take chondrites as starting materials in the study of the chemical evolution of the early earth.The sillicate phase in the Jilin chondrite (H5)was chosen for this purpose because it possesses a chemical composition similar to that of the primitive mantle.The melting experiment was carried out at 20-30 k bar and has rsulted in a product which contains1-5% melts in addition to solid cryustal phase.The chemical composition of the melt phases and the partitioning of various elements between the coexisting silicate melts are geochemically similar to those of anatectic rocks on the earth.This can thus serve as the basis for discussing the chemical evolution of the early upper mantle.
3. Effect of Alkali-Acid-Heat Chemical Surface Treatment on Electron Beam Melted Porous Titanium and Its Apatite Forming Ability
Directory of Open Access Journals (Sweden)
Suzan Bsat
2015-04-01
Full Text Available Advanced additive manufacturing techniques such as electron beam melting (EBM, can produce highly porous structures that resemble the mechanical properties and structure of native bone. However, for orthopaedic applications, such as joint prostheses or bone substitution, the surface must also be bio-functionalized to promote bone growth. In the current work, EBM porous Ti6Al4V alloy was exposed to an alkali acid heat (AlAcH treatment to bio-functionalize the surface of the porous structure. Various molar concentrations (3, 5, 10M and immersion times (6, 24 h of the alkali treatment were used to determine optimal parameters. The apatite forming ability of the samples was evaluated using simulated body fluid (SBF immersion testing. The micro-topography and surface chemistry of AlAcH treated samples were evaluated before and after SBF testing using scanning electron microscopy and energy dispersive X-ray spectroscopy. The AlAcH treatment successfully modified the topographical and chemical characteristics of EBM porous titanium surface creating nano-topographical features ranging from 200–300 nm in size with a titania layer ideal for apatite formation. After 1 and 3 week immersion in SBF, there was no Ca or P present on the surface of as manufactured porous titanium while both elements were present on all AlAcH treated samples except those exposed to 3M, 6 h alkali treatment. An increase in molar concentration and/or immersion time of alkali treatment resulted in an increase in the number of nano-topographical features per unit area as well as the amount of titania on the surface.
4. Chemical Characterisation of Bulk and Melt-spun Ribbons of NiMnIn Alloy using Inductively Coupled Plasma Optical Emission Spectrometry
Directory of Open Access Journals (Sweden)
S.S. Kalyan Kamal
2011-05-01
Full Text Available Method development for the analysis of NiMnIn, a new magnetocaloric effect (MCE material using inductively-coupled plasma optical emission spectrometry (ICPOES is discussed. Spectral interference of Ni and Mn on the analysis of In were studied. The process of method validation was carried out using various analytical techniques like conventional wet chemical techniques and instrumental techniques such as atomic absorption spectrometry. All the techniques show a close agreement in values, thus this method could be applied for regular analysis of NiMnIn alloys. A comparative chemical analysis of bulk and melt-spun ribbons of this alloy is also discussed.
5. Crystal-chemical controls on the partitioning of Sr and Ba between plagioclase feldspar, silicate melts, and hydrothermal solutions
Energy Technology Data Exchange (ETDEWEB)
Blundy, J.D.; Wood, B.J. (Bristol Univ. (England))
1991-01-01
The aim of this paper is to evaluate the factors which control the partitioning of alkaline earth elements (Ba and Sr) between plagioclase feldspar and silicate melts, specifically the respective role of crystal chemistry, melt chemistry, and temperature. We have selected plagioclase because of the wealth of volcanic and experimental data, the compositional simplicity of plagioclase, and its relevance to many petrological problems. We begin our study by examining experimental data on Sr partitioning between plagioclase and hydrothermal solutions in an attempt to constrain the role of crystal chemistry. We establish a simple thermodynamic model for trace element partitioning between plagioclase and hydrothermal solutions. This treatment is then extended to the plagioclase-melt system using available data from both experimental and volcanic systems in order to derive a general equation for Sr and Ba partitioning. Finally we consider the geochemical applications and implications of our findings.
6. Effect of Alkali-Acid-Heat Chemical Surface Treatment on Electron Beam Melted Porous Titanium and Its Apatite Forming Ability
NARCIS (Netherlands)
Bsat, S.; Yavari, S.; Munsch, M.; Valstar, E.R.; Zadpoor, A.A.
2015-01-01
Advanced additive manufacturing techniques such as electron beam melting (EBM), can produce highly porous structures that resemble the mechanical properties and structure of native bone. However, for orthopaedic applications, such as joint prostheses or bone substitution, the surface must also be bi
7. Chemical Characterisation of Bulk and Melt-spun Ribbons of NiMnIn alloy using Inductively Coupled Plasma Optical Emission Spectrometry
Directory of Open Access Journals (Sweden)
S.S. Kalyan Kamal
2011-04-01
Full Text Available Method development for the analysis of NiMnIn, a new magnetocaloric effect (MCE material using inductively coupled plasma optical emission spectrometry (ICPOES is discussed. Spectral interference of Ni and Mn on the analysis of In were studied. The process of method validation was carried out using various analytical techniques like conventional wet chemical techniques and instrumental techniques such as atomic absorption spectrometry. All the techniques show a close agreement in values, thus this method could be applied for regular analysis of NiMnIn alloys. A comparative chemical analysis of bulk and melt-spun ribbons of this alloy is also discussed.Defence Science Journal, 2011, 61(3, pp.270-274, DOI:http://dx.doi.org/10.14429/dsj.61.397
8. Thermal radiation and chemical reaction effects on boundary layer slip flow and melting heat transfer of nanofluid induced by a nonlinear stretching sheet
Science.gov (United States)
Krishnamurthy, M. R.; Gireesha, B. J.; Prasannakumara, B. C.; Gorla, Rama Subba Reddy
2016-09-01
A theoretically investigation has been performed to study the effects of thermal radiation and chemical reaction on MHD velocity slip boundary layer flow and melting heat transfer of nanofluid induced by a nonlinear stretching sheet. The Brownian motion and thermophoresis effects are incorporated in the present nanofluid model. A set of proper similarity variables is used to reduce the governing equations into a system of nonlinear ordinary differential equations. An efficient numerical method like Runge-Kutta-Fehlberg-45 order is used to solve the resultant equations for velocity, temperature and volume fraction of the nanoparticle. The effects of different flow parameters on flow fields are elucidated through graphs and tables. The present results have been compared with existing one for some limiting case and found excellent validation.
9. The chemical digestion of Ti6Al7Nb scaffolds produced by Selective Laser Melting reduces significantly ability of Pseudomonas aeruginosa to form biofilm.
Science.gov (United States)
Junka, Adam F; Szymczyk, Patrycja; Secewicz, Anna; Pawlak, Andrzej; Smutnicka, Danuta; Ziółkowski, Grzegorz; Bartoszewicz, Marzenna; Chlebus, Edward
2016-01-01
In our previous work we reported the impact of hydrofluoric and nitric acid used for chemical polishing of Ti-6Al-7Nb scaffolds on decrease of the number of Staphylococcus aureus biofilm forming cells. Herein, we tested impact of the aforementioned substances on biofilm of Gram-negative microorganism, Pseudomonas aeruginosa, dangerous pathogen responsible for plethora of implant-related infections. The Ti-6Al-7Nb scaffolds were manufactured using Selective Laser Melting method. Scaffolds were subjected to chemical polishing using a mixture of nitric acid and fluoride or left intact (control group). Pseudomonal biofilm was allowed to form on scaffolds for 24 hours and was removed by mechanical vortex shaking. The number of pseudomonal cells was estimated by means of quantitative culture and Scanning Electron Microscopy. The presence of nitric acid and fluoride on scaffold surfaces was assessed by means of IR and rentgen spetorscopy. Quantitative data were analysed using the Mann-Whitney test (P ≤ 0.05). Our results indicate that application of chemical polishing correlates with significant drop of biofilm-forming pseudomonal cells on the manufactured Ti-6Al-7Nb scaffolds ( p = 0.0133, Mann-Whitney test) compared to the number of biofilm-forming cells on non-polished scaffolds. As X-ray photoelectron spectroscopy revealed the presence of fluoride and nitrogen on the surface of scaffold, we speculate that drop of biofilm forming cells may be caused by biofilm-supressing activity of these two elements.
10. MELTED BUTTER TECHNOLOGY DEVELOPMENT
Directory of Open Access Journals (Sweden)
L. V. Golubeva
2014-01-01
Full Text Available Summary. Melted butter is made from dairy butter by rendering the fat phase. It has specific taste and aroma, high-calorie content and good assimilability. Defects of butter which appeared during the storage causes by the development of microbiological processes or by the chemical oxidation. On the development of these processes influence quality and composition of fresh butter, its physical structure, content of the increased amount of gas phase and content of heavy metals, storage conditions. Microbiological spoilage of butter occurs generally due to damage of plasma which is good environment for the development of microorganisms. Defects of microbiological origin include: unclean, sour, moldy, yeasty, cheesy, bitter taste. Defects of test and smell chemical origin are formed due to hydrolytic digestion of lipids. It's prevailed at long storage of butter in the conditions of freezing temperatures. It's picked out the following main processes of spoiling: souring, acidifying and sallowness. Often these processes take place simultaneously.It has been investigated melted butter with lactated additive. The latter improves the microbiological and toxicological safety, prolongs the storage condition of the products. Technological efficiency of the additives is achieved by a multilayer products formation from the inactive bound water, preventing microorganisms growth and by the barrier layer with lactate inhibiting hydrolytic reactions. Oil samples were obtained with the batch-type butter maker application, then they were melted and after that lactated additive were supplemented. It has been studied organoleptic and physico-chemical indices of the melted butter samples. The fatty-acid composition of melted butter were studied. Comparative analysis of fatty-acid composition of cow's milk fat and produced melted butter has shown their similarity. Also in the last sample there is increased weight fraction of linoleic and linolenic acids. The obtained
11. Selective Laser Sintering And Melting Of Pristine Titanium And Titanium Ti6Al4V Alloy Powders And Selection Of Chemical Environment For Etching Of Such Materials
Directory of Open Access Journals (Sweden)
Dobrzański L.A.
2015-09-01
Full Text Available The aim of the investigations described in this article is to present a selective laser sintering and melting technology to fabricate metallic scaffolds made of pristine titanium and titanium Ti6Al4V alloy powders. Titanium scaffolds with different properties and structure were manufactured with this technique using appropriate conditions, notably laser power and laser beam size. The purpose of such elements is to replace the missing pieces of bones, mainly cranial and facial bones in the implantation treatment process. All the samples for the investigations were designed in CAD/CAM (3D MARCARM ENGINEERING AutoFab (Software for Manufacturing Applications software suitably integrated with an SLS/SLM system. Cube-shaped test samples dimensioned 10×10×10 mm were designed for the investigations using a hexagon-shaped base cell. The so designed 3D models were transferred to the machine software and the actual rapid manufacturing process was commenced. The samples produced according to the laser sintering technology were subjected to chemical processing consisting of etching the scaffolds’ surface in different chemical mediums. Etching was carried out to remove the loosely bound powder from the surface of scaffolds, which might detach from their surface during implantation treatment and travel elsewhere in an organism. The scaffolds created were subjected to micro- and spectroscopic examinations
12. Effect of melting conditions on striae in iron-bearing silicate melts
DEFF Research Database (Denmark)
Jensen, Martin; Yue, Yuanzheng
2012-01-01
Chemical striae are present in a broad range of glass products, but due to their negative impact on e.g., the optical and mechanical properties, elimination of striae from melts is a key issue in glass technology. By varying melting temperatures, retentions times and redox conditions of an iron......-bearing calciumaluminosilicate melt, we quantify the effect of each of the three melting parameters on the stria content in the melt. The quantification of the stria content in the melt is conducted by means of image analysis on casted melt samples. We find that in comparison to an extension of retention time an increase...... factors such as compositional fluctuation of melts and bubbling due to iron reduction on the stria content. During the melting process, striae with a chemical gradient in a more mobile species equilibrate faster than striae caused by a chemical gradient in a less mobile species. The temperature and time...
13. Growth and Evolution of the Kerala Khondalite Belt, Southern India: Mineral and Whole rock Chemical Evidence for Intracrustal Melting and Magmatic Petrogenesis
Science.gov (United States)
Gundlupet Rangasetty, R.; Chettootty, S.
2011-12-01
The Kerala Khondalite Belt (KKB) constitutes an important lower crustal segment in the southern Indian granulite terrain. Dominant rock types, except sillimanite bearing gneisses, are classified as sodic and potassic granitoids and a general supracrustal origin is ascribed to these rocks. We present here new results from our studies on mineral and whole rock major- and trace-element and REE systematic of major litho units of the belt. We address the petrogenesis, physical conditions during crystallization and tectonic setting of KKB rocks. Granitoids (gneiss and variants of charnockites) makeup more than 70% of exposed rock types in KKB. They are classified as sodic and potassic groups based on K2O/Na2O ratios. Mineral chemical analysis of granitoids, especially biotites from different groups document igneous parentage and as potential indicator of nature of the magma. Biotites from sodic group are Mg2+-rich (XMg:0.47-0.63), denote calc-alkaline host in contrast to those from potassic groups, which are Fe2+-types with much lower XMg (0.37-0.44) and suggest an alkaline host. Biotites in potassic group are poorer in A12O3 than sodic, indicating evolved nature of the magmatic protolith. Decrease in ΣAl with increasing Fe/(Fe+Mg) values of biotites indicate progressive oxidising condition during magma evolution. Compositional variation of biotite allow us to speculate that the host magmas of sodic charnockites as calc-alkaline, arc-type with features typical of Archaean TTGs and potassic groups as partial melts of meta-igneous lower crust with little mantle contribution. The sodic group has geochemical affinity to Archaean tonalities with low-K, calc-alkaline, metaluminous to peraluminous chemistry. Compositionally contrasting K-rich rocks are essentially of granitic composition. Most oxides in both the groups, with exceptions of K2O and Na2O, show negative correlation with SiO2. The sodic group is enriched in Sr and depleted in Rb and Th. They exhibit geochemical
14. Study on the Physical and Chemical Conditions of Ore Formation of Hetai Ductile Shear Zone—Hosted Gold Deposit and Discovery of Melt Inclusions
Institute of Scientific and Technical Information of China (English)
李兆麟; 翟伟; 等
2002-01-01
The Hetai ductile shear zone-hosted gold deposit occurs in the deep-seated falut mylonite zone of the Sinian-Silurian metamorphic rock series.In this study there have been discovered melt inclusions,fluid-melt inclusions and organic inclusions in ore-bearing ruartz veins of the ore deposit and mylonite for the first time.The homogenization temperatures of the various types of inclusions are 160℃,180-350℃，530℃and 870℃ for organic inclusions,liquid inclsions two-phase immiscible liquid inclusions and melt inclusion,respectively,Ore fluid is categoriezed as the neutral to basic K+-Ca2+-Mg2+-Na+-SO42--HCO3-Cl- system.The contents of trace gases follow a descending order of H2O>CO2>CH4>(orCO>C2H2>C2H6>O2>N2.The concentrations of K+,Ca2+,SO42-,HCO3-,Cl-,H2O and C2H2 in fluid inclusions are related to the contents of gold and the Au/Ag ratios in from different levels of the gold deposit.This is significant for deep ore prospecting in the region.Daughter minerals in melt inclusions were analyzed using SEM.Quartz,orthoclase,wollastonite and other silicate minerals were identified.They were formed in different mineral assemblages.This analysis further proves the existence of melt inclusions in ore veins.Sedimentary metamophic rocks could form silicate melts during metamorphic anatexis and dynamic metamorphism,which possess melt-soulution characteristics.Ore formation is related to the multi-stage forming process of silicate melt and fluid.
15. Study on the Physical and Chemical Conditions of Ore Formation of Hetai Ductile Shear Zone-Hosted Gold Deposit and Discovery of Melt Inclusions
Institute of Scientific and Technical Information of China (English)
李兆麟; 翟伟; 李文; 石贵勇; 文拥军
2002-01-01
The Hetai ductile shear zone-hosted gold deposit occurs in the deep-seated fault mylonite zone of the Sinian-Silurian metamorphic rock series. In this study there have been discovered melt inclusions, fluid-melt inclusions and organic inclusions in ore-bearing quartz veins of the ore deposit and mylonite for the first time. The homogenization temperatures of the various types of inclusions are 160℃, 180 - 350℃, 530℃ and 870℃ for organic inclusions, liquid inclusions, two-phase immiscible liquid inclusions and melt inclusions, respectively. Ore fluid is categorized as the neutral to basic K+ -Ca2+ -Mg2+ -Na+ - SO2- 4-HCO3-Cl- system. The contents of trace gases follow a descending order of H2O＞CO2＞CH4＞(or ＜ ) H2＞CO＞C2H2＞C2I-I6＞O2＞N2.The concentrations of K , Ca2 + ,SO2-4,HCO3-,Cl- H2O and C2H2 in fluid inclusions are related to the contents of gold and the Au/Ag ratios in ores from different levels of the gold deposit. This is significant for deep ore prospecting in the region. Daughter minerals in melt inclusions were analyzed using SEM. Quartz, orthoclase, wollastonite and other silicate minerals were identified. They were formed in different mineral assemblages.This analysis further proves the existence of melt inclusions in ore veins. Sedimentary metamorphic rocks could form silicate melts during metamorphic anatexis and dynamic metamorphism, which possess melt-solution characteristics. Ore formation is related to the multi-stage forming process of silicate melt and fluid.
16. [Chemical composition and daily variation of melt water during ablation season in monsoonal temperate Glacier region: a case study of Baishui Glacier No. 1].
Science.gov (United States)
Zhu, Guo-Feng; Pu, Tao; He, Yuan-Qing; Wang, Pei-Zhen; Kong, Jian-Long; Zhang, Ning-Ning; Xin, Hui-Juan
2012-12-01
Melt water samples collected continuously from 29 August to 3 September 2009 in the Baishui Glacier No. 1 at elevation of 4750 m were analyzed for pH, conductivity, delta18O and inorganic ions. The results showed that the pH had obvious diurnal variations and was increased slightly by the influence of precipitation. The dissolution of alkaline soluble salts in the dust was the main reason for the increase of melt water conductivity; the value of delta18O was relatively low in strong ablation period and high in slight ablation period. Different from other research areas, the concentrations of Na+, K+, which were influenced by lithological and marine water vapor, were higher than that of Mg2+ in the study area; HCO3- and Ca2+ accounted for more than 80% of total ions in snow and ice melt water, indicating that the ions mainly came from limestone and the melt water was a typical carbonate solution; The content of melt water had an obvious daily change with temperature change, but the response amplitudes were different; Monsoon transport, local rock lithology, human industrial and agricultural activities were the main sources of inorganic ions and the deciding factors of the ion composition in the Baishui Glacier No. 1.
17. Methods for Melting Temperature Calculation
Science.gov (United States)
Hong, Qi-Jun
Melting temperature calculation has important applications in the theoretical study of phase diagrams and computational materials screenings. In this thesis, we present two new methods, i.e., the improved Widom's particle insertion method and the small-cell coexistence method, which we developed in order to capture melting temperatures both accurately and quickly. We propose a scheme that drastically improves the efficiency of Widom's particle insertion method by efficiently sampling cavities while calculating the integrals providing the chemical potentials of a physical system. This idea enables us to calculate chemical potentials of liquids directly from first-principles without the help of any reference system, which is necessary in the commonly used thermodynamic integration method. As an example, we apply our scheme, combined with the density functional formalism, to the calculation of the chemical potential of liquid copper. The calculated chemical potential is further used to locate the melting temperature. The calculated results closely agree with experiments. We propose the small-cell coexistence method based on the statistical analysis of small-size coexistence MD simulations. It eliminates the risk of a metastable superheated solid in the fast-heating method, while also significantly reducing the computer cost relative to the traditional large-scale coexistence method. Using empirical potentials, we validate the method and systematically study the finite-size effect on the calculated melting points. The method converges to the exact result in the limit of a large system size. An accuracy within 100 K in melting temperature is usually achieved when the simulation contains more than 100 atoms. DFT examples of Tantalum, high-pressure Sodium, and ionic material NaCl are shown to demonstrate the accuracy and flexibility of the method in its practical applications. The method serves as a promising approach for large-scale automated material screening in which
18. Crystal chemical control of clinopyroxene-melt partitioning in the Di-Ab-An system: implications for elemental fractionations in the depleted mantle
Energy Technology Data Exchange (ETDEWEB)
Lundstrom, C. C.; Shaw, H. F.; Ryerson, F. J.; Williams, Q.; Gill, J.
1998-08-01
The partitioning of fifteen trace elements (Rb, Sr, Zr, Nb, Ba, La, Ce, Nd, Sm, Gd, Yb, Hf, Ta, Pb and Th) between clinopyroxene and synthetic melt has been studied in two compositions along an isotherm in the diopside-albite-anorthite ternary at 1 bar pressure. The two compositions correspond to ~ Di65An35 and ~ Di55Ab45 and produce clinopyroxenes distinct in chemistry while melt compositions range from 49 wt % SiO2 to 61 wt. % SiO2. The partition coefficients of high field strength elements (HFSE) increase by factors of 2 to 8 in Di-An experiments relative to Di-Ab experiments while other elements show very little change (+/- 20%) between compositions. The change in HFSE partitioning correlates with increases in tetrahedral Al2O3 (IVAl) content of clinopyroxenes in the anorthite-bearing experiments. Changes in DTa/DNb also correlate with IVA1 based on a survey of previously published determinations.
19. Quantifying melting and mobilistaion of interstitial melts in crystal mushes
Science.gov (United States)
Veksler, Ilya; Dobson, Katherine; Hess, Kai-Uwe; Ertel-Ingrisch, Werner; Humphreys, Madeleine
2015-04-01
The deformation of crystals mushes and separation of melts and crystals in is critical to understanding the development of physical and chemical heterogeneity in magma chambers and has been invoked as an eruption trigger mechanism. Here we investigate the behaviour of the melt in the well characterised, classic crystal mush system of the Skaergaard intrusion by combining experimental petrology and the non-destructive 3D imaging methods. Starting materials for partial melting experiments were four samples from the upper Middle Zone of the Layered Series. Cylinders, 15 mm in diameter and 20 mm in length, were drilled out of the rock samples, placed in alumina crucibles and held for 5 days in electric furnaces at atmospheric pressure and 1050-1100 °C. Redox conditions set by the CO-CO2 gas mixture were kept close to those of the FMQ buffer. We then use spatially registered 3D x-ray computed tomography images, collected before and after the experiment, to determine the volume and distribution of the crystal framework and interstitial phases, and the volume, distribution and connectivity the interstitial phases that undergo melting and extraction while at elevated temperature. Image analysis has allowed us to quantify these physical changes with high spatial resolution. Our work is a first step towards quantitative understanding of the melt mobilisation and migration processes operating in notionally locked crystal rich magmatic systems.
20. Importance of the Small-Scale Processes Melting, Plate Boundary Formation and Mineralogy on the Large-Scale, Long-Term Thermo-Chemical Evolution of Earth's Mantle-Plate System
Science.gov (United States)
Tackley, P.
2015-12-01
Seismic observations of the deep Earth reveal the presence of two large low shear velocity provinces (LLSVPs) that are typically inferred to be dense chemically-distinct material, as well as discontinuities that are typically linked to the post-perovskite (pPv) phase transition. Several possible origins of chemically-dense material have been proposed, including recycling of mid-ocean ridge basalt (MORB), primordial differentiation events, crystallisation of a basal magma ocean, or some combination of these creating a basal melange (BAM; Tackley 2012 Earth Sci. Rev.). Each of these possibilities would result in a different composition hence different mineralogy. In order to constrain this we have been running calculations of thermo-chemical mantle evolution over 4.5 billion years that include melting-induced differentiation, plate tectonics induced by strongly temperature-dependent viscosity and plastic yielding, core cooling and compressibility with reasonable assumptions about the pressure-dependence of other material properties. Some of our simulations start from a magma ocean state so initial layering is developed self-consistently. Already-published results (Nakagawa et al., 2009 GCubed, 2010 PEPI, 2012 GCubed) already indicate the importance of exact MORB composition on the amount of MORB segregating above the CMB, which in turn influences mantle thermal structure and the evolution of the core and geodynamo. In more recent results we have been additionally including primordial material. We find that melting-induced differentiation has several first-order effects on the dynamics, including (i) making plate tectonics easier (through stresses associated with lateral variations in crustal thickness) and (ii) reducing heat flux through the CMB (due to the build-up of dense material above the CMB); also (iii) tectonic mode (continuous plate tectonics, episodic lid or stagnant lid) also makes a first-order difference to mantle structure and dynamics. This emphasises
1. Melting of Transition Metals
Energy Technology Data Exchange (ETDEWEB)
Ross, M; Japel, S; Boehler, R
2005-04-11
We review the transition melting studies carried out at Mainz, and describe a recently developed model used to explain that the relatively low melting slopes are due to the partially filled d-bands, and the persistence of the pressure induced s-d transition. The basic tenets of the model have now been reconfirmed by new measurements for Cu and Ni. The measurements show that Cu which has a filled 3d-band, has a melt slope that is about 2.5 greater than its neighbor Ni. In the case of Mo, the apparent discrepancy of DAC melting measurements with shock melting can be explained by accounting for the change in melt slope due to the bcc-cp transition observed in the shock studies. The Fe melt curve is revisited. The possible relevance of the Jahn-Teller effect and recently observed transition metal melts with Icosahedral Short-Range Order (ISRO) is discussed.
2. Do Melt Inclusions Answer Big Questions?
Science.gov (United States)
Hofmann, A. W.; Sobolev, A. V.
2009-12-01
In a pioneering paper, Sobolev and Shimizu (1993) demonstrated the existence of ultra-depleted melt inclusions in olivine phenocrysts in MORB. They interpreted these as evidence for the preservation of parental melts formed by progressive near-fractional melting. Subsequently many cases have been described where melt inclusions from single basalt samples display enormous chemical and isotopic heterogeneity. The interpretation of these observations hinges critically on whether such melt inclusions can faithfully preserve primary or parental melt composition. If they do, melt inclusion data can truly answer big questions from small-scale observations. If they do not, they answer rather small questions. Favoring the second possibility, Danyushevsky et al. (2004) have suggested that much of the observed variability of highly incompatible trace elements in melt inclusions “may not represent geologically significant melts, but instead reflect localized, grain-scale reaction processes within the magmatic plumbing system.” We disagree and show that this mechanism cannot, for example, explain isotopic heterogeneity measured in several suites of melt inclusions, nor does it not account for the presence of ultra-depleted melts and "ghost" plagioclase signatures in other inclusions. More recently, Spandler et al. (2007) have suggested on the basis of experimental evidence that diffusion rates for REE in olivine are so rapid that parental melt compositions in melt inclusions are rapidly falsified by diffusional exchange with (evolved) host lava. We show that the very fact that extreme chemical and isotopic heterogeneities are routinely preserved in melt inclusions demonstrates that this conclusion is unwarranted, either because residence times of the olivine phenocrysts are much shorter than assumed by Spandler et al. or because the high experimental diffusion rates are caused by an unknown experimental artifact. Although there is no obvious flaw in design and execution of
3. CHEMICALS
CERN Multimedia
Medical Service
2002-01-01
It is reminded that all persons who use chemicals must inform CERN's Chemistry Service (TIS-GS-GC) and the CERN Medical Service (TIS-ME). Information concerning their toxicity or other hazards as well as the necessary individual and collective protection measures will be provided by these two services. Users must be in possession of a material safety data sheet (MSDS) for each chemical used. These can be obtained by one of several means : the manufacturer of the chemical (legally obliged to supply an MSDS for each chemical delivered) ; CERN's Chemistry Service of the General Safety Group of TIS ; for chemicals and gases available in the CERN Stores the MSDS has been made available via EDH either in pdf format or else via a link to the supplier's web site. Training courses in chemical safety are available for registration via HR-TD. CERN Medical Service : TIS-ME :73186 or [email protected] Chemistry Service : TIS-GS-GC : 78546
4. Physics of the Lindemann melting rule
Energy Technology Data Exchange (ETDEWEB)
Lawson, Andrew C [Los Alamos National Laboratory
2008-01-01
We investigate the thermodynamics of melting for 74 distinct chemical elements including several actinides and rare earths. We find that the observed melting points are consistent with a linear relationship between the correlation entropy of the liquid and the Grueneisen constant of the solid, and that the Lindemann rule is well obeyed for the elements with simple structures and less well obeyed for the less symmetric more open structures. No special assumptions are required to explain the melting points of the rare earths or light actinides.
5. Rapidly solidified titanium alloys by melt overflow
Science.gov (United States)
Gaspar, Thomas A.; Bruce, Thomas J., Jr.; Hackman, Lloyd E.; Brasmer, Susan E.; Dantzig, Jonathan A.; Baeslack, William A., III
1989-01-01
A pilot plant scale furnace was designed and constructed for casting titanium alloy strips. The furnace combines plasma arc skull melting techniques with melt overflow rapid solidification technology. A mathematical model of the melting and casting process was developed. The furnace cast strip of a suitable length and width for use with honeycomb structures. Titanium alloys Ti-6Al-4V and Ti-14Al-21 Nb were successfully cast into strips. The strips were evaluated by optical metallography, microhardness measurements, chemical analysis, and cold rolling.
6. Melting and Sintering of Ashes
DEFF Research Database (Denmark)
Hansen, Lone Aslaug
1997-01-01
obtained during coal/straw co-firing, substantive sintering strength was observed to build up in the ashes below the melting onset. The strength obtained was thus assumed to be due to viscous flow sintering, and the sintering onset was for the four ashes investigated simultaneous to a calculated ash......The thesis contains an experimental study of the fusion and sintering of ashes collected during straw and coal/straw co-firing.A laboratory technique for quantitative determination of ash fusion has been developed based on Simultaneous Thermal Analysis (STA). By means of this method the fraction...... of melt in the investigated ashes has been determined as a function of temperature. Ash fusion results have been correlated to the chemical and mineralogical composition of the ashes, to results from a standard ash fusion test and to results from sintering experiments. Furthermore, the ash fusion results...
7. Signatures of nonthermal melting
Directory of Open Access Journals (Sweden)
Tobias Zier
2015-09-01
Full Text Available Intense ultrashort laser pulses can melt crystals in less than a picosecond but, in spite of over thirty years of active research, for many materials it is not known to what extent thermal and nonthermal microscopic processes cause this ultrafast phenomenon. Here, we perform ab-initio molecular-dynamics simulations of silicon on a laser-excited potential-energy surface, exclusively revealing nonthermal signatures of laser-induced melting. From our simulated atomic trajectories, we compute the decay of five structure factors and the time-dependent structure function. We demonstrate how these quantities provide criteria to distinguish predominantly nonthermal from thermal melting.
8. Improved procedures for separating crystals from the melt
NARCIS (Netherlands)
Verdoes, D.; Arkenbout, G.J.; Bruinsma, O.S.L.; Koutsoukos, P.G.; Ulrich, J.
1997-01-01
Innovative separation techniques like melt crystallization have the potential to fulfil two important demands, namely: a significant reduction of energy consumption by the chemical industry, and the production of high quality products required by industry. Several industrial applications of melt cry
9. Effect of stirring on striae in glass melts
DEFF Research Database (Denmark)
Jensen, Martin; Yue, Yuanzheng
2012-01-01
Chemical striae have often negative effect on the glass properties, and hence, elimination of striae has been a key issue in glass science and technology. To produce highly homogeneous glasses, it is necessary to stir melts during the melting process. To explore the physical origin of the stria e...
10. Melting of sodium clusters
CERN Document Server
Reyes-Nava, J A; Beltran, M R; Michaelian, K
2002-01-01
Thermal stability properties and the melting-like transition of Na_n, n=13-147, clusters are studied through microcanonical molecular dynamics simulations. The metallic bonding in the sodium clusters is mimicked by a many-body Gupta potential based on the second moment approximation of a tight-binding Hamiltonian. The characteristics of the solid-to-liquid transition in the sodium clusters are analyzed by calculating physical quantities like caloric curves, heat capacities, and root-mean-square bond length fluctuations using simulation times of several nanoseconds. Distinct melting mechanisms are obtained for the sodium clusters in the size range investigated. The calculated melting temperatures show an irregular variation with the cluster size, in qualitative agreement with recent experimental results. However, the calculated melting point for the Na_55 cluster is about 40 % lower than the experimental value.
11. Organic contaminant release from melting snow. 2. Influence of snow pack and melt characteristics.
Science.gov (United States)
Meyer, Torsten; Lei, Ying Duan; Muradi, Ibrahim; Wania, Frank
2009-02-01
Large reservoirs of organic contaminants in seasonal snowpack can be released in short pulses during spring snowmelt, potentially impacting the receiving ecosystems. Laboratory experiments using artificial snow spiked with organic target substances were conducted to investigate the behavior of six organic contaminants with widely variable distribution properties in melting snow. Whereas the influence of a chemical's equilibrium phase partitioning on the elution behavior is explored in a companion paper, we discuss here the impact of snow properties and melt features, including the snowpack depth, the temperature at the interface between soil and snow, the meltwater content the internal ice surface area, and the existence of distinct snow layers. Water-soluble organic substances are released in high concentrations at the beginning of a melt period when a deep and aged snowpack undergoes intense melting. Warm ground can cause notable melting at the snow bottom leading to a delayed and dampened concentration peak. Hydraulic barriers in layered snow packs cause preferential meltwater flow which also mitigates the early contaminant flush. Hydrophobic organic pollutants that are associated with particles accumulate near the snow surface and are released at the end of melting. Dirt cones at the surface of a dense snowpack enhance this enrichment. The findings of this laboratory study will aid in the understanding of the behavior of organic pollutants during the melting of more complex, natural snow covers.
12. A Model for Scrap Melting in Steel Converter
Science.gov (United States)
Kruskopf, Ari
2015-03-01
A process model for basic oxygen furnace is in development. The full model will include a 2-D axisymmetric turbulent flow model for iron melt, a steel scrap melting model, and a chemical reaction model. A theoretical basis for scrap melting model is introduced in this paper and an in-house implementation of the model is tested in this article independently from the other parts of the full process model. The model calculates a melting curve for the scrap piece and the heat and carbon mass exchange between the melt and the scrap. A temperature and carbon concentration-dependent material data are used for heat capacity, thermal conductivity, and diffusion coefficient. The equations are discretized into a moving grid, which is uncommon in literature in the context of scrap melting. A good agreement is found between the modeling results and experiments from literature. Also a heat transfer correlation for dimensionless Nusselt number is determined using the numerical results.
13. Melt Rate Improvement for DWPF MB3: Foaming Theory and Mitigation Techniques
Energy Technology Data Exchange (ETDEWEB)
Peeler, D.K.
2001-07-24
The objective of this research is to enhance the basic understanding of the role of glass chemistry, including the chemical kinetics of pre-melting, solid state reactions, batch melting, and the reaction pathways in glass and/or acid addition strategy changes on the overall melting process for the Defense Waste Processing Facility (DWPF) Macrobatch 3 (MB3).
14. GLASS MELTING PHENOMENA, THEIR ORDERING AND MELTING SPACE UTILISATION
Directory of Open Access Journals (Sweden)
Němec L.
2013-12-01
Full Text Available Four aspects of effective glass melting have been defined – namely the fast kinetics of partial melting phenomena, a consideration of the melting phenomena ordering, high utilisation of the melting space, and effective utilisation of the supplied energy. The relations were defined for the specific melting performance and specific energy consumption of the glass melting process which involve the four mentioned aspects of the process and indicate the potentials of effective melting. The quantity “space utilisation” has been treated in more detail as an aspect not considered in practice till this time. The space utilisation was quantitatively defined and its values have been determined for the industrial melting facility by mathematical modelling. The definitions of the specific melting performance and specific energy consumption have been used for assessment of the potential impact of a controlled melt flow and high space utilisation on the melting process efficiency on the industrial scale. The results have shown that even the partial control of the melt flow, leading to the partial increase of the space utilisation, may considerably increase the melting performance, whereas a decrease of the specific energy consumption was determined to be between 10 - 15 %.
15. Thermoacoustic Streaming and Ultrasonic Processing of Low Melting Melts
Science.gov (United States)
Trinh, E. H.
1997-01-01
Ultrasonic levitation allows the processing of low melting materials both in 1 G as well as in microgravity. The free suspension of the melts also facilitates undercooling, permitting the measurements of the physical properties of the metastable liquids.
16. A multi-component evaporation model for beam melting processes
Science.gov (United States)
Klassen, Alexander; Forster, Vera E.; Körner, Carolin
2017-02-01
In additive manufacturing using laser or electron beam melting technologies, evaporation losses and changes in chemical composition are known issues when processing alloys with volatile elements. In this paper, a recently described numerical model based on a two-dimensional free surface lattice Boltzmann method is further developed to incorporate the effects of multi-component evaporation. The model takes into account the local melt pool composition during heating and fusion of metal powder. For validation, the titanium alloy Ti-6Al-4V is melted by selective electron beam melting and analysed using mass loss measurements and high-resolution microprobe imaging. Numerically determined evaporation losses and spatial distributions of aluminium compare well with experimental data. Predictions of the melt pool formation in bulk samples provide insight into the competition between the loss of volatile alloying elements from the irradiated surface and their advective redistribution within the molten region.
17. Thermodynamics of Oligonucleotide Duplex Melting
Science.gov (United States)
Schreiber-Gosche, Sherrie; Edwards, Robert A.
2009-01-01
Melting temperatures of oligonucleotides are useful for a number of molecular biology applications, such as the polymerase chain reaction (PCR). Although melting temperatures are often calculated with simplistic empirical equations, application of thermodynamics provides more accurate melting temperatures and an opportunity for students to apply…
18. Melting of polydisperse hard disks
NARCIS (Netherlands)
Pronk, S.; Frenkel, D.
2004-01-01
The melting of a polydisperse hard-disk system is investigated by Monte Carlo simulations in the semigrand canonical ensemble. This is done in the context of possible continuous melting by a dislocation-unbinding mechanism, as an extension of the two-dimensional hard-disk melting problem. We find th
19. Pavement Snow Melting
Energy Technology Data Exchange (ETDEWEB)
Lund, John W.
2005-01-01
The design of pavement snow melting systems is presented based on criteria established by ASHRAE. The heating requirements depends on rate of snow fall, air temperature, relative humidity and wind velocity. Piping materials are either metal or plastic, however, due to corrosion problems, cross-linked polyethylene pipe is now generally used instead of iron. Geothermal energy is supplied to systems through the use of heat pipes, directly from circulating pipes, through a heat exchanger or by allowing water to flow directly over the pavement, by using solar thermal storage. Examples of systems in New Jersey, Wyoming, Virginia, Japan, Argentina, Switzerland and Oregon are presented. Key words: pavement snow melting, geothermal heating, heat pipes, solar storage, Wyoming, Virginia, Japan, Argentina, Klamath Falls.
20. Primary carbonatite melt from deeply subducted oceanic crust
Energy Technology Data Exchange (ETDEWEB)
Walter, M.J.; Bulanova, G.P.; Armstrong, L.S.; Keshav, S.; Blundy, J.D.; Gudfinnesson, G.; Lord, O.T.; Lennie, A.R.; Clark, S.M.; Smith, C.B.; Gobbo, L.
2008-07-01
Partial melting in the Earth's mantle plays an important part in generating the geochemical and isotopic diversity observed in volcanic rocks at the surface. Identifying the composition of these primary melts in the mantle is crucial for establishing links between mantle geochemical 'reservoirs' and fundamental geodynamic processes. Mineral inclusions in natural diamonds have provided a unique window into such deep mantle processes. Here they provide exper8imental and geochemical evidence that silicate mineral inclusions in diamonds from Juina, Brazil, crystallized from primary and evolved carbonatite melts in the mantle transition zone and deep upper mantle. The incompatible trace element abundances calculated for a melt coexisting with a calcium-titanium-silicate perovskite inclusion indicate deep melting of carbonated oceanic crust, probably at transition-zone depths. Further to perovskite, calcic-majorite garnet inclusions record crystallization in the deep upper mantle from an evolved melt that closely resembles estimates of primitive carbonatite on the basis of volcanic rocks. Small-degree melts of subducted crust can be viewed as agents of chemical mass-transfer in the upper mantle and transition zone, leaving a chemical imprint of ocean crust that can possibly endure for billions of years.
1. MULTIPLE MELTING IN NYLON 1010
Institute of Scientific and Technical Information of China (English)
FU Shuren; CHEN Taoyung
1983-01-01
Multiple melting behavior of nylon 1010 has been investigated by using DSC instrument. Effects of partial scanning, partial scanning and annealing, heating rate, cooling rate and stepwise annealing on the melting curve were studied. Experimental results indicate that the sample undergoes a process of continuous melting and recrystallization during DSC scanning. Nylon 1010 contains a distribution of crystallites of different degrees of perfection which is strongly dependent on its previous thermal history. From the structural reorganization point of view, the origin of double and multiple peaks of the melting curve is explained.
2. Viscosity of ring polymer melts
KAUST Repository
Pasquino, Rossana
2013-10-15
We have measured the linear rheology of critically purified ring polyisoprenes, polystyrenes, and polyethyleneoxides of different molar masses. The ratio of the zero-shear viscosities of linear polymer melts η0,linear to their ring counterparts η0,ring at isofrictional conditions is discussed as a function of the number of entanglements Z. In the unentangled regime η0,linear/η 0,ring is virtually constant, consistent with the earlier data, atomistic simulations, and the theoretical expectation η0,linear/ η0,ring = 2. In the entanglement regime, the Z-dependence of ring viscosity is much weaker than that of linear polymers, in qualitative agreement with predictions from scaling theory and simulations. The power-law extracted from the available experimental data in the rather limited range 1 < Z < 20, η0,linear/η0,ring ∼ Z 1.2±0.3, is weaker than the scaling prediction (η0,linear/η0,ring ∼ Z 1.6±0.3) and the simulations (η0,linear/ η0,ring ∼ Z2.0±0.3). Nevertheless, the present collection of state-of-the-art experimental data unambiguously demonstrates that rings exhibit a universal trend clearly departing from that of their linear counterparts, and hence it represents a major step toward resolving a 30-year-old problem. © 2013 American Chemical Society.
3. Evolution of Shock Melt Compositions in Lunar Agglutinates
Science.gov (United States)
Vance, A. M.; Christoffersen, R.; Keller, L. P.
2015-01-01
Lunar agglutinates are aggregates of regolith grains fused together in a glassy matrix of shock melt produced during smaller-scale (mostly micrometeorite) impacts. Agglutinate formation is a key space weathering process under which the optically-active component of nanophase metallic Fe (npFe(sup 0)) is added to the lunar regolith. Here we have used energy-dispersive X-ray (EDX) compositional spectrum imaging in the SEM to quantify the chemical homogeneity of agglutinitic glass, correlate its homogeneity to its parent soil maturity, and identify the principle chemical components contributing to the shock melt compositional variations.
4. 氯盐融雪剂对城市道路绿化带土壤性状的影响%Effect of Snow Melt Agent Containing Chloride-salt on Soil Chemical Characters of Urban Road Greenbelt
Institute of Scientific and Technical Information of China (English)
王艳春; 白雪薇; 李芳
2011-01-01
2009年底至2010年初,北京市降雪非常集中且强度较大,为保障交通畅通,大量的氯盐融雪剂在北京城区的绿地上应用,其用量达3万t.路面撒施的融雪剂不可避免地进入分车带、绿化带等绿地,对绿地植物正常生长造成威胁.文章通过实地采集了45个绿地土样,研究了道路绿地土壤盐分等相关指标,结果表明,与对照相比,撒施融雪剂对道路绿化带土壤造成了严重的污染,土壤全盐量范围为0.11％～2.79％,最高值出现在西城区金融街；表层土壤氯化物含量范围为222～19 548 mg/kg;表层土壤水溶性钠分别达到了对照的18～780倍.从不同土层来看,0～10 cm的表层土壤全盐量、氯化物、水溶性钠的含量远远高于10～20 cm土层；地理分布上呈现出中心城区表层土壤全盐量总体高于外围城区,交通主干道高于次干道和交通支线的特点.最后,提出了减缓氯盐融雪剂危害的建议措施.%There were several heavy snowfalls during winter of 2009-2010 in Beijing and nearly 30,000 tons of snow melt agent containing chloride salt were used to guarantee the smooth and safe traffic flow. Snow melt agent containing chloride salt inevitably entered the greenbelt soil by the road, which* greatly threatened the growth of plants. Soil salt and chloride content were studied and analyzed after typical greenbelt soil samples were collected from main arterial traffic such as the 2nd, 3rd and 4th rings road. Results showed that snow melt agent containing chloride salt had caused serious soil pollution and soil salt, chloride and water soluble sodium content greatly increased, compared to check soil, with the highest salt content of 2.79% in Beijing Financial Street, chloride content in surface soil as 222 ~19,548mg/kg. Water soluble sodium content reached 18-780 times of the check. The contents of investigated indexes in surface soil (0-10 cm) were greatly higher than that in 10-20 cm soil. Central
5. Crystallization behavior during melt-processing of ceramic waste forms
Science.gov (United States)
Tumurugoti, Priyatham; Sundaram, S. K.; Misture, Scott T.; Marra, James C.; Amoroso, Jake
2016-05-01
Multiphase ceramic waste forms based on natural mineral analogs are of great interest for their high chemical durability, radiation resistance, and thermodynamic stability. Melt-processed ceramic waste forms that leverage existing melter technologies will broaden the available disposal options for high-level nuclear waste. This work reports on the crystallization behavior in selected melt-processed ceramics for waste immobilization. The phase assemblage and evolution of hollandite, zirconolite, pyrochlore, and perovskite type structures during melt processing were studied using thermal analysis, x-ray diffraction, and electron microscopy. Samples prepared by melting followed by annealing and quenching were analyzed to determine and measure the progression of the phase assemblage. Samples were melted at 1500 °C and heat-treated at crystallization temperatures of 1285 °C and 1325 °C corresponding to exothermic events identified from differential scanning calorimetry measurements. Results indicate that the selected multiphase composition partially melts at 1500 °C with hollandite coexisting as crystalline phase. Perovskite and zirconolite phases crystallized from the residual melt at temperatures below 1350 °C. Depending on their respective thermal histories, different quenched samples were found to have different phase assemblages including phases such as perovskite, zirconolite and TiO2.
6. Melt pool dynamics during selective electron beam melting
Science.gov (United States)
Scharowsky, T.; Osmanlic, F.; Singer, R. F.; Körner, C.
2014-03-01
Electron beam melting is a promising additive manufacturing technique for metal parts. Nevertheless, the process is still poorly understood making further investigations indispensable to allow a prediction of the part's quality. To improve the understanding of the process especially the beam powder interaction, process observation at the relevant time scale is necessary. Due to the difficult accessibility of the building area, the high temperatures, radiation and the very high scanning speeds during the melting process the observation requires an augmented effort in the observation equipment. A high speed camera in combination with an illumination laser, band pass filter and mirror system is suitable for the observation of the electron beam melting process. The equipment allows to observe the melting process with a high spatial and temporal resolution. In this paper the adjustment of the equipment and results of the lifetime and the oscillation frequencies of the melt pool for a simple geometry are presented.
7. Photoluminescence dynamics in singlet fission chromophore liquid melts
Science.gov (United States)
Piland, Geoffrey B.; Bardeen, Christopher J.
2017-02-01
The effect of high temperature melting on the photophysics of three prototypical singlet fission molecules is investigated. Time-resolved photoluminescence is used to look at the melt phase of the molecules tetracene, diphenylhexatriene and rubrene. Chemical decomposition of tetracene precluded any detailed measurements on this molecule. In the diphenylhexatriene melt, a rapid singlet state nonradiative relaxation process outcompetes singlet fission. In the rubrene melt, singlet fission occurs at a rate similar to that of the crystal, but the decay of the delayed fluorescence is much more rapid. The rapid decay of the delayed fluorescence suggests that either the triplet lifetime is shortened, or the fusion probability decreases, or that both factors are operative at higher temperatures.
8. Beyond the Melting Pot Reconsidered.
Science.gov (United States)
Anderson, Elijah
2000-01-01
Discusses the 1963 book, "Beyond the Melting Pot," which suggested that eventually the problem of different ethnicities in the U.S. would be resolved and society would become one melting pot. Examines how changes in immigration and economic structures have affected the issue, noting the devastating effect of the dominant culture's…
9. Survival times of anomalous melt inclusions from element diffusion in olivine and chromite.
Science.gov (United States)
Spandler, C; O'Neill, H St C; Kamenetsky, V S
2007-05-17
The chemical composition of basaltic magma erupted at the Earth's surface is the end product of a complex series of processes, beginning with partial melting and melt extraction from a mantle source and ending with fractional crystallization and crustal assimilation at lower pressures. It has been proposed that studying inclusions of melt trapped in early crystallizing phenocrysts such as Mg-rich olivine and chromite may help petrologists to see beyond the later-stage processes and back to the origin of the partial melts in the mantle. Melt inclusion suites often span a much greater compositional range than associated erupted lavas, and a significant minority of inclusions carry distinct compositions that have been claimed to sample melts from earlier stages of melt production, preserving separate contributions from mantle heterogeneities. This hypothesis is underpinned by the assumption that melt inclusions, once trapped, remain chemically isolated from the external magma for all elements except those that are compatible in the host minerals. Here we show that the fluxes of rare-earth elements through olivine and chromite by lattice diffusion are sufficiently rapid at magmatic temperatures to re-equilibrate completely the rare-earth-element patterns of trapped melt inclusions in times that are short compared to those estimated for the production and ascent of mantle-derived magma or for magma residence in the crust. Phenocryst-hosted melt inclusions with anomalous trace-element signatures must therefore form shortly before magma eruption and cooling. We conclude that the assumption of chemical isolation of incompatible elements in olivine- and chromite-hosted melt inclusions is not valid, and we call for re-evaluation of the popular interpretation that anomalous melt inclusions represent preserved samples of unmodified mantle melts.
10. Using a Spreadsheet To Explore Melting, Dissolving and Phase Diagrams.
Science.gov (United States)
Goodwin, Alan
2002-01-01
Compares phase diagrams relating to the solubilities and melting points of various substances in textbooks with those generated by a spreadsheet using data from the literature. Argues that differences between the diagrams give rise to new chemical insights. (Author/MM)
11. Electrical Conductivity of Cryolite Melts
Science.gov (United States)
Fellner, P.; Grjotheim, K.; Kvande, H.
1985-11-01
This paper proposes an equation for the electrical conductivity of multicomponent cryolite-based mixtures. The equation is based on a physical model which assumes that the conductivity is proportional to the number density of the effective electric charges in the melt. The various authors in the available literature show a great discrepancy in conductivity data of cryolite-based melts. The equation based on the physical model enables determination of which set of data is preferable. Special consideration in this respect is given to the influence of magnesium flouride and lithium flouride additions to the melt.
12. Synthesis of Refractory Materials by Skull Melting Technique
Science.gov (United States)
Osiko, Vyacheslav V.; Borik, Mikhail A.; Lomonova, Elena E.
This chapter discusses methods of growing refractory oxide single crystals and synthesis of refractory glasses by skull melting technique in a cold crucible. It shows the advantages of radiofrequency (RF) heating of dielectric materials in a cold crucible and points out some specific problems regarding the process of growing crystals by directional crystallization from the melt and by pulling on a seed from the melt. The distinctive features of the method of directional crystallization from the melt are discussed in detail on the example of technology of materials based on zirconia, i.e., cubic single crystals and partly stabilized single crystals. It is shown that the size and quality of crystals are functions of the process conditions, such as thermal conditions under crystallization, growth rate, and chemical composition. We provide an overview of research on the structure, phase composition, and physicochemical properties of crystals based on zirconia. The optical, mechanical, and electric properties of these crystals make them suitable for a number of technical and industrial applications in optics, electronics, materials processing, and medicine. In this chapter, we also consider some problems regarding the synthesis of refractory glasses by skull melting technique. The physicochemical and optical properties of glasses are given and their practical applications in technology are discussed. We note that one of the better developed and most promising applications of skull melting technique is the immobilization of liquid and solid waste (also radioactive waste) into solid-state materials by vitrification.
13. Scaleable Clean Aluminum Melting Systems
Energy Technology Data Exchange (ETDEWEB)
Han, Q.; Das, S.K. (Secat, Inc.)
2008-02-15
The project entitled 'Scaleable Clean Aluminum Melting Systems' was a Cooperative Research and Development Agreements (CRADAs) between Oak Ridge National Laboratory (ORNL) and Secat Inc. The three-year project was initially funded for the first year and was then canceled due to funding cuts at the DOE headquarters. The limited funds allowed the research team to visit industrial sites and investigate the status of using immersion heaters for aluminum melting applications. Primary concepts were proposed on the design of furnaces using immersion heaters for melting. The proposed project can continue if the funding agency resumes the funds to this research. The objective of this project was to develop and demonstrate integrated, retrofitable technologies for clean melting systems for aluminum in both the Metal Casting and integrated aluminum processing industries. The scope focused on immersion heating coupled with metal circulation systems that provide significant opportunity for energy savings as well as reduction of melt loss in the form of dross. The project aimed at the development and integration of technologies that would enable significant reduction in the energy consumption and environmental impacts of melting aluminum through substitution of immersion heating for the conventional radiant burner methods used in reverberatory furnaces. Specifically, the program would couple heater improvements with furnace modeling that would enable cost-effective retrofits to a range of existing furnace sizes, reducing the economic barrier to application.
14. Laser melting of uranium carbides
Science.gov (United States)
Utton, C. A.; De Bruycker, F.; Boboridis, K.; Jardin, R.; Noel, H.; Guéneau, C.; Manara, D.
2009-03-01
In the context of the material research aimed at supporting the development of nuclear plants of the fourth Generation, renewed interest has recently arisen in carbide fuels. A profound understanding of the behaviour of nuclear materials in extreme conditions is of prime importance for the analysis of the operation limits of nuclear fuels, and prediction of possible nuclear reactor accidents. In this context, the main goal of the present paper is to demonstrate the feasibility of laser induced melting experiments on stoichiometric uranium carbides; UC, UC1.5 and UC2. Measurements were performed, at temperatures around 3000 K, under a few bars of inert gas in order to minimise vaporisation and oxidation effects, which may occur at these temperatures. Moreover, a recently developed investigation method has been employed, based on in situ analysis of the sample surface reflectivity evolution during melting. Current results, 2781 K for the melting point of UC, 2665 K for the solidus and 2681 K for the liquidus of U2C3, 2754 K for the solidus and 2770 K for the liquidus of UC2, are in fair agreement with early publications where the melting behaviour of uranium carbides was investigated by traditional furnace melting methods. Further information has been obtained in the current research about the non-congruent (solidus-liquidus) melting of certain carbides, which suggest that a solidus-liquidus scheme is followed by higher ratio carbides, possibly even for UC2.
15. Studying regimes of convective heat transfer in the production of high-temperature silicate melts
Science.gov (United States)
Volokitin, O. G.; Sheremet, M. A.; Shekhovtsov, V. V.; Bondareva, N. S.; Kuzmin, V. I.
2016-09-01
The article presents the results of theoretical and experimental studies of the production of high-temperature silicate melts using the energy of low-temperature plasma in a conceptually new setup. A mathematical model of unsteady regimes of convective heat and mass transfer is developed and numerically implemented under the assumption of non-Newtonian nature of flow in the melting furnace with plasma-chemical synthesis of high-temperature silicate melts. Experiments on melting silicate containing materials were carried out using the energy of low-temperature plasma. The dependence of dynamic viscosity of various silicate materials (basalt, ash, waste of oil shale) was found experimentally.
16. Chicxulub Impact Melts: Geochemical Signatures of Target Lithology Mixing and Post-Impact Hydrothermal Fluid Processes
Science.gov (United States)
Kring, David A.; Zurcher, Lukas; Horz, Freidrich; Mertzmann, Stanley A.
2004-01-01
Impact melts within complex impact craters are generally homogeneous, unless they differentiated, contain immiscible melt components, or were hydrothermally altered while cooling. The details of these processes, however, and their chemical consequences, are poorly understood. The best opportunity to unravel them may lie with the Chicxulub impact structure, because it is the world s most pristine (albeit buried) large impact crater. The Chicxulub Scientific Drilling Project recovered approx. 100 meters of impactites in a continuous core from the Yaxcopoil-1 (YAX-1) borehole. This dramatically increased the amount of melt available for analyses, which was previously limited to two small samples N17 and N19) recovered from the Yucatan-6 (Y-6) borehole and one sample (N10) recovered from the Chicxulub-1 (C-1) borehole. In this study, we describe the chemical compositions of six melt samples over an approx. 40 m section of the core and compare them to previous melt samples from the Y-6 and C-1 boreholes.
17. Phase change nanocomposites with tunable melting temperature and thermal energy storage density
Science.gov (United States)
Liu, Minglu; Wang, Robert Y.
2013-07-01
Size-dependent melting decouples melting temperature from chemical composition and provides a new design variable for phase change material applications. To demonstrate this potential, we create nanocomposites that exhibit stable and tunable melting temperatures through numerous melt-freeze cycles. These composites consist of a monodisperse ensemble of Bi nanoparticles (NPs) embedded in a polyimide (PI) resin matrix. The Bi NPs operate as the phase change component whereas the PI resin matrix prevents nanoparticle coalescence during melt-freeze cycles. We tune melting temperature and enthalpy of fusion in these composites by varying the NP diameter. Adjusting the NP volume fraction also controls the composite's thermal energy storage density. Hence it is possible to leverage size effects to tune phase change temperature and energy density in phase change materials.Size-dependent melting decouples melting temperature from chemical composition and provides a new design variable for phase change material applications. To demonstrate this potential, we create nanocomposites that exhibit stable and tunable melting temperatures through numerous melt-freeze cycles. These composites consist of a monodisperse ensemble of Bi nanoparticles (NPs) embedded in a polyimide (PI) resin matrix. The Bi NPs operate as the phase change component whereas the PI resin matrix prevents nanoparticle coalescence during melt-freeze cycles. We tune melting temperature and enthalpy of fusion in these composites by varying the NP diameter. Adjusting the NP volume fraction also controls the composite's thermal energy storage density. Hence it is possible to leverage size effects to tune phase change temperature and energy density in phase change materials. Electronic supplementary information (ESI) available: Experimental details and additional DSC data on nanocomposites and pure PI resin. See DOI: 10.1039/c3nr02842a
18. Lattice cluster theory for polymer melts with specific interactions
Energy Technology Data Exchange (ETDEWEB)
Xu, Wen-Sheng, E-mail: [email protected] [James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States); Freed, Karl F., E-mail: [email protected] [James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States); Department of Chemistry, The University of Chicago, Chicago, Illinois 60637 (United States)
2014-07-28
Despite the long-recognized fact that chemical structure and specific interactions greatly influence the thermodynamic properties of polymer systems, a predictive molecular theory that enables systematically addressing the role of chemical structure and specific interactions has been slow to develop even for polymer melts. While the lattice cluster theory (LCT) provides a powerful vehicle for understanding the influence of various molecular factors, such as monomer structure, on the thermodynamic properties of polymer melts and blends, the application of the LCT has heretofore been limited to the use of the simplest polymer model in which all united atom groups within the monomers of a species interact with a common monomer averaged van der Waals energy. Thus, the description of a compressible polymer melt involves a single van der Waals energy. As a first step towards developing more realistic descriptions to aid in the analysis of experimental data and the design of new materials, the LCT is extended here to treat models of polymer melts in which the backbone and side groups have different interaction strengths, so three energy parameters are present, namely, backbone-backbone, side group-side group, and backbone-side group interaction energies. Because of the great algebraic complexity of this extension, we retain maximal simplicity within this class of models by further specializing this initial study to models of polymer melts comprising chains with poly(n-α-olefin) structures where only the end segments on the side chains may have different, specific van der Waals interaction energies with the other united atom groups. An analytical expression for the LCT Helmholtz free energy is derived for the new model. Illustrative calculations are presented to demonstrate the degree to which the thermodynamic properties of polymer melts can be controlled by specific interactions.
19. Detection of structural heterogeneity of glass melts
DEFF Research Database (Denmark)
Yue, Yuanzheng
2004-01-01
The structural heterogeneity of both supercooled liquid and molten states of silicate has been studied using calorimetric method. The objects of this study are basaltic glasses and liquids. Two experimental approaches are taken to detect the structural heterogeneity of the liquids. One is the hyp......The structural heterogeneity of both supercooled liquid and molten states of silicate has been studied using calorimetric method. The objects of this study are basaltic glasses and liquids. Two experimental approaches are taken to detect the structural heterogeneity of the liquids. One...... and the crystal-memory effect of the liquids above their liquidus temperature are detected. Clear dependences of the structural heterogeneity of the liquids on the maximum upscan temperature and on the chemical composition are found by conducting calorimetric measurements. The origin of such dependences...... is discussed. The ordered structure of glass melts above the liquidus temperature is indirectly characterized by use of X-ray diffraction method. The new approaches are of importance for monitoring the glass melting and forming process and for improving the physical properties of glasses and glass fibers....
20. Impact melting of the largest known enstatite meteorite: Al Haggounia 001, a fossil EL chondrite
Science.gov (United States)
Rubin, Alan E.
2016-09-01
Al Haggounia 001 and paired specimens (including Northwest Africa [NWA] 2828 and 7401) are part of a vesicular, incompletely melted, EL chondrite impact melt rock with a mass of ~3 metric tons. The meteorite exhibits numerous shock effects including (1) development of undulose to weak mosaic extinction in low-Ca pyroxene; (2) dispersion of metal-sulfide blebs within silicates causing "darkening"; (3) incomplete impact melting wherein some relict chondrules survived; (4) vaporization of troilite, resulting in S2 bubbles that infused the melt; (5) formation of immiscible silicate and metal-sulfide melts; (6) shock-induced transportation of the metal-sulfide melt to distances >10 cm (7) partial resorption of relict chondrules and coarse silicate grains by the surrounding silicate melt; (8) crystallization of enstatite in the matrix and as overgrowths on relict silicate grains and relict chondrules; (9) crystallization of plagioclase from the melt; and (10) quenching of the vesicular silicate melt. The vesicular samples lost almost all of their metal during the shock event and were less susceptible to terrestrial weathering; in contrast, the samples in which the metal melt accumulated became severely weathered. Literature data indicate the meteorite fell ~23,000 yr ago; numerous secondary phases formed during weathering. Both impact melting and weathering altered the meteorite's bulk chemical composition: e.g., impact melting and loss of a metal-sulfide melt from NWA 2828 is responsible for bulk depletions in common siderophile elements and in Mn (from alabandite); weathering of oldhamite caused depletions in many rare earth elements; the growth of secondary phases caused enrichments in alkalis, Ga, As, Se, and Au.
1. Melt-Enhanced Rejuvenation of Lithospheric Mantle: Insights from the Colorado Plateau
CERN Document Server
Roy, Mousumi; Holtzman, Ben; Gaherty, James
2012-01-01
The stability of the lithospheric mantle beneath the ancient cratonic cores of continents is primarily a function of chemical modification during the process of melt extraction. Processes by which stable continental lithosphere may be destabilized are not well-understood, although destabilization by thickening and removal of negatively-buoyant lithospheric mantle in "delamination" events has been proposed in a number of tectonic settings. In this paper we explore an alternative process for destabilizing continents, namely, thermal and chemical modification during infiltration of metasomatic fluids and melts into the lithospheric column. We consider observations pertinent to the structure and evolution of the Colorado Plateau within the western United States to argue that the physical and chemical state of the margins of the plateau have been variably modified and destabilized by interaction with melts. In the melt-infiltration process explored here, the primary mechanism for weakening and rejuvenating the pla...
2. Toward a coherent model for the melting behavior of the deep Earth's mantle
Science.gov (United States)
Andrault, D.; Bolfan-Casanova, N.; Bouhifd, M. A.; Boujibar, A.; Garbarino, G.; Manthilake, G.; Mezouar, M.; Monteux, J.; Parisiades, P.; Pesce, G.
2017-04-01
Knowledge of melting properties is critical to predict the nature and the fate of melts produced in the deep mantle. Early in the Earth's history, melting properties controlled the magma ocean crystallization, which potentially induced chemical segregation in distinct reservoirs. Today, partial melting most probably occurs in the lowermost mantle as well as at mid upper-mantle depths, which control important aspects of mantle dynamics, including some types of volcanism. Unfortunately, despite major experimental and theoretical efforts, major controversies remain about several aspects of mantle melting. For example, the liquidus of the mantle was reported (for peridotitic or chondritic-type composition) with a temperature difference of ∼1000 K at high mantle depths. Also, the Fe partitioning coefficient (DFeBg/melt) between bridgmanite (Bg, the major lower mantle mineral) and a melt was reported between ∼0.1 and ∼0.5, for a mantle depth of ∼2000 km. Until now, these uncertainties had prevented the construction of a coherent picture of the melting behavior of the deep mantle. In this article, we perform a critical review of previous works and develop a coherent, semi-quantitative, model. We first address the melting curve of Bg with the help of original experimental measurements, which yields a constraint on the volume change upon melting (ΔVm). Secondly, we apply a basic thermodynamical approach to discuss the melting behavior of mineralogical assemblages made of fractions of Bg, CaSiO3-perovskite and (Mg,Fe)O-ferropericlase. Our analysis yields quantitative constraints on the SiO2-content in the pseudo-eutectic melt and the degree of partial melting (F) as a function of pressure, temperature and mantle composition; For examples, we find that F could be more than 40% at the solidus temperature, except if the presence of volatile elements induces incipient melting. We then discuss the melt buoyancy in a partial molten lower mantle as a function of pressure
3. Magnetic Biocomposites for Remote Melting.
Science.gov (United States)
Zhou, Mengbo; Liebert, Tim; Müller, Robert; Dellith, Andrea; Gräfe, Christine; Clement, Joachim H; Heinze, Thomas
2015-08-10
A new approach toward the fabrication of biocompatible composites suitable for remote melting is presented. It is shown that magnetite nanoparticles (MNP) can be embedded into a matrix of biocompatible thermoplastic dextran esters. For that purpose, fatty acid esters of dextran with adjustable melting points in the range of 30-140 °C were synthesized. Esterification of the polysaccharide by activation of the acid as iminium chlorides guaranteed mild reaction conditions leading to high quality products as confirmed by FTIR- and NMR spectroscopy as well as by gel permeation chromatography (GPC). A method for the preparation of magnetically responsive bionanocomposites was developed consisting of combined dissolution/suspension of the dextran ester and hydrophobized MNPs in an organic solvent followed by homogenization with ultrasonication, casting of the solution, drying and melting of the composite for a defined shaping. This process leads to a uniform distribution of MNPs in nanocomposite as revealed by scanning electron microscope. Samples of different geometries were exposed to high frequency alternating magnetic field. It could be shown that defined remote melting of such biocompatible nanocomposites is possible for the first time. This may lead to a new class of magnetic remote control systems, which are suitable for controlled release applications or self-healing materials.
4. Thermodynamics of freezing and melting
DEFF Research Database (Denmark)
Pedersen, Ulf Rørbæk; Costigliola, Lorenzo; Bailey, Nicholas
2016-01-01
phases at a single thermodynamic state point provide the basis for calculating the pressure, density and entropy of fusion as functions of temperature along the melting line, as well as the variation along this line of the reduced crystalline vibrational mean-square displacement (the Lindemann ratio...
5. Multi-stage melt-rock interaction in the Mt. Maggiore (Corsica, France) ophiolitic peridotites: microstructural and geochemical evidence
Science.gov (United States)
Rampone, Elisabetta; Piccardo, Giovanni B.; Hofmann, Albrecht W.
2008-10-01
Spinel and plagioclase peridotites from the Mt.Maggiore (Corsica, France) ophiolitic massif record a composite asthenosphere-lithosphere history of partial melting and subsequent multi-stage melt-rock interaction. Cpx-poor spinel lherzolites are consistent with mantle residues after low-degree fractional melting ( F = 5-10%). Opx + spinel symplectites at the rims of orthopyroxene porphyroclasts indicate post-melting lithospheric cooling ( T = 970-1,100°C); this was followed by formation of olivine embayments within pyroxene porphyroclasts by melt-rock interaction. Enrichment in modal olivine (up to 85 wt%) at constant bulk Mg values, and variable absolute REE contents (at constant LREE/HREE) indicate olivine precipitation and pyroxene dissolution during reactive porous melt flow. This stage occurred at spinel-facies depths, after incorporation of the peridotites in the thermal lithosphere. Plagioclase-enriched peridotites show melt impregnation microtextures, like opx + plag intergrowths replacing exsolved cpx porphyroclasts and interstitial gabbronoritic veinlets. This second melt-rock interaction stage caused systematic chemical changes in clinopyroxene (e.g. Ti, REE, Zr, Y increase), related to the concomitant effects of local melt-rock interaction at decreasing melt mass, and crystallization of small (<3%) trapped melt fractions. LREE depletion in minerals of the gabbronoritic veinlets indicates that the impregnating melts were more depleted than normal MORB. Preserved microtextural evidence of previous melt-rock interaction in the impregnated peridotites suggests that they were progressively uplifted in response to lithosphere extension and thinning. Migrating melts were likely produced by mantle upwelling and melting related to extension; they were modified from olivine-saturated to opx-saturated compositions, and caused different styles of melt-rock interaction (reactive spinel harzburgites, vs. impregnated plagioclase peridotites) depending on the
6. Impact ejecta-induced melting of surface ice deposits on Mars
Science.gov (United States)
Weiss, David K.; Head, James W.
2016-12-01
, depending on crater diameter, ice thickness, surface temperature, and geothermal heat flux. Contact melting is predicted to produce fluvial features on the surface of ejecta and the interior crater walls, whereas basal melting is predicted to produce fluvial features only on the interior crater walls. Before basal melting initiates, the ice-cemented cryosphere underlying the crater ejecta is predicted to melt and drain downwards through the substratum, generating a source of water for chemical alteration and possibly subsurface clay formation. These candidate melting processes are predicted to occur under a wide range of parameters, and provides a basis for further morphologic investigation.
7. Filament stretching rheometry of polymer melts
DEFF Research Database (Denmark)
Hassager, Ole; Nielsen, Jens Kromann; Rasmussen, Henrik Koblitz
2005-01-01
The Filament Stretching Rheometry (FSR) method developed by Sridhar, McKinley and coworkers for polymer solutions has been extended to be used also for polymer melts. The design of a melt-FSR will be described and differences to conventional melt elongational rheometers will be pointed out. Results...
8. Ash melting behavior by Fourier transform infrared spectroscopy
Institute of Scientific and Technical Information of China (English)
LI Han-xu; QIU Xiao-sheng; TANG Yong-xin
2008-01-01
A Fourier Transform Infrared Spectroscopic (FTIR) method involving a Fe2O3 flux was used to learn how China's coal ash melts. The relationship between ash fusion temperature and chemical composition, as well as the effects of Fe2O3 flux on the ash fusion temperature were studied. The relationship between ash fusion temperature and chemical composition, mineralogical phases and functional groups was analyzed with the FTIR method. The results show that the ash fusion temperature is related to the location and transmittance of certain absorption peaks, which is of great significance for the study of ash behavior.
9. Melting Behaviour of Ferronickel Slags
Science.gov (United States)
Sagadin, Christoph; Luidold, Stefan; Wagner, Christoph; Wenzl, Christine
2016-12-01
The industrial manufacturing of ferronickel in electric furnaces produces large amounts of slag with strong acidic character and high melting points, which seriously stresses the furnace refractory lining. In this study, the melting behavior of synthetically produced ferronickel slags on magnesia as refractory material was determined by means of a hot stage microscope. Therefore, slags comprising the main oxides SiO2 (35-70 wt.%), MgO (15-45 wt.%) and Fe2O3 (5-35 wt.%) were melted in a graphite crucible and afterwards analyzed by a hot stage microscope. The design of experiments, which was created by the statistic software MODDE®, included 20 experiments with varying slag compositions as well as atmospheres. The evaluation of the test results occurred at three different characteristic states of the samples like the softening point according to DIN 51730 and the temperatures at which the area of residual cross-section of the samples amounted to 30% and 40%, respectively, of the original value depending of their SiO2/MgO ratio and iron oxide content. Additionally, the thickness of the zone influenced by the slag was measured and evaluated.
10. Melting of the Primitive Mercurian Mantle, Insights into the Origin of Its Surface Composition
Science.gov (United States)
Boujibar, A.; Righter, K.; Rapp, J. F.; Ross, D. K.; Pando, K. M.; Danielson, L. R.; Fontaine, E.
2016-01-01
Recent findings of the MESSENGER mission on Mercury have brought new evidence for its reducing nature, widespread volcanism and surface compositional heteregeneity. MESSENGER also provided major elemental ratios of its surface that can be used to infer large-scale differentiation processes and the thermal history of the planet. Mercury is known as being very reduced, with very low Fe-content and high S and alkali contents on its surface. Its bulk composition is therefore likely close to EH enstatite chondrites. In order to elucidate the origin of the chemical diversity of Mercury's surface, we determined the melting properties of EH enstatite chondrites, at pressures between 1 bar and 3 GPa and oxygen fugacity of IW-3 to IW-5, using piston-cylinder experiments, combined with a previous study on EH4 melting at 1 bar. We found that the presence of Ca-rich sulfide melts induces significant decrease of Ca-content in silicate melts at low pressure and low degree of melting (F). Also at pressures lower than 3 GPa, the SiO2-content decreases with F, while it increases at 3 GPa. This is likely due to the chemical composition of the bulk silicate which has a (Mg+Fe+Ca)/Si ratio very close to 1 and to the change from incongruent to congruent melting of enstatite. We then tested whether the various chemical compositions of Mercury's surface can result from mixing between two melting products of EH chondrites. We found that the majority of the geochemical provinces of Mercury's surface can be explained by mixing of two melts, with the exception of the High-Al plains that require an Al-rich source. Our findings indicate that Mercury's surface could have been produced by polybaric melting of a relatively primitive mantle.
11. Mineralogical comparison and cooling history of lunar and chondritic vesicular melt breccias
Science.gov (United States)
Miyamoto, M.; Takeda, H.; Ishii, T.
1984-01-01
Lunar sample 77135, an impact melt breccia full of vesicles, has been reinvestigated by electron microprobe and X-ray diffraction techniques and compared with a vesicular melt LL chondrite, Yamato 790964, in an attempt to understand their impact heating processes and subsequent cooling history. Notable similarities between the lunar and chondritic melt breccias include: abundant vesicles, similar pyroxene chemical zoning trends, the presence of variable amounts of clastic material, and similar chemical compositions except for K and Na contents of glass and mesostasis. Some constraints on the cooling history are estimated from Mg-Fe diffusion profiles in olivine and pyroxene. The burial depth of lunar sample 77135 during cooling was 0.2-100 m; the depth for the chondrite was probably smaller. Impact melts were probably produced and a layer of regolith retained on the parent body sufficiently thick to allow the olivines to homogenize during slow cooling.
12. Magmatism vs mushmatism: Numerical modelling of melt migration and accumulation in partially molten crust
Science.gov (United States)
Roele, Katarina; Jackson, Matthew; Morgan, Joanna
2016-04-01
We present a quantitative model of heat and mass transport in a compacting crustal mush created by the repetitive intrusion of mantle-derived basaltic sills. At very low sill emplacement rates, we find that the maximum melt fraction remains small, far below that required to create an eruptible magma, and consistent with purely thermal models published previously. However, at intermediate (and realistic) sill emplacement rates, we observe the formation of a high melt fraction layer within a low melt fraction background. The high melt fraction layer migrates upwards towards the top of the mush (which is defined by the location of the solidus isotherm) and, despite occupying a high melt fraction, the melt in the layer has a composition corresponding to a progressively larger degree of fractionation during upwards migration, because it locally equilibrates with mush at progressively lower temperature. Thus the composition of the melt in the high melt fraction layer becomes progressively more evolved. The high melt fraction layer resembles a conventional magma chamber, but is produced by changes in bulk composition in response to melt migration, rather than the addition of heat. Indeed, such a layer can form even when the mush is cooling overall. The magma within the layer is at sufficiently high melt fraction to be eruptible, but is not located in the hottest region of the mush where the temperature is highest. This is a new method to produce a magma chamber within a crustal mush, and also to evolve the composition of the melt in the chamber. Our results show that high melt fractions need not be associated with high temperature; they also show that eruptible melt fractions can be created at much lower emplacement rates than predicted by purely thermal models. These high melt fractions are transient, and spatially localized within larger mush zones. Moreover, chemical differentiation does not require fractional crystallisation in a largely liquid magma chamber. Our
13. Highly refractory peridotites in Songshugou, Qinling orogen: Insights into partial melting and melt/fluid-rock reactions in forearc mantle
Science.gov (United States)
Cao, Yi; Song, Shuguang; Su, Li; Jung, Haemyeong; Niu, Yaoling
2016-05-01
The Songshugou ultramafic massif is located in the eastern segment of the Qinling orogenic belt, central China. It is a large spinel peridotite body dominated by coarse-grained, porphyroclastic, and fine-grained dunite with minor harzburgite, olivine clinopyroxenite, and banded/podiform chromitite. The compositions of the bulk-rock dunite and harzburgite, and the constituent olivine and spinel, together with the textures and chemical characteristics of multiphase mineral inclusions, point to the highly refractory nature of these rocks with complex histories of high-temperature boninite melt generation and boninitic melt-rock reaction, probably in a young, warm, and volatile-rich forearc lithospheric mantle setting. Additionally, a subsequent low-temperature fluid-rock reaction is also recorded by TiO2-rich spinel with Ti solubility/mobility enhanced by chloride- or fluoride-rich subduction-zone fluids as advocated by Rapp et al. (2010). The olivine clinopyroxenite, on the other hand, was likely crystallized from a residual boninitic melt that had reacted with harzburgitic residues. The ubiquitous occurrences of hydrous minerals, such as anthophyllite, tremolite, Cr-chlorite, and serpentine (stable at lower P-T crustal conditions) in the matrix, suggest that further low-temperature fluid-rock reaction (or retrograde metamorphism) has affected the original volatile-poor peridotites either in a mature and cool subduction zone, or in a continental crust during their exhumation into the Qinling collisional orogeny at early Paleozoic era, or both. The prolonged and intense ductile/brittle deformation can decrease the mineral grain size through dynamic recrystallization and fracturing, and thus aid the fluid-rock reaction or retrograde metamorphism and mineral chemical re-equilibration processes. Therefore, the Songshugou peridotites present a good example for understanding the petrogenesis and evolution of the mantle wedge, with the emphasis on the complex partial
14. Microstructural changes due to laser surface melting of an AISI 304 stainless steel
Directory of Open Access Journals (Sweden)
d?Oliveira A.S.C.M.
2001-01-01
Full Text Available Several techniques can be used to improve surface properties. These can involve changes on the surface chemical composition (such as alloying and surface welding processes or on the surface microstructure, such as hardening and melting. In the present work surface melting with a 3kW CO2 cw laser was done to alter surface features of an AISI 304 stainless steel. Microstructure characterisation was done by optical and scanning electron microscopy. Vickers and Knoop microhardness tests evaluated mechanical features after surface melting. Phase transformation during rapid solidification is analysed and discussed.
15. Production of high melt strength polypropylene by gamma irradiation
Science.gov (United States)
Lugão, A. B.; Artel, B. W. H.; Yoshiga, A.; Lima, L. F. C. P.; Parra, D. F.; Bueno, J. R.; Liberman, S.; Farrah, M.; Terçariol, W. R.; Otaguro, H.
2007-11-01
16. Effects of surface shape on the geometry and surface topography of the melt pool in low-power density laser melting
KAUST Repository
Kim, Youngdeuk
2011-04-15
The quantitative correlations between workpiece volume and melt pool geometry, as well as the flow and thermal features of the melt pool are established. Thermocapillary convections in melt pool with a deformable free surface are investigated with respect to surface shape and laser intensity. When the contact angle between the tangent to the top surface and the vertical wall at the hot center is acute, the free surface flattens, compared with that of the initial free surface. Otherwise, the free surface forms a bowl-like shape with a deep crater and a low peripheral rim when the contact angle at the hot center is obtuse. Increasing the workpiece volume at a fixed laser intensity and a negative radial height gradient cause linear decreases in the geometric size and magnitude of flow and temperature of the melt pool. Conversely, linear increases are observed with a positive radial height gradient. © 2011 American Institute of Chemical Engineers (AIChE).
17. Ocean Basalt Simulator version 1 (OBS1): Trace element mass balance in adiabatic melting of a pyroxenite-bearing peridotite
Science.gov (United States)
Kimura, Jun-Ichi; Kawabata, Hiroshi
2015-01-01
present a new numerical trace element mass balance model for adiabatic melting of a pyroxenite-bearing peridotite for estimating mantle potential temperature, depth of melting column, and pyroxenite fraction in the source mantle for a primary ocean basalt/picrite. The Ocean Basalt Simulator version 1 (OBS1) uses a thermodynamic model of adiabatic melting of a pyroxenite-bearing peridotite with experimentally/thermodynamically parameterized liquidus-solidus intervals and source mineralogy. OBS1 can be used to calculate a sequence of adiabatic melting with two melting models, including (1) melting of peridotite and pyroxenite sources with simple mixing of their fractional melts (melt-melt mixing model), and (2) pyroxenite melting, melt metasomatism in the host peridotite, and melting of the metasomatized peridotite (source-metasomatism model). OBS1 can be used to explore (1) the fractions of peridotite and pyroxenite, (2) mantle potential temperature, (3) pressure of termination of melting, (4) degree of melting, and (5) residual mode of the sources. In order to constrain these parameters, the model calculates a mass balance for 26 incompatible trace elements in the sources and in the generated basalt/picrite. OBS1 is coded in an Excel spreadsheet and runs with VBA macros. Using OBS1, we examine the source compositions and conditions of the mid-oceanic ridge basalts, Loihi-Koolau basalts in the Hawaiian hot spot, and Jurassic Shatsky Rise and Mikabu oceanic plateau basalts and picrites. The OBS1 model shows the physical conditions, chemical mass balance, and amount of pyroxenite in the source peridotite, which are keys to global mantle recycling.
18. Diffusive fractionation of trace elements in basaltic melt
Science.gov (United States)
Holycross, Megan E.; Bruce Watson, E.
2016-10-01
The chemical diffusivities of 25 trace elements (Sc, V, Rb, Sr, Y, Zr, Nb, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Yb, Lu, Hf, Ta, Th, and U) in basaltic melt were measured in diffusion couple experiments performed at 1 GPa pressure and temperatures from 1250 to 1500 °C. Trace element concentration gradients developed in the glasses were simultaneously characterized using laser ablation ICP/MS to create an internally consistent data set. A ratio-fitting technique was employed to accurately determine the relative diffusivities of the rare earth elements (REE). All diffusion coefficients conform to the expected Arrhenius relation D = D 0exp(- E a /RT), where the constant log( D 0, m2/s) ranges from -3.81 to -5.11 and E a ranges from 161.73 to 223.81 kJ/mol. The slowest diffusivities are obtained for the high-field-strength elements; the fastest diffusivities are obtained for the low-field-strength elements. Trace element diffusion in MORB follows the compensation law, where log D 0 is linearly correlated with E a. Arrhenius parameters for diffusion of trivalent REE monotonically increase from La to Lu and are near-linear functions of bond strength (the variation in Arrhenius parameters means that the diffusivities decrease monotonically from La to Lu at a given T). The new data for trace element diffusion in basaltic melt can be used to explore the potential for diffusive fractionation of trace elements using kinetic models. Concentrations of the slower-diffusing heavy REE may be altered relative to those of the faster-diffusing light REE as a diffusive boundary layer develops in melt-melt and crystal-melt systems. The results indicate that diffusion in basalt can be an effective mechanism to fractionate trace elements from one another.
19. Viscosity model for aluminosilicate melt
Directory of Open Access Journals (Sweden)
Zhang G.H.
2012-01-01
Full Text Available The structurally based viscosity model proposed in our previous study is extended to include more components, e.g. SiO2, Al2O3, FeO, MnO, MgO, CaO, Na2O and K2O. A simple method is proposed to calculate the numbers of different types of oxygen ions classified by the different cations they bonded with, which is used to characterize the influence of composition on viscosity. When dealing with the aluminosilicate melts containing several basic oxides, the priority order is established for different cations for charge compensating Al3+ ions, according to the coulombic force between cation and oxygen anion. It is indicated that basic oxides have two paradox influences on viscosity: basic oxide with a higher basicity decreases viscosity more greatly by forming weaker non-bridging oxygen bond; while it increases viscosity more greatly by forming stronger bridging oxygen bond in tetrahedron after charge compensating Al3+ ion. The present model can extrapolate its application range to the system without SiO2. Furthermore, it could also give a satisfy interpretation to the abnormal phenomenon that viscosity increases when adding K2O to CaO-Al2O3-SiO2 melt within a certain composition range.
20. Reactive Infiltration of Silicon Melt Through Microporous Amorphous Carbon Preforms
Science.gov (United States)
Sangsuwan, P.; Tewari, S. N.; Gatica, J. E.; Singh, M.; Dickerson, R.
1999-01-01
The kinetics of unidirectional capillary infiltration of silicon melt into microporous carbon preforms have been investigated as a function of the pore morphology and melt temperature. The infiltrated specimens showed alternating bands of dark and bright regions, which corresponded to the unreacted free carbon and free silicon regions, respectively. The decrease in the infiltration front velocity for increasing infiltration distances, is in qualitative agreement with the closed-form solution of capillarity driven fluid flow through constant cross section cylindrical pores. However, drastic changes in the thermal response and infiltration front morphologies were observed for minute differences in the preforms microstructure. This suggests the need for a dynamic percolation model that would account for the exothermic nature of the silicon-carbon chemical reaction and the associated pore closing phenomenon.
1. Crystal Melting and Toric Calabi-Yau Manifolds
CERN Document Server
Ooguri, Hirosi
2008-01-01
We construct a statistical model of crystal melting to count BPS bound states of D0 and D2 branes on a single D6 brane wrapping an arbitrary toric Calabi-Yau threefold. The three-dimensional crystalline structure is determined by the quiver diagram and the brane tiling which characterize the low energy effective theory of D branes. The crystal is composed of atoms of different colors, each of which corresponds to a node of the quiver diagram, and the chemical bond is dictated by the arrows of the quiver diagram. BPS states are constructed by removing atoms from the crystal. This generalizes the earlier results on the BPS state counting to an arbitrary non-compact toric Calabi-Yau manifold. We point out that a proper understanding of the relation between the topological string theory and the crystal melting involves the wall crossing in the Donaldson-Thomas theory.
2. Volcanic ash melting under conditions relevant to ash turbine interactions.
Science.gov (United States)
Song, Wenjia; Lavallée, Yan; Hess, Kai-Uwe; Kueppers, Ulrich; Cimarelli, Corrado; Dingwell, Donald B
2016-03-02
The ingestion of volcanic ash by jet engines is widely recognized as a potentially fatal hazard for aircraft operation. The high temperatures (1,200-2,000 °C) typical of jet engines exacerbate the impact of ash by provoking its melting and sticking to turbine parts. Estimation of this potential hazard is complicated by the fact that chemical composition, which affects the temperature at which volcanic ash becomes liquid, can vary widely amongst volcanoes. Here, based on experiments, we parameterize ash behaviour and develop a model to predict melting and sticking conditions for its global compositional range. The results of our experiments confirm that the common use of sand or dust proxy is wholly inadequate for the prediction of the behaviour of volcanic ash, leading to overestimates of sticking temperature and thus severe underestimates of the thermal hazard. Our model can be used to assess the deposition probability of volcanic ash in jet engines.
3. Interfacial properties of statistical copolymer brushes in contact with homopolymer melts.
Science.gov (United States)
Trombly, David M; Pryamitsyn, Victor; Ganesan, Venkat
2011-04-21
We use polymer self-consistent field theory to quantify the interfacial properties of random copolymer brushes (AB) in contact with a homopolymer melt chemically identical to one of the blocks (A). We calculate the interfacial widths and interfacial energies between the melt and the brush as a function of the relative chain sizes, grafting densities, compositions of the random copolymer in the brush, and degree of chemical incompatibility between the A and B species. Our results indicate that the interfacial energies between the melt and the brush increase (signifying expulsion of the free chains from the brush) with increasing grafting density, chemical incompatibility between A and B components, and size of the free chains relative to the grafted chains. We also compare the interfacial energies of random copolymers of different sequence characteristics and find that, except for the case of very blocky or proteinlike chains, blockiness of the copolymer has only little effect on interfacial properties. Our results for interfacial energies are rationalized based on the concept of an "effective volume fraction" of the brush copolymers, f(eff), which quantifies the chemical composition of the brush segments in the interfacial zone between the brush and melt copolymers. Using this concept, we modify the strong-stretching theory of brush-melt interfaces to arrive at a simple model whose results qualitatively agree with our results from self-consistent field theory. We discuss the ramifications of our results for the design of neutral surfaces.
4. Snow Melting and Freezing on Older Townhouses
DEFF Research Database (Denmark)
Nielsen, Anker; Claesson, Johan
2011-01-01
The snowy winter of 2009/2010 in Scandinavia prompted many newspaper articles on icicles falling from buildings and the risk this presented for people walking below. The problem starts with snow melting on the roof due to heat loss from the building. Melt water runs down the roof and some...... of it will freeze on the overhang. The rest of the water will either run off or freeze in gutters and downpipes or turn into icicles. This paper describes use of a model for the melting and freezing of snow on roofs. Important parameters are roof length, overhang length, heat resistance of roof and overhang......, outdoor and indoor temperature, snow thickness and thermal conductivity. If the snow thickness is above a specific limit value – the snow melting limit- some of the snow will melt. Another interesting limit value is the dripping limit. All the melt water will freeze on the overhang, if the snow thickness...
5. RHEOLOGY FEATURE OF SIMPLE METAL MELT
Institute of Scientific and Technical Information of China (English)
C.J. Sun; H.R. Geng; Y.S. Shen; X.Y. Teng; Z.X. Yang
2007-01-01
The rheology feature of Sb, Bi melt and alloys was studied using coaxial cylinder high-temperature viscometer. The results showed that the curve of torsion-rotational speed for Sb melt presents a linear relation in all measured temperature ranges, whereas for the Bi melt, the curve presents obvious non-Newtonian feature within the low temperature range and at relative high shear stress. The rheology feature of Sb80Bi20 and Sb20Bi80, alloy melts was well correlated with that of Sb and Bi, respectively. It is considered that the rheology behavior of Sb melt plays a crucial role in Sb80Bi20, alloy and that of Bi melt plays a crucial role in Sb20Bi80 alloy.
6. Evolution of Shock Melt Compositions in Lunar Regoliths
Science.gov (United States)
Vance, A. M.; Christoffersen, R.; Keller, L. P.; Berger, E. L.; Noble, S. K.
2016-01-01
Space weathering processes - driven primarily by solar wind ion and micrometeorite bombardment, are constantly changing the surface regoliths of airless bodies, such as the Moon. It is essential to study lunar soils in order to fully under-stand the processes of space weathering, and how they alter the optical reflectance spectral properties of the lunar surface relative to bedrock. Lunar agglutinates are aggregates of regolith grains fused together in a glassy matrix of shock melt produced during micrometeorite impacts into the lunar regolith. The formation of the shock melt component in agglutinates involves reduction of Fe in the target material to generate nm-scale spherules of metallic Fe (nanophase Fe0 or npFe0). The ratio of elemental Fe, in the form of npFe0, to FeO in a given bulk soil indicates its maturity, which increases with length of surface exposure as well as being typically higher in the finer-size fraction of soils. The melting and mixing process in agglutinate formation remain poorly understood. This includes incomplete knowledge regarding how the homogeneity and overall compositional trends of the agglutinate glass portions (agglutinitic glass) evolve with maturity. The aim of this study is to use sub-micrometer scale X-ray compositional mapping and image analysis to quantify the chemical homogeneity of agglutinitic glass, correlate its homogeneity to its parent soil maturity, and identify the principal chemical components contributing to the shock melt composition variations. An additional focus is to see if agglutinitic glass contains anomalously high Fe sub-micron scale compositional domains similar to those recently reported in glassy patina coatings on lunar rocks.
7. Carbonatitic and granitic melts produced under conditions of primary immiscibility during anatexis in the lower crust
Science.gov (United States)
Ferrero, Silvio; Wunder, Bernd; Ziemann, Martin A.; Wälle, Markus; O'Brien, Patrick J.
2016-11-01
Carbonatites are peculiar magmatic rocks with mantle-related genesis, commonly interpreted as the products of melting of CO2-bearing peridotites, or resulting from the chemical evolution of mantle-derived magmas, either through extreme differentiation or secondary immiscibility. Here we report the first finding of anatectic carbonatites of crustal origin, preserved as calcite-rich polycrystalline inclusions in garnet from low-to-medium pressure migmatites of the Oberpfalz area, SW Bohemian Massif (Central Europe). These inclusions originally trapped a melt of calciocarbonatitic composition with a characteristic enrichment in Ba, Sr and LREE. This interpretation is supported by the results of a detailed microstructural and microchemical investigation, as well as re-melting experiments using a piston cylinder apparatus. Carbonatitic inclusions coexist in the same cluster with crystallized silicate melt inclusions (nanogranites) and COH fluid inclusions, suggesting conditions of primary immiscibility between two melts and a fluid during anatexis. The production of both carbonatitic and granitic melts during the same anatectic event requires a suitable heterogeneous protolith. This may be represented by a sedimentary sequence containing marble lenses of limited extension, similar to the one still visible in the adjacent central Moldanubian Zone. The presence of CO2-rich fluid inclusions suggests furthermore that high CO2 activity during anatexis may be required to stabilize a carbonate-rich melt in a silica-dominated system. This natural occurrence displays a remarkable similarity with experiments on carbonate-silicate melt immiscibility, where CO2 saturation is a condition commonly imposed. In conclusion, this study shows how the investigation of partial melting through melt inclusion studies may unveil unexpected processes whose evidence, while preserved in stiff minerals such as garnet, is completely obliterated in the rest of the rock due to metamorphic re
8. Multiscale Models of Melting Arctic Sea Ice
Science.gov (United States)
2014-09-30
1 Multiscale Models of Melting Arctic Sea Ice Kenneth M. Golden University of Utah, Department of Mathematics phone: (801) 581-6851...feedback has played a major role in the recent declines of the summer Arctic sea ice pack. However, understanding the evolution of melt ponds and sea...Models of Melting Arctic Sea Ice 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER
9. Low Melt Height Solidification of Superalloys
Science.gov (United States)
Montakhab, Mehdi; Bacak, Mert; Balikci, Ercan
2016-06-01
Effect of a reduced melt height in the directional solidification of a superalloy has been investigated by two methods: vertical Bridgman (VB) and vertical Bridgman with a submerged baffle (VBSB). The latter is a relatively new technique and provides a reduced melt height ahead of the solidifying interface. A low melt height leads to a larger primary dendrite arm spacing but a lower mushy length, melt-back transition length, and porosity. The VBSB technique yields up to 38 pct reduction in the porosity. This may improve a component's mechanical strength especially in a creep-fatigue type dynamic loading.
10. Solute Redistribution in Directional Melting Process
Institute of Scientific and Technical Information of China (English)
2000-01-01
@@The solute redistribution in directional melting process is theoretically studied. Based on quantitative evaluations, uniform solute distribution in liquid and a quasi-steady solute distribution in solid are supposed. The discussion on the solute balance comes to a simple model for the solute redistribution in directional melting process. As an example, the variation of liquid composition during melting process of carbon steel is quantitatively evaluated using the model. Results show that the melting of an alloy starts at solidus temperature, but approaches the liquidus temperature after a very short transient process.
11. Evidence for fractional crystallization of wadsleyite and ringwoodite from olivine melts in chondrules entrained in shock-melt veins.
Science.gov (United States)
Miyahara, Masaaki; El Goresy, Ahmed; Ohtani, Eiji; Nagase, Toshiro; Nishijima, Masahiko; Vashaei, Zahra; Ferroir, Tristan; Gillet, Philippe; Dubrovinsky, Leonid; Simionovici, Alexandre
2008-06-24
Peace River is one of the few shocked members of the L-chondrites clan that contains both high-pressure polymorphs of olivine, ringwoodite and wadsleyite, in diverse textures and settings in fragments entrained in shock-melt veins. Among these settings are complete olivine porphyritic chondrules. We encountered few squeezed and flattened olivine porphyritic chondrules entrained in shock-melt veins of this meteorite with novel textures and composition. The former chemically unzoned (Fa(24-26)) olivine porphyritic crystals are heavily flattened and display a concentric intergrowth with Mg-rich wadsleyite of a very narrow compositional range (Fa(6)-Fa(10)) in the core. Wadsleyite core is surrounded by a Mg-poor and chemically stark zoned ringwoodite (Fa(28)-Fa(38)) belt. The wadsleyite-ringwoodite interface denotes a compositional gap of up to 32 mol % fayalite. A transmission electron microscopy study of focused ion beam slices in both regions indicates that the wadsleyite core and ringwoodite belt consist of granoblastic-like intergrowth of polygonal crystallites of both ringwoodite and wadsleyite, with wadsleyite crystallites dominating in the core and ringwoodite crystallites dominating in the belt. Texture and compositions of both high-pressure polymorphs are strongly suggestive of formation by a fractional crystallization of the olivine melt of a narrow composition (Fa(24-26)), starting with Mg-rich wadsleyite followed by the Mg-poor ringwoodite from a shock-induced melt of olivine composition (Fa(24-26)). Our findings could erase the possibility of the resulting unrealistic time scales of the high-pressure regime reported recently from other shocked L-6 chondrites.
12. Coarse grained model of entangled polymer melts
Science.gov (United States)
Rakshit, Abhik
reptation behavior. Constraint release is additionally implemented by tracing the position of the ends of all chains in the system and performing a local relaxation of the chain backbones once end retraction is detected. This algorithm takes advantage of the multibody nature of the model and requires no heuristic input parameters that would control, for example, the frequency and the magnitude of these fluctuations. The model is used, without additional calibration, to study start-up and step strain shear flows and reproduces features observed experimentally such as the overshoot during start-up shear flow, the Lodge-Meissner law, the monotonicity of the steady state shear stress with the strain rate, and shear thinning at large ġ . Most of the simulations reported are performed in conditions in which using a fully refined model of the same system would have been extremely computationally demanding or simply impossible with the current methods. Chain diffusion is studied in mixtures of bi-disperse linear polymers of same chemical identity by means of the coarse grained model with no additional calibration. The two sub-populations are moderately to highly entangled, with the shorter chain length NS fulfilling NS/Ne ≥ 5. Its performance in reproducing chain dynamics in a polydisperse melt is tested by extensively comparing the results with those obtained from an equivalent fine scale representation of the same system. The coarse grained model is used further to investigate for the first time by means of simulations the scaling of the diffusion coefficient with the length of the two types of chains and its dependence on the respective fractions. The model reproduces many features observed experimentally. For example, the diffusion coefficient of one of the chain types decreases with increasing the length of the other type chains. It is shown that, in this model, this effect is not linked to constraint release. When the matrix chains become sufficiently long, their length
13. Evidence for pressure-release melting beneath magmatic arcs from basalt at Galunggung, Indonesia
Science.gov (United States)
Sisson, T.W.; Bronto, S.
1998-01-01
The melting of peridotite in the mantle wedge above subduction zones is generally believed to involve hydrous fluids derived from the subducting slab. But if mantle peridotite is upwelling within the wedge, melting due to pressure release could also contribute to magma production. Here we present measurements of the volatile content of primitive magmas from Galunggung volcano in the Indonesian are which indicate that these magmas were derived from the pressure-release melting of hot mantle peridotite. The samples that we have analysed consist of mafic glass inclusions in high-magnesium basalts. The inclusions contain uniformly low H2O concentrations (0.21-0.38 wt%), yet relatively high levels of CO2 (up to 750 p.p.m.) indicating that the low H2O concentrations are primary and not due to degassing of the magma. Results from previous anhydrous melting experiments on a chemically similar Aleutian basalts indicate that the Galunggung high-magnesium basalts were last in equilibrium with peridotite at ~1,320 ??C and 1.2 GPa. These high temperatures at shallow sub-crustal levels (about 300-600 ??C hotter than predicted by geodynamic models), combined with the production of nearly H2O- free basaltic melts, provide strong evidence that pressure-release melting due to upwelling in the sub-are mantle has taken place. Regional low- potassium and low-H2O (ref. 5) basalts found in the Cascade are indicate that such upwelling-induced melting can be widespread.
14. A benchmark initiative on mantle convection with melting and melt segregation
Science.gov (United States)
Schmeling, Harro; Dannberg, Juliane; Dohmen, Janik; Kalousova, Klara; Maurice, Maxim; Noack, Lena; Plesa, Ana; Soucek, Ondrej; Spiegelman, Marc; Thieulot, Cedric; Tosi, Nicola; Wallner, Herbert
2016-04-01
In recent years a number of mantle convection models have been developed which include partial melting within the asthenosphere, estimation of melt volumes, as well as melt extraction with and without redistribution at the surface or within the lithosphere. All these approaches use various simplifying modelling assumptions whose effects on the dynamics of convection including the feedback on melting have not been explored in sufficient detail. To better assess the significance of such assumptions and to provide test cases for the modelling community we carry out a benchmark comparison. The reference model is taken from the mantle convection benchmark, cases 1a to 1c (Blankenbach et al., 1989), assuming a square box with free slip boundary conditions, the Boussinesq approximation, constant viscosity and Rayleigh numbers of 104 to 10^6. Melting is modelled using a simplified binary solid solution with linearly depth dependent solidus and liquidus temperatures, as well as a solidus temperature depending linearly on depletion. Starting from a plume free initial temperature condition (to avoid melting at the onset time) five cases are investigated: Case 1 includes melting, but without thermal or dynamic feedback on the convection flow. This case provides a total melt generation rate (qm) in a steady state. Case 2 is identical to case 1 except that latent heat is switched on. Case 3 includes batch melting, melt buoyancy (melt Rayleigh number Rm) and depletion buoyancy, but no melt percolation. Output quantities are the Nusselt number (Nu), root mean square velocity (vrms), the maximum and the total melt volume and qm approaching a statistical steady state. Case 4 includes two-phase flow, i.e. melt percolation, assuming a constant shear and bulk viscosity of the matrix and various melt retention numbers (Rt). These cases are carried out using the Compaction Boussinseq Approximation (Schmeling, 2000) or the full compaction formulation. For cases 1 - 3 very good agreement
15. Disordering and Melting of Aluminum Surfaces
DEFF Research Database (Denmark)
Stoltze, Per; Nørskov, Jens Kehlet; Landman, U.
1988-01-01
We report on a molecular-dynamics simulation of an Al(110) surface using the effective-medium theory to describe the interatomic interactions. The surface region is found to start melting ≅200 K below the bulk melting temperature with a gradual increase in the thickness of the disordered layer as...
16. Purification of Niobium by Electron Beam Melting
Science.gov (United States)
Sankar, M.; Mirji, K. V.; Prasad, V. V. Satya; Baligidad, R. G.; Gokhale, A. A.
2016-06-01
Pure niobium metal, produced by alumino-thermic reduction of niobium oxide, contains various impurities which need to be reduced to acceptable levels to obtain aerospace grade purity. In the present work, an attempt has been made to refine niobium metals by electron beam drip melting technique to achieve purity confirming to the ASTM standard. Input power to the electron gun and melt rate were varied to observe their combined effect on extend of refining and loss of niobium. Electron beam (EB) melting is shown to reduce alkali metals, trace elements and interstitial impurities well below the specified limits. The reduction in the impurities during EB melting is attributed to evaporation and degassing due to the combined effect of high vacuum and high melt surface temperature. The % removal of interstitial impurities is essentially a function of melt rate and input power. As the melt rate decreases or input power increases, the impurity levels in the solidified niobium ingot decrease. The EB refining process is also accompanied by considerable amount of niobium loss, which is attributed to evaporation of pure niobium and niobium sub-oxide. Like other impurities, Nb loss increases with decreasing melt rate or increase in input power.
17. Stability of foams in silicate melts
Science.gov (United States)
Proussevitch, Alexander A.; Sahagian, Dork L.; Kutolin, Vladislav A.
1993-12-01
Bubble coalescence and the spontaneous disruption of high-porosity foams in silicate melts are the result of physical expulsion of interpore melt (syneresis) leading to bubble coalescence, and diffusive gas exchange between bubbles. Melt expulsion can be achieved either along films between pairs of bubbles, or along Plateau borders which represent the contacts between 3 or more bubbles. Theoretical evaluation of these mechanisms is confirmed by experimental results, enabling us to quantify the relevant parameters and determine stable bubble size and critical film thickness in a foam as a function of melt viscosity, surface tension, and time. Foam stability is controlled primarily by melt viscosity and time. Melt transport leading to coalescence of bubbles proceeds along inter-bubble films for smaller bubbles, and along Plateau borders for larger bubbles. Thus the average bubble size accelerates with time. In silicate melts, the diffusive gas expulsion out of a region of foam is effective only for water (and even then, only at small length scales), as the diffusion of CO 2 is negligible. The results of our analyses are applicable to studies of vesicularity of lavas, melt degassing, and eruption mechanisms.
18. Uniaxial Elongational viscosity of bidisperse polystyrene melts
DEFF Research Database (Denmark)
Nielsen, Jens Kromann; Rasmussen, Henrik K.; Hassager, Ole
2006-01-01
The startup and steady uniaxial elongational viscosity have been measured for three bidisperse polystyrene (PS) melts, consisting of blends of monodisperse PS with molecular weights of 52 kg/mole or 103 kg/mole and 390 kg/mole. The bidisperse melts have a maximum in the steady elongational viscos...
19. Bubble Formation in Basalt-like Melts
DEFF Research Database (Denmark)
Jensen, Martin; Keding, Ralf; Yue, Yuanzheng
2011-01-01
The effect of the melting temperature on bubble size and bubble formation in an iron bearing calcium aluminosilicate melt is studied by means of in-depth images acquired by optical microscopy. The bubble size distribution and the total bubble volume are determined by counting the number of bubble...
20. Bubble Formation in Basalt-like Melts
DEFF Research Database (Denmark)
Jensen, Martin; Keding, Ralf; Yue, Yuanzheng
2011-01-01
The effect of the melting temperature on bubble size and bubble formation in an iron bearing calcium aluminosilicate melt is studied by means of in-depth images acquired by optical microscopy. The bubble size distribution and the total bubble volume are determined by counting the number of bubbles...
1. Shock-induced melting and rapid solidification
Energy Technology Data Exchange (ETDEWEB)
Nellis, W.J.; Gourdin, W.H.; Maple, M.B.
1987-08-01
Model calculations are presented to estimate that approx.50 GPa is required to completely shock melt metal powders with quenching at rates up to 10/sup 8/ K/s. Experiments are discussed for powders of a Cu-Zr alloy compacted in the usual way at 16 GPa and melted by shocking to 60 GPa. 12 refs.
2. NANOSTRUCTURAL PROCESSES OF MELTING AND MOULDING OF HYPOEUTECTIC SILUMIN
Directory of Open Access Journals (Sweden)
V. Yu. Stetsenko
2016-01-01
Full Text Available It is shown that melting and molding of hypoeutectic silumin are difficult physical and chemical nanostructural processes. In them the major role is played by the centers of crystallization of primary dendrites of aluminum, aluminum nanocrystals, the dissolved and adsorbed hydrogen. The role of the modifying crystals of an intermetallid of TiAl3 is reduced to absorption of the dissolved hydrogen and an intensification of process of a koalestsention of nanocrystals of aluminum in the centers of crystallization of primary dendrites of aluminum.
3. Size-dependent melting of Bi nanoparticles
Science.gov (United States)
Olson, E. A.; Efremov, M. Yu.; Zhang, M.; Zhang, Z.; Allen, L. H.
2005-02-01
Nanocalorimetry was used to investigate the melting of Bi nanoparticles. The particles were formed by evaporating Bi onto a silicon nitride substrate, which was then heated. The particles self-assemble into truncated spherical particles. Below 5-nm average film thickness, mean particle sizes increased linearly with deposition thickness but increased rapidly for 10-nm-thick films. As expected, small particles were found to exhibit size-dependent melting temperatures less than the bulk melting temperature (e.g., ΔT =67K for a 3-nm radius particle). The measured melting temperatures for particles below ˜7nm in radius, however, were ˜50K above the value predicted by the homogeneous melting model. We discuss this discrepancy in terms of a possible size-dependent crystal structure change and the superheating of the solid phase.
4. Nanotexturing of surfaces to reduce melting point.
Energy Technology Data Exchange (ETDEWEB)
Garcia, Ernest J.; Zubia, David (University of Texas at El Paso El Paso, TX); Mireles, Jose (Universidad Aut%C3%94onoma de Ciudad Ju%C3%94arez Ciudad Ju%C3%94arez, Mexico); Marquez, Noel (University of Texas at El Paso El Paso, TX); Quinones, Stella (University of Texas at El Paso El Paso, TX)
2011-11-01
This investigation examined the use of nano-patterned structures on Silicon-on-Insulator (SOI) material to reduce the bulk material melting point (1414 C). It has been found that sharp-tipped and other similar structures have a propensity to move to the lower energy states of spherical structures and as a result exhibit lower melting points than the bulk material. Such a reduction of the melting point would offer a number of interesting opportunities for bonding in microsystems packaging applications. Nano patterning process capabilities were developed to create the required structures for the investigation. One of the technical challenges of the project was understanding and creating the specialized conditions required to observe the melting and reshaping phenomena. Through systematic experimentation and review of the literature these conditions were determined and used to conduct phase change experiments. Melting temperatures as low as 1030 C were observed.
5. Volatile diffusion in silicate melts and its effects on melt inclusions
Directory of Open Access Journals (Sweden)
P. Scarlato
2005-06-01
Full Text Available A compendium of diffusion measurements and their Arrhenius equations for water, carbon dioxide, sulfur, fluorine, and chlorine in silicate melts similar in composition to natural igneous rocks is presented. Water diffusion in silicic melts is well studied and understood, however little data exists for melts of intermediate to basic compositions. The data demonstrate that both the water concentration and the anhydrous melt composition affect the diffusion coefficient of water. Carbon dioxide diffusion appears only weakly dependent, at most, on the volatilefree melt composition and no effect of carbon dioxide concentration has been observed, although few experiments have been performed. Based upon one study, the addition of water to rhyolitic melts increases carbon dioxide diffusion by orders of magnitude to values similar to that of 6 wt% water. Sulfur diffusion in intermediate to silicic melts depends upon the anhydrous melt composition and the water concentration. In water-bearing silicic melts sulfur diffuses 2 to 3 orders of magnitude slower than water. Chlorine diffusion is affected by both water concentration and anhydrous melt composition; its values are typically between those of water and sulfur. Information on fluorine diffusion is rare, but the volatile-free melt composition exerts a strong control on its diffusion. At the present time the diffusion of water, carbon dioxide, sulfur and chlorine can be estimated in silicic melts at magmatic temperatures. The diffusion of water and carbon dioxide in basic to intermediate melts is only known at a limited set of temperatures and compositions. The diffusion data for rhyolitic melts at 800°C together with a standard model for the enrichment of incompatible elements in front of growing crystals demonstrate that rapid crystal growth, greater than 10-10 ms-1, can significantly increase the volatile concentrations at the crystal-melt interface and that any of that melt trapped
6. Hot melt extrusion versus spray drying: hot melt extrusion degrades albendazole.
Science.gov (United States)
Hengsawas Surasarang, Soraya; Keen, Justin M; Huang, Siyuan; Zhang, Feng; McGinity, James W; Williams, Robert O
2017-05-01
The purpose of this study was to enhance the dissolution properties of albendazole (ABZ) by the use of amorphous solid dispersions. Phase diagrams of ABZ-polymer binary mixtures generated from Flory-Huggins theory were used to assess miscibility and processability. Forced degradation studies showed that ABZ degraded upon exposure to hydrogen peroxide and 1 N NaOH at 80 °C for 5 min, and the degradants were albendazole sulfoxide (ABZSX), and ABZ impurity A, respectively. ABZ was chemically stable following exposure to 1 N HCl at 80 °C for one hour. Thermal degradation profiles show that ABZ, with and without Kollidon(®) VA 64, degraded at 180 °C and 140 °C, respectively, which indicated that ABZ could likely be processed by thermal processing. Following hot melt extrusion, ABZ degraded up to 97.4%, while the amorphous ABZ solid dispersion was successfully prepared by spray drying. Spray-dried ABZ formulations using various types of acids (methanesulfonic acid, sulfuric acid and hydrochloric acid) and polymers (Kollidon(®) VA 64, Soluplus(®) and Eudragit(®) E PO) were studied. The spray-dried ABZ with methanesulfonic acid and Kollidon(®) VA 64 substantially improved non-sink dissolution in acidic media as compared to bulk ABZ (8-fold), physical mixture of ABZ:Kollidon(®) VA 64 (5.6-fold) and ABZ mesylate salt (1.6-fold). No degradation was observed in the spray-dried product for up to six months and less than 5% after one-year storage. In conclusion, amorphous ABZ solid dispersions in combination with an acid and polymer can be prepared by spray drying to enhance dissolution and shelf-stability, whereas those made by melt extrusion are degraded.
7. Evaluation of Melt Behavior with initial Melt Velocity under SFR Severe Accidents
Energy Technology Data Exchange (ETDEWEB)
Heo, Hyo; Bang, In Cheol [UNIST, Ulsan (Korea, Republic of); Jerng, Dong Wook [Chung-Ang Univ, Seoul (Korea, Republic of)
2015-10-15
In the current Korean sodium-cooled fast reactor (SFR) program, early dispersion of the molten metallic fuel within a subchannel is suggested as one of the inherent safety strategies for the initiating phase of hypothetical core disruptive accident (HCDA). The safety strategy provides negative reactivity driven by the melt dispersal, so it could reduce the possibility of the recriticality event under a severe triple or more fault scenario for SFR. Since the behavior of the melt dispersion is unpredictable, it depends on the accident condition, particularly core region. While the voided coolant channel region is usually developed in the inner core, the unvoided coolant channel region is formed in the outer core. It is important to confirm the fuel dispersion with the core region, but there are not sufficient existing studies for them. From the existing studies, the coolant vapor pressure is considered as one of driving force to move the melt towards outside of the core. There is a complexity of the phenomena during intermixing of the melt with the coolant after the horizontal melt injections. It is too difficult to understand the several combined mechanisms related to the melt dispersion and the fragmentation. Thus, it could be worthwhile to study the horizontal melt injections at lower temperature as a preliminary study in order to identify the melt dispersion phenomena. For this reason, it is required to clarify whether the coolant vapor pressure is the driving force of the melt dispersion with the core region. The specific conditions to be well dispersed for the molten metallic fuel were discussed in the experiments with the simulant materials. The each melt behavior was compared to evaluate the melt dispersion under the coolant void condition and the boiling condition. As the results, the following results are remarked: 1. The upward melt dispersion did not occur for a given melt and coolant temperature in the nonboiling range. Over current range of conditions
8. Distribution of radionuclides during melting of carbon steel
Energy Technology Data Exchange (ETDEWEB)
Thurber, W.C.; MacKinney, J.
1997-02-01
9. Viscosity of carbonate-rich melts under different oxygen fugacity conditions
Science.gov (United States)
Di Genova, Danilo; Hess, Kai-Uwe; Cimarelli, Corrado; Dingwell, Donald B.
2015-04-01
Viscosity is a fundamental property of many materials and its changes affects the fluid dynamics of natural system as well as industrial processes. The mobility of carbonatitic melts, which are carbonate-rich and very fluid melts, has attracted renewed interest in both earth science and industry. In fact, these melts are considered the main transport agent of carbon from the mantle to the crust and may be intimately linked to the generation of kimberlites. At the same time lithium, potassium and sodium carbonate are used as electrolytes in molten carbonate fuel cells which operate at high temperatures (~650° C) for the production of electricity without CO2 emissions. Accurate measurement of the transport property (i.e. viscosity) of carbonatitic melts is a priority in order to understand the carbonatite mobility and reaction rates. Additionally, obtaining accurate viscosity measurements of such low viscosity melts is however an experimental challenge due to volatility, very low torques and chemical melt instability in the viscometer. To overcome these limitations we have customized a Modular Compact Rheometer (MCR 502 from Anton Paar) ad hoc equipped with 2 narrow gap concentric-cylinder geometries of steel and Pt-Au. The rheometer is characterized by an air-bearing-supported synchronous motor with torque ranging between 0.01 μNm and 230 mNm (resolution of 0.1 nNm), achieving very low viscosity measurements in the order of mPa s, temperatures up to 1000° C and shear rates ranging between 1 and 100 sec-1. These experimental conditions well match the temperature-viscosity-shear rate window relevant for carbonate melts. Here we present the calibration of the rheometer and the results of a rheological characterization study on a series of very low viscous synthetic and natural carbonatitic melts at different oxygen fugacity (air and CO2 saturated atmosphere). Viscosity measurements on carbonate melts have been performed in the temperature range between ~650 and 1000
10. Ionic-polymeric models and the amphoteric behavior of water in silicate melts
Science.gov (United States)
Moretti, R.
2012-04-01
In silicate melts it is almost impossible to readily distinguish solute and solvent like in aqueous solutions. The anionic framework of silicate melts, in fact, makes solute and solvents so intimately related that one cannot identify a solvation shell and identify directly, from structural studies, the complexes needed to define acid-base reactions. Therefore, the distinction between solute and solvent becomes blurred in systems such as silicate melts, because speciation is not only complex but changes with the marked depolymerization of the silicate framework that obtains from pure SiO2 to metal-oxide rich compositions. These features do not allow proper understanding of the actual physico-chemical role of many species detected by conventional techniques, a fact which can lead to confusing notation. However, these may not be serious limits to account correctly for the acid-base reactions that take place in every kind of magmatic setting, provided a 'syntax' describing the effective interactions among significative cationic and anionic entities. In particular, the syntax for acid-base exchanges is needed such that constituting oxides (i.e. chemical components) can be treated independently of (but not necessarily extraneous to) structural features in defining such entities. So-called ionic-polymeric models highlight the mutual correspondence between polymerization and acid-base properties of dissolved oxides through the Lux-Flood formalism for molten oxides. They thus provide the syntax to write chemical exchanges, but have no pretension to structural description. In fact the concept of melt polymerization is used to identify basic anions and cations that can be used, along with their formal charge, to describe effectively acid-base interactions taking place in melts. In this respect, an example is given by the description of the amphoteric behavior of water dissolved on melts, hence water autoprotolysis. Although it exerts a profound influence on properties of
11. Analysis of Turf Fungicides in Snow Melt Runoff by LC/MS
Science.gov (United States)
Fungicides are applied on turf grass, in autumn, to control snow mold in the north-central United States. Fungicides of varying chemical classes have been detected in snow melt runoff from turf. A multi-residue method for simultaneous sample extraction and analysis is needed to process a large quant...
12. Melt processed high-temperature superconductors
CERN Document Server
1993-01-01
The achievement of large critical currents is critical to the applications of high-temperature superconductors. Recent developments have shown that melt processing is suitable for producing high J c oxide superconductors. Using magnetic forces between such high J c oxide superconductors and magnets, a person could be levitated.This book has grown largely out of research works on melt processing of high-temperature superconductors conducted at ISTEC Superconductivity Research Laboratory. The chapters build on melt processing, microstructural characterization, fundamentals of flux pinning, criti
13. Redox Equilibria of Chromium in Calcium Silicate Base Melts
Science.gov (United States)
2009-08-01
The oxidation state of chromium has been determined at 1600 °C in CaO-SiO2-CrO x melts with CaO/SiO2 ratios (mass pct) of 0.66, 0.93, and 1.10, and 0.15 to 3.00 pct Cr2O3 (initial). A few experiments were also carried out with CaO-SiO2-Al2O3-CrO x melts at 1430 °C. The slag samples were equilibrated with gas phases of controlled oxygen pressure. Two techniques were applied to determine the oxidation state: thermogravimetry and quenching of the samples with subsequent wet chemical analysis. In the low-oxygen pressure range, the chromium is mainly divalent. In the high-oxygen pressure range, it is trivalent and hexavalent. It was found that the Cr3+/Cr2+ and Cr6+/Cr3+ ratios depend on oxygen pressure at a constant CaO/SiO2 ratio and a constant content of total chromium, according to the ideal law of mass action. According to the respective chemical reactions, these ratios change proportional to p_{{{text{O}}2 }}{}^{1/4} or p_{{{text{O}}_{ 2} }}{}^{3/4}, respectively. They also increase with increasing basicity. The data are used to compute the fractions of the different ions in the melt. There is a certain range of oxygen pressure in which all three valence states, Cr2+, Cr3+, and Cr6+, coexist. The color of the solidified slag samples is described and is explained with the help of transmission spectra.
14. Investigation on contact melting of Cu/Al laminated composite
Directory of Open Access Journals (Sweden)
Dmitry V. Pronichev
2016-12-01
Full Text Available The study presents investigation of chemical composition, microhardness and electrical conductivity of Cu/Al laminated metal composite after heat treatment at temperatures higher than Cu–Al eutectic melting point. The Cu/Al bimetal was obtained via explosion welding. Chemical composition of the material after heat treatments was identified using EDS analysis. Eddy current testing was applied to investigate electrical conductivity of the composite’s components. Strain-hardened zones were identified in the explosion welded composite. The experimental value of electrical conductivity of explosion welded composite was in good coherence with calculated by additivity rule results. Heat treatments resulted in the formation of multiple interlayers which had high microhardness value and had intermetallics in composition. The electrical conductivity of the identified interlayers was significantly lower than of Cu and Al.
15. The Reaction of Carbonates in Contact with Superheated Silicate Melts: New Insights from MEMIN Laser Melting Experiments
Science.gov (United States)
Hamann, C.; Hecht, L.; Schäffer, S.; Deutsch, A.; Lexow, B.
2016-08-01
The reaction of carbonates in contact with silicate impact melts is discussed quite controversially in the impact community. Here, we discuss four MEMIN laser melting experiments involving carbonates in contact with superheated silicate melts.
16. Interaction mechanism between niobium-silicide-based alloy melt and Y2O3 refractory crucible in vacuum induction melting process
Directory of Open Access Journals (Sweden)
Gao Ming
2011-05-01
Full Text Available The Y2O3 crucibles were introduced in the study as an alternative to the traditional ceramic ones in vacuum induction melting of multi-component Nb-16Si-22Ti-2Al-2Hf-17Cr (at.% alloys, to reveal the possible interactions between the alloy melt and the refractory crucible. Multiple melting time lengths and two cooling schemes were designed and used for the experiments. The chemical composition and microstructure of the tested alloy and the melt-crucible interaction were investigated and evaluated. In the experiments, Y2O3 crucible displays good physical-chemical compatibility. The results indicate that the increment of O element in the as-cast ingot is 0.03at.%-0.04at.% (72-97 ppm and the increment of Y element is very insignificant. The key features of the alloy melt interacting with Y2O3 ceramics are analyzed and concluded in the paper. As a result of the dissolution reaction xY2O3 (in molten alloy + (1-xHfO2 (impurity →Hf1-xY2xO2-x, a continuous double-layer solid film consisted of HfO2 solid solution (~2 μm and pure HfO2 (~5 μm is formed on the surface of the test ingot after cooled down in the crucible. The experimental results show that the Y2O3 crucible is applicable to the vacuum induction melting of Nb-Si based alloys.
17. Origins of ultralow velocity zones through slab-derived metallic melt.
Science.gov (United States)
Liu, Jiachao; Li, Jie; Hrubiak, Rostislav; Smith, Jesse S
2016-05-17
Understanding the ultralow velocity zones (ULVZs) places constraints on the chemical composition and thermal structure of deep Earth and provides critical information on the dynamics of large-scale mantle convection, but their origin has remained enigmatic for decades. Recent studies suggest that metallic iron and carbon are produced in subducted slabs when they sink beyond a depth of 250 km. Here we show that the eutectic melting curve of the iron-carbon system crosses the current geotherm near Earth's core-mantle boundary, suggesting that dense metallic melt may form in the lowermost mantle. If concentrated into isolated patches, such melt could produce the seismically observed density and velocity features of ULVZs. Depending on the wetting behavior of the metallic melt, the resultant ULVZs may be short-lived domains that are replenished or regenerated through subduction, or long-lasting regions containing both metallic and silicate melts. Slab-derived metallic melt may produce another type of ULVZ that escapes core sequestration by reacting with the mantle to form iron-rich postbridgmanite or ferropericlase. The hypotheses connect peculiar features near Earth's core-mantle boundary to subduction of the oceanic lithosphere through the deep carbon cycle.
18. Effect of Sulfur on Siderophile Element Partitioning Between Olivine and Martian Primary Melt
Science.gov (United States)
Usui, T.; Shearer, C. K.; Righter, K.; Jones, J. H.
2011-01-01
Since olivine is a common early crystallizing phase in basaltic magmas that have produced planetary and asteroidal crusts, a number of experimental studies have investigated elemental partitioning between olivine and silicate melt [e.g., 1, 2, 3]. In particular, olivine/melt partition coefficients of Ni and Co (DNi and DCo) have been intensively studied because these elements are preferentially partitioned into olivine and thus provide a uniquely useful insight into the basalt petrogenesis [e.g., 4, 5]. However, none of these experimental studies are consistent with incompatible signatures of Co [e.g., 6, 7, 8] and Ni [7] in olivines from Martian meteorites. Chemical analyses of undegassed MORB samples suggest that S dissolved in silicate melts can reduce DNi up to 50 % compared to S-free experimental systems [9]. High S solubility (up to 4000 ppm) for primitive shergottite melts [10] implies that S might have significantly influenced the Ni and Co partitioning into shergottite olivines. This study conducts melting experiments on Martian magmatic conditions to investigate the effect of S on the partitioning of siderophile elements between olivine and Martian primary melt.
19. Cloud screening and melt water detection over melting sea ice using AATSR/SLSTR
Science.gov (United States)
Istomina, Larysa; Heygster, Georg
2014-05-01
With the onset of melt in the Arctic Ocean, the fraction of melt water on sea ice, the melt pond fraction, increases. The consequences are: the reduced albedo of sea ice, increased transmittance of sea ice and affected heat balance of the system with more heat passing through the ice into the ocean, which facilitates further melting. The onset of melt, duration of melt season and melt pond fraction are good indicators of the climate state of the Arctic and its change. In the absence of reliable sea ice thickness retrievals in summer, melt pond fraction retrieval from satellite is in demand as input for GCM as an indicator of melt state of the sea ice. The retrieval of melt pond fraction with a moderate resolution radiometer as AATSR is, however, a non-trivial task due to a variety of subpixel surface types with very different optical properties, which give non-unique combinations if mixed. In this work this has been solved by employing additional information on the surface and air temperature of the pixel. In the current work, a concept of melt pond detection on sea ice is presented. The basis of the retrieval is the sensitivity of AATSR reflectance channels 550nm and 860nm to the amount of melt water on sea ice. The retrieval features extensive usage of a database of in situ surface albedo spectra. A tree of decisions is employed to select the feasible family of in situ spectra for the retrieval, depending on the melt stage of the surface. Reanalysis air temperature at the surface and brightness temperature measured by the satellite sensor are analyzed in order to evaluate the melting status of the surface. Case studies for FYI and MYI show plausible retrieved melt pond fractions, characteristic for both of the ice types. The developed retrieval can be used to process the historical AATSR (2002-2012) dataset, as well as for the SLSTR sensor onboard the future Sentinel-3 mission (scheduled for launch in 2015), to keep the continuity and obtain longer time sequence
20. A benchmark initiative on mantle convection with melting and melt segregation
Science.gov (United States)
Schmeling, Harro; Dohmen, Janik; Wallner, Herbert; Noack, Lena; Tosi, Nicola; Plesa, Ana-Catalina; Maurice, Maxime
2015-04-01
In recent years a number of mantle convection models have been developed which include partial melting within the asthenosphere, estimation of melt volumes, as well as melt extraction with and without redistribution at the surface or within the lithosphere. All these approaches use various simplifying modelling assumptions whose effects on the dynamics of convection including the feedback on melting have not been explored in sufficient detail. To better assess the significance of such assumptions and to provide test cases for the modelling community we initiate a benchmark comparison. In the initial phase of this endeavor we focus on the usefulness of the definitions of the test cases keeping the physics as sound as possible. The reference model is taken from the mantle convection benchmark, case 1b (Blanckenbach et al., 1989), assuming a square box with free slip boundary conditions, the Boussinesq approximation, constant viscosity and a Rayleigh number of 1e5. Melting is modelled assuming a simplified binary solid solution with linearly depth dependent solidus and liquidus temperatures, as well as a solidus temperature depending linearly on depletion. Starting from a plume free initial temperature condition (to avoid melting at the onset time) three cases are investigated: Case 1 includes melting, but without thermal or dynamic feedback on the convection flow. This case provides a total melt generation rate (qm) in a steady state. Case 2 includes batch melting, melt buoyancy (melt Rayleigh number Rm), depletion buoyancy and latent heat, but no melt percolation. Output quantities are the Nusselt number (Nu), root mean square velocity (vrms) and qm approaching a statistical steady state. Case 3 includes two-phase flow, i.e. melt percolation, assuming a constant shear and bulk viscosity of the matrix and various melt retention numbers (Rt). These cases should be carried out using the Compaction Boussinseq Approximation (Schmeling, 2000) or the full compaction
1. Evolving magma storage conditions beneath Mount St. Helens inferred from chemical variations in melt inclusions from the 1980-1986 and current (2004-2006) eruptions: Chapter 33 in A volcano rekindled: the renewed eruption of Mount St. Helens, 2004-2006
Science.gov (United States)
Blundy, Jon; Cashman, Katharine V.; Berlo, Kim; Sherrod, David R.; Scott, William E.; Stauffer, Peter H.
2008-01-01
Major element, trace element, and volatile concentrations in 187 glassy melt inclusions and 25 groundmass glasses from the 1980-86 eruption of Mount St. Helens are presented, together with 103 analyses of touching FE-Ti oxide pairs from the same samples. These data are used to evaluate the temporal evolution of the magmatic plumbing system beneath the volcano during 1980-86 and so provide a framework in which to interpret analyses of melt inclusions from the current (2004-2006) eruption. Major and trace element concentrations of all melt inclusions lie at the high SiO2 end of the data array defined by eruptive products of the late Quaternary age from Mount St. Helens. For several major and trace elements, the glasses define a trend that is oblique to the whole-rock trend, indicating that different mineral assemblages were responsible for the two trends. The whole-rock trend can be ascribed to differentiation of hydrous basaltic parents in a deep-seated magma reservoir, probably at depths great enough to stabilize garnet. In contrast, the glass trends were generated by closed-system crystallization of the phenocryst and microlite mineral assemblages at low pressures. The dissolved H2O content of the melt inclusions from 1980-86, as measured by the ion microprobe, ranges from 0 to 6.7 wt. percent, with the highest values obtained from the plinian phase of May 18, 1980. Water contents decrease with increasing SiO2, consistent with decompression-driven crystallization. Preliminary data for dissolved CO2 in melt inclusions from the May 18 plinian phase from August 7, 1980, indicate that XH2O in a vapor phase was approximately constant at 0.80, irrespective of H2O content, suggestive of closed-system degassing with a high bubble fraction or gas streaming through the subvolcanic system. Temperature and f
2. Melting behavior of mixed U-Pu oxides under oxidizing conditions
Science.gov (United States)
Strach, Michal; Manara, Dario; Belin, Renaud C.; Rogez, Jacques
2016-05-01
In order to use mixed U-Pu oxide ceramics in present and future nuclear reactors, their physical and chemical properties need to be well determined. The behavior of stoichiometric (U,Pu)O2 compounds is relatively well understood, but the effects of oxygen stoichiometry on the fuel performance and stability are often still obscure. In the present work, a series of laser melting experiments were carried out to determine the impact of an oxidizing atmosphere, and in consequence the departure from a stoichiometric composition on the melting behavior of six mixed uranium plutonium oxides with Pu content ranging from 14 to 62 wt%. The starting materials were disks cut from sintered stoichiometric pellets. For each composition we have performed two laser melting experiments in pressurized air, each consisting of four shots of different duration and intensity. During the experiments we recorded the temperature at the surface of the sample with a pyrometer. Phase transitions were qualitatively identified with the help of a reflected blue laser. The observed phase transitions occur at a systematically lower temperature, the lower the Pu content of the studied sample. It is consistent with the fact that uranium dioxide is easily oxidized at elevated temperatures, forming chemical species rich in oxygen, which melt at a lower temperature and are more volatile. To our knowledge this campaign is a first attempt to quantitatively determine the effect of O/M on the melting temperature of MOX.
3. Melting behavior of mixed U–Pu oxides under oxidizing conditions
Energy Technology Data Exchange (ETDEWEB)
Strach, Michal [CEA, DEN, DTEC, SECA, LCC, Cadarache F-13108, Saint-Paul-Lez-Durance (France); IM2NP, UMR CNRS 7334 – Aix Marseille University, Case 251, Avenue Escadrille Normandie Niemen, 13397 Marseille Cedex 20 (France); Manara, Dario [European Commission, Joint Research Centre, Institute for Transuranium Elements, P.O. Box 2340, 76125 Karlsruhe (Germany); Belin, Renaud C. [CEA, DEN, DTEC, SECA, LCC, Cadarache F-13108, Saint-Paul-Lez-Durance (France); Rogez, Jacques [IM2NP, UMR CNRS 7334 – Aix Marseille University, Case 251, Avenue Escadrille Normandie Niemen, 13397 Marseille Cedex 20 (France)
2016-05-01
In order to use mixed U–Pu oxide ceramics in present and future nuclear reactors, their physical and chemical properties need to be well determined. The behavior of stoichiometric (U,Pu)O{sub 2} compounds is relatively well understood, but the effects of oxygen stoichiometry on the fuel performance and stability are often still obscure. In the present work, a series of laser melting experiments were carried out to determine the impact of an oxidizing atmosphere, and in consequence the departure from a stoichiometric composition on the melting behavior of six mixed uranium plutonium oxides with Pu content ranging from 14 to 62 wt%. The starting materials were disks cut from sintered stoichiometric pellets. For each composition we have performed two laser melting experiments in pressurized air, each consisting of four shots of different duration and intensity. During the experiments we recorded the temperature at the surface of the sample with a pyrometer. Phase transitions were qualitatively identified with the help of a reflected blue laser. The observed phase transitions occur at a systematically lower temperature, the lower the Pu content of the studied sample. It is consistent with the fact that uranium dioxide is easily oxidized at elevated temperatures, forming chemical species rich in oxygen, which melt at a lower temperature and are more volatile. To our knowledge this campaign is a first attempt to quantitatively determine the effect of O/M on the melting temperature of MOX.
4. Energy-Efficient Glass Melting: Submerged Combustion
Energy Technology Data Exchange (ETDEWEB)
None
2004-01-01
Oxy-gas-fired submerged combustion melter offers simpler, improved performance. For the last 100 years, the domestic glass industry has used the same basic equipment for melting glass on an industrial scale.
5. Principle of Melt-glue Cloth
Institute of Scientific and Technical Information of China (English)
陈人豪; 曹建达; 李济群; 张利梅; 何洋
2003-01-01
This paper advances a new concept of textile-meltglue cloth, and introduces the readers to the basic principle of melt-glue cloth. On the basis of melt spinning, the spinneret can be replaced by a spinning device that consists of an outer spinneret (a loop)and an inner spinneret ( a round plate), and between them there is an interval circle on which the centers of the holes are evenly distributed. When the machine is running, the outer spinneret (or the inner one) is fixed, the inner spinneret (or the outer one)is spinning, and a columnar net will be obtained.Then it will be excided with the help of a cutter in transporting it. Finally the once-forming melt-glue cloth will be produced. Compared with the traditional woven fabric, melt-glue cloth has a lot of special features and a bright future of application.
6. Energy Saving Melting and Revert Reduction Technology (E-SMARRT): Melting Efficiency Improvement
Energy Technology Data Exchange (ETDEWEB)
Principal Investigator Kent Peaslee; Co-PIÃÂâÃÂÃÂÃÂÃÂs: Von Richards, Jeffrey Smith
2012-07-31
Steel foundries melt recycled scrap in electric furnaces and typically consume 35-100% excess energy from the theoretical energy requirement required to pour metal castings. This excess melting energy is multiplied by yield losses during casting and finishing operations resulting in the embodied energy in a cast product typically being three to six times the theoretical energy requirement. The purpose of this research project was to study steel foundry melting operations to understand energy use and requirements for casting operations, define variations in energy consumption, determine technologies and practices that are successful in reducing melting energy and develop new melting techniques and tools to improve the energy efficiency of melting in steel foundry operations.
7. Melt Dispersion and Direct Containment Heating (DCH) Experiments für KONVOI reactors (KIT Scientific Reports ; 7567)
OpenAIRE
Meyer, Leonhard
2010-01-01
The DISCO-H test facility was used to perform scaled experiments that simulate melt ejection scenarios under low system pressure in Severe Accidents in Pressurized Water Reactors (PWR). These experiments are designed to investigate the fluid-dynamic, thermal and chemical processes during melt ejection out of a breach in the lower head of a PWR pressure vessel at pressures around and below 2 MPa with an iron-alumina melt and steam. The report presents results from a test series with the geomet...
8. Terrestrial analogues for lunar impact melt flows
Science.gov (United States)
Neish, C. D.; Hamilton, C. W.; Hughes, S. S.; Nawotniak, S. Kobs; Garry, W. B.; Skok, J. R.; Elphic, R. C.; Schaefer, E.; Carter, L. M.; Bandfield, J. L.; Osinski, G. R.; Lim, D.; Heldmann, J. L.
2017-01-01
Lunar impact melt deposits have unique physical properties. They have among the highest observed radar returns at S-Band (12.6 cm wavelength), implying that they are rough at the decimeter scale. However, they are also observed in high-resolution optical imagery to be quite smooth at the meter scale. These characteristics distinguish them from well-studied terrestrial analogues, such as Hawaiian pāhoehoe and ´a´ā lava flows. The morphology of impact melt deposits can be related to their emplacement conditions, so understanding the origin of these unique surface properties will help to inform us as to the circumstances under which they were formed. In this work, we seek to find a terrestrial analogue for well-preserved lunar impact melt flows by examining fresh lava flows on Earth. We compare the radar return and high-resolution topographic variations of impact melt flows to terrestrial lava flows with a range of surface textures. The lava flows examined in this work range from smooth Hawaiian pāhoehoe to transitional basaltic flows at Craters of the Moon (COTM) National Monument and Preserve in Idaho to rubbly and spiny pāhoehoe-like flows at the recent eruption at Holuhraun in Iceland. The physical properties of lunar impact melt flows appear to differ from those of all the terrestrial lava flows studied in this work. This may be due to (a) differences in post-emplacement modification processes or (b) fundamental differences in the surface texture of the melt flows due to the melts' unique emplacement and/or cooling environment. Information about the surface properties of lunar impact melt deposits will be critical for future landed missions that wish to sample these materials.
9. Electrochemical Studies in Aluminum Chloride Melts
Science.gov (United States)
1976-07-31
Molten Salt Systems", Symposium on Molten Salts, Symposium Volume, The Electrochemical Society , in press (1976). Manuscripts in Preparation--Related to...Fused Salt Technology, Electrochemical Society Meeting, Chicaao, May 8-13, 1973. R. A. Osteryoung, R. H. Abel, L. G. Boxall and B. H. Vassos, "An...aluminate Melts", Electrochemical Society , San Francisco, CA, May, 1974. R. A. Osteryoung, "Chemistry in Aluminum Chloride Melts", Fifth International
10. The melting and solidification of nanowires
Science.gov (United States)
Florio, B. J.; Myers, T. G.
2016-06-01
A mathematical model is developed to describe the melting of nanowires. The first section of the paper deals with a standard theoretical situation, where the wire melts due to a fixed boundary temperature. This analysis allows us to compare with existing results for the phase change of nanospheres. The equivalent solidification problem is also examined. This shows that solidification is a faster process than melting; this is because the energy transfer occurs primarily through the solid rather than the liquid which is a poorer conductor of heat. This effect competes with the energy required to create new solid surface which acts to slow down the process, but overall conduction dominates. In the second section, we consider a more physically realistic boundary condition, where the phase change occurs due to a heat flux from surrounding material. This removes the singularity in initial melt velocity predicted in previous models of nanoparticle melting. It is shown that even with the highest possible flux the melting time is significantly slower than with a fixed boundary temperature condition.
11. Melting behavior of large disordered sodium clusters
CERN Document Server
2000-01-01
The melting-like transition in disordered sodium clusters Na_N, with N=92 and 142 is studied by using a first-principles constant-energy molecular dynamics simulation method. Na_142, whose atoms are distributed in two (surface and inner) main shells with different radial distances to the center of mass of the cluster, melts in two steps: the first one, at approx. 130 K, is characterized by a high intrashell mobility of the atoms, and the second, homogeneous melting, at approx. 270 K, involves diffusive motion of all the atoms across the whole cluster volume (both intrashell and intershell displacements are allowed). On the contrary, the melting of Na_92 proceeds gradually over a very wide temperature interval, without any abrupt step visible in the thermal or structural melting indicators. The occurrence of well defined steps in the melting transition is then shown to be related to the existence of a distribution of the atoms in shells. Thereby we propose a necessary condition for a cluster to be considered r...
12. Manufacturing laser glass by continuous melting
Energy Technology Data Exchange (ETDEWEB)
Campbell, J H; Suratwala, T; krenitsky, S; Takeuchi, K
2000-07-01
A novel, continuous melting process is being used to manufacture meter-sized plates of laser glass at a rate 20-times faster, 5-times cheaper, and with 2-3 times better optical quality than with previous one-at-a-time, ''discontinuous'' technology processes. This new technology for manufacturing laser glass, which is arguably the most difficult continuously-melted optical material ever produced, comes as a result of a $60 million, six-year joint R&D program between government and industry. The glasses manufactured by the new continuous melting process are Nd-doped phosphate-based glasses and are marketed under the product names LG-770 (Schott Glass Technologies) and LHG-8 (Hoya Corporation USA). With this advance in glass manufacturing technology, it is now possible to construct high-energy, high-peak-power lasers for use in fusion energy development, national defense, and basic physics research that would have been impractical to build using the old melting technology. The development of continuously melted laser glass required technological advances that have lead to improvements in the manufacture of other optical glass products as well. For example, advances in forming, annealing, and conditioning steps of the laser glass continuous melting process are now being used in manufacture of other large-size optical glasses. 13. Si- and alkali-rich melt inclusions in minerals of mantle peridotites from eastern China: Implication for lithospheric evolution Institute of Scientific and Technical Information of China (English) FAN; Qicheng; SUI; Jianli; XU; Ping; LI; Ni; SUN; Qian; WANG; Tuanhua 2006-01-01 Minerals of spinel- and garnet-facies mantle xenoliths entrained in Cenozoic basalts from eastern China (North China, Northeastern China and Southeastern China coastal area) contains lots of melt inclusions. Studies on these melt inclusions show that the glass inclusions are rich in SiO2 (60%―68%) and alkalis (K2O+Na2O＝5%―11%, especially for K2O) as well as volatiles such as H2O and CO2 (2%―7%), which belong to dacites and andesites of the high-K calcic alkali series rocks with few shoshonites. High Al and Ca diopside in melt inclusion is the product of melt crystallization at high temperature and pressure, rather than the product of devitrification. Results show that these K-rich (in general K2O>3%) intermediate-acidic silicate melt inclusions have characteristics of continent without a genetical link to host basalts and their phenocrystic minerals. Thus, these trapped melt inclusions represent melts of Mesozoic lithospheric mantle-crust interaction and imply that the continental lithospheric mantle beneath eastern China had undergone fragmentation and recreation processes during the Mesozoic and Cenozoic periods. This result undoubtly provides important implication for the evolution of sub-continental lithosphere beneath eastern China. We propose that these Si- and alkalis-rich melts should be responsible for the mantle chemical heterogeneity underneath eastern China. 14. Target-projectile interaction during impact melting at Kamil Crater, Egypt Science.gov (United States) Fazio, Agnese; D'Orazio, Massimo; Cordier, Carole; Folco, Luigi 2016-05-01 In small meteorite impacts, the projectile may survive through fragmentation; in addition, it may melt, and chemically and physically interact with both shocked and melted target rocks. However, the mixing/mingling between projectile and target melts is a process still not completely understood. Kamil Crater (45 m in diameter; Egypt), generated by the hypervelocity impact of the Gebel Kamil Ni-rich ataxite on sandstone target, allows to study the target-projectile interaction in a simple and fresh geological setting. We conducted a petrographic and geochemical study of macroscopic impact melt lapilli and bombs ejected from the crater, which were collected during our geophysical campaign in February 2010. Two types of glasses constitute the impact melt lapilli and bombs: a white glass and a dark glass. The white glass is mostly made of SiO2 and it is devoid of inclusions. Its negligible Ni and Co contents suggest derivation from the target rocks without interaction with the projectile (<0.1 wt% of projectile contamination). The dark glass is a silicate melt with variable contents of Al2O3 (0.84-18.7 wt%), FeOT (1.83-61.5 wt%), and NiO (<0.01-10.2 wt%). The dark glass typically includes fragments (from few μm to several mm in size) of shocked sandstone, diaplectic glass, lechatelierite, and Ni-Fe metal blebs. The metal blebs are enriched in Ni compared to the Gebel Kamil meteorite. The dark glass is thus a mixture of target and projectile melts (11-12 wt% of projectile contamination). Based on recently proposed models for target-projectile interaction and for impact glass formation, we suggest a scenario for the glass formation at Kamil. During the transition from the contact and compression stage and the excavation stage, projectile and target liquids formed at their interface and chemically interact in a restricted zone. Projectile contamination affected only a shallow portion of the target rocks. The SiO2 melt that eventually solidified as white glass behaved as 15. Recent changes in Arctic sea ice melt onset, freezeup, and melt season length Science.gov (United States) Markus, Thorsten; Stroeve, Julienne C.; Miller, Jeffrey 2009-12-01 In order to explore changes and trends in the timing of Arctic sea ice melt onset and freezeup, and therefore melt season length, we developed a method that obtains this information directly from satellite passive microwave data, creating a consistent data set from 1979 through present. We furthermore distinguish between early melt (the first day of the year when melt is detected) and the first day of continuous melt. A similar distinction is made for the freezeup. Using this method we analyze trends in melt onset and freezeup for 10 different Arctic regions. In all regions except for the Sea of Okhotsk, which shows a very slight and statistically insignificant positive trend (0.4 d decade-1), trends in melt onset are negative, i.e., toward earlier melt. The trends range from -1.0 d decade-1 for the Bering Sea to -7.3 d decade-1 for the East Greenland Sea. Except for the Sea of Okhotsk all areas also show a trend toward later autumn freeze onset. The Chukchi/Beaufort seas and Laptev/East Siberian seas observe the strongest trends with 7 d decade-1. For the entire Arctic, the melt season length has increased by about 20 days over the last 30 years. Largest trends of over 10 d decade-1 are seen for Hudson Bay, the East Greenland Sea, the Laptev/East Siberian seas, and the Chukchi/Beaufort seas. Those trends are statistically significant at the 99% level. 16. Melt-intercalation studies of polystyrene ionomers in pristine montmorillonite Science.gov (United States) Bhiwankar, Nikhil N. The main objective of this study was to examine the use of ionomers, specifically alkylamine-neutralized sulfonated polystyrene (SPS) for promoting intercalation into unmodified sodium montmorillonite clay and its use as a compatabilizer for intercalating another polymer into unmodified silicate clay. The processing parameters and chemical structure of polymers which led to the formation of partially intercalated/exfoliated morphologies were investigated. Melt-intercalated polymer layered silicate nanocomposites (PLSNs) are made by mixing polymers and organically modified silicates by the application of shear forces. However, the thermal decomposition temperatures of the organic modifications are usually comparable to the processing temperatures of most of the polymers. Hence, in this work modification of the polymer, rather than the clay, for promoting melt intercalation, specifically the introduction of alkyl ammonium salt groups along the polymer chain was considered. In this study the effects of viscosity, shear rates and mixing times on the morphology of nanocomposites were investigated. The effect of ionic content in the polymer chain of SPS in the batch mixtures of SPS and PS was researched. We also compared the effect on the extent of intercalation in these silicate clay galleries as a function of size of the counter-ions by varying the alkyl chain length and as a function of basicity of these counter-ions by varying the number of alkyl substituents that are attached on the N of the amine. The melt mixing of pristine Na-Mmt with alkyl ammonium and quaternary ammonium salts of SPS ionomers, resulted in an increase in the silicate gallery spacing consistent with intercalation. Mixtures of the ionomer with PS exhibited similar gallery spacing increases, indicating that the ionomer is an effective compatibilizing agent for the melt-intercalation of hydrophobic polymers into the clay. The extent of intercalation was independent of the melt processing conditions 17. A melt inclusion study of the Sudbury Igneous Complex (Ontario, Canada): preliminary results Science.gov (United States) Watts, Kathleen; Hanley, Jacob; Kontak, Daniel; Ames, Doreen 2013-04-01 The 1.85 Ga Sudbury Igneous Complex (SIC), Ontario, Canada, is an intrusive complex representing the crystallized melt sheet that formed within a large impact crater. The SIC has been extensively studied due to its rich endowment in magmatic sulfide ores (Ni-Cu-PGEs). The nature and origin of the SIC melt sheet and its subsequent evolution still remain controversial. In this study, analyses of primary melt inclusions hosted in cumulus apatite within three mafic units of the SIC (gabbro, norite and sublayer quartz diorite) are used to decipher the thermometric and chemical characteristics of the evolving melt sheet as it crystallized. Apatite-hosted melt inclusions commonly display a negative crystal shape, occur parallel to the c-axis, and often occur within a central growth zone, which suggest a primary origin. The compositions of coeval (co-entrapped) melt inclusions are distinct and may represent either the products of immiscibility (low or high temperature field; c.f. the Skaergaard Intrusion: Jakobsen et al., Geology, 2005), or a product of early, high-temperature, impact-generated emulsification (prior to and independent of crystallization of the melt sheet). The compositions of homogenized (1100-1200oC for 3 hrs) melt inclusions, determined by SEM-EDS and EMP analyses of opened, homogenized melt inclusions, equate to two distinct compositions: (1) Type-I are SiO2-rich, ranging from tonalitic to granodioritic in composition (60-70 wt% SiO2, up to 11 wt% FeO); and (2) Type-II are Fe-rich with syenogabbroic to essexitic to alkali gabbroic compositions (27-49 wt% SiO2, 16-44 wt% FeO). Trace element data, obtained by LA-ICPMS analyses of single inclusions and surrounding host apatite, are used to infer D values between apatite and the two melt types, and between the coexisting melt types. Apparent Dap-melt values for both Type-I and Type-II inclusions show that the REE, Sr, and Y are compatible in apatite, and As is weakly compatible or incompatible in apatite 18. SUMMARY OF 2010 DOE EM INTERNATIONAL PROGRAM STUDIES OF WASTE GLASS MELT RATE ENHANCEMENT Energy Technology Data Exchange (ETDEWEB) Fox, K.; Marra, J. 2011-01-19 A collaborative study has been established under the U.S. Department of Energy (DOE) Office of Environmental Management International Program between the Savannah River National Laboratory (SRNL) and the V. G. Khlopin Radium Institute (KRI) in St. Petersburg, Russia, to investigate potential improvements in melt rate via chemical additions to the glass frit. Researchers at KRI suggested a methodology for selecting frit additives based on empirical coefficients for optimization of glass melting available in the Russian literature. Using these coefficients, KRI identified B{sub 2}O{sub 3}, CuO, and MnO as frit additives that were likely to improve melt rate without having adverse effects on crystallization of the glass or its chemical durability. The results of the melt rate testing in the SMK melter showed that the slurry feed rate (used as a gauge of melt rate) could be significantly increased when MnO or CuO were added to Frit 550 with the SMR-2 sludge. The feed rates increased by about 27% when MnO was added to the frit and by about 26% when CuO was added to the frit, as compared to earlier results for Frit 550 alone. The impact of adding additional B{sub 2}O{sub 3} to the frit was minor when added with CuO. The additional B{sub 2}O{sub 3} showed a more significant, 39% improvement in melt rate when added with MnO. The additional B{sub 2}O{sub 3} also reduced the viscosity of the glasses during pouring. Samples of the glasses from the melt rate testing characterized at SRNL showed that there were no significant impacts on crystallization of the glasses. All of the glasses had very good chemical durability. Chemical composition measurements showed that the frit additives were present in concentrations below the targeted values in some of the glasses. Therefore, it is possible that higher concentrations of these additives may further improve melt rate, although the impacts of higher concentrations of these components on crystallization and durability would need to 19. Vacuum Arc Melting Processes for Biomedical Ni-Ti Shape Memory Alloy Directory of Open Access Journals (Sweden) Tsai De-Chang 2015-01-01 Full Text Available This study primarily involved using a vacuum arc remelting (VAR process to prepare a nitinol shape-memory alloy with distinct ratios of alloy components (nitinol: 54.5 wt% to 57 wt%. An advantage of using the VAR process is the adoption of a water-cooled copper crucible, which effectively prevents crucible pollution and impurity infiltration. Optimising the melting production process enables control of the alloy component and facilitates a uniformly mixed compound during subsequent processing. This study involved purifying nickel and titanium and examining the characteristics of nitinol alloy after alloy melt, including its microstructure, mechanical properties, phase transition temperature, and chemical components. 20. Patterns in new dimensionless quantities containing melting temperature, and their dependence on pressure Directory of Open Access Journals (Sweden) U. WALZER 1980-06-01 Full Text Available The relationships existing between melting temperature and other macroscopic physical quantities are investigated. A new dimensionless quantity Q(1 not containing the Grtineisen parameter proves to be suited for serving in future studies as a tool for the determination of the melting temperature in the outer core of the Earth. The pressure dependence of more general dimensionless quantities Q„ is determined analytically and, for the chemical elements, numerically, too. The patterns of various interesting dimensionless quantities are shown in the Periodic Table and compared. 1. Magnetic properties of ND Rich Melt-Spun ND-FE-B alloy Directory of Open Access Journals (Sweden) Grujić Aleksandar 2005-01-01 Full Text Available As a part of these experimental investigations of melt-spun Nd-Fe-B alloy with Nd rich content in relation to Nd2Fe14B prepared by rapid quenching process for optimally selected cooling rate and heat treatment, the influence of the chosen chemical composition on magnetic properties was observed. The results of X-ray diffraction, Mössbauer spectroscopy phase analysis and magnetic measurement of investigated melt-spun Nd14.5Fe78.5B7 alloy are presented to bring some new information concerning the relation between their structure and magnetic properties. 2. Ingredient Losses during Melting Binary Ni-Ti Shape Memory Alloys Institute of Scientific and Technical Information of China (English) S.K. Sadrnezhaad; S. Badakhshan Raz 2005-01-01 Losses of the alloying elements during vacuum induction melting of the binary NiTi alloys were evaluated by visual observation and chemical analysis of the NiTi melted specimens and the scalp formed on the internal surface of the crucible. The results indicated that the major sources of the losses were (a) evaporation of the metals, (b) formation of the NiTi scalp and (c) the sprinkling drops splashed out of the melt due to the exothermic reactions occurring between Ni and Ti to form the NiTi parent phase. Quantitative evaluations were made for the metallic losses by holding the molten alloy for 0.5, 3, 5, 10 and 15 min at around 100℃ above the melting point inside the crucible.Chemical analysis showed that there existed an optimum holding time of 3 min during which the alloying elements were only dropped to a predictable limit. Microstructure, chemical composition, shape memory and mechanical properties of the cast metal ingots were determined to indicate the appropriate achievements with the specified 3 min optimum holding time. 3. Integral coolant channels supply made by melt-out method Science.gov (United States) Escher, W. J. D. 1964-01-01 Melt-out method of constructing strong, pressure-tight fluid coolant channels for chambers is accomplished by cementing pins to the surface and by depositing a melt-out material on the surface followed by two layers of epoxy-resin impregnated glass fibers. The structure is heated to melt out the low-melting alloy. 4. Energy Saving Melting and Revert Reduction Technology: Melting Efficiency in Die Casting Operations Energy Technology Data Exchange (ETDEWEB) David Schwam 2012-12-15 This project addressed multiple aspects of the aluminum melting and handling in die casting operations, with the objective of increasing the energy efficiency while improving the quality of the molten metal. The efficiency of melting has always played an important role in the profitability of aluminum die casting operations. Consequently, die casters need to make careful choices in selecting and operating melting equipment and procedures. The capital cost of new melting equipment with higher efficiency can sometimes be recovered relatively fast when it replaces old melting equipment with lower efficiency. Upgrades designed to improve energy efficiency of existing equipment may be well justified. Energy efficiency is however not the only factor in optimizing melting operations. Melt losses and metal quality are also very important. Selection of melting equipment has to take into consideration the specific conditions at the die casting shop such as availability of floor space, average quantity of metal used as well as the ability to supply more metal during peaks in demand. In all these cases, it is essential to make informed decisions based on the best available data. 5. Comparative Study on Two Melting Simulation Methods: Melting Curve of Gold Science.gov (United States) Liu, Zhong-Li; Sun, Jun-Sheng; Li, Rui; Zhang, Xiu-Lu; Cai, Ling-Cang 2016-05-01 Melting simulation methods are of crucial importance to determining melting temperature of materials efficiently. A high-efficiency melting simulation method saves much simulation time and computational resources. To compare the efficiency of our newly developed shock melting (SM) method with that of the well-established two-phase (TP) method, we calculate the high-pressure melting curve of Au using the two methods based on the optimally selected interatomic potentials. Although we only use 640 atoms to determine the melting temperature of Au in the SM method, the resulting melting curve accords very well with the results from the TP method using much more atoms. Thus, this shows that a much smaller system size in SM method can still achieve a fully converged melting curve compared with the TP method, implying the robustness and efficiency of the SM method. Supported by the National Natural Science Foundation of China under Grant No. 41574076 and the NSAF of China under Grant No. U1230201/A06, and the Young Core Teacher Scheme of Henan Province under Grant No. 2014GGJS-108 6. Polyether Based Thermoplastic Polyurethane Melt Blown Nonwovens Directory of Open Access Journals (Sweden) Terezie Zapletalova 2006-08-01 Full Text Available A series of melt blown samples were produced from three hardness grades of ether based thermoplastic polyurethane elastomers (TPU. The fabrics were tested to investigate their structure-property relationship in a melt blown process. Solution viscosities of the web were only 20-26% of there original values indicating a large loss in polymer molecular weight during melt blowing. Fiber diameter distributions measured on melt blown samples were found comparable to those made with more conventional polymers. The fiber orientation distribution functions (ODF suggest slight fiber orientation in machine direction. Tensile and elongation properties depended on die-to-collector distance (DCD, polymer hardness and fiber ODF. A strong relationship between the tensile strength and die-to-collector distance was identified and attributed to reduced interfiber adhesion in the web with increasing DCD. The reduction in adhesion was attributed to greater extents of solidification before reaching the forming belt for longer DCDs. This paper is the first in a series relating the influence of the melt blowing process parameters on the polymer properties and the nonwoven fabric properties for block thermoplastic elastomers. 7. CRYSTALLIZATION AND MELTING OF NYLON 610 Institute of Scientific and Technical Information of China (English) 1998-01-01 Differential scanning calorimetry was used to study the crystallization and melting of nylon 610. For nylon 610 crystallized from the melt state (260℃), the overall rate of bulk crystallization can be described by a simple Avrami equation with Avrami exponent n≈2, independent of crystallization temperature. With the experimentally obtained Tm0 (235℃～255℃) of nylon 610, the fold surface free energy σe was determined to be 35～38 erg/cm2. The effects of annealing temperature and time on the melting of quenched nylon 610 were also investigated. For nylon 610 quenched at room temperature there is only one DSC endotherm peak DSC scans on annealed samples exhibited an endotherm peak at approximately 10℃ above the annealing temperature. The size and position of the endothermic peak is strongly related to annealing temperature and time. An additional third melting was observed when quenched nylon 610 was annealed at high temperature for a sufficiently long residence time. The existence of the third melting peak suggests that more than one kind of distribution of lamella thickness may occur when quenched nylon610 is annealed. The implications of these results in terms of crystal thickening mechanism were discussed. 8. Melting of the Earth's inner core. Science.gov (United States) Gubbins, David; Sreenivasan, Binod; Mound, Jon; Rost, Sebastian 2011-05-19 The Earth's magnetic field is generated by a dynamo in the liquid iron core, which convects in response to cooling of the overlying rocky mantle. The core freezes from the innermost surface outward, growing the solid inner core and releasing light elements that drive compositional convection. Mantle convection extracts heat from the core at a rate that has enormous lateral variations. Here we use geodynamo simulations to show that these variations are transferred to the inner-core boundary and can be large enough to cause heat to flow into the inner core. If this were to occur in the Earth, it would cause localized melting. Melting releases heavy liquid that could form the variable-composition layer suggested by an anomaly in seismic velocity in the 150 kilometres immediately above the inner-core boundary. This provides a very simple explanation of the existence of this layer, which otherwise requires additional assumptions such as locking of the inner core to the mantle, translation from its geopotential centre or convection with temperature equal to the solidus but with composition varying from the outer to the inner core. The predominantly narrow downwellings associated with freezing and broad upwellings associated with melting mean that the area of melting could be quite large despite the average dominance of freezing necessary to keep the dynamo going. Localized melting and freezing also provides a strong mechanism for creating seismic anomalies in the inner core itself, much stronger than the effects of variations in heat flow so far considered. 9. Origin of impact melt rocks in the Bununu howardite Science.gov (United States) Klein, L. C.; Hewins, R. H. 1979-01-01 The Bununu howardite is a polymict regolith breccia which contains impact melt that is largely restricted to a 1-cm thick intrusion containing residual glass. As in Malvern, the melt rock contains melt with meteoritic Ni-Co contents. The cooling rate, interpreted for forming glass from this composition, is a few tenths of a degree per minute. The intrusive melts rock, which is a feature unique to Bununu, may indicate that Bununu was consolidated at the time of impact melting. 10. Studies on Hot-Melt Prepregging of PMR-II-50 Polyimide Resin with Graphite Fibers Science.gov (United States) Shin, E. Eugene; Sutter, James K.; Juhas, John; Veverka, Adrienne; Klans, Ojars; Inghram, Linda; Scheiman, Dan; Papadopoulos, Demetrios; Zoha, John; Bubnick, Jim 2003-01-01 A Second generation PMR (in situ Polymerization of Monomer Reactants) polyimide resin, PMR-II-50, has been considered for high temperature and high stiffness space propulsion composites applications for its improved high temperature performance. As part of composite processing optimization, two commercial prepregging methods: solution vs. hot-melt processes were investigated with M40J fabrics from Toray. In a previous study a systematic chemical, physical, thermal and mechanical characterization of these composites indicated that poor resin-fiber interfacial wetting, especially for the hot-melt process, resulted in poor composite quality. In order to improve the interfacial wetting, optimization of the resin viscosity and process variables were attempted in a commercial hot-melt prepregging line. In addition to presenting the results from the prepreg quality optimization trials, the combined effects of the prepregging method and two different composite cure methods, i.e., hot press vs. autoclave on composite quality and properties are discussed. 11. On the Mechanism of Ultrasound-Driven Deagglomeration of Nanoparticle Agglomerates in Aluminum Melt Science.gov (United States) Kudryashova, Olga; Vorozhtsov, Sergey 2016-05-01 One of the promising directions in the technology of composite alloys with improved mechanical properties is reinforcement of the metallic matrix with nanopowders introduced in the liquid metal. Ultrasonic processing is known to significantly improve the introduction of submicrone particles to the metallic melt. This study focuses on the mechanisms of deagglomeration and wettability of such particles by the melt under the action of ultrasound. The suggested mechanism involves the penetration of the liquid metal into the pores and cracks of the agglomerates under the excess pressure created by imploding cavitation bubbles and further destruction of the agglomerate by the sound wave. The main dependences connecting the acoustic parameters and processing time with the physical and chemical properties of particles and the melt are obtained through analytical modeling. The mathematical description of the ultrasonic deagglomeration in liquid metal is presented; a dependence of the threshold intensity of ultrasound for the break-up of agglomerates on their size is reported. 12. Studies on Hot-Melt Prepregging on PRM-II-50 Polyimide Resin with Graphite Fibers Science.gov (United States) Shin, E. Eugene; Sutter, James K.; Juhas, John; Veverka, Adrienne; Klans, Ojars; Inghram, Linda; Scheiman, Dan; Papadopoulos, Demetrios; Zoha, John; Bubnick, Jim 2004-01-01 A second generation PMR (in situ Polymerization of Monomer Reactants) polyimide resin PMR-II-50, has been considered for high temperature and high stiffness space propulsion composites applications for its improved high temperature performance. As part of composite processing optimization, two commercial prepregging methods: solution vs. hot-melt processes were investigated with M40J fabrics from Toray. In a previous study a systematic chemical, physical, thermal and mechanical characterization of these composites indicated the poor resin-fiber interfacial wetting, especially for the hot-melt process, resulted in poor composite quality. In order to improve the interfacial wetting, optimization of the resin viscosity and process variables were attempted in a commercial hot-melt prepregging line. In addition to presenting the results from the prepreg quality optimization trials, the combined effects of the prepregging method and two different composite cure methods, i.e. hot press vs. autoclave on composite quality and properties are discussed. 13. Noble metal nanoclusters and nanoparticles precede mineral formation in magmatic sulphide melts. Science.gov (United States) Helmy, Hassan M; Ballhaus, Chris; Fonseca, Raúl O C; Wirth, Richard; Nagel, Thorsten; Tredoux, Marian 2013-01-01 In low temperature aqueous solutions, it has long been recognized by in situ experiments that many minerals are preceded by crystalline nanometre-sized particles and non-crystalline nanophases. For magmatic systems, nanometre-sized precursors have not yet been demonstrated to exist, although the suggestion has been around for some time. Here we demonstrate by high temperature quench experiments that platinum and arsenic self-organize to nanoparticles, well before the melt has reached a Pt-As concentration at which discrete Pt arsenide minerals become stable phases. If all highly siderophile elements associate to nanophases in undersaturated melts, the distribution of the noble metals between silicate, sulphide and metal melts will be controlled by the surface properties of nano-associations, more so than by the chemical properties of the elements. 14. Study on melting conditions of radioactive miscellaneous solid waste. Contract research Energy Technology Data Exchange (ETDEWEB) Fukui, Toshiki; Nakashio, Nobuyuki; Isobe, Motoyasu; Otake, Atsushi; Wakui, Takuji; Nakashima, Mikio [Department of Decommissioning and Waste Management, Tokai Research Establishment, Japan Atomic Energy Research Institute, Tokai, Ibaraki (Japan); Hirabayashi, Takakuni [Radiation Application Develpment Association, Tokai, Ibaraki (Japan) 2001-02-01 Improvement of fluidity of molten slag is one of the most important factors for plasma melting treatment of low level radioactive miscellaneous wastes generated from nuclear facilities. In general, it is considered that elevating molten slag temperature of addition of flux is of certain use in improvement of fluidity of molten slag. However, these ways are not necessarily suitable from the viewpoints of refractory erosion or reduction of waste volume. In this report, we suggested that fluidity of molten slag could be improved by controlling chemical compositions of molten slag. On the Basic of the investigation using phase diagram and viscosity data, FeO was selected as a key component for improving fluidity: Viscosity and melting point of molten slag decreased with increasing relative concentration of FeO in molten slag. Accordingly, we concluded that it is important to adjust basicity of molten slag for melting treatment of low-level radioactive miscellaneous solid wastes. (author) 15. Microstructure, texture, and mechanical properties of electron-beam melted Ti-6Al-4V Energy Technology Data Exchange (ETDEWEB) Kalinyuk, A.N.; Trigub, N.P.; Zamkov, V.N.; Ivasishin, O.M.; Markovsky, P.E.; Teliovich, R.V.; Semiatin, S.L 2003-04-15 The chemical homogeneity, microstructure, texture, and mechanical properties of Ti-6Al-4V ingots synthesized via electron-beam melting were established. Despite large aluminum losses during melting, very uniform compositions well within the specification for the alloy were obtained in both 200- and 400-mm diameter ingots. The local conditions of melting and solidification produced essentially texture-free as-cast material with a largely equiaxed beta grain structure. Following hot working via rolling at various temperatures, a wide range of microstructures and textures similar to those found in conventionally-processed Ti-6Al-4V was obtained. The resulting mechanical properties were comparable to or better than those found in Ti-6Al-4V synthesized via vacuum arc remelting. 16. On the occurrence and implications of Jurassic primary continental boninite-like melts in the Zagros orogen Science.gov (United States) Esna-Ashari, A.; Tiepolo, M.; Hassanzadeh, J. 2016-08-01 Ultramafic rocks, ranging from pyroxenites to hornblendites, are associated with granitoids of the Aligoodarz intrusive complex in the central Sanandaj-Sirjan Zone, representing the Mesozoic continental arc segment of the Zagros orogen. As inferred from the ultramafic whole rock composition and the most primitive clinopyroxene composition in pyroxenites, the geochemical signature of primary melt is significantly different from that of the continental arc basalts. In particular, primary melt is characterized by extremely low concentrations of incompatible elements and high concentrations of Mg and refractory elements typical of boninites. Amphibole is a late crystallizing mineral in these rocks and is in textural and chemical disequilibrium with olivine + orthopyroxene + clinopyroxene. Amphibole crystallized from a liquid underwent differentiation through a process of melt-rock reaction. In particular, early differentiated boninitic cumulates reacted with later melts with a strong crustal signature similar to Aligoodarz granodiorite. Usbnd Pb zircon geochronology from ultramafic rocks and surrounding quartz-diorite yield similar ages and indicate that they are coeval with Aligoodarz granitoids (ca. 165-170 Ma). However, the occurrence of a marked negative Eu anomaly in zircon from the ultramafic rocks, which is absent in the boninitic primary melt, indicates that zircons crystallized from the infiltrating melt and in turn date the timing of melt infiltration. The interaction between ultramafic cumulates and infiltrated melt has generated a new liquid compositionally similar to high-Mg andesites and to the quartz-diorites hosting the ultramafic cumulates. The scenario that better account for the genesis of boninitic melts in the Sanandaj-Sirjan Zone is partial melting of a depleted mantle wedge in response to the onset of NeoTethys subduction. According to this hypothesis, middle Jurassic calc-alkaline magmatism in the Sanandaj-Sirjan Zone represents the mature stage 17. Melting Processes and Mantle Heterogeneity Recorded by Individual Phases from Mid-Ocean Ridge Basalts Science.gov (United States) Burton, K. W.; Parkinson, I. J. 2014-12-01 Isotope and elemental studies of mantle rocks and oceanic basalts demonstrate that Earth's mantle is heterogeneous, comprising distinct components that have experienced isolated long-term evolution, on both global and local scales. In principle, such heterogeneity will control the onset of melting and at least some of the chemical variation seen in Mid-Ocean Ridge Basalts (MORB) (e.g. [1]). But, the high degrees of melting that generate MORB, together with magma mixing and assimilation, have the effect of homogenising the compositions of lavas erupted at the surface, concealing the true extent of the variability in the mantle source. This study presents high-precision double-spike Pb isotope data for the consituent phases of MORB from a single ridge segment from the FAMOUS region (36°50'N) on the Mid-Atlantic ridge. Separated phases from individual basalts show a remarkable variation in Pb isotope composition, greater than that seen for all samples previously analysed from this ridge segment, and encompassing >70% of the variation seeen globally in MORB. These variations cannot be explained by assimilation of seawater altered oceanic crust or by contamination from the Azores, both of which carry a radiogenic Pb isotope siganture. Rather they indicate mixing between an early extremely unradiogenic melt, from which plagioclase, clinopyroxene and sulphide crystallised, sourced by material showing long-term depletion of U, and a later more radiogenic melt that produced the final glass host. Elemental and isotope data suggest that the source of this early melt was ancient, enriched, with a crust-like chemical signature, producing a relatively volatile-rich melt. This study confirms that signficant information may be preserved in the early crystallising minerals at slow spreading ridges, either phenocryst phases or the melt inclusions that they host (e.g. [2]). Overall, these results suggest that there is a simple relationship between the scale and nature of mantle 18. Chemical Emergencies Science.gov (United States) When a hazardous chemical has been released, it may harm people's health. Chemical releases can be unintentional, as in the case of an ... the case of a terrorist attack with a chemical weapon. Some hazardous chemicals have been developed by ... 19. Melting and Reactive Flow of Carbonated Peridotite Beneath Mid-Ocean Ridges Science.gov (United States) Keller, T.; Katz, R. F. 2015-12-01 The mantle carbon reservoir is four orders of magnitude more massive than that of the atmosphere and ocean combined. The behaviour of carbon in the mantle, especially its transport and extraction, is thus of crucial importance to understanding the coupling between the deep interior and the surface environment of Earth. Laboratory experiments indicate that even small concentrations of carbon dioxide (and other volatiles like H2O) in the upper mantle significantly affect silicate melting [HK96,DH06] by stabilising carbon-rich melt at high pressure. The presence of carbon in the mantle substantially extends the region where partial melt is stable and has important consequences for the dynamics of magma transport and chemical differentiation [H10,DH10]. We have developed theory and numerical implementation to simulate thermo-chemically coupled magma/mantle dynamics in terms of a two-phase (rock+melt), three component (dunite+MORB+carbonated MORB) physical model. The fluid dynamics is based on McKenzie's equations [McK84]. The thermo-chemical formulation of the system is represented by a novel, disequilibrium, multi-component melting model based on thermodynamic theory [RBS11]. This physical model is implemented as a parallel, two-dimensional, finite-volume code that leverages tools from the PETSc toolkit. First results show that carbon and other volatiles cause a qualitative difference to the style of melt transport, potentially enhancing its extraction efficiency - measured in the carbon mass flux arriving at the mid-ocean ridge axis - by at least an order of magnitude. The process that controls magma transport in our models is a volatile flux-induced reactive infiltration instability, causing carbonated melt to rise from depth in localized channels. These results add to our understanding of melt formation and transport at mid-ocean ridges (the most important magmatic system in the mantle) and may have important implications for subduction zones. REFERENCESHK96 Hirth 20. A model for melting of confined DNA CERN Document Server Werner, E; Ambjörnsson, T; Mehlig, B 2015-01-01 When DNA molecules are heated they denature. This occurs locally so that loops of molten single DNA strands form, connected by intact double-stranded DNA pieces. The properties of this "melting" transition have been intensively investigated. Recently there has been a surge of interest in this question, caused by experiments determining the properties of partially bound DNA confined to nanochannels. But how does such confinement affect the melting transition? To answer this question we introduce, and solve a model predicting how confinement affects the melting transition for a simple model system by first disregarding the effect of self-avoidance. We find that the transition is smoother for narrower channels. By means of Monte-Carlo simulations we then show that a model incorporating self-avoidance shows qualitatively the same behaviour and that the effect of confinement is stronger than in the ideal case. 1. Analysis of Picosecond Pulsed Laser Melted Graphite Science.gov (United States) Steinbeck, J.; Braunstein, G.; Speck, J.; Dresselhaus, M. S.; Huang, C. Y.; Malvezzi, A. M.; Bloembergen, N. 1986-12-01 A Raman microprobe and high resolution TEM have been used to analyze the resolidified region of liquid carbon generated by picosecond pulse laser radiation. From the relative intensities of the zone center Raman-allowed mode for graphite at 1582 cm{sup -1} and the disorder-induced mode at 1360 cm{sup -1}, the average graphite crystallite size in the resolidified region is determined as a function of position. By comparison with Rutherford backscattering spectra and Raman spectra from nanosecond pulsed laser melting experiments, the disorder depth for picosecond pulsed laser melted graphite is determined as a function of irradiating energy density. Comparisons of TEM micrographs for nanosecond and picosecond pulsed laser melting experiments show that the structure of the laser disordered regions in graphite are similar and exhibit similar behavior with increasing laser pulse fluence. 2. Scleral melt following Retisert intravitreal fluocinolone implant Directory of Open Access Journals (Sweden) Georgalas I 2014-11-01 Full Text Available Ilias Georgalas,1 Chrysanthi Koutsandrea,1 Dimitrios Papaconstantinou,1 Dimitrios Mpouritis,1 Petros Petrou1,2 1Ophthalmology Department, University of Athens, Athens, Greece; 2Moorfields Eye Hospital, London, UKAbstract: Intravitreal fluocinolone acetonide implant (Retisert has a high potency, a low solubility, and a very short duration of action in the systemic circulation, enabling the steroid pellet to be small and reducing the risk of systemic side effects. Scleral melt has not been reported as a possible complication of Retisert implant. The authors describe the occurrence of scleral melt 18 months after the implantation of fluocinolone acetonide implant in a 42-year-old Caucasian woman. To the authors’ knowledge, this is the first report of this possible complication.Keywords: Retisert, scleral melt, complication, surgical management 3. First Kinetic Reactive-Flow and Melting Calculations for Entropy Budget and Major Elements in Heterogeneous Mantle Lithologies (Invited) Science.gov (United States) Asimow, P. D. 2009-12-01 The consequences of source heterogeneity and reactive flow during melt transport in the mantle can be classified by scale. At the smallest spatial and longest temporal scales, we can assume complete equilibrium and use batch melting of homogenized sources or equilibrium porous flow treatments. At large enough spatial scale or short enough temporal scale to prevent any thermal or chemical interaction between heterogeneities or between melt and matrix, we can assume perfectly fractional melting and transport and apply simple melt-mixing calculations. At a somewhat smaller spatial or longer temporal scale, thermal but not chemical interactions are significant and various lithologies and channel/matrix systems must follow common pressure-temperature paths, with energy flows between them. All these cases are tractable to model with current tools, whether we are interested in the energy budget, major elements, trace elements, or isotopes. There remains, however, the very important range of scales where none of these simple theories applies because of partial chemical interaction among lithologies or along the flow path. Such disequilibrium or kinetic cases have only been modeled, in the case of mantle minerals and melts, for trace elements and isotopes, with fixed melting rates instead of complete energy budgets. In order to interpret volumes of magma production and major element basalt and residue compositions that might emerge from a heterogeneous mantle in this last range of scales, we must develop tools that can combine a kinetic formulation with a major element and energy-constrained thermodynamic calculation. The kinetics can be handled either with a chemical kinetic approach with rate constants for various net transfer and exchange reactions, or with a physical diffusion-limited approach. A physical diffusion-limited approach can be built with the following elements. At grain scale, spherical grains of an arbitrary number of solid phases can evolve zoning profiles 4. Water content variability in Ignimbrite Campana melts. New insights on magma chamber history Science.gov (United States) Marianelli, P.; Proto, M.; Sbrana, A. 2003-04-01 The Ignimbrite Campana (39 ka) represents the most powerful eruption characterizing the volcanic history of the Campi Flegrei caldera. The study is based on melt inclusions investigations in phenocrysts of juvenile pumice from the fallout unit and from the Breccia Museo Unit. The aim of this work is the determination of both the chemical composition and the pre-eruptive volatile content of Ignimbrite Campana magmas. Glass compositions fall in the trachyte field close to the trachyte-phonolite boundary, similarly to the others Ignimbrite Campana products. FTIR analyses on double-polished melt inclusions were carried out in order to investigate H_2O and CO_2 contents. CO_2 was below detection limit. Melt inclusions from Breccia Museo products and from the fallout layer show a very large range of H_2O contents with a mode of 2--4wt% and higher values of about 5--6%wt%. The variability of water content is independent of the evolutive degree of the melt (CaO=2.5--1.5wt%), and therefore cannot be ascribed to differentiation processes. Minimum pressures of crystallization are estimated assuming saturation conditions for the trapped melts and using the H_2O solubility model of Carroll and Blank (1997). Most of crystallization pressures are in the range 20--60 MPa, whereas a few values are between 100 and 150 MPa. We suggest that the higher values could indicate the pressure of crystallization in a magma chamber, located at a depth of about 4.5--6 Km. The abundance of melt inclusions with lower water content could testify an abrupt change in pre-eruptive conditions of the Ignimbrite Campana magma chamber, such as degassing due to magma rising or opening and decompression of the magma chamber. References Carroll M.R. and Blank J.G. (1997): The solubility of H_2O in phonolitic melts. American Mineralogist, 82: 549--556. 5. How to identify garnet lherzolite melts and distinguish them from pyroxenite melts Science.gov (United States) Grove, T. L.; Holbig, E.; Barr, J. A.; Till, C.; Krawczynski, M. J. 2013-12-01 Liquids form in equilibrium with garnet lherzolite sources when the Earth's mantle melts at depths of greater than ~ 60 km. We present a phase equilibrium investigation of Tibetan plateau olivine leucitites from 2.2 to 2.8 GPa and 1380 to 1480 °C. The resulting liquids were multiply saturated with spinel and garnet lherzolite assemblages (olivine, orthopyroxene, clinopyroxene and spinel +/-garnet) under nominally anhydrous conditions. These SiO2-undersaturated liquids and published experimental data have been used to develop a new model that parameterizes the major element compositions of garnet lherzolite partial melts, allowing the prediction of melt compositions from depleted to metasomatically enriched peridotite. The model is calibrated over the pressure range of 1.9 to 6 GPa. The model also predicts the suprasolidus pressure and temperature of the spinel to garnet lherzolite phase transition for natural peridotite compositions. Combined with the recent parameterization of melting in the plagioclase- and spinel- lherzolite facies (Till et al., 2012, JGR, 117, B06206), the new model distinguishes between melts of garnet vs. spinel vs. plagioclase lherzolites, but can also be used to distinguish between melts of lherzolitic vs. pyroxenitic source regions, allowing source lithology to be uniquely identified. Pyroxenite melts fall into two compositionally distinct groups; an olivine-normative, SiO2-undersaturated group and quartz-normative, SiO2-oversaturated group. Melts of plagioclase, spinel, and garnet lherzolite plot between these two types of pyroxenitic melts in mineral normative composition space. When our model is applied to high-K lavas erupted in the Tibetan plateau, we find that these magmas are derived from both pyroxenite and lherzolite source regions. Distinctive enrichments in compatible trace elements (Ni, Cr) are observed in the lherzolite-derived magmas. Applied to Hawaiian basalts, our model suggests the transitional and weakly alkaline pre 6. Stress Relaxation in Entangled Polymer Melts DEFF Research Database (Denmark) Hou, Ji-Xuan; Svaneborg, Carsten; Everaers, Ralf 2010-01-01 and into the terminal relaxation regime for Z=10. Using the known (Rouse) mobility of unentangled chains and the melt entanglement length determined via the primitive path analysis of the microscopic topological state of our systems, we have performed parameter-free tests of several different tube models. We find......We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts. The data allow us to explore the chain dynamics and the shear relaxation modulus, G(t), into the plateau regime for chains with Z=40 entanglements... 7. Experimental observation of Minkowski spacetime melting CERN Document Server Smolyaninov, Igor I 2015-01-01 Cobalt nanoparticle-based ferrofluid in the presence of an external magnetic field forms a self-assembled hyperbolic metamaterial, which may be described as an effective 3D Minkowski spacetime for extraordinary photons. If the magnetic field is not strong enough, this effective Minkowski spacetime gradually melts under the influence of thermal fluctuations. On the other hand, it may restore itself if the magnetic field is increased back to its original value. Here we present direct microscopic visualization of such a Minkowski spacetime melting/crystallization, which is somewhat similar to hypothesized formation of the Minkowski spacetime in loop quantum cosmology. 8. Influence of Grain Boundary on Melting Institute of Scientific and Technical Information of China (English) 王暾; 周富信; 刘曰武 2001-01-01 The temperature behaviour of an Al bicrystal with surfaces consisting of (110) and (111) crystals is simulated using molecular dynamics. The result shows that the (110) crystal losses its crystalline order at 820K, whereas the disorder does not propagate through the (111) crystal at this temperature. Instead, some disordered atoms are recrystallized into the (111) crystal and the initial grain boundary changes into a stable order-disorder interface. Thus, it was discovered that at a temperature near its melting point, the (111) crystal grew and obstructed the propagation of disorder. Such an obstruction is helpfulfor understanding melting. 9. Thermal melting studies of ligand DNA interactions. Science.gov (United States) Guédin, Aurore; Lacroix, Laurent; Mergny, Jean-Louis 2010-01-01 A simple thermal melting experiment may be used to demonstrate the stabilization of a given structure by a ligand (usually a small molecule, sometimes a peptide). Preparation of the sample is straightforward, and the experiment itself requires an inexpensive apparatus. Furthermore, reasonably low amounts of sample are required. A qualitative analysis of the data is simple: An increase in the melting temperature (T(m)) indicates preferential binding to the folded form as compared to the unfolded form. However, it is perilous to derive an affinity constant from an increase in T(m) as other factors play a role. 10. 3He melting pressure temperature scale DEFF Research Database (Denmark) Halperin, W.P.; Archie, C.N.; Richardson, R.C.; 1976-01-01 The latent heat for solidification of **3He has been measured along the **3He melting curve between 23 and 1 mK. A temperature scale is established which depends only on measurements of heat, pressure and volume, and on the condition that the entropy of solid **3He approaches R ln 2 at high...... temperatures. The A feature of the melting curve which suggests itself as a thermometric fixed point is found to be T//A equals 2. 75 plus or minus 0. 11 mK. The agreement between this value and independent measurements of T//A, based on nuclear or electronic paramagnetism, Johnson noise thermometry... 11. U-238 - Th-230 - Ra-226 disequilibria in volcanics: A new insight into melting conditions Science.gov (United States) Chabaux, Francois; Allegre, Claude J. 1994-08-01 Using new mass spectrometry techniques developed for the analysis of Ra isotopes, we present U-238 - Th-230 - Ra-226 disequilibria data from a variety of volcanic settings, and compare them with previously published data. Two correlations are observed with alkali volcanic data, one between (Th-230/U-238) and (Th-230/Ra-226) and another between the intensity of the disequilibria and the buoyancy flux of the underlying plume. These two correlations prove that partial melting is the major cause of U-Th-Ra fractionations in this volcanic context. The U-238 - Th-230 - Ra-226 disequilibria then place new constraints on some parameters of the classical melting models (batch melting and dynamic melting). The comparison of U-238 - Th-230 - Ra-226 disequilibria in alkali volcanics, carbonatites and subduction zones shows a clear parallel between the disequilibria value and the type of volcanic context. Such a parallel reflects the diversity of the conditions of magma generation, and shows that the U-238 - Th-230 - Ra-226 disequilibria systematics are very dependent on the chemical composition of liquids produced during magmatic processes. A systematic difference is observed between disequilibria in MORB and in alkali volcanics, which could indicate that the melting processes in these two volcanic contexts are very different. 12. The Origin of the Compositional Diversity of Mercury's Surface Constrained From Experimental Melting of Enstatite Chondrites Science.gov (United States) Boujibar, A.; Righter, K.; Pando, K.; Danielson, L. 2015-01-01 Mercury is known as an endmember planet as it is the most reduced terrestrial planet with the highest core/mantle ratio. MESSENGER spacecraft has shown that its surface is FeO-poor (2-4 wt%) and Srich (up to 6-7 wt%), which confirms the reducing nature of its silicate mantle. Moreover, high resolution images revealed large volcanic plains and abundant pyroclastic deposits, suggesting important melting stages of the Mercurian mantle. This interpretation was confirmed by the high crustal thickness (up to 100 km) derived from Mercury's gravity field. This is also corroborated by a recent experimental result that showed that Mercurian partial melts are expected to be highly buoyant within the Mercurian mantle and could have risen from depths as high as the core-mantle boundary. In addition MESSENGER spacecraft provided relatively precise data on major elemental compositions of Mercury's surface. These results revealed important chemical and mineralogical heterogeneities that suggested several stages of differentiation and re-melting processes. However, the extent and nature of compositional variations produced by partial melting remains poorly constrained for the particular compositions of Mercury (very reducing conditions, low FeO-contents and high sulfur-contents). Therefore, in this study, we investigated the processes that lead to the various compositions of Mercury's surface. Melting experiments with bulk Mercury-analogue compositions were performed and compared to the compositions measured by MESSENGER. 13. Viscosity Measurements of Eclogite Melt up to 5.6 GPa and 2000 K Science.gov (United States) Liu, H.; Fei, Y.; Han, L.; Kono, Y.; Hou, M.; Zhao, Z.; Du, J. 2014-12-01 The melting and rheology of eclogite is critical for understanding the dynamics of the subduction zone and plate tectonic. Viscosity of eclogite melt as a function of depth is a key parameter to model the long-term chemical evolution of the subduction zone and volcanic magma. It also plays an important role in earthquakes and continent formation. However, the viscosity and rheology of eclogite melt remain poorly understood at high pressure and temperature. In this study, we have carried out in-situ falling-sphere viscometry measurements to determine the viscosity of eclogite melt from 1.3 to 5.6 GPa at temperatures between 1500 and 2000 K, using the Paris-Edinburgh cell at the 16-BM-B beamline of the High Pressure Collaborative Access Team (HPCAT) at the Advanced Photon Source. We used a natural eclogite sample with 47.7wt% SiO2. The viscosity (η) was calculated with the Stokes' equation. The viscosity of eclogite melt decreases between 1.3 and 5.6 GPa at 2000K. At 1.4 GPa and 2000K the viscosity is 0.43 Pa·s, whereas at 5.6 GPa and 2000 K it is 0.13Pa·s. No minimum in the viscosity of eclogite was found in the measured pressure range up to 5.6 GPa. 14. Surface valence transformation during thermal activation and hydrogenation thermodynamics of Mg-Ni-Y melt-spun ribbons Science.gov (United States) Zhang, Tiebang; Song, Wenjie; Kou, Hongchao; Li, Jinshan 2016-05-01 In this work, phase compositions and chemical valence states on the surface and subsurface of Mg67Ni33-xYx (x = 0, 1, 3, 6) ribbons during thermal activation have been investigated by X-ray photoelectron spectroscopy (XPS). The results indicate that the surface contaminants of melt-spun ribbons are mainly MgO, NiO, Y2O3 and organics. The oxides/hydroxides of Mg67Ni33-xYx (x = 0, 1, 3, 6) melt-spun ribbons are removed from the surface during thermal activation. Surface chemical valence firstly transforms from oxidized state to the metallic one during thermal activation, which accounts for hydrogenation of Mg67Ni33-xYx melt-spun ribbons. Hydrogen absorption capacities of Mg67Ni33-xYx (x = 0, 1, 3, 6) melt-spun ribbons are enhanced with the increase of cycle numbers during thermal activation. Hydrogenation thermodynamics of activated Mg67Ni33-xYx (x = 0, 1, 3, 6) melt-spun ribbons have been also compared and correlated with the surface valence transformation. The obtained enthalpy of hydride formation is -55.5, -50.5, -46.9 and -48.6 kJ/mol for Mg67Ni33-xYx melt-spun ribbons with x = 0, 1, 3 and 6, respectively. 15. Evolution of melt-vapor surface tension in silicic volcanic systems: Experiments with hydrous melts Science.gov (United States) Mangan, M.; Sisson, T. 2005-01-01 We evaluate the melt-vapor surface tension (??) of natural, water-saturated dacite melt at 200 MPa, 950-1055??C, and 4.8-5.7 wt % H2O. We experimentally determine the critical supersaturation pressure for bubble nucleation as a function of dissolved water and then solve for ?? at those conditions using classical nucleation theory. The solutions obtained give dacite melt-vapor surface tensions that vary inversely with dissolved water from 0.042 (??0.003) J m-2 at 5.7 wt% H2O to 0.060 (??0.007) J m-2 at 5.2 wt% H2O to 0.073 (??0.003) J m-2 at 4.8 wt% H2O. Combining our dacite results with data from published hydrous haplogranite and high-silica rhyolite experiments reveals that melt-vapor surface tension also varies inversely with the concentration of mafic melt components (e.g., CaO, FeOtotal, MgO). We develop a thermodynamic context for these observations in which melt-vapor surface tension is represented by a balance of work terms controlled by melt structure. Overall, our results suggest that cooling, crystallization, and vapor exsolution cause systematic changes in ?? that should be considered in dynamic modeling of magmatic processes. 16. High Power Selective Laser Melting (HP SLM) of Aluminum Parts Science.gov (United States) Buchbinder, D.; Schleifenbaum, H.; Heidrich, S.; Meiners, W.; Bültmann, J. Selective Laser Melting (SLM) is one of the Additive Manufacturing (AM) technologies that enables the production of light weight structured components with series identical mechanical properties without the need for part specific tooling or downstream sintering processes, etc. Especially aluminum is suited for such eco-designed components due to its low weight and superior mechanical and chemical properties. However, SLM's state-of-the-art process and cost efficiency is not yet suited for series-production. In order to improve this efficiency it is indispensable to increase the build rate significantly. Thus, aluminum is qualified for high build rate applications using a new prototype machine tool including a 1 kW laser and a multi-beam system. 17. Universality between Experiment and Simulation of a Diblock Copolymer Melt Science.gov (United States) Beardsley, Thomas M.; Matsen, Mark W. 2016-11-01 The equivalent behavior among analogous block copolymer systems involving chemically distinct molecules or mathematically different models has long hinted at an underlying universality, but only recently has it been rigorously demonstrated by matching results from different simulations. The profound implication of universality is that simple coarse-grained models can be calibrated so as to provide quantitatively accurate predictions to experiment. Here, we provide the first compelling demonstration of this by simulating a polyisoprene-polylactide diblock copolymer melt using a previously calibrated lattice model. The simulation successfully predicts the peak in the disordered-state structure function, the position of the order-disorder transition, and the latent heat of the transition in excellent quantitative agreement with experiment. This could mark a new era of precision in the field of block copolymer research. 18. Effect of impurities in industrial salts on aluminum scrap melting Energy Technology Data Exchange (ETDEWEB) Ye, J.; Sahai, Y. [Ohio State Univ., Columbus, OH (United States). Dept. of Materials Science and Engineering; Revet, A. [Kalium Canada, ltd., Regina, Saskatchewan (Canada) 1996-10-01 Aluminum scrap such as Used Beverage Containers (UBC) is melted under a protective molten salt cover. An appropriate salt protects metal from oxidation, promotes coalescence of molten droplets, and separates clean metal from the oxide contamination. Generally, the salt compositions for aluminum scrap recycling are based on equimolar mixtures of NaCl and KCl. A small amount of fluoride is also added in the salt. In the past, laboratory research at universities and industrial laboratories have been limited to pure salts. However, the industrial salts have impurities such as sulfates and other insoluble materials. These impurities have a pronounced effect on the efficiency of the scrap remelting process. In this paper, the role of impurities in industrial salts in terms of their chemical interactions with the metal are summarized. The efficiency of different industrial grade salts containing varying amounts of sulfates and other insoluble impurities for scrap recycling is compared. 19. InP Bulk Crystals Grown from Various Stoichiometric Melt Institute of Scientific and Technical Information of China (English) 2006-01-01 InP crystal was grown from stoichiometric or non-stoichiometric melt, including P-rich and In-rich condition by the P-injection synthesis LEC method. Owing to the non-stoichiometric condition, there are many pores in the tail of the P-rich ingot. Samples were characterized by high speed photoluminescence mapping and E.P.D. mapping. The perfection (dislocation, stoichiometry and uniformity) of these samples were studied and compared. The PL peak intensity standard deviation of the 4-inch InP wafer is higher. The EPDs around the pores are higher than the other regions. Besides the stress releasing, the pores and the high concentration of dislocations around them are the leading factors causing the inhomogeneity of the wafer. By adjusting the thermal field and ensuring the chemical stoichiometry, InP crystals of larger diameters and better performance can be developed. 20. A Comparison of Biocompatibility of a Titanium Alloy Fabricated by Electron Beam Melting and Selective Laser Melting Science.gov (United States) Wang, Hong; Zhao, Bingjing; Liu, Changkui; Wang, Chao; Tan, Xinying; Hu, Min 2016-01-01 Electron beam melting (EBM) and selective laser melting (SLM) are two advanced rapid prototyping manufacturing technologies capable of fabricating complex structures and geometric shapes from metallic materials using computer tomography (CT) and Computer-aided Design (CAD) data. Compared to traditional technologies used for metallic products, EBM and SLM alter the mechanical, physical and chemical properties, which are closely related to the biocompatibility of metallic products. In this study, we evaluate and compare the biocompatibility, including cytocompatibility, haemocompatibility, skin irritation and skin sensitivity of Ti6Al4V fabricated by EBM and SLM. The results were analysed using one-way ANOVA and Tukey’s multiple comparison test. Both the EBM and SLM Ti6Al4V exhibited good cytobiocompatibility. The haemolytic ratios of the SLM and EBM were 2.24% and 2.46%, respectively, which demonstrated good haemocompatibility. The EBM and SLM Ti6Al4V samples showed no dermal irritation when exposed to rabbits. In a delayed hypersensitivity test, no skin allergic reaction from the EBM or the SLM Ti6Al4V was observed in guinea pigs. Based on these results, Ti6Al4V fabricated by EBM and SLM were good cytobiocompatible, haemocompatible, non-irritant and non-sensitizing materials. Although the data for cell adhesion, proliferation, ALP activity and the haemolytic ratio was higher for the SLM group, there were no significant differences between the different manufacturing methods. PMID:27391895 1. A Comparison of Biocompatibility of a Titanium Alloy Fabricated by Electron Beam Melting and Selective Laser Melting. Directory of Open Access Journals (Sweden) Hong Wang Full Text Available Electron beam melting (EBM and selective laser melting (SLM are two advanced rapid prototyping manufacturing technologies capable of fabricating complex structures and geometric shapes from metallic materials using computer tomography (CT and Computer-aided Design (CAD data. Compared to traditional technologies used for metallic products, EBM and SLM alter the mechanical, physical and chemical properties, which are closely related to the biocompatibility of metallic products. In this study, we evaluate and compare the biocompatibility, including cytocompatibility, haemocompatibility, skin irritation and skin sensitivity of Ti6Al4V fabricated by EBM and SLM. The results were analysed using one-way ANOVA and Tukey's multiple comparison test. Both the EBM and SLM Ti6Al4V exhibited good cytobiocompatibility. The haemolytic ratios of the SLM and EBM were 2.24% and 2.46%, respectively, which demonstrated good haemocompatibility. The EBM and SLM Ti6Al4V samples showed no dermal irritation when exposed to rabbits. In a delayed hypersensitivity test, no skin allergic reaction from the EBM or the SLM Ti6Al4V was observed in guinea pigs. Based on these results, Ti6Al4V fabricated by EBM and SLM were good cytobiocompatible, haemocompatible, non-irritant and non-sensitizing materials. Although the data for cell adhesion, proliferation, ALP activity and the haemolytic ratio was higher for the SLM group, there were no significant differences between the different manufacturing methods. 2. A Comparison of Biocompatibility of a Titanium Alloy Fabricated by Electron Beam Melting and Selective Laser Melting. Science.gov (United States) Wang, Hong; Zhao, Bingjing; Liu, Changkui; Wang, Chao; Tan, Xinying; Hu, Min 2016-01-01 Electron beam melting (EBM) and selective laser melting (SLM) are two advanced rapid prototyping manufacturing technologies capable of fabricating complex structures and geometric shapes from metallic materials using computer tomography (CT) and Computer-aided Design (CAD) data. Compared to traditional technologies used for metallic products, EBM and SLM alter the mechanical, physical and chemical properties, which are closely related to the biocompatibility of metallic products. In this study, we evaluate and compare the biocompatibility, including cytocompatibility, haemocompatibility, skin irritation and skin sensitivity of Ti6Al4V fabricated by EBM and SLM. The results were analysed using one-way ANOVA and Tukey's multiple comparison test. Both the EBM and SLM Ti6Al4V exhibited good cytobiocompatibility. The haemolytic ratios of the SLM and EBM were 2.24% and 2.46%, respectively, which demonstrated good haemocompatibility. The EBM and SLM Ti6Al4V samples showed no dermal irritation when exposed to rabbits. In a delayed hypersensitivity test, no skin allergic reaction from the EBM or the SLM Ti6Al4V was observed in guinea pigs. Based on these results, Ti6Al4V fabricated by EBM and SLM were good cytobiocompatible, haemocompatible, non-irritant and non-sensitizing materials. Although the data for cell adhesion, proliferation, ALP activity and the haemolytic ratio was higher for the SLM group, there were no significant differences between the different manufacturing methods. 3. High-temperature apparatus for chaotic mixing of natural silicate melts Energy Technology Data Exchange (ETDEWEB) Morgavi, D.; Petrelli, M.; Vetere, F. P.; González-García, D.; Perugini, D., E-mail: [email protected] [Department of Physics and Geology, Petro-Volcanology Research Group (PVRG), University of Perugia, Piazza Università, Perugia 06100 (Italy) 2015-10-15 A unique high-temperature apparatus was developed to trigger chaotic mixing at high-temperature (up to 1800 °C). This new apparatus, which we term Chaotic Magma Mixing Apparatus (COMMA), is designed to carry out experiments with high-temperature and high-viscosity (up to 10{sup 6} Pa s) natural silicate melts. This instrument allows us to follow in time and space the evolution of the mixing process and the associated modulation of chemical composition. This is essential to understand the dynamics of magma mixing and related chemical exchanges. The COMMA device is tested by mixing natural melts from Aeolian Islands (Italy). The experiment was performed at 1180 °C using shoshonite and rhyolite melts, resulting in a viscosity ratio of more than three orders of magnitude. This viscosity ratio is close to the maximum possible ratio of viscosity between high-temperature natural silicate melts. Results indicate that the generated mixing structures are topologically identical to those observed in natural volcanic rocks highlighting the enormous potential of the COMMA to replicate, as a first approximation, the same mixing patterns observed in the natural environment. COMMA can be used to investigate in detail the space and time development of magma mixing providing information about this fundamental petrological and volcanological process that would be impossible to investigate by direct observations. Among the potentials of this new experimental device is the construction of empirical relationships relating the mixing time, obtained through experimental time series, and chemical exchanges between the melts to constrain the mixing-to-eruption time of volcanic systems, a fundamental topic in volcanic hazard assessment. 4. Recent Changes in Arctic Sea Ice Melt Onset, Freeze-Up, and Melt Season Length Science.gov (United States) Markus, Thorsten; Stroeve, Julienne C.; Miller, Jeffrey 2010-01-01 In order to explore changes and trends in the timing of Arctic sea ice melt onset and freeze-up and therefore melt season length, we developed a method that obtains this information directly from satellite passive microwave data, creating a consistent data set from 1979 through present. We furthermore distinguish between early melt (the first day of the year when melt is detected) and the first day of continuous melt. A similar distinction is made for the freeze-up. Using this method we analyze trends in melt onset and freeze-up for 10 different Arctic regions. In all regions except for the Sea of Okhotsk, which shows a very slight and statistically insignificant positive trend (O.4 days/decade), trends in melt onset are negative, i.e. towards earlier melt. The trends range from -1.0day/decade for the Bering Sea to -7.3 days/decade for the East Greenland Sea. Except for the Sea of Okhotsk all areas also show a trend towards later autumn freeze onset. The Chukchi/Beaufort Seas and Laptev/East Siberian Seas observe the strongest trends with 7 days/decade. For the entire Arctic, the melt season length has increased by about 20 days over the last 30 years. Largest trends of over 1O days/decade are seen for Hudson Bay, the East Greenland Sea the Laptev/East Siberian Seas, and the Chukchi/Beaufort Seas. Those trends are statistically significant a1 the 99% level. 5. Development of melt dilute technology for disposition of aluminum based spent nuclear fuel Energy Technology Data Exchange (ETDEWEB) Swift, W.F. [Nuclear Material Management Division Westinghouse Savannah River Company, Savannah River Site Building 707-C, Aiken, SC 29808 (United States) 2002-07-01 The US Department of Energy (DOE) has for many years had a program for receipt and disposition of spent nuclear fuels of US origin from research reactors around the world. The research reactor spent nuclear fuel that consists of aluminum alloy composition has historically been returned to the Savannah River Site (SRS) and dispositioned via chemical reprocessing. In 1995, the DOE evaluated a number of alternatives to chemical reprocessing. In 2000, the DOE selected the melt-dilute alternative as the primary disposition path and direct disposal as the backup path. The melt-dilute technology has been developed from lab-scale demonstration up through the construction of a pilot-scale facility. The pilot-scale L-Area Experimental Facility (LEF) has been constructed and is ready for operation. The LEF will be used primarily, to confirm laboratory research on zeolite media for off- gas trapping and remote operability. Favorable results from the LEF are expected to lead to final design of the production melt-dilute facility identified as the Treatment and Storage Facility (TSF). This paper will describe the melt-dilute process and provide a status of the program development. (author) 6. Analysis of an EBeam melting process Science.gov (United States) Schunk, P. R. Electron-Beam (EBeam) melting furnaces are routinely used to minimize the occurrence of second-phase particles in the processing of segregation-sensitive alloys. As one part of the process, a circulating electron beam impinges the surface of a crucible melt pool to help control the shape of the solidification front below. By modeling melt pool hydrodynamics, heat transfer, and the shape of solidification boundaries, we plan to optimize the dwell pattern of the beam so that the material solidifies with a composition as spatially homogeneous as possible. Both two-and three-dimensional models are being pursued with FIDAP 5.02, the former serving as a test bed for various degrees of model sophistication. A heat flux distribution is specified on the top of the domain to simulate the EBeam dwell pattern. In two dimensions it is found that an inertially-driven recirculation in the melt pool interacts with a counter-rotating buoyancy-driven recirculation, and that both recirculation influence heavily the shape of the solidification front. In three dimensions the inertial cell decays quickly with distance from the position of the inlet stream. Because the Rayleigh number can exceed 10(exp 7) for materials and operating conditions of interest, stability and the possibility of spontaneous transients are explored. 7. Surface-Induced Melting of Metal Nanoclusters Institute of Scientific and Technical Information of China (English) YANG Quan-Wen; ZHU Ru-Zeng; WEI Jiu-An; WEN Yu-Hua 2004-01-01 @@ We investigate the size effect on melting of metal nanoclusters by molecular dynamics simulation and thermodynamic theory based on Kofman's melt model. By the minimization of the free energy of metal nanoclusters with respect to the thickness of the surface liquid layer, it has been found that the nanoclusters of the same metal have the same premelting temperature Tpre = T0 - T0(γsv -γlv -γst)/(ρLξ) (T0 is the melting point of bulk metal, γsv the solid-vapour interfacial free energy, γlv the liquid-vapour interfacial free energy, γsl the solid-liquid interfacial free energy, ρ the density of metal, L the latent heat of bulk metal, and ξ the characteristic length of surface-interface interaction) to be independent of the size of nanoclusters, so that the characteristic length ξ ofa metal can be obtained easily by Tpre, which can be obtained by experiments or molecular dynamics (MD) simulations. The premelting temperature Tpre of Cu is obtained by MD simulations, then ξ is obtained.The melting point Tcm is further predicted by free energy analysis and is in good agreement with the result of our MD simulations. We also predict the maximum premelting-liquid width of Cu nanoclusters with various sizes and the critical size, below which there is no premelting. 8. Pressure-induced melting of micellar crystal DEFF Research Database (Denmark) Mortensen, K.; Schwahn, D.; Janssen, S. 1993-01-01 that pressure improves the solvent quality of water, thus resulting in decomposition of the micelles and consequent melting of the micellar crystal. The combined pressure and temperature dependence reveals that in spite of the apparent increase of order on the 100 angstrom length scale upon increasing... 9. Using Melting Ice to Teach Radiometric Dating. Science.gov (United States) Wise, Donald Underkofler 1990-01-01 Presented is an activity in which a mystery setting is used to motivate students to construct their own decay curves of melting ice used as an analogy to radioactive decay. Procedures, materials, apparatus, discussion topics, presentation, and thermodynamics are discussed. (CW) 10. Spontaneous Breakup of Extended Monodisperse Polymer Melts DEFF Research Database (Denmark) Rasmussen, Henrik K.; Yu, Kaijia 2011-01-01 We apply continuum mechanical based, numerical modeling to study the dynamics of extended monodisperse polymer melts during the relaxation. The computations are within the ideas of the microstructural ‘‘interchain pressure’’ theory. The computations show a delayed necking resulting in a rupture... 11. Melting Metal on a Playing Card Science.gov (United States) Greenslade, Thomas B., Jr. 2016-01-01 Many of us are familiar with the demonstration of boiling water in a paper cup held over a candle or a Bunsen burner; the ignition temperature of paper is above the temperature of 100°C at which water boils under standard conditions. A more dramatic demonstration is melting tin held in a playing card. This illustration is from Tissandier's book on… 12. Intracavity DNA melting analysis with optofluidic lasers. Science.gov (United States) Lee, Wonsuk; Fan, Xudong 2012-11-01 DNA melting analysis holds great promise for simple and fast DNA sequence discrimination. However, conventional fluorescence-based methods suffer from a small differential signal and demanding melting curve analysis, both of which make it difficult to distinguish the target DNA from the mismatched one. Herein, we propose and demonstrate a highly specific intracavity DNA melting analysis scheme utilizing an optofluidic laser. The laser optically amplifies the small yet intrinsic thermal dynamic difference between the target and the single-base-mismatched DNA, resulting in a differential signal that is orders of magnitude greater than with fluorescence-based methods. In particular, the existence of a phase transition between the stimulated laser emission and fluorescence (i.e., spontaneous emission) enables accurate determination of the DNA transition temperature difference. Furthermore, the high differential signal in the intracavity detection allows for scanning of the laser excitation at a fixed temperature to distinguish two DNA sequences, which provides another means for rapid DNA analysis. In this paper, we first theoretically investigate DNA melting analysis using an optofluidic laser and then experimentally explore this scheme with a high-quality optofluidic ring resonator. Distinction of two DNA sequences of up to 100 bases long is demonstrated. The intracavity detection developed here will lead to novel optofluidic devices that enable rapid and simple analysis of DNAs with very long sequences. 13. Catastrophic failure of polymer melts during extension DEFF Research Database (Denmark) Rasmussen, Henrik K. 2013-01-01 Numerical flow modeling has been applied to study the break of monodisperse polymer melts during extension. These continuum mechanical based computations are within the ideas of the microstructural ’interchain pressure’ theory. Calculated breaks, a result of small initial sample imperfections, ag... 14. Record Summer Melt in Greenland in 2010 NARCIS (Netherlands) Tedesco, M.; Fettweis, X.; van den Broeke, M.R.; van de Wal, R.S.W.; Smeets, C.J.P.P.; van de Berg, W.J.; Serreze, M.C.; Box, J.E. 2011-01-01 As Arctic temperatures increase, there is growing concern about the melting of the Greenland ice sheet, which reached a new record during the summer of 2010. Understanding the changing surface mass balance of the Greenland ice sheet requires appreciation of the close links among changes in surface a 15. Geometry and Combinatorics of Crystal Melting CERN Document Server Yamazaki, Masahito 2011-01-01 We survey geometrical and especially combinatorial aspects of generalized Donaldson-Thomas invariants (also called BPS invariants) for toric Calabi-Yau manifolds, emphasizing the role of plane partitions and their generalizations in the recently proposed crystal melting model. We also comment on equivalence with a vicious walker model and the matrix model representation of the partition function. 16. Electrical conductivity measurements on silicate melts using the loop technique Science.gov (United States) Waff, H. S. 1976-01-01 A new method is described for measurement of the electrical conductivity of silicate melts under controlled oxygen partial pressure at temperatures to 1550 C. The melt samples are suspended as droplets on platinum-rhodium loops, minimizing iron loss from the melt due to alloying with platinum, and providing maximum surface exposure of the melt to the oxygen-buffering gas atmosphere. The latter provides extremely rapid equilibration of the melt with the imposed oxygen partial pressure. The loop technique involves a minimum of setup time and cost, provides reproducible results to within + or - 5% and is well suited to electrical conductivity studies on silicate melts containing redox cations. 17. Glacier melt on the Third Pole Science.gov (United States) Yao, T. 2015-12-01 With an average elevation above 4,000 metres, the Third Pole (TP) is a unique region with many high mountains centered on the Tibetan Plateau stretching over 5 million square kilometers. Major environmental changes are taking place on the TP characterized by complex interactions of atmospheric, cryospheric, hydrological, geological and environmental processes. These processes are critical for the well-being of the three billion people inhabiting the plateau and the surrounding regions. Glacier melt is one of the most significant environmental changes observed on the TP. Over the past decade, most of the glaciers on the TP have undergone considerable melt. The Third Pole Environment (TPE) has focused on the causes of the glacier melt by conducting large-scale ground in-situ observation and monitoring, analyzing satellite images and remote sensing data, and applying numerical modeling to environmental research on the TP. The studies of long-term record of water stable isotopes in precipitation and ice core throughout the TP have revealed different features with regions, thus proposing significant influence of atmospheric circulations on spatial precipitation pattern over the TP. Validation of the result by isotope-equipped general circulation models confirms the spatial distribution of different atmospheric circulation dominances on the TP, with northern part dominated by the westerlies, southern part by the summer monsoon, and central part featuring the influences of both circulation systems. Such unique circulation patterns also bear directly on the status of glaciers and lakes over the TP and its surroundings. The studies therefore found the largest glacier melt in the monsoon-dominated southern part, moderate melt in the central part of transition, and the least melt, or even slight advance in the westerlies-dominated northern TP. It is clear that some mountains on the TP are undergoing rapid melt and the consequence of without ice and snow will be very soon. The 18. Chemical Composition and Daily Variation of Melt Water During Ablation Season in Monsoonal Temperate Glacier Region:A Case Study of Baishui Glacier No.1%典型季风型温冰川消融期融水化学日变化特征 Institute of Scientific and Technical Information of China (English) 朱国锋; 蒲焘; 何元庆; 王培震; 孔建龙; 张宁宁; 辛惠娟 2012-01-01 Melt water samples collected continuously from 29 August to 3 September 2009 in the Baishui Glacier No.1 at elevation of 4 750 m were analyzed for pH,conductivity,δ18 O and inorganic ions.The results showed that the pH had obvious diurnal variations and was increased slightly by the influence of precipitation.The dissolution of alkaline soluble salts in the dust was the main reason for the increase of melt water conductivity;the value of δ18 O was relatively low in strong ablation period and high in slight ablation period.Different from other research areas,the concentrations of Na+,K+,which were influenced by lithological and marine water vapor,were higher than that of Μg2+ in the study area;HCO-3 and Ca2+ accounted for more than 80% of total ions in snow and ice melt water,indicating that the ions mainly came from limestone and the melt water was a typical carbonate solution;The content of melt water had an obvious daily change with temperature change,but the response amplitudes were different;Monsoon transport,local rock lithology,human industrial and agricultural activities were the main sources of inorganic ions and the deciding factors of the ion composition in the Baishui Glacier No.1.%分析了玉龙雪山白水1号冰川区2009年8月29日～9月3日4 750 m处冰雪融水的pH、电导率、无机离子和δ18O的化学特征,结果表明,消融期日尺度上pH值受气温变化影响较大.碱性尘埃中的可溶盐溶解导致融水电导率增大.一天中消融速率快时δ18O值较低,消融速率慢时δ18O值较高.受岩石岩性和海洋水汽影响,研究区Na＋、K＋的平均浓度高于Μg2＋的平均浓度.融水中阳离子主要来源于石灰岩风化,属典型的碳酸盐溶滤水.融水中无机离子的总含量随气温的变化而变化,具有明显的周期性,但是不同可溶性离子对气温变化所导致的消融速率响应幅度不一致.局地岩石岩性、季风输送和人类活动是白水1号冰川融水中无机离子的主要来源. 19. Communication: Theory of melt-memory in polymer crystallization Science.gov (United States) Muthukumar, M. 2016-07-01 Details of crystallization processes of a polymer at the crystallization temperature Tc from its melt kept initially at the melt temperature Tm depend profoundly on the nature of the initial melt state and often are accompanied by memory effects. This phenomenon is in contrast to small molecular systems where the supercooling (Tm0-Tc), with Tm0 being the equilibrium melting temperature, and not (Tm - Tc), determines the nature of crystallization. In addressing this five-decade old puzzle of melt-memory in polymer crystallization, we present a theory to describe melt-memory effects, by invoking an intermediate inhomogeneous melt state in the pathway between the melt and crystalline states. Using newly introduced dissolution temperature T10 for the inhomogeneous melt state and the transition temperature Tt0 for the transition between the inhomogeneous melt and crystalline states, analytical formulas are derived for the nucleation rate as a function of the melt temperature. The theory is general to address different kinds of melt-memory effects depending on whether Tm is higher or lower than Tm0. The derived results are in qualitative agreement with known experimental data, while making predictions for further experiments on melt-memory. 20. The influence of partial melting and melt migration on the rheology of the continental crust Science.gov (United States) Cavalcante, Geane Carolina G.; Viegas, Gustavo; Archanjo, Carlos José; da Silva, Marcos Egydio 2016-11-01 The presence of melt during deformation produces a drastic change in the rheological behavior of the continental crust; rock strength is decreased even for melt fractions as low as ∼7%. At pressure/temperature conditions typical of the middle to lower crust, melt-bearing systems may play a critical role in the process of strain localization and in the overall strength of the continental lithosphere. In this contribution we focus on the role and dynamics of melt flow in two different mid-crustal settings formed during the Brasiliano orogeny: (i) a large-scale anatectic layer in an orthogonal collision belt, represented by the Carlos Chagas anatexite in southeastern Brazil, and (ii) a strike-slip setting, in which the Espinho Branco anatexite in the Patos shear zone (northeast Brazil) serves as an analogue. Both settings, located in eastern Brazil, are part of the Neoproterozoic tectonics that resulted in widespread partial melting, shear zone development and the exhumation of middle to lower crustal layers. These layers consist of compositionally heterogeneous anatexites, with variable former melt fractions and leucosome structures. The leucosomes usually form thick interconnected networks of magma that reflect a high melt content (>30%) during deformation. From a comparison of previous work based on detailed petrostructural and AMS studies of the anatexites exposed in these areas, we discuss the rheological implications caused by the accumulation of a large volume of melt "trapped" in mid-crustal levels, and by the efficient melt extraction along steep shear zones. Our analyses suggest that rocks undergoing partial melting along shear settings exhibit layers with contrasting competence, implying successive periods of weakening and strengthening. In contrast, regions where a large amount of magma accumulates lack clear evidence of competence contrast between layers, indicating that they experienced only one major stage of dramatic strength drop. This comparative 1. Modeling the Temperature Fields of Copper Powder Melting in the Process of Selective Laser Melting Science.gov (United States) Saprykin, A. A.; Ibragimov, E. A.; Babakova, E. V. 2016-08-01 Various process variables influence on the quality of the end product when SLM (Selective Laser Melting) synthesizing items of powder materials. The authors of the paper suggest using the model of distributing the temperature fields when forming single tracks and layers of copper powder PMS-1. Relying on the results of modeling it is proposed to reduce melting of powder particles out of the scanning area. 2. Thermodynamic Calculations of Melt in Melt Pool During Laser Cladding High Silicon Coatings Institute of Scientific and Technical Information of China (English) DONG Dan-yang; LIU Chang-sheng; ZHANG Bin 2008-01-01 Based on the Miedema's formation heat model for binary alloys and the Toop's asymmetric model for terna-ry alloys, the formation heat, excess entropy, and activity coefficients of silicon ranging from 1 900 K to 4 100 K in the Fe-Si-C melt formed during the laser cladding high silicon coatings process were calculated. The results indicated that all values of InγOSi, εCSi, ρSiSi and ρCSi are negative in the temperature range and these values increase as the tempera-ture increases. And all values of εSiSi and ρSi-CSi are positive and these values decrease with increasing temperature. The iso-activity lines of silicon are distributed axisymmetrically to the incident laser beam in the melt pool vertical to the laser scanning direction. And the iso-activity lines of silicon in the front of the melt pool along the laser scanning direction are more intensive than those in the back of the melt pool. The activity of silicon on the bottom of the melt pool is lower than that in the effecting center of laser beam on the top surface of the melt pool and it may be the im-portant reason for the formation of the silicides and excellent metallurgical bonding between the laser cladding coating and the substrate. 3. Formation of melt droplets, melt fragments, and accretionary impact lapilli during a hypervelocity impact Science.gov (United States) Johnson, B. C.; Melosh, H. J. 2014-01-01 We present a model that describes the formation of melt droplets, melt fragments, and accretionary impact lapilli during a hypervelocity impact. Using the iSALE hydrocode, coupled to the ANEOS equation of state for silica, we create high-resolution two-dimensional impact models to track the motion of impact ejecta. We then estimate the size of the ejecta products using simple analytical expressions and information derived from our hydrocode models. Ultimately, our model makes predictions of how the size of the ejecta products depends on impactor size, impact velocity, and ejection velocity. In general, we find that larger impactor sizes result in larger ejecta products and higher ejection velocities result in smaller ejecta product sizes. We find that a 10 km diameter impactor striking at a velocity of 20 km/s creates millimeter scale melt droplets comparable to the melt droplets found in the Chicxulub ejecta curtain layer. Our model also predicts that melt droplets, melt fragments, and accretionary impact lapilli should be found together in well preserved ejecta curtain layers and that all three ejecta products can form even on airless bodies that lack significant volatile content. This prediction agrees with observations of ejecta from the Sudbury and Chicxulub impacts as well as the presence of accretionary impact lapilli in lunar breccia. 4. Dynamic properties of Aluminum-Lithium and Aluminum-Magnesium melts Science.gov (United States) Kiselev, A. I. 2010-08-01 A comparison of calculated concentration dependences of the electrical resistivities of the Al-Li and Al-Mg systems suggests that a metal-nonmetal phase transition takes place in the Al-Li system. This assumption casts some doubt on the mechanism of quasi-chemical electron localization used to explain the metal-nonmetal phase transition in Pb-Li and Sn-Li melts. 5. Hot-Melt Extrusion: from Theory to Application in Pharmaceutical Formulation OpenAIRE Patil, Hemlata; Tiwari, Roshan V.; Repka, Michael A. 2015-01-01 Hot-melt extrusion (HME) is a promising technology for the production of new chemical entities in the developmental pipeline and for improving products already on the market. In drug discovery and development, industry estimates that more than 50% of active pharmaceutical ingredients currently used belong to the biopharmaceutical classification system II (BCS class II), which are characterized as poorly water-soluble compounds and result in formulations with low bioavailability. Therefore, th... 6. Melting and reactive flow of a volatilized mantle beneath mid-ocean ridges: theory and numerical models Science.gov (United States) Keller, Tobias; Katz, Richard F. 2015-04-01 Laboratory experiments indicate that even small concentrations volatiles (H2O or CO2) in the upper mantle significantly affect the silicate melting behavior [HK96,DH06]. The presence of volatiles stabilizes volatile-rich melt at high pressure, thus vastly increasing the volume of the upper mantle expected to be partially molten [H10,DH10]. These small-degree melts have important consequences for chemical differentiation and could affect the dynamics of mantle flow. We have developed theory and numerical implementation to simulate thermo-chemically coupled magma/mantle dynamics in terms of a two-phase (rock+melt), three component (dunite+MORB+volatilized MORB) physical model. The fluid dynamics is based on McKenzie's equations [McK84], while the thermo-chemical formulation of the system is represented by a novel disequilibrium multi-component melting model based on thermo-dynamic theory [RBS11]. This physical model is implemented as a parallel, two-dimensional, finite-volume code that leverages tools from the PETSc toolkit. Application of this simulation code to a mid-ocean ridge system suggests that the methodology captures the leading-order features of both hydrated and carbonated mantle melting, including deep, low-degree, volatile-rich melt formation. Melt segregation leads to continuous dynamic thermo-chemical dis-equilibration, while phenomenological reaction rates are applied to continually move the system towards re-equilibration. The simulations will be used first to characterize volatile extraction from the MOR system assuming a chemically homogeneous mantle. Subsequently, simulations will be extended to investigate the consequences of heterogeneity in lithology [KW12] and volatile content. These studies will advance our understanding of the role of volatiles in the dynamic and chemical evolution of the upper mantle. Moreover, they will help to gauge the significance of the coupling between the deep carbon cycle and the ocean/atmosphere system. REFERENCES 7. Modeling the summertime evolution of sea-ice melt ponds DEFF Research Database (Denmark) Lüthje, Mikael; Feltham, D.L.; Taylor, P.D.; 2006-01-01 We present a mathematical model describing the summer melting of sea ice. We simulate the evolution of melt ponds and determine area coverage and total surface ablation. The model predictions are tested for sensitivity to the melt rate of unponded ice, enhanced melt rate beneath the melt ponds......, vertical seepage, and horizontal permeability. The model is initialized with surface topographies derived from laser altimetry corresponding to first-year sea ice and multiyear sea ice. We predict that there are large differences in the depth of melt ponds and the area of coverage between the two types...... of ice. We also find that the vertical seepage rate and the melt rate of unponded ice are important in determining the total surface ablation and area covered by melt ponds.... 8. Sea Ice Melt Pond Data from the Canadian Arctic Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains observations of albedo, depth, and physical characteristics of melt ponds on sea ice, taken during the summer of 1994. The melt ponds studied... 9. Primitive, high-Mg basaltic andesites: direct melts of the shallow, hot, wet mantle Science.gov (United States) Andrews, A.; Grove, T. L. 2013-12-01 Direct mantle melts are rare in subduction zone settings. Such melts are identified by Mg #s (Mg # = Mg / (Mg+Fe)) greater than ~0.73, indicating chemical equilibrium with Fo90 mantle olivine. Most of these primitive arc melts are basaltic, characterized by SiO2 contents of ~48-50 wt % and MgO contents ranging from 8-10 wt %. However, primitive basaltic andesites with mantle-equilibrated Mg #s have also been found at subduction zones worldwide. These basaltic andesites have higher SiO2 contents (53-58 wt %) than typical primitive basalts as well as high MgO (8-10 wt %). Because these rocks have high SiO2 contents and yet retain evidence for chemical equilibrium with the mantle (Mg #s), their petrogenesis has sparked intense debate as researchers have tried to discern how these samples fit into the paradigm of mantle melting at subduction zones. Through an understanding of the conditions and processes that produce the SiO2 enrichment in these rocks, we also aim to understand the role of these melts in producing the observed andesitic compositional characteristics of the continental crust. To understand the petrogenesis of primitive, high-Mg basaltic andesites, this study investigates the experimental melts of undepleted mantle peridotite plus a slab component (Na-2O + K2O) from 1,205-1,470°C at 1.0-2.0 GPa under water-undersaturated conditions (0-5 wt % H2O). At 1.0 and 1.2 GPa, the experimental melts reproduce the compositions of natural primitive, high-Mg basaltic andesites in all major elements (SiO2, TiO2, Al2O3, FeO, MnO, MgO, and Na2O+K2O) except CaO. CaO contents are higher than the range of the natural samples by ~2 wt % at the highest silica contents of the experiments (54-56 wt% SiO2). This suggests that at 1.0-1.2 GPa, a higher percent of melting (30-35 %) with 3-5 wt % H2O is required to drive the chemical compositions of the experiments toward the representative compositions of the natural rocks. The experimental melts also show that mantle-wall rock 10. The Global Array of Primitve Arc Melts Science.gov (United States) Schmidt, M. W.; Jagoutz, O. E. 2015-12-01 A longstanding question concerns the nature of the melts forming in the subarc mantle and giving rise to arc magmatism. The global array of primitive arc melts (1180 volcanic rocks in 25 arcs extracted from the georoc database, calculated to be in equilibrium with mantle olivine) yields five principal melt types: calc-alkaline basalts and high-Mg andesites, tholeiitic basalts and high-Mg andesites, and shoshonitic or alkaline arc melts; many arcs have more than one type. Primitive calc-alkaline basalts occur in 11 arcs but most strikingly, 8 continental arcs (incl. Aleutians, Cascades, Japan, Mexico, Kamtschatka) have a continuous range of calc-alkaline basalts to high-Mg andesites with mostly 48-58 wt% SiO2. In each arc, these are spatially congruent, trace element patterns overlap, and major elements form a continuum. Their Ca-Mg-Si systematics suggests saturation in olivine+opx+cpx. We hence interpret the large majority of high-Mg andesites as derived from primitive calc-alkaline basalts through fractionation and reaction in the shallower mantle. Removal of anhydrous mantle phases at lower pressures increases SiO2 and H2O-contents while Mg# and Ni remain buffered to mantle values. Primitive tholeiitic basalts (Cascades, Kermadec, Marianas, Izu-Bonin, Japan, Palau, Sunda) have a much lesser subduction signal (e.g. in LILE) than the calc-alkaline suite. These tholeiites have been interpreted to form through decompression melting, but also characterize young intraoceanic arcs. In the two continental arcs with both tholeiitic and calc-alkaline primitive basalts (clearly distinct in trace patterns), there is no clear spatial segregation (Casacades, Japan). Three intraoceanic arcs (Marianas, Izu-Bonin, Tonga) have primitive tholeiitic, highly depleted high-Mg andesites (boninites) with HFSE and HREE slightly above primitive mantle values. These deviate in majors from the array formed by the basalts and calc-alkaline andesites suggesting that only these formed from a 11. Conditions of crystallization of the Ural platinum-bearing ultrabasic massifs: evidence from melt inclusions Science.gov (United States) Simonov, Vladimir; Puchkov, Victor; Prikhod'ko, Vladimir; Stupakov, Sergey; Kotlyarov, Alexey 2013-04-01 Conditions of the Ural platinum-bearing ultramafic massifs formation attract attention of numerous researchers. A most important peculiarity of such plutons is their dunite cores, to which commercial Pt deposits are related. There are a different opinions about genesis of these massifs and usual methods not always can solve this question. As a result of melt inclusions study in the Cr-spinel the new data on physical and chemical parameters of dunite crystallization of the Nizhnii Tagil platinum-bearing ulrabasic massif (Ural) was obtained. The comparative analysis of Cr-spinels, containing melt inclusions, has shown essential differences of these minerals from chromites of the ultrabasic ophiolite complexes and of modern oceanic crust. Contents of major chemical components in the heated and quenched melt inclusions are close to those in the picrite and this testifies dunite crystallization from ultrabasic (to 24 wt.% MgO) magma. On the variation diagrams for inclusions in Cr-spinel the following changes of chemical compositions are established: during SiO2 growth there is falling of FeO, MgO, and increase of CaO, Na2O contents. Values of TiO2, Al2O3, K2O and P2O5 remain as a whole constant. Comparing to the data on the melt inclusions in Cr-spinel from the Konder massif, we see that values of the most part of chemical components (SiO2, TiO2, K2O, P2O5) are actually overlapped. At the same time, for the Nizhnii Tagil platinum-bearing massif the big maintenances of FeO and CaO in inclusions are marked. Distinct dependence of the majority of components from the MgO content in inclusions is observed: values TiO2, Al2O3 FeO, CaO and Na2O fall at transition to more magnesia melts. On the peculiarities of distribution of petrochemical characteristics melt inclusions in considered Cr-spinels are co-ordinated with the data on evolution of compositions of melts and rocks of model stratified ultramafic plutons during their crystallization in the magmatic chambers. On the 12. Multiple Melting Endotherms of Syndiotactic Polystyrene in β Crystalline Form Institute of Scientific and Technical Information of China (English) 2000-01-01 A series of syndiotactic polystyrene (SPS) samples in β crystalline form were prepared by cooling from the melt at various cooling rates. The effects of cooling rate from the melt, and DSC heating rate on the multiple melting behaviors of β crystals were investigated by differential scanning calorimetry (DSC) and modulated differential scanning calorimetry (MDSC), from which the nature of the multiple melting behavior was ascribed to the occurring of a recrystallization process. 13. Transition in the fractal geometry of Arctic melt ponds OpenAIRE Hohenegger, C.; B. Alali; K. R. Steffen; D. K. Perovich; K. M. Golden 2012-01-01 During the Arctic melt season, the sea ice surface undergoes a remarkable transformation from vast expanses of snow covered ice to complex mosaics of ice and melt ponds. Sea ice albedo, a key parameter in climate modeling, is determined by the complex evolution of melt pond configurations. In fact, ice–albedo feedback has played a major role in the recent declines of the summer Arctic sea ice pack. However, understanding melt pond evolution remains a significant challenge to improving climate... 14. A Disequilibrium Melting Spectrum: Partially Melted Crustal Xenoliths from the Wudalianchi Volcanic Field, NE China. Science.gov (United States) McLeod, C. L.; McGee, L. E. 2015-12-01 Disequilibrium melting has been established as a common process occurring during crustal anatexis and thus demonstrates that crustal assimilation by ascending mantle-derived magmas is likley not a closed system. Observations of extreme compositional heterogeneity within partial melts derived from crustal xenoliths have been documented in several recent examples, however, the retention or transfer of elements to and from residues and glasses, and their relative contributions to potential crustal contaminants warrants further investigation. Sampled lavas from the Huoshaoshan volcano in the Holocene Wudalianchi volcanic field of Northeast China contain crustal xenoliths which preserve a spectrum of partial melting both petrographically and geochemically, thus providing an excellent, natural example of crustal anatexis. Correlations exist between the volume of silicic glass preserved within the xenoliths and bulk rock SiO2 (70-83 wt%), Al2O3 (16-8 wt%), glass 87Sr/86Sr (0.715-0.908), abundances of elements common in feldspars and micas (Sr, Ba, Rb) and elements common in accessory minerals (Y, Zr, Nb). These correlations are likely associated with the consumption of feldspars and micas and the varying retention of accessory phases during partial melting. The xenoliths which contain the greater volumes of silicic glass and residual quartz (interpreted as being the most melted) were found within pahoehoe lava, whilst the least melted xenoliths were found within scoria of the summit cone of Huoshaoshan; thus it is interpreted that the extent of melting is linked to the immersion time in the lava. Small-scale (mm) mingling and transfer of material from the enclosing lava to the xenolith is observed, however, modelling of potential contaminant compositions is inconsistent with crustal contamination during lava petrogenesis. It is inferred that crustal contamination in sampled lavas is localized within the open magmatic system and most likely occurs at the contact zone 15. Peridotite-melt interaction: A key point for the destruction of cratonic lithospheric mantle Institute of Scientific and Technical Information of China (English) ZHANG HongFu 2009-01-01 This paper presents an overview of recent studies dealing with different ages of mantle peridotitic xenoliths and xenocrysts from the North China Craton, with aim to provide new ideas for further study on the destruction of the North China Craton. Re-Os isotopic studies suggest that the lithospheric mantle of the North China Craton is of Archean age prior to its thinning. The key reason why such a low density and highly refractory Archean lithospheric mantle would be thinned is changes in composition, thermal regime, and physical properties of the lithospheric mantle due to interaction of peridotites with melts of different origins. Inward subducUon of circum craton plates and collision with the North China Craton provided not only the driving force for the destruction of the craton, but also continuous melts derived from partial melting of subducted continental or oceanic crustal materials that resulted in the compositional change of the lithospheric mantle. Regional thermal anomaly at ca. 120 Ma led to the melting of highly modified iithospheric mantle. At the same time or subsequently lithospheric extension and asthenospheric upwelling further reinforced the melting and thinning of the lithospheric mantle. Therefore, the destruction and thinning of the North China Craton is a combined result of peridotite-melt interaction (addition of volatile), enhanced regional thermal anomaly (temperature increase) and lithospheric extension (decompression). Such a complex geological process finally produced a "mixed" lithospheric mantle of highly chemical heterogeneity during the Mesozoic and Cenozoic. It also resulted in significant difference in the composition of mantle peridotitic xenoliths between different regions and times. 16. Melting mechanism in monolayers of flexible rod-shaped molecules DEFF Research Database (Denmark) Hansen, Flemming Yssing; Taub, H. 1992-01-01 mechanism for melting in monolayers of flexible rod-shaped molecules. Melting requires the formation of vacancies in the monolayer by molecular motion perpendicular to the surface. This ‘‘footprint reduction’’ mechanism implies that strictly two-dimensional theories of melting are inapplicable... 17. How to detect melting in laser heating diamond anvil cell Institute of Scientific and Technical Information of China (English) 杨留响 2016-01-01 Research on the melting phenomenon is the most challenging work in the high pressure/temperature field. Until now, large discrepancies still exist in the melting curve of iron, the most interesting and extensively studied element in geoscience research. Here we present a summary about techniques detecting melting in the laser heating diamond anvil cell. 18. Elongational viscosity of monodisperse and bidisperse polystyrene melts DEFF Research Database (Denmark) Nielsen, Jens Kromann; Rasmussen, Henrik K.; Hassager, Ole 2006-01-01 The start-up and steady uniaxial elongational viscosity have been measured for two monodisperse polystyrene melts with molecular weights of 52 and 103 kg/mole, and for three bidisperse polystyrene melts. The monodisperse melts show a maximum in the steady elongational viscosity vs. the elongation... 19. The thermal physical properties and structure of In-In2Bi eutectic at melting-crystallization process Directory of Open Access Journals (Sweden) V. Prokhorenko 2007-04-01 Full Text Available The physical properties of In-In2Bi liquid eutectic alloy as well as structure has been studied at different temperature. Structure data are used for calculation of configuration entropy. The change of structure upon melting is analyzed in comparison with change chemical bonding. The data on acoustic emission studies at meting and crystallization processes are analyzed too. 20. Stress Relaxation in Entangled Polymer Melts DEFF Research Database (Denmark) Hou, Ji-Xuan; Svaneborg, Carsten; Everaers, Ralf; 2010-01-01 We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts. The data allow us to explore the chain dynamics and the shear relaxation modulus, G(t), into the plateau regime for chains with Z=40 entanglements and into the t......We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts. The data allow us to explore the chain dynamics and the shear relaxation modulus, G(t), into the plateau regime for chains with Z=40 entanglements...... excellent agreement for the Likhtman-McLeish theory using the double reptation approximation for constraint release, if we remove the contribution of high-frequency modes to contour length fluctuations of the primitive chain.... 1. Are polymer melts “ideal”? Science.gov (United States) Wittmer, J. P.; Beckrich, P.; Crevel, F.; Huang, C. C.; Cavallo, A.; Kreer, T.; Meyer, H. 2007-07-01 It is commonly accepted that in concentrated solutions or melts high-molecular weight polymers display random-walk conformational properties without long-range correlations between subsequent bonds. This absence of memory means, for instance, that the bond-bond correlation function, P(s), of two bonds separated by s monomers along the chain should exponentially decay with s. Presenting numerical results and theoretical arguments for both monodisperse chains and self-assembled (essentially Flory size-distributed) equilibrium polymers we demonstrate that some long-range correlations remain due to self-interactions of the chains caused by the chain connectivity and the incompressibility of the melt. Suggesting a profound analogy with the well-known long-range velocity correlations in liquids we find, for instance, P(s) to decay algebraically as s. Our study suggests a precise method for obtaining the statistical segment length b in a computer experiment. 2. Melting of metallic intermediate level waste Energy Technology Data Exchange (ETDEWEB) Huutoniemi, Tommi; Larsson, Arne; Blank, Eva [Studsvik Nuclear AB, Nykoeping (Sweden) 2013-08-15 This report presents a feasibility study of a melting facility for core components and reactor internals. An overview is given of how such a facility for treatment of intermediate level waste might be designed, constructed and operated and highlights both the possibilities and challenges. A cost estimate and a risk analysis are presented in order to make a conclusion of the technical feasibility of such a facility. Based on the authors' experience in operating a low level waste melting facility, their conclusion is that without technical improvements such a facility is not feasible today. This is based on the cost of constructing and operating such a facility, in conjunction with the radiological risks associated with operation and the uncertain benefits to disposal and long term safety. 3. Melts at the Lithosphere-Asthenosphere Boundary beneath the Basin and Range, US (Invited) Science.gov (United States) Plank, T.; Gazel, E.; Bendersky, C.; Forsyth, D. W.; Rau, C. J.; Lee, C. 2010-12-01 The Transportable Array component of EarthScope is providing an unparalleled view of the seismic structure of the mantle beneath the North American continent. In volcanically active regions such as the Basin and Range province of the western US, petrological data can also be used to constrain the temperature, water content, and depth of melting within the mantle, all of which may contribute to seismic velocity anomalies. Of particular interest to dynamic models is the location and evolution of the lithosphere-asthenosphere boundary (LAB), for which petrological and seismological data yield complementary constraints. The LAB is a rheological boundary that may strongly relate to the locus and mode of melting, whether by upwelling, hydration or extension. Here we present a preliminary integration of mantle melting depths, derived from the chemical composition of basaltic scoria from recent cinder cones across the Basin and Range, with shear velocity structure derived from inversion of Rayleigh waves. Primitive basaltic magmas record in their major element composition the pressures and temperatures of last equilibration in the mantle. Specifically, the Fe content of primary melts scales with melting temperature (through olivine-melt equilibrium) and the Si content scales inversely with pressure (through olivine-orthopyroxene melt equilibrium). Independent of these relationships, the water content of magmas affects estimated temperatures (roughly 100 C per 3 wt percent H2O), and the ferric Fe component affects estimated pressures or depths (15-20 km per 15 percent Fe3+). Our efforts have thus gone into measuring the pre-eruptive H2O content of Basin and Range magmas, using undegassed melt inclusions trapped in olivine, and their oxidation state, based on sulfur and vanadium speciation. Our results thus far for volcanic fields in the Western Grand Canyon (AZ), St. George (UT), and Crater Flat (NV) regions, indicate melt equilibration depths around 55-70 km. These depths 4. Nuclear reactor melt arrest and coolability device Energy Technology Data Exchange (ETDEWEB) Theofanous, Theo G.; Dinh, Nam Truc; Wachowiak, Richard M. 2016-06-14 Example embodiments provide a Basemat-Internal Melt Arrest and Coolability device (BiMAC) that offers improved spatial and mechanical characteristics for use in damage prevention and risk mitigation in accident scenarios. Example embodiments may include a BiMAC having an inclination of less than 10-degrees from the basemat floor and/or coolant channels of less than 4 inches in diameter, while maintaining minimum safety margins required by the Nuclear Regulatory Commission. 5. Holographic picture of heavy vector meson melting Energy Technology Data Exchange (ETDEWEB) Braga, Nelson R.F.; Diles, Saulo [Universidade Federal do Rio de Janeiro, Instituto de Fisica, Rio de Janeiro, RJ (Brazil); Martin Contreras, Miguel Angel [Universidad de los Andes, High Energy Group, Department of Physics, Bogota (Colombia) 2016-11-15 The fraction of heavy vector mesons produced in a heavy ion collision, as compared to a proton-proton collision, serves as an important indication of the formation of a thermal medium, the quark-gluon plasma. This sort of analysis strongly depends on understanding the thermal effects of a medium like the plasma on the states of heavy mesons. In particular, it is crucial to know the temperature ranges where they undergo a thermal dissociation, or melting. AdS/QCD models are know to provide an important tool for the calculation of hadronic masses, but in general are not consistent with the observation that decay constants of heavy vector mesons decrease with excitation level. It has recently been shown that this problem can be overcome using a soft wall background and introducing an extra energy parameter, through the calculation of correlation functions at a finite position of anti-de Sitter space. This approach leads to the evaluation of masses and decay constants of S wave quarkonium states with just one flavor dependent and one flavor independent parameter. Here we extend this more realistic model to finite temperatures and analyze the thermal behavior of the states 1S, 2S and 3S of bottomonium and charmonium. The corresponding spectral function exhibits a consistent picture for the melting of the states where, for each flavor, the higher excitations melt at lower temperatures. We estimate for these six states the energy ranges in which the heavy vector mesons undergo a transition from a well-defined peak in the spectral function to complete melting in the thermal medium. A very clear distinction between the heavy flavors emerges, with the bottomonium state Υ(1S) surviving a deconfinement transition at temperatures much larger than the critical deconfinement temperature of the medium. (orig.) 6. Polarization effects in ionic solids and melts OpenAIRE Salanne, Mathieu; Madden, Paul A. 2015-01-01 Ionic solids and melts are compounds in which the interactions are dominated by electrostatic effects. However, the polarization of the ions also plays an important role in many respects as has been clarified in recent years thanks to the development of realistic polarizable interaction potentials. After detailing these models, we illustrate the importance of polarization effects on a series of examples concerning the structural properties, such as the stabilization of particular crystal stru... 7. Melts of garnet lherzolite: experiments, models and comparison to melts of pyroxenite and carbonated lherzolite Science.gov (United States) Grove, Timothy L.; Holbig, Eva S.; Barr, Jay A.; Till, Christy B.; Krawczynski, Michael J. 2013-01-01 Phase equilibrium experiments on a compositionally modified olivine leucitite from the Tibetan plateau have been carried out from 2.2 to 2.8 GPa and 1,380–1,480 °C. The experiments-produced liquids multiply saturated with spinel and garnet lherzolite phase assemblages (olivine, orthopyroxene, clinopyroxene and spinel ± garnet) under nominally anhydrous conditions. These SiO2-undersaturated liquids and published experimental data are utilized to develop a predictive model for garnet lherzolite melting of compositionally variable mantle under anhydrous conditions over the pressure range of 1.9–6 GPa. The model estimates the major element compositions of garnet-saturated melts for a range of mantle lherzolite compositions and predicts the conditions of the spinel to garnet lherzolite phase transition for natural peridotite compositions at above-solidus temperatures and pressures. We compare our predicted garnet lherzolite melts to those of pyroxenite and carbonated lherzolite and develop criteria for distinguishing among melts of these different source types. We also use the model in conjunction with a published predictive model for plagioclase and spinel lherzolite to characterize the differences in major element composition for melts in the plagioclase, spinel and garnet facies and develop tests to distinguish between melts of these three lherzolite facies based on major elements. The model is applied to understand the source materials and conditions of melting for high-K lavas erupted in the Tibetan plateau, basanite–nephelinite lavas erupted early in the evolution of Kilauea volcano, Hawaii, as well as younger tholeiitic to alkali lavas from Kilauea. 8. Glass forming ability of calcium aluminosilicate melts DEFF Research Database (Denmark) Moesgaard, Mette; Yue, Yuanzheng 2011-01-01 The glass forming ability (GFA) of two series of calcium aluminosilicate melts is studied by measuring their viscous behavior and crystallization tendency. The first series consists of five compositions on the joining line between the eutectic point of anorthite-wollastonite-tridymite and that of......The glass forming ability (GFA) of two series of calcium aluminosilicate melts is studied by measuring their viscous behavior and crystallization tendency. The first series consists of five compositions on the joining line between the eutectic point of anorthite......-wollastonite-tridymite and that of anorthite-wollastonite-gehlenite. The series includes the eutectic compositions as end members. The second series consists of five compositions on a line parallel to the joining line on the alumina rich side. In the present work, GFA is described in terms of glass stability, i.e., the ability of a glass....... However, this proportionality is only valid for comparison of the glasses in the same series of compositions. The eutectic composition of anorthite-wollastonite-tridymite is found to exhibit the highest GFA of the melts under investigation.... 9. Processing metallic glasses by selective laser melting Directory of Open Access Journals (Sweden) Simon Pauly 2013-01-01 Full Text Available Metallic glasses and their descendants, the so-called bulk metallic glasses (BMGs, can be regarded as frozen liquids with a high resistance to crystallization. The lack of a conventional structure turns them into a material exhibiting near-theoretical strength, low Young's modulus and large elasticity. These unique mechanical properties can be only obtained when the metallic melts are rapidly cooled to bypass the nucleation and growth of crystals. Most of the commonly known and used processing routes, such as casting, melt spinning or gas atomization, have intrinsic limitations regarding the complexity and dimensions of the geometries. Here, it is shown that selective laser melting (SLM, which is usually used to process conventional metallic alloys and polymers, can be applied to implement complex geometries and components from an Fe-base metallic glass. This approach is in principle viable for a large variety of metallic alloys and paves the way for the novel synthesis of materials and the development of parts with advanced functional and structural properties without limitations in size and intricacy. 10. Nucleation and undercooling of metal melt Institute of Scientific and Technical Information of China (English) 2000-01-01 The effects of thermodynamic and dynamic factors on nucleation process have been integrated in a theoretical formula representing the dependence of undercooling on parameters concerned. Moreover, a method to determine the kind and amount of the most effective catalyst in an undercooled melt has been acquired. The results show that the undercooling increases with the decreasing surface area of the most effective catalyst and the increasing cooling rate as the kind of the most effective catalyst is constant. It increases to a maximum value when the ratio of the surface area of catalyst (SvV) to the cooling rate of melt (Rc) decreases to a critical value. The maximum undecooling not only depends on the ratio of non-dimensional factor of activation energy for an atom to diffuse (φ) to non-dimensional factor of driving force for nucleus to form (ψ), but also depends on the contact angle of the most effective catalyst; the smaller the ratio of φ to ψ, the higher the maximum undercooling, but it does not exceed the value of 2/3 melting point; the smaller the contact angle of the most effective catalyst, the lower the maximum undercooling, and the smaller the requisite value of SvV/Rc for the maximum undercooling also. 11. Energetics of melts from thermal diffusion studies. Final report Energy Technology Data Exchange (ETDEWEB) Lesher, C.E. 1998-12-01 Most processes in geology are a consequence at some level of the flow of energy or mass. Heat conduction and chemical diffusion are examples of two of these sorts of flows which are driven by temperature and chemical potential imbalances, respectively. In the general case these flows may be coupled so that, for instance, a temperature gradient may result in a flow of mass as well as heat. This effect in liquids was demonstrated by Soret (1879) and bears his name. In gases or solids the phenomenon is given the general name thermal diffusion. It was the purpose of this research program to examine the Soret effect in molten silicates under laboratory conditions. Results of these experiments are used to evaluate the form and quantitative values of many thermodynamic and kinetic properties of silicate melts over a range of temperature, pressure, and bulk composition. The author published a comprehensive review and synthesis with a microscopic theoretical explanation for the effect at low pressure in silicate liquids of geological interest. He conducted experimental investigations of molecular diffusion in the absence of a thermal gradient through experiments involving dissolution of solid silicates in molten silicate and interdiffusion of species between miscible silicate liquids. Collectively these results enable the author to construct a more comprehensive model of molecular diffusion in magmatic liquids. He has applied this model to problems of magma mixing and crustal assimilation. 12. Studies of thermal dissolution of RDX in TNT melt Science.gov (United States) Suvorova, N. A.; Hamilton, V. T.; Oschwald, D. M.; Balakirev, F. F.; Smilowitz, L. B.; Henson, B. F. 2017-01-01 The thermal response of energetic materials is studied due to its importance in issues of material safety and surety. Secondary high explosives which melt before they thermally decompose present challenging systems to model due to the addition of material flow. Composition B is a particularly challenging system due to its multiphase nature with a low melt component (TNT) and a high melt component (RDX). The dissolution of RDX crystals in molten TNT at the temperature below RDX melting point has been investigated using hot stage microscopy. In this paper, we present data on the dissolution rate of RDX crystals in molten TNT as a function of temperature above the TNT melt. 13. Regional variability in sea ice melt in a changing Arctic OpenAIRE Perovich, Donald K.; Richter-Menge, Jacqueline A. 2015-01-01 In recent years, the Arctic sea ice cover has undergone a precipitous decline in summer extent. The sea ice mass balance integrates heat and provides insight on atmospheric and oceanic forcing. The amount of surface melt and bottom melt that occurs during the summer melt season was measured at 41 sites over the time period 1957 to 2014. There are large regional and temporal variations in both surface and bottom melting. Combined surface and bottom melt ranged from 16 to 294 cm, with a mean of... 14. New Evidences on the Process Sensitivity of Some Renewable Blends Based on Starch considering Their Melt Rheological Properties Directory of Open Access Journals (Sweden) Doina Dimonie 2016-01-01 Full Text Available The degradability and processability of new renewable materials based on starch and PVOH were studied using the melt flow index (MFI method by measuring the melt rheological properties which depend not only on the extrusion conditions and material formulation but also on the macromolecule characteristics which can be modified by chemical degradation. These results were correlated with other material properties like color and cross-linking degree. The obtained results show that flowing in the melted state of the studied materials is accompanied by a second process of chains chemical degradation. It was observed that, at the same level of additivation, under identical extrusion conditions, the melted blends with corn starch as main component are highly mechanically sensitive and degrade mostly by chains scission and those with PVOH as major component are highly temperature sensitive and degrade mainly by cross-linking. The obtained results show also that each PVOH-starch blend requires particular formulation and individual windows of melt processing conditions. These results are a good proof that the MFI method is a good path to study the degradability and moldability of process sensitive polymeric materials like those based on starch and PVOH. 15. Continental Crust Growth as a Result of Continental Collision: Ocean Crust Melting and Melt Preservation Science.gov (United States) Niu, Y.; Zhao, Z.; Zhou, S.; Zhu, D.; Dong, G.; Mo, X.; Xie, G.; Dong, X. 2010-12-01 The significance of the continental crust (CC) on which we live is self-evident. However, our knowledge remains limited on its origin, its way and rate of growth, and how it has acquired the “andesitic” composition from mantle derived magmas. Compared to rocks formed from mantle derived magmas in all tectonic settings, volcanic arc rocks associated with oceanic lithosphere subduction share some common features with the CC; both are relatively depleted in “fluid-insoluble” elements (e.g., Nb, Ta and Ti), but enriched in “fluid-soluble” elements (e.g., U, K and Pb). These chemical characteristics are referred to as the “arc-like signature”, and point to a genetic link between subduction-zone magmatism and CC formation, thus leading to the “island-arc” model widely accepted for the origin of the CC over the past 40 years. However, it has been recognized also that this “island-arc” model has several difficulties. These include (1) bulk arc crust (AC) is basaltic, whereas the bulk CC is andesitic [1]; (2) AC has a variably large Sr excess whereas the CC is Sr deficient [2]; and (3) AC production is mass-balanced by subduction-erosion and sediment recycling, thus contributing no new mass to CC growth, at least in the Phanerozoic [3,4]. Our data on magmatic rocks (both volcanic and intrusive) formed during the India-Asia continental collision (~65 - ~45Ma) [5] show a remarkable compositional similarity to the bulk CC with the typical “arc-like signature” [6]. Also, these syncollisional felsic rocks exhibit strong mantle isotopic signatures, implying that they were recently derived from a mantle source. The petrology and geochemistry of these syncollisional felsic rocks is most consistent with an origin via partial melting of upper oceanic crust (i.e., last fragments of underthrusting oceanic crust) under amphibolite facies conditions, adding net mantle-derived materials to form juvenile CC mass. This leads to the logical and testable hypothesis 16. Crystallization, recrystallization, and melting lines in syndiotactic polypropylene crystallized from quiescent melt and semicrystalline state due to stress-induced localized melting and recrystallization. Science.gov (United States) Lu, Ying; Wang, Yaotao; Fu, Lianlian; Jiang, Zhiyong; Men, Yongfeng 2014-11-13 Crystalline lamellar thickness in syndiotactic polypropylene (sPP) during crystallization from either isothermal molten or stretching induced localized melt states and during subsequent heating was investigated by means of temperature dependent small-angle X-ray scattering techniques. Well-defined crystallization lines where the reciprocal lamellar thickness is linearly dependent on crystallization temperature were observed. Unlike in the case of polybutene-1 where stretching crystallization line was shifted to direction of much smaller lamellar thickness (Macromolecules 2013, 46, 7874), the stretching induced crystallization line for sPP deviates from its corresponding isothermal crystallization line only slightly. Such phenomenon could be attributed to the fact that both crystallization processes from quiescent melt and stress induced localized melt are mediated in a mesomorphic phase in sPP. Subsequent heating of sPP after crystallization revealed the same melting behavior in both systems for the two kinds of crystallites obtained from either quiescent melt or stretching induced localized melt. Both of them underwent melting and recrystallization when the lamellar thickness was smaller than a critical value and melting directly without changing in thickness when the lamellar thickness was larger than the critical value. The melting behavior in sPP systems can be understood by considering the chain relaxation ability within crystalline phase and also can be used as evidence that the crystallization from molten state and stress-induced crystallization passed through the intermediate phase before forming crystallites. 17. Calculation Model of Mass Action Concentration for Mg-Al, Sr-Al and Ba-Al Melts and Determination of Their Thermodynamic Parameters Institute of Scientific and Technical Information of China (English) 2003-01-01 Based on the phase diagrams and the mass action law in combination with the coexistence theory of metallic melts structure, the calculation model of mass action concentration for Mg-Al, Sr-Al and Ba-Al was built, and their thermodynamic parameters were determined. The agreement between calculated and measured results shows that the model and the determined thermodynamic parameters can reflect the structural characteristics of relevant melts. However, the fact that the thermodynamic parameters from literature don′t give the value agree with the measured result may be due to unconformity of these parameters to real chemical reactions in metallic melts. 18. Lessons learnt from FARO/TERMOS corium melt quenching experiments Energy Technology Data Exchange (ETDEWEB) Magallon, D.; Huhtiniemi, I.; Hohmann, H. [Commission of the European Communities, Ispra (Italy). Joint Research Center 1998-01-01 The influence of melt quantity, melt composition, water depth and initial pressure on quenching is assessed on the basis of seven tests performed in various conditions in the TERMOS vessel of the FARO facility at JRC-Ispra. Tests involved UO{sub 2}-based melt quantities in the range 18-176 kg at a temperature of approximately 3000 K poured into saturated water. The results suggest that erosion of the melt jet column is an efficient contributor to the amount of break-up, and thus quenching, for large pours of corium melt. The presence of Zr metal in the melt induced a much more efficient quenching than in a similar test with no Zr metal, attributed to the oxidation of the Zr. Significant amounts of H{sub 2} were produced also in tests with pure oxidic melts (e.g. about 300 g for 157 kg melt). In the tests at 5.0 and 2.0 MPa good mixing with significant melt break-up and quenching was obtained during the penetration in the water. At 0.5 MPa, good penetration of the melt into the water could still be achieved, but a jump in the vessel pressurisation occurred when the melt contacted the bottom and part (5 kg) of the debris was re-ejected from the water. (author) 19. Regional variability in sea ice melt in a changing Arctic. Science.gov (United States) Perovich, Donald K; Richter-Menge, Jacqueline A 2015-07-13 In recent years, the Arctic sea ice cover has undergone a precipitous decline in summer extent. The sea ice mass balance integrates heat and provides insight on atmospheric and oceanic forcing. The amount of surface melt and bottom melt that occurs during the summer melt season was measured at 41 sites over the time period 1957 to 2014. There are large regional and temporal variations in both surface and bottom melting. Combined surface and bottom melt ranged from 16 to 294 cm, with a mean of 101 cm. The mean ice equivalent surface melt was 48 cm and the mean bottom melt was 53 cm. On average, surface melting decreases moving northward from the Beaufort Sea towards the North Pole; however interannual differences in atmospheric forcing can overwhelm the influence of latitude. Substantial increases in bottom melting are a major contributor to ice losses in the Beaufort Sea, due to decreases in ice concentration. In the central Arctic, surface and bottom melting demonstrate interannual variability, but show no strong temporal trends from 2000 to 2014. This suggests that under current conditions, summer melting in the central Arctic is not large enough to completely remove the sea ice cover. 20. Gallery of melt textures developed in Westerly Granite during high-pressure triaxial friction experiments Science.gov (United States) Moore, Diane E.; Lockner, David A.; Kilgore, Brian D.; Beeler, Nicholas M. 2016-09-23 IntroductionMelting occurred during stick-slip faulting of granite blocks sheared at room-dry, room-temperature conditions in a triaxial apparatus at 200–400 megapascals (MPa) confining pressure. Petrographic examinations of melt textures focused largely on the 400-MPa run products. This report presents an overview of the petrographic data collected on those samples, followed by brief descriptions of annotated versions of all the images.Scanning electron microscope (SEM) images of the starting materials and the three examined 400-MPa samples are presented in this report. Secondary-electron (SE) and backscattered-electron (BSE) imaging techniques were used on different samples. The SE images look down on the sawcut surfaces, yielding topographic and three-dimensional textural information. The BSE imaging was done on samples cut to provide cross-sectional views of the glass-filled shear band (or zone) that developed along the sawcut. Brightness in the BSE images increases with increasing mean atomic number of the material. Additional chemical information about the quenched melt and adjoining minerals was obtained using the energy dispersive system of the SEM during BSE examinations. However, the very narrow shear-band thicknesses and common occurrence of very fine lamellar compositional layering limited the usefulness of this technique for estimating melt chemistry. 1. Can slabs melt beneath forearcs in hot subduction zones? Science.gov (United States) Ribeiro, J.; Maury, R.; Gregoire, M. 2015-12-01 At subduction zones, thermal modeling predict that the shallow part of the downgoing oceanic crust (test the hypothesis that adakites are pristine slab melts. We find that adakites from Baja California and Philippines formed by two distinct petrogenetic scenarios. In Baja California, hydrous mantle melts mixed/mingled with high-pressure (HP) adakite-type, slab melts within a lower crustal (~30 km depth) magma storage region before stalling into the upper arc crust (~7-15 km depth). In contrast, in the Philippines, primitive mantle melts stalled and crystallized within lower and upper crustal magma storage regions to produce silica-rich melts with an adakitic signature. Thereby, slab melting is not required to produce an adakitic geochemical fingerprint in hot subduction zones. However, our results also suggest that the downgoing crust potentially melted beneath Baja California. 2. PRELIMINARY FRIT DEVELOPMENT AND MELT RATE TESTING FOR SLUDGE BATCH 6 (SB6) Energy Technology Data Exchange (ETDEWEB) Fox, K.; Miller, D.; Edwards, T. 2009-07-21 The Liquid Waste Organization (LWO) provided the Savannah River National Laboratory (SRNL) with a Sludge Batch 6 (SB6) composition projection in March 2009. Based on this projection, frit development efforts were undertaken to gain insight into compositional effects on the predicted and measured properties of the glass waste form and to gain insight into frit components that may lead to improved melt rate for SB6-like compositions. A series of Sludge Batch 6 (SB6) based glasses was selected, fabricated and characterized in this study to better understand the ability of frit compositions to accommodate uncertainty in the projected SB6 composition. Acceptable glasses (compositions where the Product Composition Control System (PCCS) Measurement Acceptability Region (MAR) predicted acceptable properties, good chemical durability was measured, and no detrimental nepheline crystallization was observed) can be made using Frit 418 with SB6 over a range of Na{sub 2}O and Al{sub 2}O{sub 3} concentrations. However, the ability to accommodate variation in the sludge composition limits the ability to utilize alternative frits for potential improvements in melt rate. Frit 535, which may offer improvements in melt rate due to its increased B2O3 concentration, produced acceptable glasses with the baseline SB6 composition at waste loadings of 34 and 42%. However, the PCCS MAR results showed that it is not as robust as Frit 418 in accommodating variation in the sludge composition. Preliminary melt rate testing was completed in the Melt Rate Furnace (MRF) with four candidate frits for SB6. These four frits were selected to evaluate the impacts of B{sub 2}O{sub 3} and Na{sub 2}O concentrations in the frit relative to those of Frit 418, although they are not necessarily candidates for SB6 vitrification. Higher concentrations of B{sub 2}O{sub 3} in the frit relative to that of Frit 418 appeared to improve melt rate. However, when a higher concentration of B{sub 2}O{sub 3} was coupled 3. Trace element evidence for anatexis at oceanic magma chamber roofs and the role of partial melts for contamination of fresh MORB Science.gov (United States) Fischer, Lennart A.; Erdmann, Martin; France, Lydéric; Wolff, Paul E.; Deloule, Etienne; Zhang, Chao; Godard, Marguerite; Koepke, Jürgen 2016-09-01 At oceanic spreading centers, interactions between magma and hydrothermal convecting systems trigger major physical, thermal, and chemical exchanges. The two-pyroxene hornfels recovered from the base of the sheeted dike sequence at Integrated Ocean Drilling Program (IODP) Site 1256 (equatorial Eastern Pacific) are interpreted as a conducting boundary layer between the underlying axial melt lens and the hydrothermally cooled sheeted dikes. They are cut by numerous small, felsic veins, which were recently interpreted as a product of hydrous partial melting of sheeted dikes. Here, we present trace element compositions of products (melts and residues) of hydrous partial melting experiments using basalts and hornfels from IODP Site 1256 as starting material. The experimental products generated between 910 °C and 970 °C match the natural lithologies from Site 1256 in terms of major and trace element compositions. The compositions of the anatectic melts correspond to the compositions of the felsic veins, while the residual minerals match the compositions of the two-pyroxene hornfels, evidencing that hydrous partial melting is an important magmatic process in the gabbro/dike transition of fast-spreading mid-oceanic ridges. Our results complement previous experimental studies on anatectic processes occurring at the roof of the magma chambers from fast-spreading mid-ocean ridges. Moreover, calculations of mixing and assimilation fractional crystallization using the experimental partial melts as contaminant/assimilant showed that anatectic melts can only be a minor contributor to the contamination process. 4. Experimental Results on Pouring and Underwater Liquid Melt Spreading and Energetic Melt-coolant Interaction OpenAIRE Konovalenko, Alexander; Karbojian, Aram; Kudinov, Pavel 2012-01-01 In a hypothetical light water reactor (LWR) core-melt accident with corium release from the reactor vessel, the ultimate containment integrity is contingent on coolability of the decay-heated core debris. Pouring of melt into a pool of water located in the reactor cavity is considered in several designs of existing and new LWRs as a part of severe accident (SA) management strategies. At certain conditions of melt release into the pool (e.g. large ratio of the vessel breach size... 5. Zircon saturation in silicate melts: a new and improved model for aluminous and alkaline melts Science.gov (United States) Gervasoni, Fernanda; Klemme, Stephan; Rocha-Júnior, Eduardo R. V.; Berndt, Jasper 2016-03-01 The importance of zircon in geochemical and geochronological studies, and its presence not only in aluminous but also in alkaline rocks, prompted us to think about a new zircon saturation model that can be applied in a wide range of compositions. Therefore, we performed zircon crystallization experiments in a range of compositions and at high temperatures, extending the original zircon saturation model proposed by Watson and Harrison (Earth Planet Sci Lett 64:295-304, 1983) and Boehnke et al. (Chem Geol 351:324-334, 2013). We used our new data and the data from previous studies in peraluminous melts, to describe the solubility of zircon in alkaline and aluminous melts. To this effect, we devised a new compositional parameter called G [ {( {3 \\cdot {{Al}}2 {{O}}3 + {{SiO}}2 )/({{Na}}2 {{O}} + {{K}}2 {{O}} + {{CaO}} + {{MgO}} + {{FeO}}} )} ] (molar proportions), which enables to describe the zircon saturation behaviour in a wide range of rock compositions. Furthermore, we propose a new zircon saturation model, which depends basically on temperature and melt composition, given by (with 1σ errors): ln [ {{Zr}} ] = ( {4.29 ± 0.34} ) - ( {1.35 ± 0.10} ) \\cdot ln G + ( {0.0056 ± 0.0002} ) \\cdot T( °C ) where [Zr] is the Zr concentration of the melt in µg/g, G is the new parameter representing melt composition and T is the temperature in degrees Celsius. The advantages of the new model are its straightforward use, with the G parameter being calculated directly from the molar proportions converted from electron microprobe measurements, the temperature calculated given in degrees Celsius and its applicability in a wider range of rocks compositions. Our results confirm the high zircon solubility in peralkaline rocks and its dependence on composition and temperature. Our new model may be applied in all intermediate to felsic melts from peraluminous to peralkaline compositions. 6. Effect of low temperature melt on solidification structure of A356 alloy with melt thermal treatment Institute of Scientific and Technical Information of China (English) 何树先; 王俊; 孙宝德; 周尧和 2001-01-01 The influence of the low temperature melt (LTM) structure on solidification structure of the sample with melt thermal treatment (MTT) process was studied. And the mechanism of the MTT process was analyzed with cluster theory. It is shown that the final solidification structure is dependent mainly on the structure of LTM. Dendrites will appear in the solidification structure if the structure of LTM is dendritic before MTT. Otherwise, non-dendritic grains will appear in the solidification structure. And the lower the temperature of LTM, the more remarkable the effect of the LTM structure is. 7. Silicic Arc Magmas And Silicic Slab Melts: The Melt-Rock Reaction Link Science.gov (United States) Straub, S. M.; Gomez-Tuena, A.; Bolge, L. L.; Espinasa-Perena, R.; Bindeman, I. N.; Stuart, F. M.; Zellmer, G. F. 2013-12-01 While a genetic link between silicic arc magmas and silicic melts from the subducted slab has long been proposed, this hypothesis is commonly refuted because most arc magmas lack a 'garnet-signature' which such slab melts must have. A comprehensive geochemical study of high-Mg# arc magmas from the Quaternary central Mexican Volcanic Belt (MVB), however, shows that this conflict can be reconciled if melt-rock reaction processes in the mantle wedge were essential to arc magma formation. In the central MVB, monogenetic and composite volcanoes erupt high-Mg# basalts to andesites with highly variable trace element patterns. These magmas contain high-Ni olivines (olivine Ni higher than permissible for olivines in partial peridotite melts) with high 3He/4He = 7-8 Ra that provide strong evidence for silicic slab components that infiltrate the subarc mantle to produce olivine-free segregations of 'reaction pyroxenite' in the sources of individual volcanoes. Melting of silica-excess and silica-deficient reaction pyroxenites can then produce high-Mg# basaltic and dacitic primary melts that mix during ascent through mantle and crust to form high-Mg# andesites. Mass balance requires that reaction pyroxenites contain at least >15-18 wt%, and likely more, of slab component. However, because the HREE of the slab component are efficiently retained in the eclogitic slab, elements Ho to Lu in partial melts from reaction pyroxenites remain controlled by the mantle and maintain MORB-normalized Ho/Lun ˜1.15 close to unity. In contrast, the MREE to LREE and fluid mobile LILE of the arc magmas are either controlled, or strongly influenced, by slab-contributions. The origin from hybrid sources also shows in the major elements that are blends of mantle-derived elements (Mg, Ca, Mn, Fe, Ti) and elements augmented by slab contributions (Si, Na, K, P, and possibly Al). Moreover, strong correlations between bulk rock SiO2, 87Sr/86Sr and δ18O (olivines) can be interpreted as mixtures of subarc 8. Study of macro- and micro-segregation of iridium in molybdenum single crystals after electron beam zone melting Energy Technology Data Exchange (ETDEWEB) Drapala, Jaromir; Skotnicova, Katerina [VSB-Technical University of Ostrava (Czech Republic). Dept. of Non-ferrous Metals, Refining and Recycling 2013-01-15 The aim of the work was to study the creation of micro- and macro-segregation of iridium in low-alloyed molybdenum single crystals after electron beam zone melting (floating zone technique) depending on various conditions of crystallization. In order to evaluate relations between the chemical inhomogeneity and structural defects and their influence on properties of single crystals, the dependence of concentration and character of distribution of admixtures under various crystallization conditions on the origin of concentration undercooling and dislocation substructure of molybdenum single crystals prepared by electron beam floating zone melting was experimentally investigated. 9. Lithosphere and Asthenosphere Properties beneath Oceans and Continents and their Relationship with Domains of Partial Melt Stability in the Mantle Science.gov (United States) Dasgupta, R. 2014-12-01 The depth of the lithosphere-asthenosphere boundary (LAB) and the change in properties across the lithosphere, asthenosphere, and LAB in various tectonic settings are captured in a variety of geophysical data, including seismic velocities and electrical conductivity. A sharp drop in shear wave velocity and increase in electrical conductivity can potentially be caused by the appearance of partial melt at or below the LAB but the chemical and dynamic stability of partial melt across lithosphere and at LAB remain debated. Here I apply the recent models of mantle melting in the presence of water and carbon [1, 2] to evaluate the domains of stability of partial melt both beneath continents and oceans. The model allows prediction of the possible presence, the fraction, and composition of partial melt as a function of depth, bulk C and H2O content, and fO2 [3] in various geologic/tectonic settings. The results show that while a hydrous, carbonated melt is stable only beneath LAB and in the asthenospheric mantle beneath oceans, continental mantle can contain a carbonate-rich melt within the lithosphere. For geotherms corresponding to surface heat flux (SHF) of 40-50 mW m-2, which also match P-T estimates beneath cratons based on thermo-barometry of peridotite xenoliths [4], the solidus of fertile peridotite with trace amount of CO2 and H2O is crossed at depths as shallow as 80-120 km [5]. If elevated geotherms of the Proterozoic and Phanerozoic terrains are applied, carbonatitic melt becomes stable somewhat shallower. These depths are similar to those argued for a mid-lithospheric discontinuity (MLD) where a negative velocity gradient has been detected much shallower than the proposed depth of LAB in many places. With a drop in oxygen fugacity with depth, a freezing of carbonatitic melt may be expected at intermediate depths (~150-200 km). At 200-250 km a hydrous, carbonated silicate melt may reappear owing to the interplay of fO2 and freezing point depression effect of CO 10. Critical porosity of melt segregation during crustal melting: Constraints from zonation of peritectic garnets in a dacite volcano Science.gov (United States) Yu, Xun; Lee, Cin-Ty A. 2016-09-01 The presence of leucogranitic dikes in orogenic belts suggests that partial melting may be an important process in the lower crust of active orogenies. Low seismic velocity and low electrical resistivity zones have been observed in the lower crust of active mountain belts and have been argued to reflect the presence of partial melt in the deep crust, but volcanoes are rare or absent above many of these inferred melt zones. Understanding whether these low velocity zones are melt-bearing, and if so, why they do not commonly erupt, is essential for understanding the thermal and rheologic structure of the crust and its dynamic evolution. Central to this problem is an understanding of how much melt can be stored before it can escape from the crust via compaction and eventually erupt. Experimental and theoretical studies predict trapped melt fractions anywhere from 30%. Here, we examine Mn growth-zoning in peritectic garnets in a Miocene dacite volcano from the ongoing Betic-Rif orogeny in southern Spain to estimate the melt fraction at the time of large-scale melt extraction that subsequently led to eruption. We show that the melt fraction at segregation, corresponding approximately to the critical melt porosity, was ∼30%, implying significant amounts of melt can be stored in the lower crust without draining or erupting. However, seismic velocities in the lower crust beneath active orogenic belts (southern Spain and Tibet) as well as beneath active magmatic zones (e.g., Yellowstone hotspot) correspond to average melt porosities of <10%, suggesting that melt porosities approaching critical values are short-lived or that high melt porosity regions are localized into heterogeneously distributed sills or dikes, which individually cannot be resolved by seismic studies. 11. Chemistry of Impact-Generated Silicate Melt-Vapor Debris Disks CERN Document Server Visscher, Channon 2013-01-01 In the giant impact theory for lunar origin, the Moon forms from material ejected by the impact into an Earth-orbiting disk. Here we report the initial results from a silicate melt-vapor equilibrium chemistry model for such impact-generated planetary debris disks. In order to simulate the chemical behavior of a two-phase (melt+vapor) disk, we calculate the temperature-dependent pressure and chemical composition of vapor in equilibrium with molten silicate from 2000 to 4000 K. We consider the elements O, Na, K, Fe, Si, Mg, Ca, Al, Ti, and Zn for a range of bulk silicate compositions (Earth, Moon, Mars, eucrite parent body, angrites, and ureilites). In general, the disk atmosphere is dominated by Na, Zn, and O2 at lower temperatures (< 3000 K) and SiO, O2, and O at higher temperatures. The high-temperature chemistry is consistent for any silicate melt composition, and we thus expect abundant SiO, O2, and O to be a common feature of hot, impact-generated debris disks. In addition, the saturated silicate vapor... 12. Manufacturing of implants by selective laser melting Directory of Open Access Journals (Sweden) Cosma Sorin Cosmin 2012-09-01 Full Text Available In recent years, digitizing and automation have gained an important place in fabrication of medical parts. Rapid Prototyping could be very suitable for medical applications due to their complex geometry, low volume and strong individualization. The presented study investigates the possibility to produce medical or dental parts by Selective Laser Melting (SLM. The SLM process is optimized and fully characterized for different biocompatible metal alloys, such as: TiAl6V4 and CoCrMo. The potential of SLM as medical manufacturing technique is proved by a developed procedure to fabricate frameworks for complex dental prostheses. 13. Thermodynamic Properties of Mn-C Melts Institute of Scientific and Technical Information of China (English) CHEN Er-bao; WANG Shi-jun 2008-01-01 Carbon solubility in Mn-Fe melts (xMn=0.161-0.706, xFe=0.034-0.633) was measured experimentally at various temperatures. By thermodynamic derivation and calculation, the relationship between activity coefficient of carbon in infinite dilute solution of manganese in Mn-C system and temperature was obtained. Using Gibbs-Duhem relationship, the experimental results of this study, and experimental data reported in references, the relationship between other thermodynamic properties in Mn-C system and temperature were obtained by thermodynamic derivation and calculation. 14. Analogue models of melt-flow networks in folding migmatites Science.gov (United States) Barraud, Joseph; Gardien, Véronique; Allemand, Pascal; Grandjean, Philippe 2004-02-01 We have modelled the formation and the layer-parallel shortening of layered (stromatic) migmatites. The model consists of thin superposed layers of partially molten microcrystalline wax. The melt (30 vol.%) has a negative buoyancy and a high viscosity contrast with its solid matrix. As soon as the shortening begins, melt-filled veins with high aspect ratios open along foliation. The melt is segregated into the veins, forming a stromatic layering. During incipient folding, crescent-shaped saddle reefs open at the hinges of open sinusoidal folds. Further shortening and melt-enhanced shear displacements on interlayer interfaces cause chevron folds to develop and the saddle reefs to become triangular. In comparison, a melt-free experiment shows only a few layer-parallel openings and no saddle reefs in chevron folds. On the basis of our experimental results, we propose that in migmatites: (1) mesoscale melt migration is a combination of flow in immobile veins and movements of veins as a whole; (2) the changes in the geometry of the mesoscale melt-flow network create the pressure gradients that drive melt migration; (3) the melt-flow network does not need to be fully interconnected to allow local expulsion; (4) melt expulsion is episodic because the temporal evolution of the network combines with the spatial heterogeneity of the deformation. 15. Chemical use Data.gov (United States) US Fish and Wildlife Service, Department of the Interior — This is a summary of research and activities related to chemical use on Neal Smith National Wildlife Refuge between 1992 and 2009. The chemicals used on the Refuge... 16. Chemical Reactors. Science.gov (United States) Kenney, C. N. 1980-01-01 Describes a course, including content, reading list, and presentation on chemical reactors at Cambridge University, England. A brief comparison of chemical engineering education between the United States and England is also given. (JN) 17. Exploring new concepts in directional solidification by electron beam melting and selective laser melting Science.gov (United States) Martinez, Edwin Unlike more conventional directional solidification, electron and laser-beam melting technologies involve building 3D components through layer-by-layer melt/solidification thermal cycling which creates novel, directional microstructural architectures. In this study we compared various the columnar microstructures of various components manufactured by EBM and SLM; image composite observations of columnar microstructural architectures in Cu, Co-29-Cr-6Mo-0.2C alloy, Ni-22Cr-9Mo-4Nb (alloy 625) fabricated by electron beam melting (EBM), and Ni-19Cr-19Fe-5Nb-1Al (alloy 718) by selective laser melting (SLM) as well as stainless steel 17-4 PH (SLM). Cu produced discontinuous columns of Cu2O precipitates while the Co-base alloy exhibited similar columns of Cr 23C6 precipitates. The alloy 625 produced columns of Ni 3Nb (Upsilon"-bct) precipitates. All of the EBM-produced columnar microstructure arrays were spaced ˜2 microm. In contrast, the SLM fabricated alloy 718 contained columnar microstructural arrays of Ni3 Nb (Upsilon") spaced ˜ 0.8microm, the 17-4 PH stainless steel produced martensitic structures dependent on the gas used for manufacturing. The manufactured components were observed by optical microscopy, SEM, XRD and by TEM in order to understand the microstructural development. 18. Rheological signatures of gelation and effect of shear melting on aging colloidal suspension Energy Technology Data Exchange (ETDEWEB) Jatav, Shweta; Joshi, Yogesh M, E-mail: [email protected] [Department of Chemical Engineering, Indian Institute of Technology, Kanpur (India) 2014-09-01 Colloidal suspensions that are out of thermodynamic equilibrium undergo physical aging wherein their structure evolves to lower the free energy. In aqueous suspension of Laponite, physical aging accompanies increases of elastic and viscous moduli as a function of time. In this work, we study temporal evolution of elastic and viscous moduli at different frequencies and observe that freshly prepared aqueous suspension of Laponite demonstrates identical rheological behavior reported for the crosslinking polymeric materials undergoing chemical gelation. Consequently at a certain time, tan δ is observed to be independent of frequency. However, for samples preserved under rest condition for longer duration before applying the shear melting, the liquid to solid transition subsequent to shear melting shows greater deviation from classical gelation. We also obtain continuous relaxation time spectra from the frequency dependence of viscous modulus. We observe that, with an increase in the rest time, continuous relaxation time spectrum shows gradual variation from negative slope, describing dominance of fast relaxation modes to positive slope representing dominance of slow relaxation modes. We propose that the deviation from gelation behavior for the shear melted suspensions originates from inability of shear melting to completely break the percolated structure thereby creating unbroken aggregates. The volume fraction of such unbroken aggregates increases with the rest time. For small rest times presence of fewer number of unbroken aggregates cause deviation from the classical gelation. On the other hand, at high rest times presence of greater fraction of unbroken aggregates subsequent to shear melting demonstrate dynamic arrest leading to inversion of relaxation time spectra. 19. Densification and grain coarsening of melting snow Institute of Scientific and Technical Information of China (English) 周石硚; 中尾正义; 桥本重将; 坂井亚规子; 成田英器; 石川信敬 2003-01-01 A field work was conducted at Moshiri in Japan.The work included intensive snow pit work, taking snow grain photos, recording snow and air temperatures, as well as measuring snow water content.By treating the snow as a viscous fluid, it is found that the snow compactive viscosity decreases as the density increases, which is opposite to the relation for dry snow.Based on the measurements of snow grain size, it is shown that, similar to the water-saturated snow, the frequency distributions of grain size at different times almost have the same shape.This reveals that the water-unsaturated melting snow holds the same grain-coarsening behavior as the water-saturated snow does.It is also shown that the water-unsaturated melting snow coarsens much more slowly than the water-saturated snow.The C value, which is the viscosity when the snow density is zero, is related to the mean grain size and found to decrease with increasing grain size.The decreasing rate of C value increases with decreasing grain-coarsening rate. 20. Nucleation and undercooling of metal melt Institute of Scientific and Technical Information of China (English) 坚增运; 常芳娥; 马卫红; 严文; 杨根仓; 周尧和 2000-01-01 The effects of thermodynamic and dynamic factors on nucleation process have been integrated in a theoretical formula representing the dependence of undercooling on parameters concerned. Moreover, a method to determine the kind and amount of the most effective catalyst in an undercooled melt has been acquired. The results show that the undercooling increases with the decreasing surface area of the most effective catalyst and the increasing cooling rate as the kind of the most effective catalyst is constant. It increases to a maximum value when the ratio of the surface area of catalyst ( Sv V) to the cooling rate of melt ( Rc) decreases to a critical value. The maximum undecooling not only depends on the ratio of non-dimensional factor of activation energy for an atom to diffuse (φ) to non-dimensional factor of driving force for nucleus to form (ψ), but also depends on the contact angle of the most effective catalyst; the smaller the ratio of φ to ψ, the higher the maximum undercooling, but it does not 1. Melting curve of materials: theory versus experiments Science.gov (United States) Alfè, D.; Vocadlo, L.; Price, G. D.; Gillan, M. J. 2004-04-01 A number of melting curves of various materials have recently been measured experimentally and calculated theoretically, but the agreement between different groups is not always good. We discuss here some of the problems which may arise in both experiments and theory. We also report the melting curves of Fe and Al calculated recently using quantum mechanics techniques, based on density functional theory with generalized gradient approximations. For Al our results are in very good agreement with both low pressure diamond-anvil-cell experiments (Boehler and Ross 1997 Earth Planet. Sci. Lett. 153 223, Hänström and Lazor 2000 J. Alloys Compounds 305 209) and high pressure shock wave experiments (Shaner et al 1984 High Pressure in Science and Technology ed Homan et al (Amsterdam: North-Holland) p 137). For Fe our results agree with the shock wave experiments of Brown and McQueen (1986 J. Geophys. Res. 91 7485) and Nguyen and Holmes (2000 AIP Shock Compression of Condensed Matter 505 81) and the recent diamond-anvil-cell experiments of Shen et al (1998 Geophys. Res. Lett. 25 373). Our results are at variance with the recent calculations of Laio et al (2000 Science 287 1027) and, to a lesser extent, with the calculations of Belonoshko et al (2000 Phys. Rev. Lett. 84 3638). The reasons for these disagreements are discussed. 2. Synthesis of SiC/Al Co-Continuous Composite by Spontaneous Melt Infiltration Institute of Scientific and Technical Information of China (English) 2000-01-01 @@Investigation has been made on the process of synthesizing SiC/Al co-continuous composite by spontaneous melt infiltration. It is found that nitrogen atmosphere is an indispensable factor for spontaneous infiltration of melt Al into SiC preform with continuous porosity. The critical temperature for spontaneous infiltration occurrence can be lowered and spontaneous infiltration rate increased by doping a small amount of Mg into the Al alloy. Adding fine SiO2 powders into the ceramic preform can play the similar role as Mg-doping by increasing wetting through the chemical reaction of 3SiO2+4Al=2Al2O3+3Si at the infiltration front. Infiltration rate can also be increased by Si-doping to lower the viscosity of the molten Al alloy. In addition, sufficient Si content in the molten Al is also indispensable to avoid the formation of Al4C in the synthesized composite. 3. Separation of primary solid phases from Al-Si alloy melts Directory of Open Access Journals (Sweden) Ki Young Kim 2014-07-01 Full Text Available The iron-rich solids formed during solidification of Al-Si alloys which are known to be detrimental to the mechanical, physical and chemical properties of the alloys should be removed. On the other hand, Al-Si hypereutectic alloys are used to extract the pure primary silicon which is suitable for photovoltaic cells in the solvent refining process. One of the important issues in iron removal and in solvent refining is the effective separation of the crystallized solids from the Al-Si alloy melts. This paper describes the separation methods of the primary solids from Al-Si alloy melts such as sedimentation, draining, filtration, electromagnetic separation and centrifugal separation, focused on the iron removal and on the separation of silicon in the solvent refining process. 4. Study of Reactive Melt Processing Behavior of Externally Plasticized Cellulose Acetate in Presence of Isocyanate Directory of Open Access Journals (Sweden) Rafael Erdmann 2014-12-01 Full Text Available Two types of externally plasticized cellulose acetate (CA were chemically modified using 4,4'-methylene diphenyl diisocyanate (MDI as crosslinking agent. Crosslinking was performed in the molten state by means of melt mixing in an internal mixer. The viscoelastic properties of the non-crosslinked, externally plasticized CA show typical temperature dependence, similar to conventional thermoplastics. A strong increase in storage modulus is observed with increasing crosslink density indicating that the crosslinked compounds exhibit predominately elastic response. The complex viscosity also increases considerably with increasing crosslink density and does not reach the typical Newtonian plateau at low radial frequencies any more. The viscoelastic properties correlate well with the data recorded online during reactive melt processing in the internal mixer. In comparison to the non-crosslinked CA, the crosslinked compounds show higher glass transition temperature, higher VICAT softening temperatures, improved thermal stability and lower plasticizer evaporation at evaluated temperatures. 5. Separation of primary solid phases from Al-Si alloy melts Institute of Scientific and Technical Information of China (English) Ki Young Kim 2014-01-01 The iron-rich solids formed during solidification of Al-Si aloys which are known to be detrimental to the mechanical, physical and chemical properties of the aloys should be removed. On the other hand, Al-Si hypereutectic alloys are used to extract the pure primary silicon which is suitable for photovoltaic cells in the solvent refining process. One of the important issues in iron removal and in solvent reifning is the effective separation of the crystalized solids from the Al-Si aloy melts. This paper describes the separation methods of the primary solids from Al-Si aloy melts such as sedimentation, draining, ifltration, electromagnetic separation and centrifugal separation, focused on the iron removal and on the separation of silicon in the solvent refining process. 6. Facile synthesis of a melt-spinnable polyborazine from asymmetric alkylaminoborazine Institute of Scientific and Technical Information of China (English) Yong Peng Lei; Ying De Wang; Yong Cai Song; Yi He Li; Hao Wang; Cheng Deng; Zheng Fang Xie 2010-01-01 A novel asymmetric alkylaminoborazine monomer,2-propylamino-4,6-bis(methylamino)borazine,was synthesized for the first time,and directly polymerized to give a melt-spinnable polyborazine(PBN).This asymmetric alkylaminoborazine was synthesized by an aminolysis reaction of 2,4,6-trichloroborazine(TCB)with different amines under mild conditions.This route turns out to be much cheaper and simpler than the conventional routes.The chemical composition,structure,molecular weights and ceramic yield were investigated by EA,FTIR,NMR,GPC and TG analysis.The PBN exhibits suitable rheological property for melt-spinning,which suggests that it is a potential precursor for BN fibers. 7. Distribution of siderophile and other trace elements in melt rock at the Chicxulub impact structure Science.gov (United States) Schuraytz, B. C.; Lindstrom, D. J.; Martinez, R. R.; Sharpton, V. L.; Marin, L. E. 1994-01-01 Recent isotopic and mineralogical studies have demonstrated a temporal and chemical link between the Chicxulub multiring impact basin and ejecta at the Cretaceous-Tertiary boundary. A fundamental problem yet to be resolved, however, is identification of the projectile responsible for this cataclysmic event. Drill core samples of impact melt rock from the Chichxulub structure contain Ir and Os abundances and Re-Os isotopic ratios indicating the presence of up to approx. 3 percent meteoritic material. We have used a technique involving microdrilling and high sensitivity instrumental neutron activation analysis (INAA) in conjunction with electron microprobe analysis to characterize further the distribution of siderophile and other trace elements among phases within the C1-N10 melt rock. 8. The Gao-Guenie impact melt breccia—Sampling a rapidly cooled impact melt dike on an H chondrite asteroid? Science.gov (United States) Schmieder, Martin; Kring, David A.; Swindle, Timothy D.; Bond, Jade C.; Moore, Carleton B. 2016-06-01 The Gao-Guenie H5 chondrite that fell on Burkina Faso (March 1960) has portions that were impact-melted on an H chondrite asteroid at ~300 Ma and, through later impact events in space, sent into an Earth-crossing orbit. This article presents a petrographic and electron microprobe analysis of a representative sample of the Gao-Guenie impact melt breccia consisting of a chondritic clast domain, quenched melt in contact with chondritic clasts, and an igneous-textured impact melt domain. Olivine is predominantly Fo80-82. The clast domain contains low-Ca pyroxene. Impact melt-grown pyroxene is commonly zoned from low-Ca pyroxene in cores to pigeonite and augite in rims. Metal-troilite orbs in the impact melt domain measure up to ~2 mm across. The cores of metal orbs in the impact melt domain contain ~7.9 wt% of Ni and are typically surrounded by taenite and Ni-rich troilite. The metallography of metal-troilite droplets suggest a stage I cooling rate of order 10 °C s-1 for the superheated impact melt. The subsolidus stage II cooling rate for the impact melt breccia could not be determined directly, but was presumably fast. An analogy between the Ni rim gradients in metal of the Gao-Guenie impact melt breccia and the impact-melted H6 chondrite Orvinio suggests similar cooling rates, probably on the order of ~5000-40,000 °C yr-1. A simple model of conductive heat transfer shows that the Gao-Guenie impact melt breccia may have formed in a melt injection dike ~0.5-5 m in width, generated during a sizeable impact event on the H chondrite parent asteroid. 9. Greenland Ice Sheet Melt from MODIS and Associated Atmospheric Variability Science.gov (United States) Hakkinen, Sirpa; Hall, Dorothy K.; Shuman, Christopher A.; Worthen, Denise L.; DiGirolamo, Nicolo E. 2014-01-01 Daily June-July melt fraction variations over the Greenland Ice Sheet (GIS) derived from the MODerate-resolution Imaging Spectroradiometer (MODIS) (2000-2013) are associated with atmospheric blocking forming an omega-shape ridge over the GIS at 500hPa height (from NCEPNCAR). Blocking activity with a range of time scales, from synoptic waves breaking poleward ( 5 days) to full-fledged blocks (5 days), brings warm subtropical air masses over the GIS controlling daily surface temperatures and melt. The temperature anomaly of these subtropical air mass intrusions is also important for melting. Based on the largest MODIS melt years (2002 and 2012), the area-average temperature anomaly of 2 standard deviations above the 14-year June-July mean, results in a melt fraction of 40 or more. Summer 2007 had the most blocking days, however atmospheric temperature anomalies were too small to instigate extreme melting. 10. Temperature dependence of densities of Sb and Bi melts Institute of Scientific and Technical Information of China (English) GENG HaoRan; SUN ChunJing; WANG Rui; QI XiaoGang; ZHANG Ning 2007-01-01 The densities of Sb and Bi melts were investigated by an improved Archimedean method. The results show that the density of the Sb melt decreases linearly with increasing temperature, but the density of the Bi melt firstly increases and then decreases as the temperature increases. There is a maximum density value of 10.002 g/cm3 at 310℃, about 39℃ above the melting point. The temperature dependence of the Sb melt is well fitted with the expression ρ= 6.8590-5.8105×10-4T, and that of the Bi melt is fitted with ρ=10.3312-1.18×10-3T. The results were discussed from a microstructure viewpoint. 11. Surface reconstruction precursor to melting in Au309 clusters OpenAIRE Fuyi Chen; Li, Z. Y.; Roy L. Johnston 2011-01-01 The melting of gold cluster is one of essential properties of nanoparticles and revisited to clarify the role played by the surface facets in the melting transition by molecular dynamics simulations. The occurrence of elaborate surface reconstruction is observed using many-body Gupta potential as energetic model for 309-atom (2.6 nm) decahedral, cuboctahedral and icosahedral gold clusters. Our results reveal for the first time a surface reconstruction as precursor to the melting transitions. ... 12. Theoretical study of a melting curve for tin Institute of Scientific and Technical Information of China (English) Xi Feng; Cai Ling-Cang 2009-01-01 The melting curve of Sn has been calculated using the dislocation-mediated melting model with the 'zone-linking method'. The results are in good agreement with the experimental data. According to our calculation, the melting temperature of γ-Sn at zero pressure is about 436 K obtained by the extrapolation of the method from the triple point of Sn. The results show that this calculation method is better than other theoretical methods for predicting the meltingcurve of polymorphic material Sn. 13. Melting of the Abrikosov flux lattice in anisotropic superconductors Science.gov (United States) Beck, R. G.; Farrell, D. E.; Rice, J. P.; Ginsberg, D. M.; Kogan, V. G. 1992-01-01 It has been proposed that the Abrikosov flux lattice in high-Tc superconductors is melted over a significant fraction of the phase diagram. A thermodynamic argument is provided which establishes that the angular dependence of the melting temperature is controlled by the superconducting mass anisotropy. Using a low-frequency torsional-oscillator technique, this relationship has been tested in untwinned single-crystal YBa2Cu3O(7-delta). The results offer decisive support for the melting proposal. 14. Study of Contact Melting Inside Isothermally Heated Vertical Cylindrical Capsules Institute of Scientific and Technical Information of China (English) ChenWenzhen; ChengShangmo; 等 1993-01-01 Close-contact melting processes of phase change material(PCM) inside vertical cylindrical capsule are studied.PCM are heated bhy the capsule isothermalyy at the bottom and side.The theoretical formulas of the melting rate and thickness of liquid layer during the heat transfer process are obtained by analysis,which are convenient for engineering predictions.Finally,the factors that affect melting are discussed.and conclusions are drawn. 15. Retrograde Melting and Internal Liquid Gettering in Silicon Energy Technology Data Exchange (ETDEWEB) Hudelson, Steve; Newman, Bonna K.; Bernardis, Sarah; Fenning, David P.; Bertoni, Mariana I.; Marcus, Matthew A.; Fakra, Sirine C.; Lai, Barry; Buonassisi, Tonio 2011-07-01 Retrograde melting (melting upon cooling) is observed in silicon doped with 3d transition metals, via synchrotron-based temperature-dependent X-ray microprobe measurements. Liquid metal-silicon droplets formed via retrograde melting act as efficient sinks for metal impurities dissolved within the silicon matrix. Cooling results in decomposition of the homogeneous liquid phase into solid multiple-metal alloy precipitates. These phenomena represent a novel pathway for engineering impurities in semiconductor-based systems. 16. CFD Modeling of Melt Spreading on the Reactor Cavity Floor Energy Technology Data Exchange (ETDEWEB) Yeon, Wan Sik; Bang, Kwang Hyun [Korea Maritime University, Busan (Korea, Republic of); Cho, Young Jo; Lee, Jae Gon [Korea Hydro and Nuclear Power Co., Daejeon (Korea, Republic of) 2010-05-15 In the very unlikely event of a severe reactor accident involving core melt and reactor pressure vessel failure, it is important to provide an accident management strategy that would allow the molten core material to cool down, resolidify and bring the core debris to a stable coolable state for Light Water Reactors (LWRs). One approach to achieve a stable coolable state is to quench the core melt after its relocation from the reactor pressure vessel into the reactor cavity. This approach typically requires a large cavity floor area on which a large amount of core melt spreads well and forms a shallow melt thickness for small thermal resistance across the melt pool. Spreading of high temperature (approx3000 K), low superheat (approx200 K) core melt over a wide cavity floor has been a key question to the success of the ex-vessel core coolability and it has brought a number of experimental work (CORINE, ECOKATS, VULCANO) and analytical work (CORFLOW, MELTSPREAD, THEMA). These computational models are currently able to predict well the spreading of stimulant materials but yet have shown a limitation for prototypic core melt of UO{sub 2}+ZrO{sub 2} mixture. A computational model for the melt spreading requires a multiphase treatment of liquid melt, solidified melt, and air. Also solidification and thermal radiation physics should be included. The present work uses ANSYS-CFX code to simulate core melt spreading on the reactor cavity. The CFX code is a general-purpose multiphase code and the present work is focused on exploring the code's capability to model melt spreading problem in a step by step approach 17. Tidal Heating and Melt Segregation and Migration within Io Science.gov (United States) Rajendar, A.; Paty, C. S.; Dufek, J.; Roberts, J. H. 2014-12-01 Io's volcanic activity is driven by the dissipation of energy in its interior due to tidal forces exerted by Jupiter, maintained by its orbital resonances with Europa and Ganymede. The 2011 discovery of a global partial melt layer beneath Io's surface has raised further questions about the structure of the Galilean moon and the processes that shape it. In this study we use two coupled simulations, the MFIX multiphase dynamics and the TiRADE tidal heating models, to investigate the location and extent, thermal state, melt fraction, stability, and migration of melt Io's viscous asthenosphere. We explore the feedback between melt migration and production, taking into account the rate of tidal heating and melt migration through the magma ocean layer. We begin with an assumed 1D layered internal structure based on previous investigations. This structure is input into TiRADE, which solves the equations of motion for forced oscillations in a layered spherical body using the propagator matrix method to obtain the displacements and strains due to tidal forcing. From this, we obtain the radial distribution of tidal heat generation within Io. This heating profile is then used as input for the MFIX multiphase fluid model in order to obtain the vertical flow of partially molten material, as well as the radial temperature distribution and thus the material properties and melt fractions. In the multiphase model, individual phases (melt and solid residue) separately conserve mass, momentum and enthalpy allowing us to explore melt segregation phenomena. Enthalpy closure is provided by the MELTS thermodynamics algorithm, which is called at each point in space, accounting for the partitioning between latent and sensible heat, and updating the physical properties of the melt and solid phases. This approach allows us to explore the sensitivity of melt generation to internal structure, as well as the time scales that govern melt production and eruption (i.e.: the residence and migration 18. Nitrogen distribution between aqueous fluids and silicate melts Science.gov (United States) Li, Yuan; Huang, Ruifang; Wiedenbeck, Michael; Keppler, Hans 2015-02-01 The partitioning of nitrogen between hydrous fluids and haplogranitic, basaltic, or albitic melts was studied at 1-15 kbar, 800-1200 °C, and oxygen fugacities (fO2) ranging from the Fe-FeO buffer to 3log units above the Ni-NiO buffer. The nitrogen contents in quenched glasses were analyzed either by electron microprobe or by secondary ion mass spectrometry (SIMS), whereas the nitrogen contents in fluids were determined by mass balance. The results show that the nitrogen content in silicate melt increases with increasing nitrogen content in the coexisting fluid at given temperature, pressure, and fO2. Raman spectra of the silicate glasses suggest that nitrogen species change from molecular N2 in oxidized silicate melt to molecular ammonia (NH3) or the ammonium ion (NH4+) in reduced silicate melt, and the normalized Raman band intensities of the nitrogen species linearly correlate with the measured nitrogen content in silicate melt. Elevated nitrogen contents in silicate melts are observed at reduced conditions and are attributed to the dissolution of NH3/NH4+. Measured fluid/melt partition coefficients for nitrogen (DNfluid/ melt) range from 60 for reduced haplogranitic melts to about 10 000 for oxidized basaltic melts, with fO2 and to a lesser extent melt composition being the most important parameters controlling the partitioning of nitrogen. Pressure appears to have only a minor effect on DNfluid/ melt in the range of conditions studied. Our data imply that degassing of nitrogen from both mid-ocean ridge basalts and arc magmas is very efficient, and predicted nitrogen abundances in volcanic gases match well with observations. Our data also confirm that nitrogen degassing at present magma production rates is insufficient to accumulate the atmosphere. Most of the nitrogen in the atmosphere must have degassed very early in Earth's history and degassing was probably enhanced by the oxidation of the mantle. 19. Differential melt scaling for oblique impacts on terrestrial planets Science.gov (United States) Abramov, Oleg; Wong, Stephanie M. Wong; Kring, David A. Kring 2012-01-01 Analytical estimates of melt volumes produced by a given projectile and contained in a given impact crater are derived as a function of impact velocity, impact angle, planetary gravity, target and projectile densities, and specific internal energy of melting. Applications to impact events and impact craters on the Earth, Moon, and Mars are demonstrated and discussed. The most probable oblique impact (45°) produces ∼1.6 times less melt volume than a vertical impact, and ∼1.6 and 3.7 times more melt volume than impacts with 30° and 15° trajectories, respectively. The melt volume for a particular crater diameter increases with planetary gravity, so a crater on Earth should have more melt than similar-size craters on Mars and the Moon. The melt volume for a particular projectile diameter does not depend on gravity, but has a strong dependence on impact velocity, so the melt generated by a given projectile on the Moon is significantly larger than on Mars. Higher surface temperatures and geothermal gradients increase melt production, as do lower energies of melting. Collectively, the results imply thinner central melt sheets and a smaller proportion of melt particles in impact breccias on the Moon and Mars than on Earth. These effects are illustrated in a comparison of the Chicxulub crater on Earth, linked to the Cretaceous–Tertiary mass extinction, Gusev crater on Mars, where the Mars Exploration Rover Spirit landed, and Tsiolkovsky crater on the Moon. The results are comparable to those obtained from field and spacecraft observations, other analytical expressions, and hydrocode simulations. 20. Melt dispersion and direct containment heating (DCH) experiments in the DISCO-H test facility Energy Technology Data Exchange (ETDEWEB) Meyer, L.; Albrecht, G.; Kirstahler, M.; Schwall, M.; Wachter, E.; Woerner, G. 2004-05-01 The DISCO-H Test Facility at Forschungszentrum Karlsruhe was set up to perform scaled experiments that simulate melt ejection scenarios under low system pressure in Severe Accidents in Pressurized Water Reactors (PWR). These experiments are designed to investigate the fluid-dynamic, thermal and chemical processes during melt ejection out of a breach in the lower head of a PWR pressure vessel at pressures below 2 MPa with an iron-alumina melt and steam. In the past, a detailed study of pressure and geometry effects on the fluid dynamics of the melt dispersion process had been performed with cold model fluids in the facility DISCO-C. The main components of the facility are scaled about 1:18 linearly to a large European pressurized water reactor. Standard test results are: pressure and temperature history in the RPV, the cavity, the reactor compartment and the containment, post test melt fractions in all locations with size distribution of the debris, video film in reactor compartment and containment (timing of melt flow and hydrogen burning), and pre- and post test gas analysis in the cavity and the containment. The results of six experiments are presented here. All experiments were done with 10.6 kg of iron-alumina melt (scaling to 16 m{sup 3} corium), and a hole of 56 mm diameter (1 m scaled) or 28 mm at the center of the lower head. For comparison with a similar experiment conducted in a larger scale (1:10), the basis experiment was performed with an open path from the reactor pit to the containment (open pit), with prototypical conditions concerning the steam driven ejection out of the RPV, and a containment atmosphere, that was part air and part steam at an elevated pressure, with 3 mole-% hydrogen. In this and other tests, hydrogen production and combustion occurred. In one experiment the hydrogen effect was excluded by using only nitrogen as driving gas and a pure air atmosphere in the containment. In some tests the direct path to the containment was closed 1. Creep of mafic dykes infiltrated by melt in the lower continental crust (Seiland Igneous Province, Norway) Science.gov (United States) Degli Alessandrini, G.; Menegon, L.; Malaspina, N.; Dijkstra, A. H.; Anderson, M. W. 2017-03-01 A dry mafic dyke from a continental lower-crustal shear zone in the Seiland Igneous Province (northern Norway) experienced syn-kinematic melt-rock interaction. Viscous shearing occurred at T ≈ 800 °C, P ≈ 0.75-0.95 GPa and was coeval with infiltration of felsic melt from adjacent migmatitic metapelites. The dyke has a mylonitic microstructure where porphyroclasts of orthopyroxene, clinopyroxene and plagioclase are wrapped by a fine-grained (4-7 μm) polyphase mixture of clinopyroxene + orthopyroxene + plagioclase + quartz + ilmenite ± K-feldspar ± apatite. Microstructural observations and electron backscatter diffraction analysis indicate that the porphyroclasts deformed by a combination of dislocation glide and fracturing, with only a limited record of dislocation creep, recovery and dynamic recrystallization. We identified diffusion creep as the dominant deformation mechanism in the mixture based on the small grain size, phase mixing and weak crystallographic preferred orientation of all phases (interpreted as the result of oriented grain growth during viscous flow). The polyphase mixture did not form by dynamic recrystallization or by mechanical fragmentation of the porphyroclasts, but rather by melt-rock interaction. Thermodynamic models indicate that the syn-kinematic mineral assemblage results from the chemical interaction between a pristine mafic dyke and ca. 10 vol.% of felsic melt infiltrating from the adjacent partially molten metapelites. Extrapolation of laboratory-derived flow laws to natural conditions indicates that the formation of interconnected layers of fine-grained reaction products deforming by diffusion creep induces a dramatic weakening in the mafic granulites, with strain rates increasing up to 2-3 orders of magnitude. The reaction weakening effect is more efficient than the weakening associated with melt-assisted diffusion creep in the presence of up to 10 vol.% of infiltrated melt without formation of fine-grained reaction products 2. Impact melt of the lunar Crisium multiring basin Science.gov (United States) Spudis, P. D.; Sliz, M. U. 2017-02-01 New geological mapping of the Crisium basin on the Moon has revealed exposures of the basin impact melt sheet. The melt sheet has a feldspathic highland composition, somewhat more mafic than the melt sheet of the Orientale basin, but less mafic than comparable deposits around the Imbrium basin. These newly recognized deposits would be ideal locations to directly sample Crisium basin impact melt, material whose study would yield insight into the composition of the lunar crust, the time of formation of the basin, and the large impact process. 3. Variation of hydrogen level in magnesium alloy melt Institute of Scientific and Technical Information of China (English) XU Si-xiang; WU Shu-sen; MAO You-wu; AN Ping; GAO Pei-qing 2006-01-01 At present there is no commercial instrument available for measurement of hydrogen level in magnesium alloy melt in front of melting fumace. In this paper the equations of solubility of hydrogen in pure magnesium and magnesium alloy have been modified based on thermodynamic analysis. A fast measurement system for hydrogen content in magnesium melt was set up. With this instrument,measurement experiments have been carried out to determine hydrogen level in AZ91 melt. The hydrogen level varies from 6 cm3/100 g to 14 cm3/100 g at the temperature range between 650 ℃and 750 ℃. 4. Unified analysis of pressure melting of ice around horizontal columns Institute of Scientific and Technical Information of China (English) LIU Feng; CHEN Wenzhen; MENG Bin; GONG Miao 2007-01-01 The contact melting processes of ice, caused by pressure under the two-dimension axisymmetric horizontal columns, are generally studied. The unified mathematical expressions of the characteristic parameters for the pressure contact melting processes are obtained. Applying these expressions to the analysis of the pressure contact melting of ice around the horizontal cylinder, elliptical cylinder and flat plate, the related results in the published literatures are obtained, which prove the correctness and validity of the expressions. In addition, the expressions for the pressure contact melting of ice around the wedge-shaped object are also derived. 5. Melting of bcc Transition Metals and Icosahedral Clustering Energy Technology Data Exchange (ETDEWEB) Ross, M; Boehler, R; Japel, S 2006-05-26 In contrast to polyvalent metals, transition metals have low melting slopes(dT/dP) that are due to partially filled d-bands that allow for a lowering of liquid phase energy through s-d electron transfer and the formation of local structures. In the case of bcc transition metals we show the apparent discrepancy of DAC melting measurements with shock melting of Mo can be understood by reexamining the shock data for V and Ta and introducing the presence of an icosahedral short range order (ISRO) melt phase. 6. Surface reconstruction precursor to melting in Au309 clusters Directory of Open Access Journals (Sweden) Fuyi Chen 2011-09-01 Full Text Available The melting of gold cluster is one of essential properties of nanoparticles and revisited to clarify the role played by the surface facets in the melting transition by molecular dynamics simulations. The occurrence of elaborate surface reconstruction is observed using many-body Gupta potential as energetic model for 309-atom (2.6 nm decahedral, cuboctahedral and icosahedral gold clusters. Our results reveal for the first time a surface reconstruction as precursor to the melting transitions. The surface reconstruction lead to an enhanced melting temperature for (100 faceted decahedral and cuboctahedral cluster than (111 faceted icosahedral gold cluster, which form a liquid patch due to surface vacancy. 7. Experimental Studies on Partial Melting of Massive Samples of Granite Institute of Scientific and Technical Information of China (English) 林强; 吴福元 1994-01-01 As a basis of modern petrology,the equilibrium relations describing the melting of granite were established mainly on melting experiments of Powder samples.Such experiments,however,have serious limitations in providing information about the variations in compositional and fabric features of the minerals and in the composition and distribution of the melt.Our experiments using massive samples indicate that melt occure mainly at the quartz-plagioclase and quartz-potash feldspar boundaries and the composition of the melt is dependent on local characteristics in the melting system,showing no correlation with the bulk composition of the rock samples.At lower temperatures(740-760℃,0.2GPa),the melt plots at or near the eutectic point in Q-Ab-Or-An-H2O diagram,indicating equilibrium melting.At higher temperatures(790-800℃，0.2GPa)the melt becomes lower in SiO2 and higher in Na2O,deviating makedly from the eutectic line but without disappearance of any mineral phase,suggesting a non-equilibrium process.It is obvious that the phase-equilibrium relations in natural massive granites may be greatly different from those deduced from powder experiments. 8. Partial melting of metavolcanics in amphibolite facies regional metamorphism Indian Academy of Sciences (India) Alan Bruce Thompson 2001-12-01 Metavolcanic rocks containing low-Ca amphiboles (gedrite, cummingtonite) and biotite can undergo substantial dehydration-melting. This is likely to be most prominent in Barrovian Facies Series (kyanite-sillimanite) and occurs at the same time as widespread metapelite dehydration- melting. In lower pressure facies series, metavolcanics will be represented by granulites rich in orthopyroxene when dehydration occurs at much lower temperatures than melting. In higher pressure facies series it is not well known whether metavolcanic rocks dehydrate or melt at temperatures lower or similar to that of metapelites. 9. Mg Alloy Foam Fabrication via Melt Foaming Method Institute of Scientific and Technical Information of China (English) Donghui YANC; Changhwan SEO; Bo-Young HUR 2008-01-01 For the first time AZ91 (MgAl9Zn1) and AM60 (MgAl6) Mg alloy foams with homogeneous pore structures were prepared successfully via melt foaming method using CaCO3 as blowing agent. It is revealed that the blowing gas to foam the melt is not CO2 but CO, which comes from liquid-solid reaction between Mg melt. The reaction temperature is more than 100℃ lower than CaCO3 decomposition, which makes Mg alloy melts foam into cellular structure much more easily in the temperature range from 690℃ to 750℃. 10. Analysis of solidification and melting of Pcm with energy generation Energy Technology Data Exchange (ETDEWEB) Jiji, Latif M. [Department of Mechanical Engineering, The City College of the City University of New York, New York, NY 10031 (United States); Gaye, Salif [Ecole Superieure Polytechnique, Enseignant a l' ESP BP A10, Universite Cheikh Anta Diop, Thies (Senegal) 2006-04-01 One-dimensional solidification and melting of a slab with uniform volumetric energy generation is examined analytically. A sudden change in surface temperature triggers phase transformation and interface motion. Analytic solutions are obtained using a quasi-steady approximation. Unlike solidification, the melting case is characterized by a pure liquid phase and a mixture of solid and liquid at the fusion temperature. The solution is governed by a single energy generation parameter. Temperature profiles, interface location and steady state conditions are presented for solidification and melting. Results are applied to two examples: solidification of a nuclear material and melting of ice. [Author]. 11. Arctic melt ponds and bifurcations in the climate system CERN Document Server Sudakov, Ivan; Golden, Kenneth M 2014-01-01 Understanding how sea ice melts is critical to climate projections. In the Arctic, melt ponds that develop on the surface of sea ice floes during the late spring and summer largely determine their albedo$-$a key parameter in climate modeling. Here we explore the possibility of a simple sea ice climate model passing through a bifurcation point$-an irreversible critical threshold as the system warms, by incorporating geometric information about melt pond evolution. This study is based on a nonlinear phase transition model for melt ponds, and bifurcation analysis of a simple climate model with ice - albedo feedback as the key mechanism driving the system to a potential bifurcation point. 12. Redox Equilibrium of Niobium in Calcium Silicate Base Melts Science.gov (United States) Mirzayousef-Jadid, A.-M.; Schwerdtfeger, Klaus 2010-10-01 The oxidation state of niobium has been determined at 1873 K (1600 °C) in CaO-SiO2-NbO x melts with CaO/SiO2 ratios (mass pct) of 0.66, 0.93 and 1.10, and 5.72 to 11.44 pct Nb2O5 (initial). The slag samples were equilibrated with gas phases of controlled oxygen pressure, then quenched to room temperature and analyzed chemically. The niobium is mainly pentavalent with small amounts in the tetravalent state. It was found that the Nb5+/Nb4+ ratio increases with oxygen pressure at a constant CaO/SiO2 ratio and constant content of total niobium, closely according to the ideal law of mass action, which is proportional to {text{p}}_{{{text{O}}2 }}^{1/4} . The ratio also increases with total niobium content, and it seems to have a maximum at a basicity of about 0.93. The color of the solidified slag samples is described and is explained with the help of transmission spectra. 13. The Dynamics of Nanoparticles in Polymer Solutions and Melts Science.gov (United States) Mukhopadhyay, Ashis; Alam, Sharmine; Kohli, Indermeet 2014-03-01 Polymer nanocomposites (PNCs) has received a lot of attention in the recent years because of their potential applications in fabricating materials with novel mechanical, electrical, and photonic properties. The mobility of nanoparticles (NPs) play crucial role in determining various properties of PNC systems. Computer simulations and recent experiments have suggested that properties such as the toughness of a composite depend upon particle mobility. Even nanocomposites with self-healing'' properties that can restore strength in damaged regions have been proposed and some early work of their feasibility has been demonstrated. In this talk I will present some of our experimental work on the diffusion of nano-sized gold particles in polymer solutions and melt. Unusually fast diffusion of NPs when their size is smaller than the tube diameter in an entangled polymer was observed. Comparison with current theories and simulations will be shown. If time permits, our recent results on gold nanorod diffusion in polymer solution using polarized fluorescence correlation spectroscopy will be presented. Acknowledgements are made to the Donors of the American Chemical Society Petroleum Research fund (PRF # 51694-ND10) for support of this research. 14. Hot-melt extrusion technology and pharmaceutical application. Science.gov (United States) Wilson, Matthew; Williams, Marcia A; Jones, David S; Andrews, Gavin P 2012-06-01 The use of hot-melt extrusion (HME) within the pharmaceutical industry is steadily increasing, due to its proven ability to efficiently manufacture novel products. The process has been utilized readily in the plastics industry for over a century and has been used to manufacture medical devices for several decades. The development of novel drugs with poor solubility and bioavailability brought the application of HME into the realm of drug-delivery systems. This has specifically been shown in the development of drug-delivery systems of both solid dosage forms and transdermal patches. HME involves the application of heat, pressure and agitation through an extrusion channel to mix materials together, and subsequently forcing them out through a die. Twin-screw extruders are most popular in solid dosage form development as it imparts both dispersive and distributive mixing. It blends materials while also imparting high shear to break-up particles and disperse them. HME extrusion has been shown to molecularly disperse poorly soluble drugs in a polymer carrier, increasing dissolution rates and bioavailability. The most common difficulty encountered in producing such dispersions is stabilization of amorphous drugs, which prevents them from recrystallization during storage. Pharmaceutical industrial suppliers, of both materials and equipment, have increased their development of equipment and chemicals for specific use with HME. Clearly, HME has been identified as an important and significant process to further enhance drug solubility and solid-dispersion production. 15. Steroid monochloroacetates : Physical-chemical characteristics and use in gas-liquid chromatography NARCIS (Netherlands) Molen, H.J. van der; Groen, D.; Maas, J.H. van der 1965-01-01 Synthesis and physical-chemical characteristics (melting points, infrared-, visible- and ultraviolet spectra, paper-,thin-layer- and gas-liquid Chromatographie behaviour) of monochloroacetate derivatives of steroids representing the androstane-, pregnane-, estrane- and cholestane series are describe 16. Thermal barrier ZrO2 - Y2O3 obtained by plasma spraying method and laser melting Directory of Open Access Journals (Sweden) K. Kobylańska–Szkaradek 2006-04-01 Full Text Available Purpose: Purpose: The aim of the paper is to determine the influence of laser melting upon the selected physical properties of ZrO2 - Y2O3 ceramic coatings deposited by APS (Air Plasma Spraying method on super-alloys which function as TBC (Thermal Barriers Coatings.Design/methodology/approach: Laser melting which helps eliminate pores and other structural defects of coatings should contribute to the improvement of their density and durability as thermal barriers. In order to prove the assumptions made in the paper, coatings featuring varied porosity and deposited upon the nickel base super-alloys surface with the initially sprayed NiCrAlY bond coat have been subjected to laser melting and then their structure, thermal conductivity and thermal life prediction in the conditions of cyclic temperature changes from 20 to 1200ºC have been examined.Findings: It has been revealed that the coatings featuring low porosity laser melted on part of their thickness and heated up to about 700ºC demonstrate the highest thermal life prediction under the conditions mentioned and at slightly lower thermal conductivity.Research limitations/implications: Low wettability of metal by ceramic which results from various surface tensions of these materials is the cause of their lower adhesion to the substrate during laser melting all through their thickness. It is so because delaminations occur between phases the boundary and cracks.Practical implications: The worked out conditions of laser melting might be used in the process of creation of TBC which feature high working durability upon super-alloy elements.Originality/value: It has been found that homogenization of chemical composition of coatings occurs during laser melting leading to the reduction of ZrO2 - Y2O3 phase with monoclinic lattice participation as well as to the reduction of structural stresses which accompany this phase transformation during heating and cooling process. 17. Melting curve of the deep mantle applied to properties of early magma ocean and actual core-mantle boundary Science.gov (United States) Andrault, Denis; Lo Nigro, Giacomo; Bolfan-Casanova, Nathalie; Bouhifd, Mohamed A.; Garbarino, Gaston; Mezouar, Mohamed 2010-05-01 Our planet experienced partial melting early in its history as a consequence of energy release due to accretion. Partial mantle melting could still happen today in the lowermost mantle. Occurrence of melting is primordial for the chemical segregation between the different Earth's reservoirs and for the dynamics of the whole planet. Melting of iron-alloys is relatively easy to achieve, but the silicated mantle happens to be more refractory. We investigated experimentally melting properties of two starting material, forsterite and chondritic-mantle, at pressures ranging from 25 to 140 GPa, using laser-heated diamond anvil cell coupled with synchrotron radiation. We show that partial melting in the lowermost mantle, as suggested by seismology on the basis of the ultra-low velocity zones (ULVZ), requires temperatures above 4200 K at the core-mantle boundary. At low pressures, our curve plots significantly lower than previous reports. Compared to recent estimates of mantle geotherm, while this temperature remains possible if the Earth's core is very hot, it is more likely that ULVZs correspond to high concentration of incompatible elements driven down to the D"-layer by subducting slabs or extracted out from the outer core. When our chondritic melting curve is coupled with recent isentropic temperature profiles for a magma ocean, we obtain a correlation between magma ocean depth and the potential temperature (Tp) at its surface; an ocean depth of 1000 km (equivalent to ~40 GPa) corresponds to Tp=2000 K, which happens to be significantly hotter than the estimated surface temperature of a sustained magma ocean. It emphasizes the importance of a lid at the magma ocean surface at an epoch as early as that of core-mantle segregation. 18. Using a low melting solvent mixture to extract value from wood biomass Science.gov (United States) Hiltunen, Jaakko; Kuutti, Lauri; Rovio, Stella; Puhakka, Eini; Virtanen, Tommi; Ohra-Aho, Taina; Vuoti, Sauli 2016-09-01 Green chemistry, sustainability and eco-efficiency are guiding the development of the next generation of industrial chemical processes. The use of non-edible lignocellulosic biomass as a source of chemicals and fuels has recently raised interest due to the need for an alternative to fossil resources. Valorisation mainly focuses on cellulose, which has been used for various industrial scale applications for decades. However, creating an economically more viable value chain would require the exploitation of the other main components, hemicellulose and lignin. Here, we present a new low melting mixture composition based in boric acid and choline chloride, and demonstrate its efficiency in the fractionation of wood-based biomass for the production of non-condensed lignin, suitable for further use in the search for sustainable industrial applications, and for the selective conversion of hemicelluloses into valuable platform chemicals. 19. Constraints on Structure and Melting of Heterogeneous Plumes From Laboratory Experiments With Three Components Science.gov (United States) Harris, A. C.; Kincaid, C.; Kelley, K. A. 2007-12-01 Many studies of chemical geodynamics consider the fate of a single, compositionally distinct layer at the base of the mantle, but subducted oceanic lithosphere introduces two distinct lithologies (higher-density eclogite and lower-density harzburgite) into the mantle (a third lithology, intermediate-density lherzolitic peridotite). To address the dynamic complexities of interactions between these materials, we conducted three-dimensional laboratory experiments that use glucose syrup (Rayleigh number: 106\\)) to model the mantle and a two-layer subducted lithosphere. The viscosity and density of the syrup are controlled by its water content, which is varied to simulate the distinct physical properties of each of the three lithologies. Experiments were conducted in a 20cc tank, heated from below to create a basal thermal boundary layer (BTBL). The two-layer glucose slab was frozen and placed within the tank, where it sank into the BTBL. These experiments produced heterogeneous upwellings with temporal and spatial variations in both temperature and composition that are much more complex than predicted by classic plume theory. Temperature, composition, and distribution of material in the tank through space and time were recorded during each experiment. We scale these data to mantle-equivalent conditions and address the observational implication for melting such heterogeneous plumes, both within larger (200 - 600 km) plume heads and smaller (<100 km) trailing conduits. Results show length scales of chemical heterogeneity range from <10 km up to 300 km. Thermal heterogeneity was often correlated with composition, where the denser, eclogite analog had higher temperatures than the lighter, harzburgite analog. Distinct domains form within plumes and melting begins at different depths, dependent on the temperature and composition of each domain and the solidus of each composition (e.g. eclogite melts at lower temperatures than harzburgite). The combination of thermo-chemical 20. Mantle differentiation and chemical cycling in the Archean (Invited) Science.gov (United States) Lee, C. 2010-12-01 Differentiation of Earth’s silicate mantle is largely controlled by solid-state convection. Today, upwelling mantle leads to decompression melting. Melts, being of low density, rise to form the continental and oceanic crusts. Because many trace elements, such as heat-producing U, Th and K, as well as the noble gases, preferentially partition into melts, melt extraction concentrates these elements into the crust or atmosphere. However, one by-product of whole-mantle convection is that melting during the Earth’s first billion years was likely deep and hot. Such high pressure melts may have been dense, allowing them to stall, crystallize and later founder back into the lower mantle. These sunken lithologies would have ‘primordial’ chemical signatures despite a non-primordial origin. As the Earth cools, the proportion of upwards melt segregation relative to downwards melt segregation increases, removing volatiles and other incompatible elements to the surface. Recycling of these elements back into the Earth’s interior occurs by subduction, but because of chemical weathering, hydrothermal alteration and photosynthetic reactions occurring in the Earth’s exosphere, these recycled materials may re-enter the mantle already chemically transformed. In particular, photosynthetic production of oxygen and, especially, the progressive oxygenation of the Earth’s atmosphere require removal of reduced carbon from the Earth’s surface. If such removal occurred by subduction, the mantle would have become progressively reduced. During the Archean and early Proterozoic, much of this material may have contributed to making cratonic mantle, and if so, cratonic mantle may have been assembled by reduced building blocks, perhaps explaining the origin of diamonds with organic carbon isotopic signatures. The origin of peridotitic diamonds in cratonic mantle could then be explained if the underlying convecting mantle was in fact more oxidizing such that carbonatitic liquids 1. Kinetic Pathways of the DNA Melting Transition CERN Document Server Santos, Aaron 2012-01-01 We investigate kinetic pathways of the DNA melting transition using variable-range versions of the Poland-Scheraga (PS) and Peyrard-Dauxois-Bishop (PDB) models of DNA. In the PS model, we construct a phi^4-field theory to calculate the critical droplet profile, the initial growth modes, and the exponent characterizing the divergence of the susceptibility near the spinodal. In the PDB model, we use a mean field analysis to calculate susceptibility exponent. We compare these theoretical results with Monte Carlo and Brownian dynamic simulations on the PS and PDB models, respectively. We find that by increasing the range of interaction, the system can be brought close to a pseudospinodal, and that in this region the nucleating droplet is diffuse in contrast to the compact droplets predicted by classical nucleation theory. 2. Pb isotopes during mingling and melting DEFF Research Database (Denmark) Waight, Tod Earle; Lesher, Charles E. 2010-01-01 Pb isotopic data are presented for hybrid rocks formed by mingling between mantle-derived tholeiitic magma of the Eocene Miki Fjord macrodike (East Greenland) and melt derived from the adjacent Precambrian basement. Bulk mixing and AFC processes between end-members readily identified in the field...... fail to model the Pb isotope systematics. Selective contamination during diffusional exchange, which can explain the complex Sr and Nd isotope compositions of the hybrid rocks (Blichert-Toft et al., 1992), cannot fully account for the variability of the Pb isotopic data using the identified crustal end......-members. The crustal anatectic end-member, although similar in Sr and Nd isotope composition, has a markedly different Pb isotopic composition than its source gneiss. The differences are consistent with preferential incorporation of radiogenic Pb from accessory phases such as metamict zircon or loosely-bound Pb from... 3. Spherical foam growth in Al alloy melt Institute of Scientific and Technical Information of China (English) SHANG; Jintang; HE; Deping 2005-01-01 Due to the demand of high-tech Al alloy foam with spherical pores, high strength and high energy-absorption capacity has become one of the research foci. The aim of this study is to ascertain the growth regularity of spherical foam in Al alloy melt. Three-dimensional packing model such as face-centered cubic is established to study the spherical foam growth. Theoretical results are compared with experimental ones, and the face-centered cubic model corresponds well with the experiment. It is reasonable to assume that the pores have the same radius, the total pore number keeps unchanged and spherical foam grows with face-centered cubic packing mode. This study presents a useful help to control the average pore radius and film thickness. 4. Entangled Polymer Melts in Extensional Flow DEFF Research Database (Denmark) Hengeller, Ludovica Many commercial materials derived from synthetic polymers exhibit a complex response under different processing operations such as fiber formation, injection moulding,film blowing, film casting or coatings. They can be processed both in the solid or in the melted state. Often they may contain two...... or more different polymers in addition to additives, fillers or solvents in order to modify the properties of the final product. Usually, it is also desired to improve the processability. For example the supplement of a high molecular weight component improves the stability in elongational flows....... On the other hand, addition of low-volatility solvents to polymers is also a common industrial practice that others a means for lowering the Tg of the polymers. Moreover industrial polymers present a wide distribution of chain lengths and/or branched architectures that strongly influence their response... 5. Partial melting and the efficiency of mantle outgasing in one-plate planets Science.gov (United States) Plesa, Ana-Catalina; Breuer, Doris 2013-04-01 The generation of partial melting can have a major impact on the thermo-chemical evolution of a terrestrial body by the depletion of the mantle material in incompatible elements such as radioactive elements and volatiles, crust formation and volcanic outgassing. During some period in the thermal history of a terrestrial planet, the temperature in regions of the upper mantle, either below tectonic plates or a stagnant lid, rises above the solidus - the temperature at which the mineral with the lowest melting temperature among those that form the silicate mantle mixture starts to melt. The melt than rises toward the surface, forms the crust, and releases volatiles into the atmosphere. In case of one-plate (stagnant lid) planets the thickness of the present-day crust can 'tell' us already about the efficiency of mantle melting and mantle degassing - the thicker the crust the more mantle material experienced melting and thus the more efficient can be the outgassing. However, it has been shown with parameterized convection models [1] but also 2-3D convection models [2] that crustal delamination is a common process in one-plate planets. Crustal delamination allows that possibly much more crust is produced during the entire evolution (and thus more mantle material experienced differentiation) than what is observed today, implying also more efficient outgassing than expected. Crustal delamination is therefore a process that may help to generate a substantial planetary atmosphere. In the present work we investigate the influence of partial melt on mantle dynamics and the volcanic outgassing of one-plate planets using the mantle convection code GAIA [3] in a 2D cylindrical geometry. We consider the depletion of the mantle, redistribution of radioactive heat sources between mantle and crust, as well as mantle dehydration and volcanic outgassing [4]. When melt is extracted to form the crust, the mantle material left behind is more buoyant than its parent material and depleted 6. Uranium and neodymium partitioning in alkali chloride melts using low-melting gallium-based alloys Directory of Open Access Journals (Sweden) Melchakov Stanislav Yu. 2015-12-01 Full Text Available Partitioning of uranium and neodymium was studied in a ‘molten chloride salt - liquid Ga-X (X = In or Sn alloy’ system. Chloride melts were based on the low-melting ternary LiCl-KCl-CsCl eutectic. Nd/U separation factors were calculated from the thermodynamic data as well as determined experimentally. Separation of uranium and neodymium was studied using reductive extraction with neodymium acting as a reducing agent. Efficient partitioning of lanthanides (Nd and actinides (U, simulating fission products and fissile materials in irradiated nuclear fuels, was achieved in a single stage process. The experimentally observed Nd/U separation factor valued up to 106, depending on the conditions. 7. Accretional Impact Melt From the L-Chondrite Parent Body Science.gov (United States) Wittmann, A.; Weirich, J. R.; Swindle, T. D.; Rumble, D.; Kring, D. A. 2009-05-01 MIL 05029, a unique achondritic Antarctic meteorite with L-chondritic affinity, has a medium-grained, well equilibrated texture of large poikilitic low-Ca pyroxenes that overgrew smaller, euhedral olivines. Plagioclase filled interstitial spaces and has an abundance that is twice that typical for L-chondrites, while Fe-Ni metal and troilite are strongly depleted in that respect. No relic clasts or shock features were found in the thin section analyzed. However, based on its chemical affinity to L-chondrites, MIL 05029 was classified as an impact melt. This is confirmed by its olivine and low-Ca pyroxene compositions, the Co content in Fe-Ni metal, and its oxygen isotopic composition that lies very close to that of L-chondrites. An igneous origin of MIL 05029 cannot be ruled out but would have to be reconciled with thermochronometric constraints for the formation of the ordinary chondrite parent bodies. These studies infer delayed accretion of the parent asteroids of the ordinary chondrites and, thus, insufficient heating from short-lived radiogenic isotopes to produce endogenic magmatism. Metallographic cooling rates of ˜2-22 °C/Ma in the temperature range between ˜700-400°C were determined on five zoned metal particles of MIL 05029. Thermal modeling showed that such cooling rates relate to metamorphic conditions at depths of 5-12 km on the L-chondrite parent body. For an impact to deposit material at this depth, scaling relationships for an impact event on the 100-200 km diameter parent asteroid require a 15 to 60 km diameter simple crater that produced a basal melt pool, in which MIL 05029 crystallized. Further constraints for the formation conditions of MIL 05029 were derived from three whole-rock samples that gave well-defined Ar-Ar plateau ages of 4.53±0.02 Ga. This age indicates the time at which MIL 05029 cooled below ˜180°C, the Ar-closure temperature of plagioclase. Considering its slow metallographic cooling, the impact event that formed MIL 05029 8. Water isotopic ratios from a continuously melted ice core sample Directory of Open Access Journals (Sweden) V. Gkinis 2011-06-01 Full Text Available A new technique for on-line high resolution isotopic analysis of liquid water, tailored for ice core studies is presented. We build an interface between an Infra Red Cavity Ring Down Spectrometer (IR-CRDS and a Continuous Flow Analysis (CFA system. The system offers the possibility to perform simultaneuous water isotopic analysis of δ18O and δD on a continuous stream of liquid water as generated from a continuously melted ice rod. Injection of sub μl amounts of liquid water is achieved by pumping sample through a fused silica capillary and instantaneously vaporizing it with 100 % efficiency in a home made oven at a temperature of 170 °C. A calibration procedure allows for proper reporting of the data on the VSMOW scale. We apply the necessary corrections based on the assessed performance of the system regarding instrumental drifts and dependance on humidity levels. The melt rates are monitored in order to assign a depth scale to the measured isotopic profiles. Application of spectral methods yields the combined uncertainty of the system at below 0.1 ‰ and 0.5 ‰ for δ18O and δD, respectively. This performance is comparable to that achieved with mass spectrometry. Dispersion of the sample in the transfer lines limits the resolution of the technique. In this work we investigate and assess these dispersion effects. By using an optimal filtering method we show how the measured profiles can be corrected for the smoothing effects resulting from the sample dispersion. Considering the significant advantages the technique offers, i.e. simultaneuous measurement of δ18O and δD, potentially in combination with chemical components that are traditionally measured on CFA systems, notable reduction on analysis time and power consumption, we consider it as an alternative to traditional isotope ratio mass spectrometry with the possibility to be deployed for field ice core studies. We present data acquired in the 9. Water isotopic ratios from a continuously melted ice core sample Directory of Open Access Journals (Sweden) V. Gkinis 2011-11-01 Full Text Available A new technique for on-line high resolution isotopic analysis of liquid water, tailored for ice core studies is presented. We built an interface between a Wavelength Scanned Cavity Ring Down Spectrometer (WS-CRDS purchased from Picarro Inc. and a Continuous Flow Analysis (CFA system. The system offers the possibility to perform simultaneuous water isotopic analysis of δ18O and δD on a continuous stream of liquid water as generated from a continuously melted ice rod. Injection of sub μl amounts of liquid water is achieved by pumping sample through a fused silica capillary and instantaneously vaporizing it with 100% efficiency in a~home made oven at a temperature of 170 °C. A calibration procedure allows for proper reporting of the data on the VSMOW–SLAP scale. We apply the necessary corrections based on the assessed performance of the system regarding instrumental drifts and dependance on the water concentration in the optical cavity. The melt rates are monitored in order to assign a depth scale to the measured isotopic profiles. Application of spectral methods yields the combined uncertainty of the system at below 0.1‰ and 0.5‰ for δ18O and δD, respectively. This performance is comparable to that achieved with mass spectrometry. Dispersion of the sample in the transfer lines limits the temporal resolution of the technique. In this work we investigate and assess these dispersion effects. By using an optimal filtering method we show how the measured profiles can be corrected for the smoothing effects resulting from the sample dispersion. Considering the significant advantages the technique offers, i.e. simultaneuous measurement of δ18O and δD, potentially in combination with chemical components that are traditionally measured on CFA systems, notable reduction on analysis time and power consumption, we consider it as an alternative to traditional isotope ratio mass spectrometry with the possibility to 10. Alternatives to SF{sub 6} for magnesium melt protection Energy Technology Data Exchange (ETDEWEB) Ricketts, N.J. [CAST CRC-CSIRO Manufacturing and Materials Technology, Pullenvale (Australia) 2007-07-01 Molten magnesium is typically protected from oxidation with sulphur hexafluoride (SF{sub 6}), an extremely potent greenhouse gas (GHG) with a long atmospheric lifetime. This paper examined gas alternatives to SF{sub 6} and discussed reasons why alternative systems have not been readily adopted by manufacturers. AM-cover is a blend of HFC-134a that uses either carbon dioxide (CO{sub 2}) or nitrogen (N) as a carrier gas. AM-cover was designed as a drop-in replacement for SF{sub 6}, and has been demonstrated to work as well or better than SF{sub 6}. However, a license fee must be paid for its use, and the active gas still produces GHGs. The use of CO{sub 2} and nitrogen can also be prohibitively expensive for some operators. Novec 612 is a liquid fluorinated ketone for use in magnesium cover gas applications. Novec 612 has been tested in a number of primary magnesium production facilities, and has been shown to provide effective protection against oxidation. However, the active component is expensive, and is only available from 1 supplier. Air is added to the gas to reduce the potential for the formation of toxic PFCs and PFIBs. CO{sub 2} snow is used to cool the surface of molten magnesium, lowering the magnesium vapour pressure to the point where oxygen exclusion is an effective melt protection system. A significant amount of CO{sub 2} is needed to start the process. While boron trifluoride has been successfully used to protect molten magnesium, it is highly toxic, and decomposes readily in moist air. Sulphuryl fluoride (SO{sub 2}F{sub 2}) has been considered as a magnesium melt protection device. However, it is a toxic chemical traditionally used to fumigate houses. Hydrofluoroethers (HFEs) are volatile liquids that evaporate into a moving stream of diluent gas. However, the ready availability of HFE makes it an attractive option for further research. A wide range of HFC and HFE gases are both commercially available and have the potential as cover gases for 11. Melt segregation evidence from a young pluton, Takidani Granodiorite (Japan) Science.gov (United States) Hartung, Eva; Caricchi, Luca; Floess, David; Wallis, Simon; Harayama, Satoru; Chiaradia, Massimo; Kouzmanov, Kalin 2016-04-01 We are presenting new petrological data from one of the youngest exposed plutons in the world, the Takidani Granodiorite (Japan), which has been suggested as a source for large volume ignimbrites (> 300km3). Takidani Granodiorite (1.54 Ma ± 0.23 Ma) is located within the active Norikura Volcanic Chain in the Northen Japan Alps and has been previously linked to large andesitic (1.76 Ma ± 0.17 Ma) and rhyolitic eruptions (1.75 Ma ± 0.17 Ma). The pluton is vertically zoned and consists of granites (67 to 68 wt.% SiO2) in the lower section, granodiorites (65 to 66 wt.% SiO2) in the middle section, a chemically more evolved fine-grained porphyritic unit (67 to 71 wt.% SiO2) near the roof and a marginal granodiorite at the roof (67 to 68 wt.% SiO2). The porphyritic texture of the more evolved unit near the roof indicates rapid crystallisation, which could be the result of the late intrusion of this unit at the roof of the magmatic system. However, no sharp contact is found between the underlying granodiorite and the porphyritic unit. Instead, a gradual change in rock fabric, whole-rock chemistry and mineralogy is observed suggesting that melt was extracted from the granodiorite. Electron microprobe analyses of plagioclases show three main crystal populations (Type I, II and III) with distinct anorthite and Fe contents. Type I plagioclase (An30-40) occurs dominantly within the marginal granodiorite at the roof. Type II plagioclase (An40-45) are common in the granodiorite and porphyritic unit. Type III plagioclase (An45-50) is predominantly present in the granite. All plagioclase populations share a common sodic rim (An22) across the different units. Takidani Granodiorite rocks are compared to crystallisation experiments from similar magmatic suites. Emplacement conditions of the Takidani Granodiorite are obtained from the latter as well as barometry, thermometry and hygrometry indicating that magmas were ultimately emplaced at around 200 MPa, 850° C to 875° C and 12. Observation of melting conditions in selective laser melting of metals (SLM) Science.gov (United States) Thombansen, U.; Abels, Peter 2016-03-01 Process observation in 3D printing of metals currently is one of the central challenges. Many companies strive to employ this additive manufacturing process in their production chains in order to gain competitive advantages through added flexibility in product design and embedded features. The new degrees of freedom are accompanied with the challenge to manufacture every detail of the product to the predefined specifications. Products with filigree internal structures for example require a perfect build to deliver the performance that was designed into these structures. Melting conditions determine properties such as grain structure and density of the finished part before it is sent to post processing steps. Monitoring of such melting conditions is still a challenge where the use of photodiodes, pyrometry and camera systems contribute to an overall picture that might identify errors or deviations during the build process. Additional considerations must be made to decide if these sensors are applied coaxially or from a lateral perspective. Furthermore, setting parameters of focal plane array (FPA) sensors are discussed and events that are seen in the machine vision image are compared against the pyrometry data. The resume of the experiments suggests the application of multiple sensors to the selective laser melting process (SLM) as they jointly contribute to an identification of events. These events need to be understood in order to establish cause effect relationships in the future. 13. Carbon-Carbon High Melt Coating for Nozzle Extensions Project Data.gov (United States) National Aeronautics and Space Administration — The High Melt Coating system is applied to a carbon-carbon structure and embeds HfC, ZrB2 in the outer layers. ACC High Melt builds on the time tested base material... 14. The investigation of melting process on the solar furnace Energy Technology Data Exchange (ETDEWEB) Suleimanov, S.Kh.; Bugakov, A.G. [Uubek Academy of Sciences, Materials Science Institute, Tashkent (Uzbekistan); Boehmer, M.; Fend, T. [DLR MD-ET, Cologne (Germany) 1999-03-01 The outcomes of a trial of new melting method on the solar furnace with horizontal optical axis by means of side fusion of rotatable ceramic sample with continuous restoration of the surface by charge is presented. The different development of the melting processes on the sample depending on the it's rotation speed is detected. (authors) 15. Joint electroreduction of lanthanum, gadolinium and boron in halide melts Directory of Open Access Journals (Sweden) Khushkhov KH.B. 2003-01-01 Full Text Available The joint electroreduction of La, Gd and B from chloride-fluoride melts has been studied by cyclic voltametry. Based on the analysis of voltamograms the possibility of electrosynthesis of lanthanum-gadolinium borides from chloride-fluoride melts has been shown. 16. Coatings with laser melt injection of ceramic particles NARCIS (Netherlands) de Hosson, J.T.M.; Ocelik, V.; de Oliveira, U.; Seal, S; Dahotre, NB; Moore, JJ; Suryanarayana, C; Agarwal, A 2003-01-01 The conditions for a successful Laser Melt Injection (LMI) of SiC and WC particles into the melt pool of Al8Si and Ti6Al4V alloys were studied experimentally and theoretically by FEM calculations. The laser employed is a high power Nd:YAG The formation of a relatively thick aluminium oxide layer on 17. Single scan vector prediction in selective laser melting NARCIS (Netherlands) Wits, W.W.; Bruins, R.; Terpstra, L.; Huls, R.A.; Geijselaers, H.J.M. 2015-01-01 In selective laser melting (SLM) products are built by melting layers of metal powder successively. Optimal process parameters are usually obtained by scanning single vectors and subsequently determining which settings lead to a good compromise between product density and build speed. This paper pro 18. Dislocations and melting in two and three dimensions DEFF Research Database (Denmark) Tallon, Jeffery L. 1980-01-01 Comments are presented on the recent theories of two-dimensional melting which envisage melting as proceeding via two second-order transitions comprising dislocation dipole dissociation followed by disclination dipole dissociation. It is suggested that if the configurational entropy is properly i... 19. Electrochemistry of the Oxofluoro Complexes of Boron in Fluoride Melts DEFF Research Database (Denmark) Polyakova, L.P.; Bukatova, G.A.; Polyakov, E.G. 1997-01-01 Electrochemical behavior of oxofluoro complexes of boron, synthesized both in situ in FLINAK melt and added into the melt as Na3B3O3F6 compound, was by linear voltammetry within the range of 570-750 oC. It was shown that in lower part of this range the electrochemical reduction of BOF2- complexes... 20. Heredity of Aluminum Melt Caused by Electric Pulse Modification (Ⅰ) Institute of Scientific and Technical Information of China (English) WANG Jian-zhong; QI Jin-gang; DU Hui-ling; ZHANG Zhen-bin 2007-01-01 The heredity of aluminum melt under the action of pulse electric field was investigated by means of the remelt experiment. A new hereditary criterion under this condition was proposed; in the meantime, the differential transferability of genetic carrier in activated melt among filial generations was validated with the aid of DSC. 1. Hexa-n-alkylcyclotrisiloxanes - synthesis, melting behaviour and polymerization NARCIS (Netherlands) Out, Gerardus J.J.; Klok, Harm-Anton; Möller, Martin; Oelfin, Dieter 1995-01-01 A homologous series of hexa-n-alkylcyclotrisiloxanes and poly(di-n-alkylsiloxane)s has been prepared with alkyl side groups varying in length between 4 and 10 carbon atoms. Melting transition enthalpies of the hexa-n-alkylcyclotrisiloxanes indicated a reversed odd-even effect, showing higher melting 2. Morphology and melt rheology of nylon 11/clay nanocomposites NARCIS (Netherlands) He, Xiaofeng; Yang, Jun; Zhu, Lianchao; Wang, Biao; Sun, Guangping; Lv, Pengfei; Phang, In Yee; Liu, Tianxi 2006-01-01 Nylon 11 (PA11)/clay nanocomposites have been prepared by melt-blending, followed by melt-extrusion through a capillary. Transmission electron microscopy shows that the exfoliated clay morphology is dominant for low nanofiller content, while the intercalated one is prevailing for high filler loading 3. Melt onset over Arctic sea ice controlled by atmospheric moisture transport Science.gov (United States) Mortin, Jonas; Svensson, Gunilla; Graversen, Rune G.; Kapsch, Marie-Luise; Stroeve, Julienne C.; Boisvert, Linette N. 2016-06-01 The timing of melt onset affects the surface energy uptake throughout the melt season. Yet the processes triggering melt and causing its large interannual variability are not well understood. Here we show that melt onset over Arctic sea ice is initiated by positive anomalies of water vapor, clouds, and air temperatures that increase the downwelling longwave radiation (LWD) to the surface. The earlier melt onset occurs; the stronger are these anomalies. Downwelling shortwave radiation (SWD) is smaller than usual at melt onset, indicating that melt is not triggered by SWD. When melt occurs early, an anomalously opaque atmosphere with positive LWD anomalies preconditions the surface for weeks preceding melt. In contrast, when melt begins late, clearer than usual conditions are evident prior to melt. Hence, atmospheric processes are imperative for melt onset. It is also found that spring LWD increased during recent decades, consistent with trends toward an earlier melt onset. 4. Analysis of Contact Melting Driven by Surface Heat Flux Around a Cylinder Institute of Scientific and Technical Information of China (English) Y.S. Zhao; W.Z. Chen; F.R. Sun; Z.Y. Chen 2008-01-01 The contact melting of phase change material around a moving horizontal cylindrical heat source, which descended under its own weight, is investigated in this article. A melting model under constant surface heat flux is established. The analytical results for thickness and pressure distributions inside melt layer and steady melting velocity are obtained by using contact melting theory. The melting law is discussed, and compared with that of contact melting driven by temperature difference. It is found that quasi-steady melting velocity is determined by heat flux of heat source, and the variation of heat source density has less effect on melting velocity. 5. Melting in the FeOsbnd SiO2 system to deep lower-mantle pressures: Implications for subducted Banded Iron Formations Science.gov (United States) Kato, Chie; Hirose, Kei; Nomura, Ryuichi; Ballmer, Maxim D.; Miyake, Akira; Ohishi, Yasuo 2016-04-01 Banded iron formations (BIFs), consisting of layers of iron oxide and silica, are far denser than normal mantle material and should have been subducted and sunk into the deep lower mantle. We performed melting experiments on Fe2SiO4 from 26 to 131 GPa in a laser-heated diamond-anvil cell (DAC). The textural and chemical characterization of a sample recovered from the DAC revealed that SiO2 is the liquidus phase for the whole pressure range examined in this study. The chemical compositions of partial melts are very rich in FeO, indicating that the eutectic melt compositions in the FeOsbnd SiO2 binary system are very close to the FeO end-member. The eutectic temperature is estimated to be 3540 ± 150 K at the core-mantle boundary (CMB), which is likely to be lower than the temperature at the top of the core at least in the Archean and Paleoproterozoic eons, suggesting that subducted BIFs underwent partial melting in a thermal boundary layer above the CMB. The FeO-rich melts formed by partial melting of the BIFs were exceedingly dense and therefore migrated downward. We infer that such partial melts have caused iron enrichment in the bottom part of the mantle, which may have contributed to the formation of ultralow velocity zones (ULVZs) observed today. On the other hand, solid residues left after the segregation of the FeO-rich partial melts have been almost pure SiO2, and therefore buoyant in the deep lower mantle to be entrained in mantle upwellings. They have likely been stretched and folded repeatedly by mantle flow, forming SiO2 streaks within the mantle "marble cake". Mantle packages enhanced by SiO2 streaks may be the origin of seismic scatterers in the mid-lower mantle. 6. Enhancing the Dyeability of Polypropylene Fibers by Melt Blending with Polyethylene Terephthalate Directory of Open Access Journals (Sweden) Fereshteh Mirjalili 2013-01-01 Full Text Available Attempts were made to modify polypropylene fibers by melt blending with polyethylene terephthalate in order to enhance the dyeability of the resultant fiber. Five blends of polypropylene/polyethylene terephthalate/compatibilizer were prepared and subsequently spun into fibers. Three disperse dyes were used to dye such modified fibers at boiling and 130°C. The dyeing performance of the blend fibers, as well as the morphological, chemical, thermal, and mechanical properties, of the corresponding blends was characterized by means of spectrophotometry, polarized optical microscopy, scanning electron microscopy (SEM, FT-IR spectroscopy, differential scanning calorimetry (DSC, and tensile testing. 7. Thermodynamic Modeling of Sulfide Capacity of Na2O-Containing Oxide Melts Science.gov (United States) Moosavi-Khoonsari, Elmira; Jung, In-Ho 2016-10-01 Thermodynamic modeling of the sulfide dissolution in the Na2O-FetO-CaO-MgO-MnO-Al2O3-SiO2 multicomponent slags was performed to investigate the desulfurization of hot metal using Na2O-containing fluxes. The dissolution behavior of sulfur in the melts was modeled using the modified quasi-chemical model in the quadruplet approximation. This model can take into account the short-range ordering and the reciprocal exchange reaction of cations and anions in oxy-sulfide slags. Experimental sulfide capacity data were well predicted from the model with only three model parameters. 8. Continuous melting and ion chromatographic analyses of ice cores. Science.gov (United States) Huber, T M; Schwikowski, M; Gäggele, H W 2001-06-22 A new method for determining concentrations of organic and inorganic ions in ice cores by continuous melting and contemporaneous ion chromatographic analyses was developed. A subcore is melted on a melting device and the meltwater produced is collected in two parallel sample loops and then analyzed simultaneously by two ion chromatographs, one for anions and one for cations. For most of the analyzed species, lower or equal blank values were achieved with the continuous melting and analysis technique compared to the conventional analysis. Comparison of the continuous melting and ion chromatographic analysis with the conventional analysis of a real ice core segment showed good agreement in concentration profiles and total amounts of ionic species. Thus, the newly developed method is well suited for ice core analysis and has the advantages of lower ice consumption, less time-consuming sample preparation and lower risk of contamination. 9. Effects of Melt Thermal Treatment on A356 Alloy Institute of Scientific and Technical Information of China (English) 2003-01-01 To increase the casting quality of hypoeutectic Al-Si alloys, the effects of melt thermal treatment on the solidification structure of the A356 alloy were analyzed by a factorial experiment, in which the overheated melt was mixed with the low temperature melt. Experimental results show that the elongation ratio and strength of the treated samples increase remarkably compared with the control sample. The primary dendrite size reduces dramatically and the dendrite changes from columnar to equiaxed, with a little change of the secondary dendrite arm spacing (SDAS).Combined with the measurement of the nucleation undercooling, it is concluded that the solidification structure and refining effect are dependent primarily on the low temperature melt. The refining mechanism is believed as a result of the multiplication of the nuclei in the melt thermal treatment procedure. 10. Crystallisation and Melting Behavior of Methyl Esters of Palm Oil Directory of Open Access Journals (Sweden) Cheng S. Foon 2006-01-01 Full Text Available The methyl esters of palm oil, which consists of saturated and unsaturated esters (0.6 to 95.9% unsaturation of the C12 to C18 fatty acids, solidify at the two temperature ranges, -52 to -45°C and -24 to 21°C, when the esters are cooled. When the esters are heated, they melt at two distinct temperatures, -25 and -33°C and a broad peak at -9 to 28°C. The heating thermograms also showed an exothermic crystallisation peak in between two endothermic melting peaks, indicating the occurrence of re-crystallisation of low melting methyl esters into higher melting point crystal and then melt again at higher temperature. 11. Modeling of velocity field for vacuum induction melting process Institute of Scientific and Technical Information of China (English) CHEN Bo; JIANG Zhi-guo; LIU Kui; LI Yi-yi 2005-01-01 The numerical simulation for the recirculating flow of melting of an electromagnetically stirred alloy in a cylindrical induction furnace crucible was presented. Inductive currents and electromagnetic body forces in the alloy under three different solenoid frequencies and three different melting powers were calculated, and then the forces were adopted in the fluid flow equations to simulate the flow of the alloy and the behavior of the free surface. The relationship between the height of the electromagnetic stirring meniscus, melting power, and solenoid frequency was derived based on the law of mass conservation. The results show that the inductive currents and the electromagnetic forces vary with the frequency, melting power, and the physical properties of metal. The velocity and the height of the meniscus increase with the increase of the melting power and the decrease of the solenoid frequency. 12. Melting Characteristics and Wettability of Binding Phase in Sinter Institute of Scientific and Technical Information of China (English) SHEN Feng-man; LI Guang-sen; DING Zhi-min; MU Lin 2009-01-01 The melting characteristics and wettability of the binding phase in high basicity sinter were studied.By changing nCaO:nFe2O3 (molar ratio of CaO to Fe2O3) as well as the percentage of MgO,SiO2,and Al2O3,the melting characteristics and wettability of the binding phase were discussed.The results indicated that the characteristic melting temperature was the lowest and wettability was the best at nCaO:nFe2O3=1:1 (without addition); the addition of MgO increased the characteristic melting temperature and contact angles; when the percentage of SiO2 or Al2O3 was 3%,the characteristic melting temperature was the lowest,whereas the contact angles increased with an increase in SiO2 and Al2O3 contents. 13. Finite size melting of spherical solid-liquid aluminium interfaces DEFF Research Database (Denmark) Chang, J.; Johnson, Erik; Sakai, T.; 2009-01-01 We have investigated the melting of nano-sized cone shaped aluminium needles coated with amorphous carbon using transmission electron microscopy. The interface between solid and liquid aluminium was found to have spherical topology. For needles with fixed apex angle, the depressed melting...... to the conclusion that the depressed melting temperature is not controlled solely by the inverse radius 1/R. Instead, we found a direct relation between the depressed melting temperature and the ratio between the solid-liquid interface area and the molten volume....... temperature of this spherical interface, with radius R, was found to scale linearly with the inverse radius 1/R. However, by varying the apex angle of the needles we show that the proportionality constant between the depressed melting temperature and the inverse radius changes significantly. This led us... 14. Controlled Growth of Rubrene Nanowires by Eutectic Melt Crystallization Science.gov (United States) Chung, Jeyon; Hyon, Jinho; Park, Kyung-Sun; Cho, Boram; Baek, Jangmi; Kim, Jueun; Lee, Sang Uck; Sung, Myung Mo; Kang, Youngjong 2016-03-01 Organic semiconductors including rubrene, Alq3, copper phthalocyanine and pentacene are crystallized by the eutectic melt crystallization. Those organic semiconductors form good eutectic systems with the various volatile crystallizable additives such as benzoic acid, salicylic acid, naphthalene and 1,3,5-trichlorobenzene. Due to the formation of the eutectic system, organic semiconductors having originally high melting point (Tm > 300 °C) are melted and crystallized at low temperature (Te = 40.8–133 °C). The volatile crystallizable additives are easily removed by sublimation. For a model system using rubrene, single crystalline rubrene nanowires are prepared by the eutectic melt crystallization and the eutectic-melt-assisted nanoimpinting (EMAN) technique. It is demonstrated that crystal structure and the growth direction of rubrene can be controlled by using different volatile crystallizable additives. The field effect mobility of rubrene nanowires prepared using several different crystallizable additives are measured and compared. 15. Spontaneous corneal melting in pregnancy: a case report Directory of Open Access Journals (Sweden) Arya Sudesh K 2007-11-01 Full Text Available Abstract Background To report a case of spontaneous corneal melting in pregnancy. We reviewed the literature on corneal melting and the effect of pregnancy on cornea and collagen containing tissues. Case presentation A 29-year-old woman who underwent radial keratotomy in both eyes followed by trabeculectomy in her left eye developed corneal melting in the same eye, in her seventh month of pregnancy. Despite screening, no infectious or immune mediated condition could be identified. She was managed conservatively with cyanoacrylate glue, bandage contact lens, lubricants and antibiotics. Conclusion It may not always be possible to find the underlying cause of corneal melting but the more common underlying causes should be ruled out by proper investigations. Pregnancy with its host of hormonal changes could potentially have some effect on corneal collagen leading to corneal melting in compromised corneas. 16. Melting of Boltzmann particles in different 2D trapping potential Science.gov (United States) Bhattacharya, Dyuti; Filinov, Alexei; Ghosal, Amit; Bonitz, Michael 2015-03-01 We analyze the quantum melting of two dimensional Wigner solid in several confined geometries and compare them with corresponding thermal melting in a purely classical system. Our results show that the geometry play little role in deciding the crossover quantum parameter nX, as the effects from boundary is well screened by the quantum zero point motion. The unique phase diagram in the plane of thermal and quantum fluctuations determined from independent melting criteria separates out the Wigner molecule phase'' from the classical and quantum liquids''. An intriguing signature of weakening liquidity with increasing temperature T have been found in the extreme quantum regime (n). This crossover is associated with production of defects, just like in case of thermal melting, though the role of them in determining the mechanism of the crossover appears different. Our study will help comprehending melting in a variety of experimental realization of confined system - from quantum dots to complex plasma. 17. Chemical sensors Science.gov (United States) Lowell, J.R. Jr.; Edlund, D.J.; Friesen, D.T.; Rayfield, G.W. 1991-07-02 Sensors responsive to small changes in the concentration of chemical species are disclosed. The sensors comprise a mechanochemically responsive polymeric film capable of expansion or contraction in response to a change in its chemical environment. They are operatively coupled to a transducer capable of directly converting the expansion or contraction to a measurable electrical response. 9 figures. 18. Single-molecule study on polymer diffusion in a melt state: Effect of chain topology KAUST Repository Habuchi, Satoshi 2013-08-06 We report a new methodology for studying diffusion of individual polymer chains in a melt state, with special emphasis on the effect of chain topology. A perylene diimide fluorophore was incorporated into the linear and cyclic poly(THF)s, and real-time diffusion behavior of individual chains in a melt of linear poly(THF) was measured by means of a single-molecule fluorescence imaging technique. The combination of mean squared displacement (MSD) and cumulative distribution function (CDF) analysis demonstrated the broad distribution of diffusion coefficient of both the linear and cyclic polymer chains in the melt state. This indicates the presence of spatiotemporal heterogeneity of the polymer diffusion which occurs at much larger time and length scales than those expected from the current polymer physics theory. We further demonstrated that the cyclic chains showed marginally slower diffusion in comparison with the linear counterparts, to suggest the effective suppression of the translocation through the threading-entanglement with the linear matrix chains. This coincides with the higher activation energy for the diffusion of the cyclic chains than of the linear chains. These results suggest that the single-molecule imaging technique provides a powerful tool to analyze complicated polymer dynamics and contributes to the molecular level understanding of the chain interaction. © 2013 American Chemical Society. 19. Experimental investigation and modelling of heat capacity, heat of fusion and melting interval of rocks Energy Technology Data Exchange (ETDEWEB) Leth-Miller, R.; Jensen, A.D.; Glarborg, P.; Jensen, L.M.; Hansen, P.B.; Joergensen, S.B 2003-11-28 The heat capacity and heat of fusion were measured for a number of minerals using differential scanning calorimetry (DSC). The DSC measurements showed that the heat of fusion for the minerals is very low compared to the heat of fusion for pure crystalline phases reported elsewhere. A model for the melting behaviour of mineral materials in terms of melting interval, heat capacities and heat of fusion has been developed. The only model input is the chemical composition of the mineral material. The model was developed to be implemented in a detailed model of a cupola furnace, thus the focus for the development was not only precision but also to obtain a model that was continuous and differentiable. The model is based on several different submodels that each covers a part of the heating and melting of rocks. Each submodel is based on large amounts of empirical data. Comparison of the model and the DSC measurements showed reasonable agreement for the model to be used when a fast estimate is needed and experimental data is not available. 20. Monoclinic tridymite in clast-rich impact melt rock from the Chesapeake Bay impact structure Science.gov (United States) Jackson, J.C.; Horton, J.W.; Chou, I.-Ming; Belkin, H.E. 2011-01-01 X-ray diffraction and Raman spectroscopy confirm a rare terrestrial occurrence of monoclinic tridymite in clast-rich impact melt rock from the Eyreville B drill core in the Chesapeake Bay impact structure. The monoclinic tridymite occurs with quartz paramorphs after tridymite and K-feldspar in a microcrystalline groundmass of devitrified glass and Fe-rich smectite. Electron-microprobe analyses revealed that the tridymite and quartz paramorphs after tridymite contain different amounts of chemical impurities. Inspection by SEM showed that the tridymite crystal surfaces are smooth, whereas the quartz paramorphs contain irregular tabular voids. These voids may represent microporosity formed by volume decrease in the presence of fluid during transformation from tridymite to quartz, or skeletal growth in the original tridymite. Cristobalite locally rims spherulites within the same drill core interval. The occurrences of tridymite and cristobalite appear to be restricted to the thickest clast-rich impact melt body in the core at 1402.02-1407.49 m depth. Their formation and preservation in an alkali-rich, high-silica melt rock suggest initially high temperatures followed by rapid cooling. 1. High-temperature corrosion of metals in the salt and metallic melts containing rare earths Science.gov (United States) Karpov, V. V.; Abramov, A. V.; Zhilyakov, A. Yu.; Belikov, S. V.; Volkovich, V. A.; Polovov, I. B.; Rebrin, O. I. 2016-09-01 A complex of independent methods was employed to study the corrosion resistance of molybdenum, zirconium, tantalum and tungsten in chloride, chloride-fluoride and fluoride-oxide melts based on LiCl, CaCl2, NaCl- KCl, LiF, and containing rare earths. Tests were conducted for 30 h at 750-1050 °C. The metals showed excellent corrosion resistance in fused chlorides (the corrosion rates were below 0.0005 g/(m2 h). Despite the presence of chemically active fluoride ions in the chloride-fluoride melts, the metals studied also showed very low corrosion rates, except molybdenum, for which the rate of corrosion was 0,8 g/(m2 h). The corrosion resistance of tantalum was considerably reduced in the fluoride-oxide melts; the corrosion rate was over 1 g/(m2 h) corresponding to the 8-th grade of stability and placing tantalum to the group of "low stability" materials. 2. Morphologies of ABC triblock terpolymer melts containing poly(Cyclohexadiene): Effects of conformational asymmetry KAUST Repository Kumar, Rajeev Senthil 2013-02-12 We have synthesized linear ABC triblock terpolymers containing poly(1,3-cyclohexadiene), PCHD, as an end block and characterized their morphologies in the melt. Specifically, we have studied terpolymers containing polystyrene (PS), polybutadiene (PB), and polyisoprene (PI) as the other blocks. Systematically varying the ratio of 1,2- /1,4-microstructures of poly(1,3-cyclohexadiene), we have studied the effects of conformational asymmetry among the three blocks on the morphologies using transmission electron microscopy (TEM), small-angle X-ray scattering (SAXS), and self-consistent field theory (SCFT) performed with PolySwift++. Our work reveals that the triblock terpolymer melts containing a high percentage of 1,2-microstructures in the PCHD block are disordered at 110 C for all the samples, independent of sequence and volume fraction of the blocks. In contrast, the triblock terpolymer melts containing a high percentage of 1,4-microstructure form regular morphologies known from the literature. The accuracy of the SCFT calculations depends on calculating the χ parameters that quantify the repulsive interactions between different monomers. Simulations using χ values obtained from solubility parameters and group contribution methods are unable to reproduce the morphologies as seen in the experiments. However, SCFT calculations accounting for the enhancement of the χ parameter with an increase in the conformational asymmetry lead to an excellent agreement between theory and experiments. These results highlight the importance of conformational asymmetry in tuning the χ parameter and, in turn, morphologies in block copolymers. © 2012 American Chemical Society. 3. Fluid-present disequilibrium melting in Neoarchean arc-related migmatites of Daeijak Island, western Gyeonggi Massif, Korea Science.gov (United States) Lee, Yuyoung; Cho, Moonsup 2013-10-01 The melting process of meta-igneous rocks was investigated via field, petrographic and geochemical analyses of the Neoarchean (~ 2.51 Ga) migmatite complex in Daeijak Island, western Gyeonggi Massif. This complex consists primarily of garnet-free amphibolites and tonalitic migmatites, both of which contain hornblende, plagioclase and quartz as major constituents. Neosomes and leucosomes in the migmatite have dioritic-tonalitic and tonalitic-trondhjemitic compositions, respectively. Compositions of hornblende (XFe = 0.39-0.42) and plagioclase (An24-27) vary little between the neosomes and leucosomes. The amphibolites show distinct depletions in Nb, Ta, Zr, and Ti relative to large ion lithophile elements, suggesting an arc-related origin for their basaltic protolith. Leucosomes have lower contents of K2O, MgO, FeO*, TiO2, Zr, Rb, and rare earth elements (REE) than amphibolites and neosomes, but are higher in SiO2, Na2O, and Sr contents. Leucosomes and neosomes have positive [(Eu/Eu*)N = 1.32-7.26] and negative (0.71-0.97) Eu anomalies, respectively, which are attributed to the variable degree of plagioclase fractionation during the partial melting. The P-T condition for the migmatite formation was estimated to be ~ 700-730 °C and 4.7-5.5 kbar, primarily based on the hornblende-plagioclase thermobarometry and phase equilibria. Various lines of textural evidence, such as the channel flow of melt along migmatitic layers and the segregation of melt into shear bands or boudin necks suggest a syn-deformation crystallization of melt. Chemical disequilibrium in migmatites is documented not only by petrographic and geochemical data but also by the REE modeling between melt product and source rock. Disequilibrium process is most likely attributed to the rapidity of melt extraction or migration, compared to chemical diffusion rate. In summary, the fluid-present disequilibrium melting of dioritic-tonalitic protoliths has produced tonalitic-trondhjemitic leucosomes in a dynamic 4. Slab melting and magma generation beneath the southern Cascade Arc Science.gov (United States) Walowski, K. J.; Wallace, P. J.; Clynne, M. A. 2014-12-01 Magma formation in subduction zones is interpreted to be caused by flux melting of the mantle wedge by fluids derived from dehydration of the downgoing oceanic lithosphere. In the Cascade Arc and other hot-slab subduction zones, however, most dehydration reactions occur beneath the forearc, necessitating a closer investigation of magma generation processes in this setting. Recent work combining 2-D steady state thermal models and the hydrogen isotope composition of olivine-hosted melt inclusions from the Lassen segment of the Cascades (Walowski et al., 2014; in review) has shown that partial melting of the subducted basaltic crust may be a key part of the subduction component in hot arcs. In this model, fluids from the slab interior (hydrated upper mantle) rise through the slab and cause flux-melting of the already dehydrated MORB volcanics in the upper oceanic crust. In the Shasta and Lassen segments of the southern Cascades, support for this interpretation comes from primitive magmas that have MORB-like Sr isotope compositions that correlate with subduction component tracers (H2O/Ce, Sr/P) (Grove et al. 2002, Borg et al. 2002). In addition, mass balance calculations of the composition of subduction components show ratios of trace elements to H2O that are at the high end of the global arc array (Ruscitto et al. 2012), consistent with the role of a slab-derived melt. Melting of the subducted basaltic crust should contribute a hydrous dacitic or rhyolitic melt (e.g. Jego and Dasgupta, 2013) to the mantle wedge rather than an H2O-rich aqueous fluid. We are using pHMELTS and pMELTS to model the reaction of hydrous slab melts with mantle peridotite as the melts rise through the inverted thermal gradient in the mantle wedge. The results of the modeling will be useful for understanding magma generation processes in arcs that are associated with subduction of relatively young oceanic lithosphere. 5. Chemical and thermal unfolding of calreticulin. Science.gov (United States) Duus, K; Larsen, N; Tran, T A T; Güven, E; Skov, L K; Jespersgaard, C; Gajhede, M; Houen, G 2013-05-01 Calreticulin is a soluble endoplasmic reticulum chaperone, which has a relatively low melting point due to its remarkable structure with a relatively high content of flexible structural elements. Using far ultraviolet circular dichroism (CD) spectroscopy and a fluorescent dye binding thermal shift assay, we have investigated the chemical and thermal stability of calreticulin. When the chemical stability of calreticulin was assessed, a midpoint for calreticulin unfolding was calculated to 3.0M urea using CD data at 222 nm. Using the fluorescent dye binding thermal shift assay, calreticulin was found to obtain a molten structure in urea concentrations between 1-1.5 M urea, and to unfold/aggregate at high and low pH values. The results demonstrated that the fluorescent dye binding assay could measure the thermal stability of calreticulin in aqueous buffers with results comparable to melting points obtained by other techniques. 6. Melt inclusion record of immiscibility between silicate, hydrosaline, and carbonate melts: Applications to skarn genesis at Mount Vesuvius Science.gov (United States) Fulignati, Paolo; Kamenetsky, Vadim S.; Marianelli, Paola; Sbrana, Alessandro; Mernagh, Terrence P. 2001-11-01 Foid-bearing syenites and endoskarn xenoliths of the A.D. 472 Vesuvius eruption represent the magma chamber carbonate wall-rock interface. Melt inclusions hosted in crystals from these rocks offer a rare opportunity to depict the formation and the composition of metasomatic skarn-forming fluids at the peripheral part of a growing K-alkaline magma chamber disrupted by an explosive eruption. Four principal types of melt inclusions represent highly differentiated phonolite (type 1), hydrosaline melt (type 3), unmixed silicate salt melts (type 2), and a complex chloride-carbonate melt with minor sulfates (type 4). The high-temperature (700 800 °C) magmatic-derived hydrosaline melt is considered to be the main metasomatic agent for the skarn-forming reactions. The interaction between this melt (fluid) and carbonate wall rocks produces a Na-K-Ca carbonate-chloride melt that shows immiscibility between carbonate and chloride constituents at ˜700 °C in 1 atm experiments. This unmixing can be viewed as a possible mechanism for the origin of carbonatites associated with intrusion-related skarn systems. 7. Channelling of Melt Above Plumes and Beneath MORs Science.gov (United States) Mueller, K.; Schmeling, H. 2003-12-01 We investigate melt transportation in partially molten rocks under different stress fields above the head of a mantle plume or beneath a spreading mid-oceanic ridge under hydrous and anhydrous conditions. We model such aggregates with the 2D-FD code FDCON [1] by means of a porous deformable matrix with melt under the influence of a given stress field to clarify the following key questions: Could channeling occur in a matrix containing a random melt distribution under a given stress field? Which orientation does it take? Is it possible to achieve a focusing of melt towards a MOR (dykes)? Does applying simple or pure shear to the matrix result in a difference in the formation and orientation of channels? How does the channel instability evolve during finite simple shear? In a deforming partially molten aggregate, weakening of the solid matrix due to the presence of melt creates an instability in which melt is localized by the following mechanism: regions of initially high melt fraction are areas of low viscosity and pressure, so that melt is drawn into these regions from higher pressure surroundings. This further enhances the melt weakening, producing a self-excited localization mechanism [2]. The channeling developing in models with a random melt distribution of 3.5 +/- 0.5% shows that melt is accumulated preferably in inclined channels. For both, simple as well as pure shear, the growth rate is highest for an orientation parallel to the direction of the maximum compressive stress and proportional to applied stress and the reverse of the Melt Retention Number. This also confirms the theoretical growth rate found by Stevenson [2]. In our isothermal models we found that the influence of water reduces the growth rate, in contrast to non-isothermal models of Hall [3]. Under simple shear melt channels evolve from an irregular melt distribution at angles of 45 degrees to the direction of shear. Upon further straining they rotate out of the orientation of maximum growth 8. Pressure-dependent compatibility of iron in garnet: Insights into the origin of ferropicritic melt Science.gov (United States) Zhang, JunBo; Liu, YongSheng; Ling, WenLi; Gao, Shan 2017-01-01 Iron-rich silicate melts in the Earth's deep mantle have been seismologically and geochemically inferred in recent years. The origin of local enrichments in iron and low-velocity seismic anomalies that have been detected in dense mantle domains are critical to understanding the mantle's evolution, which has been canonically explained by long-term chemical reactions between the Earth's silicate mantle and its liquid iron outer core. However, the Pleistocene alkaline ferropicrites (∼0.73 Ma) from Wudi, North China, show chemical and Sr-Nd-Os isotopic features that suggest derivation from the preferential melting of silica-deficient eclogite, a lithology of delaminated mafic lower continental crust that had stagnated at mid-upper mantle depths during the Mesozoic decratonization of the North China block. These rocks are characterized by substantial enrichment in iron (14.9-15.2 wt% Fe2O3), relative depletion in silica (40-41 wt% SiO2) and decoupled Y and heavy rare earth element (HREE) compositions. These ferropicrites have particularly higher Y/Yb ratios than the other Cenozoic basalts from North China. The pressure-dependent compatibility of Fe, Y and Yb in eclogitic garnet can adequately explain the Fe-enrichment and Y-HREE decoupling of the Wudi ferropicrites and indicates that the eclogites were melted at pressures of 5-8 GPa, as also constrained by previous high-P-T experiments. This melting depth ties together a seismically imaged high-velocity anomaly that extends from 150 km to 350 km in depth under the study area, which has been commonly interpreted as evidence for the stagnation of the missing, delaminated continental lithosphere. Our findings provide an alternative mechanism to produce an extremely iron-rich mantle reservoir in addition to core-mantle interaction. Iron-rich silicate melts that form by this process are likely to be denser than the ambient mantle peridotite (and therefore drive flow downward) and may play a more significant role in the 9. Making Ceramic Fibers By Chemical Vapor Science.gov (United States) Revankar, Vithal V. S.; Hlavacek, Vladimir 1994-01-01 Research and development of fabrication techniques for chemical vapor deposition (CVD) of ceramic fibers presented in two reports. Fibers of SiC, TiB2, TiC, B4C, and CrB2 intended for use as reinforcements in metal-matrix composite materials. CVD offers important advantages over other processes: fibers purer and stronger and processed at temperatures below melting points of constituent materials. 10. In situ determination of binary alloy melt compositions in the LHDAC by X- Radiography Science.gov (United States) Lord, O. T.; Walter, M. J.; Walker, D.; Clark, S. M. 2008-12-01 based on various ex situ techniques. We measured the eutectic composition between Fe and Fe3C up to 44 GPa, and found that the carbon content of the eutectic drops rapidly above about 10 GPa, dropping to less that 1 wt% by 44 GPa. This result is generally consistent with the thermodynamic calculations of Wood [2]. Experiments on the Fe-FeSi eutectic yielded an increase in the Si content of the eutectic to 35 GPa, consistent with data from large volume press experiments [3] Notably, melting experiments at 35-43 GPa and ~2500 K on a boundary between Fe and FeO failed to yield evidence of a melt with a composition distinguishable from pure iron. However, an experiment at 12 GPa and 2700 K between Fe and FeO(OH) did yield a melt with a composition intermediate between the two end members. This suggests that O solubility in the Fe-O eutectic melt is low at mid-mantle pressures, but that H may dissolve into the melt by itself or in combination with O. [1] Walker, D., 2005. Core-Mantle chemical issues. Canad. Min., 43, 1553-1564 [2] Wood, B. J., 1993. Carbon in the core. Earth Planet Sci. Lett., 117, 593-607 [3] Kuwayama, Y. & Hirose, K., 2004. Phase relations in the system Fe-FeSi at 21 GPa. Am. Min., 89, 273-276. 11. A dearth of intermediate melts at subduction zone volcanoes and the petrogenesis of arc andesites. Science.gov (United States) Reubi, Olivier; Blundy, Jon 2009-10-29 Andesites represent a large proportion of the magmas erupted at continental arc volcanoes and are regarded as a major component in the formation of continental crust. Andesite petrogenesis is therefore fundamental in terms of both volcanic hazard and differentiation of the Earth. Andesites typically contain a significant proportion of crystals showing disequilibrium petrographic characteristics indicative of mixing or mingling between silicic and mafic magmas, which fuels a long-standing debate regarding the significance of these processes in andesite petrogenesis and ultimately questions the abundance of true liquids with andesitic composition. Central to this debate is the distinction between liquids (or melts) and magmas, mixtures of liquids with crystals, which may or may not be co-genetic. With this distinction comes the realization that bulk-rock chemical analyses of petrologically complex andesites can lead to a blurred picture of the fundamental processes behind arc magmatism. Here we present an alternative view of andesite petrogenesis, based on a review of quenched glassy melt inclusions trapped in phenocrysts, whole-rock chemistry, and high-pressure and high-temperature experiments. We argue that true liquids of intermediate composition (59 to 66 wt% SiO(2)) are far less common in the sub-volcanic reservoirs of arc volcanoes than is suggested by the abundance of erupted magma within this compositional range. Effective mingling within upper crustal magmatic reservoirs obscures a compositional bimodality of melts ascending from the lower crust, and masks the fundamental role of silicic melts (>/=66 wt% SiO(2)) beneath intermediate arc volcanoes. This alternative view resolves several puzzling aspects of arc volcanism and provides important clues to the integration of plutonic and volcanic records. 12. Trace element mass balance in hydrous adiabatic mantle melting: The Hydrous Adiabatic Mantle Melting Simulator version 1 (HAMMS1) Science.gov (United States) Kimura, Jun-Ichi; Kawabata, Hiroshi 2014-06-01 numerical mass balance calculation model for the adiabatic melting of a dry to hydrous peridotite has been programmed in order to simulate the trace element compositions of basalts from mid-ocean ridges, back-arc basins, ocean islands, and large igneous provinces. The Excel spreadsheet-based calculator, Hydrous Adiabatic Mantle Melting Simulator version 1 (HAMMS1) uses (1) a thermodynamic model of fractional adiabatic melting of mantle peridotite, with (2) the parameterized experimental melting relationships of primitive to depleted mantle sources in terms of pressure, temperature, water content, and degree of partial melting. The trace element composition of the model basalt is calculated from the accumulated incremental melts within the adiabatic melting regime, with consideration for source depletion. The mineralogic mode in the primitive to depleted source mantle in adiabat is calculated using parameterized experimental results. Partition coefficients of the trace elements of mantle minerals are parameterized to melt temperature mostly from a lattice strain model and are tested using the latest compilations of experimental results. The parameters that control the composition of trace elements in the model are as follows: (1) mantle potential temperature, (2) water content in the source mantle, (3) depth of termination of adiabatic melting, and (4) source mantle depletion. HAMMS1 enables us to obtain the above controlling parameters using Monte Carlo fitting calculations and by comparing the calculated basalt compositions to primary basalt compositions. Additionally, HAMMS1 compares melting parameters with a major element model, which uses petrogenetic grids formulated from experimental results, thus providing better constraints on the source conditions. 13. Why Permafrost Is Thawing, Not Melting Science.gov (United States) Grosse, Guido; Romanovsky, Vladimir; Nelson, Frederick E.; Brown, Jerry; Lewkowicz, Antoni G. 2010-03-01 As global climate change is becoming an increasingly important political and social issue, it is essential for the cryospheric and global change research communities to speak with a single voice when using basic terminology to communicate research results and describe underlying physical processes. Experienced science communicators have highlighted the importance of using the correct terms to communicate research results to the media and general public [e.g., Akasofu, 2008; Hassol, 2008]. The consequences of scientists using improper terminology are at best oversimplification, but they more likely involve misunderstandings of the facts by the public. A glaring example of scientifically incorrect terminology appearing frequently in scientific and public communication relates to reports on the degradation of permafrost. Numerous research papers have appeared in recent years, broadly echoed in the news media, describing the “melting of permafrost,” its effects in the Arctic, and its feedbacks on climate through the carbon cycle. Although permafrost researchers have attempted to distinguish between the appropriate term “permafrost thawing” and the erroneous “permafrost melting” [e.g., van Everdingen, 2005; French, 2002], the latter is still used widely. A Web-based search using the phrase “permafrost melting” reveals hundreds of occurrences, many from highly regarded news and scientific organizations, including Reuters, New Scientist, ABC, The Guardian, Discovery News, Smithsonian magazine, the National Science Foundation, and others. 14. Glass Furnace Combustion and Melting Research Facility. Energy Technology Data Exchange (ETDEWEB) Connors, John J. (PPG Industries, Inc., Pittsburgh, PA); McConnell, John F. (JFM Consulting, Inc., Pittsburgh, PA); Henry, Vincent I. (Henry Technology Solutions, LLC, Ann Arbor, MI); MacDonald, Blake A.; Gallagher, Robert J.; Field, William B. (Lilja Corp., Livermore, CA); Walsh, Peter M.; Simmons, Michael C. (Lilja Corp., Livermore, CA); Adams, Michael E. (Lilja Corp., Rochester, NY); Leadbetter, James M. (A.C. Leadbetter and Son, Inc., Toledo, OH); Tomasewski, Jack W. (A.C. Leadbetter and Son, Inc., Toledo, OH); Operacz, Walter J. (A.C. Leadbetter and Son, Inc., Toledo, OH); Houf, William G.; Davis, James W. (A.C. Leadbetter and Son, Inc., Toledo, OH); Marvin, Bart G. (A.C. Leadbetter and Son, Inc., Toledo, OH); Gunner, Bruce E. (A.C. Leadbetter and Son, Inc., Toledo, OH); Farrell, Rick G. (A.C. Leadbetter and Son, Inc., Toledo, OH); Bivins, David P. (PPG Industries, Inc., Pittsburgh, PA); Curtis, Warren (PPG Industries, Inc., Pittsburgh, PA); Harris, James E. (PPG Industries, Inc., Pittsburgh, PA) 2004-08-01 The need for a Combustion and Melting Research Facility focused on the solution of glass manufacturing problems common to all segments of the glass industry was given high priority in the earliest version of the Glass Industry Technology Roadmap (Eisenhauer et al., 1997). Visteon Glass Systems and, later, PPG Industries proposed to meet this requirement, in partnership with the DOE/OIT Glass Program and Sandia National Laboratories, by designing and building a research furnace equipped with state-of-the-art diagnostics in the DOE Combustion Research Facility located at the Sandia site in Livermore, CA. Input on the configuration and objectives of the facility was sought from the entire industry by a variety of routes: (1) through a survey distributed to industry leaders by GMIC, (2) by conducting an open workshop following the OIT Glass Industry Project Review in September 1999, (3) from discussions with numerous glass engineers, scientists, and executives, and (4) during visits to glass manufacturing plants and research centers. The recommendations from industry were that the melting tank be made large enough to reproduce the essential processes and features of industrial furnaces yet flexible enough to be operated in as many as possible of the configurations found in industry as well as in ways never before attempted in practice. Realization of these objectives, while still providing access to the glass bath and combustion space for optical diagnostics and measurements using conventional probes, was the principal challenge in the development of the tank furnace design. The present report describes a facility having the requirements identified as important by members of the glass industry and equipped to do the work that the industry recommended should be the focus of research. The intent is that the laboratory would be available to U.S. glass manufacturers for collaboration with Sandia scientists and engineers on both precompetitive basic research and the 15. Magnesium melt protection by covering gas Directory of Open Access Journals (Sweden) M. Holtzer 2008-03-01 Full Text Available Thc protcclion of liquid light metals Cmm oxidation is a major issue in recycling and mclting proccsscs in rhc light mctal industry. Thcprorcction of liquid magncsirrm surfacc was carried out by using salts. alloying clemcnts, incrt gascs or rcactivc gas mixture. Snlt bnscdprorcction is still ~hcm ost widely uscd technology in the recycling of magnesium, but gases arc more frcqucntly uscd in magnesiumc;lszing industry. Protcczing thc mottcn mctal undcr a blanket of an inert gas such as argon or helium is dangerous. bccausc no protcctivctaycr is hrrnorl on thc mctr surface and mctal is frcc to cvaporatc, resulting in safcty hazards when furnace ambicncc is cxposcd to air ducto a violcnt rcaction. Thc disadvantagcs of t hcse methods have been partially ovcrcomc by using reactive gas systcrn, in which n chcmicnlrcaction hctwccn a gas and thc moltcn mctal produces a fhin protective film on the surface of the melt. Rcaclive gascs likc SFI, or SOz donot mccr cnvironmcnral standards due to their cxtrcrnely high global warming ptentiat or toxicity. Thcreforc thc altcrnativc covcringgascs ror magncsium mclrbng arc ol big intcrcst. Gas mixturcs containing HE%-1 34a, Novec 6 12. BF3 (Magshictd systcrn and solid C02have hccn succcssfi~lyl ~cstcdin I he world. 16. Slicing Strategy for Selective Laser Melting Institute of Scientific and Technical Information of China (English) SONG Xin; LIU Ji-quan; FAN Shu-qian 2014-01-01 Selective laser melting (SLM) is one of the most popular additive manufacturing (AM) technologies for metal parts. Slicing result, especially for the different dimensional slicing geometry and its topology, plays an important role because of the thermodynamic behavior of metal powders. To get correct geometry and reliable topology, a slicing strategy for SLM is proposed. The unavoidable numerical error caused by sampling and geometric transformation is suppressed firstly, according to shifting the z-coordinate of a vertex with a small value such the shifted vertex is on a slicing plane. The result of vertex-shifting makes it possible to identify different geometric features such as skin surfaces, overhang surfaces, extreme edges and volumetric solid. Second, from geometric primitives a hierarchy of axis-aligned bounding boxes (AABBs) is constructed and used to speed up intersection of slicing planes against sets of triangles. All intersecting segments are given different signs to depict their geometric or topological information. Based the different signs, the different dimensional geometry that is eventually represented by simple and anticlockwise oriented polygons, are identified. Finally, the polygons are classified and nested in a multi-tree data structure set to produce correct topological relations. The result of digital and physical experiments shows the proposed slicing strategy is feasible and robust. 17. Holographic Picture of Heavy Vector Meson Melting CERN Document Server Braga, Nelson R F; Diles, Saulo 2016-01-01 The fraction of heavy vector mesons produced in a heavy ion collision, as compared to a proton proton collision, serves as an important indication of the formation of a thermal medium, the quark gluon plasma. This sort of analysis strongly depends on understanding the thermal effects of a medium like the plasma on the states of heavy mesons. In particular, it is crucial to know the temperature ranges where they undergo a thermal dissociation, or melting. AdS/QCD models are know to provide an important tool for the calculation of hadronic masses, but in general are not consistent with the observation that decay constants of heavy vector mesons decrease with excitation level. It has recently been shown that this problem can be overcome using a soft wall background and introducing an extra energy parameter, through the calculation of correlation functions at a finite position of anti-de Sitter space. This approach leads to the evaluation of masses and decay constants of S wave quarkonium states with just one fla... 18. Charged Water Droplets can Melt Metallic Electrodes Science.gov (United States) Elton, Eric; Rosenberg, Ethan; Ristenpart, William 2016-11-01 A water drop, when immersed in an insulating fluid, acquires charge when it contacts an energized electrode. Provided the electric field is strong enough, the drop will move away to the opposite electrode, acquire the opposite charge, and repeat the process, effectively 'bouncing' back and forth between the electrodes. A key implicit assumption, dating back to Maxwell, has been that the electrode remains unaltered by the charging process. Here we demonstrate that the electrode is physically deformed during each charge transfer event with an individual water droplet or other conducting object. We used optical, electron, and atomic force microscopy to characterize a variety of different metallic electrodes before and after drops were electrically bounced on them. Although the electrodes appear unchanged to the naked eye, the microscopy reveals that each charge transfer event yielded a crater approximately 1 micron wide and 50 nm deep, with the exact dimensions proportional to the applied field strength. We present evidence that the craters are formed by localized melting of the electrodes via Joule heating in the metal and concurrent dielectric breakdown of the surrounding fluid, suggesting that the electrode locally achieves temperatures exceeding 3400°C. Present address: Dept. Materials Sci. Engineering, MIT. 19. Bidirectional optimization of the melting spinning process. Science.gov (United States) Liang, Xiao; Ding, Yongsheng; Wang, Zidong; Hao, Kuangrong; Hone, Kate; Wang, Huaping 2014-02-01 A bidirectional optimizing approach for the melting spinning process based on an immune-enhanced neural network is proposed. The proposed bidirectional model can not only reveal the internal nonlinear relationship between the process configuration and the quality indices of the fibers as final product, but also provide a tool for engineers to develop new fiber products with expected quality specifications. A neural network is taken as the basis for the bidirectional model, and an immune component is introduced to enlarge the searching scope of the solution field so that the neural network has a larger possibility to find the appropriate and reasonable solution, and the error of prediction can therefore be eliminated. The proposed intelligent model can also help to determine what kind of process configuration should be made in order to produce satisfactory fiber products. To make the proposed model practical to the manufacturing, a software platform is developed. Simulation results show that the proposed model can eliminate the approximation error raised by the neural network-based optimizing model, which is due to the extension of focusing scope by the artificial immune mechanism. Meanwhile, the proposed model with the corresponding software can conduct optimization in two directions, namely, the process optimization and category development, and the corresponding results outperform those with an ordinary neural network-based intelligent model. It is also proved that the proposed model has the potential to act as a valuable tool from which the engineers and decision makers of the spinning process could benefit. 20. Rheometry of polymer melts using processing machines Science.gov (United States) Friesenbichler, Walter; Neunhäuserer, Andreas; Duretek, Ivica 2016-08-01 The technology of slit-die rheometry came into practice in the early 1960s. This technique enables engineers to measure the pressure drop very precisely along the slit die. Furthermore, slit-die rheometry widens up the measurable shear rate range and it is possible to characterize rheological properties of complicated materials such as wall slipping PVCs and high-filled compounds like long fiber reinforced thermoplastics and PIM-Feedstocks. With the use of slit-die systems in polymer processing machines e.g., Rauwendaal extrusion rheometer, by-pass extrusion rheometer, injection molding machine rheometers, new possibilities regarding rheological characterization of thermoplastics and elastomers at processing conditions near to practice opened up. Special slit-die systems allow the examination of the pressure-dependent viscosity and the characterization of cross-linking elastomers because of melt preparation and reachable shear rates comparable to typical processing conditions. As a result of the viscous dissipation in shear and elongational flows, when performing rheological measurements for high-viscous elastomers, temperature-correction of the apparent values has to be made. This technique was refined over the last years at Montanuniversitaet. Nowadays it is possible to characterize all sorts of rheological complicated polymeric materials under process- relevant conditions with viscosity values fully temperature corrected. 1. Chemical intolerance DEFF Research Database (Denmark) Dantoft, Thomas Meinertz; Andersson, Linus; Nordin, Steven; 2015-01-01 Chemical intolerance (CI) is a term used to describe a condition in which the sufferer experiences a complex array of recurrent unspecific symptoms attributed to low-level chemical exposure that most people regard as unproblematic. Severe CI constitutes the distinguishing feature of multiple...... chemical sensitivity (MCS). The symptoms reported by CI subjects are manifold, involving symptoms from multiple organs systems. In severe cases of CI, the condition can cause considerable life-style limitations with severe social, occupational and economic consequences. As no diagnostic tools for CI... 2. Hazardous Chemicals Centers for Disease Control (CDC) Podcasts 2007-04-10 Chemicals are a part of our daily lives, providing many products and modern conveniences. With more than three decades of experience, The Centers for Disease Control and Prevention (CDC) has been in the forefront of efforts to protect and assess people's exposure to environmental and hazardous chemicals. This report provides information about hazardous chemicals and useful tips on how to protect you and your family from harmful exposure. Created: 4/10/2007 by CDC National Center for Environmental Health. Date Released: 4/13/2007. 3. Melting the hydrous, subarc mantle: the origin of primitive andesites Science.gov (United States) Mitchell, Alexandra L.; Grove, Timothy L. 2015-08-01 This experimental study is the first comprehensive investigation of the melting behavior of an olivine + orthopyroxene ± spinel—bearing fertile mantle (FM) composition as a function of variable pressure and water content. The fertile composition was enriched with a metasomatic slab component of ≤0.5 % alkalis and investigated from 1135 to 1470 °C at 1.0-2.0 GPa. A depleted lherzolite with 0.4 % alkali addition was also studied from 1225 to 1240 °C at 1.2 GPa. Melts of both compositions were water-undersaturated: fertile lherzolite melts contained 0-6.4 wt% H2O, and depleted lherzolite melts contained ~2.5 wt% H2O. H2O contents of experimental glasses are measured using electron microprobe, secondary ion mass spectrometry, and synchrotron-source reflection Fourier transform infrared spectroscopy, a novel technique for analyzing H2O in petrologic experiments. Using this new dataset in conjunction with results from previous hydrous experimental studies, a thermobarometer and a hygrometer-thermometer are presented to determine the conditions under which primitive lavas were last in equilibration with the mantle. These predictive models are functions of H2O content and pressure, respectively. A predictive melting model is also presented that calculates melt compositions in equilibrium with an olivine + orthopyroxene ± spinel residual assemblage (harzburgite). This model quantitatively predicts the following influences of H2O on mantle lherzolite melting: (1) As melting pressure increases, melt compositions become more olivine-normative, (2) as melting extent increases, melt compositions become depleted in the normative plagioclase component, and (3) as melt H2O content increases, melts become more quartz-normative. Natural high-Mg# [molar Mg/(Mg + Fe2+)], high-MgO basaltic andesite and andesite lavas—or primitive andesites (PAs)—contain high SiO2 contents at mantle-equilibrated Mg#s. Their compositional characteristics cannot be readily explained by melting 4. Seismic Evidence for Possible Slab Melting from Strong Scattering Waves Directory of Open Access Journals (Sweden) Cheng-Horng Lin 2011-01-01 Full Text Available Slab melting in young and hot subduction zones has been studied using geochemical observations and thermal modelling, but there are few data from seismic studies to confirm slab melting. Also the detailed geometry in the deep part of the melting slab is often ambiguous in that the intraslab earthquakes within the Wadati-Benioff zone are only limited to shallower depths. To improve our understanding of both the seismic features and geometry found in a young and hot subducted slab, I analyzed anomalous moonquake-like seismograms that were generated by an intermediate-depth earthquake recorded in central Japan. For this study, possible reflected (or scattered sources were examined using detailed analyses of particle motions and a grid search for travel-time differences between the direct and later P-waves. The results show that using strong seismic scattering, slab melting is likely occurring in the deeper, flexing part of the subducted Philippine Sea plate. Because the subducted Philippine Sea plate in central Japan is young and therefore hot, partial melting might have taken place to produce abundant melting spots in the subducted slab. Melting spots, identified as ¡§bright spots,¡¨ could efficiently reflect or scatter seismic energy and generate many later phases with large amplitudes. 5. Greenland Ice Sheet surface melt:A review Institute of Scientific and Technical Information of China (English) Kang Yang; ManChun Li 2014-01-01 Surface melt has great impacts on the Greenland Ice Sheet (GrIS) mass balance and thereby has become the focus of significant GrIS research in recent years. The production, transport, and release processes of surface meltwater are the keys to understanding the poten-tial impacts of the GrIS surface melt. These hydrological processes can elucidate the following scientific questions:How much melt-water is produced atop the GrIS? What are the characteristics of the meltwater-formed supraglacial hydrological system? How does the meltwater influence the GrIS motion? The GrIS supraglacial hydrology has a number of key roles and yet continues to be poorly understood or documented. This paper summarizes the current understanding of the GrIS surface melt, emphasizing the three essential supraglacial hydrological processes:(1) meltwater production:surface melt modeling is an important approach to acquire surface melt information, and areas, depths, and volumes of supraglacial lakes extracted from remotely sensed imagery can also provide surface melt information;(2) meltwater transport:the spatial distributions of supraglacial lakes, supraglacial streams, moulins, and crevasses demonstrate the characteristics of the supraglacial hydrological system, revealing the meltwater transport process;and (3) meltwater release:the release of meltwater into the englacial and the subglacial ice sheet has important but undetermined impacts on the GrIS motion. The correlation between surface runoff and the GrIS motion speed is employed to understand these influences. 6. Ice-sheet acceleration driven by melt supply variability. Science.gov (United States) Schoof, Christian 2010-12-09 Increased ice velocities in Greenland are contributing significantly to eustatic sea level rise. Faster ice flow has been associated with ice-ocean interactions in water-terminating outlet glaciers and with increased surface meltwater supply to the ice-sheet bed inland. Observed correlations between surface melt and ice acceleration have raised the possibility of a positive feedback in which surface melting and accelerated dynamic thinning reinforce one another, suggesting that overall warming could lead to accelerated mass loss. Here I show that it is not simply mean surface melt but an increase in water input variability that drives faster ice flow. Glacier sliding responds to melt indirectly through changes in basal water pressure, with observations showing that water under glaciers drains through channels at low pressure or through interconnected cavities at high pressure. Using a model that captures the dynamic switching between channel and cavity drainage modes, I show that channelization and glacier deceleration rather than acceleration occur above a critical rate of water flow. Higher rates of steady water supply can therefore suppress rather than enhance dynamic thinning, indicating that the melt/dynamic thinning feedback is not universally operational. Short-term increases in water input are, however, accommodated by the drainage system through temporary spikes in water pressure. It is these spikes that lead to ice acceleration, which is therefore driven by strong diurnal melt cycles and an increase in rain and surface lake drainage events rather than an increase in mean melt supply. 7. Melt processed multiphase ceramic waste forms for nuclear waste immobilization Energy Technology Data Exchange (ETDEWEB) Amoroso, Jake, E-mail: [email protected] [Savannah River National Laboratory, Aiken, SC 29808 (United States); Marra, James C. [Savannah River National Laboratory, Aiken, SC 29808 (United States); Tang, Ming [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Lin, Ye; Chen, Fanglin [University of South Carolina, Columbia, SC 29208 (United States); Su, Dong [Brookhaven National Laboratory, Upton, NY 11973 (United States); Brinkman, Kyle S. [Clemson University, Clemson, SC 29634 (United States) 2014-11-15 Highlights: • We explored the feasibility of melt processing multiphase titanate-based ceramics. • Melt processing produced phases obtained by alternative processing methods. • Phases incorporated multiple lanthanides and transition metals. • Processing in reducing atmosphere suppressed un-desirable Cs–Mo coupling. • Cr partitions to and stabilizes the hollandite phase, which promotes Cs retention. - Abstract: Ceramic waste forms are promising hosts for nuclear waste immobilization as they have the potential for increased durability and waste loading compared with conventional borosilicate glass waste forms. Ceramics are generally processed using hot pressing, spark plasma sintering, and conventional solid-state reaction, however such methods can be prohibitively expensive or impractical at production scales. Recently, melt processing has been investigated as an alternative to solid-state sintering methods. Given that melter technology is currently in use for High Level Waste (HLW) vitrification in several countries, the technology readiness of melt processing appears to be advantageous over sintering methods. This work reports the development of candidate multi-phase ceramic compositions processed from a melt. Cr additions, developed to promote the formation and stability of a Cs containing hollandite phase were successfully incorporated into melt processed multi-phase ceramics. Control of the reduction–oxidation (Redox) conditions suppressed undesirable Cs–Mo containing phases, and additions of Al and Fe reduced the melting temperature. 8. The Melting Curve and Premelting of MgO CERN Document Server Cohen, R E 1996-01-01 The melting curve for MgO was obtained using molecular dynamics and a non-empirical, many-body potential. We also studied premelting effects by computing the dynamical structure factor in the crystal on approach to melting. The melting curve simulations were performed with periodic boundary conditions with cells up to 512 atoms using the ab-initio Variational Induced Breathing (VIB) model. The melting curve was obtained by computing% \\Delta H_m$and agreement with previous estimates and we obtain a reasonable$\\Delta V_m$, but our melting slope dT/dP (114 K/GPa) is three times greater than that of Zerr and Boehler [1994] (35 K/GPa), suggesting a problem with the experimental melting curve, or an indication of exotic, non-ionic behavior of MgO liquid. We computed$S(q,\\omega )$from simulations of 1000 atom clusters using the Potential Induced Breathing (PIB) model. A low frequency peak in the dynamical structure factor$% S(q,\\omega )\$ arises below the melting point which appears to be related to the onset ...
9. Interaction of rhyolite melts with monazite, xenotime, and zircon surfaces
Science.gov (United States)
2015-05-01
The interfacial contact region between a rhyolite melt and the accessory minerals monazite, xenotime, and zircon is investigated using molecular dynamics simulations. On all surfaces, major structural rearrangement extends about 1 nm into the melt from the interface. As evidenced by the structural perturbations in the ion distribution profiles, the affinity of the melt for the surface increases in going from monazite to xenotime to zircon. Alkali ions are enriched in the melt in contact with an inert wall, as well as at the mineral surfaces. Melt in contact with zircon has a particularly strong level of aluminum enrichment. In xenotime, the enrichment of aluminum is less than that in zircon, but still notable. In monazite, the aluminum enrichment in the contact layer is much less. It is expected that the relative surface energies of these accessory minerals will be a strong function of the aluminum content of the melt and that nucleation of zircon, in particular, would be easier for melts with higher aluminum concentration. The crystal growth rate for zircon is expected to be slower at a higher aluminum concentration because of the effectiveness of aluminum in solvating the zircon surface. The variable interfacial concentration profiles across the series of accessory minerals will likely affect the kinetics of trace element incorporation, as the trace elements must compete with the major elements for surface sites on the growing accessory minerals.
10. Experiments on melt droplets falling into a water pool
Energy Technology Data Exchange (ETDEWEB)
Okkonen, T.; Sehgal, B.R. [Royal Inst. of Tech., Stockholm (Sweden). Div. of Nuclear Power Safety
1998-01-01
This paper presents experimental data and analysis related to melt droplets falling into a water pool. A binary CaO-B{sub 2}O{sub 3} melt mixture is used to study the influence of melt superheat and water subcooling on droplet deformation and fragmentation. For the conditions studied (We {<=} 1000), the surface tension of the melt droplet and the film boiling stability greatly affect the fragmentation behaviour. If the melt temperature is between the liquidus and solidus point (mushy zone) or if the film boiling is stable due to a relatively low subcooling, the droplet deformation and fragmentation are mitigated. This behaviour can be related to the effective Weber number (We) of the melt droplet upon entry into the water pool. Similar phenomena can be expected also for interactions of corium (UO{sub 2}-ZrO{sub 2}) and water, which are characterized by a potentially fast transformation of melt into the mushy zone and by particularly stable film boiling. (author)
11. The Partitioning of Tungsten bwtween Aqueous Fluids and Silicate Melts
Institute of Scientific and Technical Information of China (English)
许永胜; 张本仁; 等
1993-01-01
An experimental study has been carried out to determine the partition coefficients of tungsten between aqueous fluids and granitic melts at 800℃ and 1.5kb with natural granite as the starting material,The effects of the solution on the partition coefficients of tungsten show a wequence of P>co32->B>H2O.The effects are limited(generally KD<0.3)and the tungsten shows a preferential trend toward the melt over the aqueous fiuid.The value of KD increases with increasing concentration of phosphorus;the KD increases first and then reduces with the concentration of CO32-;when temperature decreases,the KD between the solution of CO32- and the silicate melt increases,and that between the solution of B4O72- and the silicate melt decreases.The partition coefficients of phosphorus and sodium between fluids and silicate melts have been calculated from the concentrations of the elements in the melts.The KD value for phosphorus is 0.38 and that for sodium is 0.56.Evidence shows that the elements tend to become richer and richer in the melts.
12. Research on low emission MSW gasification and melting system
Institute of Scientific and Technical Information of China (English)
XIAO Gang; NI Mingjiang; CHI Yong; JIN Yuqi; ZHANG Jiaquan; MIAO Qi; CEN Kefa
2007-01-01
In order to eliminate secondary pollution caused by municipal solid waste (MSW) incineration,a MSW gasification and melting process is proposed.The process is expected to reduce the emission of pollutants,especially heavy-metals and dioxins.In this paper,the combustible components of MSW and simulated MSW were gasified in a lab-scale fluidized bed at 400℃-700℃ when the excess air ratio (ER) was between 0.2 and 0.8.The experimental results indicated that the MSW could be gasified effectively in a fluidized bed at approximately 600℃-700℃ when excess air ratio was 0.2-0.4.The melting characteristics of two typical fly ash samples from MSW incinerators were investigated.The results indicated that fly ash of pure MSW incineration could be melted at approximately 1,300℃ and that of MSW and coal co-combustion could be melted at approximately 1,400℃.When temperature was over 1,100℃,more than 99.9% of the dioxins could be decomposed and most of the heavy-metals could be solidified in the slag.Based on the above experiments,two feasible MSW gasification and melting processes were proposed for low calorific value MSW:(1) sieved MSW gasification and melting system,which was based on an idea of multi-recycle;(2) gasification and melting scheme of MSW adding coal as assistant fuel.
13. Analysis of melt ejection during long pulsed laser drilling
Science.gov (United States)
Ting-Zhong, Zhang; Zhi-Chao, Jia; Hai-Chao, Cui; De-Hua, Zhu; Xiao-Wu, Ni; Jian, Lu
2016-05-01
In pulsed laser drilling, melt ejection greatly influences the keyhole shape and its quality as well, but its mechanism has not been well understood. In this paper, numerical simulation and experimental investigations based on 304 stainless steel and aluminum targets are performed to study the effects of material parameters on melt ejection. The numerical method is employed to predict the temperatures, velocity fields in the solid, liquid, and vapour front, and melt pool dynamics of targets as well. The experimental methods include the shadow-graphic technique, weight method, and optical microscope imaging, which are applied to real-time observations of melt ejection phenomena, measurements of collected melt and changes of target mass, observations of surface morphology and the cross-section of the keyhole, respectively. Numerical and experimental results show that the metallic material with high thermal diffusivity like aluminum is prone to have a thick liquid zone and a large quantity of melt ejection. Additionally, to the best of our knowledge, the liquid zone is used to illustrate the relations between melt ejection and material thermal diffusivity for the first time. The research result in this paper is useful for manufacturing optimization and quality control in laser-material interaction. Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. KYLX_0341) and the National Natural Science Foundation of China (Grant No. 61405147).
14. Transition in the fractal geometry of Arctic melt ponds
Directory of Open Access Journals (Sweden)
C. Hohenegger
2012-10-01
Full Text Available During the Arctic melt season, the sea ice surface undergoes a remarkable transformation from vast expanses of snow covered ice to complex mosaics of ice and melt ponds. Sea ice albedo, a key parameter in climate modeling, is determined by the complex evolution of melt pond configurations. In fact, ice–albedo feedback has played a major role in the recent declines of the summer Arctic sea ice pack. However, understanding melt pond evolution remains a significant challenge to improving climate projections. By analyzing area–perimeter data from hundreds of thousands of melt ponds, we find here an unexpected separation of scales, where pond fractal dimension D transitions from 1 to 2 around a critical length scale of 100 m2 in area. Pond complexity increases rapidly through the transition as smaller ponds coalesce to form large connected regions, and reaches a maximum for ponds larger than 1000 m2, whose boundaries resemble space-filling curves, with D ≈ 2. These universal features of Arctic melt pond evolution are similar to phase transitions in statistical physics. The results impact sea ice albedo, the transmitted radiation fields under melting sea ice, the heat balance of sea ice and the upper ocean, and biological productivity such as under ice phytoplankton blooms.
15. Calving on tidewater glaciers amplified by submarine frontal melting
CERN Document Server
O'Leary, Martin
2012-01-01
While it has been shown repeatedly that ocean conditions exhibit an important control on the behaviour of grounded tidewater glaciers, modelling studies have focused largely on the effects of basal and surface melting. Here, a finite-element model of stresses near the front of a tidewater glacier is used to investigate the effects of frontal melting on calving, independently of the calving criterion used. Applications of the stress model to idealized scenarios reveal that undercutting of the ice front due to frontal melting can drive calving at up to ten times the mean melt rate. Factors which cause increased frontal melt-driven calving include a strong thermal gradient in the ice, and a concentration of frontal melt at the base of the glacier. These properties are typical of both Arctic and Antarctic tidewater glaciers. The finding that frontal melt near the base is a strong driver of calving leads to the conclusion that water temperatures near the bed of the glacier are critically important to the glacier f...
16. Transition in the fractal geometry of Arctic melt ponds
Directory of Open Access Journals (Sweden)
C. Hohenegger
2012-06-01
Full Text Available During the Arctic melt season, the sea ice surface undergoes a remarkable transformation from vast expanses of snow covered ice to complex mosaics of ice and melt ponds. Sea ice albedo, a key parameter in climate modeling, is determined by the complex evolution of melt pond configurations. In fact, ice-albedo feedback has played a major role in the recent declines of the summer Arctic sea ice pack. However, understanding melt pond evolution remains a significant challenge to improving climate projections. By analyzing area-perimeter data from hundreds of thousands of melt ponds, we find here an unexpected separation of scales, where pond fractal dimension D transitions from 1 to 2 around a critical length scale of 100 m2 in area. Pond complexity increases rapidly through the transition as smaller ponds coalesce to form large connected regions, and reaches a maximum for ponds larger than 1000 m2 whose boundaries resemble space filling curves with D ≈ 2. These universal features of Arctic melt pond evolution are similar to phase transitions in statistical physics. The results impact sea ice albedo, the transmitted radiation fields under melting sea ice, the heat balance of sea ice and the upper ocean, and biological productivity such as under ice phytoplankton blooms.
17. Calving on tidewater glaciers amplified by submarine frontal melting
Directory of Open Access Journals (Sweden)
M. O'Leary
2012-08-01
Full Text Available While it has been shown repeatedly that ocean conditions exhibit an important control on the behaviour of grounded tidewater glaciers, modelling studies have focused largely on the effects of basal and surface melting. Here, a finite-element model of stresses near the front of a tidewater glacier is used to investigate the effects of frontal melting on calving, independently of the calving criterion used. Applications of the stress model to idealized scenarios reveal that undercutting of the ice front due to frontal melting can drive calving at up to ten times the mean melt rate. Factors which cause increased frontal melt-driven calving include a strong thermal gradient in the ice, and a concentration of frontal melt at the base of the glacier. These properties are typical of both Arctic and Antarctic tidewater glaciers. The finding that frontal melt near the base is a strong driver of calving leads to the conclusion that water temperatures near the bed of the glacier are critically important to the glacier front, and thus the flow of the glacier. These conclusions are robust against changes in the basal boundary condition and the choice of calving criterion, as well as variations in the glacier size or level of crevassing.
18. Influence of processing parameters on laser penetration depth and melting/re-melting densification during selective laser melting of aluminum alloy
Science.gov (United States)
Yu, Guanqun; Gu, Dongdong; Dai, Donghua; Xia, Mujian; Ma, Chenglong; Chang, Kun
2016-10-01
A three-dimensional mesoscopic model, considering the powder-to-solid transition, motion of gas bubbles within molten pool and the effect of surface tension, has been established in order to investigate the evolution rule of pores and re-melting densification mechanism during selective laser melting of AlSi10Mg. The results indicated that re-melting phenomenon of previous fabricated layer induced by laser melting of current powder layer played a crucial role on the increase in densification rate. During the re-melting process, the trapped gas pores in previous layer rose up swiftly and came to the surface consequently, resulting in remarkably elevated densification in previous layer. The influences of laser scan speed on the single-track morphology, types of pores and laser penetration depth have also been studied. It showed that the maximum re-melting depth (31 µm) was attained, and meanwhile, pores left in preceding layer got eliminated completely due to the mass transfer within molten pool, when an appropriate laser scan speed (150 mm/s) was applied. In this case, reasonable laser energy per unit length and irradiation time tended to enhance the laser penetration depth for powder bed and decrease the porosity in as-fabricated layer. A series of experimental study were performed to verify the reliability of the above mesoscopic simulation, including the surface topography of single track and the types of pores. The redistribution of bubbles between the adjacent layers as well as the localized re-melting densification, which were observed from the longitudinal section of samples, was in good agreement with simulation results.
19. ZnO homoepitaxy on the O polar face of hydrothermal and melt-grown substrates by pulsed laser deposition
Energy Technology Data Exchange (ETDEWEB)
Rogers, D.J. [Nanovation SARL, Orsay (France); Technical Univ. of Troyes (France); CNRS, Troyes (France); Hosseini Teherani, F. [Nanovation SARL, Orsay (France); Largeteau, A.; Demazeau, G. [ICMCB-CNRS, Bordeaux 1 University (Science and Technology), Pessac (France); Moisson, C.; Turover, D. [Novasic, Savoie Technolac, Arche Bat. 4, BP 267, Le Bourget du Lac (France); Nause, J. [Cermet Inc., Atlanta, GA (United States); Garry, G. [Thales Research, Domaine de Corbeville, Orsay (France); Kling, R.; Gruber, T. [Ulm University, Department of Semiconductor Physics, Ulm (Germany); Waag, A. [Braunschweig Technical University, Institute of Semiconductor Technology, Braunschweig (Germany); Jomard, F.; Galtier, P.; Lusson, A. [LPSC-CNRS, Meudon (France); Monteiro, T.; Soares, M.J.; Neves, A.; Carmo, M.C.; Peres, M. [University of Aveiro, Physics Department, Aveiro (Portugal); Lerondel, G.; Hubert, C. [Technical University of Troyes-CNRS (FRE2671), 12 rue Marie Curie, BP 2060, Troyes (France)
2007-07-15
2 cm diameter hydrothermal ZnO crystals were grown and then made into substrates using both mechanical and chemical-mechanical polishing (CMP). CMP polishing showed superior results with an (0002) {omega} scan full width half maximum (FWHM) of 67 arcsec and an root mean square (RMS) roughness of 2 Aa. In comparison, commercial melt-grown substrates exhibited broader X-ray diffraction (XRD) linewidths with evidence of sub-surface crystal damage due to polishing, including a downward shift of c-lattice parameter. Secondary ion mass spectroscopy revealed strong Li, Fe, Co, Al and Si contamination in the hydrothermal crystals as opposed to the melt-grown substrates, for which glow discharge mass spectroscopy studies had reported high levels of Pb, Fe, Cd and Si. Low temperature photoluminescence (PL) studies indicated that the hydrothermal crystal had high defect and/or impurity concentrations compared with the melt-grown substrate. The dominant bound exciton for the melt-grown substrate was indexed to Al. ZnO films were grown using pulsed laser deposition. The melt-grown substrates gave superior results with XRD (0002) {omega} and 2{theta}/{omega} WHM of 124 and 34 arcsec, respectively. Atomic force microscope measurements indicated a low RMS roughness (1.9 nm) as confirmed by fringes in the XRD 2{theta}/{omega} scan. It was suggested that the improvement in XRD response relative to the substrate might be due to ''healing'' of sub-surface polishing damage due to the elevated T{sub s} used for the growth. Indeed the c-lattice parameter for the homoepitaxial layer on the melt-grown substrate had become that which would be expected for strain-free ZnO. Furthermore, the stability of the PL peak positions relative to bulk ZnO, confirmed that the films appear practically strain free. (orig.)
20. [Perilla nankinensis Decne by using melt granulation method].
Science.gov (United States)
Shashiashvili, N B; Berashvili, D T; Bakuridze, L A; Bakuridze, A D
2013-12-01
The aim of the research was to work out the technology and tablet composition from the overground parts of the Perilla nankinensis Decne on the base of complex research. The dry extract was prepared from dried overground parts of perilla introduced in Georgia. The structural-mechanical and technological character of tablets and their masses were identified by the known methodic. Friability was studied by defining the fluctuation and bending corner. Volume density was established by using vibration cylinder. Volume density of powders was studied by pyknometers. Porosity was calculated by the bearing of volume density of the masses. The size of pressing was established by defining the firmness of tablets. The granule composition was defined by analysis. Disintegration and dissolution were studied by using "rotating basket" and "basket-rack assembly". From the result we got it was clear that the dry extract for research don't have good fluctuation and pressing. It should be mentioned that it contained moisture and is hygroscopic. As the character of substances is not satisfied it was necessary to select new assisting substances and studying and using additional technological method. We have selected some more additional substances for optimal firmness and for the purpose of shortening the time of tablet dissolution. There were also selected parameters of optimal pressing force. Assisting substances are practically selected and theoretically accepted on the base of studying technological and physical-chemical character features of the substances of the dry extract from the over ground parts of Perilla nankinensis Decne. As a result optimal composition of tablets is delivered. It is also scientifically proved and practically offered optimal technological parameters of tablets forming melt granulation method.
1. Modification of Nanocomposites by Melting Intercalation of Polypropylene in Montmorillonite
Institute of Scientific and Technical Information of China (English)
2002-01-01
The polypropylene was modified by ultraviolet irradiation.The polypropylene-montmorillonite nanocomposites were prepared by direct melting intercalation of polypropylene powders.The structure of polypropylene,the polyproprlene irradiated, montmorillinote and polypropylene-montmorillonite composites were studied by XRD, IR and DSC. The results show that the PP molecules can are oxidized during ultraviolet irradiation,melt polypropylene can intercalate into montmorillonite layer.As a result,the layered distance (d001) of montmorillonite increases, and the melt absorption peak of polypropylene in layer is eliminated.
2. Energy Efficient Glass Melting - The Next Generation Melter
Energy Technology Data Exchange (ETDEWEB)
David Rue
2008-03-01
The objective of this project is to demonstrate a high intensity glass melter, based on the submerged combustion melting technology. This melter will serve as the melting and homogenization section of a segmented, lower-capital cost, energy-efficient Next Generation Glass Melting System (NGMS). After this project, the melter will be ready to move toward commercial trials for some glasses needing little refining (fiberglass, etc.). For other glasses, a second project Phase or glass industry research is anticipated to develop the fining stage of the NGMS process.
3. Slab melting and magma formation beneath the southern Cascade arc
Science.gov (United States)
Walowski, K. J.; Wallace, P. J.; Clynne, M. A.; Rasmussen, D. J.; Weis, D.
2016-07-01
The processes that drive magma formation beneath the Cascade arc and other warm-slab subduction zones have been debated because young oceanic crust is predicted to largely dehydrate beneath the forearc during subduction. In addition, geochemical variability along strike in the Cascades has led to contrasting interpretations about the role of volatiles in magma generation. Here, we focus on the Lassen segment of the Cascade arc, where previous work has demonstrated across-arc geochemical variations related to subduction enrichment, and H-isotope data suggest that H2O in basaltic magmas is derived from the final breakdown of chlorite in the mantle portion of the slab. We use naturally glassy, olivine-hosted melt inclusions (MI) from the tephra deposits of eight primitive (MgO > 7 wt%) basaltic cinder cones to quantify the pre-eruptive volatile contents of mantle-derived melts in this region. The melt inclusions have B concentrations and isotope ratios that are similar to mid-ocean ridge basalt (MORB), suggesting extensive dehydration of the downgoing plate prior to reaching sub-arc depths and little input of slab-derived B into the mantle wedge. However, correlations of volatile and trace element ratios (H2O/Ce, Cl/Nb, Sr/Nd) in the melt inclusions demonstrate that geochemical variability is the result of variable addition of a hydrous subduction component to the mantle wedge. Furthermore, correlations between subduction component tracers and radiogenic isotope ratios show that the subduction component has less radiogenic Sr and Pb than the Lassen sub-arc mantle, which can be explained by melting of subducted Gorda MORB beneath the arc. Agreement between pMELTS melting models and melt inclusion volatile, major, and trace element data suggests that hydrous slab melt addition to the mantle wedge can produce the range in primitive compositions erupted in the Lassen region. Our results provide further evidence that chlorite-derived fluids from the mantle portion of the
4. Hysteresis in the melting kinetics of Bi nanoparticles
Energy Technology Data Exchange (ETDEWEB)
Haro-Poniatowski, E.; Serna, R.; Afonso, C.N.; Jouanne, M.; Morhange, J.F.; Bosch, P.; Lara, V.H
2004-04-01
Structural properties as a function of temperature of bismuth nanocrystals embedded in amorphous germanium thin films, synthesised by laser ablation are investigated by Raman spectroscopy and X-ray diffraction. In addition to temperature anharmonic effects, Raman spectroscopy results reveal a melting solidification hysteresis, which takes place below the melting point of bulk bismuth. Furthermore, preliminary X-ray diffraction results suggest that the nanocrystals change in structure upon heating until melting occurs. However, the nanocrystals recover their original structure once the sample is cooled at room temperature.
5. Molecular dynamics simulation of Ni3Al melting
Institute of Scientific and Technical Information of China (English)
Rongshan Wang; Huaiyu Hou; Xiaodong Ni; Guoliang Chen
2008-01-01
With the Voter-Chert version of embedded-atom model (EAM) potential and molecular dynamics, the melting of Ni3A1 alloy was simulated by one-phase (conventional) and two-phase approaches. It is shown that the simulated melting point is dependent on the potential and the simulation method. The structures of the melts obtained by different simulation methods were analyzed by the pair correlation function, the coordination number, and the distribution of atom pair type (indexed by the Honeycutt-Andersen pair analysis technique). The results show that the structures are very similar.
6. ELM induced tungsten melting and its impact on tokamak operation
Science.gov (United States)
Coenen, J. W.; Arnoux, G.; Bazylev, B.; Matthews, G. F.; Jachmich, S.; Balboa, I.; Clever, M.; Dejarnac, R.; Coffey, I.; Corre, Y.; Devaux, S.; Frassinetti, L.; Gauthier, E.; Horacek, J.; Knaup, M.; Komm, M.; Krieger, K.; Marsen, S.; Meigs, A.; Mertens, Ph.; Pitts, R. A.; Puetterich, T.; Rack, M.; Stamp, M.; Sergienko, G.; Tamain, P.; Thompson, V.
2015-08-01
In JET-ILW dedicated melt exposures were performed using a sequence of 3MA/2.9T H-Mode JET pulses with an input power of PIN = 23 MW, a stored energy of ∼6 MJ and regular type I ELMs at ΔWELM = 0.3 MJ and fELM ∼ 30 Hz. In order to assess the risk of starting ITER operations with a full W divertor, one of the task was to measure the consequences of W transients melting due to ELMs. JET is the only tokamak able to produce transients/ ELMs large enough (>300 kJ per ELM) to facilitate melting of tungsten. Such ELMs are comparable to mitigated ELMs expected in ITER. By moving the outer strike point (OSP) onto a dedicated leading edge the base temperature was raised within ∼1 s to allow transient ELM-driven melting during the subsequent 0.5 s. Almost 1 mm (∼6 mm3) of W was moved by ∼ 150 ELMs within 5 subsequent discharges. Significant material losses in terms of ejections into the plasma were not observed. There is indirect evidence that some small droplets (∼ 80 μm) were ejected. The impact on the main plasma parameters is minor and no disruptions occurred. The W-melt gradually moved along the lamella edge towards the high field side, driven by j × B forces. The evaporation rate determined is 100 times less than expected from steady state melting and thus only consistent with transient melting during individual ELMs. IR data, spectroscopy, as well as melt modeling point to transient melting. Although the type of damage studied in these JET experiments is unlikely to be experienced in ITER, the results do strongly support the design strategy to avoid exposed edges in the ITER divertor. The JET experiments required a surface at normal incidence and considerable pre-heating to produce tungsten melting. They provide unique experimental evidence for the absence of significant melt splashing at events resembling mitigated ELMs on ITER and establish a unique experimental benchmark for the simulations being used to study transient shallow melting on ITER W
7. Molecular dynamics of MgSiO3 perovskite melting
Institute of Scientific and Technical Information of China (English)
Liu Zi-Jiang; Cheng Xin-Lu; Yang Xiang-Dong; Zhang Hong; Cai Ling-Cang
2006-01-01
The melting curve of MgSiO3 perovskite is simulated using molecular dynamics simulations method at high pressure. It is shown that the simulated equation of state of MgSiO3 perovskite is very successful in reproducing accurately the experimental data. The pressure dependence of the simulated melting temperature of MgSiO3 perovskite reproduces the stability of the orthorhombic perovskite phase up to high pressure of 13OGPa at ambient temperature, consistent with the theoretical data of the other calculations. It is shown that its transformation to the cubic phase and melting at high pressure and high temperature are in agreement with recent experiments.
8. STABILIZATION, REFORMATION AND MELTING OF POLY(L-LACTIDE) CRYSTALLITES
Institute of Scientific and Technical Information of China (English)
Tai-Yon Cho; Barbara Heck; Gert Strobl
2007-01-01
The large size of the crystallites in poly(L-lactide) and the low growth rate enable detailed time- and temperaturedependent X-ray scattering studies of the ordering processes to be carried out. A layer located intermediate between crystals and melt-like regions is observed which finally takes on crystalline order. Recrystallization processes during heating change the complete stack structure rather than the crystallites individually and produce voids in the stacks. Establishment of a new stable structure after a temperature jump in the melting range can be followed in time. DSC experiments indicate times of melting of the order of minutes.
9. On the fluctuation mechanism of melting of supported gold nanoclusters.
Science.gov (United States)
Pushkin, M A; Troyan, V I; Borisyuk, P V; Borman, V D; Tronin, V N
2012-11-01
The size dependence of the melting temperature of Au nanoclusters deposited on SiO2 and HOPG substrates, measured by the elastic-peak electron spectroscopy (EPES) is discussed. The observed behavior of the melting temperature with decrease in clusters' size is qualitatively explained in the framework of the fluctuation mechanism for surface melting. The interaction of nanoclusters with substrate is taken into account by means of the effective surface tension for spherical-segment shaped particles, corresponding to the contact angle of supported nanocluster.
10. Gas atomization of cobalt ferrite-phosphate melts
Science.gov (United States)
De Guire, Mark R.; O'Handley, R. C.; Kalonji, G.
1989-01-01
XRD, Moessbauer spectroscopy, and EDXS have been used to characterize a rapidly-solidified (Co,Fe)3O4 spinel generated in a cobalt-iron-phosphate glass matrix by gas atomization of melts. Of the two compositions tested, that containing 20 mol pct P2O5 exhibited randomly-oriented ferrite crystallization whose growth appears to have been diffusion-controlled. Unlike the ferrite, in which the iron has both tetrahedral and octahedral coordination, the iron in the glassy matrix was primarily of distorted-octahedral coordination. Calculations indicate that the cooling rates obtained with oxide melts vary strongly with droplet size, but less strongly with melt temperature.
11. Arctic melt ponds and energy balance in the climate system
Science.gov (United States)
Sudakov, Ivan
2017-02-01
Elements of Earth's cryosphere, such as the summer Arctic sea ice pack, are melting at precipitous rates that have far outpaced the projections of large scale climate models. Understanding key processes, such as the evolution of melt ponds that form atop Arctic sea ice and control its optical properties, is crucial to improving climate projections. These types of critical phenomena in the cryosphere are of increasing interest as the climate system warms, and are crucial for predicting its stability. In this paper, we consider how geometrical properties of melt ponds can influence ice-albedo feedback and how it can influence the equilibria in the energy balance of the planet.
12. Research of Snow-Melt Process on a Heated Platform
Directory of Open Access Journals (Sweden)
Vasilyev Gregory P.
2016-01-01
Full Text Available The article has shown the results of experimental researches of the snow-melt on a heated platform-near building heat-pump snow-melt platform. The near-building (yard heat pump platforms for snow melt with the area up to 10-15 m2 are a basis of the new ideology of organization of the street cleaning of Moscow from snow in the winter period which supposes the creation in the megalopolis of the «distributed snow-melt system» (DSMS using non-traditional energy sources. The results of natural experimental researches are presented for the estimation of efficiency of application in the climatic conditions of Moscow of heat pumps in the snow-melt systems. The researches were conducted on a model sample of the near-building heat-pump platform which uses the low-potential thermal energy of atmospheric air. The conducted researches have confirmed experimentally in the natural conditions the possibility and efficiency of using of atmospheric air as a source of low-potential thermal energy for evaporation of the snow-melt heat pump systems in the climatic conditions of Moscow. The results of laboratory researches of snow-melt process on a heated horizontal platform are presented. The researches have revealed a considerable dependence of efficiency of the snow-melt process on its piling mode (form-building and the organization of the process of its piling mode (form-building and the organization of the process of its (snow mass heat exchange with the surface of the heated platform. In the process of researches the effect of formation of an «ice dome» under the melting snow mass called by the fact that in case of the thickness of snow loaded on the platform more than 10 cm the water formed from the melting snow while the contact with the heating surface don’t spread on it, but soaks into the snow, wets it due to capillary effect and freezes. The formation of «ice dome» leads to a sharp increase of snow-melt period and decreases the operating
13. Occurrence of silicate melt, carbonate-rich melt and fluid during medium pressure anatexis of metapelitic gneisses (Oberpfalz, Bavaria) revealed by melt and fluid inclusions study
Science.gov (United States)
Ferrero, Silvio; O'Brien, Patrick; Hecht, Lutz; Wunder, Bernd
2014-05-01
In the last decades our understanding of partial melting processes in the lower crust profited from the investigation of fluid inclusions (Touret et al., 2009) and more recently of anatectic melt inclusions (Cesare et al., 2011) within enclaves and high-grade terranes. The latter finding allowed us to directly analyse the original anatectic melt (Ferrero et al., 2012; Bartoli et al., 2013) preserved within peritectic phases, i.e. mainly garnet, but also ilmenite and spinel, before fractionation, mixing and contamination processes took place. Furthermore, the occurrence of primary fluid inclusions (FI) and anatectic melt inclusions (MI) within enclaves allowed the characterization of the COH fluid present during anatexis under fluid+melt immiscibility conditions (Ferrero et al., 2014). Primary crystallized MI, or "nanogranites", and FI have been identified to occur as clusters in garnet from stromatic migmatites (Zeilengneise) from Oberpfalz, Eastern Bavaria (Moldanubian Zone). During the late Carboniferous, these Grt+Bt+Sill+Crd+Spl metapelitic gneisses underwent HT/MP metamorphism, followed by a HT/LP event (Tanner & Behrmann, 1995). Nanogranites, ≤20 µm in size, consist of Qtz+Bt+Wm+Ab±Ap, and show abundant nanoporosity, localized in the quartz. Fluid inclusions are smaller, generally ≤10 µm, and contain CO2+N2+CH4 plus siderite, pyrophillite and cristobalite, mineral phases not observed in the surrounding rock or as mineral inclusion in garnet. Polycrystalline inclusions containing Cc+Wm+Opx±Qz, commonly ≤10 µm in diameter, occur in the same cluster with MI and FI. Microstructural features, negative-crystal shape and the well-developed crystalline faces of calcite within inclusions suggest that they may result from the crystallization of a carbonate-rich melt. The lack of arrays of carbonate-bearing MI, verified by cathodoluminiscence investigation, supports their primary nature, i.e. they formed during garnet growth. This would suggest the occurrence
14. Chemical and thermal unfolding of calreticulin
DEFF Research Database (Denmark)
Duus, K.; Larsen, N.; Tran, T. A. T.;
2013-01-01
was found to obtain a molten structure in urea concentrations between 1-1.5 M urea, and to unfold/aggregate at high and low pH values. The results demonstrated that the fluorescent dye binding assay could measure the thermal stability of calreticulin in aqueous buffers with results comparable to melting...... assay, we have investigated the chemical and thermal stability of calreticulin. When the chemical stability of calreticulin was assessed, a midpoint for calreticulin unfolding was calculated to 3.0M urea using CD data at 222 nm. Using the fluorescent dye binding thermal shift assay, calreticulin...
15. Peltier Heats in Cryolite Melts With Alumina
Energy Technology Data Exchange (ETDEWEB)
Flem, B.E.
1996-12-31
In the production of aluminium, improving the heat balance at the electrolytic cell may contribute to improve the energy conversion efficiency and the current efficiency of the process. The main purpose of this doctoral thesis was to measure Seebeck coefficients, or thermoelectric powers, to settle the question of reversible cooling or heating of the aluminium electrode and to decide the magnitude of the reversible Peltier effect of both the aluminium and the carbon electrode. The irreversible thermodynamics of thermocells is outlined. A thermocell using the binary system AlF{sub 3}-NaF and aluminium electrodes is described and the temperature dependence of the thermoelectric power is given. The system is extended by adding Al{sub 2}O{sub 3} to the molten electrolyte. Both thermocells with aluminium electrodes and oxygen electrodes are treated. The relevance of the thermocell measurements to the Hall-Heroult cell is discussed and an overview of trends in other thermocell systems is given. Measuring thermocell potentials of fluoride melts is complicated and so the experiments are covered in great detail. It is found that there is a reversible heat production at the cathode and a reversible cooling at the anode, which indicates that maximum temperature in the cell occurs at the cathode surface, not in the electrolyte as previously believed. When the electrolyte is saturated with both Al oxide and Al fluoride, the reversible heat effect at the cathode is approximately zero. This means that the cooling of the anode corresponds to the change of entropy in the reduction of Al oxide to Al and carbon dioxide. 186 refs., 23 figs., 25 tabs.
16. Origin of Inhomogeneity in Glass Melts
DEFF Research Database (Denmark)
Jensen, Martin; Keding, Ralf; Yue, Yuanzheng
The homogeneity of a glass plays a crucial role in many applications as the inhomogeneities can provide local changes in mechanical properties, optical properties, and thermal expansion coefficient. Homogeneity is not a single property of the glass, instead, it consists of several factors...... such as bubbles, striae, trace element concentration, undissolved species, and crystallised species. As it is not possible to address all the factors in a single study, this work focuses on one of the major factors: chemical striae. Up to now, the quantification of chemical striae in glasses, particularly......, in less transparent glasses, has been a challenge due to the lack of an applicable method. In this study, we have established a simple and accurate method for quantifying the extent of the striae, which is based on the scanning and picture processing through the Fourier transformation. By performing...
17. Melting behavior of low-level radioactive miscellaneous solid waste and characteristics of solidified products
Energy Technology Data Exchange (ETDEWEB)
Nakashio, Nobuyuki; Isobe, Motoyasu; Wakui, Takuji [Department of Decommissioning and Waste Management, Tokai Research Establishment, Japan Atomic Energy Research Institute, Tokai, Ibaraki (Japan)] (and others)
2001-02-01
Melting tests of simulated miscellaneous solid wastes were conducted to clarify melting behavior of wastes and to characterize solidified products. Two heating modes were adopted in the tests: hybrid heating and induction heating modes. In the former, wastes were heated with both an induction furnace and a plasma torch, and in the latter, an electrical-conductive crucible was used with the induction furnace. The solidified products with no void, which may reduce the mechanical strength of them, were obtained by addition of deoxidizer. It was found that slag and metallic layers of the solidified products were almost homogeneous from the results of measurement of chemical composition and specific gravity. It was confirmed that the solidified products possessed compressive strength required for disposal. Chemical composition of solidified products was changed by corrosion of crucible or refractory material. Cobalt and cesium tracers were uniformly distributed in metallic and slag layers, respectively. It was found that the residual fraction of cesium is influenced by the heating mode. (author)
18. Partial melting of apatite-bearing charnockite, granulite, and diorite: Melt compositions, restite mineralogy, and petrologic implications
Science.gov (United States)
Beard, James S.; Lofgren, Gary E.; Sinha, A. Krishna; Tollo, Richard P.
1994-01-01
Melting experiments (P = 6.9 kbar, T = 850-950 deg C, NNO is less than fO2 is less than HM) were done on mafic to felsic charnockites, a dioritic gneiss, and a felsic garnet granulite, all common rock types in the Grenville basement of eastern North America. A graphite-bearing granulite gneiss did not melt. Water (H2O(+) = 0.60 to 2.0 wt %) is bound in low-grade, retrograde metamorphic minerals and is consumed during the earliest stages of melting. Most melts are water-undersaturated. Melt compositions range from metaluminous, silicic granodiorite (diorite starting composition) to peraluminous or weakly metaluminous granites (all others). In general, liquids become more feldspathic, less silicic, and less peraluminous and are enriched in FeO, MgO, and TiO2 with increasing temperature. Residual feldspar mineralogy controls the CaO, K2O, and Na2O contents of the partial melts and the behavior of these elements can be used, particularly if the degree of source melting can be ascertained, to infer some aspects of the feldspar mineralogy of the source. K-feldspar, a common restite phase in the charnockite and granulite (but not the diorite) should control the behavior of Ba and, possibly, Eu in these systems and yield signatures of these elements that can distinguish source regions and, in some cases, bulk versus melt assimilation. Apatite, a common restite phase, is enriched in rare earth elements (REE), especially middle REE. Retention of apatite in the restite will result in steep, light REE-enriched patterns for melts derived from the diorite and charnockites.
19. Modeling the viscosity of silicate melts containing manganese oxide
Directory of Open Access Journals (Sweden)
Kim Wan-Yi
2013-01-01
Full Text Available Our recently developed model for the viscosity of silicate melts is applied to describe and predict the viscosities of oxide melts containing manganese oxide. The model requires three pairs of adjustable parameters that describe the viscosities in three systems: pure MnO, MnO-SiO2 and MnO-Al2O3-SiO2. The viscosity of other ternary and multicomponent silicate melts containing MnO is then predicted by the model without any additional adjustable model parameters. Experimental viscosity data are reviewed for melts formed by MnO with SiO2, Al2O3, CaO, MgO, PbO, Na2O and K2O. The deviation of the available experimental data from the viscosities predicted by the model is shown to be within experimental error limits.
20. Mechanisms of acoustic processing of a metal melt containing nanoparticles
Science.gov (United States)
Kudryashova, O.; Vorozhtsov, S.; Dubkova, Ya.; Stepkina, M.
2016-11-01
Wave processing with the frequencies from subsound (vibration) to ultrasound is used to produce nanopowder-modified composite alloys. This work considers mechanisms of such processing of metal melts, which lead to deagglomeration and wettability of particles of a metal melt and to the destruction of growing crystals during solidification. The main dependences for the threshold of the turbulence and cavitation were obtained. Resonance phenomena that contribute to positive changes in the melt are discussed. Possible mechanisms of the destruction of growing crystals and agglomerates of particles at the high-frequency processing of the melt are considered, including the destruction of agglomerates in the front of an acoustic wave and the destruction of crystals by oscillating solid particles.
1. Electrical conductivity and viscosity of borosilicate glasses and melts
DEFF Research Database (Denmark)
Ehrt, Doris; Keding, Ralf
2009-01-01
, 0 to 62·5 mol% B2O3, and 25 to 85 mol% SiO2. The glass samples were characterised by different methods. Refractive indices, density and thermal expansion were measured. Phase separation effects were investigated by electron microscopy. The electrical conductivity of glasses and melts were determined...... by impedance measurements in a wide temperature range (250 to 1450°C). The activation energies were calculated by Arrhenius plots in various temperature regions: below the glass transition temperature, Tg, above the melting point, Tl, and between Tg and Tl. Viscosity measurements were carried out...... with different methods from Tg to the melt. The measured data were fitted and the activation energies calculated. Simple exponential behaviour was found only in very narrow temperature ranges. The effect of B2O3 in sodium borosilicate glasses and melts is discussed in comparison with sodium silicate glasses...
2. Glassy dynamics of nanoparticles in semiflexible ring polymer nanocomposite melts
Science.gov (United States)
Zhou, Xiaolin; Jiang, Yangwei; Deng, Zhenyu; Zhang, Linxi
2017-01-01
By employing molecular dynamics simulations, we explore the dynamics of NPs in semiflexible ring polymer nanocomposite melts. A novel glass transition is observed for NPs in semiflexible ring polymer melts as the bending energy (Kb) of ring polymers increases. For NPs in flexible ring polymer melts (Kb = 0), NPs move in the classic diffusive behavior. However, for NPs in semiflexible ring polymer melts with large bending energy, NPs diffuse very slowly and exhibit the glassy state in which the NPs are all irreversibly caged be the neighbouring semiflexible ring polymers. This glass transition occurs well above the classical glass transition temperature at which microscopic mobility is lost, and the topological interactions of semiflexible ring polymers play an important role in this non-classical glass transition. This investigation can help us understand the nature of the glass transition in polymer systems. PMID:28290546
3. Purification effects of glass flux on A356 melt
Institute of Scientific and Technical Information of China (English)
倪红军; 孙宝德; 蒋海燕; 陈晨; 丁文江
2002-01-01
In order to remove hydrogen and inclusions from A356 alloy melt,a low melting-point glass flux,JDN-Ⅱ,was developed.The results indicated that JDN-Ⅱ flux has distinct effect of purification and protection on A356 alloy melt.When the dosage of the flux was 3%,the content of hydrogen in A356 melt was only 2.6 mL/kg at 857 ℃ and 0.7 mL/kg even at 750 ℃.In the meantime,the mechanical properties of the alloy increase greatly with the covering of 3% JDN-Ⅱ flux.Compared with no flux,the tensile strength of A356 alloy increases by 9.42% and the elongation increases by 22%.The purification mechanism of JDN-Ⅱ glass flux was discussed too.
4. ROLE OF MELT EXTRUSION IN THE ENHANCEMENT OF BIOAVAILABILITY
Directory of Open Access Journals (Sweden)
Sahil Bansode* and S. S. Poddar
2012-11-01
Full Text Available Starting from plastic industry, today melt extrusion has found its place in the array of pharmaceutical manufacturing processes. Melt extrusion processes are currently applied in the pharmaceutical field for the formulation of variety of dosage forms such as granules, pellets, tablets, implants, transdermal systems & ophthalmic inserts. This technology represents an efficient pathway for increasing the solubility of poorly soluble drugs. The process forms a solid dispersion where the drug is presented in an amorphous & molecularly dispersed state in a carrier. This leads to an increase in solubility, as no lattice energy has to be overcome during dissolution. Melt extrusion is considered to be an efficient technology in the field of formulation of solid dispersions to improve bioavailability with particular advantages over solvent processes. This article highlights on the technology of Hot Melt Extrusion (HME.
5. Impact-induced melting during accretion of the Earth
CERN Document Server
de Vries, Jellie; Melosh, H Jay; Jacobson, Seth A; Morbidelli, Alessandro; Rubie, David C
2016-01-01
Because of the high energies involved, giant impacts that occur during planetary accretion cause large degrees of melting. The depth of melting in the target body after each collision determines the pressure and temperature conditions of metal-silicate equilibration and thus geochemical fractionation that results from core-mantle differentiation. The accretional collisions involved in forming the terrestrial planets of the inner Solar System have been calculated by previous studies using N-body accretion simulations. Here we use the output from such simulations to determine the volumes of melt produced and thus the pressure and temperature conditions of metal-silicate equilibration, after each impact, as Earth-like planets accrete. For these calculations a parametrised melting model is used that takes impact velocity, impact angle and the respective masses of the impacting bodies into account. The evolution of metal-silicate equilibration pressures (as defined by evolving magma ocean depths) during Earth's ac...
6. Wear behaviour of laser melted an ion implanted materials.
NARCIS (Netherlands)
Beurs, Hans de
1988-01-01
The emphasis in this thesis is on the development of wear resistant materials by laser melting. Furthermore, the principle aim is to search for the dislocation characteristics common to the wear process in heterogeneous materials. ... Zie: Summary
7. Modeling the melting temperature of nanoscaled bimetallic alloys.
Science.gov (United States)
Li, Ming; Zhu, Tian-Shu
2016-06-22
The effect of size, composition and dimension on the melting temperature of nanoscaled bimetallic alloys was investigated by considering the interatomic interaction. The established thermodynamics model without any arbitrarily adjustable parameters can be used to predict the melting temperature of nanoscaled bimetallic alloys. It is found that, the melting temperature and interatomic interaction of nanoscaled bimetallic alloys decrease with the decrease in size and the increasing composition of the lower surface energy metal. Moreover, for the nanoscaled bimetallic alloys with the same size and composition, the dependence of the melting temperature on the dimension can be sequenced as follows: nanoparticles > nanowires > thin films. The accuracy of the developed model is verified by the recent experimental and computer simulation results.
8. VIBROCASTING CRUCIBLES OF DIFFERENT COMPOSITION FOR FRYING INDUCTION MELTING ALLOYS
Directory of Open Access Journals (Sweden)
V. V. Primachenko
2012-01-01
Full Text Available It is shown that PSC «UKRNIIO them. A.S.Berezhnogo has developed technologies for a wide range of induction melting temperature alloys and started commercial production of crucibles of different composition.
9. Shocked Feldspar in L Chondrites: Deformation, Transformation and Local Melting
Science.gov (United States)
Fudge, C.; Sharp, T. G.
2016-08-01
We present textures and compositional profiles of partially to completely transformed plagioclase to maskelynite. Evidence for transformation mechanisms, including solid state transformation and crystallization from melt will be discussed.
10. Close—COntact Melting Around a Hot Sphere
Institute of Scientific and Technical Information of China (English)
YaojiangHu; MinghengShi
1997-01-01
A more general model describing PCM close-contact melting outside a hot sphere is developed with the aid of introducing a paramter α and presenting a supplementary equation for the first time in this paper.The governing integral-differential equations are solved by numerical method.The melt-film thickness variation along the surface of sphere is obtained reasonably due to the consideration of the interface shape more precisely,The calculation resultes of Peclet number,heat transferred and pressure distribution are also compared with that in literature,The model presented in this paper can describe the whole close-contact region and the whole contact melting process.Close-contact melting in spherical or cylindrical capsules to which the model can be extended is also discussed briefly.
11. Dynamic and kinetic properties of Al-Li melts
Science.gov (United States)
Kiselev, A. I.
2008-12-01
The dynamic and kinetic properties of Al-Li melts are calculated. The liquid phase of this system is shown to be characterized by three states with different ion distributions and different degrees of electron localization.
12. A Modeling Approach to Fiber Fracture in Melt Impregnation
Science.gov (United States)
Ren, Feng; Zhang, Cong; Yu, Yang; Xin, Chunling; Tang, Ke; He, Yadong
2017-02-01
The effect of process variables such as roving pulling speed, melt temperature and number of pins on the fiber fracture during the processing of thermoplastic based composites was investigated in this study. The melt impregnation was used in this process of continuous glass fiber reinforced thermoplastic composites. Previous investigators have suggested a variety of models for melt impregnation, while comparatively little effort has been spent on modeling the fiber fracture caused by the viscous resin. Herein, a mathematical model was developed for impregnation process to predict the fiber fracture rate and describe the experimental results with the Weibull intensity distribution function. The optimal parameters of this process were obtained by orthogonal experiment. The results suggest that the fiber fracture is caused by viscous shear stress on fiber bundle in melt impregnation mold when pulling the fiber bundle.
13. Thermodynamic properties of under-cooled silver melts
Institute of Scientific and Technical Information of China (English)
2010-01-01
Differential scanning calorimeter technique combined with the traditional fluxing treatment was used to investigate the specific heat and related thermodynamic properties of under-cooled pure silver melts. The specific heat of the under-cooled melt showed a linear dependence on the temperature in the range of the obtained under-cooling from 0 to 198 K. The related thermodynamic properties of silver, such as the entropy change, the enthalpy change and the Gibbs free energy difference between the under-cooled melt and the solid phase, were derived from the measured specific heat. The relations between the temperature and the thermal diffusion or the thermal conductivity of the under-cooled melt were analyzed respectively.
14. High Quality Silica Bricks for Glass Melting Furnace
Institute of Scientific and Technical Information of China (English)
Zhang Xiaohui; Chai Junlan
2008-01-01
@@ 1 Scope This standard specifies the classification, technical requirements, test method, inspection rules,marking,packing,transportation,storage and quality certification of high quality silica bricks for glass melting furnace.
15. Investigation of the stability of melt flow in gating systems
DEFF Research Database (Denmark)
Tiedje, Niels Skat; Larsen, Per
2011-01-01
of the gating system causes pressure waves to form that eventually lead to defective castings. It is clear that sharp corners and dead ends in gating systems should be avoided, and that more stream lined, organic designs based on fluid dynamic principles will are necessary to design gating systems......Melt flow in four different gating systems designed for production of brake discs was analysed experimentally and by numerical modelling. In the experiments moulds were fitted with glass fronts and melt flow was recorded on video. The video recordings were compared with modelling of melt flow...... in the gating systems. Particular emphasis was on analysing local pressure and formation of pressure waves in the gating system. It was possible to compare melt flow patterns in experiments directly to modelled flow patterns. Generally there was good agreement between flow patterns and filling times. However...
16. Plastic Melt Waste Compactor Flight Demonstrator Payload (PFDP) Project
Data.gov (United States)
National Aeronautics and Space Administration — The PMWC Flight Demonstrator Payload is a trash dewatering and volume reduction system that uses heat melt compaction to remove nearly 100% of water from trash while...
17. Shallow Melting and Underground Drainage in Utopia Planitia, Mars
Science.gov (United States)
Costard, F.; Sejourne, A.; Kargel, J.; Soare, R.
2012-03-01
Based on the identification of sinuous and elongated pits in Utopia Planitia, we suggest that shallow melting and underground drainage are possible. We test that hypothesis using a thermal model that comprises a thick insulating dusty layer.
18. In situ viscosity measurements of albite melt under high pressure
CERN Document Server
Funakoshi, K I; Terasaki, H
2002-01-01
The viscosities of albite (NaAlSi sub 3 O sub 8) melt under high pressures have been measured using an x-ray radiography falling sphere method with synchrotron radiation. This method has enabled us to determine the precise sinking velocity directly. Recent experiments of albite melt showed the presence of a viscosity minimum around 5 GPa (Poe et al 1997 Science 276 1245, Mori et al 2000 Earth Planet. Sci. Lett. 175 87). We present the results for albite melt up to 5.2 GPa at 1600 and 1700 deg. C. The viscosity minimum is clearly observed to be around 4.5 GPa, and it might be explained not by the change of the compression mechanism in albite melt but by change of the phase itself.
19. Sulfur solubility in reduced mafic silicate melts: Implications for the speciation and distribution of sulfur on Mercury
Science.gov (United States)
Namur, Olivier; Charlier, Bernard; Holtz, Francois; Cartier, Camille; McCammon, Catherine
2016-08-01
Chemical data from the MESSENGER spacecraft revealed that surface rocks on Mercury are unusually enriched in sulfur compared to samples from other terrestrial planets. In order to understand the speciation and distribution of sulfur on Mercury, we performed high temperature (1200-1750 °C), low- to high-pressure (1 bar to 4 GPa) experiments on compositions representative of Mercurian lavas and on the silicate composition of an enstatite chondrite. We equilibrated silicate melts with sulfide and metallic melts under highly reducing conditions (IW-1.5 to IW-9.4; IW = iron-wüstite oxygen fugacity buffer). Under these oxygen fugacity conditions, sulfur dissolves in the silicate melt as S2- and forms complexes with Fe2+, Mg2+ and Ca2+. The sulfur concentration in silicate melts at sulfide saturation (SCSS) increases with increasing reducing conditions (from 10 wt.% S at IW-8) and with increasing temperature. Metallic melts have a low sulfur content which decreases from 3 wt.% at IW-2 to 0 wt.% at IW-9. We developed an empirical parameterization to predict SCSS in Mercurian magmas as a function of oxygen fugacity (fO2), temperature, pressure and silicate melt composition. SCSS being not strictly a redox reaction, our expression is fully valid for magmatic systems containing a metal phase. Using physical constraints of the Mercurian mantle and magmas as well as our experimental results, we suggest that basalts on Mercury were free of sulfide globules when they erupted. The high sulfur contents revealed by MESSENGER result from the high sulfur solubility in silicate melt at reducing conditions. We make the realistic assumption that the oxygen fugacity of mantle rocks was set during equilibration of the magma ocean with the core and/or that the mantle contains a minor metal phase and combine our parameterization of SCSS with chemical data from MESSENGER to constrain the oxygen fugacity of Mercury's interior to IW- 5.4 ± 0.4. We also calculate that the mantle of Mercury
20. Enthalpies of DNA melting in the presence of osmolytes.
Science.gov (United States)
Spink, Charles H; Garbett, Nichola; Chaires, Jonathan B
2007-03-01
The melting of DNA in the presence of osmolytes has been studied with the intention of obtaining information about how base pair stability is affected by changes in solution conditions. In previous investigations, the melting enthalpies were assumed to be constant as osmolalities change, but no systematic evaluation of whether this condition is true has been offered. This paper presents calorimetric data on the melting of two synthetic DNA samples in the presence of a number of common osmolytes. Poly(dAdT)*poly(dTdA) and poly(dGdC)*poly(dCdG) melting have been examined by differential scanning calorimetry in solutions containing ethylene glycol, glycerol, sucrose, urea, betaine, PEG 200 and PEG 1450 at increasing osmolalities. The results show small, but significant changes in the enthalpy of melting of the two polynucleotides that are different, depending on the structure of the cosolvent. The polyols, ethylene glycol, glycerol, PEG 200 and also urea all show decreases in melting enthalpy, while betaine and sucrose display increases with increasing concentration of cosolvent. The large stabilizing PEG 1450 shows no change within the experimental errors. Using concepts relating to preferential interactions of the cosolvents with the DNA base pairs, it is possible to interpret some of the observed changes in the thermodynamic properties of melting. The results indicate that there is strong entropy-enthalpy compensation upon melting base pairs, but entropy increases dominate to cause the decreases in stability with increased cosolvent concentration. Excess hydration parameters are evaluated and their magnitudes discussed in terms of changes in cosolvent interactions with the DNA base pairs.
1. MELT RATE FURNACE TESTING FOR SLUDGE BATCH 5 FRIT OPTIMIZATION
Energy Technology Data Exchange (ETDEWEB)
Miller, D; Fox, K; Pickenheim, B; Stone, M
2008-10-03
Savannah River National Laboratory (SRNL) was requested to provide the Defense Waste Processing Facility (DWPF) with a frit composition for Sludge Batch 5 (SB5) to optimize processing. A series of experiments were designed for testing in the Melt Rate Furnace (MRF). This dry fed tool can be used to quickly determine relative melt rates for a large number of candidate frit compositions and lead to a selection for further testing. Simulated Sludge Receipt and Adjustment Tank (SRAT) product was made according to the most recent SB5 sludge projections and a series of tests were conducted with frits that covered a range of boron and alkali ratios. Several frits with relatively large projected operating windows indicated melt rates that would not severely impact production. As seen with previous MRF testing, increasing the boron concentration had positive impacts on melt rate on the SB5 system. However, there appears to be maximum values for both boron and sodium above which the there is a negative effect on melt rate. Based on these data and compositional trends, Frit 418 and a specially designed frit (Frit 550) have been selected for additional melt rate testing. Frit 418 and Frit 550 will be run in the Slurry Fed Melt Rate Furnace (SMRF), which is capable of distinguishing rheological properties not detected by the MRF. Frit 418 will be used initially for SB5 processing in DWPF (given its robustness to compositional uncertainty). The Frit 418-SB5 system will provide a baseline from which potential melt rate advantages of Frit 550 can be gauged. The data from SMRF testing will be used to determine whether Frit 550 should be recommended for implementation in DWPF.
2. Zn isotopic heterogeneity in the mantle: A melting control?
Science.gov (United States)
Doucet, Luc S.; Mattielli, Nadine; Ionov, Dmitri A.; Debouge, Wendy; Golovin, Alexander V.
2016-10-01
We present new Zn elemental and isotope data on seventeen fertile and refractory mantle peridotite xenoliths. Eleven fertile peridotites are garnet and spinel lherzolites from Vitim and Tariat (Siberia and Mongolia) and represent some of the most pristine fertile peridotites available. Six refractory peridotites are spinel harzburgites from the Udachnaya kimberlite (Siberian craton) that are nearly pristine residues of high-degree polybaric melting at high pressure (7-4 GPa). Geochemical data suggest that Zn isotopic compositions in the peridotites have not been affected by post-melting processes such as metasomatism, contamination by the host-magmas or alteration. The fertile peridotites have uniform Zn concentrations (59 ± 2 ppm) and Zn isotopic compositions with δ66Zn (relative to JMC-Lyon-03-0749l) = +0.30 ± 0.03‰ consistent with the Bulk Silicate Earth estimates of δ66Zn = +0.28 ± 0.05‰ (Chen et al., 2013). The refractory peridotites have Zn concentrations ranging from 30 to 48 ppm and δ66Zn from + 0.10 ± 0.01 ‰ to + 0.18 ± 0.01 ‰ with an average of + 0.14 ± 0.03 ‰. Our data suggest that the lithospheric mantle has a heterogeneous Zn isotopic composition. Modeling of Zn isotope partitioning during partial melting of fertile mantle suggests that high degrees of melt extraction (>30%) may significantly fractionate Zn isotopes (up to 0.16‰) and that during mantle melting, Zn concentrations and isotopic compositions are mainly controlled by the stability of clinopyroxene and garnet within the melting residue. Because the stability of clinopyroxene and garnet is mainly pressure dependent we suggest that both the depth and the degrees of melt extraction may control Zn isotope fractionation during mantle melting.
3. Primary carbonatite melt from deeply subducted oceanic crust
OpenAIRE
Walter, Michael J.; Bulanova, Galina; Armstrong, Lora S; Keshav, S; Blundy, Jon D; Gudfinnsson, G; Lord, Oliver T.; Lennie, A; Clark, SM; Smith, C; Gobbo, L
2008-01-01
Partial melting in the Earth’s mantle plays an important part in generating the geochemical and isotopic diversity observed in volcanic rocks at the surface. Identifying the composition of these primary melts in the mantle is crucial for establishing links between mantle geochemical ‘reservoirs’ and fundamental geodynamic processes. Mineral inclusions in natural diamonds have provided a unique window into such deep mantle processes. Here we provide experimental and geochemical evidence that s...
4. Melting Point Of Metals In Relation Io Electron Charge Density
Directory of Open Access Journals (Sweden)
Boczkal G.
2015-09-01
Full Text Available The concept of spatial criterion of the electron charge concentration is applied to determine the metal melting point. Based on the model proposed for bcc metals, a model for hcp metals and general form for others has been developed. To calculate the melting point, only structural data and atomic number are required. The obtained results show good consistency with the experimental data for metals with atomic number Z < 70.
5. Reactive Melt Infiltration Of Silicon Into Porous Carbon
Science.gov (United States)
Behrendt, Donald R.; Singh, Mrityunjay
1994-01-01
Report describes study of synthesis of silicon carbide and related ceramics by reactive melt infiltration of silicon and silicon/molybdenum alloys into porous carbon preforms. Reactive melt infiltration has potential for making components in nearly net shape, performed in less time and at lower temperature. Object of study to determine effect of initial pore volume fraction, pore size, and infiltration material on quality of resultant product.
6. H2O diffusion in Mount Changbai peralkaline rhyolitic melt
Science.gov (United States)
Zhang, Y.; Xu, Z.; Wang, H.; Behrens, H.
2008-05-01
For quantitative modeling of bubble growth and volcanic eruption dynamics, it is necessary to know H2O diffusivity in the melt. Mount Changbai Volcano at the border of China and North Korea has produced explosive peralkaline rhyolitic eruptions, including a 30-km3 eruption with an age of 1 ky (Horn and Schmincke, 2000). H2O diffusivity is expected to be greater in a peralkaline rhyolitic melt than a calc-alkaline rhyolitic melt. We have experimentally investigated H2O diffusion in Mount Changbai peralkaline rhyolite. Because phenocryst-free glass is not available from Mount Changbai eruption products, the starting materials (nominally dry and hydrous) are synthesized. The diffusion couple technique, with one half dry and the other half wet, is adopted. Three high- temperature experiments have been carried out at 500 MPa and one at 1500 MPa in a piston-cylinder apparatus. After the experiment, the sample is prepared into a doubly-polished section of about 0.2 mm thickness, which is analyzed by a Perkin-Elmer FTIR microscope. The data are fit following the procedures of Zhang and Behrens (2000) and Ni and Zhang (2008). Preliminary data show that H2O diffusivity in peralkaline rhyolitic melt is greater than that in calc-alkaline rhyolitic melt (Zhang and Behrens, 2000), as expected. The exact difference depends on temperature and pressure, and the ratio of diffusivity in the peralkaline rhyolitic melt to that in the calc-alkaline rhyolitic melt ranges from 1 to 3. More experiments will be conducted on this melt to provide the basic data for specific modeling of bubble growth and volcanic eruption dynamics in past and future Mount Changbai eruptions and other peralkaline rhyolitic eruptions. References: Horn S and Schmincke H U (2000) Bull. Volcanol., 61, 537. Ni H and Zhang Y (2008) Chem. Geol., doi: 10.1016/j.chemgeo.2008.01.011. Zhang Y and Behrens H (2000) Chem. Geol., 169, 243.
7. Floating Ice-Algal Aggregates below melting Arctic Sea Ice
OpenAIRE
Philipp Assmy; Jens K. Ehn; Mar Fernández-Méndez; Haakon Hop; Christian Katlein; Arild Sundfjord; Katrin Bluhm; Malin Daase; Anja Engel; Agneta Fransson; Granskog, Mats A.; Hudson, Stephen R.; Svein Kristiansen; Marcel Nicolaus; Ilka Peeken
2013-01-01
During two consecutive cruises to the Eastern Central Arctic in late summer 2012, we observed floating algal aggregates in the melt-water layer below and between melting ice floes of first-year pack ice. The macroscopic (1 – 15 cm in diameter) aggregates had a mucous consistency and were dominated by typical ice-associated pennate diatoms embedded within the mucous matrix. Aggregates maintained buoyancy and accumulated just above a strong pycnocline that separated meltwater and seawater layer...
8. Impact History on Vesta: Petrographic, Compositional and Future Chronological Studies of Melt Clasts in Howardites
Science.gov (United States)
Cartwright, J. A.; Mittlefehldt, D. W.; Hodges, K. V.; Wadhwa, M.
2015-01-01
Howardite meteorites are polymict breccias composed mainly of eucritic and diogenitic material that likely originate from the surface of the Asteroid 4 Vesta. They can be separated into two subtypes: Regolithic, which represent the lithified remains of the active vestan regolith; Fragmental, which represent simpler polymict breccias. Amongst the regolithic features observed in the former, melt clasts are particularly striking for their appearance and compositional variability. They range from glassy spherules to finely crystalline (i.e., devitrified) clasts, and clasts containing only relict mineral grains to those containing only phenocrysts. Glasses can be separated into compositional sub-types including those with low FeO/MgO ratios (less than 5) -low alkali glasses, K-rich (K2O greater than 0.2 wt.%), Na-rich (Na2O greater than 0.6 wt.%) and CaO-rich, and those with high FeO/MgO ratios (greater than 10). There is also a distinction to be made between primary volcanic melt clasts and those produced by impacts. While suggested that a lack of chemical homogeneity among their studied melt clasts ruled out a primary volcanic origin, the low siderophile element contents observed in such clasts suggest less compositional influence from impactors than commonly assumed. Studying the chronology of the impact melt clasts in howardites can help us to better determine the timing of impact events on Vesta and the asteroid belt. In this research, we are launching an investigation into the petrology, composition (major/trace element and noble gas) and chronology of melt clasts in howardites. We have selected a set of howardites known to contain large quantities of melt clasts, and have begun the petrological and compositional studies of these materials. Once the melt clasts have been fully classified, we aim to perform chronological studies of individual clasts using both the Ar-40/Ar-39 and Pb-Pb chronometers, as well as determine the noble gas components present. Of
9. Contrasting sediment melt and fluid signatures for magma components in the Aeolian Arc: Implications for numerical modeling of subduction systems
Science.gov (United States)
Zamboni, Denis; Gazel, Esteban; Ryan, Jeffrey G.; Cannatelli, Claudia; Lucchi, Federico; Atlas, Zachary D.; Trela, Jarek; Mazza, Sarah E.; De Vivo, Benedetto
2016-06-01
The complex geodynamic evolution of Aeolian Arc in the southern Tyrrhenian Sea resulted in melts with some of the most pronounced along the arc geochemical variation in incompatible trace elements and radiogenic isotopes worldwide, likely reflecting variations in arc magma source components. Here we elucidate the effects of subducted components on magma sources along different sections of the Aeolian Arc by evaluating systematics of elements depleted in the upper mantle but enriched in the subducting slab, focusing on a new set of B, Be, As, and Li measurements. Based on our new results, we suggest that both hydrous fluids and silicate melts were involved in element transport from the subducting slab to the mantle wedge. Hydrous fluids strongly influence the chemical composition of lavas in the central arc (Salina) while a melt component from subducted sediments probably plays a key role in metasomatic reactions in the mantle wedge below the peripheral islands (Stromboli). We also noted similarities in subducting components between the Aeolian Archipelago, the Phlegrean Fields, and other volcanic arcs/arc segments around the world (e.g., Sunda, Cascades, Mexican Volcanic Belt). We suggest that the presence of melt components in all these locations resulted from an increase in the mantle wedge temperature by inflow of hot asthenospheric material from tears/windows in the slab or from around the edges of the sinking slab.
10. Partial crystallization of picritic melt and its applications for the genesis of high-Ti and low-Ti basalts
Science.gov (United States)
Yang, J.; WANG, C.; Jin, Z.; Jin, S.; Yan, S.
2015-12-01
Geochemical and petrological studies have revealed the existence of high-Ti and low-Ti basalts in large igneous provinces (LIPs). However the originate of these high-Ti and low-Ti magmas are still under debate. Several different mechanisms have been proposed: (1) the high-Ti basalts are formed by the melting of mantle plume containing recycled oceanic crust (Spandler et al., 2008) while low-Ti basalts are formed by the melting of subcontinental lithospheric mantle (Xiao et al., 2004); (2) both high-Ti and low-Ti basalts are from mantle plume source, but the production of high-Ti basalts are associated with the thick lithosphere while the low-Ti basalts are controlled by the thin lithosphere (Arndt et al., 1993); (3) they are derived from the different degrees of melting, with high-Ti basalts representing low degree of partial melting of mantle plume (Xu et al., 2004). The low Mg# (below 0.7) of high-Ti and low-Ti basalts provides that they are far away from direct melting of mantle peridotite. In addition, seismic data indicate unusually high seismic velocities bodies beneath the LIPs which explained by the fractionated cumulates from picritic magmas (Farnetani et al., 1996). Therefore, we believed that the crystallization differentiation process might play a more significant role in the genesis of high-Ti and low-Ti basalts.In order to investigate the generation of high-Ti and low-Ti basalts, a series of high pressure and high temperature partial crystallization experiments were performed at pressures of 1.5, 3.0 and 5.0 GPa and a temperature range of 1200-1700℃. The starting material is picrate glass with relative high TiO2 (2.7 wt %), which is synthesized according to the chemical composition of primary magmas of Emeishan LIP (Xu et al., 2001). The experimental results show that: (1) At a given pressure, the TiO2 content is decreased with increasing melt fraction; (2) At a given melt fraction, the TiO2 content of melts is increased with increasing pressure. On
11. Mantle refertilization by melts of crustal-derived garnet pyroxenite: Evidence from the Ronda peridotite massif, southern Spain
Science.gov (United States)
Marchesi, Claudio; Garrido, Carlos J.; Bosch, Delphine; Bodinier, Jean-Louis; Gervilla, Fernando; Hidas, Károly
2013-01-01
-peridotite interaction, such as secondary spinel lherzolite in Ronda, may nucleate magmatic channels that remain chemically isolated from the ambient mantle and act as preferential pathways for melts with the signature of recycled crust.
12. Relationship between Oxygen Chemical Potential and Steel Cleanliness
Institute of Scientific and Technical Information of China (English)
Mansour Soltanieh; Yousef Payandeh
2005-01-01
To investigate inclusion formation in each step during steel making process, several samples were taken in different steps of the production of steel at Mobarakeh Steel Co of Esfahan to measure the oxygen chemical potential of the molten steel in each stage. The chemical compositions of the inclusions in samples were investigated lby scanning electron microscope. The chemical composition of the slag was analyzed. With the use of thermodynamic calculations and chemical analysis of the melt, at the working temperature, the relationship between dissolved oxygen and other elements were determined. Finally, it was found that there is a close relationship between inclusions formed in each step with the oxygen partial pressure.
13. MONOBLOCK EMITTERS FOR MELTING OF SYNTHETIC FATTY ACIDS
Directory of Open Access Journals (Sweden)
A. N. Cherepanov
2014-03-01
Full Text Available The paper deals with usage of monoblock emitters for melting of synthetic fatty acids, which are delivered to plants in a solid state and are used in the production of detergents as liquids. In such emitters all lamps are arranged in a common case. Irradiation of the solid phase in the direction of the channel melting axis is done through an output quartz window. This method excludes the possibility of slowing down or stopping the process when one of the tubes is overheated. Halogen lamps are used as light sources, each one is placed in individual transparent body. Combined effect of thermal power supply and the light emission should provide a significant increase in the rate of the channel melting in the solid phase of the synthetic fatty acid. The results of evaluations for achievable rates of the channel melting in the solid phase of the synthetic fatty acids are presented. Melting of the channel with one meter depth can be reached in less than an hour when eight halogen lamps of 100 W power are used. To exclude the possibility of self-ignition of the liquid phase of synthetic fatty acid it is proposed to adjust the luminosity of the emitter and the surface temperature by selecting the number of lamps in the monoblock emitter cavity. The usage of cylindrical quartz tube as a case for monoblock emitter increases the diameter of the melting channel due to side effects of light on the solid and liquid phases.
14. Melting and casting of FeAl-based cast alloy
Energy Technology Data Exchange (ETDEWEB)
Sikka, V.K. [Oak Ridge National Lab., TN (United States); Wilkening, D. [Columbia Falls Aluminum Co., Columbia Falls, MT (United States); Liebetrau, J.; Mackey, B. [AFFCO, L.L.C., Anaconda, MT (United States)
1998-11-01
The FeAl-based intermetallic alloys are of great interest because of their low density, low raw material cost, and excellent resistance to high-temperature oxidation, sulfidation, carburization, and molten salts. The applications based on these unique properties of FeAl require methods to melt and cast these alloys into complex-shaped castings and centrifugal cast tubes. This paper addresses the melting-related issues and the effect of chemistry on the microstructure and hardness of castings. It is concluded that the use of the Exo-Melt{trademark} process for melting and the proper selection of the aluminum melt stock can result in porosity-free castings. The FeAl alloys can be melted and cast from the virgin and revert stock. A large variation in carbon content of the alloys is possible before the precipitation of graphite flakes occurs. Titanium is a very potent addition to refine the grain size of castings. A range of complex sand castings and two different sizes of centrifugal cast tubes of the alloy have already been cast.
15. Melting and casting of FeAl-based cast alloy
Energy Technology Data Exchange (ETDEWEB)
Sikka, V.K. [Oak Ridge National Lab., TN (United States). Metals and Ceramics Div.; Wilkening, D. [Columbia Falls Aluminum Co., 2000 Aluminum Dr., Columbia Falls, MT 59912 (United States); Liebetrau, J.; Mackey, B. [AFFCO, L.L.C., P.O. Box 1071, Anaconda, MT 59711 (United States)
1998-12-31
The FeAl-based intermetallic alloys are of great interest because of their low density, low raw material cost, and excellent resistance to high-temperature oxidation, sulfidation, carburization, and molten salts. The applications based on these unique properties of FeAl require methods to melt and cast these alloys into complex-shaped castings and centrifugal cast tubes. This paper addresses the melting-related issues and the effect of chemistry on the microstructure and hardness of castings. It is concluded that the use of the Exo-Melt{sup TM} process for melting and the proper selection of the aluminum melt stock can result in porosity-free castings. The FeAl alloys can be melted and cast from the virgin and revert stock. A large variation in carbon content of the alloys is possible before the precipitation of graphite flakes occurs. Titanium is a very potent addition to refine the grain size of castings. A range of complex sand castings and two different sizes of centrifugal cast tubes of the alloy have already been cast. (orig.) 18 refs.
16. Voronoi Structural Evolution of Bulk Silicon upon Melting
Institute of Scientific and Technical Information of China (English)
ZHANG Shi-Liang; ZHANG Xin-Yu; WANG Lin-Min; QI Li; ZHANG Su-Hong; ZHU Yan; LIU Ri-Ping
2011-01-01
@@ The Voronoi structural evolution of silicon upon melting is investigated using a molecular dynamics simulation.At temperatures below the melting point, the solid state system is identified to have a four-fold coordination structure .As the temperature increases, the five-fold coordination and six-fold coordination structures and are observed.This is explained in terms of increasing atomic displacement due to thermal motion and the trapping of the moving atoms by others.At temperatures above the melting point, nearly ali of the four-fold coordination structures grows into multiple-fold coordination ones.%The Voronoi structural evolution of silicon upon melting is investigated using a molecular dynamics simulation. At temperatures below the melting point, the solid state system is identified to have a four-told coordination structure (4,0,0,0). As the temperature increases, the five-fold coordination (2,3,0,0) and six-fold coordination structures (2,2,2,0) and (0,6,0,0) are observed. This is explained in terms of increasing atomic displacement due to thermal motion and the trapping of the moving atoms by others. At temperatures above the melting point, nearly all of the four-fold coordination structures grows into multiple-fold coordination ones.
17. Determination of Reactive Surface Area of Melt Glass
Energy Technology Data Exchange (ETDEWEB)
Bourcier,W.L.; Roberts, S.; Smith, D.K.; Hulsey, S.; Newton,L.; Sawvel, A.; Bruton, C.; Papelis, C.; Um, W.; Russell, C. E.; Chapman,J.
2000-10-01
A comprehensive investigation of natural and manmade silicate glasses, and nuclear melt glass was undertaken in order to derive an estimate of glass reactive surface area. Reactive surface area is needed to model release rates of radionuclides from nuclear melt glass in the subsurface. Because of the limited availability of nuclear melt glasses, natural volcanic glass samples were collected which had similar textures and compositions as those of melt glass. A flow-through reactor was used to measure the reactive surface area of the analog glasses in the presence of simplified NTS site ground waters. A measure of the physical surface area of these glasses was obtained using the BET gas-adsorption method. The studies on analog glasses were supplemented by measurement of the surface areas of pieces of actual melt glass using the BET method. The variability of the results reflect the sample preparation and measurement techniques used, as well as textural heterogeneity inherent to these samples. Based on measurements of analog and actual samples, it is recommended that the hydraulic source term calculations employ a range of 0.001 to 0.01 m{sup 2}/g for the reactive surface area of nuclear melt glass.
18. Experimental study on MSW gasification and melting technology
Institute of Scientific and Technical Information of China (English)
2007-01-01
In order to develop municipal solid waste (MSW) gasification and melting technology, two preliminary experiments and a principle integrated experiment were fulfilled respectively. The gasification characteristics of MSW are studied at 500-750℃ when equivalence ratio (ER) was 0.2-0.5 using a fluidized-bed gasifier. When temperature was 550-700℃ and ER was 0.2-0.4, low heat value (LHV) of syngas reaches 4000-12000 kJ/Nm3. The melting characteristics of fly ash were investigated at 1100-1460℃ using a fixed-bed furnace. It was proved that over 99.9% of dioxins could be decomposed and most heavy-metals could be solidified when temperature was 1100-1300℃. The principle integrated experiment was carried out in a fluidized-bed gasification and swirl-melting system. MSW was gasified efficiently at 550-650℃, swirl-melting furnace maintains at 1200-1300℃ stably and over 95% of fly ash could be caught by the swirl-melting furnace. The results provided much practical experience and basic data to develop MSW gasification and melting technology.
19. Melt Protection of Mg-Al Based Alloys
Directory of Open Access Journals (Sweden)
María J. Balart
2016-05-01
Full Text Available This paper reports the current status of Mg melt protection in view to identify near-future challenges, but also opportunities, for Mg melt protection of Mg-Al based alloys. The goal is to design and manufacture sustainable Mg alloys for resource efficiency, recycling and minimising waste. Among alternative cover gas technologies for Mg melt protection other than SF6: commercially available technologies containing―HFC-134a, fluorinated ketone and dilute SO2―and developed technologies containing solid CO2, BF3 and SO2F2, can potentially produce toxic and/or corrosive by-products. On the other hand, additions of alkaline earth metal oxides to Mg and its alloys have developed a strong comparative advantage in the field of Mg melt protection. The near-future challenges and opportunities for Mg-Al based alloys include optimising and using CO2 gas as feedstock for both melt protection and grain refinement and TiO2 additions for melt protection.
20. Modified enthalpy method for the simulation of melting and solidification
Niranjan N Gudibande; Kannan N Iyer
2013-12-01
Enthalpy method is commonly used in the simulation of melting and solidification owing to its ease of implementation. It however has a few shortcomings. When it is used to simulate melting/solidification on a coarse grid, the temperature time history of a point close to the interface shows waviness. While simulatingmelting with natural convection, in order to impose no-slip and impermeability boundary conditions, momentum sink terms are used with some arbitrary constants called mushy zone constants. The values of these are very large and have no physical basis. Further, the chosen values affect the predictions and hence have to be tuned for satisfactory comparison with experimental data. To overcome these deficiencies, a new cell splitting method under the framework of the enthalpy method has been proposed. This method does not produce waviness nor requires mushy zone constants for simulating melting with natural convection. The method is then demonstrated for a simple onedimensional melting problem and the results are compared with analytical solutions. The method is then demonstrated to work in two-dimensions and comparisons are shown with analytical solutions for problems with planar and curvilinear interfaces. To further benchmark the present method, simulations are performed for melting in a rectangular cavity with natural convection in the liquid melt. The solid–liquid interface obtained is compared satisfactorily with the experimental results available in literature.
1. A metastable liquid melted from a crystalline solid under decompression
Science.gov (United States)
Lin, Chuanlong; Smith, Jesse S.; Sinogeikin, Stanislav V.; Kono, Yoshio; Park, Changyong; Kenney-Benson, Curtis; Shen, Guoyin
2017-01-01
A metastable liquid may exist under supercooling, sustaining the liquid below the melting point such as supercooled water and silicon. It may also exist as a transient state in solid–solid transitions, as demonstrated in recent studies of colloidal particles and glass-forming metallic systems. One important question is whether a crystalline solid may directly melt into a sustainable metastable liquid. By thermal heating, a crystalline solid will always melt into a liquid above the melting point. Here we report that a high-pressure crystalline phase of bismuth can melt into a metastable liquid below the melting line through a decompression process. The decompression-induced metastable liquid can be maintained for hours in static conditions, and transform to crystalline phases when external perturbations, such as heating and cooling, are applied. It occurs in the pressure–temperature region similar to where the supercooled liquid Bi is observed. Akin to supercooled liquid, the pressure-induced metastable liquid may be more ubiquitous than we thought. PMID:28112152
2. Widespread Refreezing of Both Surface and Basal Melt Water Beneath the Greenland Ice Sheet
Science.gov (United States)
Bell, R. E.; Tinto, K. J.; Das, I.; Wolovick, M.; Chu, W.; Creyts, T. T.; Frearson, N.
2013-12-01
The isotopically and chemically distinct, bubble-free ice observed along the Greenland Ice Sheet margin both in the Russell Glacier and north of Jacobshavn must have formed when water froze from subglacial networks. Where this refreezing occurs and what impact it has on ice sheet processes remain unclear. We use airborne radar data to demonstrate that freeze-on to the ice sheet base and associated deformation produce large ice units up to 700 m thick throughout northern Greenland. Along the ice sheet margin, in the ablation zone, surface meltwater, delivered via moulins, refreezes to the ice sheet base over rugged topography. In the interior, water melted from the ice sheet base is refrozen and surrounded by folded ice. A significant fraction of the ice sheet is modified by basal freeze-on and associated deformation. For the Eqip and Petermann catchments, representing the ice sheet margin and interior respectively, extensive airborne radar datasets show that 10%-13% of the base of the ice sheet and up to a third of the catchment width is modified by basal freeze-on. The interior units develop over relatively subdued topography with modest water flux from basal melt where conductive cooling likely dominates. Steps in the bed topography associated with subglacial valley networks may foster glaciohydraulic supercooling. The ablation zone units develop where both surface melt and crevassing are widespread and large volumes of surface meltwater will reach the base of the ice sheet. The relatively steep topography at the upslope edge of the ablation zone units combined with the larger water flux suggests that supercooling plays a greater role in their formation. The ice qualities of the ablation zone units should reflect the relatively fresh surface melt whereas the chemistry of the interior units should reflect solute-rich basal melt. Changes in basal conditions such as the presence of till patches may contribute to the formation of the large basal units near the
3. Deep mixing of mantle melts beneath continental flood basalt provinces: Constraints from olivine-hosted melt inclusions in primitive magmas
Science.gov (United States)
Jennings, Eleanor S.; Gibson, Sally A.; Maclennan, John; Heinonen, Jussi S.
2017-01-01
We present major and trace element compositions of 154 re-homogenised olivine-hosted melt inclusions found in primitive rocks (picrites and ferropicrites) from the Mesozoic Paraná-Etendeka and Karoo Continental Flood Basalt (CFB) provinces. The major element compositions of the melt inclusions, especially their Fe/Mg ratios, are variable and erratic, and attributed to the re-homogenisation process during sample preparation. In contrast, the trace element compositions of both the picrite and ferropicrite olivine-hosted melt inclusions are remarkably uniform and closely reflect those of the host whole-rocks, except in a small subset affected by hydrothermal alteration. The Paraná-Etendeka picrites and ferropicrites are petrogenetically related to the more evolved and voluminous flood basalts, and so we propose that compositional homogeneity at the melt inclusion scale implies that the CFB parental mantle melts were well mixed prior to extensive crystallisation. The incompatible trace element homogeneity of olivine-hosted melt inclusions in Paraná-Etendeka and Karoo primitive magmatic rocks has also been identified in other CFB provinces and contrasts with findings from studies of basalts from mid-ocean ridges (e.g. Iceland and FAMOUS on the Mid Atlantic Ridge), where heterogeneity of incompatible trace elements in olivine-hosted melt inclusions is more pronounced. We suggest that the low variability in incompatible trace element contents of olivine-hosted melt inclusions in near-primitive CFB rocks, and also ocean island basalts associated with moderately thick lithosphere (e.g. Hawaii, Galápagos, Samoa), may reflect mixing along their longer transport pathways during ascent and/or a temperature contrast between the liquidus and the liquid when it arrives in the crust. These thermal paths promote mixing of mantle melts prior to their entrapment by growing olivine crystals in crustal magma chambers. Olivine-hosted melt inclusions of ferropicrites from the Paran
4. Termochemical Models For Slags and Silicate Melts, Review and Perspectives
Science.gov (United States)
Ottonello, G.
Thermochemical models devoted to the comprehension of reactive and mixing properties of silicate melts and slags may be roughly grouped into four main classes: 1) fictive chemical; 2) quasi chemical; 3) fictive structural; 4) polymeric. In the first class we may group the fictive regular mixture approach of Ghiorso and Carmichael [1,2]and its extensions [3-5]and the subregular model of Berman and Brown [6]. To the second class belong the modified quasi chemical approach of Pelton and coworkers [7,8] , and the Kapoor - Froberg cellular model and its extensions [9-11]. The third class has much to share with the second one (and indeed the cellular model could be ascribed to this class as well). To this class belong the "central surround model" of Sastri and Lahiri [12] , the associated solution models of Bjorkman [13], Hastie and coworkers [14]and Goel and coworkers [15], the two sublattice model of Hillert and coworkers [16]and the polynomial expansions of Hoch and Arpshofen [17] . The fourth class encompasses the models of Masson[18-20] , Toop-Samis [21,22]and its extensions [23-25] . The phylosophy beyond each one of the four classes is basically different. Benefits and drawbacks are present in any of them, and applications are often limited to simple systems (or to sufficiently complex systems, in the case of arbitrary deconvolutions of type 1) and to limited P-T ranges. The crucial aspects of the various models will be outlined to some extent. It will be shown that, often, model conflictuality is only appartent and that, in some cases, model failure is unperceived by acritical utilizers. New perspectives in the future research devoted to the comprehension of melt reactivity in compositionally complex systems, with special enphasis on the solubility of gaseous components and unmixing, will be finally discussed. References: [1] Ghiorso M.S. and Carmichael I.S.E. (1980) Contrib. Mineral. Petrol., 71, 323-342. [2] Ghiorso M.S., Carmichael I.S.E., Rivers M.L. and Sack
5. Mixing Experiments with Natural Shoshonitic and Trachytic Melts
Science.gov (United States)
de Campos, C. P.; Perugini, D.; Kolzenburg, S.; Petrelli, M.; Dorfman, A.; Dingwell, D. B.
2010-12-01
end-members, in different proportions, have been mixed together using a concentric cylinder viscometer. For the 2nd set of experiments forced convection has been simulated by stirring with a spindle. Experimental conditions were constrained by: 1) constant angular velocity (0.5 rotations per minute) and 2) constant temperature (1,300°C). The experiments terminated by stopping all movement, extracting the spindle from the sample and letting the sample cool to room temperature. Cylinders of the resultant mixed glasses were recovered by drilling and, prepared for microprobe analysis. Microprobe and ICP-MS analyses along longitudinal lines from sections of all the resulting products reveal a complex non-linear mixing process with different mobility for different elements. Chemical data from both experiments (with the centrifuge and the viscometer) will be discussed in a comparative way. Our results highlight the importance of chaotic dynamics for the efficiency of the mixing process in silicate melts.
6. Chemical Mahjong
Science.gov (United States)
Cossairt, Travis J.; Grubbs, W. Tandy
2011-01-01
An open-access, Web-based mnemonic game is described whereby introductory chemistry knowledge is tested using mahjong solitaire game play. Several tile sets and board layouts are included that are themed upon different chemical topics. Introductory tile sets can be selected that prompt the player to match element names to symbols and metric…
7. Chemical dispersants
NARCIS (Netherlands)
Rahsepar, Shokouhalsadat; Smit, Martijn P.J.; Murk, Albertinka J.; Rijnaarts, Huub H.M.; Langenhoff, Alette A.M.
2016-01-01
Chemical dispersants were used in response to the Deepwater Horizon oil spill in the Gulf of Mexico, both at the sea surface and the wellhead. Their effect on oil biodegradation is unclear, as studies showed both inhibition and enhancement. This study addresses the effect of Corexit on oil biodeg
8. Melt Segregation & LPO in Anorthite-Basalt Deformed in Torsion
Science.gov (United States)
Zimmerman, M. E.; Kohlstedt, D. L.
2003-12-01
Deformation in the middle and lower crust is in large part controlled by the rheology of feldspar. Seismic studies have shown that the middle crust of orogenic belts is partially molten. Structural studies of mylonites and migmatites from these terrains record large strain deformation. Therefore, we performed torsional shear deformation experiments on fine grained (10 μ m) samples of Beaver Bay anorthite (An70) +/- 10 vol% basalt to shear strains γ = 2-6 to investigate the development of lattice preferred orientation (LPO) and melt segregation at large shear strains. We performed experiments in a gas medium apparatus equipped with an internal torque cell at T = 1450 K, P = 300 MPa, and constant twist rate. Melt segregated in the An70 + basalt samples into melt-rich bands oriented at ˜20° to the shear plane and antithetic to the shear direction. The spacing between bands is ˜0.5 mm. Distortion of the iron jacket demonstrates that strain localized in the melt-rich bands. We determined the LPO of An70 with scanning electron microscopy using electron back scatter diffraction (SEM-EBSD). In patterns from an An70+ basalt sample deformed to γ ≈ 2.5, (001) planes are aligned subparallel to the shear plane and [100] axes are concentrated close to the shear direction. Both the (001) and the [100] are rotated counter clockwise from the shear direction by 20-25° . The formation of melt-rich bands is consistent with results from simple shear experiments on olivine + chromite + basalt and olivine + FeS +/- basalt, as well as An70 + basalt and indicates that deformation can drive melt segregation. Deformation drives the self organization of melt-rich bands and decreases the effective viscosity of the rock. The LPO is consistent with results from experiments on albite in shear and anorthite in compression and compatible with slip dominantly on (001) with [100] as the slip direction. A similar back rotation, attributed to partitioning of the strain between melt-rich and
9. Transient refractory material dissolution by a volumetrically-heated melt
Energy Technology Data Exchange (ETDEWEB)
Seiler, Jean Marie, E-mail: [email protected] [CEA, DEN, DTN, 17 Rue des Martyrs, 38054 Grenoble Cedex 9 (France); Ratel, Gilles [CEA, DEN, DTN, 17 Rue des Martyrs, 38054 Grenoble Cedex 9 (France); Combeau, Hervé [Institut Jean Lamour, UMR 7198, Lorraine University, Ecole des Mines de Nancy, Parc de Saurupt, 54042 Nancy Cedex (France); Gaus-Liu, Xiaoyang; Kretzschmar, Frank; Miassoedov, Alexei [Karlsruhe Institut of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany)
2014-12-15
Highlights: • We describe a test investigating ceramic dissolution by a molten non-eutectic melt. • The evolution of the interface temperature between melt and refractory is measured. • A theoretical model describing dissolution kinetics is proposed. • When dissolution stops, interface temperature is the liquidus temperature of the melt. - Abstract: The present work addresses the question of corium–ceramic interaction in a core catcher during a core-melt accident in a nuclear power plant. It provides an original insight into transient aspects concerning dissolution of refractory material by a volumetrically heated pool. An experiment with simulant material (LIVECERAM) is presented. Test results clearly show that dissolution of solid refractory material can occur in a non-eutectic melt at a temperature which is lower than the melting temperature of the refractory material. During the dissolution transient, the interface temperature rises above the liquidus temperature, corresponding to the instantaneous average composition of the melt pool. With constant power dissipation in the melt and external cooling of the core-catcher, a final steady-state situation is reached. Dissolution stops when the heat flux (delivered by the melt to the refractory) can be removed by conduction through the residual thickness of the ceramic, with T{sub interface} = T{sub liquidus} (calculated for the average composition of the final liquid pool). The final steady state corresponds to a uniform pool composition and uniform interface temperature distribution. Convection in the pool is governed by natural thermal convection and the heat flux distribution is therefore similar to what would be obtained for a single component pool. An interpretation of the experiment with two model-based approaches (0D and 1D) is presented. The mass transfer kinetics between the interface and the bulk is controlled by a diffusion sublayer within the boundary layer. During the dissolution transient
10. The effect of melt overheating on the melt structure transition and solidified structures of Sn-Bi40 alloy
Institute of Scientific and Technical Information of China (English)
2008-01-01
Evolution of the electrical resistivity of Sn-40wt%Bi melt with time under different overheating temperatures during isothermal experiments has been studied, and the relationship between different melt state, solidification behavior and solidified structure has also been investigated. The results show that the melt structure transition revealed by the abnormal change of resistivity would take place within a certain holding time just when the holding temperature is above a certain critical, and that the higher the temperature above the critical, the shorter the "incubation period" of the melt structure transition, and the faster the transition speed. The results of solidification experiments suggest that the melt structure transition caused by different holding time at the same temperature can lead to a higher so-lidification undercooling degree, finer grain size and change of microscopic pattern. Further exploration indicates that the solidification undercooling degree can come to a head when the melt is held at the specific temperature for a given time. The functionary mechanism of the phenomena above is also discussed briefly.
11. The effect of melt overheating on the melt structure transition and solidified structures of Sn-Bi40 alloy
Institute of Scientific and Technical Information of China (English)
CHEN HongSheng; ZU FangQiu; OHEN Jie; ZOU Li; DING GuoHua; HUANG ZhongYue
2008-01-01
Evolution of the electrical resistivity of Sn-4Owt%Bi melt with time under different overheating temperatures during isothermal experiments has been studied, and the relationship between different melt state, solidification behavior and solidified structure has also been investigated. The results show that the melt structure transition revealed by the abnormal change of resistivity would take place within a certain holding time just when the holding temperature is above a certain critical, and that the higher the temperature above the critical, the shorter the "incubation period" of the melt structure transition, and the faster the transition speed. The results of solidification experiments suggest that the melt structure transition caused by different holding time at the same temperature can lead to a higher so- lidification undercooling degree, finer grain size and change of microscopic pattern. Further exploration indicates that the solidification undercooling degree can come to a head when the melt is held at the specific temperature for a given time. The functionary mechanism of the phenomena above is also discussed briefly.
12. Interpreting chemical compositions of small scale basaltic systems: A review
Science.gov (United States)
McGee, Lucy E.; Smith, Ian E. M.
2016-10-01
Small scale basaltic magmatic systems occur in all of the major tectonic environments of planet Earth and are characteristically expressed at the Earth's surface as fields of small monogenetic cones. The chemical compositions of the materials that make up these cones reflect processes of magma generation and differentiation that occur in their plumbing system. The volumes of magmas involved are very small and significantly their compositional ranges reveal remarkably complex processes which are overwhelmed or homogenized in larger scale systems. Commonly, compositions are basaltic, alkalic and enriched in light rare earth elements and large ion lithophile elements, although the spectrum extends from highly enriched nephelinites to subalkalic and tholeiitic basalts. Isotopic analyses of rocks from volcanic fields almost always display compositions which can only be explained by the interaction of two or more mantle sources. Ultimately their basaltic magmas originate by small scale melting of mantle sources. Compositional variety is testament to melting processes at different depths, a range of melting proportions, a heterogeneous source and fractionation, magma mixing and assimilation within the plumbing system that brings magmas to the surface. The fact that such a variety of compositions is preserved in a single field shows that isolation of individual melting events and their ascent is an important and possibly defining feature of monogenetic volcanism, as well as the window their chemical behavior provides into the complex process of melt generation and extraction in the Earth's upper mantle.
13. Mineralogical and textural evidences of melt transfer in a granulite from the Paleoproterozoic Itabuna-Salvador-Curaça belt (Salvador da Bahia, Brazil)
Science.gov (United States)
Goncalves, Philippe; Santos de Souza, Jailma; Barbosa, Johildo; Bourque, Hugo; Floess, David
2014-05-01
In pelitic rocks, the effect of melt transfer (loss and/or gain) on phase relations can be successfully predicted via phase equilibrium modeling and more particularly using pseudosections with bulk composition as a variable (e.g. White et al., 2001). One of the most obvious effect of melt loss is the dehydration of the rock that limits further melting and favors the preservation of peak metamorphic assemblage. However, in most cases, melt loss has a limited effect that can be hardly seen mineralogically. Indeed, composition of phases like garnet, cordierite or plagioclase, that are first-order metamorphic phase, will not be affected significantly by melt loss. Therefore, evidences of melt extraction must be evidenced texturally. The goal of this contribution is to present an example where both mineralogical and textural evidences of melt extraction have been inferred. The studied sample is a pelitic granulite from the Paleoproterozoic Itabuna-Salvador-Curaça belt (Salvador da Bahia, Brazil). It is located in the city of Salvador da Bahia, next to the Farol da Bara. Structurally, it is located in a steeply deeping high strain zone that could have play a major role on the segregation and transfer of melt. The gneissic foliation is marked by a compositional banding with centimer-wide quartzo-feldspathic leucosomes in a garnet-bearing granulite. Leucosomes are almost systematically surrounded by a darker layer that is quartz-undersaturated and enriched in spinel and primatic sillimanite. This silica undersaturation is interpreted as the effect of extreme melt extraction and was modeled using phase diagram section. An interesting feature of the rock is that garnet grain size decreases and the number of garnet grains increases in the melanosome away from the leucosome. Furthermore, the type, amount and shape of inclusions in garnet, chemical composition and zoning in garnet also varies greatly and continuously across the gneissic foliation. Texturally, the presence of
14. Revisiting the compositions and volatile contents of olivine-hosted melt inclusions from the Mount Shasta region: implications for the formation of high-Mg andesites
Science.gov (United States)
Ruscitto, D. M.; Wallace, P. J.; Kent, A. J. R.
2011-07-01
Primitive chemical characteristics of high-Mg andesites (HMA) suggest equilibration with mantle wedge peridotite, and they may form through either shallow, wet partial melting of the mantle or re-equilibration of slab melts migrating through the wedge. We have re-examined a well-studied example of HMA from near Mt. Shasta, CA, because petrographic evidence for magma mixing has stimulated a recent debate over whether HMA magmas have a mantle origin. We examined naturally quenched, glassy, olivine-hosted (Fo87-94) melt inclusions from this locality and analyzed the samples by FTIR, LA-ICPMS, and electron probe. Compositions (uncorrected for post-entrapment modification) are highly variable and can be divided into high-CaO (>10 wt%) melts only found in Fo > 91 olivines and low-CaO ( 90 olivines. Restored low-CaO melt inclusions are HMAs (57-61 wt% SiO2; 4.9-10.9 wt% MgO), whereas high-CaO inclusions are primitive basaltic andesites (PBA) (51-56 wt% SiO2; 9.8-15.1 wt% MgO). HMA and PBA inclusions have distinct trace element characteristics. Importantly, both types of inclusions are volatile-rich, with maximum values in HMA and PBA melt inclusions of 3.5 and 5.6 wt% H2O, 830 and 2,900 ppm S, 1,590 and 2,580 ppm Cl, and 500 and 820 ppm CO2, respectively. PBA melts are comparable to experimental hydrous melts in equilibrium with harzburgite. Two-component mixing between PBA and dacitic magma (59:41) is able to produce a primitive HMA composition, but the predicted mixture shows some small but significant major and trace element discrepancies from published whole-rock analyses from the Shasta locality. An alternative model that involves incorporation of xenocrysts (high-Mg olivine from PBA and pyroxenes from dacite) into a primary (mantle-derived) HMA magma can explain the phenocryst and melt inclusion compositions but is difficult to evaluate quantitatively because of the complex crystal populations. Our results suggest that a spectrum of mantle-derived melts, including
15. Melt segregation in the Muroto Gabbroic Intrusion, Cape Muroto - Japan
Science.gov (United States)
Floess, David; Caricchi, Luca; Wallis, Simon
2014-05-01
Melt segregation is a crucial process in igneous petrology and is commonly used to explain characteristic geochemical trends of magmatic rocks (e.g. Brophy 1991), as well as the accumulation of large amounts of eruptible magma (e.g. Bachmann & Bergantz, 2008). In order to gain further insight into the physical processes behind melt segregation we investigated a small-scale, natural setting. The Miocene Muroto Gabbroic Intrusion (MGI) is a 230m thick, layered sill located at Cape Muroto (Shikoku Island - Japan; Yoshizawa, 1953). It was rotated into a near-vertical (~70°) orientation after horizontal emplacement, allowing for easy sampling of the entire sill from bottom to top. We collected ~70 oriented samples for petrographic and geochemical analysis, as well as for structural analysis using Anisotropy of Magnetic Susceptibility (AMS). A well-defined horizon (zone I) between 50 and 125m from the bottom shows spectacular evidence for the segregation of felsic melts from the mafic mush (Hoshide et al. 2006). Individual, cm- to m-sized, anorthositic melt lenses mainly consist of plagioclase laths with minor cpx. Small diapirs emanate from the melt lenses and clearly indicate the paleo-upward direction of the sill. Zone I is overlaid by a coarse-grained gabbro (zone II) with cm-sized crystals of plag+cpx and no anorthositic segregations can be found. The MGI grades into fine-grained dolerite towards the top and bottom margins of the sill. We modeled the phase relations of a representative MGI gabbro composition (chilled margin) upon cooling using MELTS (Gualda et al. 2012). Extracted physical parameters (i.e. melt and solid densities, melt viscosity) were used as a proxy for melt mobility (Sakamaki et al. 2013). The temporal and spatial evolution of melt mobility within the sill was investigated using the temperature-time curve obtained through a thermal model for the MGI. We observed several peaks for the melt mobility, implying zones of melt drainage (when mobility
16. 7 CFR 58.318 - Butter, frozen or plastic cream melting machines.
Science.gov (United States)
2010-01-01
... 7 Agriculture 3 2010-01-01 2010-01-01 false Butter, frozen or plastic cream melting machines. 58... Service 1 Equipment and Utensils § 58.318 Butter, frozen or plastic cream melting machines. Shavers, shredders or melting machines used for rapid melting of butter, frozen or plastic cream shall be...
17. On edge melting under the Colorado Plateau margin
Science.gov (United States)
Rudzitis, Sean; Reid, Mary R.; Blichert-Toft, Janne
2016-07-01
Asthenosphere beneath the relatively thin lithosphere of the Basin and Range province appears to be juxtaposed in step-like fashion against the Colorado Plateau's thick lithospheric keel. Primary to near-primary basalts are found above this edge, in the San Francisco-Morman Mountain volcanic fields, north central Arizona, western USA. We show that at least two distinct peridotite-dominated mantle end-members contributed to the origin of the basalts. One has paired Nd and Hf isotopic characteristics that cluster near the mantle array and trace element patterns as expected for melts generated in the asthenosphere, possibly in the presence of garnet. The second has isotopic compositions displaced above the ɛHf - ɛNd mantle array which, together with its particular trace element characteristics, indicate contributions from hydrogenous sediments and/or melt (carbonatite or silicate)-related metasomatism. Melt equilibration temperatures obtained from Si- and Mg-thermobarometry are mostly 1340-1425°C and account for the effects of water (assumed to be 2 wt.%) and estimated CO2 (variable). Melt equilibration depths cluster at the inferred location of the lithosphere-asthenosphere boundary at ˜70-75 km beneath the southwestern margin of the Colorado Plateau but scatter to somewhat greater values (˜100 km). Melt generation may have initiated in or below the garnet-spinel facies transition zone by edge-driven convection and continued as mantle and/or melts upwelled, assimilating and sometimes equilibrating with shallower contaminated mantle, until melts were finally extracted.
18. Application of direct laser melting to restore damaged steel dies
Science.gov (United States)
Jang, Jeong Hwan; Joo, Byeong Don; Mun, Sung Min; Sung, Min Young; Moon, Young Hoon
2011-02-01
Direct laser melting (DLM) technology can be applied to restore damaged steel dies. To understand the effects of DLM process parameters such as the laser power and scan rate, a series of experiments was conducted to determine the optimal operating parameters. To investigate the laser melting characteristics, the depth/height ratio, depth/width ratio and micro-hardness as a function of the laser energy density were analyzed. Fe-Cr and Fe-Ni layers were deposited on a steel die with 11.38 J/mm2 of energy input. The wear-resistance and the friction coefficient of the deposited layer were investigated by a pin-on-disk test. The penetration depth decreased as the scan rate increased as a consequence of the shorter interaction time. The depth/height ratio of the deposited layer decreased with an increase in the scan rate. The depth/width ratio increased as laser power increased and the scan rate decreased. The deposition shape of the Fe-Ni powder was relatively shallow and wide compared with that of the Fe-Cr powder. The scan rate had a substantial effect upon the deposition height, with the Fe-Cr powder melting more than the Fe-Ni powder. The micro-hardness of the layer melted from the powders is higher than that of the substrate, and the hardness of the laser-surface-melted layer without any metal powder is higher compared to that of the metal-powder-melted layer. The direct laser melting process with Fe-Ni powder represents a superior method when restoring a steel die when the bead shape and hardness of the restored surface are important outcome considerations.
19. Mathematical Modelling of Melt Lake Formation On An Ice Shelf
Science.gov (United States)
Buzzard, Sammie; Feltham, Daniel; Flocco, Daniela
2016-04-01
The accumulation of surface meltwater on ice shelves can lead to the formation of melt lakes. These structures have been implicated in crevasse propagation and ice-shelf collapse; the Larsen B ice shelf was observed to have a large amount of melt lakes present on its surface just before its collapse in 2002. Through modelling the transport of heat through the surface of the Larsen C ice shelf, where melt lakes have also been observed, this work aims to provide new insights into the ways in which melt lakes are forming and the effect that meltwater filling crevasses on the ice shelf will have. This will enable an assessment of the role of meltwater in triggering ice-shelf collapse. The Antarctic Peninsula, where Larsen C is situated, has warmed several times the global average over the last century and this ice shelf has been suggested as a candidate for becoming fully saturated with meltwater by the end of the current century. Here we present results of a 1-D mathematical model of heat transfer through an idealized ice shelf. When forced with automatic weather station data from Larsen C, surface melting and the subsequent meltwater accumulation, melt lake development and refreezing are demonstrated through the modelled results. Furthermore, the effect of lateral meltwater transport upon melt lakes and the effect of the lakes upon the surface energy balance are examined. Investigating the role of meltwater in ice-shelf stability is key as collapse can affect ocean circulation and temperature, and cause a loss of habitat. Additionally, it can cause a loss of the buttressing effect that ice shelves can have on their tributary glaciers, thus allowing the glaciers to accelerate, contributing to sea-level rise.
20. Biodegradable polyester films from renewable aleuritic acid: surface modifications induced by melt-polycondensation in air
Science.gov (United States)
Jesús Benítez, José; Alejandro Heredia-Guerrero, José; Inmaculada de Vargas-Parody, María; Cruz-Carrillo, Miguel Antonio; Morales-Flórez, Victor; de la Rosa-Fox, Nicolás; Heredia, Antonio
2016-05-01
Good water barrier properties and biocompatibility of long-chain biopolyesters like cutin and suberin have inspired the design of synthetic mimetic materials. Most of these biopolymers are made from esterified mid-chain functionalized ω-long chain hydroxyacids. Aleuritic (9,10,16-trihydroxypalmitic) acid is such a polyhydroxylated fatty acid and is also the major constituent of natural lac resin, a relatively abundant and renewable resource. Insoluble and thermostable films have been prepared from aleuritic acid by melt-condensation polymerization in air without catalysts, an easy and attractive procedure for large scale production. Intended to be used as a protective coating, the barrier's performance is expected to be conditioned by physical and chemical modifications induced by oxygen on the air-exposed side. Hence, the chemical composition, texture, mechanical behavior, hydrophobicity, chemical resistance and biodegradation of the film surface have been studied by attenuated total reflection-Fourier transform infrared spectroscopy (ATR-FTIR), atomic force microscopy (AFM), nanoindentation and water contact angle (WCA). It has been demonstrated that the occurrence of side oxidation reactions conditions the surface physical and chemical properties of these polyhydroxyester films. Additionally, the addition of palmitic acid to reduce the presence of hydrophilic free hydroxyl groups was found to have a strong influence on these parameters.
1. Three Petrologic Classes of Impact Melt on Large Atmosphereless Bodies
Science.gov (United States)
Warren, P. H.; Kallemeyn, G. W.
2005-12-01
Impacts have been important in the evolution of the Moon's crust and regolith, and impact melt products (breccias, glasses, and "highland basalts") account for a huge fraction of all sampled nonmare materials. As we endeavor to unravel the history of the Moon using these materials, it is important to understand that three fundamentally distinct types of impact melt occur. This discussion will focus on the Moon, but the same tripartite classification of impact melts should be applicable to Mercury. However, on Earth, Venus and to some extent Mars, atmosphere and even hydrosphere have major complicating influences. The fate of impact melt is closely tied to a parameter that Melosh has termed melting/displacement ratio, i.e., volume of impact melt over volume of transient crater; hereafter m/d. For any given energy of impact in large-scale cratering events, d is sensitive to the local gravity, g. As a result, m/d is systematically lower on a planet with modest g, such as the Moon, than it is on Earth. But also, for any given g, m/d increases with the energy (crater size) of the impact. As one consequence, it is easy to show that most of the total volume of impact melt throughout lunar history, M, was generated by a very small number (probably much less than 10) of the largest impacts. In "small" lunar events, with final crater D < ~ 100 km and m/d of order 1-4%, calculations based on Maxwell's z model indicate that roughly half of the impact melt is ejected from the transient crater; and the fraction not ejected will be dispersed within the thoroughly disintegrated but relatively cool shallow-subcrater crust. In the largest events (most notably South Pole-Aitken) that contribute most to M, m/d can be as high as 50%. The z models show that only about 1/4 of m is ejected from the transient crater, yet these largest events so dominate M that they still dominate the total inventory of ejected impact melt, M*. The ejected impact melt winds up cooling rapidly, dispersed in
2. Stepwise magma migration and accumulation processes and their effect on extracted melt chemistry
Directory of Open Access Journals (Sweden)
Urtson, Kristjan
2009-12-01
Full Text Available Numerical and analogue models suggest that melt production, its segregation from the solid matrix and subsequent transport and accumulation are highly dynamic and stepwise processes exhibiting scale invariant patterns in both time and length scales, which is characteristic of self-organized critical systems. This phenomenon is also observed in migmatites at several localities, where the leucosome thickness statistics obey power laws. Stepwise melt transport and deformation-enhanced melt mobility affect melt production dynamics by determining the distribution of extracted melt batch sizes and residence times of melt pockets within the host rock, which in turn would influence the geochemistry of extracted melts. We introduce a numerical approach, which enables qualitative and quantitative assessment of the effects of stress-induced melt migration and accumulation on the chemistry of partial melts. The model suggests that apart from different sources and melting percentages, deformation can be an important factor in producing geochemical variations within and between intrusive/extrusive complexes.
3. Tracking the Martian Mantle Signature in Olivine-Hosted Melt Inclusions of Basaltic Shergottites Yamato 980459 and Tissint
Science.gov (United States)
Peters, T. J.; Simon, J. I.; Jones, J. H.; Usui, T.; Moriwaki, R.; Economos, R.; Schmitt, A.; McKeegan, K.
2014-01-01
The Martian shergottite meteorites are basaltic to lherzolitic igneous rocks that represent a period of relatively young mantle melting and volcanism, approximately 600-150 Ma (e.g. [1,2]). Their isotopic and elemental composition has provided important constraints on the accretion, evolution, structure and bulk composition of Mars. Measurements of the radiogenic isotope and trace element concentrations of the shergottite meteorite suite have identified two end-members; (1) incompatible trace element enriched, with radiogenic Sr and negative epsilon Nd-143, and (2) incompatible traceelement depleted, with non-radiogenic Sr and positive epsilon 143-Nd(e.g. [3-5]). The depleted component represents the shergottite martian mantle. The identity of the enriched component is subject to debate, and has been proposed to be either assimilated ancient martian crust [3] or from enriched domains in the martian mantle that may represent a late-stage magma ocean crystallization residue [4,5]. Olivine-phyric shergottites typically have the highest Mg# of the shergottite group and represent near-primitive melts having experienced minimal fractional crystallization or crystal accumulation [6]. Olivine-hosted melt inclusions (MI) in these shergottites represent the most chemically primitive components available to understand the nature of their source(s), melting processes in the martian mantle, and origin of enriched components. We present trace element compositions of olivine hosted melt inclusions in two depleted olivinephyric shergottites, Yamato 980459 (Y98) and Tissint (Fig. 1), and the mesostasis glass of Y98, using Secondary Ionization Mass Spectrometry (SIMS). We discuss our data in the context of understanding the nature and origin of the depleted martian mantle and the emergence of the enriched component.
4. Infrared emissivity studies of melting thresholds and structural changes of aluminium and copper samples heated by femtosecond laser pulses
Energy Technology Data Exchange (ETDEWEB)
Hallo, L; Riou, O; Stenz, C; Tikhonchuk, V T [Centre Lasers Intenses et Applications, UMR 5107 CNRS-Universite Bordeaux 1-CEA, Universite Bordeaux 1, 351 Cours de la Liberation, 33405 Talence Cedex (France)
2006-12-21
We propose a new method for studies of laser-induced heating and melting of metallic foils. The method is based on time-integrated measurements of the surface infrared thermal emission. The experimental data are compared with a model where two equations describe the evolution of electron and lattice temperatures and the emissivity is found from the Drude model with the temperature-dependent electron collision frequency. A good agreement between the experimental data and the model is found for the aluminium samples. It is less satisfactory for the copper, but a signature of phase melting can also be pointed out. A multi-pulse laser irradiation study indicates significant changes in the surface emittance, related to preheating, oxidation and/or chemical modification of the copper sample. The proposed method is relatively simple and complementary to the pump-probe technique.
5. Peridotitic lithosphere metasomatised by volatile-bearing melts, and its association with intraplate alkaline HIMU-like magmatism
DEFF Research Database (Denmark)
Scott, James; Brenna, Marco; Crase, Jordan;
2016-01-01
.4 and eHf 0 +5 to +8) indistinguishable from the host low-silica basalts and, except for 207Pb/204Pb, overlapping with the HIMU mantle reservoir. Laser line scans across grain boundaries in the xenoliths show, however, that the host magma contribution is restricted to minor degrees of melt infiltration...... along grain boundaries during ascent, with the distinctive peridotite isotopic compositions having been imparted earlier by mantle metasomatism. Two mantle metasomatic styles are distinguished from pyroxene trace element concentrations (in particular, rare earth elements, Ti, Zr and Hf......) and are interpreted to be the result of reaction of peridotite with CO2- bearing magmas. The occurrence of two subtly chemically different but isotopically indistinguishable styles of metasomatism in rocks with the same equilibrium temperatures within the same mantle column may be due to separate volatile-rich melts...
6. Rare-element pegmatite-forming melt during Variscan orogeny: genesis, propagation and consolidation
Science.gov (United States)
Deveaud, Sarah; Guillou-Frottier, Laurent; Millot, Romain
2015-04-01
the main role of tectonic context during pegmatite-forming melt genesis and their propagation through activated shear-bands, opening of tensions gashes, magma pumping and space filling by pegmatite-melt crystallisation. Based on field observation such as mineralised ptygmatic veins, the role of chemistry and rheology of hosting-rocks on pegmatite differentiation type and on their morphology can be constrained. In particular, high permeability shear zones could play a crucial role in the ascent of low viscosity pegmatite-forming melts. To refine our results, preliminary numerical models have been developed to constrain the ascent of a pegmatitic melt from a deep crustal source. The "exotic" physico-chemical properties (large viscosity contrasts due to temperature- and water content-dependence) have been accounted for, and the experiments with large Peclet numbers reproduce individual patches of low viscosity melts disconnected from the parental source.
7. Melt processed multiphase ceramic waste forms for nuclear waste immobilization
Science.gov (United States)
Amoroso, Jake; Marra, James C.; Tang, Ming; Lin, Ye; Chen, Fanglin; Su, Dong; Brinkman, Kyle S.
2014-11-01
Ceramic waste forms are promising hosts for nuclear waste immobilization as they have the potential for increased durability and waste loading compared with conventional borosilicate glass waste forms. Ceramics are generally processed using hot pressing, spark plasma sintering, and conventional solid-state reaction, however such methods can be prohibitively expensive or impractical at production scales. Recently, melt processing has been investigated as an alternative to solid-state sintering methods. Given that melter technology is currently in use for High Level Waste (HLW) vitrification in several countries, the technology readiness of melt processing appears to be advantageous over sintering methods. This work reports the development of candidate multi-phase ceramic compositions processed from a melt. Cr additions, developed to promote the formation and stability of a Cs containing hollandite phase were successfully incorporated into melt processed multi-phase ceramics. Control of the reduction-oxidation (Redox) conditions suppressed undesirable Cs-Mo containing phases, and additions of Al and Fe reduced the melting temperature.
8. Experimental evidence supports mantle partial melting in the asthenosphere.
Science.gov (United States)
Chantel, Julien; Manthilake, Geeth; Andrault, Denis; Novella, Davide; Yu, Tony; Wang, Yanbin
2016-05-01
The low-velocity zone (LVZ) is a persistent seismic feature in a broad range of geological contexts. It coincides in depth with the asthenosphere, a mantle region of lowered viscosity that may be essential to enabling plate motions. The LVZ has been proposed to originate from either partial melting or a change in the rheological properties of solid mantle minerals. The two scenarios imply drastically distinct physical and geochemical states, leading to fundamentally different conclusions on the dynamics of plate tectonics. We report in situ ultrasonic velocity measurements on a series of partially molten samples, composed of mixtures of olivine plus 0.1 to 4.0 volume % of basalt, under conditions relevant to the LVZ. Our measurements provide direct compressional (V P) and shear (V S) wave velocities and constrain attenuation as a function of melt fraction. Mantle partial melting appears to be a viable origin for the LVZ, for melt fractions as low as ~0.2%. In contrast, the presence of volatile elements appears necessary to explaining the extremely high V P/V S values observed in some local areas. The presence of melt in LVZ could play a major role in the dynamics of plate tectonics, favoring the decoupling of the plate relative to the asthenosphere.
9. Continuous manufacturing of solid lipid nanoparticles by hot melt extrusion.
Science.gov (United States)
Patil, Hemlata; Kulkarni, Vijay; Majumdar, Soumyajit; Repka, Michael A
2014-08-25
Solid lipid nanoparticles (SLN) can either be produced by hot homogenization of melted lipids at higher temperatures or by a cold homogenization process. This paper proposes and demonstrates the formulation of SLN for pharmaceutical applications by combining two processes: hot melt extrusion (HME) technology for melt-emulsification and high-pressure homogenization (HPH) for size reduction. This work aimed at developing continuous and scalable processes for SLN by mixing a lipid and aqueous phase containing an emulsifier in the extruder barrel at temperatures above the melting point of the lipid and further reducing the particle size of emulsion by HPH linked to HME in a sequence. The developed novel platform demonstrated better process control and size reduction compared to the conventional process of hot homogenization (batch process). Varying the process parameters enabled the production of SLN below 200 nm (for 60 mg/ml lipid solution at a flow rate of 100ml/min). Among the several process parameters investigated, the lipid concentration, residence time and screw design played major roles in influencing the size of the SLN. This new process demonstrates the potential use of hot melt extrusion technology for continuous and large-scale production of SLN.
10. Microstructure analysis of magnesium alloy melted by laser irradiation
Science.gov (United States)
Liu, S. Y.; Hu, J. D.; Yang, Y.; Guo, Z. X.; Wang, H. Y.
2005-12-01
The effects of laser surface melting (LSM) on microstructure of magnesium alloy containing Al8.57%, Zn 0.68%, Mn0.15%, Ce0.52% were investigated. In the present work, a pulsed Nd:YAG laser was used to melt and rapidly solidify the surface of the magnesium alloy with the objective of changing microstructure and improving the corrosion resistance. The results indicate that laser-melted layer contains the finer dendrites and behaviors good resistance corrosion compared with the untreated layer. Furthermore, the absorption coefficient of the magnesium alloy has been estimated according to the numeral simulation of the thermal conditions. The formation process of fine microstructure in melted layers was investigated based on the experimental observation and the theoretical analysis. Some simulation results such as the re-solidification velocities are obtained. The phase constitutions of the melted layers determined by X-ray diffraction were β-Mg 17Al 12 and α-Mg as well as some phases unidentified.
11. Experimental evidence supports mantle partial melting in the asthenosphere
Science.gov (United States)
Chantel, Julien; Manthilake, Geeth; Andrault, Denis; Novella, Davide; Yu, Tony; Wang, Yanbin
2016-01-01
The low-velocity zone (LVZ) is a persistent seismic feature in a broad range of geological contexts. It coincides in depth with the asthenosphere, a mantle region of lowered viscosity that may be essential to enabling plate motions. The LVZ has been proposed to originate from either partial melting or a change in the rheological properties of solid mantle minerals. The two scenarios imply drastically distinct physical and geochemical states, leading to fundamentally different conclusions on the dynamics of plate tectonics. We report in situ ultrasonic velocity measurements on a series of partially molten samples, composed of mixtures of olivine plus 0.1 to 4.0 volume % of basalt, under conditions relevant to the LVZ. Our measurements provide direct compressional (VP) and shear (VS) wave velocities and constrain attenuation as a function of melt fraction. Mantle partial melting appears to be a viable origin for the LVZ, for melt fractions as low as ~0.2%. In contrast, the presence of volatile elements appears necessary to explaining the extremely high VP/VS values observed in some local areas. The presence of melt in LVZ could play a major role in the dynamics of plate tectonics, favoring the decoupling of the plate relative to the asthenosphere. PMID:27386548
12. Differentiation of Planetesimals and the Thermal Consequences of Melt Migration
CERN Document Server
Moskovitz, Nicholas
2011-01-01
We model the heating of a primordial planetesimal by decay of the short-lived radionuclides Al-26 and Fe-60 to determine (i) the timescale on which melting will occur; (ii) the minimum size of a body that will produce silicate melt and differentiate; (iii) the migration rate of molten material within the interior; and (iv) the thermal consequences of the transport of Al-26 in partial melt. Our models incorporate results from previous studies of planetary differentiation and are constrained by petrologic (i.e. grain size distributions), isotopic (e.g. Pb-Pb and Hf-W ages) and mineralogical properties of differentiated achondrites. We show that formation of a basaltic crust via melt percolation was limited by the formation time of the body, matrix grain size and viscosity of the melt. We show that low viscosity (100 km in size. Differentiation would be mos t likely for planetesimals larger than 20 km in diameter that accreted within ~2.7 Myr of CAI formation.
13. Component Evaporation of Ti-15-3 Melt during ISM Processing
Institute of Scientific and Technical Information of China (English)
2001-01-01
How to control melt composition is the key for getting high quality alloy melt. The paper made the following efforts: (1) The activity coefficients in Ti-15-3 melt have been calculated. (2)Taking advantage of the activity coefficients, the evaporation losses of components in Ti-15-3melt during ISM process have been studied. The calculated results show that there is a critical vacuum degree (about 1.33 Pa) during melting process.
14. Experimental studies of crystal-melt differentiation in planetary basalt compositions
Science.gov (United States)
Grove, T. L.
1987-01-01
An important process that controls the evolution of magmas on and within planetary bodies is crystal-melt differentiation. Experimental studies of silicate melt solidification were performed on several planetary and terrestrial melt compositions, and experiments on one of these compositions in the microgravity environment of the space station would provide an opportunity to understand the factors that control crystal growth and crystal-melt exchange processes at crystal-melt interfaces during solidification. Experimental requirements are presented.
15. MELTS_Excel: A Microsoft Excel-based MELTS interface for research and teaching of magma properties and evolution
Science.gov (United States)
Gualda, Guilherme A. R.; Ghiorso, Mark S.
2015-01-01
thermodynamic modeling software MELTS is a powerful tool for investigating crystallization and melting in natural magmatic systems. Rhyolite-MELTS is a recalibration of MELTS that better captures the evolution of silicic magmas in the upper crust. The current interface of rhyolite-MELTS, while flexible, can be somewhat cumbersome for the novice. We present a new interface that uses web services consumed by a VBA backend in Microsoft Excel©. The interface is contained within a macro-enabled workbook, where the user can insert the model input information and initiate computations that are executed on a central server at OFM Research. Results of simple calculations are shown immediately within the interface itself. It is also possible to combine a sequence of calculations into an evolutionary path; the user can input starting and ending temperatures and pressures, temperature and pressure steps, and the prevailing oxidation conditions. The program shows partial updates at every step of the computations; at the conclusion of the calculations, a series of data sheets and diagrams are created in a separate workbook, which can be saved independently of the interface. Additionally, the user can specify a grid of temperatures and pressures and calculate a phase diagram showing the conditions at which different phases are present. The interface can be used to apply the rhyolite-MELTS geobarometer. We demonstrate applications of the interface using an example early-erupted Bishop Tuff composition. The interface is simple to use and flexible, but it requires an internet connection. The interface is distributed for free from http://melts.ofm-research.org.
16. Thermal analysis as an aid to forensics: Alkane melting and oxidative stability of wool
Energy Technology Data Exchange (ETDEWEB)
Alan Riga, D. [Professor of Chemistry, Cleveland State University and TechCon Inc., 6325 Aldenham Dr., Cleveland, OH 44143-3331 (United States)
1998-12-21
Interdisciplinary methods and thermal analytical techniques in particular are effective tools in aiding the identification and characterization of materials in question involved in civil or criminal law. Forensic material science uses systematic knowledge of the physical or material world gained through analysis, observation and experimentation. Thermal analytical data can be used to aid the legal system in interpreting technical variations in quite often a complex system.Calorimetry and thermal microscopic methods helped define a commercial product composed of alkanes that was involved in a major law suit. The solid-state structures of a number of normal alkanes have unique crystal structures. These alkanes melt and freeze below room temperature to more than 60C below zero. Mixtures of specific alkanes have attributes of pure chemicals. The X-ray diffraction structure of a mixture of alkanes is the same as a pure alkane, but the melting and freezing temperature are significantly lower than predicted. The jury ruled that the product containing n-alkanes had the appropriate melting characteristics. The thermal-physical properties made a commercial fluid truly unique and there was no advertising infringement according to the law and the jury trialA combination of thermogravimetry, differential thermal analysis, infrared spectroscopy and macrophotography were used to conduct an extensive modeling and analysis of physical evidence obtained in a mobile home fire and explosion. A person's death was allegedly linked to the misuse of a kerosene space heater. The thermal analytical techniques showed that external heating was the cause of the space heater's deformation, not a firing of the heater with gasoline and kerosene. (Copyright (c) 1998 Elsevier Science B.V., Amsterdam. All rights reserved.)
17. Melting point prediction employing k-nearest neighbor algorithms and genetic parameter optimization.
Science.gov (United States)
Nigsch, Florian; Bender, Andreas; van Buuren, Bernd; Tissen, Jos; Nigsch, Eduard; Mitchell, John B O
2006-01-01
We have applied the k-nearest neighbor (kNN) modeling technique to the prediction of melting points. A data set of 4119 diverse organic molecules (data set 1) and an additional set of 277 drugs (data set 2) were used to compare performance in different regions of chemical space, and we investigated the influence of the number of nearest neighbors using different types of molecular descriptors. To compute the prediction on the basis of the melting temperatures of the nearest neighbors, we used four different methods (arithmetic and geometric average, inverse distance weighting, and exponential weighting), of which the exponential weighting scheme yielded the best results. We assessed our model via a 25-fold Monte Carlo cross-validation (with approximately 30% of the total data as a test set) and optimized it using a genetic algorithm. Predictions for drugs based on drugs (separate training and test sets each taken from data set 2) were found to be considerably better [root-mean-squared error (RMSE)=46.3 degrees C, r2=0.30] than those based on nondrugs (prediction of data set 2 based on the training set from data set 1, RMSE=50.3 degrees C, r2=0.20). The optimized model yields an average RMSE as low as 46.2 degrees C (r2=0.49) for data set 1, and an average RMSE of 42.2 degrees C (r2=0.42) for data set 2. It is shown that the kNN method inherently introduces a systematic error in melting point prediction. Much of the remaining error can be attributed to the lack of information about interactions in the liquid state, which are not well-captured by molecular descriptors.
18. Experimental Constraints on the Chemical Differentiation of Mercurys Mantle
Science.gov (United States)
Boujibar, A.; Righter, K.; Pando, K.; Danielson, L.
2015-01-01
Mercury is known as being the most reduced terrestrial planet with the highest core/mantle ratio. Results from MESSENGER spacecraft have shown that its surface is FeO-poor (2-4 wt%) and S-rich (up to 6-7 wt%), which confirms the reducing nature of its silicate mantle. In addition several features suggest important melting stages of the Mercurian mantle: widespread volcanic deposits on its surface, a high crustal thickness (approximately 10% of the planet's volume) and chemical compositions of its surface suggesting several stages of differentiation and remelting processes. Therefore it is likely that igneous processes like magma ocean crystallization and continuous melting have induced chemical and mineralogical heterogeneities in the Mercurian mantle. The extent and nature of compositional variations produced by partial melting remains poorly constrained for the particular compositions of Mercury (very reducing conditions, low FeO-contents and high sulfur-contents). Melting experiments with bulk Mercury-analogue compositions are scarce and with poorly con-trolled starting compositions. Therefore additional experimental data are needed to better understand the differentiation processes that lead to the observed chemical compositions of Mercury's surface.
19. The Formation of Yanshanian Granitic Magma in Dabie Mountains:Dehydration or Aquifer Melting with Tiantangzhai and Jiuzihe Granites as Examples
Institute of Scientific and Technical Information of China (English)
WANG Qiang; ZHAO Zhenhua; QIU Jiaxiang; WANG Renjing; XU Jifeng
2001-01-01
There are large-areas of late Yanshanian granites in the Dabie Orogen, but the formation mode of the relevant granitic magma is still under discussion. Taking the typical Yanshanian granites in the North Dabie Block The TG and JG as examples, the Writers endeavor to discuss contain aspects of the formation mode of the granitic magma by studying the characteristics of the chemical compositions of biotite and amphibole of the granites and petrological features of enclaves in the intrusions, in the light of recent results of experimental petrology on dehydration melting and aquifer melting. It is suggested that: (1) Some biotites in the Tiantangzhai and the JGs and their enclaves were residual minerals; (2) Some of the amphiboles could be new-born minerals, and others, residual ones.(3) the banded bodies in granites were residuals of anatexis. (4) The TG and JG were formed by aquifer melting, and the South Dabie Block could be the important source region of water.
20. Use of detailed thermochemical databases to model chemical interactions in the Severe Accident codes
Energy Technology Data Exchange (ETDEWEB)
Barrachin, M. [IPSN/DRS, CEA Cadarache (France)
2001-07-01
For the prevention, mitigation and management of severe accidents, many problems related to core melt have to be solved: fuel degradation, melting and relocation, convection in the core melt(s), coolability of the core melt(s), fission product release, hydrogen production, behavior of the materials of the protective layers, ex-vessel spreading of the core melt(s).. To solve these problems such properties like thermal conductivity, heat capacity, density, viscosity, evaporation or sublimation of melts, the solidification behavior (solid/liquid fraction), the tendency to trap or to release the fission products, the stratification of melts notably metallic and oxide, must be known. However most of these properties are delicate to measure directly at high temperature and/or in the radio-active environment produced by the fission products. Therefore some of them must be derived by calculations from the physical-chemical description of the melt: number of phases, phase compositions, proportions of solids and liquids and their respective oxidation state, miscibility of the liquids, solubility of one phase in another, etc. This information is given by the phase diagrams of the materials in presence. Since more than ten years, IPSN has developed in collaboration with THERMODATA (Grenoble, France) a very detailed thermochemical database for the complex system U-O-Zr-Fe-Ni-La-Ba-Ru-Sr-Si-Mg-Ca-Al-(H-Ar). The direct coupling between the severe accident (SA) Codes and a thermochemical code with its database is not actually possible because of the computer time consuming and the size of the database. For this reason, most of the Severe Accident codes usually have a very simplified description for the phase diagrams which are not in agreement with the status of the art. In this presentation, alternative methodologies are detailed with their respective difficulties, the goal being to build an interface between a thermochemical database and a SA Code and to get a fast, accurate and | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7516894936561584, "perplexity": 6144.920775981168}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187822145.14/warc/CC-MAIN-20171017163022-20171017183022-00251.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/introductory-algebra-for-college-students-7th-edition/chapter-1-section-1-5-addition-of-real-numbers-exercise-set-page-63/17 | ## Introductory Algebra for College Students (7th Edition)
$-1.3$
In adding two numbers with the same sign, perform the following steps: (1) Add their absolute values. $|-0.4| + |-0.9| = 0.4 + 0.9 = 1.3$ (2) The sum must have sign common to the addends. $-0.4+(-0.9) = -1.3$ Thus, the sum is $-1.3$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.550398051738739, "perplexity": 727.4965208456113}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203464.67/warc/CC-MAIN-20190324165854-20190324191854-00318.warc.gz"} |
https://math.stackexchange.com/questions/1805301/how-do-curves-consist-of-points/1805304 | # How do curves consist of points?
According to Euclid, a point is something which has no dimensions. And we know that all curves of any type consists of points. Now this thing bothers me because if a point has no dimensions, i.e. in other words there is nothing, then how is it possible to draw any curve? The thing I could imagine is that maybe a point is not as Euclid thought. I mean a point can be thought of as a small line segment whose length is approaching zero but never becomes exactly zero. In this way, we can say that curves consist of points (the line segment with length approaching zero). But then it breaks the fact as given by Euclid that a point has no dimensions. Please help me to get out of this dilemma.
• You are wrong by thinking that the union of $n$-dimensional objects must be $n$-dimensional as well. Think of $\mathbb{R}^2$: It is the union of all lines $\mathbb{R}(x,0)$ which are parallel to the $y$-axis. These lines are all one-dimensional objects, but their union $\mathbb{R}^2$ is a 2-dimensional vector space. – lattice May 30 '16 at 5:34
• Ah okay, then I agree with the others: We live in 3-dimensional space, and however you "draw" something, it will in fact be 3-dimensional. The point is that "drawing" is hard to be defined/modeled in a mathematically correct way. you are merely moving a pen around space, and through some mechanism the ink is coming out and sticking on a sheet of paper after a certain period of time. So as soon as you want to imagine a (not really existing) pen that draws single points, it raises the question of how you even define that. – lattice May 30 '16 at 6:35
• But isn't this the same as saying: How can the integral of a function over an interval $[a,b]$ have a positive value if the integral of the same function over ${a}$ (as a "interval with length 0") is zero? How can the probability that an (arbitrary) integer is even be 1/2 if the probability for an arbitrary integer to be 0 equals 0? And I think your dilemma is also a similar problem as that the union of $n$-dimensional sets can build a $n+k$ dimensional vector space. – lattice May 30 '16 at 7:43
• I think the point is: Just because the points are lines of length zero, it doesn't mean that they do not exist. The "length" is just a function assigning every line some value. Usually you probably define it such that it always takes non-negative values, but of course there may be objects with length 0, which Euclid defines as points. – lattice May 30 '16 at 7:45
• @user306288 No, it means the "paradox" was based on faulty assumptions and/or understanding to begin with. – jpmc26 May 31 '16 at 9:03
Euclid did say that that "A point is that which has no part". It is nothing more that a whisper of an indication that "You are here." You can't really see a point since there is nothing there.
"...if point has no dimensions, i.e. in other words there is nothing,
then how is it possible to draw any curve?"
If you're thinking in terms of "connecting the dots", it isn't physically possible. Pick a ridiculously small positive number, $\delta$. It doesn't matter how small. It is a fact that there are as many points in the interval $(0, \delta)$ as there are points in the universe. There is no way you can physically enumerate all of the points in the smallest of curves. I don't believe that Euclid had our understanding of infinity, but I think he was aware of its paradoxical abundance.
But you don't have to draw curves. They are just a set of points. A graph is just a representation of that set and only serves to fuel our intuition.
Euclid's definitions of point, line, and segments, have zero functionality. They may sound nice but they don't really say anything useful.
If you want to know what a point really is, propositions like the following are much more useful.
"Two distinct points determine a unique line."
"If two distinct lines intersect, then they intersect at a single point."
Having reread your question for the upteenth time, it occurs to me that you may be thinking of infinitesimals. Infinitesimals are basically numbers that are smaller in magnitude than any real number but are not equal to zero. You may want to check out THIS and THIS.
• So what should I conclude from all of this ? – user306288 May 30 '16 at 10:38
• @user306288 - You should read about Zeno's Paradoxes. – steven gregory May 30 '16 at 11:31
• I know about zeno paradox . So at the end I should conclude that what I asked is a paradox only?!! – user306288 May 30 '16 at 11:43
• @user306288 I think the point is that intuition is fine, but when it starts to get confusing (like in this case) stick to the rigorous (modern) definition of points and lines. Euclid's definition may be intuitive but is clearly not rigorous.. "A point is that which has no part", how are you supposed to work with that? What does part even mean? Is the null set a point then? And so on.. – Ant May 30 '16 at 13:22
• @user306288 - A line is not a physical thing. When you talk about the point with coordinate $(2,3)$, the point is the location, not what is at that location. When you talk about the line defined by $x+y=1$ you are talking about an infinite set of pairs of numbers that point at the graph and say "here, here, here, ...". – steven gregory May 30 '16 at 15:00
Intuitive interpretation:
A curve has an infinity of points. So many that the amount counteracts the abscence of dimensions, like an $0\times\infty$ undeterminacy.
More precisely, a curve still has no dimension transversally, but a finite (or infinite) dimension longitudinally.
You can think of it as the limit of a necklace of pearls (points of finite area) in contact, getting smaller and smaller but more and more numerous. In the end, an infinitely thin but continuous string remains.
• IMO, your final paragraph is more important than the initial paragraph -- if you forget how points are related, then their union is always a zero dimensional discrete space, no matter how many. – user14972 May 30 '16 at 18:44
• @Hurkyl : I agree with you on this. How can 0*infinity counteract the absence of dimensions. It is undefined first of all. The second sentence does indeed make sense. – novice May 31 '16 at 11:56
• @Yves Daoust , Could you please explain, how to get a line segment out of a set of points. I am hopelessly stuck at understanding infinities. – novice May 31 '16 at 12:00
You are confusing theory with parctise.
A point does not exist in the real universe.
Anything you draw will have some dimensions.
• I am shocked if point has no existence then what is its worth? – user306288 May 30 '16 at 5:32
• As you have already mentioned a line segment with length rending to 0. But this is within the realm of logic/maths and may not apply to the real world. – novice May 30 '16 at 5:34
• Well even straight lines or perfect circles do not exist in the real world. But we can use them to model real world curves/lines etc. – novice May 30 '16 at 5:35
• "I am shocked if point has no existence then what is its worth?" Negative numbers have no existence, so what are they worth? – Aiman Al-Eryani May 30 '16 at 8:21
• Yeah, though sometimes it's good to have a look at the bigger picture, the place which inspired maths. – novice May 30 '16 at 19:32
A curve is completely determined by two facts:
• Knowledge of all of the points lying on the curve
• Knowledge that the curve is drawn on the Euclidean plane
When it's said that a curve is made out of points, one really means to include in the latter fact too, or something similar (e.g. a topology or a metric on the collection of points).
There are more sophisticated geometric techniques (e.g. tangent spaces, halos, germs, stalks) that probe the "infinitesimal" shape of the curve at the point;
For example, studying the tangent space to the curve would indeed allow you to say that, at each point where the curve is smooth, it consists of an infinitesimal line.
But just to reinforce my initial point, the shape of that infinitesimal line can be ascertained simply by knowing the curve is being drawn on the plane along with which 'nearby' points lie on the curve.
A point in an n-dimensional Euclidean space is that point which consists of n coordinates which give a distinct location of that point.
A function in Euclidean space essentially provides a rule for defining a set coordinates in space for which that function is true.
You are correct in that the physical realization of a collection of 0-dimensional points is nonsense to create a physical 1-D curve, however, it makes tons of sense when you learn a bit more math in topics like set and measure theory
You are confusing reality and the idealized world of maths. In an ideal world, a point has no dimensions. You could never actually draw a point. In reality, you can. You take a pencil, make a point on a piece of paper and say "that is the point". But the fact that you can see the point already means that is has some dimensions (the ink occupies a non-empty area in our real, three dimensional world). You have not actually drawn the point, but a representation of the (idealized) point.
Similar, if you draw a curve, you need to draw it with some thickness. This means you don't draw the actual idealized curve, but a real life representation of that curve.
Maths is founded in the real world, but goes one step further. Maths discovers the rules behind things, and abstracts them into an idealized world. This ideal world does not exist in reality, but it is nevertheless useful.
For example, infinity is a purely mathematical concept, yet it is tremendously useful for real-life applications, e.g. physics.
• The question is not about curves and points in reality versus ideal curves and points. It is about how "ideal" points, which have zero dimension, can together form an "ideal" curve, which is not zero dimensional. – M. Vinay May 30 '16 at 8:27
• Which is precisely the same question?! Sorry, but if you have a curve, you have some term that all points that lie on the curve have to satisfy. There is nothing else a curve can consist of then the infinite amount of points that lie on it. You have to get rid of the notion grounded in reality that the curve actually is some object you can physically grab. Its not. You just map some numbers to others, and if you let the curve segment be infinitely small you asymptotically approach a point. – Polygnome May 30 '16 at 9:01
• Not the same question at all. Even someone who perfectly understands that mathematical, "ideal" points and curves can't be "drawn" in reality, might have the same question about the relation between ideal points and ideal curves. That has nothing to do with the difference between physical reality and mathematics. – M. Vinay May 30 '16 at 9:06
As at least one other answer has mentioned, it takes an infinitude of points to make up a curve. (Or to make up any other interval, like the rather simple "curve" of the closed interval [0,1], for example.)
At least one other answer has also mentioned the notion of "measure," and that's probably the more appropriate way to think about the small-ness of a point: it's said to have "measure zero." If you've taken calculus, then you may recall that you can remove a finite number of points from the interval that you're integrating over, and it won't affect the value of the integral. Why? Because each point only has "measure zero," so its contribution to the total value of the integral is negligible, when compared to the infinitely-many contributions made by all the other points in the interval.
Don't forget, when you have a closed interval (or, once you get to topology-level stuff, a "compact" interval), those intervals will have infinitely-many points in them. Like take [0,1] again; there are infinitely many points in that interval. But cut it in half; say, to [0,1/2]. There's still infinitely many points in that interval. Cut it in half again, to [0,1/4]; still infinitely many points in that interval. You can keep cutting it in half as many times as you can imagine, and you'll still be looking at an interval with infinitely many points in there.
All this "infinitely many" stuff that you encounter in math; it may not seem to line up with the real world all that well, but it's necessary for doing calculus (because it's at the heart of the concept of continuity).
This article by Prof. Lawrence Spector helped me a lot and I think it addresses exactly what your confusion is. I'm not sure what the policy is on just posting links, but I don't think i would do a great job paraphrasing what he wrote, so here goes: http://www.themathpage.com/aCalc/apoint.htm
I would also highly recommend reading on the same site: http://www.themathpage.com/areal/real-numbers.htm, about the historical evolution of the real numbers. I think it'll clear up a lot of the questions you probably already have or will have.
• The commonly accepted policy here is to briefly summarize the relevant points of links, so that your answer is self-contained and useful even if the link goes down. But if you've no time to do that, it might be better to just leave a few comments instead of an answer. – user21820 May 31 '16 at 11:19
Some other answers have already mentioned the distinction between the ideal geometric world (which we can describe by mathematical rules) and the real world (which our ideal world is intended to approximate).
However, an interesting point is that Euclid never talked about dimension but merely said:
[Euclid Book 1 Def 1] σημειον εστιν ου μερος ουθεν
[a] mark is that of which [there] [is] no part // A point is that which has no part.
It is amusing that we can force a set-theoretic interpretation onto this as:
A point is a non-empty set with no proper subset. // A point is a singleton.
This coincides with the notion that two different straight lines that intersect do so at a point.
If $A,B$ are distinct straight lines with an intersection, then $A \cap B$ is a point.
In more set-theoretic terms:
If $A,B$ are distinct straight lines such that $A \cap B \ne \varnothing$, then $A \cap B$ is a singleton.
Nice? Furthermore, a line can then be said to be a union of points! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6862266659736633, "perplexity": 373.6326154191308}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371624083.66/warc/CC-MAIN-20200406102322-20200406132822-00173.warc.gz"} |
https://existentialtype.wordpress.com/2011/03/27/the-holy-trinity/ | ## The Holy Trinity
The Christian doctrine of trinitarianism states that there is one God that is manifest in three persons, the Father, the Son, and the Holy Spirit, who together form the Holy Trinity. The doctrine of computational trinitarianism holds that computation manifests itself in three forms: proofs of propositions, programs of a type, and mappings between structures. These three aspects give rise to three sects of worship: Logic, which gives primacy to proofs and propositions; Languages, which gives primacy to programs and types; Categories, which gives primacy to mappings and structures. The central dogma of computational trinitarianism holds that Logic, Languages, and Categories are but three manifestations of one divine notion of computation. There is no preferred route to enlightenment: each aspect provides insights that comprise the experience of computation in our lives.
Computational trinitarianism entails that any concept arising in one aspect should have meaning from the perspective of the other two. If you arrive at an insight that has importance for logic, languages, and categories, then you may feel sure that you have elucidated an essential concept of computation—you have made an enduring scientific discovery. Advances in our understanding of computation may arise from insights gained in many ways (any data is useful and relevant), but their essential truth does not depend on their popularity.
Logic tells us what propositions exist (what sorts of thoughts we wish to express) and what constitutes a proof (how we can communicate our thoughts to others). Languages (in the sense of programming) tells us what types exist (what computational phenomena we wish to express) and what constitutes a program (how we can give rise to that phenomenon). Categories tell us what structures exist (what mathematical models we have to work with) and what constitutes a mapping between them (how they relate to one another). In this sense all three have ontological force; they codify what is, not how to describe what is already given to us. In this sense they are foundational; if we suppose that they are merely descriptive, we would be left with the question of where these previously given concepts arise, leading us back again to foundations. It is the foundations that I wish to describe here, because I believe it will help to clarify some common misunderstandings about the notions of proposition, type, and structure. Of particular interest here is that a “type system” is not, under this conception, an arbitrary collection of conditions imposed on a previously given notion of program (whether written with horizontal lines, or not). It is, rather, a way to say what the programs are in the first place, and what they mean as proofs and as mappings.
Here I will outline the basic correspondences between logic, languages, and categories by examining their structural properties (and, for now, nothing more).
The fundamental notion in logic is that of entailment, written $P_1,\dots,P_n\vdash P$, expressing derivability of $P$ from $P_1,\dots, P_n$. This means that $P$ is derivable from the rules of logic, given the $P_i$ as axioms. In contrast to admissibility (which I will not discuss further here) this form of entailment does not express implication! In particular, an entailment is never vacuously true. Entailment enjoys at least two crucial structural properties, making it a pre-order:
$\displaystyle{\strut\over{P\vdash P}}$
$\displaystyle{{P\vdash Q\quad Q\vdash R}\over{P\vdash R}}$.
$\displaystyle{{P_1,\dots,P_n\vdash Q}\over{P_1,\dots,P_n,P_{n+1}\vdash Q}}$
$\displaystyle{{P_1,\dots,P_i,P_{i+1},\dots,P_n\vdash Q}\over{P_1,\dots,P_{i+1},P_{i},\dots,P_n\vdash Q}}$
$\displaystyle{{P_1,\dots,P_i,P_i,\dots,P_n\vdash Q}\over{P_1,\dots,P_i,\dots,P_n\vdash Q}}$.
These state that “extra” axioms do not affect deduction; the “order” of axioms does not matter; “duplication” of axioms does not matter. (These may seem inevitable, but in substructural logics any or all of these may be denied.)
In languages we have the fundamental concept of a typing judgement, written $x_1{:}A_1,\dots,x_n{:} A_n\vdash M{:}A$, stating that $M$ is an expression of type $A$ involving variables $x_i$ of type $A_i$. A typing judgement must satisfy the following basic structural properties:
$\displaystyle{\strut\over{x:A\vdash x:A}}$
$\displaystyle{{y:B\vdash N:C \quad x:A\vdash M:B}\over{x:A\vdash [M/y]N:C}}$
We may think of the variables as names for “libraries”, in which case the first states that we may use any library we wish, and the second states closure under “linking” (as in the Unix tool ld or its relatives), with $[M/x]N$ being the result of linking $x$ in $N$ to the library $M$. Typically we expect analogues of the “extra”, “reordering”, and “duplication” axioms to hold as well, though this ain’t necessarily so. I will leave their formulation as an exercise for the reader.
In categories we have the fundamental concept of a mapping $f:X\longrightarrow Y$ between structures $X$ and $Y$. The most elementary structures, perhaps, are sets, and mappings are functions, but it is more common to consider, say, that $X$ and $Y$ are topological spaces, and $f$ is a continuous function between them. Mappings satisfy analogous structural properties:
$\displaystyle{\strut\over{\textit{id}_X : X \longrightarrow X}}$
$\displaystyle{{f:X\longrightarrow Y \quad g : Y\longrightarrow Z}\over{g\circ f:X\longrightarrow Z}}$
These express, respectively, the existence of the identity map, and the closure of maps under composition. They correspond to reflexivity and transitivity of entailment, and to the library and linking rule of languages. As with types, one may expect additional closure conditions corresponding to the “extra”, “reordering”, and “duplication” axioms by giving suitable meaning to multiple assumptions. I will not go into this here, but numerous standard sources treat these conditions in detail.
What I find captivating about computational trinitarianism is that it is beautiful! Imagine a world in which logic, programming, and mathematics are unified, in which every proof corresponds to a program, every program to a mapping, every mapping to a proof! Imagine a world in which the code is the math, in which there is no separation between the reasoning and the execution, no difference between the language of mathematics and the language of computing. Trinitarianism is the central organizing principle of a theory of computation that integrates, unifies, and enriches the language of logic, programming, and mathematics. It provides a framework for discovery, as well as analysis, of computational phenomena. An innovation in one aspect must have implications for the other; a good idea is a good idea, in whatever form it may arise. If an idea does not make good sense logically, categorially, and typically (sorry for the neologism), then it cannot be a manifestation of the divine.
### 33 Responses to The Holy Trinity
1. […] Suggested Reading: Immanuel Kant, ‘Introduction’, Critique of Pure Reason (https://ebooks.adelaide.edu.au/k/kant/immanuel/k16p/introduction.html); Per Martin-Lof, ‘Analytic and Synthetic Judgments in Type Theory’ (http://archive-pml.github.io/martin-lof/pdfs/Martin-Lof-Analytic-and-Synthetic-Judgements-in-Type-Theory.pdf); Pei Wang, ‘Artificial General Intelligence: A Gentle Introduction’ (https://sites.google.com/site/narswang/home/agi-introduction); Robert Harper ‘The Holy Trinity’ (https://existentialtype.wordpress.com/2011/03/27/the-holy-trinity/) […]
2. […] Harper refers to the inter-referential nature of type theory, proof theory, and category theory as computational trinitarianism. To quote […]
3. […] by Bob Harper’s recent postings, I too have a confession to make. I know what is morally right; but sometimes the […]
4. […] I never thought of it this way […]
5. Bogdan Barbu says:
If we use a common framework for both mathematics and computation, then the former becomes part of the latter. The way mathematics looks should then be dependent on its computational model. If we consider mathematics an abstraction, switching the underlying computational model would be an elegant way to tell whether something can be expressed in that model and, if so, how efficiently it can be evaluated.
Sometimes, we will be interested in purely mathematical results, in which case, only expressiveness should be relevant. An example would be defining a computational model. We do, however, get “for free” how efficiently that new model can be simulated in terms of the old.
6. […] The Holy Trinity In the process of making plans for actually going to graduate school, I’ve been spending some thinking about what I want to research and what motivations and goals are. Apart from the technical things I’m interested in, I’m starting to believe that what we need more than ever is a “philosophy of computation” — ideas and concepts that define computation and our relationship to it at a higher level. Robert Harper’s recent blog post is a milestone on that journey. […]
7. The functional programming languages are again becoming popular and your blog deals with the CS behind them. What is your recommendation for a programmer in the industry who wishes to learn the science behind such languages ? Attending a CS course in a college might not be possible for working people. What else can one do ?
Even to understand your blog entries fully one requires a strong foundation in CS.
8. phookdk says:
Computer Scientists are often caught up in the seduction of types and categorizations (as your argument in “Dynamic languages are static languages”).
I would argue the reverse, that “Static languages are dynamic languages”, because the type is a de facto unit test performed by the compiler. This means that the single type of the dynamic language is a simplification, because types can not replace unit testing (IMO).
A language with dynamic run-time features and unit testing at compile-time, would provide the best of both worlds.
• abstract type says:
It’s not a matter of methodology or opinion, it’s a matter of fact. See PFPL for technical details.
• phookdk says:
Im a bit confused – you say yourself that in a one type system you have to do the type checking yourself – and if you read my post Im not really arguing against your statement.
No matter how beautiful types are (and I dont disagree with that), I have come to the startling insight that they are merely compile time unit tests. Lambda calculus is also very beautiful from a mathematical standpoint and I share your exitement about them, however Im heading down a different road, which I would like to discuss with someone but your religion analogy apparently goes deep because everyone thinks functional lazy lambda calculus is THE ONE WAY.
A totally reductionist view would state that there IS only one type and it is the boolean; everything else is just compositions and conventions.
Ah, well – now im just waiting for your “Lambda Calculus is THE ONE WAY – its a fact” – reply :-)
• abstract type says:
My point is technical: static typing is the prior notion; dynamic typing is a mode of use of static typing (in which one focuses on one type, for some reason). One can retrofit a dynamic language with a system of predicates governing the behavior of expressions of dynamic type, but this is not a static type discipline in my sense. (That was already present in the very definition of the dynamic language.) On this point there can be no dispute; it’s not a matter of opinion.
Methodologically, one may reasonably argue about the role of dynamic typing (that is, of a particular static type of dynamically classified values) relative to the role of a richer concept of typing (that embraces classified values as but one static type of many). It is clear to me, at least, that the benefits of admitting more than one type are enormous. In particular, a static type discipline is fundamental to modular decomposition of programs (it’s how you state the api for the separate code that may not even exist at the moment you compiler your code). Once you take the catholic view that I advocate, you quickly realize that dynamic classification is occasionally useful, but is hardly the most important thing around. If, for example, you want to “get down to the metal”, eg give access to machine integers as such, not classified as numbers, then you have no choice but to use a static type discipline. And once you realize that type inference eliminates the bureaucracy of static typing (contrary to what one sees in Java, for example), then you realize that static types are your friend, and that you rarely have need of dynamic classifcation—but it’s there if you want it, as a special case.
9. rafael111 says:
From a software engineering perspective, it´s interesting that all three views are needed.
In analysis and testing, it´s important to find out how input is mapped to output. In design, what thoughts we want to express. And in programming, what do we need to invoke, and how do we abstract that which we invoke.
Thanks.
10. n7yz5rhdanth says:
another nice little story: Wadler, Proofs are Programs, 2000
11. johnwcowan says:
The trouble is that CS degrees have become a kind of gate for high-level programming jobs, except for grandfathered old farts like me (I don’t have any degrees, though I do have a descendant in the second degree). I enjoy the Classics very much, and am glad that people can study them, but I don’t want to live in a society in which the ability to compose Latin verses is a prerequisite for a mid-level government position.
12. rafael111 says:
What about machines ? Are they under structure ?
• abstract type says:
See my post on languages and machines please. Also the second half of my post on parallelism.
• rafael111 says:
Machine models maybe important to hardware implementors, but they are of essentially no practical importance for programming. The λ-calculus is directly useful for programming. I agree, but I never thought I would read
this from a computer science professor. Thanks for the honesty!
Rafael
• marklillibridge says:
> “Machine models maybe important to hardware implementors, but they are of essentially no practical importance for programming.”
?!? This is totally untrue for many programming tasks. If having to take a TLB miss will cause you to miss your performance target (a recent real example), I assure you knowing exactly how your CPU implements page tables is extremely relevant. Likewise, try and implement a hypervisor without understanding the hardware you’re running on and/or simulating.
• rafael111 says:
“I assure you knowing exactly how your CPU implements page tables is extremely relevant”
In language, a page table could be thought of as a type. Execution time and memory use could be seen as values given to the semantics of the language.
The knowledge of the machine you simulate is a knowledge of application domain…From a programming perspective, the relevant details of the machine you are running can be thought of as an augmentation to the basic grammar of its language. Is there something important about machines-unless they are part of the application
domain- that can´t be abstracted as a value and attached to the language (What Robert calls giving a cost semantics to it) ?
What knowledge about how the cpu implements page tables-not present in an augmented language-did you
need for the aforementioned task ? Knowing how it implements page tables seems to be a problem of semantics…
• abstract type says:
Current research by Guy Blelloch is concerned with precisely this: giving a cost semantics for a language that allows you to make useful predictions about locality (cache behavior) at the implementation level. It seems plausible to me that one can factor concerns, putting memory hierarchy effects into the “provable implementation” part of the setup, and providing a cost semantics that allows the programmer to understand the program’s interaction with memory hierarchies.
13. marklillibridge says:
your second rule for type judgments does not hold for translucent sums… (M must be restricted to a value)
• abstract type says:
Such restrictions can be postulated in the general framework I’m sketching by adding the hypothesis “x_i value” for those variables (perhaps all) that must be bound to values. It doesn’t change my basic outline.
14. mitchwand says:
Bob,
I’m going to take your post seriously, at face value, and offer a different point of view.
The Map is Not the Territory
You appear to be not only a Trinitarian, but a Platonist: you appear to believe that the things we see in the real world are just imperfect manifestations of some ideal forms.
I propose a different view: programs and computations are things in the real world, and our job is to construct useful models of those things. Our models are useful insofar as they reflect the features of the world that are of interest, and provide predictions about the behavior of those real-world objects that are accurate within the bounds of our model.
This is the point of view of physics. A model in physics is always an approximate model of the real world, which yields accurate predictions if applied within the limits of the model. Thus Newtonian mechanics is a good model for objects that are not too small and not travelling too fast. If the objects are too small, you need quantum mechanics, and if they are travelling too fast you need relativistic mechanics. And if your objects are travelling too close to the beginning of the universe, then you need string theory or who-knows-what.
When we build a model, we must choose what aspects of nature we wish to model. We build a model to work in a certain domain and to make certain kinds of predictions. (As Will Clinger likes to put it: every good model is a lie. The art is in knowing what it’s lying about.)
An architect, for example, will use a variety of models to predict the behavior of the structure he or she is designing. He or she will make design drawings or even foam-core models to communicate issues of concern to the client. He/she will make detailed construction drawings to communicate issues of concern to the builder. The structural engineer will use a different set of models to predict whether the building will fall down. The seismological engineer will use a still different set of models. And during construction, somebody will X-ray the concrete and use yet another model to determine whether the concrete has set correctly.
Similarly, we can choose different models to reflect different aspects of computation, or to make either finer or coarser predictions about the behavior of a program. A Un(i)typed model can express certain propositions, and therefore make certain predictions, about the behavior of a program; a simply-typed model can make different predictions. These predictions are in general finer than those made by the Un(i)typed model, but at the expense of excluding some programs about which it can make no predictions at all. The same story applies to System F or your favorite dependent type theory.
Furthermore, other type systems and other program analyses make predictions that may be entirely different in kind from those suggested so far. You allude to this in your post with your mention of substructural logics.
So it seems entirely unfair to assert that a type system is, as you say, “a way to say what the programs are in the first place.”
I am not a philosopher but sometimes I play one on the Internet. Those with a better background in philosophy can set me straight.
I look forward to more discussion.
–Mitch
• bowaggoner says:
Hi Mitch, it seems to me that a big difference between computing and, say, physics is that in computing we can prove that our physical and hypothetical models are equivalent in many cases.
Assuming no defects in your machine, you can execute a certain program and get exactly the correct results, every time. (Let’s say the algorithm is deterministic.) If you send me your code, I can in theory deduce it’s output a priori. If I run it on my machine, the output will be the same. The “model” is reality.
One thing I don’t understand is how, as you say, “type systems and other program analyses make predictions that may be entirely different in kind from those suggested so far.” It seems to me that either two programs are provably equivalent, or they’re not. Could you explain?
Anyway, I’m no pro at philosophy, but my main point is that our field is very special in that the hypothetical model and the physical reality are basically equivalent — that’s pretty cool, and also means that this theorizing applies directly to real programs.
• abstract type says:
Well put. Herb Simon described CS as a “science of the artificial”.
• abstract type says:
I don’t see the disagreement. I struggled a lot with the wording in that post. Perhaps I should have said that logic codifies principles of reasoning, to make clear that it is not a once-and-for-all, finished classification. I believe that as we explore and discover new computational phenomena we should subject them to the rigors of being seen as logical, programming, and mathematical concepts in order to clarify them and isolate the core contribution (if any).
My point about typed and un(i)typed is simply this: many people seem to believe that untyped languages are somehow in opposition to typed languages, and that a type system is something that can be bolted on after the fact onto a so-called untyped language. Both of these claims are simply false. The only correct view is that computation comes to us in typed form, with some types being perhaps more interesting to some people than to others. One can choose to be myopic, and consider only one type, but I argue that this is idiotic, born of ideological attachments and plain old ignorance. It is much better to understand the whole context in which such languages arise, because then one sees that (a) there is no opposition, and (b) it is natural and productive to embrace the existence of more than one type.
• marklillibridge says:
In the real world, machines do not obey any “theoretical specification”. See for example one of the CS papers on the *actual* failure models of disk drives. Firmware bugs can do weird things…
The entire subfield of CS dealing with fault tolerance is concerned with these sort of issue.
If you need to be concerned with your programs’ performance — even within an order of magnitude — this can be intractable to understand from the program source using traditional models. (E.g., nasty effects due to prefetch branch table thrashing.)
15. climatecode says:
Shouldn’t that be M/y ?
16. johnwcowan says:
If programming is equivalent to proving, it is no longer programming, but something else, just as geometry is not land-surveying, but something else. I have no trouble with people wishing to study the something else, but I fail to see that it’s a good, never mind the only, preparation for a career with chain and theodolite.
• climatecode says:
CMU’s SCS is not in the business of training grunt programmers (at least, it wasn’t when I worked there). It teaches Computer Science, which is largely a branch of mathematics. If you want programmer training, go to an evening class. If you want to understand computation, study Computer Science.
• destrius says:
In fact, if I remember from a class with Bob some years ago, he explained (perhaps tongue-firmly-in-cheek) that mathematics was really a branch of computer science. I can’t remember the explanation he gave for that though; it probably involved category theory.
• jonathanaldrich says:
climatecode-
Yes, CMU teaches computer science, not grunt programming. But be careful about your claims. CMU by its very structure recognizes that CS is not a subdiscipline of math, but rather a discipline that combines mathematics with engineering and other fields. One of the great things about SCS is that it is its own school, not part of the college of engineering or the college of arts & sciences. It is thus a place where great mathematicians can work with great engineers, psychologists, linguists, biologists, and many interdisciplinary researchers, all on CS-related topics.
Reading the historical Carnegie Plan for Education (still summarized in the CMU undergraduate catalog), you’ll find an emphasis on “fundamentals useful in later learning” but also “pride in educating students who display excellence in application–students who can do useful things with their learning.” It takes both, and I think our curriculum viewed as a whole strives to deliver both immediate competency and knowledge of enduring value.
Follow | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 26, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.59172523021698, "perplexity": 1098.2866726730704}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469258951764.94/warc/CC-MAIN-20160723072911-00261-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://mathematica.stackexchange.com/questions/70120/systemexceptionmemoryallocationfailure-with-nmaximize/70157 | SystemException["MemoryAllocationFailure", ...] with NMaximize
I have a complicated analytical expression that needs to be maximized with respect to a parameter t:
qfB[t_,\[Lambda]_,\[Gamma]_,a_]=Uncompress["1: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"];
For certain values of the parameters, for example with the following command
NMaximize[{qfB[t, 1, 2, 0.5162124455872646], t > 0}, t][[1]]
I obtain the following error
SystemException["MemoryAllocationFailure", {NMaximize[{qfB[t, 1, 2,
0.516212], t > 0}, t][[1]], OutputSizeLimitSkeleton[52], -1 + 4.5*10^-24300380321879}]
(very long output, even if compressed). This error doesn't appear in the documentation, and it causes the whole evaluation to stop.
I would like to understand why it comes up, and if there is a way around it or at least a way to handle it inside a computation.
EDIT
Following Oleksandr's suggestion I have filed a support request to Wolfram technical support and it has been forwarded to the developers as a bug.
• I got this as a Maximized answer after several trials, {0.0175048, {t -> 0.570513}}. Jan 4 '15 at 17:26
• @OleksandrR. Thanks for your comment. I'll investigate the analytical form of my function to fix the numerical instability. I've noticed that FindMaximum can be slow for certain parameters. I will try with NelderMeadMinimize. Jan 4 '15 at 22:13
• The kernel crashes after a minute in V10.1 (Mac OSX, Macbook Pro, 2.7 GHz Intel Core i7, 16 GB RAM). Does that count as the bug being "fixed"? :) Jul 18 '15 at 16:26
This error should probably be reported to WRI as a bug, most likely in ExperimentalNumericalFunction; you should not be seeing this come back up to the top level. I see no obvious reason why memory allocation should fail, as this is not really a large or difficult problem, despite the apparent complexity of the expression.
However, we do not really need the full global optimization machinery of NMaximize anyway, as the function is seen to be unimodal by plotting. Thus, we can manage with only local minimizers.
For what it's worth, neither FindMaximum or NelderMeadMinimize have a problem with this function--so it seems confined to NMinimize:
FindMaximum[{qfB[t, 1, 2, 0.5162124455872646], t > 0}, {t, 1}]
(* -> { 0.017504782445427220, {t -> 0.5705059672138650}} *)
NelderMeadMinimize[-qfB[t, 1, 2, 0.5162124455872646], t]
(* -> {-0.017504782449431693, {t -> 0.5705132464216982}} *)
If FindMaximum seems too slow, it's probably because it starts too close to $t=0$, where the expression diverges. This causes overflows and other numerical problems, which FindMaximum may attempt to deal with by ramping up the precision. Constrained optimization is also slower than unconstrained, although constraints are not really necessary here. We can fix any problem FindMaximum has by giving it a more favorable starting region:
FindMaximum[qfB[t, 1, 2, 0.516212445587264625], {t, 1/2, 1}]
(* -> {0.017504782449430056, {t -> 0.5705133885275231}} *)
This way is about 100 times faster than using the constraint, and actually a bit (~30%) faster even than NelderMeadMinimize, using the Mathematica VM. (NelderMeadMinimize is faster when using a C compiler, but most compilers will take a long time to compile this complicated expression, so there is no benefit unless you need to maximize this for very many combinations of parameters.)
• I have reported the problem with the error message to Wolfram. I've also tried your NelderMeadMinimize function and it works great, much faster than FindMaximum! Jan 4 '15 at 22:31
• @Pincopallino if they confirm it is a bug, could you please update the question to add the "bugs" tag? Also, see my update about the poor performance of FindMaximum. Even though NelderMeadMinimize can be a bit faster, personally I think the difference is not large enough to be worth bothering with; just use FindMaximum without the constraint instead. Jan 4 '15 at 23:23
This is the best I can get:
qfB = Uncompress["You expression here"];
myfun = qfB /. {\[Lambda] -> 1., \[Gamma] -> 2., a -> 0.5162124455872646} // N;
(* so that the expression only involves t *)
NMaximize[{myfun, t > 0}, t]
{0.0175048, {t -> 0.570513}}
Hope this helps.
• Thank you! However, I would like to understand the source of the error, because it appears to be undocumented. Does the error appear on you system? Jan 4 '15 at 20:19
• @Pincopallino I had a similar error once. If I use your code, I got the same error as yours. I think it is just that the expression is too 'complicated' for MMA to handle. Sometimes, we have to give MMA a 'minimal' things to calculate. In this case, I have fixed other parameters before passing it on to NMaximize`. Jan 4 '15 at 21:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46920186281204224, "perplexity": 1414.5082874925656}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964360803.6/warc/CC-MAIN-20211201143545-20211201173545-00540.warc.gz"} |
https://www.physicsforums.com/threads/hamiltonian-noethers-theorem-in-classical-mechanics.762187/ | # Hamiltonian Noether's theorem in classical mechanics
1. Jul 18, 2014
### bolbteppa
How does one think about, and apply, in the classical mechanical Hamiltonian formalism?
From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity
$$\sum_{i=1}^n \frac{\partial \mathcal{L}}{\partial ( \frac{d y_i}{dx})} \frac{\partial y_i^*}{\partial \varepsilon} - \left[\sum_{j=1}^n \frac{\partial \mathcal{L}}{\partial ( \frac{d y_j}{dx})} \frac{d y_j }{\partial x} - \mathcal{L}\right]\frac{\partial x^*}{\partial \varepsilon}$$
is conserved if the Lagrangian $\mathcal{L}(x,y_i,y_i')$ is invariant under a continuous one-parameter group of infinitesimal transformations of the form
$$T(x,y_i,\varepsilon) = (x^*,y_i^*) = (x^*(x,y_i,\varepsilon),y_i^*(x,y_i,\varepsilon)).$$
From the action perspective, Noether's theorem states the equality of the 1-forms:
$$\mathcal{L}(x,y_i,y_i')dx = \sum_{j=1}^n p_i d y_j - \mathcal{H}dx = \mathcal{L}(x^*,y_i^*,y_i'^*)dx^* = \sum_{i=1}^n p_i d y_i^* - \mathcal{H}dx^*$$
which can be used to determine (additive) symmetries nicely.
How do I use this formalism to understand the Hamiltonian Noether theorem in a general context? I'll usually see a claim that $dA/dt = [H,A]$ is the Hamiltonian Noether's theorem, and I can't make sense of this in the context of my description of Noether above. This appears to derive the Poisson brackets as part of Noether from what I've developed above, but I can't make much sense of it to be honest I'm sure the answer is supposed to link the local Lie algebra tangent vector structure to the global Lie group transformation in the Lagrangian, but saying that in words is one thing, in math it's another, thanks. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9677489399909973, "perplexity": 330.58253725364017}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647280.40/warc/CC-MAIN-20180320033158-20180320053158-00104.warc.gz"} |
https://www.distance-calculator.co.uk/towns-within-a-radius-of.php?t=Ciplet&c=Belgium | Cities, Towns and Places within a 60 mile radius of Ciplet, Belgium
Get a list of towns within a 60 mile radius of Ciplet or between two set distances, click on the markers in the satelitte map to get maps and road trip directions. If this didn't quite work how you thought then you might like the Places near Ciplet map tool (beta).
The radius entered failed to produce results - we reset it to a max of 60 miles - apologies for any inconvenience
# Distance Calculator > World Distances > Radius Distances > Ciplet distance calculator > Ciplet (Belgium ) Radius distances
Get towns between and Miles KM
Click to View Visual Places on Map or View Visual Radius on Map
miles
Showing 0100 places between 10 and 60 miles of Ciplet
(Increase the miles radius to get more places returned *)
< 25 miles > 25 miles
Ampsin, Belgium is 10 miles away
Attenhoven, Belgium is 10 miles away
Borlo, Belgium is 10 miles away
Coutisse, Belgium is 10 miles away
Donceel, Belgium is 10 miles away
Gelbressee, Belgium is 10 miles away
Grand-rosiere, Belgium is 10 miles away
Grand-rosiere-hottomont, Belgium is 10 miles away
Haneffe, Belgium is 10 miles away
Jehay, Belgium is 10 miles away
Jehay-bodegnee, Belgium is 10 miles away
Longchamps, Belgium is 10 miles away
Marchovelette, Belgium is 10 miles away
Mechelen-bovelingen, Belgium is 10 miles away
Mehaigne, Belgium is 10 miles away
Mielen-boven-aalst, Belgium is 10 miles away
Mont-saint-andre, Belgium is 10 miles away
Noduwez, Belgium is 10 miles away
Pousset, Belgium is 10 miles away
Rhion, Belgium is 10 miles away
Rukkelingen-loon, Belgium is 10 miles away
Sclayn, Belgium is 10 miles away
Verlaine, Belgium is 10 miles away
Amay, Belgium is 11 miles away
Boninne, Belgium is 11 miles away
Bonneville, Belgium is 11 miles away
Cognelee, Belgium is 11 miles away
Flone, Belgium is 11 miles away
Huppaye, Belgium is 11 miles away
Kerkom, Belgium is 11 miles away
Kerkom-bij-sint-truiden, Belgium is 11 miles away
Lantremange, Belgium is 11 miles away
Les Boscailles, Belgium is 11 miles away
Marche-les-dames, Belgium is 11 miles away
Muizen, Belgium is 11 miles away
Namache, Belgium is 11 miles away
Nameche, Belgium is 11 miles away
Neerheylissem, Belgium is 11 miles away
Neerwinden, Belgium is 11 miles away
Oleye, Belgium is 11 miles away
Opheers, Belgium is 11 miles away
Opheylissem, Belgium is 11 miles away
Petit Sart, Belgium is 11 miles away
Pietrain, Belgium is 11 miles away
Pietremau, Belgium is 11 miles away
Remicourt, Belgium is 11 miles away
Stockay, Belgium is 11 miles away
Thon, Belgium is 11 miles away
Upigny, Belgium is 11 miles away
Aische, Belgium is 12 miles away
Aische-en-refail, Belgium is 12 miles away
Barse, Belgium is 12 miles away
Brumagne, Belgium is 12 miles away
Daussoulx, Belgium is 12 miles away
Dhuy, Belgium is 12 miles away
Dommartin, Belgium is 12 miles away
Eliksem, Belgium is 12 miles away
Engelmanshoven, Belgium is 12 miles away
Ereffe, Belgium is 12 miles away
Ezemaal, Belgium is 12 miles away
Gelinden, Belgium is 12 miles away
Goetsenhoven, Belgium is 12 miles away
Haltinne, Belgium is 12 miles away
Heers, Belgium is 12 miles away
Hodeige, Belgium is 12 miles away
Horion, Belgium is 12 miles away
Horion-hozemont, Belgium is 12 miles away
Jauchelette, Belgium is 12 miles away
Jeneffe, Belgium is 12 miles away
Jodoigne, Belgium is 12 miles away
Jodoigne-souveraine, Belgium is 12 miles away
Marchin, Belgium is 12 miles away
Neerlanden, Belgium is 12 miles away
Perwez, Belgium is 12 miles away
Perwez, Belgium is 12 miles away
Saint-georges, Belgium is 12 miles away
Saint-germain, Belgium is 12 miles away
Saint-jean-geest, Belgium is 12 miles away
Samson, Belgium is 12 miles away
Velm, Belgium is 12 miles away
Vierset-barse, Belgium is 12 miles away
Wange, Belgium is 12 miles away
Warisoulx, Belgium is 12 miles away
Alveaux, Belgium is 13 miles away
Awirs, Belgium is 13 miles away
Beez, Belgium is 13 miles away
Bost, Belgium is 13 miles away
emines, Belgium is 13 miles away
Glimes, Belgium is 13 miles away
Gussenhoven, Belgium is 13 miles away
Haillot, Belgium is 13 miles away
Halle-booienhoven, Belgium is 13 miles away
Hermalle-sous-huy, Belgium is 13 miles away
Horpmaal, Belgium is 13 miles away
Hozemont, Belgium is 13 miles away
Jallet, Belgium is 13 miles away
Klein-gelmen, Belgium is 13 miles away
Labas, Belgium is 13 miles away
Lambert, Belgium is 13 miles away
Les Tombes, Belgium is 13 miles away
Click to See place names or View Visual Places on Map
Click to go to the top or View Visual Radius on Map
World Distances
Need to calculate a distance for Ciplet, Belgium - use this Ciplet distance calculator.
To view distances for Belgium alone this Belgium distance calculator
If you have a question relating to this area then we'd love to hear it! Chec out our facebook, G+ or Twitter pages above!
Don't forget you can increase the radius in the tool above to 50, 100 or 1000 miles to get a list of towns or cities that are in the vicinity of or are local to Ciplet. You can also specify a list of towns or places that you want returned between two distances in both Miles(mi) or Kilometres (km) .
Europe Distances
* results returned are limited for each query | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.976056694984436, "perplexity": 13850.707593897372}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989820.78/warc/CC-MAIN-20210518033148-20210518063148-00496.warc.gz"} |
https://www.physicsforums.com/threads/change-of-basis-help.657817/ | # Change of basis help?
1. Dec 9, 2012
### bonfire09
1. The problem statement, all variables and given/known data
Problem is assuming the mapping T: P2---->P2 defined by T(a0+a1t+a2t2)=3a0+(5a0-2a1)t+(4a1+a2)t^2 is linear. Find the matrix representation of T relative to Basis B={1,t,t^2}.
The part that im confused on is when I go plug in the basis values T(1),T(t),and T(t^2)? I don't know how to do it?
2. Relevant equations
3. The attempt at a solution
So to find T(1) its just T(1+0t+0t2)=3a0+5a0t
To find T(t) is just T(0+a1(t)+0T2)=3(0)+(5(0)-2a1)t+(4a1+0)t^2=-2a1t+4a1t^2
T(t^2)= T(0+0t+a2t^2)=3(0)+(5(0)-2(0))t+(4(0)+a2)t^2=a2T2
Usually in lots of books they omit steps like these and I'm trying to figure them out. Is this a correct way?
2. Dec 9, 2012
### pasmith
This is the right idea, but to get $T(1)$ you take $a_0 = 1$, $a_1 = 0$, and $a_2 = 0$ so that $T(1) = 3 + 5t$. Similarly for the other two basis vectors.
3. Dec 9, 2012
### bonfire09
Oh ok. So for T(t) just let a0=0, a1=1 and a2=0 and for T(t^2) just let a0=0,a1=0 and a2=1?
That looks like the standard basis {e1,e2,e3}
Similar Discussions: Change of basis help? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9538803100585938, "perplexity": 1698.8922484049285}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823482.25/warc/CC-MAIN-20171019231858-20171020011858-00788.warc.gz"} |
http://clay6.com/qa/46302/if-a-and-b-are-two-sets-such-that-a-subset-b-then-what-is-a-cup-b- | Browse Questions
Home >> AIMS >> Class11 >> Math >> Sets
# If A and B are two sets such that A $\subset$ B, then what is A $\cup$ B?
A $\cup$ B = B. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8763307332992554, "perplexity": 75.3604740067964}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720760.76/warc/CC-MAIN-20161020183840-00058-ip-10-171-6-4.ec2.internal.warc.gz"} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.