url
stringlengths 15
1.13k
| text
stringlengths 100
1.04M
| metadata
stringlengths 1.06k
1.1k
|
|---|---|---|
http://learninglover.com/blog/?m=201307 | # Term Frequency Inverse Document Frequency
I recently found myself at a gathering where there was a presentation followed by a question and answer session. The presenter spoke about how recent advents in technology had allowed for questions to be submitted online, which led to many more questions than they normally receive. He then stated that rather than attempt to answer each question individually, that the questions would be grouped together to attempt to cover as many areas as possible. I must say that while the presentation and the Q & A sessions in themselves were informative, I was probably most excited when I heard the speaker present this problem. I immediately began analyzing the problem, developing a strategy and decided to speak with the presenter afterwards.
I like to think of three trains of thought when it comes to computers. There are those who watch science fiction movies and believe that computers can do literally anything; there are those who haven’t seen computers tackle complex tasks, so they think of computers as simple “adding machines”; and then there are those of us who work with computers on a day to day basis. There is an extremely long list of things that computers can do – a list which far outnumbers the things that people in the second category try to limit computers to. However, the fact that computers have not gotten to an “I, Robot” mentality does not make them useless.
As a case in point, one of the more popular and thus more important areas of data mining is that of text analytics. This area attempts to combine the fields of computer science and natural language processing to build tools that gather meaning from text documents. Several algorithms have emerged in this field and the one I choose to write about today is the Term Frequency Inverse Document Frequency Matrix. This is the means by which I suggested to help with the question and answer session I mentioned earlier.
The Term Frequency Inverse Document Frequency (TF-IDF) Matrix considers as input a list of documents. Each of these documents consists of words (or terms). Two important things are computed for each term, the “term frequency” and the “inverse document frequency”. There are several ways to compute each of these, but the most basic way of computing each is to let the term frequency of a given word and document tf(w, d) be the number of times the word w appears in the document d. In a similar manner, the inverse document frequency idf(w, D) tells how common the word w is across all the documents d \in D. The calculation of the TF-IDF matrix consists of creating a column corresponding to each word and a row for each document. The tf and idf values are then computed for each cell and the value in the cell is the product tf(w, d)*idf(w, D).
Once the TF-IDF matrix has been computed, we can use a metric like Cosine Similarity to determine how similar two documents are. When every pair of document is compared using the cosine similarity metric, it forms a similarity matrix that shows how the documents relate to one another. This matrix can be clustered via k-means clustering or hierarchal clustering show the similar documents. | {"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": 0.8980292677879333, "perplexity": 615.273401750342}, "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/1505818695375.98/warc/CC-MAIN-20170926085159-20170926105159-00196.warc.gz"} |
https://socratic.org/questions/how-do-you-find-the-discriminant-and-how-many-solutions-does-11x-2-9x-1-0-have | Algebra
Topics
# How do you find the discriminant and how many solutions does 11x^2-9x-1=0? have?
May 1, 2015
The discriminant is the thing you take the square root of in the
$a {x}^{2} + b x + c = 0$ has solution(s): $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
The discriminant is ${b}^{2} - 4 a c$
If $a , b$ and $c$ are real numbers, then:
If the discriminant is positive, then there are two real solutions.
$\textcolor{w h i t e}{\text{ssss}}$ One when we add and another when we subtract.
If the discriminant is 0, then there is one real solutions.
$\textcolor{w h i t e}{\text{ssss}}$ Since $\sqrt{0} = 0$, adding and subtracting do not give us different answers.
If the discriminant is positive, then there are two imaginary solutions.
$\textcolor{w h i t e}{\text{ssss}}$ Since the square root of a negative is imaginary, we get imaginary solutions.
In $11 {x}^{2} - 9 x - 1 = 0$, we have
$a = 11$, $b = - 9$ and $c = - 1$, so the discriminant is:
${b}^{2} - 4 a c = {\left(- 9\right)}^{2} - 4 \left(11\right) \left(- 1\right)$, which is equal to :
$81 + 44 = 125$
The equation has two real solutions.
$\textcolor{w h i t e}{\text{ssss}}$ One when we add $\sqrt{125}$ and another when we subtract $\sqrt{125}$.
##### Impact of this question
847 views around the world | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 18, "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": 0.9535253047943115, "perplexity": 412.56500520078396}, "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-2019-51/segments/1575541157498.50/warc/CC-MAIN-20191214122253-20191214150253-00541.warc.gz"} |
http://math.stackexchange.com/questions/200967/i-am-confused-about-bayes-rule-in-mcmc?answertab=votes | # I am confused about Bayes' rule in MCMC
Bayes' rule appears to bevery simple at first sight, but when studied deeply I find it is difficult and confusing, especially in MCMC applications when multiple parameters need to be estimated.
For example, assuming $x,y,z,t$ are four parameters, which of the following three expressions are true (or true under some specifications)?
1. $P(x)P(z\mid x,y)=P(x,z\mid y)$
2. $P(x\mid y)P(z\mid x,y)=P(x,z\mid y)$
3. $P(x\mid y)P(z\mid x,t)=P(x,z\mid y,t)$
I usually see formulas similar with 3, but I wonder why it hold. Could someone explain it in detail?
If there are any excellent books that could help me, pls list them.
-
The generalization of the formula $$\Pr(A \cap B) = \Pr(A \mid B)\Pr(B)$$ for a conditional probability $\Pr(\cdot \mid C)$ is the following one: $$\Pr(A \cap B \mid C) = \Pr(A \mid B\cap C)\Pr(B \mid C).$$
Your formula number 2 is analogous to the above formula (with $P(\cdot \mid y)$ substituted for $\Pr(\cdot \mid C)$), and it is the correct one. | {"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": 0.936557412147522, "perplexity": 389.91308886989}, "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/1429246635639.11/warc/CC-MAIN-20150417045715-00309-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://physics.stackexchange.com/questions/280154/where-is-the-mass-and-gravitational-influence-of-dark-matter | # Where is the mass and gravitational influence of dark matter? [duplicate]
I'll have to ask an elementary level question about orbital motion and the mass/gravity that influences it.
In solar systems, the large mass of the sun pulls on the planets and we see the velocity of the outer planets traveling far slower than the inner planets because the mass in the rest of the solar system is far lower than the mass of the sun. If dark matter is spread throughout a galaxy, and not just at the center, would that not be like having massive planets in the outer part of a solar system, like a lot of jupiters that can have an effect on the planetary motion of the outer planets in the solar system? i.e. if there were a lot of jupiters in the outer regions of a solar system, would they cause the velocity of the outer planets to speed up, like we see in a galaxy with dark matter located throughout the galaxy?
• Probably a duplicate. See answe in physics.stackexchange.com/q/107764 Sep 14 '16 at 18:40
• Possible duplicates: physics.stackexchange.com/q/1008/2451 and links therein. Sep 14 '16 at 18:43
• @BobBee I don't think it is a duplicate of that question: it seems to be asking whether the solar solar system is affected by dark matter, while I think this question is asking whether solar systems with a lot of distant mass -- lots of Jupiters -- would have markedly different rotation curves for other planets.
– user107153
Sep 14 '16 at 18:44
• @tfb I have to say that the answers provided by DavePhDa and Alan under the proposed duplicate are fine and explicit answers to this question: the size of the possible effect is below the sensitivity of current measurements so we can only tell you the theoretical answer. Sep 14 '16 at 19:14
• @dmckee And I think the theoretical answer is what they are after: how are the rotation curves of galaxies (or planetary systems) dependent on their mass distributions, not how our solar system's curve in how much dark matter we expect to exist, which is obviously 'not very much at all'.
– user107153
Sep 14 '16 at 19:30 | {"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": 0.8085104823112488, "perplexity": 389.2617704867456}, "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-2021-43/segments/1634323585380.70/warc/CC-MAIN-20211021005314-20211021035314-00567.warc.gz"} |
http://www.physicsforums.com/showthread.php?t=377018 | # What type of energy is transfered in a circuit?
by p.tryon
Tags: circuit, energy, transfered, type
P: 51 In an electrical circuit the electrons kinetic energy is transfered to other forms of energy at the components. True or false? If it is false what type of energy do the electrons transfer? Thanks
Mentor P: 22,234 False. Electrons transfer electrical energy. Electrical energy has nothing to do with kinetic energy in electrons. Electromagnetism is one of the four fundamental forces and electrical energy is due to moving charges with that force.
P: 51 Thanks for that ;-)
P: 132
What type of energy is transfered in a circuit?
Quote by russ_watters False. Electrons transfer electrical energy. Electrical energy has nothing to do with kinetic energy in electrons. Electromagnetism is one of the four fundamental forces and electrical energy is due to moving charges with that force.
So by your definition of fundamental forces, no such thing as "kinetic energy" exists!
And that implies that the energy expressed when large masses smash into each other is simply electromagnetic transfers and radiation. Well, that is obviously true, but then how does one explain the term "kinetic energy"? Just perhaps, electromagnetic energy just might in some way be related to the effects that have been defined in some circles as "kinetic energy"?
That is rather a different answer than "has nothing to do with kinetic energy" isn't it?
But I take it what you are really saying is that energy in an electrical circuit is transferred in ways different from the simplistic "kinetic" model of ball bearings going down a hose. I'd agree with that.
Mentor
P: 16,947
Quote by bjacoby Just perhaps, electromagnetic energy just might in some way be related to the effects that have been defined in some circles as "kinetic energy"? That is rather a different answer than "has nothing to do with kinetic energy" isn't it?
No, russ is correct. The point is that electrons are so light and their drift velocity is so small that there is never a significant amount of energy in the form of kinetic energy. It is not that kinetic energy does not exist, simply that it is not relevant for electrical circuits.
Here is an example I worked out a while back in a similar thread:
http://www.physicsforums.com/showpos...3&postcount=27
Mentor
P: 22,234
Quote by bjacoby So by your definition of fundamental forces, no such thing as "kinetic energy" exists!
Good point - Kinetic energy isn't really related to one of the fundamental forces, so that part of the sentence is somewhat misleading.
P: 35 I'm not quite sure how this works. Isn't the reason that electrons possess low average KE because they've transferred most of their KE to other forms in the components? For example, in the absence of components(hence no or negligible resistance), an electron traveling through a circuit with a 6V potential across it would gain a KE of 6 eV, which is a quite a large amount of KE for an electron. Hence its maximum drift speed would be 1.03 x 10^6 m/s, and assuming it starts at rest and is uniformly accelerated through the circuit, its average drift speed would be half of that, 5.13 x 10^5 m/s. This agrees with the fact that a circuit with near zero resistance would have almost infinite current flowing through it, since I = nAve and all. Because of this I concluded that the electrons lose their KE within the components of a circuit converting it to heat and light or whatever the components do, causing them to move at a much lower average drift speed. Is this reasoning flawed?
PF Gold
P: 1,756
Quote by Repainted I'm not quite sure how this works. Isn't the reason that electrons possess low average KE because they've transferred most of their KE to other forms in the components? For example, in the absence of components(hence no or negligible resistance), an electron traveling through a circuit with a 6V potential across it would gain a KE of 6 eV, which is a quite a large amount of KE for an electron. Hence its maximum drift speed would be 1.03 x 10^6 m/s, and assuming it starts at rest and is uniformly accelerated through the circuit, its average drift speed would be half of that, 5.13 x 10^5 m/s. This agrees with the fact that a circuit with near zero resistance would have almost infinite current flowing through it, since I = nAve and all. Because of this I concluded that the electrons lose their KE within the components of a circuit converting it to heat and light or whatever the components do, causing them to move at a much lower average drift speed. Is this reasoning flawed?
I would say yes because outside of DC circuits, the energy in a circuit is transferred via electromagnetic waves. If we have an AC signal, then the charges have a zero net displacement. In addition, the propagation of the signal (the group velocity, not just the phase velocity), is much much higher than the drift velocities of the charges. As such, the energy cannot be transferred via kinetic energy. The mechanism for drawing out energy from the circuit in elements like a resistor do rely on the kinetic energy of electrons as they rely on the Drude model to transfer the energy from the charges to heat. However, that is not the mechanism for all devices (like an antenna) nor is it the mechanism for how the energy is transferred between components.
P: 35 So what happens to the KE that the electrons are supposed to gain? The E-field produced by the battery exerts a force on the electrons, causing them to accelerate and hence gain KE. Even in an AC circuit, while the electrons have no net displacement, the direction of the force due to the AC source is changing as well, hence it always(I think?) points in the same direction as the displacement at anytime?
Sci Advisor PF Gold P: 1,756 In an AC circuit, you are not driving the charges. Instead, you excite an electromagnetic wave that you input into the circuit. The electromagnetic wave induces currents in the circuit's waveguide. These are the currents that we measure, but they are not directly created by the source but rather by the electromagnetic signals. When the wave reaches a component, it sets up a voltage potential that induces the movement of carriers in the component. In addition, most components will also allow the wave to migrate through the component (IC chip). The kinetic energy of the electrons is given up by their collisions with the conductor's lattice. These phonons transfer the charges' energy into heat in what is known as the Drude model. Still, this is unsatisfactory for how energy is extracted for all but the most basic circuit elements (resistors). This does not explain how energy is stored in a capacitor by building up a potential difference, how antennas work by accelerating charges to excite electromagnetic waves, or how signals are propagated between circuit components when we are not discussing true DC circuits.
P: 35 I am confused by the AC part. Isn't an AC produced by a coil of wire placed within a uniform magnetic field and rotated to change the magnetic flux through it, inducing a potential? Or is this a simplified explanation of how an AC generator works that doesn't talk about EM waves and such? Also, if this Drude model is inaccurate at describing how energy is transferred to most components, then how is energy transferred from the moving electrons to the components? Or is it something that varies for every component?
P: 4,513
Quote by p.tryon In an electrical circuit the electrons kinetic energy is transfered to other forms of energy at the components. True or false? If it is false what type of energy do the electrons transfer? Thanks
Potential Energy. Specifically electric potential energy, eV.
Mentor
P: 16,947
Quote by Repainted Isn't the reason that electrons possess low average KE because they've transferred most of their KE to other forms in the components? ... Is this reasoning flawed?
Let's say that we have 2 masses attached by a light rope with a pulley arranged to pull the second mass up as we move the first mass to the left (see Fig 30). Now, suppose we want to lift the second mass to the top of the table, but can only directly do work on the first mass. We have two basic options:
1) we can start with a little slack in the rope, suddenly do work on the first mass, accelerating it very quickly to a high KE, let it snap the line taut, and pull the second mass up by exchanging its KE for gravitational PE.
2) we can start with no slack in the rope, do work on the first mass, which will be transferred directly to the second mass via the rope with no significant amount of KE needed to effect the transfer.
Remember, work is force times distance, so as long as you can exert a force on something you can do work on it, regardless of KE. True, you can use KE to do work, but it is not necessary, and true if you don't have some other interaction then when you do work on something it will gain KE. But neither of those statements imply that you must use KE to do work nor that the first mass had a significant amount of KE in option 2) at any time.
So, in the case of electrical circuits, the rope is equivalent to the electromagnetic forces, the first mass is equivalent to the electrons, and the second mass is equivalent to whatever the electrons do work on. As I showed in my previous calculation there is never any significant amount of KE in the electrons, the electromagnetic "rope" is always taut and the energy which the power source supplies to the electrons is transferred directly to the circuit without gaining and losing KE.
Sci Advisor PF Gold P: 11,899 I think the AC factor is a red herring. The (mean) KE of the electrons is constant DC and varies in AC but it is negligible in both cases. But the notion that the energy is transferred in the form of electronic KE is like saying that the energy transmitted through a bicycle chain is due to the KE of the links in the chain. That KE would only contribute (briefly) a bit of drive if you took your feet off the pedals! (edit: this is more ore less what dalespam is saying - I think I was writing whilst his post went up) In the case of a stream of electrons, the KE gained during acceleration would be transferred, on impact with the collector. If you apply Kirchhoff 2 to the two situations - the PD across a copper supply wire is very small- the majority of the PD is dropped across the load. In the case of an electron beam, the majority PD is across the acceleration gap and a small bit at the surface of the metal in the collector. In the first case, the energy transferred to the load is in the form of electrical. In the second case, the energy transferred to the collector is KE.
P: 35 Yeah I sort of meant something like that. Not exactly colliding and stuff. More like an electron moving against another force while still under the force of the E-field. Like that the block on the table, if there was no load attached to it, it would have gained more KE, but work has to be done to gain GPE of the load, it doesn't end up with as much KE as it should. So negative work is done on the electron while it is moving through the component, it does positive work on the component causing heat or light to be given off or whatever the component does while positive work is still being done on it by the E-field due to the battery... Is this more accurate?
PF Gold
P: 1,756
Quote by Repainted I am confused by the AC part. Isn't an AC produced by a coil of wire placed within a uniform magnetic field and rotated to change the magnetic flux through it, inducing a potential? Or is this a simplified explanation of how an AC generator works that doesn't talk about EM waves and such? Also, if this Drude model is inaccurate at describing how energy is transferred to most components, then how is energy transferred from the moving electrons to the components? Or is it something that varies for every component?
How the original electromagnetic wave is generated is immaterial. For low frequency signals we can be rather basic with the generation of the wave. A simple generator works by physically rotating magnets about stationary wires. The changing magnetic field automatically creates an electromagnetic wave and the wires act as the waveguides to propagate the wave in the desired direction. At normal AC frequencies associated with residential electricity, the wavelength is so long that no real thought needs to be given in terms of designing a waveguide. It is not until we start going to higher frequencies like RF that we need to pay closer attention to waveguide design and start thinking about other ways of generating the signal. But the physics never change.
The Drude model is the classical model for normal ohmic losses. Whenever we lose energy due to the resistance of the device, it is typically the Drude model at work. However, outside of a resistor, we are not interested in converting the electrical energy into heat. As such, the mechanisms for extracting power vary from component to component. For example, a transistor works by first setting up a voltage difference between the desired terminals. This voltage difference then induces the movement of carriers within the transistor. Energy is spent to move these charges so that we build up voltages on the outputs, this can be lost due to phonon collisions akin to the Drude model but we can also emit electromagnetic radiation like with an LED. An inductor stores energy by inducing a magnetic field or locally constrained electromagnetic waves. And as I mentioned before, an antenna can work by providing a way to move the electromgantice wave from a guided mode to a propagating mode. The current side to this theory is that the accelerating currents in the antenna, say like in a simple dipole antenna, will gnerate the electromagnetic waves. It is the acceleration that matters, not their velocity or collision rate (which would affect the losses predicted by the Drude model). We can also extract power from the fields by coupling with another inductor to induce a current in the other inductor, like what we do in a simple transformer.
Energy can be extracted by the electromagnetic fields that are created by the induced currents, from the electromagnetic fields of the signals itself, or from quantum mechanical behavior of the charges themselves (dropping down from an excited state to a lower state and thus emitting a photon). Since heat itself is very rarely a desirable output from a circuit outside of a heating element, most desirable work is done via different mechanisms.
P: 35 Okay I think this sort of clears it up. Thanks a lot. So to sum it up, the collisions in the Drude model are simply useful in portraying power output due to resistance, but for everyday uses like my computer for instance, it depends on how the individual circuitry is designed to extract power for the power source. Am I right to say this? Oh and are these 'collisions' in the Drude model really collisions? or as DaleSpam showed with an example, the E-field causing the electrons to simply doing work against another agent continuously and not some haphazard movement through the circuitry? | {"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": 0.8762233257293701, "perplexity": 358.3448569314269}, "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/1405997894275.63/warc/CC-MAIN-20140722025814-00208-ip-10-33-131-23.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/multilayer-thickness.104206/ | # Multilayer thickness
1. Dec 15, 2005
### vinhphysics
Hi!
I am doing research on TiAlSiN coatings. The coatings are multilayers of crystalline TiN and amorphous (Al,Si)N. The thickness of each layer is estimated about some nano-meters. The question is How can I measure the thickness of each layer? and What measurement of method is the best?
Thanks you!
2. Dec 15, 2005
### inha
X-ray fluorescence can be used to measure the layer thicknesses(is this even a word?). The analysis of the spectra to extract the thicknesses from a multilayer system isn't a trivial procedure though. X-ray absorption should do the trick too. I'm sure there are easier ways but those two were the first that I though of.
3. Dec 19, 2005
### PerennialII
Simplest methods are probably the likes of ball indentation, but don't know whether you can get the resolution you want with plain mechanical based ones.
4. Dec 19, 2005
### Staff: Mentor
I presume the interest is for a non-destructive method, otherwise it would be simple to do a ceramograph/metalograph and measure optically with something like an electron microscope.
Are there multiple (alternating) layers? e.g. T/A/T/A/. . . . where T = TiN and A = (Al,Si).
5. Dec 25, 2005
### vinhphysics
Thanks you!
I think TEM cross section can be used to estimate the thickness of layer. I will try to do it in near future. | {"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": 0.8996425867080688, "perplexity": 2298.839630648924}, "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/1498128320386.71/warc/CC-MAIN-20170625013851-20170625033851-00157.warc.gz"} |
https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Book%3A_Analytical_Chemistry_2.0_(Harvey)/15_Quality_Assurance/15.4%3A_Evaluating_Quality_Assurance_Data | # 15.4: Evaluating Quality Assurance Data
In the previous section we described several internal methods of quality assessment that provide quantitative estimates of the systematic errors and the random errors in an analytical method. Now we turn our attention to how we incorporate this quality assessment data into a complete quality assurance program. There are two general approaches to developing a quality assurance program: a prescriptive approach, in which we prescribe an exact method of quality assessment, and a performance-based approach in which we can use any form of quality assessment, provided that we can demonstrate an acceptable level of statistical control.3
## 15.4.1 Prescriptive Approach
With a prescriptive approach to quality assessment, duplicate samples, blanks, standards, and spike recoveries are measured following a specific protocol. We compare the result for each analysis to a single predetermined limit, taking an appropriate corrective action if the limit is exceeded. Prescriptive approaches to quality assurance are common for programs and laboratories subject to federal regulation. For example, the Food and Drug Administration (FDA) specifies quality assurance practices that must be followed by laboratories analyzing products regulated by the FDA.
Figure 15.2 provides a typical example of a prescriptive approach to quality assessment. Two samples, A and B, are collected at the sample site. Sample A is split into two equal-volume samples, A1 and A2. Sample B is also split into two equal-volume samples, one of which, BSF, is spiked in the field with a known amount of analyte. A field blank, DF, also is spiked with the same amount of analyte. All five samples (A1, A2, B, BSF, and DF) are preserved if necessary and transported to the laboratory for analysis.
After returning to the lab, the first sample that is analyzed is the field blank. If its spike recovery is unacceptable—an indication of a systematic error in the field or in the lab—then a laboratory method blank, DL, is prepared and analyzed. If the spike recovery for the method blank is unsatisfactory, then the systematic error originated in the laboratory; this is something we can find and correct before proceeding with the analysis. An acceptable spike recovery for the method blank, however, indicates that the systematic error occurred in the field or during transport to the laboratory, casting uncertainty on the quality of the samples. The only recourse is to discard the samples and return to the field to collect new samples.
If the field blank is satisfactory, then sample B is analyzed. If the result for B is above the method’s detection limit, or if it is within the range of 0.1 to 10 times the amount of analyte spiked into BSF, then a spike recovery for BSF is determined. An unacceptable spike recovery for BSF indicates the presence of a systematic error involving the sample. To determine the source of the systematic error, a laboratory spike, BSL, is prepared using sample B, and analyzed. If the spike recovery for BSL is acceptable, then the systematic error requires a long time to have a noticeable effect on the spike recovery. One possible explanation is that the analyte has not been properly preserved or it has been held beyond the acceptable holding time. An unacceptable spike recovery for BSL suggests an immediate systematic error, such as that due to the influence of the sample’s matrix. In either case the systematic errors are fatal and must be corrected before the sample is reanalyzed.
This is one reason that environmental testing is so expensive.
If the spike recovery for BSF is acceptable, or if the result for sample B is below the method’s detection limit, or outside the range of 0.1 to 10 times the amount of analyte spiked in BSF, then the duplicate samples A1 and A2 are analyzed. The results for A1 and A2 are discarded if the difference between their values is excessive. If the difference between the results for A1 and A2 is within the accepted limits, then the results for samples A1 and B are compared. Because samples collected from the same sampling site at the same time should be identical in composition, the results are discarded if the difference between their values is unsatisfactory, and accepted if the difference is satisfactory.
Figure 15.2: Example of a prescriptive approach to quality assurance for laboratories monitoring waters and wastewaters. Adapted from Environmental Monitoring and Support Laboratory, U. S. Environmental Protection Agency, “Handbook for Analytical Quality Control in Water and Wastewater Laboratories,” March 1979.
The protocol in Figure 15.2 requires four to five evaluations of quality assessment data before the result for a single sample is accepted, a process that we must repeat for each analyte and for each sample. Other prescriptive protocols are equally demanding. For example, Figure 3.7 in Chapter 3 shows a portion of a quality assurance protocol for the graphite furnace atomic absorption analysis of trace metals in aqueous solutions. This protocol involves the analysis of an initial calibration verification standard and an initial calibration blank, followed by the analysis of samples in groups of ten. Each group of samples is preceded and followed by continuing calibration verification (CCV) and continuing calibration blank (CCB) quality assessment samples. Results for each group of ten samples are accepted only if both sets of CCV and CCB quality assessment samples are acceptable.
The advantage of a prescriptive approach to quality assurance is that all laboratories use a single consistent set of guideline. A significant disadvantage is that it does not take into account a laboratory’s ability to produce quality results when determining the frequency of collecting and analyzing quality assessment data. A laboratory with a record of producing high quality results is forced to spend more time and money on quality assessment than is perhaps necessary. At the same time, the frequency of quality assessment may be insufficient for a laboratory with a history of producing results of poor quality.
## 15.4.2 Performance-Based Approach
In a performance-based approach to quality assurance, a laboratory is free to use its experience to determine the best way to gather and monitor quality assessment data. The quality assessment methods remain the same—duplicate samples, blanks, standards, and spike recoveries—because they provide the necessary information about precision and bias. What a laboratory can control is the frequency with which it analyzes quality assessment samples and the conditions it chooses to identify when an analysis falls out of a state of statistical control.
The principal tool for performance-based quality assessment is a control chart, which provides a continuous record of quality assessment results. Our fundamental assumption is that if an analysis is under statistical control, individual quality assessment results are randomly distributed around a known mean with a known standard deviation. When an analysis moves out of statistical control, the quality assessment data is influenced by additional sources of error, increasing the standard deviation or changing the mean value.
Control charts were originally developed in the 1920s as a quality assurance tool for the control of manufactured products.4 Although there are many types of control charts, two are common in quality assessment programs: a property control chart, in which we record single measurements or the means for several replicate measurements, and a precision control chart, in which we record ranges or standard deviations. In either case, the control chart consists of a line representing the mean value for the measured property or the precision, and two or more boundary lines whose positions are determined by the precision of the measurement process. The position of the data points about the boundary lines determines whether the analysis is in statistical control.
### Constructing a Property Control Chart
The simplest property control chart is a sequence of points, each representing a single determination of the property we are monitoring. To construct the control chart, we analyze a minimum of 7–15 samples while the system is under statistical control. The center line (CL) of the control chart is the average of these n samples.
$CL=\overline X=\dfrac{\sum X_i}{n}$
The more samples in the original control chart, the easier it is to detect when an analysis is beginning to drift out of statistical control. Building a control chart with an initial run of 30 or more samples is not an unusual choice.
Boundary lines around the center line are determined by the standard deviation, S, of the n points
$S=\sqrt \frac{\large{\sum (X_i-\overline X)^2}}{\large{n-1}}$
The upper and lower warning limits (UWL and LWL) and the upper and lower control limits (UCL and LCL) are given by the following equations.
$UWL= CL + 2S \hspace{30px} LWL = CL - 2S$
$UCL= CL + 3S \hspace{30px} LCL = CL - 3S$
Why these limits? Examine Table 4.12 in Chapter 4 and consider your answer to this question. We will return to this point later in this chapter when we consider how to use a control chart.
Example 15.4
Construct a property control chart using the following spike recovery data (all values are for percentage of spike recovered).
sample: 1 2 3 4 5
result: 97.3 98.1 100.3 99.5 100.9
sample: 6 7 8 9 10
result: 98.6 96.9 99.6 101.1 100.4
sample: 11 12 13 14 15
result: 100.0 95.9 98.3 99.2 102.1
sample: 16 17 18 19 20
result: 98.5 101.7 100.4 99.1 100.3
Solution
The mean and the standard deviation for the 20 data points are 99.4% and 1.6%, respectively. Using these values, we find that the UCL is 104.2%, the UWL is 102.6%, the LWL is 96.2%, and the LCL is 94.6%. To construct the control chart, we plot the data points sequentially and draw horizontal lines for the center line and the four boundary lines. The resulting property control chart is shown in Figure 15.3.
Figure 15.3 Property control chart for Example 15.4. The warning limits are shown in yellow and the control limits in red.
Practice Exercise 15.3
A control chart is a useful method for monitoring a glucometer’s performance over time. One approach is to use the glucometer to measure the glucose level of a standard solution. An initial analysis of the standard yields a mean value of 249.4 mg/100 mL and a standard deviation of 2.5 mg/100 mL. An analysis of the standard over 20 consecutive days gives the following results.
day:
result:
1
248.1
2
246.0
3
247.9
4
249.4
5
250.9
6
249.7
7
250.2
8
250.3
9
247.3
10
245.6
day:
result:
11
246.2
12
250.8
13
249.0
14
254.3
15
246.1
16
250.8
17
248.1
18
246.7
19
253.5
20
251.0
Construct a control chart and evaluate the glucometer’s performance.
We also can construct a control chart using the means for a set of replicate determinations on each sample. The mean for the ith sample is
$\overline X_i=\dfrac{\sum_{j}X_{ij} }{n_\ce{rep}}$
where Xij is the jth replicate and nrep is the number of replicate determinations for each sample.
When using means to construct a property control chart, all samples must have the same number of replicates.
The control chart’s center line is
$CL=\dfrac{\sum \overline X_i}{n}$
where n is the number of samples used in constructing the control chart. To determine the standard deviation for the warning limits and the control limits, we first calculate the variance for each sample.
$s_i^2=\dfrac{\sum_{j}(X_{ij}-\overline X_i)^2}{n_\ce{rep}-1}$
The overall standard deviation, S, is the square root of the average variance for the samples used in constructing the control plot.
$S=\sqrt\frac{\large{\sum s_i^2}}{\large{n}}$
The resulting warning and control limits are given by the following four equations.
$UWL=CL+\dfrac{2S}{\sqrt{n_\ce{rep}}}\hspace{5mm}LWL=CL-\dfrac{2S}{\sqrt{n_\ce{rep}}}$
$UCL=CL+\dfrac{3S}{\sqrt{n_\ce{rep}}}\hspace{5mm}LCL=CL-\dfrac{3S}{\sqrt{n_\ce{rep}}}$
### Constructing a Precision Control Chart
A precision control chart shows how the precision of an analysis changes over time. The most common measure of precision is the range, R, between the largest and the smallest results for nrep analyses on a sample.
$R=X_\ce{largest}-X_\ce{smallest}$
To construct the control chart, we analyze a minimum of 15–20 samples while the system is under statistical control. The center line (CL) of the control chart is the average range of these n samples.
$\overline R=\dfrac{\sum R_i}{n}$
The more samples in the original control chart, the easier it is to detect when an analysis is beginning to drift our of statistical control. Building a control chart with an initial run of 30 or more samples is not an unusual choice.
The upper warning line and the upper control line are given by the following equations
$UWL=f_\ce{UWL}\times \overline R$
$UCL=f_\ce{UCL}\times \overline R$
where fUWL and fUCL are statistical factors determined by the number of replicates used in determining the range. Table 15.2 provides representative values for fUWL and fUCL. Because the range is greater than or equal to zero, there is no lower control limit or lower warning limit.
Table 15.2: Statistical Factors for the Upper Warning Limit and the Upper Control Limit of a Precision Control Chart
replicates fUWL fUCL
2 2.512 3.267
3 2.050 2.575
4 1.855 2.282
5 1.743 2.115
6 1.669 2.004
Example 15.5
Construct a precision control chart using the following ranges, each determined from a duplicate analysis of a 10.0-ppm calibration standard.
sample: 1 2 3 4 5
result: 0.36 0.09 0.11 0.06 0.25
sample: 6 7 8 9 10
result: 0.15 0.28 0.27 0.03 0.28
sample: 11 12 13 14 15
result: 0.21 0.19 0.06 0.13 0.37
sample: 16 17 18 19 20
result: 0.01 0.19 0.39 0.05 0.05
Solution
The average range for the duplicate samples is 0.177. Because two replicates were used for each point the UWL and UCL are
$UWL = 2.512 × 0.177 = 0.44$
$UCL = 3.267 × 0.177 = 0.58$
The resulting property control chart is shown in Figure 15.4.
Figure 15.4 Precision control chart for Example 15.5. The warning limits are shown in yellow and the control limits in red.
The precision control chart in Figure 15.4 is strictly valid only for the replicate analysis of identical samples, such as a calibration standard or a standard reference material. Its use for the analysis of nonidentical samples—as often is the case in clinical analyses and environmental analyses—is complicated by the fact that the range usually is not independent of the magnitude of the measurements. For example, Table 15.3 shows the relationship between the average range and the concentration of chromium in 91 water samples. The significant difference in the average range for different concentrations of chromium makes a single precision control chart impossible. As shown in figure 15.5, one solution is to prepare separate precision control charts, each of which covers a range of concentrations for which R is approximately constant.
Table 15.3 Average Range for the Concentration of Chromium in Duplicate Water Samples
[Cr] (ppb) number of duplicate samples R
5 to < 10 32 0.32
10 to < 25 15 0.57
25 to < 50 16 1.12
50 to < 150 15 3.80
150 to < 500 8 5.25
> 500 5 76.0
Figure 15.5 Example showing the use of a precision control chart for samples that span a range of analyte concentrations. The precision control charts are for (a) low concentrations of analyte; (b) intermediate concentrations of analyte; and (c) high concentrations of analyte.
### Interpreting Control Charts
The purpose of a control chart is to determine if an analysis is in a state of statistical control. We make this determination by examining the location of individual results relative to the warning limits and the control limits, and by examining the distribution of results around the central line. If we assume that the individual results are normally distributed, then the probability of finding a point at any distance from the control limit is determined by the properties of a normal distribution.5 We set the upper and lower control limits for a property control chart to CL ± 3S because 99.74% of a normally distributed population is within three standard deviations of the population’s mean. This means that there is only a 0.26% probability of obtaining a result larger than the UCL or smaller than the LCL. When a result exceeds a control limit, the most likely explanation is a systematic error in the analysis or a loss of precision. In either case, we assume that the analysis no longer is in a state of statistical control.
Rule 1. An analysis is no longer under statistical control if any single point exceeds either the UCL or the LCL.
By setting the upper and lower warning limits to CL ± 2S, we expect that no more than 5% of the results will exceed one of these limits; thus
Rule 2. An analysis is no longer under statistical control if two out of three consecutive points are between the UWL and the UCL or between the LWL and the LCL.
If an analysis is under statistical control, then we expect a random distribution of results about the center line. The presence of an unlikely pattern in the data is another indication that the analysis is no longer under statistical control.
Rule 3. An analysis is no longer under statistical control if seven consecutive results fall completely above or completely below the center line.
Rule 4. An analysis is no longer under statistical control if six consecutive results increase or decrease in value.
Rule 5. An analysis is no longer under statistical control if 14 consecutive alternate up and down in value.
Rule 6. An analysis is no longer under statistical control if there is any obvious nonrandom patter to the results.
Figure 15.6 shows three examples of control charts in which the results show an analysis that has fallen out of statistical control. The same rules apply to precision control charts with the exception that there are no lower warning limits and lower control limits.
Figure 15.6 Examples of property control charts that show a sequence of results—indicated by the highlighting—that violate (a) rule 3; (b) rule 4; and (c) rule 5.
Exercise 15.4
In Practice Exercise 15.3 you created a property control chart for a glucometer. Examine your property control chart and evaluate the glucometer’s performance. Does your conclusion change if the next three results are 255.6, 253.9, and 255.8 mg/100 mL? | {"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": 0.809408962726593, "perplexity": 939.3219895376758}, "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/1568514574377.11/warc/CC-MAIN-20190921084226-20190921110226-00465.warc.gz"} |
https://mathoverflow.net/questions/22182/analytical-steady-state-solution-of-a-complex-ode | # Analytical steady-state solution of a complex ODE
I'm a biologist in the process of modeling a fairly simple biological system using a system of ODEs. To verify the simulations, I'm attempting to obtain an analytical steady-state solution that I can check the simulations against. My attempts so far haven't borne fruit, so I thought I'd toss the question out to mathematicians. This is my first post, so apologies if the question isn't right for this site.
The equation is of the form:
## $${dS_7\over dt} = Xv_{max} \Bigg[4{S_1 - {S_3^2S_7^4\over K_{eq,3}}\over K_m+S_1+{S_3^2S_7^4\over K_{eq,3}}} + 2{S_1 - {S_4S_7^2\over K_{eq,4}}\over K_m+S_1+{S_4S_7^2\over K_{eq,4}}}\Bigg] + D(S_{7,in}-S_7)$$
Where S1, S3, S4 and S7 and X are variables
and
Km, Keq,3, Keq,4, vmax, S1,in, S3,in, S4,in, S7,in, Xin, D and Y are constants.
This system models the change in the substrate Sn or the microbial population X in a perfectly-stirred vessel with microbes acting upon a substrate S1 to produce S3, S4 and S7 when the kinetics of the chemical reactions are thermodynamically reversible.
Sn,in is the input concentration of Sn. Km and vmax are constants that describe the "affinity" of the microbe to S1 and the maximum rate of the reaction respectively and Keq,n is the thermodynamic equilibrium constant for the reaction S1 -> A Sn + B S7. I need to solve this system for Sn where n=1,3,4,7.
Is this even possible, or am I barking up the wrong tree here?
-
I presume $D$ is a constant too. Or is it a function? – Harald Hanche-Olsen Apr 22 '10 at 22:14
Sorry, D is a constant... Fixed now. – Chinmay Kanchi Apr 23 '10 at 1:07
As Andrey mentioned, you shouldn't expect an analytical solution since you're dealing with a system of algebraic equation in several variables. (Just to be clear, what we're envisioning here is the system of equations you get by setting all the left-hand-sides to be zero). In your case, I believe you have 5 variables (X, $S_i$) and 5 equations, whose denominators can be cleared to make everything polynomial.
Such systems can be solved numerically (once you specify numerical values for your constants). One tool that I've used before is PHCpack, though for your purposes maybe Mathematica or something similar will be just fine.
Perhaps an expert can describe how to calculate resultants of your system of polynomials which will give you information on when the nature of the roots of this system change as you change your parameters...
-
already have numerical solutions using Python and SciPy. Not being a mathematician however, figuring out analytical solutions by setting LHS=0 seemed like the best way to check if the system was programmed correctly. An expression like $S_3 = f(S_1, S_4, S_7, X)$ for each of the variables is what I'm looking for... – Chinmay Kanchi Apr 22 '10 at 19:14
Right, though what you probably mean is $S_3=f(K_m,K_{eq},\dots)$, etc. But those kinds of expressions don't exist in closed form in elementary functions for general polynomial systems, unless you have a very special set of equations. It is possible to write down perturbative series solutions which will be valid in certain regimes, though. If that would be interesting to you I might give it some thought. – j.c. Apr 22 '10 at 22:14
The values for the constants are actually known. What I'm after is a solution for each variable in terms of the other variables. It should then be possible to compute the intersection(s) of the solution-spaces to determine if my numerical solution arrives at a valid steady-state, given a particular set of constants. – Chinmay Kanchi Apr 23 '10 at 1:19
Perhaps the closest thing to what you want to do is compute the Groebner basis en.wikipedia.org/wiki/Gr%C3%B6bner_basis#Solving_equations of the polynomial system then. Since you are using python, perhaps you would be interested in using Sage (sagemath.org) which contains some algorithms for computing these. – j.c. Apr 23 '10 at 1:46
Looks promising, thanks! – Chinmay Kanchi Apr 26 '10 at 13:22
Abbreviate $R_3={S_1 - {S_3^2S_7^4\over K_{eq,3}}\over K_m+S_1+{S_3^2S_7^4\over K_{eq,3}}}$ and $R_4={S_1 - {S_4S_7^2\over K_{eq,4}}\over K_m+S_1+{S_4S_7^2\over K_{eq,4}}}$. Then observing the positions of the $R$'s in your equations, set $C_1 = {1\over 2}S_3+S_4+S_1$, $C_2 = 2S_3+2S_4-S_7$ and $C_3=2YS_3+3YS_4-X$.
Then the $R$s cancel from your equations to give ${dC\over dt} = D(C_{in}-C)$ for each of $C_1$, $C_2$, and $C_3$. You can solve these explicitly, which ought to give you a good check.
In particular, if "input" means the same as "initial condition", then all three $C$'s are constants, conserved quantities.
- | {"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": 0.8342344164848328, "perplexity": 522.8376269931827}, "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-2015-40/segments/1443737864605.51/warc/CC-MAIN-20151001221744-00237-ip-10-137-6-227.ec2.internal.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/174416-prove-t-linear-transformation.html | # Math Help - Prove that T is a linear transformation
1. ## Prove that T is a linear transformation
Hello,
T: P2(R) -> P3(R) defined by T(f(x)) = xf(x) + f`(x).
Let A,B,C,a,b,c be elements of R and x,y elements of P2, where f(x) = (a + bx + cx^2) and f(y) = (A + By + Cy^2)
Can't I write this as a matrix vector product and prove it to be linear that way? I can also calculate the rank and null this way, right?
T(f(x)) = x(a + bx + cx^2) + b + 2x
= b + 2ax + bx^2 + cx^3
is this right so far? I really want to use the matrix vector product method though, but I'm having a hard time making it into a matrix, any advice?
2. Originally Posted by zodiacbrave
Can't I write this as a matrix vector product and prove it to be linear that way?
Better:
$T[\lambda f(x)+\mu g(x)]=x (\lambda f(x)+\mu g(x))+(\lambda f(x)+\mu g(x))'=$
$\ldots =\lambda T[f(x)]+\mu T[g(x)]$
3. Fernando Revilla is correct that the best way to prove something is a linear transformation is to show that it satisfies the definition of a linear transformation.
Since you specifically ask about writing it as a matrix, remember that a linear transformation from vector space U to vector space V depends on specific choices of (ordered) bases for U and V. Now, apply the linear transformation to each of the basis vector of U in turn, writing the result in terms of the basis for V. The coefficients will be the columns of the matrix.
Here, U is the function space P2 of quadratic polynomials and V is the function space P3 of cubic polynomials. The standard basis for the first is 1, x, and $x^2$ and for the second, 1, x, $x^2$, and $x^3$.
Applying the linear transformation to "1" we get $x(1)+ 0= x= 0(1)+ 1(x)+ 0(x^2)+ 0(x^3)$. The first column of the matrix representation is $\begin{bmatrix}0 \\ 1\\ 0 \\ 0\end{bmatrix}$.
Applying the linear transformation to "x" we get $x(x)+ 1= x^2+ 1= 1(1)+ 0(x)+ 1(x^2)+ 0(x^3)$. The second column of the matrix representation is $\begin{bmatrix}1 \\ 0 \\ 1 \\ 0\end{bmatrix}$.
Applying the linear transformation to " $x^2$" we get $x(x^2)+ 2x= x^3+ 2x= 0(1)+ 2(x)+ 0(x^2)+ 1(x^3)$. The third column of the matrix representation is $\begin{bmatrix}0 \\ 2 \\ 0 \\ 1\end{bmatrix}$.
The matrix representing the linear transformation, using these bases in these orders, is
$\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 2\\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$. | {"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": 13, "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": 0.9426034092903137, "perplexity": 230.00029977912396}, "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-2015-27/segments/1435375094451.94/warc/CC-MAIN-20150627031814-00079-ip-10-179-60-89.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/42404/expressing-a-graph-property-with-counting-quantifiers | Expressing a graph property with counting quantifiers
Assuming that one needs $k$ quantifiers to express that a graph contains an $k$-cycle, $\lfloor n/2 \rfloor$ counting quantifiers suffice to express that a graph is an $n$-cycle:
G has exactly $n$ nodes, each node has exactly 2 neighbors, and G doesn't contain a 3-cycle, a 4-cycle, ... and an $\lfloor n/2 \rfloor$-cycle.
Question: Can be shown, that one needs at least $\lfloor n/2 \rfloor$ counting quantifiers to express that a graph is an $n$-cylce? And how?
-
The previous answer showed that quantifier rank $\log_2(k) \pm 1$ is sufficient and necessary for expressing "A is a $k$-cycle". This implies a lower bound of at least $\log_2(k)$ quantifiers, but not an upper bound since quantifier rank counts nesting-depth of quantifiers and not the number of quantifiers. However, it is possible to express "A is a $k$-cycle" with $O(\log k)$ quantifiers. Here is an explicit expression:
You start saying that every vertex has degree exactly two. These are $4$ quantifiers. Next we need to say that every two vertices $x$ and $y$ of the graph are connected by a path of length at most $k$. Let $P_k(x,y)$ denote this predicate. The naive way to express $P_k(x,y)$ requires $k$ quantifiers. A less naive way could use divide-and-conquer but, if we do it directly without any additional trick, the result would still be $k$ quantifiers. The final solution will be to add a trick to the divide and conquer solution.
The divide and conquer solution goes as follows: you quantify the middle vertex $z$ and then recurse on the halfs $x$-$z$ and $z$-$y$ by requiring that both $P_{k/2}(x,z)$ and $P_{k/2}(z,y)$ hold. An easy computation shows that this method produces $k$ quantifiers. To improve and achieve $O(\log k)$ quantifiers we make use of a "reusing trick" that those familiar with computational complexity will recognize from the proof that QBF is PSPACE-complete: you quantify the middle vertex $z$ and then say: for every $u$ and $v$, if $u = x$ and $v = z$, or $u = z$ and $v = y$, then $P_{k/2}(u,v)$. This recursive formula expresses the same as before but now $P_{k/2}$ is used recursively only once. This gives the $O(\log k)$ quantifiers that we want.
Finally, in order to complete the formula expressing "A is a $k$-cycle" we need to say that every vertex $x$ is connected by a path of length exactly $k$ to itself. This we can do with $O(\log k)$ quantifiers using the same trick that we used for $P_k$.
(Note: all this is much easier to argue if $k$ is an exact power of $2$ but can be made to work for any $k$).
-
If A and B are cycles of length m, n, then the duplicator can win the k-long Ehrenfeucht-Fraisse game iff m, n > 2^(k-1).
Basically, whatever player I moves in A, player II choose an arbitrary element in B. The rest of the strategy is the same as for linear orders.
This means that A and B are elementarily equivalent up to quantifier-rank [log_2 min(n,m)] + 1. In particular, need at least log_2 k + 1 quantifiers to express "A is a k-cycle".
(I may have gotten the quantifier-rank wrong by +- 1, but should still be basically log2 k )
-
Can the expression "A is a k-cycle" be made explicit with log_2 k quantifiers? I'd like to see it. – Hans Stricker Oct 16 2010 at 20:25 | {"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": 0.9175862669944763, "perplexity": 284.751906871278}, "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-2013-20/segments/1368701638778/warc/CC-MAIN-20130516105358-00088-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://mathhelpboards.com/threads/covariant-and-contravariant-vector.1597/ | # Covariant and Contravariant Vector
#### AA23
##### New member
Aug 6, 2012
10
I have been given the following problem:
The covariant vector field is:
$$v_{i}$$ = \begin{matrix} x+y\\ x-y\end{matrix}
What are the components for this vector field at (4,1)?
$$v_{i}$$ = \begin{matrix} 5\\ 3\end{matrix}
Now I can use this information to solve the following:
$$\bar{V_\alpha}$$
But am unsure for $$\bar{V^\alpha}$$.
I imagine it would be a similar approach with a few changes. Any help would be brilliant thank you
#### Fantini
MHB Math Helper
Feb 29, 2012
342
If you mean to write a matrix, you could have used
Code:
\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}
to output
$$\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$
Let us fix some notation here: are you using lower indexes to indicate covariant tensors and upper to indicate contravariant, or the other way around? Also, what are $\overline{V_\alpha}$ and $\overline{V}^{\alpha}$? I'm a little confused, if you could clarify perhaps we could arrive at an answer together.
At a first glance though, your calculations look correct, although I can't see where they headed because I don't understand what the symbols are meant to represent.
#### AA23
##### New member
Aug 6, 2012
10
My calculations are quite long and would take me a very long time to write them out in LaTeX. I would like to include an attachment but am unsure how to delete old ones to make room.
Thanks
#### Fantini
MHB Math Helper
Feb 29, 2012
342
Hey AA23, you still haven't answered my last questions: what do these $\overline{V_\alpha}$, $\overline{V}^{\alpha}$ mean? Also, it seemed you had
$$v_i = \begin{bmatrix} x+y \\ x-y \end{bmatrix},$$
to which you applied at the point $(4,1)$, getting
$$v_i (4,1) = \begin{bmatrix} 5+1 \\ 5-1 \end{bmatrix}.$$
Are there other calculations? Also, we let column matrices denote vectors and we use line matrices to denote covetors, so perhaps that would be
$$v^i = \begin{bmatrix} x+y & x-y \end{bmatrix} .$$
#### AA23
##### New member
Aug 6, 2012
10
$$\bar{V_{\alpha}}$$ represents a covariant tensor
$$\bar{V^{\alpha}}$$ represents a contravariant tensor
Yes I can solve the question to find the components of
$$\bar{V_{\alpha}}$$
But come stuck when finding them for
$$\bar{V^{\alpha}}$$ | {"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": 2, "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": 0.964746356010437, "perplexity": 1108.6604055809278}, "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-2020-50/segments/1606141652107.52/warc/CC-MAIN-20201201043603-20201201073603-00561.warc.gz"} |
https://www.physicsforums.com/threads/supplementary-angles-for-spherical-trigonometry.57775/ | # Supplementary Angles for Spherical Trigonometry
1. Dec 25, 2004
### jaycob1997
I'm trying to review spherical trinometry on my own and I'm stuck where it says the supplement of the solved dihedral angle can be implemented. I'm using "PLANE AND SPHERICAL TRIGONOMETRY" by Paul Rider. Can anyone explain the concept behind that statement, because the examples that I have are quite confusing
Thanks!
Last edited: Dec 25, 2004
2. Dec 25, 2004
### jaycob1997
Let me just add some other information:
I'm using Napier's rules to solve for spherical angles and spherical sides for right spherical triangles. Now my problem is, when will I use the acute angles and not the supplement angles(Obtuse). Or are there any rule/s to follow on which angle to use.
3. Dec 25, 2004
### Staff: Mentor
4. Dec 25, 2004
### jaycob1997
Thanks for the link. Do you know other sites that I can go to regarding the same subject matter (Spherical Trigonometry), or if you know of any sites that have problems to solve so I can apply the concepts that I just learned. By the way, I'm self studying for my licensure examination, and a great deal of the exams comes from all fields of math.
Thanks again
5. Dec 25, 2004
### jaycob1997
I did further reading on the subject matter. This is where I got lost, the problem goes:
In a right spherical triangle (C=90 degrees), A=69 degrees and 50.8minutes, c=72 degrees and 15.4minutes, find B, a, b.
Using Napier's rules, I get
a=63 degrees and 23.8 minutes
b= 47 degrees7.0 minutes,
B=50 degrees and 17.7 minutes
a note is given at the end of the question stating that "The supplementary value is not admissible since 'A' (angle A) and 'a' (side a) do not terminate at the same quadrant" - but by inspection, the two values are both on the first quadrant. I'm totally lost | {"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": 0.8029488325119019, "perplexity": 1659.0467791772155}, "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-2016-50/segments/1480698542939.6/warc/CC-MAIN-20161202170902-00104-ip-10-31-129-80.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/26071/when-is-the-image-of-a-linear-operator-closed/26082 | # When is the image of a linear operator closed?
Let $X$, $Y$ be Banach spaces. Let $T:X\rightarrow Y$ be a bounded linear operator.
Under what circumstances is the image of $T$ closed in $Y$ (except finite-dimensional image).
In particular, I wonder, under which assumptions $T:X\rightarrow T(X)$ is a bounded linear bijection between Banach spaces, so it is at least an isomorphism onto its image by bounded inverse theorem.
-
Probably the most useful criterion is en.wikipedia.org/wiki/Closed_range_theorem but that may not be exactly what you're looking for. It also is a nice exercise to show that an operator whose image has finite codimension has closed range (this has some use in Fredholm theory). – t.b. Mar 9 '11 at 23:10
An answer to your last question is that a bounded linear map $T$ between Banach spaces is injective with closed range if and only if it is bounded below, meaning that there is a constant $c>0$ such that for all $x$ in the domain, $\|Tx\|\geq c\|x\|$. You can read more about this in Chapter 2 of An invitation to operator theory by Abramovich and Aliprantis.
-
Thrm 1: Suppose $X$ is a Banach space, $Y$ is a normed vector space, and $T:X\to Y$ is a bounded linear operator. Then the range of $T$ is closed in $Y$ if $T$ is open.
Proof: Suppose $\mathrm{ran}(T)$ is not closed in $Y$. Let $\delta>0$ be given. The goal is to show that there exists $x\in X$ such that $\|T(x)\|/\|x\|<\delta$. Since $\delta$ is arbitrary this will demonstrate that $T$ is not open.
Since $\mathrm{ran}(T)$ is not closed there is a sequence $\{y_n\}$ in $\mathrm{ran}(T)$ and point $y\in Y\setminus\mathrm{ran}(T)$ such that $y_n\to y$. This means that there are corresponding $x_n\in X$ such that $y_n=T(x_n)$. Since $T$ is continuous it cannot be that $\{x_n\}$ is a convergent sequence or $y$ would be in the range of $T$.
Since $\{x_n\}$ does not converge it is not Cauchy. So there exists an $\epsilon>0$ such that $\forall N\in\mathbb{N} \ \ \exists n,m \ge N$ s.t. $\|x_n-x_m\|>\epsilon$. On the other hand, since $y_n\to y$, there is an $M\in\mathbb{N}$ such that $\forall k\ge M \ \ \ \|T(x_k)-y\|<\delta\frac{\epsilon}{2}$. By choosing $N=M$, there exist $n,m\ge N$ such that $\|x_n-x_m\|>\epsilon$, $\ \|T(x_n)-y\|<\delta\frac{\epsilon}{2}$, and $\|T(x_m)-y\|<\delta\frac{\epsilon}{2}$. By the Triangle Inequality, $\|T(x_n)-T(x_m)\|=\|T(x_n-x_m)\|<\delta \ \epsilon$.
Let $x=(x_n-x_m) \in X$. Then \begin{align*} \frac{\|T(x)\|}{\|x\|} &< \frac{\delta \ \epsilon}{\epsilon} \\ &= \delta. \end{align*}
Thrm 2: Suppose $X$ and $Y$ are both Banach spaces, and $T:X\to Y$ is a bounded linear operator. Then $\mathrm{ran}(T)$ is closed in $Y$ if and only if $T$ is open.
Proof: If $\mathrm{ran}(T)$ is closed then $Y$ is a surjective map onto this subspace so by the Open Mapping Theorem $T$ is open.
The other direction is just the first Theorem.
- | {"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": 0.9949085116386414, "perplexity": 35.17085865399423}, "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-2016-30/segments/1469257828283.6/warc/CC-MAIN-20160723071028-00169-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://warwick.ac.uk/fac/sci/masdoc/current/msc-modules/ma916/uq/results/ | # Numerical Results
Table 1: Dimension 1
In dimension 1 we choose training sets where the average distance between two neigbouring points is relatively small. This is the reason we get better approximation comparing to higher dimensions. It is clear from Table 1 that the least accurate points are the randomly chosen ones probably because they ignore the fact that there is an underlying structure to the solutions. Thus we expect that the other points have a distribution complimentary to our problem. However, in Table 2 we observe that the Random points perform as well as the other training sets, probably because they become denser.
Table 2: Dimension 1
It is difficult to distinguish between different training sets because of the their density in parameter space $\Gamma$. Thus we now turn our attention to dimension 2.
Table 3: Dimension 2
The Uniform grid minimises the maximum distance between any point in $\Gamma$ and a point in our training set. This might lead someone to expect that it would be a good training set. However, it is only as accurate as using the Random
points. This fact suggests that there are some parts of $\Gamma$ which are more important to sample from. Due to the nature of the Lagrange optimal points we are forced to choose a number of the form $\binom{\beta+2}{2}$ (see Table 3). We observe that Order 8 points perform as well as the Random points and the Uniform grid because there are fewer of them compared to the latter points. On the other hand, Order 9 points clearly outperform all the other families despite the fact that there are families with more points. Such a performance can be explained in terms of what was discussed in [3].
Regarding the Clenshaw-Curtis points, in the case of the tensor product we expect such a performance since they are nearly optimal for the minimisation problem (3) and the heuristic explanation above, in terms of what was discussed in [3], applies to this case as well. About the sparse Clenshaw-Curtis, given that they are a good approximation to the full tensor product, one would still expect that they perform well and they do.
Table 4: Dimension 3
In dimensions 3 and 4 we are beginning to face the curse of dimensionality. For example in dimension 4 if we were to take the tensor product of 1 dimensional training sets, we would have $10^8$ points per training set rather than the approximately 80 that we use. The Lagrange optimal points are quite accurate considering their number and we observe that in dimension 4 the Clenshaw-Curtis sparse grid perform similarly to the Random points even if they are less than half in size. This might be explained again in terms of the reason mentioned in the previous paragraphs.
Table 5: Dimension 4
Figures 1,2 and 3
In Figure 1 we notice that the value of the Greedy error is what we expected. The smaller coefficients lead to smaller error. This is basically because the actual coefficient $a(x)=a_0(x)+\sum_{k=1}^K~y_k~\alpha_k~\sin(2\pi~kx)$ varies less over $\Gamma$ where $\alpha_k$ are smaller. The decay rates of $\alpha_k=\frac{1}{k^8}$ and $\alpha_k=\frac{1}{4^k}$ are quite similar, while $\alpha_k=\frac{1}{2^k}$ decay at a slower rate.
In Figures 2 and 3 we notice that $\alpha_k=\frac{1}{k^8}$ quickly becomes the coefficient with the smallest error as we increase the dimension. This is basically due to the fact that the value of $a(x)$ does not change much as we increase the dimension whereas it does change significantly for the other two coefficients. Furthermore, we see that $\alpha_k=\frac{1}{4^k}~and~\alpha_k=\frac{1}{k^8}$ have similar decay rates whereas $\alpha_k=\frac{1}{2^k}$ seems to decay with a slower rate, as we previously observed.
At this point we would like to explore the coefficients individually because the behaviour as we increase the dimension seems to be
relevant to what we discussed above.
Figures 4,5 and 6
In Figures 4 and 5 we can see that in higher dimensions we have larger error terms, as we expected. In addition as the dimension increases the decay is getting slower, but looks like it's changing less as the dimension is increasing.
In Figure 6 we observe a more interesting behaviour. From results in our report, we expect an algebriac decay of the form $N^{-7}$. Instead we get an exponential decay which is consistent across all three dimensions, this is probably because with so few dimensions the model cannot "see" that the coefficients have an algebriac decay.
Instead we will look at a slower decay of the coefficients but in higher dimensions specifically sixteen dimensions with $a_k~=~\frac{1}{k^3}$.
Figure 7
First note that Figure 7 is a log-log scale and so algebraic decay looks linear. The theory form our report indicates that we should expect a decay rate of less than $N^{-2}$, where in the above figure we got a decay rate of $N^{-2.4}$.
Figure 8
We know that the error estimator is effective (see RBM) in the sense that it bounds the true error and in Figure 8 we can see that this particular error estimator is less than $1.35$ times the true error. Despite this fact the error estimator seems to be systematically worse near the boundary, which implies that the Greedy Algorithm favours points near the boundary. | {"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": 19, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9727551937103271, "perplexity": 204.28205535430791}, "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-2018-51/segments/1544376823318.33/warc/CC-MAIN-20181210055518-20181210081018-00137.warc.gz"} |
https://forum.allaboutcircuits.com/threads/fourier-convolution.62345/ | # fourier / convolution
Discussion in 'Homework Help' started by hamza324, Nov 22, 2011.
1. ### hamza324 Thread Starter Member
Jul 10, 2011
33
1
HI
My prof gave a question
$x= \delta(t-1) + 5Cos(2t) \ \ \ \longrightarrow \ \ \ \ \ \fbox{H( \omega)= \frac {1}{j\omega +1}} \ \ \ \longrightarrow \ \ \ y=find \ using \ super \ position$
Now for the solution , he treats each of the input functions separately with the boxed function.
he writes
$x_1 = \delta(t-1) \longrightarrow \fbox{h(t)=e^{-t} u(t)} \longrightarrow h(t-1)=e^{-(t-1)}u(t-1) = y_1$
Then,
$x_2 = 5Cos(2t) \longrightarrow \fbox {H(\omega)=\frac{1}{j\omega+1}} \longrightarrow 5\ \mid H(\omega)\mid \ Cos(2t + \theta)$
$where \mid H(\omega) \mid=( \frac{1}{(2)^2+1})^{\frac{1}{2}}and \theta =- tan^{-1} ( \frac{2}{1})=-63^o$
So using super sposition , we get
$y(t)=\ e^{-(t-1)} u(t-1)\ \ \ + \ \ \ \frac{5}{\sqrt{5}} Cos(2t-63^o)$
Now my question is that,
1 - Why did he used time domain for the impulse function and frequency domain for cos(2t).
2 - How did he get expression for $y_2$ , the one with magnitude of H(w).
thnx
2. ### steveb Senior Member
Jul 3, 2008
2,433
469
For question 1, one is free to use either the frequency domain or them time domain, depending on which is easier. Note that the first input is a delayed impulse function, so the output of that will be a delayed impulse response. So, he transforms the H(w) of the system and then delays the time domain impulse response function.
For question 2, he simply noted that H(w) is the frequency domain response and the input is a pure cosine wave, with frequency 2 and no phase delay. So, he can quickly calculate that the output will be scaled in magnitude and phase shifted by using H(w).
3. ### hamza324 Thread Starter Member
Jul 10, 2011
33
1
Thanks for explanation.
I have another similar question regarding discrete time
I have an expression
$e^{j \Omega n} \longrightarrow \fbox{h[n] \longleftrightarrow H(e^{j \Omega})} \longrightarrow H(e^{j \Omega}) e^{j \Omega n}$
I know this is frequeny response but i dont understand the expression at the output
Can you please provide me with some simpler explanation for this expression and some kind of example if possible.
4. ### steveb Senior Member
Jul 3, 2008
2,433
469
This is similar to the analysis of the second component of the input signal above (i.e. the 5cos(2t) part). That example was a continuous time cosine wave going through a system with known frequency response.
This problem is pretty much the same, only it is a complex sine wave, and the problem is in discrete time.
For background, in continuous time the frequency response is obtained by taking the Laplace s-domain transfer function $H(s)$, where $s=\sigma+j\omega$, and substituting $s=j\omega$, which puts you on the jw-axis. In discrete time, the frequency response is obtained by taking the Laplace z-domain transfer function $H(z)$, where $z=r\; {\rm e}^{j\Omega}$, and substituting $z={\rm e}^{j\Omega}$, which puts you on the unit circle.
hamza324 likes this.
Related Forum Posts:
1. Replies:
17
Views:
2,591
2. Replies:
1
Views:
991
3. Replies:
4
Views:
1,894
4. Replies:
2
Views:
1,352
5. Replies:
11
Views:
2,506 | {"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": 20, "/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": 0.939541220664978, "perplexity": 1202.192369698149}, "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/1534221215077.71/warc/CC-MAIN-20180819110157-20180819130157-00281.warc.gz"} |
https://www.emathhelp.net/en/calculators/algebra-2/parabola-calculator/ | # Parabola Calculator
This calculator will find either the equation of the parabola from the given parameters or the vertex, focus, directrix, axis of symmetry, latus rectum, length of the latus rectum, focal parameter, focal length (distance), eccentricity, x-intercepts, y-intercepts, domain, and range of the entered parabola. Also, it will graph the parabola. Steps are available.
Related calculators: Circle Calculator, Ellipse Calculator, Hyperbola Calculator, Conic Section Calculator
If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.
Find the vertex, focus, directrix, axis of symmetry, latus rectum, length of the latus rectum, focal parameter, focal length, eccentricity, x-intercepts, y-intercepts, domain, and range of the parabola $y = \left(x - 2\right)^{2} + 5$.
## Solution
The equation of a parabola is $y = \frac{1}{4 \left(f - k\right)} \left(x - h\right)^{2} + k$, where $\left(h, k\right)$ is the vertex and $\left(h, f\right)$ is the focus.
Our parabola in this form is $y = \frac{1}{4 \left(\frac{21}{4} - 5\right)} \left(x - 2\right)^{2} + 5$.
Thus, $h = 2$, $k = 5$, $f = \frac{21}{4}$.
The standard form is $y = x^{2} - 4 x + 9$.
The general form is $x^{2} - 4 x - y + 9 = 0$.
The vertex form is $y = \left(x - 2\right)^{2} + 5$.
The directrix is $y = d$.
To find $d$, use the fact that the distance from the focus to the vertex is the same as the distance from the vertex to the directrix: $5 - \frac{21}{4} = d - 5$.
Thus, the directrix is $y = \frac{19}{4}$.
The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: $x = 2$.
The focal length is the distance between the focus and the vertex: $\frac{1}{4}$.
The focal parameter is the distance between the focus and the directrix: $\frac{1}{2}$.
The latus rectum is parallel to the directrix and passes through the focus: $y = \frac{21}{4}$.
The length of the latus rectum is four times the distance between the vertex and the focus: $1$.
The eccentricity of a parabola is always $1$.
The x-intercepts can be found by setting $y = 0$ in the equation and solving for $x$ (for steps, see intercepts calculator).
Since there are no real solutions, there are no x-intercepts.
The y-intercepts can be found by setting $x = 0$ in the equation and solving for $y$: (for steps, see intercepts calculator).
y-intercept: $\left(0, 9\right)$.
Standard form: $y = x^{2} - 4 x + 9$A.
General form: $x^{2} - 4 x - y + 9 = 0$A.
Vertex form: $y = \left(x - 2\right)^{2} + 5$A.
Focus-directrix form: $\left(x - 2\right)^{2} + \left(y - \frac{21}{4}\right)^{2} = \left(y - \frac{19}{4}\right)^{2}$A.
Graph: see the graphing calculator.
Vertex: $\left(2, 5\right)$A.
Focus: $\left(2, \frac{21}{4}\right) = \left(2, 5.25\right)$A.
Directrix: $y = \frac{19}{4} = 4.75$A.
Axis of symmetry: $x = 2$A.
Latus rectum: $y = \frac{21}{4} = 5.25$A.
Length of the latus rectum: $1$A.
Focal parameter: $\frac{1}{2} = 0.5$A.
Focal length: $\frac{1}{4} = 0.25$A.
Eccentricity: $1$A.
x-intercepts: no x-intercepts.
y-intercept: $\left(0, 9\right)$A.
Domain: $\left(-\infty, \infty\right)$A.
Range: $\left[5, \infty\right)$A. | {"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": 0.9650465250015259, "perplexity": 1078.618285374662}, "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-2022-05/segments/1642320301063.81/warc/CC-MAIN-20220118213028-20220119003028-00239.warc.gz"} |
https://www.physicsforums.com/threads/question-about-information-change-as-gas-expands-and-contracts.719689/ | # Question about information change as gas expands and contracts
1. Oct 29, 2013
### absolutenoob
seeing the information is a form of entropy, what happens when gas confined to one corner of a cubic volume expands to fill the whole volume? Is information created? Would the reverse destroy information? I dont understand how a group of air molecules could change the amount of information they contain just by expanding/contracting. Does it have more to do with the system of the cubic volume? What information is there that could be transferred from the expanded volume of gas that could not be transferred from the confined gas? What is wrong with my thinking of this?
2. Oct 29, 2013
### Staff: Mentor
If it expands (perfectly) adiabatically, entropy stays the same.
If it does not, entropy can change.
Chaos has an important role here. If you suddenly open a shutter and let the gas expand, for example, you won't be able to reconstruct the initial state (whole gas in some smaller volume) based on the final state (gas fills some larger volume). Entropy is not information, even if the concepts are related. Entropy is a measurement how much information about the system you do not have - and that value can increase*.
*that is true for many systems - even for our everday life. Don't watch/read news and the amount of information you don't have will increase with time.
3. Oct 30, 2013
### TumblingDice
The relationship between entropy and information is that higher entropy levels require more information to completely define all states in the system. So moving from lower to higher entropy 'creates' information in the sense that it represents more information.
Moving a system to a lower entropy would require less information to completely describe the system.
4. Oct 30, 2013
### absolutenoob
I have read this in other places and the overwhelming response is that this is not true. Most sources i have read have stated that higher entropy= more information. I agree that your statement does make sense, but from what i have read it isnt true.
5. Oct 30, 2013
### absolutenoob
I guess it does make more sense though that entropy is how much information you dont know about a system when you think of the probability that all the gas in a cubic volume is contained in a small corner of it. The probability of that state is low, so the information is high correct? Is it just that the majority of people misunderstand information theory? Arg this is so frustrating. I hope more experts weigh in
6. Oct 30, 2013
### Staff: Mentor
The probability of all microscopic states is low (there are many of those states). The probability of the macroscopic description (all atoms in one corner) is small, corresponding to a small amount of microscopic states. It is easier to fully describe this system (if you know the macroscopic description), therefore it has a lower entropy.
7. Oct 30, 2013
### TumblingDice
It makes no difference whether you know the information or not. If you could measure every last state of a system so you knew everything about it, that wouldn't change the entropy.
You can look at this either way: Higher entropy system requires more information to describe it completely, or represents more information. Same thing...
[Edit: I spoke too soon. It seems physicists count knowing everything about a system as that it has no information to offer them. My opportunity to learn, too]
Last edited: Oct 30, 2013
8. Oct 30, 2013
### craigi
The problem we have here, is that information is a seemingly well defined term in everyday language. When you use the term for a physical system, or in a pure mathematical sense, it can take on a number of quite contradictory meanings. If entropy is the quantitiy that you're talking about, then it's best to use the word entropy, to avoid ambiguity.
Both answers that you have been given are correct. Entropy is a measure of uncertainty, ie. information that you do not have. Also, to fully describe a higher entropy system requires a higher minimal amount of information.
Last edited: Oct 30, 2013
9. Oct 30, 2013
### absolutenoob
Could you give me an example of what a microstate would be in a volume of gas? Also your first sentence, does that mean when you have the low entropy case, you KNOW more information than you do in the high entropy case?
10. Oct 30, 2013
### craigi
A microstate describes the positions of the molecules in the gas.
Try Susskind's lectures on Statistical Mechanics:
Last edited by a moderator: Sep 25, 2014
11. Oct 30, 2013
### TumblingDice
Important to recognize that my posts #3 and #7 were misleading. Mfb explained well and craigi advised correctly not to mix terminologies. As I noted in my edit on post #7. I think the reason that knowing all of the microstates (e.g., information) reduces to zero entropy is because that could only be done by influencing the system whether it be measuring or reordering, and that means entropy will be raised elsewhere, like in the instruments used to gain the knowledge.
Sorry to interrupt the good info from mfb and craigi. :(
12. Oct 30, 2013
### craigi
It's ok to talk of the entropy of a subsystem and we can non-destructively obtain knowledge of a subsystem ie. without changing it's entropy. The issue of increasing entropy elsewhere, applies to acting on an open subsystem within a closed system and is pertinent the second law of thermodynamics.
13. Oct 30, 2013
### absolutenoob
So let me get this straight- gas confined to one corner= higher information you know, lower total information. Gas expanded= lower information you know, higher total information. Is this correct? Or does the gas confined to one corner mean you know a greater proportion of the total information there is?
Last edited: Oct 30, 2013
14. Oct 30, 2013
### TumblingDice
I'm thinking:
Gas confined to one corner means less uncertainty (position microstate) than in larger volume. It is lower total unknown information, and lower entropy.
Expanded gas means more uncertainty - more total unknown information and higher entropy.
15. Oct 30, 2013
### TumblingDice
Those sound to be true statements. I wouldn't say that quantity of info you know or don't know is correlated to quantity of total information.
16. Oct 30, 2013
### kith
Information entropy can be viewed as the number of yes-or-no questions you need to get from a state of limited knowledge to a state of maximum knowledge. In thermodynamics, we have states of limited knowledge because we know only macro variables like temperature, volume or the chemical potential. We don't know the true microscopic state of the system but in thermodynamic equilibrium, we know the probability distribution of the possible microstates. Their number is constrained by the values of macro variables.
In physics, a yes-or-no question corresponds to a measurement which has only two outcomes. So entropy is a measure of how many such measurements you would have to perform in principle, to determine the true microscopic state of the system. In equilibrium, a gas in a small volume has a lower entropy than a gas in a big volume. You know more about the gas in the small volume, because you have to ask less questions to get to its true microstate.
If entropy is high, the information content of the system is high in the sense that you would have to perform lots of measurements to determine the microstate. Up to a factor, it is the maximum number of bits you can "learn" about the system by performing measurements. | {"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": 0.817044734954834, "perplexity": 711.1977859269373}, "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/1526794867995.55/warc/CC-MAIN-20180527024953-20180527044953-00246.warc.gz"} |
http://pub.acta.hu/acta/showCustomerArticle.action?id=2634&dataObjectType=article&returnAction=showCustomerVolume&sessionDataSetId=532d56d837f0b79c&style= | ACTA issues
## Continuity implies differentiability for solutions of functional equations --- even with few variables
Antal Járai
Acta Sci. Math. (Szeged) 67:3-4(2001), 719-734
2813/2009
Abstract. It is proved that --- under certain conditions --- continuous solutions $f$ of the functional equation $$f(x)=h(x,y,f(g_1(x,y)),\ldots,f(g_n(x,y))), (x,y)\in D\subset{{\msbm R}^s}\times{\msbm R}^l,$$ are ${{\cal C}^\infty }$, even if $1\le l\le s$. As a tool we introduce new function classes which --- roughly speeking --- interpolate between differentiable and continuous functions. AMS Subject Classification (1991): 39B05, 26B05 Received October 27, 2000. (Registered under 2813/2009.) | {"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": 0.8545328378677368, "perplexity": 1634.4441016923522}, "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/1590347387155.10/warc/CC-MAIN-20200525001747-20200525031747-00290.warc.gz"} |
https://cstheory.stackexchange.com/questions/42581/partition-into-c-and-1-c | # Partition into c and 1-c
Let $$c\in(0,1/2]$$ be a constant. Given a set of positive integers with sum $$S$$, is there a partition into two subsets such that both subsets have sum at least $$cS$$?
If $$c=1/2$$, this is the famous partition problem which is NP-complete. What is known about the complexity for other values of $$c$$?
• It is NP-hard for every fixed constant $c$ with $0<c<1/2$. – Gamow Mar 24 '19 at 17:42
• @Gamow Thanks. Could you please give a reference? – user52378 Mar 24 '19 at 18:10
• @Gamow This is incorrect, according to Tom van der Zanden's answer on CS SE. – David Richerby Jun 19 '19 at 15:07 | {"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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8632220029830933, "perplexity": 478.55017473022826}, "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-2020-24/segments/1590347391309.4/warc/CC-MAIN-20200526191453-20200526221453-00568.warc.gz"} |
https://talkstats.com/threads/chi-square-with-2-dependent-variables.73797/ | # Chi-square with 2 Dependent Variables
##### New Member
This may seem like a very silly question, but can you conduct a chi-square when you have 2 dependent variables? | {"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": 0.9934757351875305, "perplexity": 1596.6086147458989}, "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-2020-24/segments/1590348523476.97/warc/CC-MAIN-20200607013327-20200607043327-00061.warc.gz"} |
https://tex.stackexchange.com/questions/359502/adding-brackets-above-below-and-left-right-of-array-matrix?noredirect=1 | # Adding brackets above/below and left/right of array matrix
I'm trying to add brackets to portions of a matrix, like so:
where the arrowed bars are replaced with brackets, and the red bar would be moved to the bottom. If it helps, here's the portion I have now:
\left[
\begin{array}{c c c c|c c c}
1 & 0 & \cdots & 0 & 0 & \cdots & 0\\
0 & 1 & \ddots & \vdots & \vdots & \ddots & \vdots \\
\vdots & \ddots & \ddots & \vdots & \vdots & \ddots & \vdots\\
0 & \cdots & 0 & 1 & 0 & \cdots & 0\\
\hline
0 & \cdots & \cdots & 0 & 0 & \cdots & 0\\
\vdots & \ddots & \ddots & \vdots & \vdots & \ddots & \vdots \\
0 & \cdots & \cdots & 0 & 0 &\cdots & 0
\end{array}
\right]
\begin{matrix*}[l]
\left. \vphantom{\begin{pmatrix}
0 \\
\vdots \\
\vdots\\
0\\
0\\
\vdots\\
0
\end{pmatrix} } \right\} \text{Rank } C_{p-1} = s_{p-1}\\
\end{matrix*}
Where I have the right-side bracket working, but I'm unsure how to get the others in place... I tried adding this before my matrix:
\begin{matrix*}[r]
b_{p-1} = \text{Rank } B_{p-1}\left\{\vphantom{\begin{pmatrix}{c}
1\\
0\\
\vdots\\
0\\
\hline
\end{pmatrix}}\right.
\left.
\vphantom{\begin{pmatrix}{c}
0\\
\vdots\\
0
\end{pmatrix}}\right.
\end{matrix*}
but that places a bracket in the middle of my matrix, instead of portion of diagonal 1's. Thanks!!
• Welcome to TeX.SX! I guess that TikZ would be your friend. – egreg Mar 20 '17 at 22:02
• @egreg Thanks! I was hoping to avoid TikZ, but I'm starting to think this might be my only option... Would you happen to know where I should start looking? – Brad Flynn Mar 20 '17 at 22:05
• I'm sure our TikZ experts will soon come to the rescue. – egreg Mar 20 '17 at 22:08
This is a possible TikZ solution
\documentclass[tikz,border=2mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{matrix}
\usepackage{mathtools}
\DeclareMathOperator{\rk}{rank}
\begin{document}
\begin{tikzpicture}
\matrix (A) [
matrix of math nodes]{
1 & 0 & \dots & 0 & 0 & \dots & 0\\
0 & 1 & \ddots & \vdots & \vdots & \ddots & \vdots \\
\vdots & \ddots &\ddots & \vdots & \vdots & \ddots & \vdots \\
0 & \dots & 0 & 1 & 0 & \dots & 0\\
0 & \dots & \dots & 0 & 0 & \dots & 0\\
\vdots & \ddots & \ddots & \vdots & \vdots & \ddots & \vdots \\
0 & \dots & \dots & 0& 0 & \dots & 0\\
};
\draw[gray] (A-1-1.north west) rectangle (A-4-4.south east);
\draw[gray] (A-4-4.south east) rectangle (A-7-7.south east);
\draw[shorten >=2pt, shorten <=2pt] (A-1-1.north west) --++(180:3mm)|-(A-4-1.south west) node[pos=.25, rotate=90, above]{$b_{p-1}=\rk B_{p-1}$};
\draw[shorten >=2pt, shorten <=2pt] (A-1-1.north west) --++(90:3mm)-|(A-1-7.north east) node[pos=.25, above]{$s_p=\rk C_p$};
\draw[shorten >=2pt, shorten <=2pt] (A-7-4.south west) --++(270:3mm)-|(A-7-7.south east) node[pos=.25, below]{$\rk Z_p=z_p$};
\draw[shorten >=2pt, shorten <=2pt] (A-1-7.north east) --++(0:3mm)|-(A-7-7.south east) node[pos=.25, rotate=270, above]{$\rk C_{p-1}=s_{p-1}$};
\end{tikzpicture}
\end{document}
• how would I go about editing the vertical alignment of this inside of an equation? Like if I were to have \text{SNF}([\partial_p]) = \begin{tikzpic...? – Brad Flynn Mar 21 '17 at 15:02
• @BradFlynn Try with \begin{tikzpicture}[baseline] and see what happens. If the default baseline for tikzpicture doesn't fit your needs, you can use any anchor or page reference as baseline. It's explained in page 124 in pgfmanual. – Ignasi Mar 21 '17 at 15:17
• That worked perfectly! Thanks again for your help! One more thing, if I were wanting to learn more about tikz, would you happen to know of a good place to start? Seems pretty useful, would love to know more! – Brad Flynn Mar 21 '17 at 15:32
• And, not to be nit-picky, but is there any way to shorten the bottom bar? seems like it extends past the column that I'd like. (EDIT never mind, I just edited the drawn location!) – Brad Flynn Mar 21 '17 at 15:34
• @BradFlynn To start learning TikZ my best suggestion is reading the tutorials at beginning of pgfmanual. Later on you can find more information in tex.stackexchange.com/a/9123/1952 – Ignasi Mar 21 '17 at 15:42
Here is a solution with pstricks: it consists in adding nodes at relevant places in the matrix, and joining them with node connections:
\documentclass[x11names, svgnames]{article}
\usepackage{mathtools}
\usepackage{pst-node}
\usepackage{auto-pst-pdf}
\DeclareMathOperator{\rk}{rank}
\pagestyle{empty}
\begin{document}
\begin{equation*}
\begin{postscript}\everypsbox{\footnotesize}
\begin{bmatrix*}%{c c c c|c c c}
\pnode[-0.3ex, 2.4ex]{r1}\Rnode{R1}{1}\rule{0pt}{3ex} & 0 & \cdots & \Rnode{S1}{0} & 0 & \cdots & \Rnode{T1}{0}\\
0 & 1 & \ddots & \vdots & \vdots & \ddots & \vdots \\
\vdots & \ddots & \ddots & \vdots & \vdots & \ddots & \vdots \\
\Rnode{R2}{0} & \cdots & 0 & \Rnode{S2}{1}\pnode[1.25ex, -0.8ex]{s2} & 0 & \cdots & 0\\
0 & \cdots & \cdots & 0 & 0 & \cdots & 0\\
\vdots & \ddots & \ddots & \vdots & \vdots & \ddots & \vdots \\
0 & \cdots & \cdots &0 & \Rnode{R3}{0} & \cdots & \Rnode{S3}{0}\pnode[0.2ex, -0.3ex]{s3}
\end{bmatrix*}
\psset{ linejoin=1, linearc=0.08, arm=1ex, nodesep=1.5ex}
\ncbar[angle=90]{R1}{T1}\naput{$s_p = \rk C_p$}
\ncbar{T1}{S3}\naput[nrot=:U]{$\rk C_{p-1} = s_{p-1}$}
\ncbar[angle=180]{R2}{R1}\naput[nrot=:U]{$b_{p-1} =\rk B_{p-1}$}
\ncbar[angle=-90]{R3}{S3}\nbput{$\rk Z_p = z_p$}
\psset{linecolor=LightSteelBlue3!50}
\psframe(r1)(s2)
\psframe[dimen=inner](s2)(s3)
\end{postscript}%
\end{equation*}
\end{document} | {"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": 0.9542841911315918, "perplexity": 395.8505980943199}, "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/1558232260161.91/warc/CC-MAIN-20190526225545-20190527011545-00015.warc.gz"} |
http://mathhelpforum.com/calculus/70498-calculus-theorems.html | # Math Help - Calculus Theorems
1. ## Calculus Theorems
A car's odometer (mileage counter) reads exactly 59,024 miles at 8:00am and 59,094 miles at 10:00am. Assuming the car's position and velocity functions are differentiable, what theorem can be used to show that the car was traveling at exactly 35mph at some time between 8:00am and 10:00am?
a) Intermediate Value Theorem for Derivatives
b) Extreme Value Theorem
c) Mean Value Theorem
2. Just in case anyone's interested, it's the Mean Value Theorem. | {"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": 0.8881789445877075, "perplexity": 1879.244130531836}, "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-2014-41/segments/1410657135777.13/warc/CC-MAIN-20140914011215-00042-ip-10-234-18-248.ec2.internal.warc.gz"} |
https://slideplayer.com/slide/6981707/ | # Sources of Energy – Part 2 Glencoe - Chapter 16 Pages 484-515.
## Presentation on theme: "Sources of Energy – Part 2 Glencoe - Chapter 16 Pages 484-515."— Presentation transcript:
Sources of Energy – Part 2 Glencoe - Chapter 16 Pages 484-515
Renewable Energy Resources 1. Solar energy – capturing the energy given off by the sun - Photovoltaic cells (solar cells) convert sunlight into electricity as electrons gain energy and move - The electricity is stored in batteries
Photovoltaic Solar Cell
Renewable Energy Resources 2. Hydroelectric energy – produced by running / moving water from rivers flowing - Water is held behind a dam and released in a controlled way to spin turbines
Cross-section of a Hydroelectric Dam
Renewable Energy Resources 3. Tidal energy – produced by moving water as tides rise and fall and spins a turbine
Tidal Energy Turbines
Renewable Energy Resources 4. Wind energy – produced by moving air spinning a windmill which spins a turbine
Two Types of Windmills
Renewable Energy Resources 5. Geothermal energy – produced by harnessing the heat from hot magma near the surface of the earth Cold water is pumped down into the ground, heated by the magma, and then the hot water is pumped up to be used and turned into steam
Geyser
Geothermal Energy
Renewable Energy Resources 6. Biomass energy – organic waste / trash materials Sources include: wood, manure, food wastes, and some types of trash These wastes can be burned to release energy as heat
Types of Biomass
Renewable Energy Resources 7. Hydrogen gas fuel – hydrogen gas (H 2 ) is burned to release energy Hydrogen gas is burned in the presence of oxygen gas, which releases energy from chemical bonds, and forms water as a waste product
How We Get Electricity From Sources of Energy. No matter what energy source you use (except solar energy), to get electricity from it, a turbine must spin around.
How We Get Electricity From Sources of Energy. The turbine is attached to a generator, so as the turbine spins, the generator also spins.
How We Get Electricity From Sources of Energy. The generator is composed of wires spinning inside magnets. As the wires spin, an electric current is formed in the wires, which is transferred to the consumers in power lines.
Download ppt "Sources of Energy – Part 2 Glencoe - Chapter 16 Pages 484-515."
Similar presentations | {"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": 0.8006901144981384, "perplexity": 2620.7435261619444}, "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/1581875145438.12/warc/CC-MAIN-20200221014826-20200221044826-00389.warc.gz"} |
http://www.ams.org/joursearch/servlet/DoSearch?f1=msc&v1=11E57 | # American Mathematical Society
Publications Meetings The Profession Membership Programs Math Samplings Policy and Advocacy In the News About the AMS
You are here: Home > Publications
AMS eContent Search Results
Matches for: msc=(11E57) AND publication=(all) Sort order: Date Format: Standard display
Results: 1 to 15 of 15 found Go to page: 1
[1] Gabriel Dospinescu and Benjamin Schraen. Endomorphism algebras of admissible $p$-adic representations of $p$-adic Lie groups. Represent. Theory 17 (2013) 237-246. Abstract, references, and article information View Article: PDF [2] Jodi Black. Implications of the Hasse principle for zero cycles of degree one on principal homogeneous spaces. Proc. Amer. Math. Soc. 139 (2011) 4163-4171. MR 2823061. Abstract, references, and article information View Article: PDF [3] Brendan Foreman. Discrete groups and the complex contact geometry of $Sl(2,\mathbb {C})$. Trans. Amer. Math. Soc. 362 (2010) 4191-4200. MR 2608401. Abstract, references, and article information View Article: PDF [4] Curtis T. McMullen. Minkowski's conjecture, well-rounded lattices and topological dimension. J. Amer. Math. Soc. 18 (2005) 711-734. MR 2138142. Abstract, references, and article information View Article: PDF This article is available free of charge [5] Mohamed Elhamdadi. A note on $\lambda$-operations in orthogonal K-theory. Proc. Amer. Math. Soc. 128 (2000) 1-4. MR 1670434. Abstract, references, and article information View Article: PDF This article is available free of charge [6] Donald G. James. Conjugacy classes of $SU(h,\mathcal O_S)$ in $SL(2,\mathcal O_S)$. Trans. Amer. Math. Soc. 351 (1999) 825-835. MR 1451605. Abstract, references, and article information View Article: PDF This article is available free of charge [7] Donald G. James. Conjugacy classes of symmetries in orthogonal groups. Proc. Amer. Math. Soc. 125 (1997) 747-753. MR 1416090. Abstract, references, and article information View Article: PDF This article is available free of charge [8] G. Nebe and W. Plesken. Finite rational matrix groups. Memoirs of the AMS 116 (1995) MR 1265024. Book volume table of contents [9] Christian Wenzel. Classification of all parabolic subgroup-schemes of a reductive linear algebraic group over an algebraically closed field . Trans. Amer. Math. Soc. 337 (1993) 211-218. MR 1096262. Abstract, references, and article information View Article: PDF This article is available free of charge [10] John Smillie and Karen Vogtmann. Automorphisms of ${\rm SL}\sb 2$ of imaginary quadratic integers . Proc. Amer. Math. Soc. 112 (1991) 691-699. MR 1065094. Abstract, references, and article information View Article: PDF This article is available free of charge [11] Douglas Costa and Gordon Keller. Normal subgroups of ${\text{SL}}\left( {2,A} \right)$. Bull. Amer. Math. Soc. 24 (1991) 131-135. MR 1056153. Abstract, references, and article information View Article: PDF [12] Roger Howe. Erratum to: Remarks on classical invariant theory'' . Trans. Amer. Math. Soc. 318 (1990) MR 1019521. Abstract, references, and article information View Article: PDF This article is available free of charge [13] Roger Howe. Remarks on classical invariant theory . Trans. Amer. Math. Soc. 313 (1989) 539-570. MR 986027. Abstract, references, and article information View Article: PDF This article is available free of charge [14] C. Maclachlan, P. L. Waterman and N. J. Wielenberg. Higher-dimensional analogues of the modular and Picard groups . Trans. Amer. Math. Soc. 312 (1989) 739-753. MR 965301. Abstract, references, and article information View Article: PDF This article is available free of charge [15] Donald G. James. Representations of anisotropic unitary groups . Trans. Amer. Math. Soc. 306 (1988) 791-804. MR 933318. Abstract, references, and article information View Article: PDF This article is available free of charge
Results: 1 to 15 of 15 found Go to page: 1 | {"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": 0.8871752023696899, "perplexity": 2012.231831662284}, "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-2014-41/segments/1410657120057.96/warc/CC-MAIN-20140914011200-00218-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
https://gitlab.mpcdf.mpg.de/ift/nifty/-/commit/23eb44534daf5874802ece28eea9d381dbe7b078?view=parallel | Commit 23eb4453 by Martin Reinecke
### line breaks and small adjustments
parent baed911d
Pipeline #44859 passed with stages
in 9 minutes and 59 seconds
... @@ -166,9 +166,15 @@ NIFTy aids you in constructing your own log-likelihood by providing methods like ... @@ -166,9 +166,15 @@ NIFTy aids you in constructing your own log-likelihood by providing methods like An integral over a :class:~field.Field :code:s can be performed by calling :code:s.weight(1).sum(), which is equivalent to :code:s.integrate(). An integral over a :class:~field.Field :code:s can be performed by calling :code:s.weight(1).sum(), which is equivalent to :code:s.integrate(). Volume factors are also applied automatically in the following places: Volume factors are also applied automatically in the following places: - :class:~operators.harmonic_operators.FFTOperator as well as all other harmonic operators. Here the zero mode of the transformed field is the integral over the original field, thus the whole field is weighted once. - :class:~operators.harmonic_operators.FFTOperator as well as all other harmonic operators. - Some response operators, such as the :class:~library.los_response.LOSResponse. In this operator a line integral is discretised, so a 1-dimensional volume factor is applied. Here the zero mode of the transformed field is the integral over the original field, thus the whole field is weighted once. - In :class:~library.correlated_fields.CorrelatedField as well :class:~library.correlated_fields.MfCorrelatedField both describing fields with a smooth, a priori unknown correlation structure specified by a power spectrum. The field is multiplied by the square root of the total volume of it domain's harmonic counterpart. This ensures that the same power spectrum can be used regardless of the chosen resolution, provided the total volume of the space remains the same. It also guarantees that the power spectra in NIFTy behave according to their definition, i.e. the power of a mode :math:s_k is the expectation value of that mode squared, divided by the volume of its space :math:P(k) = \left\langle s_k^2 \right\rangle / V_k - Some response operators, such as the :class:~library.los_response.LOSResponse. In this operator a line integral is discretised, so a 1-dimensional volume factor is applied. - In :class:~library.correlated_fields.CorrelatedField as well as :class:~library.correlated_fields.MfCorrelatedField. Both describe fields with a smooth, a priori unknown correlation structure specified by a power spectrum. The field is multiplied by the square root of the total volume of it domain's harmonic counterpart. This ensures that the same power spectrum can be used regardless of the chosen resolution, provided the total volume of the space remains the same. It also guarantees that the power spectra in NIFTy behave according to their definition, i.e. the power of a mode :math:s_k is the expectation value of that mode squared, divided by the volume of its space :math:P(k) = \left\langle s_k^2 \right\rangle / V_k. Note that in contrast to some older versions of NIFTy, the dot product :code:s.vdot(t) of fields does **not** apply a volume factor, but instead just sums over the field components, Note that in contrast to some older versions of NIFTy, the dot product :code:s.vdot(t) of fields does **not** apply a volume factor, but instead just sums over the field components, ... ...
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment | {"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": 0.9602749943733215, "perplexity": 1016.7776605245672}, "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-2021-10/segments/1614178362899.14/warc/CC-MAIN-20210301182445-20210301212445-00237.warc.gz"} |
http://mathhelpforum.com/discrete-math/130064-set-theory-simplification.html | ## set theory simplification
1. Simplify the following using the set rules of inference. Show all your work:
[ ( (A - B)
È (A Ç C )) Ç (A Ç B)c]c
Where A, B, and C are subsets of the Universe | {"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": 0.8532871007919312, "perplexity": 1710.4537334992447}, "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-2015-11/segments/1424936462202.69/warc/CC-MAIN-20150226074102-00180-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/gauss-law-for-finite-line-plate.810888/ | Gauss Law for finite line/plate
1. Apr 27, 2015
henry3369
1. The problem statement, all variables and given/known data
I just noticed that whenever I'm doing a problem involving Gauss Law, it always involves an infinite line/plate. I can't seem to figure out why it must be infinite large/long.
Here is an explanation I read, but don't quite understand:
http://physics.stackexchange.com/qu...nd-the-electric-field-of-a-finite-length-char
2. Relevant equations
∫E⋅A = Qenc
3. The attempt at a solution
I don't see why E becomes unpredictable and nonuniform on a finite line of charge. If the charge is still uniformly distributed, then the field should still be the same along the wire. Also, what causes the direction of E, to branch off into random directions rather than being radial like in an infinite line of charge? And, if the position of the Gaussian cylinder along the line of charge matters, why not just move it to the middle?
2. Apr 27, 2015
henry3369
The problem I was trying to solve with Gauss law is a finite line of charge Q distributed uniformly with length 2a, where one end is at +a, and one is at -a on the y-axis and I have to compute the electric field at point P, along the x-axis.
Why can't I just choose a Gaussian cylinder, centered at the origin, with length a, and compute it as if it was an infinite line of charge?
3. Apr 27, 2015
henry3369
Or even better, a Gaussian cylinder that encompasses the entire line of charge, so charge enclosed would be Q.
EA = Q/ε.
A = 4πr^2
E = Q/ε*4πr^2
Where r = x, the distance from the line of charge to the position P.
4. Apr 27, 2015
haruspex
In the OP you mentioned charge along a finite wire (a conductor). In a later post you wrote uniformly distributed along a finite wire. Which is it? The two are in conflict.
5. Apr 28, 2015
henry3369
Don't they mean the same thing? Don't the electrons distribute themselves in a way to decrease interactions with each other along the wire?
6. Apr 28, 2015
henry3369
Here is the exact wording of the question:
Positive charge Q is distributed uniformly along the y-axis between y = -a and y = +a. Find the electric field at point P on the x-axis at a distance x from the origin.
7. Apr 28, 2015
henry3369
Either way, in a Gauss law problem, isn't the distribution irrelevant?
8. Apr 28, 2015
SammyS
Staff Emeritus
Charge distribution is important anytime you want to determine the Electric field it produces.
9. Apr 28, 2015
haruspex
Yes, the electrons move in a conductor so as to make the potential uniform, but that does not mean the charge will be uniform. In fact, the only finite case I can think of where the charge would be uniform is a thin spherical shell. As you should know, for any solid conductor all charge will be on the surface.
In the case of a finite wire, the charges (in their attempts to get away from each other) will tend to be comcentrated to wards the ends of the wire. As far as I know, the charge distribution in a finite wire is a hard problem. http://www.colorado.edu/physics/phy...MPapers_030612/Griffiths_ConductingNeedle.pdf
Anyway, it seems the problem at hand is for a uniform distribution, not a conductor. As SammyS says, the distribution is important for finding the field. The field from a single point charge 2q will be different from that from of two charges of q each a short distance apart.
Perform the integration.
Draft saved Draft deleted
Similar Discussions: Gauss Law for finite line/plate | {"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": 0.937615156173706, "perplexity": 434.74042346189447}, "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-2017-34/segments/1502886110792.29/warc/CC-MAIN-20170822143101-20170822163101-00314.warc.gz"} |
http://wiki.chemprime.chemeddl.org/index.php/Equations_Related_to_Food_Additives | Equations Related to Food Additives - ChemPRIME
# Equations Related to Food Additives
back to Balancing Chemical Equations
We've examined the properties of cuprous iodide while discussing its use as a salt additive. From these properties it can be identified as CuI. The equation for the formation of cuprous iodide would look like this:
Cu + I2 → CuI (1)
But we must be sure that the law of conservation of mass is obeyed. The same number of atoms (or moles of atoms) of a given type must appear on each side of the equation. This reflects our belief in Dalton’s third postulate that atoms are neither created, destroyed, nor changed from one kind to another during a chemical process. When the law of conservation of mass is obeyed, the equation is said to be balanced.
## Balancing Equations
Equation (1) is not balanced because there are 2 iodine atoms (in I2) on the left side of the equation and only 1 on the right.
An incorrect way of obtaining a balanced equation is to change this to
Cu + I2CuI2 (2)
This equation is wrong because we had already determined from the properties of the product that the product was CuI. Equation (2) is balanced, but it refers to a different reaction which produces a different product. The equation might also be incorrectly written as
Cu + I → CuI (3)
The symbol I suggests that iodine atoms were involved, but we know that iodine exists as diatomic molecules.
In balancing an equation you must remember that the subscripts in the formulas have been determined experimentally. Changing them indicates a change in the nature of the reactants or products. It is permissible, however, to change the amounts of reactants or products involved. For example, the equation in question is correctly balanced as follows:
2 Cu + I2 → 2 CuI (4)
The 2 written before the symbol Cu is called a coefficient. It indicates that on the microscopic level 2 Cu atoms are required to react with one iodine molecule. On a macroscopic scale the coefficient 2 means that 2 mol Cu atoms are required to react with 1 mol I2 molecules.
To summarize: Once the formulas (subscripts) have been determined, an equation is balanced by adjusting coefficients. Nothing else may be changed.
## Decomposion of CuI2
EXAMPLE 1 We have seen that copper may form an unstable cupric iodide (CuI2), but this decomposes immediately to cuprous iodide and iodine. Balance the equation for this process:
CuI2 → CuI + I2
Solution Although Cu is balanced, there are 3 I atoms on the right and only 2 on the left. A coefficient of 2 with CuI2 will help:
2 CuI2 → CuI + I2
Now I is still not balanced. We need 2 CuI molecules on the right:
2 CuI2 + → 2 CuI + I2
We now have 2 Cu atoms and 4 I atoms on each side, and so balancing is complete.
Most chemists use several techniques for balancing equations.[1] For example, it helps to know which element you should balance first. When each chemical symbol appears in a single formula on each side of the equation (as Example 1), you can start wherever you want and the process will work. When a symbol appears in three or more formulas, however, that particular element will be more difficult to balance and should usually be left until last.
## Metabolism of Sorbitol and Xylol
The sugar substitutes sorbitol and xylitol appear frequently on labels of packaged snack foods. They are sugar alcohols that occur naturally in fruits, but are probably made synthetically for many products. They are roughly as sweet as sucrose, and made by hydrogenating one C=O group on a sugar to a C-OH group, as shown below. They are nutritive sweeteners because they do have calories--about 2.6 Cal per gram compared to 4 Cal per gram for most sugars, so they are often found in "diet" foods like soft drinks, sugar-free gum, and ice cream.[2] These are both laxatives to some degree, and sometimes lead to bloating, flatulence, and diarrhea.[3]
Xylitol Glucose
EXAMPLE 2 When sorbitol (C6H14O6) is metabolized, or burned in oxygen gas (O2), the only products are carbon dioxide(CO2) and water. Write a balanced equation to describe this reaction.
Solution First write an unbalanced equation showing the correct formulas of all the reactants and products:
C6H14O6 + O2 → CO2 + H2O
We note that O atoms appear in all formulas, two on the left and two on the right. Therefore we balance C and H first. The formula C6H14O6 determines how many C and H atoms must remain after the reaction, and so we write coefficients of 6 for CO2 and 7 for H2O:
C6H14O6 + O26 CO2 + 7 H2O
We now have a total of 19 O atoms on the right-hand side, and 6 in the sorbitol, so we're lacking 13 on the left. At first, the fact that O atoms come in pairs as O2 seems to present a problem but we can balance the equation by using a coefficient of $\tfrac{13}{2}$ in front of O2:
C6H14O6 + $\tfrac{13}{2}$ O2 → 6 CO2 + 7 H2O
Usually it is preferable to remove fractional coefficients since they might be interpreted to mean a fraction of a molecule. (One-half of an O2 molecule would be an O atom, which has quite different chemical reactivity.) Therefore we multiply all coefficients on both sides of the equation by two to obtain the final result:
2 C6H14O6 + 13 O212 CO2 + 14 H2O
(Sometimes, when we are interested in moles rather than individual molecules, it may be useful to omit this last step. Obviously the idea of half a mole of O2 molecules, that is, 3.011 × 1023 molecules, is much more tenable than the idea of half a molecule.)
Another useful technique is illustrated in Example 2. When an element (such as O2) appears by itself, it is usually best to choose its coefficient last. Furthermore, groups such as NO3, SO4, etc., often remain unchanged in a reaction and can be treated as if they consisted of a single atom. When such a group of atoms is enclosed in parentheses followed by a subscript, the subscript applies to all of them. That is, the formula involves Ca(NO3)2 involves 1Ca, 2N and 2 × 3 = 6 O atoms.
## Potassium Bromate in Flour
Potassium Bromate (KBrO3) is added to flour as a conditioner which enhances the structure of bread.[4] It may do this by forming disulfide bonds in a reaction like the one in Example 3, between two cysteine amino acids. The actual mechanism for bromate action is still not known, but it may involve oxidation of glutathione to give a disulfide link (analagous to cysteine)[5] This mechanism has been demonstrated in pound cake, where the links are in egg proteins[6][7] The function of the KBrO3 is to remove the 2 electrons, which is necessary to form the disulfide bond, as shown in the figure below. Each of the cysteine amino acids would be in a protein chain, so the reaction would link two chains, imparting cohesion to the dough.
Cysteine,C3H6NO2)SH. The S atom is in yellow Formation of a disulfide bond. "R" represents the C3H6NO2) part of cysteine The S-S linkage between cysteine molecules
But potassium bromate is a proven carcinogen,[8] [9] and it is only allowed in foods in the US because it is assumed that bakers will add the right amount and provide the correct conditions of temperature and baking time so that the equation below goes to completion, producing only Br-, which is harmful only at levels high enough so that it competes with iodine uptake. Bromate is banned in most of Europe; UK banned bromate in bread in 1990, Canada in 1994. Many US bakers still use it; look at the label!
EXAMPLE 3 Balance the for the reaction of potassium bromate with 2 cysteine molecules (C3H6NO2)SH, where the part of the molecule in parentheses is unchanged, so it can be balanced as a single unit.
KBrO3 + (C3H6NO2)SH → KBr + H2O + (C3H6NO2)2S2
Solution
The K and Br are balanced. We note that 3 oxygen atoms are found in KBrO3 on the left, but only 1 in H2O on the right. So one starting place would be to balance the oxygen:
KBrO3 + (C3H6NO2)SH → KBr + 3 H2O + (C3H6NO2)2S2
Now there are 6 H in the 3 H2O on the right, but only 1 in the (C3H6NO2)SH molecules on the left, so we can add a coefficient of 6:
KBrO3 + 6 (C3H6NO2)SH → KBr + 3 H2O + (C3H6NO2)2S2
But now we have 6 (C3H6NO2)SH, so we'll need 3 of the sulfur bridged species on the right:
KBrO3 + 6 (C3H6NO2)SH → KBr + 3 H2O + 3 (C3H6NO2)2S2
Notice that, in this example, the rule of balancing first those elements whose symbols appeared in the smallest number of formulas doesn't help, because H and O both appear in two of them. But if we started by balancing H, (say by adding 2 before (C3H6NO2)SH, that step would have to be redone as soon as we went back to balance O. More algorithms for balancing equations will be developed later, in reactions in aqueous solutions.
The balancing of chemical equations has an important environmental message for us. If atoms are conserved in a chemical reaction, then we cannot get rid of them. In other words we cannot throw anything away. There are only two things we can do with atoms: Move them from place to place or from compound to compound. Thus when we "dispose" of something by burning it, dumping it, or washing it down the sink, we have not really gotten rid of it at all. The atoms which constituted it are still around someplace, and it is just as well to know where they are and what kind of molecule they are in. Discarded atoms in places where we do not want them and in undesirable molecules are known as pollution.
## References
1. Laurence E. Strong, Balancing Chemical Equations, Chemistry, vol. 47, no. 1, pp. 13-16, January 1974, discusses some techniques in more detail.
2. http://en.wikipedia.org/wiki/Sorbitol
3. http://en.wikipedia.org/wiki/Xylitol
4. http://www.inchem.org/documents/jecfa/jecmono/v18je13.htm
5. H.-D. Belitz, W. Grosch, P. Schieberle, Food Chemistry,Springer; 4th ed. 2009, p. 719
6. http://pubs.acs.org/doi/full/10.1021/jf100340j
7. http://pubs.acs.org/doi/abs/10.1021/jf100340j
8. http://www.cspinet.org/new/bromate.html
9. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1567851/ | {"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": 2, "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": 0.812583863735199, "perplexity": 1552.767539431013}, "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-2015-11/segments/1424936463708.99/warc/CC-MAIN-20150226074103-00248-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://www.nature.com/articles/s41467-021-26619-8?error=cookies_not_supported&code=d81be0a5-c47c-4ee6-b744-39984157d8a6 | ## Introduction
The revolutionary topological classification of matter (e.g., topological insulators and topological semimetals) is underpinned by the concept of band topology formed by Bloch eigenstates, commonly calculated by the Bloch theorem in an infinitely large system without a boundary1,2. Introducing a boundary will only lead to boundary states, but will not change any bulk property, including the band topology, as considered universally true for all Hermitian, or energy-conservative, systems. However, the recently discovered NHSE has shown that non-Hermiticity, originating from loss/gain or non-reciprocity, can cause all the bulk eigenstates to collapse towards the introduced boundary3,4,5,6,7,8,9,10,11,12,13,14,15,16. The complete collapse of bulk bands in NHSE has posed a challenge to the bulk-boundary correspondence3—a fundamental principle of topological physics—which states that the band topology derived from the bulk dictates the topological phenomena at the boundary.
Understanding the NHSE requires non-Hermitian band topology, a newly introduced set of topological descriptions with features distinct from the Hermitian counterpart6,17,18,19,20,21. For example, the nontrivial topology can arise from a non-Hermitian single band, with no symmetry protection, while a Hermitian band topology requires two or more bands, generally under some symmetry protection. So far, all NHSE observations are based on one type of non-Hermitian band topology, in which the complex energy spectrum winds along a closed loop in the complex plane7,8,9,15. The winding direction, characterized by the winding number of +1 or −1, determines which boundary, the left or right, all bulk eigenstates shall collapse toward in the NHSE4,6 (see Fig. 1a). In a simplified picture, the collapse direction is consistent with the direction of dominant coupling22.
Topological windings beyond the simplest single-loop configuration can generate much more complex topology. For example, as recently demonstrated along a frequency synthetic dimension in a photonic resonator, non-Hermitian topological winding can exhibit almost arbitrary topology in momentum space, including a twisted winding that produces two oppositely oriented loops in contact rather than a single loop23 (see the right panel in Fig. 1b). However, since the characterization assumes an infinitely large system without a boundary, the corresponding actual physical phenomena in a finite system still remain uncharacterized. On the other hand, as predicted by recent theories, the twisted winding may dramatically change the NHSE: the bulk eigenstates can collapse towards two directions, exhibiting the bipolar localization that is inconsistent with the dominant coupling direction; and the contact point between the two loops, named as the Bloch point, corresponds to a Bloch-wave-like extended state, interpolating the left-localized and right-localized eigenstates22,24 (see the left panel in Fig. 1b). None of these phenomena has been observed.
Here, we experimentally demonstrate the NHSE in a 1D non-reciprocal acoustic crystal exhibiting the twisted non-Hermitian winding topology. Topological acoustics is an ideal platform to explore various topological phenomena, due to the ease with which the properties and couplings of acoustic crystals can be engineered25,26. The non-reciprocal coupling, while difficult in other crystal lattices such as photonic crystals, is realized here with directional acoustic amplifiers. With non-reciprocal nearest-neighbor coupling, the crystal exhibits conventional single-winding-type NHSE, similar to previous observations7,8,9,15. When non-reciprocity is applied to the next-nearest-neighbor coupling, the crystal’s NHSE transits to the bipolar type that corresponds to the twisted winding topology22. A discrete Bloch-wave-like extended mode is also observed at the Bloch point. As the non-reciprocal coupling can be applied between two arbitrary sites, our acoustic platform provides a versatile platform to directly observe physical phenomena arising from more complex unconventional topological windings (see Supplementary Information Note 1).
## Results
### Implementation of acoustic non-Hermitian non-reciprocal coupling
We start with the design of non-reciprocal coupling. As shown in Fig. 2a, two identical acoustic resonators (labeled “1” and “2”) with resonance frequency ω0 are connected by two narrow waveguides that provide reciprocal coupling κ1 (see Supplementary Information Note 2). Note that the two waveguides can enhance the coupling strength. The unidirectional coupling, denoted as $${\tilde{\kappa }}_{a}$$, is introduced by an additional setup that consists of a directional amplifier (equipped with a direct current (DC) power supply), a speaker (output), and a microphone (input). This additional setup amplifies the sound unidirectionally: the sound is detected at resonator 1, and then coupled to resonator 2 after amplification. This unidirectional amplification introduces non-reciprocity. The tight-binding model (see Fig. 2b) can lead to the following Hamiltonian (see details in Supplementary Information Note 3):
$$H=\left[\begin{array}{cc}{\omega }_{0}-i{\gamma }_{0} & {\kappa }_{1}\\ {\kappa }_{1}+{\tilde{\kappa }}_{a} & {\omega }_{0}-i{\gamma }_{0}\end{array}\right].$$
(1)
Here, γ0 arises from the intrinsic loss, including the viscothermal loss. Note that we only consider the dipole mode in a single resonator (see Fig. 2c).
To experimentally retrieve the couplings, we measure both |S12| and |S21| transmission spectra without and with the amplifier (see experimental details in Methods), as shown in Fig. 2d, e, respectively. As expected, when the amplifier is not in operation, i.e., with only the reciprocal coupling, |S12| and |S21| are very close, and there occur two resonance peaks with almost identical amplitude. However, when the amplifier is in operation, we observe three notable features (Fig. 2e). Firstly, |S12| is higher than |S21|. This is direct evidence of non-reciprocity. Secondly, the maximum transmission is greater than unity, which comes from gain. Lastly, the two resonance frequencies are different from those in the Hermitian case, indicating that the non-reciprocal coupling has changed the eigenfrequencies of the system. By numerically fitting the measured spectra with the coupled-mode theory (see Supplementary Information Note 4), we can obtain the resonator’s resonance frequency ω0 = 1706 Hz, the reciprocal coupling κ1 = 24 Hz, the non-reciprocal coupling $${\tilde{\kappa }}_{a}$$ = −11 + 3.9i Hz, and γ0 = 2.13 Hz, respectively. The phase of $${\tilde{\kappa }}_{a}$$ results from the phase delay of the amplifier (see Supplementary Information Note 5).
### NHSE from single-winding topology
We then proceed to demonstrate the NHSE in a 1D crystal that consists of 20 acoustic resonators as shown in Fig. 3a. Here the non-reciprocal coupling is applied between nearest-neighbor resonators, following the tight-binding model in Fig. 3b (see Methods for more details). The lattice Hamiltonian of the crystal with periodic boundary conditions is $$H={\kappa }_{1}{e}^{ika}+{\kappa }_{1}{e}^{-ika}+{\tilde{\kappa }}_{a}{e}^{-ika}+{\omega }_{0}-i{\gamma }_{0}$$, where k is the wavevector, and the lattice constant a = 11.6 cm. The imaginary and real parts of the eigenfrequency spectrum are presented in Fig. 3c. The asymmetric distribution of the imaginary part (yellow curve) with respect to k = 0 indicates the non-reciprocity. The corresponding eigenfrequency spectrum in the complex frequency plane is also plotted in Fig. 3d. The spectrum winds around a tilted elliptical loop, along the direction of increasing wavenumber ka from 0 to 2π. For an arbitrary frequency ωb in the complex plane (without overlapping with the dispersion band), a quantized integer winding number v can be obtained as
$$v=\frac{1}{2\pi i}\int_{-\pi }^{\pi }\frac{\partial \omega (k)/\partial k}{\omega (k)-{\omega }_{b}}dk$$
(2)
where ω(k) is the eigenfrequency band. Geometrically, the rotation direction and the number of times of this closed-loop enclosing the reference frequency ωb determinates the sign and value of v, respectively16,18. Here, owing to the counter-clockwise winding that encloses a finite area containing an arbitrary base frequency ωb (e.g., 1700 + 5i Hz) for a single time, the winding number is v = +1, which can also be confirmed numerically by the above equation.
The winding number v = +1 determines that all eigenstates shall collapse to the left boundary. This also means that, regardless of the location of the source, all waves in the crystal shall propagate only to the left, forming a funneling effect8. For the purpose of demonstration, we first launch an acoustic pulse, covering the frequency range from 1680 to 1720 Hz, from site 1 (20), and measure the transmission at site 20 (1). As depicted in Fig. 3e, f, the transmission towards the right boundary almost vanishes, while the transmission towards the left boundary is amplified (also see the measured time-domain results in Supplementary Information Note 6 and Note 7). Such a phenomenon can be used to devise a unidirectional compact waveguide without relying on a large-size bulk to separate the one-way edge states as in Chern insulators27. Moreover, we also measure the field distributions in the acoustic crystal when the source is placed at different locations with operating frequency ω = 1713 Hz, as shown in Fig. 3g (see more results at other frequencies in Supplementary Information Note 8). There are two striking features of the NHSE. Firstly, the energy is concentered on the left boundary irrespective of the source location. This is different from a conventional Hermitian acoustic crystal, where the energy distribution generally concentrates around the source location (see Supplementary Information Note 9). Secondly, the field distribution localized at the left boundary exhibits stronger amplitude, when the source is placed further away from the left. Those two features are direct evidence of the NHSE9. We also numerically calculated the field distribution of eigenstates in the finite crystal under open boundary conditions, which further corroborates the localization of all eigenstates at the left boundary (see Fig. 3h).
### NHSE from twisted-winding topology
A remarkable advantage of our acoustic crystal is that the non-reciprocity can be conveniently applied not only to the nearest-neighbor coupling but also to the long-range coupling, the latter of which is the key element of complex topological winding of a non-Hermitian band. Here we apply the non-reciprocal coupling $${\tilde{\kappa }}_{a}$$ to the next-nearest-neighbor coupling, as shown in Fig. 4a, b. The nearest-neighbor coupling remains as κ1, which is reciprocal. The corresponding lattice Hamiltonian with periodic boundary conditions can be written as $$H={\kappa }_{1}{e}^{ika}+{\kappa }_{1}{e}^{-ika}+{\tilde{\kappa }}_{a}{e}^{-2ika}+{\omega }_{0}-i{\gamma }_{0}$$. The imaginary and real parts of the eigenfrequency spectrum are presented in Fig. 4c. The corresponding eigenfrequency spectrum in the complex frequency plane is plotted in Fig. 4d. This time the eigenfrequency spectrum does not wind along a fixed direction but instead forms a twisted topology that consists of two opposite oriented loops in contact. The loop on the left-hand side winds in the clockwise direction, indicating a negative winding number v = −1. On the contrary, the loop on the right-hand side winds in the counter-clockwise direction, indicating a positive winding number v = +1. Moreover, the twisted winding inevitably features a transition point, named the Bloch point, at ωc, between the two loops, as highlighted with the red star in Fig. 4d. According to previous predictions, such as twisted winding will lead to bipolar localization, where the eigenstates collapse to two directions simultaneously22. The Bloch point will represent a Bloch-wave-like extended state that interpolates the left-localized and right-localized states22.
Next, we experimentally measure the field distributions in the acoustic crystal exhibiting this twisted winding topology. We place a source at site 10 and measure the response at each site (see Methods). As depicted in Fig. 4e, at the frequency ω = 1666 Hz, the wave excited from site 10 is strongly suppressed towards the left boundary but is dramatically amplified towards the right boundary, implying the winding number of v = −1. On the contrary, the phenomenon is reversed at the frequency ω = 1733 Hz, indicating the flip of the sign of the winding number (see more results at different frequencies in Supplementary Information Note 10). Notably, at a frequency ω = 1696 Hz, which is between 1666 and 1733 Hz, the wave propagates towards both directions with almost identical amplitudes, with the maximum around the source. This is a manifestation of the Bloch-wave-like extended mode at the Bloch point22. The above experimental results match well with those from theoretical calculations (see Supplementary Information Note 11). Besides, we have measured the transmission of a pulse in the time domain (see Supplementary Information Note 12), and have experimentally investigated the pressure field distributions at different site numbers (see Supplementary Information Note 13). Taken together, we have thus experimentally demonstrated the twisted winding topology.
## Discussion
To conclude, we have demonstrated the NHSE in an active non-reciprocal acoustic crystal that is able to exhibit different winding topologies. By controlling the non-reciprocal coupling between arbitrary two sites, more complex unconventional topological windings can be achieved in the present acoustic platform. As the NHSE is a manifestation of the breakdown of the conventional bulk-boundary correspondence, it will be interesting to investigate the generalization of bulk-boundary correspondence and generalized Brillouin zones in non-Hermitian topological acoustics14. Though our experiments are carried out in 1D, it is feasible to extend the current design to two or three dimensions, greatly enriching the unique topology in non-Hermitian systems and enabling exotic physical phenomena such as high-order NHSE28. Furthermore, the feedback mechanism29,30 is universal and can be applied to design arbitrary lattices with non-Hermitian, time-dependent, and even nonlinear coupling, in acoustics and electromagnetics. In terms of applications, the demonstrated acoustic NHSE paves a way towards highly sensitive acoustic sensors, robust compact one-way waveguides, and amplifiers.
## Methods
### Experimental samples
The acoustic samples in this work are fabricated with the 3D-printing technique with a fabrication error ~2 mm using photosensitive resin, which can be considered as acoustically rigid for airborne sound. The parameters of each acoustic resonator are height h = 11.2 cm, width w = 7.2 cm, length l = 9.2 cm, the distance between two acoustic resonators s = 2.4 cm, the two cross-linked narrow waveguides diameter d = 3.4 cm, and the thickness of the photosensitive resin is 6 mm, as illustrated in Figs. 2a, 3a, and 4a. Each active component comprises a directional amplifier (LM386 Low Voltage Audio Power Amplifier) equipped with a DC power supply, a speaker (output), and a microphone (input). Two holes (radius 4 mm) are drilled at the top on both sides of each acoustic resonator to insert the source and detector, respectively. The active component can provide the complex unidirectional coupling (see Supplementary Information Note 3). Two holes (radius 4 mm and 6.1 mm, respectively) are drilled at the bottom in the front of each acoustic resonator. The speaker (microphone) of the active component is inserted from the small (large) hole. The holes are sealed when not in use. The sample in Fig. 2a is composed of two cross-linked acoustic resonators and one active component. The sample in Fig. 3a is composed of 20 cross-linked acoustic resonators and 19 active components connecting two nearest-neighbor cavities. The sample in Fig. (4) is composed of 20 cross-linked acoustic resonators and 18 active amplifier components connecting two next-nearest neighbor cavities. Each active component is calibrated based on the two-resonator model.
### Numerical simulations
The pressure field distribution of the acoustic resonator (Fig. 2c) is numerically calculated in the eigenfrequency of the commercial software COMSOL Multiphysics. The simulated model is the same as in Fig. 2a. The property of the materials is set as the air density ρ0 = 1.29 kg m−3 and the sound speed c = 340 × (1 + 0.0014i) m s−1.
### Measurements
A broadband sound signal is launched from a soft tube generated from the output generator module (B&K Type 3160-A-022), behaving like a point source, placed in the hole at the backside of the sample. The amplitude at each site is measured with a detector microphone (B&K Type 4182) placed in the hole at the front side of the sample, recorded with the signal acquisition module (B&K Type 3160-A-022). For the experiments in Fig. 2d and e, we measure the S12 and S21 by changing the position of the source and detector. The transmission spectra are normalized to the case when the source and the detector are directly connected. For the experiments in Figs. 3e, f, S5, S6, and S11, we place the source at sites 1 and 20, injecting a pulse ranging from 1680 to 1720 Hz, and measure the response pulse from site 20 and site 1, respectively. For the experiments in Figs. 3g, 4e, S7, S9, and S12, we measure the amplitude by changing the position of the detector at each site and polt the amplitude versus detector location. | {"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": 2, "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": 0.8742669224739075, "perplexity": 1222.0492420577984}, "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-2022-49/segments/1669446710734.75/warc/CC-MAIN-20221130092453-20221130122453-00316.warc.gz"} |
http://mathhelpforum.com/pre-calculus/3523-problem-reg-de-moivre-s-theorem.html | # Thread: Problem reg De'Moivre's theorem
1. ## De'Moivre's theorem
Hi,
Use De’Moivre’s theorem to solve the following equations:
a. X^(3) - 1 = 10
b. (x + 1)^(5) + x^(2) = 0
Lalit Chugh
2. Originally Posted by lalitchugh
Hi,
Use De’Moivre’s theorem to solve the following equations:
a. X^(3) - 1 = 10
Thus,
$x^3=11$
Express in polar form thus,
$x^3=11(\cos 2\pi k+i\sin 2\pi k)$
Thus,
$x=11^{1/3}\left( \cos \frac{2\pi k}{3}+i\sin \frac{2\pi k}{3} \right)$ for $k=0,1,2$
Thus,
$x=11^{1/3}\left( \cos \frac{2\pi \cdot 0}{3}+i\sin \frac{2\pi \cdot}{3} \right)=11^{1/3}$
$x=11^{1/3}\left( \cos \frac{2\pi \cdot 1}{3}+i\sin \frac{2\pi \cdot 1}{3} \right)=11^{1/3}\left(-\frac{1}{2}+i\frac{\sqrt{3}}{2}\right)$
$x=11^{1/3}\left( \cos \frac{2\pi \cdot 2}{3}+i\sin \frac{2\pi \cdot 2}{3} \right)=11^{1/3}\left( -\frac{1}{2}-i\frac{\sqrt{3}}{2}\right)$
3. Originally Posted by ThePerfectHacker
Thus,
$x^3=11$
Express in polar form thus,
$x^3=11(\cos 2\pi k+i\sin 2\pi k)$
Thus,
$x=11^{1/3}\left( \cos \frac{2\pi k}{3}+i\sin \frac{2\pi k}{3} \right)$ for $k=0,1,2$
I think we could take any value of k, why only 0,1 and 2, why not 3,4 and 5?
4. Originally Posted by malaygoel
I think we could take any value of k, why only 0,1 and 2, why not 3,4 and 5?
Because given,
$x^n=1$
We can then show that if,
$\zeta\in \left\{ \left{ \cos\frac{2\pi k}{n}+i\sin \frac{2\pi k}{n} \right| 0\leq k\leq n-1\right\}$
Then,
$\zeta^n=1$
Furthermore, all elements are distinct.
Thus, by the pigeonhole principle we have exactly $n$ elements in this set. But since a polynomial can have a most $n$ solution we see that all of the solution of, $x^n=1$ are found in this set.
I like to think this is as elegant as it gets.
Yes you can take other values for $k$, but I like to follow this reasoning. Because, I am certain that all the solutions are found by starting at k=0 and going to k=n-1.
5. ## Problem reg De'Moivre's theorem
Hi,
Many thanks for the solution.
May i request you to provide solution for 2nd question on De'Moivre's thoerem as well.
I will be thankful to you. It will help me in undertstanding the steps.
Best Regards,
Lalit Chugh
6. latichugh do not beg!
-=USER WARNED=-
---------------------
Your question was not answered perhaps because it has nothing with de Moiver's theorem. | {"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": 18, "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": 0.8804981112480164, "perplexity": 1462.502475739333}, "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/1512948567785.59/warc/CC-MAIN-20171215075536-20171215095536-00321.warc.gz"} |
http://www.ams.org/joursearch/servlet/DoSearch?f1=msc&v1=54E45 | American Mathematical Society
My Account · My Cart · Customer Services · FAQ
Publications Meetings The Profession Membership Programs Math Samplings Policy and Advocacy In the News About the AMS
You are here: Home > Publications
AMS eContent Search Results
Matches for: msc=(54E45) AND publication=(all) Sort order: Date Format: Standard display
Results: 1 to 30 of 32 found Go to page: 1 2
[1] Dennis J. Garity and Dušan Repovš. Inequivalent Cantor sets in $R^{3}$ whose complements have the same fundamental group. Proc. Amer. Math. Soc. 141 (2013) 2901-2911. Abstract, references, and article information View Article: PDF [2] J. Krasinkiewicz and S. Spież. Embedding of the dunce hat. Proc. Amer. Math. Soc. 141 (2013) 2537-2541. Abstract, references, and article information View Article: PDF [3] Józef Krasinkiewicz and Stanisław Spież. Extension of the Borsuk theorem on non-embeddability of spheres. Proc. Amer. Math. Soc. 140 (2012) 4035-4040. Abstract, references, and article information View Article: PDF [4] Akira Koyama, Józef Krasinkiewicz and Stanisław Spież. Generalized manifolds in products of curves. Trans. Amer. Math. Soc. 363 (2011) 1509-1532. MR 2737275. Abstract, references, and article information View Article: PDF [5] Dennis Garity, Dušan Repovš, David Wright and Matjaž Željko. Distinguishing Bing-Whitehead Cantor sets. Trans. Amer. Math. Soc. 363 (2011) 1007-1022. MR 2728594. Abstract, references, and article information View Article: PDF [6] Christina Sormani and Guofang Wei. The cut-off covering spectrum. Trans. Amer. Math. Soc. 362 (2010) 2339-2391. MR 2584603. Abstract, references, and article information View Article: PDF This article is available free of charge [7] Igor Mineyev. Metric conformal structures and hyperbolic dimension. Conform. Geom. Dyn. 11 (2007) 137-163. MR 2346214. Abstract, references, and article information View Article: PDF [8] Dennis J. Garity, Dusan Repovs and Matjaz Zeljko. Rigid cantor sets in $R^3$ with simply connected complement. Proc. Amer. Math. Soc. 134 (2006) 2447-2456. MR 2213719. Abstract, references, and article information View Article: PDF This article is available free of charge [9] Paul Larson and Stevo Todorcevic. Katetov's problem. Trans. Amer. Math. Soc. 354 (2002) 1783-1791. MR 1881016. Abstract, references, and article information View Article: PDF This article is available free of charge [10] Per Bylund and Jaume Gudayol. On the existence of doubling measures with certain regularity properties. Proc. Amer. Math. Soc. 128 (2000) 3317-3327. MR 1676303. Abstract, references, and article information View Article: PDF This article is available free of charge [11] Jang-Mei Wu. Hausdorff dimension and doubling measures on metric spaces. Proc. Amer. Math. Soc. 126 (1998) 1453-1459. MR 1443418. Abstract, references, and article information View Article: PDF This article is available free of charge [12] A. N. Dranishnikov. On the virtual cohomological dimensions of Coxeter groups. Proc. Amer. Math. Soc. 125 (1997) 1885-1891. MR 1422863. Abstract, references, and article information View Article: PDF This article is available free of charge [13] Jacek R. Jachymski. Equivalent conditions involving common fixed points for maps on the unit interval. Proc. Amer. Math. Soc. 124 (1996) 3229-3233. MR 1328352. Abstract, references, and article information View Article: PDF This article is available free of charge [14] Friedrich Wehrung. Baire paradoxical decompositions need at least six pieces . Proc. Amer. Math. Soc. 121 (1994) 643-644. MR 1209101. Abstract, references, and article information View Article: PDF This article is available free of charge [15] Leonid G. Hanin. Kantorovich-Rubinstein norm and its application in the theory of Lipschitz spaces . Proc. Amer. Math. Soc. 115 (1992) 345-352. MR 1097344. Abstract, references, and article information View Article: PDF This article is available free of charge [16] José M. Bayod and J. Martínez-Maurica. Subdominant ultrametrics . Proc. Amer. Math. Soc. 109 (1990) 829-834. MR 1015676. Abstract, references, and article information View Article: PDF This article is available free of charge [17] E. E. Grace and Eldon J. Vought. Refinable maps and $\theta\sb n$-continua . Proc. Amer. Math. Soc. 106 (1989) 231-239. MR 964455. Abstract, references, and article information View Article: PDF This article is available free of charge [18] Alan Dow. An empty class of nonmetric spaces . Proc. Amer. Math. Soc. 104 (1988) 999-1001. MR 964886. Abstract, references, and article information View Article: PDF This article is available free of charge [19] Gerald Jungck. Common fixed points for commuting and compatible maps on compacta . Proc. Amer. Math. Soc. 103 (1988) 977-983. MR 947693. Abstract, references, and article information View Article: PDF This article is available free of charge [20] A. J. Jayanthan and V. Kannan. Spaces every quotient of which is metrizable . Proc. Amer. Math. Soc. 103 (1988) 294-298. MR 938686. Abstract, references, and article information View Article: PDF This article is available free of charge [21] Katsuro Sakai. A $Q$-manifold local-compactification of a metric combinatorial $\infty$-manifold . Proc. Amer. Math. Soc. 100 (1987) 775-780. MR 894453. Abstract, references, and article information View Article: PDF This article is available free of charge [22] E. E. Grace. Generalized refinable maps . Proc. Amer. Math. Soc. 98 (1986) 329-335. MR 854042. Abstract, references, and article information View Article: PDF This article is available free of charge [23] Louis Block and Ethan M. Coven. Maps of the interval with every point chain recurrent . Proc. Amer. Math. Soc. 98 (1986) 513-515. MR 857952. Abstract, references, and article information View Article: PDF This article is available free of charge [24] Gerald Beer. Metric spaces on which continuous functions are uniformly continuous and Hausdorff distance . Proc. Amer. Math. Soc. 95 (1985) 653-658. MR 810180. Abstract, references, and article information View Article: PDF This article is available free of charge [25] E. E. Grace. Monotone decompositions of $\theta$-continua . Trans. Amer. Math. Soc. 275 (1983) 287-295. MR 678350. Abstract, references, and article information View Article: PDF This article is available free of charge [26] Gerald Beer. Which connected metric spaces are compact? . Proc. Amer. Math. Soc. 83 (1981) 807-811. MR 630059. Abstract, references, and article information View Article: PDF This article is available free of charge [27] Charles F. Mills. A simpler proof that compact metric spaces are supercompact . Proc. Amer. Math. Soc. 73 (1979) 388-390. MR 518526. Abstract, references, and article information View Article: PDF This article is available free of charge [28] William H. Chapman and Daniel J. Randtke. On the existence of compact metric subspaces with applications to the complementation of $c\sb{0}$ . Trans. Amer. Math. Soc. 219 (1976) 133-148. MR 0410688. Abstract, references, and article information View Article: PDF This article is available free of charge [29] Tim Porter. Obstructions in shape theory. Bull. Amer. Math. Soc. 79 (1973) 1206-1209. MR 0377883. Abstract, references, and article information View Article: PDF [30] B. J. Ball and R. B. Sher. A theory of proper shape for locally compact metric spaces. Bull. Amer. Math. Soc. 79 (1973) 1023-1026. MR 0334139. Abstract, references, and article information View Article: PDF
Results: 1 to 30 of 32 found Go to page: 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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9585229158401489, "perplexity": 2259.5010945605486}, "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-2016-22/segments/1464049278389.62/warc/CC-MAIN-20160524002118-00106-ip-10-185-217-139.ec2.internal.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/27160-help-w-euclidean-rings-p-i-d-s.html | # Thread: Help w/ Euclidean Rings and P.I.D.s
1. ## Help w/ Euclidean Rings and P.I.D.s
Hey, I have two questions I need some help with because I missed my recitation. Answers are fine, but I'd prefer it if someone could just tell me the procedure/give me a nudge in the right direction.
The first is: Suppose that in the Euclidean Algorithm for finding the gcd of two integers "a" and "b" we always choose "q" and "r" so a=bq+r and 0 = or < r < b. How many applications of the division algorithm are needed to find the gcd of F(n) and F(n+1) in where F is the fibonnaci sequence and F(0)=1. What is this gcd?
And the second: Show that if R is a Principal Ideal Domain and D is a multiplicatively closed subset of R, then (D^-1)R is a Principal Ideal Domain.
2. Originally Posted by Pyrrhus
The first is: Suppose that in the Euclidean Algorithm for finding the gcd of two integers "a" and "b" we always choose "q" and "r" so a=bq+r and 0 = or < r < b. How many applications of the division algorithm are needed to find the gcd of F(n) and F(n+1) in where F is the fibonnaci sequence and F(0)=1. What is this gcd?
$F(n+1) = F(n)+F(n-1)$
$F(n) = F(n-1)+F(n-2)$
$F(n-1) = F(n-2)+F(n-3)$
...
So what do you think it is?
And the second: Show that if R is a Principal Ideal Domain and D is a multiplicatively closed subset of R, then (D^-1)R is a Principal Ideal Domain.
Define what $D^{-1}$ means. And what does the juxaposition $D^{-1} R$ mean?
3. It's like a limited fraction field. (D^-1)R is the extension of R such that all the elements of D in R have multiplicative inverses in (D^-1)R. So all elements r of R get mapped to (r/1), and all elements mapped from d of D in R of the form (d/1) have an inverse in the latter ring of the form (1/d). For example, if you take R=Z and D=multiples of 3 in Z, (D^-1)R is the ring whose elements are of the formg (a/b) where "a" is an element of Z and "b" is an element of Z that is a multiple of 3.
Also, I got the answer to the first one a few hours ago so I just need to work on the second. | {"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": 5, "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": 0.8873869776725769, "perplexity": 380.7171263598337}, "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-2017-17/segments/1492917122720.81/warc/CC-MAIN-20170423031202-00176-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://en.m.wikipedia.org/wiki/SU(2) | # Special unitary group
(Redirected from SU(2))
In mathematics, the special unitary group of degree n, denoted SU(n), is the Lie group of n×n unitary matrices with determinant 1.
(More general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the special case.)
The group operation is matrix multiplication. The special unitary group is a subgroup of the unitary group U(n), consisting of all n×n unitary matrices. As a compact classical group, U(n) is the group that preserves the standard inner product on Cn.[nb 1] It is itself a subgroup of the general linear group, SU(n) ⊂ U(n) ⊂ GL(n, C).
The SU(n) groups find wide application in the Standard Model of particle physics, especially SU(2) in the electroweak interaction and SU(3) in quantum chromodynamics.[1]
The simplest case, SU(1), is the trivial group, having only a single element. The group SU(2) is isomorphic to the group of quaternions of norm 1, and is thus diffeomorphic to the 3-sphere. Since unit quaternions can be used to represent rotations in 3-dimensional space (up to sign), there is a surjective homomorphism from SU(2) to the rotation group SO(3) whose kernel is {+I, −I}.[nb 2] SU(2) is also identical to one of the symmetry groups of spinors, Spin(3), that enables a spinor presentation of rotations.
## Properties
The special unitary group SU(n) is a real Lie group (though not a complex Lie group). Its dimension as a real manifold is n2 − 1. Topologically, it is compact and simply connected.[2] Algebraically, it is a simple Lie group (meaning its Lie algebra is simple; see below).[3]
The center of SU(n) is isomorphic to the cyclic group Zn, and is composed of the diagonal matrices ζ I for ζ an nth root of unity and I the n×n identity matrix.
Its outer automorphism group, for n ≥ 3, is Z2, while the outer automorphism group of SU(2) is the trivial group.
A maximal torus, of rank n − 1, is given by the set of diagonal matrices with determinant 1. The Weyl group is the symmetric group Sn, which is represented by signed permutation matrices (the signs being necessary to ensure the determinant is 1).
The Lie algebra of SU(n), denoted by ${\displaystyle {\mathfrak {su}}(n)}$ , can be identified with the set of traceless antiHermitian n×n complex matrices, with the regular commutator as Lie bracket. Particle physicists often use a different, equivalent representation: the set of traceless Hermitian n×n complex matrices with Lie bracket given by i times the commutator.
## Lie algebra
The Lie algebra ${\displaystyle \operatorname {su} (n)}$ of ${\displaystyle \operatorname {SU} (n)}$ consists of ${\displaystyle n\times n}$ skew-Hermitian matrices with trace zero.[4] This (real) Lie algebra has dimension ${\displaystyle n^{2}-1}$ . More information about the structure of this Lie algebra can be found below in the section "Lie algebra structure."
### Fundamental representation
In the physics literature, it is common to identify the Lie algebra with the space of trace-zero Hermitian (rather than the skew-Hermitian) matrices. That is to say, the physicists' Lie algebra differs by a factor of ${\displaystyle i}$ from the mathematicians'. With this convention, one can then choose generators Ta that are traceless Hermitian complex n×n matrices, where:
${\displaystyle T_{a}T_{b}={\frac {1}{2n}}\delta _{ab}I_{n}+{\frac {1}{2}}\sum _{c=1}^{n^{2}-1}\left(if_{abc}+d_{abc}\right)T_{c}}$
where the f are the structure constants and are antisymmetric in all indices, while the d-coefficients are symmetric in all indices.
As a consequence, the anticommutator and commutator are:
{\displaystyle {\begin{aligned}\left\{T_{a},T_{b}\right\}&={\frac {1}{n}}\delta _{ab}I_{n}+\sum _{c=1}^{n^{2}-1}{d_{abc}T_{c}}\\\left[T_{a},T_{b}\right]&=i\sum _{c=1}^{n^{2}-1}f_{abc}T_{c}\,.\end{aligned}}}
The factor of ${\displaystyle i}$ in the commutation relations arises from the physics convention and is not present when using the mathematicians' convention.
We may also take
${\displaystyle \sum _{c,e=1}^{n^{2}-1}d_{ace}d_{bce}={\frac {n^{2}-4}{n}}\delta _{ab}}$
as a normalization convention.
In the (n2 − 1) -dimensional adjoint representation, the generators are represented by (n2 − 1) × (n2 − 1) matrices, whose elements are defined by the structure constants themselves:
${\displaystyle \left(T_{a}\right)_{jk}=-if_{ajk}.}$
## The group SU(2)
SU(2) is the following group,[5]
${\displaystyle \operatorname {SU} (2)=\left\{{\begin{pmatrix}\alpha &-{\overline {\beta }}\\\beta &{\overline {\alpha }}\end{pmatrix}}:\ \ \alpha ,\beta \in \mathbf {C} ,|\alpha |^{2}+|\beta |^{2}=1\right\}~,}$
where the overline denotes complex conjugation.
There is a 2:1 homomorphism from SU(2) to SO(3).
### Diffeomorphism with S3
If we consider ${\displaystyle \alpha ,\beta }$ as a pair in ${\displaystyle \mathbb {C} ^{2}}$ where ${\displaystyle \alpha =a+bi}$ and ${\displaystyle \beta =c+di}$ , then the equation ${\displaystyle |\alpha |^{2}+|\beta |^{2}=1}$ becomes
${\displaystyle a^{2}+b^{2}+c^{2}+d^{2}=1}$
This is the equation of the 3-sphere S3. This can also be seen using an embedding: the map
{\displaystyle {\begin{aligned}\varphi \colon \mathbf {C} ^{2}&\to \operatorname {M} (2,\mathbf {C} )\\\varphi (\alpha ,\beta )&={\begin{pmatrix}\alpha &-{\overline {\beta }}\\\beta &{\overline {\alpha }}\end{pmatrix}},\end{aligned}}}
where M(2, C) denotes the set of 2 by 2 complex matrices, is an injective real linear map (by considering C2 diffeomorphic to R4 and M(2, C) diffeomorphic to R8). Hence, the restriction of φ to the 3-sphere (since modulus is 1), denoted S3, is an embedding of the 3-sphere onto a compact submanifold of M(2, C), namely φ(S3) = SU(2).
Therefore, as a manifold, S3 is diffeomorphic to SU(2) and so S3 is a compact, connected Lie group.
### Isomorphism with unit quaternions
The complex matrix:
${\displaystyle {\begin{pmatrix}a+bi&-c+di\\c+di&a-bi\end{pmatrix}}\quad (a,b,c,d\in \mathbb {R} )}$
can be mapped to the quaternion:
${\displaystyle a+bi+cj+dk}$
This map is in fact an isomorphism. Additionally, the determinant of the matrix is the norm of the corresponding quaternion. Clearly any matrix in SU(2) is of this form and, since it has determinant 1, the corresponding quaternion has norm 1. Thus SU(2) is isomorphic to the unit quaternions.[6]
### Lie algebra
The Lie algebra of SU(2) consists of ${\displaystyle 2\times 2}$ skew-Hermitian matrices with trace zero.[7] Explicitly, this means
${\displaystyle {\mathfrak {su}}(2)=\left\{{\begin{pmatrix}i\ a&-{\overline {z}}\\z&-i\ a\end{pmatrix}}:\ a\in \mathbf {R} ,z\in \mathbf {C} \right\}~.}$
The Lie algebra is then generated by the following matrices,
${\displaystyle u_{1}={\begin{pmatrix}0&i\\i&0\end{pmatrix}},\quad u_{2}={\begin{pmatrix}0&-1\\1&0\end{pmatrix}},\quad u_{3}={\begin{pmatrix}i&0\\0&-i\end{pmatrix}}~,}$
which have the form of the general element specified above.
These satisfy the quaternion relationships ${\displaystyle u_{2}\ u_{3}=-u_{3}\ u_{2}=u_{1}~,}$ ${\displaystyle u_{3}\ u_{1}=-u_{1}\ u_{3}=u_{2}~,}$ and ${\displaystyle u_{1}u_{2}=-u_{2}\ u_{1}=u_{3}~.}$ The commutator bracket is therefore specified by
${\displaystyle \left[u_{3},u_{1}\right]=2\ u_{2},\quad \left[u_{1},u_{2}\right]=2\ u_{3},\quad \left[u_{2},u_{3}\right]=2\ u_{1}~.}$
The above generators are related to the Pauli matrices by ${\displaystyle u_{1}=i\ \sigma _{1}~,\,u_{2}=-i\ \sigma _{2}}$ and ${\displaystyle u_{3}=+i\ \sigma _{3}~.}$ This representation is routinely used in quantum mechanics to represent the spin of fundamental particles such as electrons. They also serve as unit vectors for the description of our 3 spatial dimensions in loop quantum gravity.
The Lie algebra serves to work out the representations of SU(2).
## The group SU(3)
### Topology
The group SU(3) is a simply-connected, compact Lie group.[8] Its topological structure can be understood by noting that SU(3) acts transitively on the unit sphere ${\displaystyle S^{5}}$ in ${\displaystyle \mathbb {C} ^{3}=\mathbb {R} ^{6}}$ . The stabilizer of an arbitrary point in the sphere is isomorphic to SU(2), which topologically is a 3-sphere. It then follows that SU(3) is a fiber bundle over the base ${\displaystyle S^{5}}$ with fiber ${\displaystyle S^{3}}$ . Since the fibers and the base are simply connected, the simple connectedness of SU(3) then follows by means of a standard topological result (the long exact sequence of homotopy groups for fiber bundles).[9]
### Representation theory
The representation theory of SU(3) is well understood.[10] Descriptions of these representations, from the point of view of its complexified Lie algebra ${\displaystyle \operatorname {sl} (3;\mathbb {C} )}$ , may be found in the articles on Lie algebra representations or the Clebsch–Gordan coefficients for SU(3).
### Lie algebra
The generators, T, of the Lie algebra su(3) of SU(3) in the defining representation, are:
${\displaystyle T_{a}={\frac {\lambda _{a}}{2}}.\,}$
where λ, the Gell-Mann matrices, are the SU(3) analog of the Pauli matrices for SU(2):
{\displaystyle {\begin{aligned}\lambda _{1}={}&{\begin{pmatrix}0&1&0\\1&0&0\\0&0&0\end{pmatrix}},&\lambda _{2}={}&{\begin{pmatrix}0&-i&0\\i&0&0\\0&0&0\end{pmatrix}},&\lambda _{3}={}&{\begin{pmatrix}1&0&0\\0&-1&0\\0&0&0\end{pmatrix}},\\\lambda _{4}={}&{\begin{pmatrix}0&0&1\\0&0&0\\1&0&0\end{pmatrix}},&\lambda _{5}={}&{\begin{pmatrix}0&0&-i\\0&0&0\\i&0&0\end{pmatrix}},\\\lambda _{6}={}&{\begin{pmatrix}0&0&0\\0&0&1\\0&1&0\end{pmatrix}},&\lambda _{7}={}&{\begin{pmatrix}0&0&0\\0&0&-i\\0&i&0\end{pmatrix}},&\lambda _{8}={\frac {1}{\sqrt {3}}}&{\begin{pmatrix}1&0&0\\0&1&0\\0&0&-2\end{pmatrix}}.\end{aligned}}}
These λa span all traceless Hermitian matrices H of the Lie algebra, as required. Note that λ2, λ5, λ7 are antisymmetric.
They obey the relations
{\displaystyle {\begin{aligned}\left[T_{a},T_{b}\right]&=i\sum _{c=1}^{8}f_{abc}T_{c},\\\left\{T_{a},T_{b}\right\}&={\frac {1}{3}}\delta _{ab}I_{3}+\sum _{c=1}^{8}d_{abc}T_{c},\end{aligned}}}
(or, equivalently, ${\displaystyle \{\lambda _{a},\lambda _{b}\}={\frac {4}{3}}\delta _{ab}I_{3}+2\sum _{c=1}^{8}{d_{abc}\lambda _{c}}}$ ).
The f are the structure constants of the Lie algebra, given by:
{\displaystyle {\begin{aligned}f_{123}&=1\\f_{147}=-f_{156}=f_{246}=f_{257}=f_{345}=-f_{367}&={\frac {1}{2}}\\f_{458}=f_{678}&={\frac {\sqrt {3}}{2}},\end{aligned}}}
while all other fabc not related to these by permutation are zero. In general, they vanish, unless they contain an odd number of indices from the set {2, 5, 7}.[nb 3]
The symmetric coefficients d take the values:
{\displaystyle {\begin{aligned}d_{118}=d_{228}=d_{338}=-d_{888}&={\frac {1}{\sqrt {3}}}\\d_{448}=d_{558}=d_{668}=d_{778}&=-{\frac {1}{2{\sqrt {3}}}}\\d_{146}=d_{157}=-d_{247}=d_{256}=d_{344}=d_{355}=-d_{366}=-d_{377}&={\frac {1}{2}}~.\end{aligned}}}
They vanish if the number of indices from the set {2, 5, 7} is odd.
A generic SU(3) group element generated by a traceless 3×3 Hermitian matrix H, normalized as tr(H2) = 2, can be expressed as a second order matrix polynomial in H[11]:
{\displaystyle {\begin{aligned}\exp(i\theta H)={}&\left[-{\frac {1}{3}}I\sin \left(\varphi +{\frac {2\pi }{3}}\right)\sin \left(\varphi -{\frac {2\pi }{3}}\right)-{\frac {1}{2{\sqrt {3}}}}~H\sin(\varphi )-{\frac {1}{4}}~H^{2}\right]{\frac {\exp \left({\frac {2}{\sqrt {3}}}~i\theta \sin(\varphi )\right)}{\cos \left(\varphi +{\frac {2\pi }{3}}\right)\cos \left(\varphi -{\frac {2\pi }{3}}\right)}}\\[4pt]{}+{}&\left[-{\frac {1}{3}}~I\sin(\varphi )\sin \left(\varphi -{\frac {2\pi }{3}}\right)-{\frac {1}{2{\sqrt {3}}}}~H\sin \left(\varphi +{\frac {2\pi }{3}}\right)-{\frac {1}{4}}~H^{2}\right]{\frac {\exp \left({\frac {2}{\sqrt {3}}}~i\theta \sin \left(\varphi +{\frac {2\pi }{3}}\right)\right)}{\cos(\varphi )\cos \left(\varphi -{\frac {2\pi }{3}}\right)}}\\[4pt]{}+{}&\left[-{\frac {1}{3}}~I\sin(\varphi )\sin \left(\varphi +{\frac {2\pi }{3}}\right)-{\frac {1}{2{\sqrt {3}}}}~H\sin \left(\varphi -{\frac {2\pi }{3}}\right)-{\frac {1}{4}}~H^{2}\right]{\frac {\exp \left({\frac {2}{\sqrt {3}}}~i\theta \sin \left(\varphi -{\frac {2\pi }{3}}\right)\right)}{\cos(\varphi )\cos \left(\varphi +{\frac {2\pi }{3}}\right)}}\end{aligned}}}
where
${\displaystyle \varphi \equiv {\frac {1}{3}}\left[\arccos \left({\frac {3{\sqrt {3}}}{2}}\det H\right)-{\frac {\pi }{2}}\right].}$
## Lie algebra structure
As noted above, the Lie algebra ${\displaystyle \operatorname {su} (n)}$ of ${\displaystyle \operatorname {SU} (n)}$ consists of ${\displaystyle n\times n}$ skew-Hermitian matrices with trace zero.[12]
The complexification of the Lie algebra ${\displaystyle \operatorname {su} (n)}$ is ${\displaystyle \operatorname {sl} (n;\mathbb {C} )}$ , the space of all ${\displaystyle n\times n}$ complex matrices with trace zero.[13] A Cartan subalgebra then consists of the diagonal matrices with trace zero,[14] which we identify with vectors in ${\displaystyle \mathbb {C} ^{n}}$ whose entries sum to zero. The roots then consist of all the n(n − 1) permutations of (1, −1, 0, ..., 0).
A choice of simple roots is
{\displaystyle {\begin{aligned}(&1,-1,0,\dots ,0,0),\\(&0,1,-1,\dots ,0,0),\\&\vdots \\(&0,0,0,\dots ,1,-1).\end{aligned}}}
So, SU(n) is of rank n − 1 and its Dynkin diagram is given by An−1, a chain of n − 1 nodes: ... .[15] Its Cartan matrix is
${\displaystyle {\begin{pmatrix}2&-1&0&\dots &0\\-1&2&-1&\dots &0\\0&-1&2&\dots &0\\\vdots &\vdots &\vdots &\ddots &\vdots \\0&0&0&\dots &2\end{pmatrix}}.}$
Its Weyl group or Coxeter group is the symmetric group Sn, the symmetry group of the (n − 1)-simplex.
## Generalized special unitary group
For a field F, the generalized special unitary group over F, SU(p, q; F), is the group of all linear transformations of determinant 1 of a vector space of rank n = p + q over F which leave invariant a nondegenerate, Hermitian form of signature (p, q). This group is often referred to as the special unitary group of signature p q over F. The field F can be replaced by a commutative ring, in which case the vector space is replaced by a free module.
Specifically, fix a Hermitian matrix A of signature p q in GL(n, R), then all
${\displaystyle M\in \operatorname {SU} (p,q,R)}$
satisfy
{\displaystyle {\begin{aligned}M^{*}AM&=A\\\det M&=1.\end{aligned}}}
Often one will see the notation SU(p, q) without reference to a ring or field; in this case, the ring or field being referred to is C and this gives one of the classical Lie groups. The standard choice for A when F = C is
${\displaystyle A={\begin{bmatrix}0&0&i\\0&I_{n-2}&0\\-i&0&0\end{bmatrix}}.}$
However, there may be better choices for A for certain dimensions which exhibit more behaviour under restriction to subrings of C.
### Example
An important example of this type of group is the Picard modular group SU(2, 1; Z[i]) which acts (projectively) on complex hyperbolic space of degree two, in the same way that SL(2,9;Z) acts (projectively) on real hyperbolic space of dimension two. In 2005 Gábor Francsics and Peter Lax computed an explicit fundamental domain for the action of this group on HC2.[16]
A further example is SU(1, 1; C), which is isomorphic to SL(2,R).
## Important subgroups
In physics the special unitary group is used to represent bosonic symmetries. In theories of symmetry breaking it is important to be able to find the subgroups of the special unitary group. Subgroups of SU(n) that are important in GUT physics are, for p > 1, np > 1 ,
${\displaystyle \operatorname {SU} (n)\supset \operatorname {SU} (p)\times \operatorname {SU} (n-p)\times \operatorname {U} (1),}$
where × denotes the direct product and U(1), known as the circle group, is the multiplicative group of all complex numbers with absolute value 1.
For completeness, there are also the orthogonal and symplectic subgroups,
{\displaystyle {\begin{aligned}\operatorname {SU} (n)&\supset \operatorname {SO} (n),\\\operatorname {SU} (2n)&\supset \operatorname {Sp} (n).\end{aligned}}}
Since the rank of SU(n) is n − 1 and of U(1) is 1, a useful check is that the sum of the ranks of the subgroups is less than or equal to the rank of the original group. SU(n) is a subgroup of various other Lie groups,
{\displaystyle {\begin{aligned}\operatorname {SO} (2n)&\supset \operatorname {SU} (n)\\\operatorname {Sp} (n)&\supset \operatorname {SU} (n)\\\operatorname {Spin} (4)&=\operatorname {SU} (2)\times \operatorname {SU} (2)\\\operatorname {E} _{6}&\supset \operatorname {SU} (6)\\\operatorname {E} _{7}&\supset \operatorname {SU} (8)\\\operatorname {G} _{2}&\supset \operatorname {SU} (3)\end{aligned}}}
See spin group, and simple Lie groups for E6, E7, and G2.
There are also the accidental isomorphisms: SU(4) = Spin(6) , SU(2) = Spin(3) = Sp(1) ,[nb 4] and U(1) = Spin(2) = SO(2) .
One may finally mention that SU(2) is the double covering group of SO(3), a relation that plays an important role in the theory of rotations of 2-spinors in non-relativistic quantum mechanics.
## Remarks
1. ^ For a characterization of U(n) and hence SU(n) in terms of preservation of the standard inner product on n, see Classical group.
2. ^ For an explicit description of the homomorphism SU(2) → SO(3), see Connection between SO(3) and SU(2).
3. ^ So fewer than 1/6 of all fabcs are non-vanishing.
4. ^ Sp(n) is the compact real form of Sp(2n, C). It is sometimes denoted USp(2n). The dimension of the Sp(n)-matrices is 2n × 2n.
## Notes
1. ^ Halzen, Francis; Martin, Alan (1984). Quarks & Leptons: An Introductory Course in Modern Particle Physics. John Wiley & Sons. ISBN 0-471-88741-2.
2. ^ Hall 2015 Proposition 13.11
3. ^ Wybourne, B G (1974). Classical Groups for Physicists, Wiley-Interscience. ISBN 0471965057 .
4. ^ Hall 2015 Proposition 3.24
5. ^ Hall 2015 Exercise 1.5
6. ^ http://alistairsavage.ca/mat4144/notes/MAT4144-5158-LieGroups.pdf
7. ^ Hall 2015 Proposition 3.24
8. ^ Hall 2015 Proposition 13.11
9. ^ Hall 2015 Section 13.2
10. ^ Hall 2015 Chapter 6
11. ^ Rosen, S P (1971). "Finite Transformations in Various Representations of SU(3)". Journal of Mathematical Physics. 12 (4): 673. Bibcode:1971JMP....12..673R. doi:10.1063/1.1665634.; Curtright, T L; Zachos, C K (2015). "Elementary results for the fundamental representation of SU(3)". Reports On Mathematical Physics. 76: 401–404. arXiv:1508.00868. Bibcode:2015RpMP...76..401C. doi:10.1016/S0034-4877(15)30040-9.
12. ^ Hall 2015 Proposition 3.24
13. ^ Hall 2015 Section 3.6
14. ^ Hall 2015 Section 7.7.1
15. ^ Hall 2015 Section 8.10.1
16. ^ Francsics, Gabor; Lax, Peter D. (September 2005). "An Explicit Fundamental Domain For The Picard Modular Group In Two Complex Dimensions". arXiv:math/0509708.
## References
• Hall, Brian C. (2015), Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, Graduate Texts in Mathematics, 222 (2nd ed.), Springer, ISBN 978-3319134666
• Iachello, Francesco (2006), Lie Algebras and Applications, Lecture Notes in Physics, 708, Springer, ISBN 3540362363 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 58, "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": 0.9682273864746094, "perplexity": 1779.667950530454}, "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/1539583515352.63/warc/CC-MAIN-20181022155502-20181022181002-00214.warc.gz"} |
https://proofwiki.org/wiki/Algebraic_Element_of_Field_Extension_is_Root_of_Unique_Monic_Polynomial_of_Minimal_Degree | Algebraic Element of Field Extension is Root of Unique Monic Polynomial of Minimal Degree
Theorem
Let $L / K$ be a field extension.
Let $\alpha \in L$ be algebraic over $K$.
Then there exists a unique monic polynomial $f \in K \sqbrk x$ of smallest degree such that $\map f \alpha = 0$, called the minimal polynomial.
Proof
Existence
Follows from Well-Ordering Principle and because $K$ is a field.
$\Box$
Uniqueness
Let $f$ and $g$ be two such monic polynomial.
Then:
$\map f \alpha - \map g \alpha = 0$
Aiming for a contradiction, suppose $f - g \ne 0$.
Let $a$ be the leading coefficient of $f-g$.
Then $\dfrac 1 {a} \paren {f - g}$ is another such polynomial of strictly smaller degree.
Thus $f - g = 0$.
$\blacksquare$ | {"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": 0.9371163845062256, "perplexity": 176.03104059654837}, "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-2021-17/segments/1618038064898.14/warc/CC-MAIN-20210411174053-20210411204053-00465.warc.gz"} |
https://www.zbmath.org/?q=ai%3Alee.siu-lun-alan | ×
zbMATH — the first resource for mathematics
On Waring’s problem: two cubes and two minicubes. (English) Zbl 1315.11088
From the text: H. Davenport proved in [Acta Math. 71, 123–143 (1939; Zbl 0021.10601)] that almost every natural number can be expressed as a sum of four positive integral cubes. It is now known, courtesy of J. Brüdern [Math. Proc. Camb. Philos. Soc. 109, No. 2, 229–256 (1991; Zbl 0729.11046)] and T. D. Wooley [Mathematika 47, No. 1–2, 53–61 (2000; Zbl 1026.11075)], that when $$N$$ is sufficiently large, the number of positive integers at most $$N$$ that fail to be written in such a way is slightly smaller than $$N^{37/42}$$ Since any integer congruent to $$4\pmod 9$$ is never a sum of three cubes, the number of summands here cannot in general be reduced. A heuristic argument shows, however, that one of the four cubes is almost redundant. This motivates the work of Brüdern and Wooley (see [Nagoya Math. J. 200, 59–91 (2010; Zbl 1238.11090)]) on the representation of almost all positive integers as a sum of four cubes, one of which is small (henceforth we call this a minicube). They have shown that, with $$n$$ being the natural number to be represented, such a minicube can be as small as $$n^5/36$$ without obstructing the existence of representations. This raises the question as to whether we can restrict not only one, but two (or even three) of the cubes in such a representation to be minicubes, and still get an almost all result. The purpose of this paper is to investigate representations of natural numbers by sums of four cubes, two of which are small.
When $$n$$ is a positive integer and $$\theta > 0$$, write $$r_\theta(n)$$ for the number of solutions to the equation $n= x_1^3+ x_2^3+ y_1^3+ y_2^3,$
where $$x_1, x_2, y_1, y_2$$ are natural numbers satisfying $$y_1, y_2 \leq n^\theta$$.
A formal application of the circle method suggests that when $$1/6 < \theta < 1/3$$, we should have $r_\theta(n) \sim \frac{\Gamma(4/3)^2}{\Gamma(2/3)} \mathfrak{S}(n) n^{2\theta-1/3},$ with $$\mathfrak{S}(n)$$ being the familiar singular series associated with the representation of positive integers as sums of four cubes.
The following theorem is proved.
Theorem. Whenever $$192/869 \leq \theta \leq 2/9$$, we have $$r_\theta(n) \geq 1$$ for almost all integers $$n$$.
An additional asymptotic formula is established.
MSC:
11P05 Waring’s problem and variants 11P55 Applications of the Hardy-Littlewood method
Full Text: | {"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": 0.8893243074417114, "perplexity": 253.592821700558}, "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/1610704835901.90/warc/CC-MAIN-20210128040619-20210128070619-00402.warc.gz"} |
http://mathhelpforum.com/discrete-math/190105-simplifying-sets-using-properties.html | # Math Help - Simplifying Sets using Properties
1. ## Simplifying Sets using Properties
First of all, n = intersection because the actual symbol would work for me
Code:
(A U B U C U D) n (A U B U C) n (A U B) n C
I need to simplify the set expression given above. I think the answer is (A U B) n C? Maybe even A n C?
Maybe the above is correct but I want to know how to show the stages of simplifying it. For example, by commutativity, associativity and idempotence.
Any help would be great, thanks.
2. ## Re: Simplifying Sets using Properties
Originally Posted by richtea9
First of all, n = intersection because the actual symbol would work for me
Code:
(A U B U C U D) n (A U B U C) n (A U B) n C
I need to simplify the set expression given above. I think the answer is (A U B) n C? Maybe even A n C?
This is always true: $(X\cup Y)\cap X=X$.
So $(A\cup B\cup C)\cap (A\cup B)=(A\cup B)$.
Can you finish?
BTW: Simple LaTeX code,
[TEX](A\cup B\cup C)\cap (A\cup B)[/TEX]
gives $(A\cup B\cup C)\cap (A\cup B)$
3. ## Re: Simplifying Sets using Properties
Originally Posted by Plato
This is always true: $(X\cup Y)\cap X=X$.
So $(A\cup B\cup C)\cap (A\cup B)=(A\cup B)$.
Can you finish?
BTW: Simple LaTeX code,
[TEX](A\cup B\cup C)\cap (A\cup B)[/TEX]
gives $(A\cup B\cup C)\cap (A\cup B)$
Hi
Thanks for the reply, am I right by thinking its just A? (Looking at the first expression you gave.) If so I don't see how this would show the same as the set expression I gave on a venn diagram.
4. ## Re: Simplifying Sets using Properties
Originally Posted by richtea9
am I right by thinking its just A? (Looking at the first expression you gave.) If so I don't see how this would show the same as the set expression I gave on a venn diagram.
The answer is $(A\cup B)\cap C$. | {"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": 7, "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": 0.974540114402771, "perplexity": 1922.976674018748}, "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-2015-35/segments/1440644064538.25/warc/CC-MAIN-20150827025424-00124-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/how-many-electrons-on-each-level-type.287076/ | # How many electrons on each level type
1. Jan 24, 2009
### transgalactic
i know s=2 p=6
what d=??
2. Jan 24, 2009
### Ygggdrasil
Each class of orbital (s, p, d, f, g, etc.) is described by a quantum number l, known as the angular quantum number. For each class of orbital, there are 2l+1 types of orbitals. For example, for the s orbital (l = 0), there is only one type of s orbital. For p orbitals (l = 1), there are three types of p orbitals (px, py, and pz). Since each orbital can hold two electrons, you can see why the s orbitals can hold only two electrons, while the p orbitals can hold six.
Based on this information, you should be able to see why the d orbitals can hold ten electrons and the f orbitals can hold 14.
3. Jan 24, 2009
### transgalactic
thanks
Similar Discussions: How many electrons on each level type | {"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": 0.921879768371582, "perplexity": 1084.5087391611216}, "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-2017-17/segments/1492917119995.14/warc/CC-MAIN-20170423031159-00269-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://boardgames.stackexchange.com/questions/22681/3-3-invasion-into-4-4-6-4 | # 3-3 invasion into 4-4,6-4
In josekipedia, they state that this exchange is a mistake
See http://www.josekipedia.com/#path:pdttpfqcpcqdqepbobrbpaqaqb for the full sequence they argue with.
But, I think that their argument is wrong! Why would white not follow making this shape, which is alive?
It is true that there are perhaps better possibilities for white's second move (in terms of points, not life & death), but the followup of the "mistake" and argument they present doesn't seem right for the above reason. Or did I miss something?
EDIT: actually, this shape works in the following joseki: http://josekipedia.com/#path:qettodqcpcqdperb
• Given your proposed S18, black would just play Q18 and while white is alive, she'd be confined completely and black's outside would have no weaknesses at all (and end in sente, of course). Compare to joseki, in which white gets more points and black gets a weakness (cut) on the outside. – mafu Jan 25 '15 at 4:30
Maybe I'm missing something, but I don't think that shape is alive.
$$B$$ ----------------------------
$$| . . . . . . . . . . . . . .$$ | . O 7 1 . . . . . . . . . .
$$| 4 . O X . . . . . . . . . .$$ | . 5 O X . . . . . , . . . .
$$| 6 2 X . . . . . . . . . . .$$ | . 3 . X . . . . . . . . . .
$$| . . . . . . . . . . . . . .$$ | . . . . . . . . . . . . . .
7 is atari, so White loses the eye in the corner.
$$B$$ ----------------------------
$$| . . . . . . . . . . . . . .$$ | . O . 1 . . . . . . . . . .
$$| 5 . O X . . . . . . . . . .$$ | . 4 O X . . . . . , . . . .
$$| . 2 X . . . . . . . . . . .$$ | . 3 . X . . . . . . . . . .
$$| . . . . . . . . . . . . . .$$ | . . . . . . . . . . . . . .
$$B$$ ----------------------------
$$| . 5 . . . . . . . . . . . .$$ | 4 O . 1 . . . . . . . . . .
$$| 3 . O X . . . . . . . . . .$$ | . 2 O X . . . . . , . . . .
$$| . . X . . . . . . . . . . .$$ | . . . X . . . . . . . . . .
$$| . . . . . . . . . . . . . .$$ | . . . . . . . . . . . . . .
And again.
Update: Turns out I didn't show the trickiest variation. When White plays 4, 5 is hard to find, but it's often a tesuji in this kind of shape.
$$B$$ ----------------------------
$$| . . . . . . . . . . . . . .$$ | . O . 1 . . . . . . . . . .
$$| . . O X . . . . . . . . . .$$ | 4 . O X . . . . . , . . . .
$$| . 2 X . . . . . . . . . . .$$ | 5 3 . X . . . . . . . . . .
$$| . . . . . . . . . . . . . .$$ | . . . . . . . . . . . . . .
I think White is still dead. If he goes this way, 4 is the tesuji:
$$W$$ ----------------------------
$$| . 3 2 . . . . . . . . . . .$$ | 4 O 1 X . . . . . . . . . .
$$| 5 . O X . . . . . . . . . .$$ | O 6 O X . . . . . , . . . .
$$| . O X . . . . . . . . . . .$$ | X X . X . . . . . . . . . .
$$| . . . . . . . . . . . . . .$$ | . . . . . . . . . . . . . .
Here he gets a false eye:
$$W$$ ----------------------------
$$| . 4 . . . . . . . . . . . .$$ | 1 O . X . . . . . . . . . .
$$| . . O X . . . . . . . . . .$$ | O 3 O X . . . . . , . . . .
$$| 2 O X . . . . . . . . . . .$$ | X X . X . . . . . . . . . .
$$| . . . . . . . . . . . . . .$$ | . . . . . . . . . . . . . .
This way, the throw in still destroys the lower eye.
$$W$$ ----------------------------
$$| . 3 . . . . . . . . . . . .$$ | . O 2 X . . . . . . . . . .
$$| 1 . O X . . . . . . . . . .$$ | O 4 O X . . . . . , . . . .
$$| . O X . . . . . . . . . . .$$ | X X . X . . . . . . . . . .
$$| . . . . . . . . . . . . . .$$ | . . . . . . . . . . . . . .
• OK, good! I was learned this shape by some 7-8k who claimed it to be alive. Thanks for making it cledar! BTW, what rank are you? – Tomas Jan 27 '15 at 19:55
• I looked into white 2 at 1-4 and couldn't find anything but death there as well. – OmnipotentEntity Feb 2 '15 at 5:01
• I'm between 1-2d AGA. – TimK Feb 2 '15 at 20:02
• Tim, what if in the 1st variant of yours white plays 4 one space below, i.e. at 1-4? I cannot find a way how black could kill this. – Tomas Jun 19 '15 at 13:09
White hanes at S15, and when Black counter hanes at S14, White plays the key move, Q18. After two hane and connection moves, White lives with T16, ending the sequence.
Black should have haned at S 18 instead of playing 1 (R15), and then connected at R18.That forces White to crawl along the second line to S14, just to live. Black plays R13, and has White running along the "line of defeat."
The corner sequence is "double sente" for either Black or White, and more to the point, relates to the life or death of White. | {"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": 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": 0.8975213170051575, "perplexity": 274.96232185938874}, "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/1573496668787.19/warc/CC-MAIN-20191117041351-20191117065351-00028.warc.gz"} |
https://www.earthdoc.org/content/papers/10.3997/2214-4609.201403091 | 1887
Abstract
The problem considered is a 3D Earth Model property prediction by well (and seismic) data. It is shown, that multimodal fuzzy presentation of the parameter (porosity) value in each elementary volume is quite adequate, when we deal with geological medium. After the region of parameter values is subdivided into n categories (n is no more than 20), the membership function f is represented by n number of discrete values f1, f2 ... fn. Presentation, when parameter value in each elementary volume is specified by a set of f1, f2 ... fn, is called a fuzzy model. <br><br>Values f1, f2 ... fn are treated as evidences in favor of different parameter categories. They can be obtained using the next three procedures: (1) fuzzy transformation of well data; (2) fuzzy transformation of seismic attributes; (3) fuzzy evidence summation by Dempster’s rule. Analytical comparison with geostatistics is done in two point example. As shown, a fuzzy model uncertainty is dependent on data contrast. A case study with 93 wells is also considered. Thanks to economic uncertainty distribution, fuzzy model realizations look like a set of deterministic models.<br>
/content/papers/10.3997/2214-4609.201403091
2007-09-10
2021-04-15 | {"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": 0.8114725947380066, "perplexity": 1780.8551468011854}, "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-2021-17/segments/1618038084765.46/warc/CC-MAIN-20210415095505-20210415125505-00225.warc.gz"} |
http://math.stackexchange.com/questions/70196/whats-the-distance-between-a-ray-and-a-sphere?answertab=votes | # What's the distance between a ray and a sphere?
I don't quite understand the shapeDistance function when dealing with spheres. What does it mean to calculate the distance between a ray and a sphere? and what is the formula?
c = the center of a sphere
r = radius of a sphere
ori = origin of a ray
dir = direction of ray
. = dot product
p = ori + (((c - ori) . dir) * dir)
d_cp = magnitude(p - c)
d = magnitude(p - ori) - sqrt(r^2 - d_cp^2)
If (d_cp >= r) OR (((p - ori) . dir) <= 0) Then
return Nothing
Else
return d
-
The page you link to doesn't mention "the distance between a ray and a sphere". It talks about "the distance to it along a given ray", and that's also what the code you quote calculates; that is, the distance from the origin of the ray along the ray up to the first point where the ray intersects the sphere. Here are the steps of the calculation, in mathematical notation and with comments:
$$\vec p=\vec o + (((\vec c -\vec o)\cdot \vec n)\vec n$$
$\vec c - \vec o$ is the vector from the origin $\vec o$ to the center $\vec c$ of the sphere, and $\vec n$ is a unit vector along the direction of the ray. Forming the dot product of a vector with a unit vector and multiplying by the unit vector yields the projection of the vector onto the direction of the unit vector. So $(((\vec c -\vec o)\cdot \vec n)\vec n$ is the projection of the vector from the origin to the centre onto the ray, and thus $\vec p$ is the point at which the ray is perpendicular to the direction to the centre.
$$d_{\mathrm cp}=|\vec p - \vec c|$$
This is the distance from $\vec p$ to the centre $\vec c$, i.e. the perpendicular distance from the centre of the sphere to the ray.
$$d=|\vec p - \vec o|-\sqrt{r^2-d_{\mathrm cp}^2}$$
This calculation is somewhat wasteful, since the first term is
\begin{align} |\vec p - \vec o| &=|(\vec o + (((\vec c -\vec o)\cdot \vec n)\vec n) - \vec o| \\ &=|((\vec c -\vec o)\cdot \vec n)\vec n| \\ &=(\vec c -\vec o)\cdot \vec n\;, \end{align}
which had already been calculated in the first step. The first term is the distance from the origin of the ray to $\vec p$. If $\vec p$ is outside the sphere, that is, if its distance from the centre of the sphere is greater than $r$, the argument of the square root in the second term is negative; in this case $d$ won't be used since the first condition in the if statement won't be fulfilled, and the value Nothing will be returned to indicate that the ray doesn't intersect the sphere. If, on the other hand, $\vec p$ is inside the sphere, that is, if its distance from the centre of the sphere is less than $r$, then the square root in the second term calculates the distance on the ray from the intersection with the sphere to $\vec p$; this is an applciation of the Pythagoraen theorem; the desired distance is one leg of a right triangle, the distance from $\vec p$ to the centre is the other, and the sphere's radius is the hypotenuse. This distance from the intersection with the sphere to $\vec p$ is then subtracted from the distance from the origin to $\vec p$, to obtain the distance from the origin to the intersection. Finally, the second condition in the if statement,
$$(\vec p - \vec o)\cdot \vec n\le 0\;,$$
checks whether $\vec p$ lies on the ray (as opposed to the line containing the ray) by checking whether it lies in the positive direction from the origin along the unit vector. If so, the distance to the intersection is returned; if not, the ray (as opposed to the line) doesn't intersect the sphere, and Nothing is returned.
Note that this only works if the origin is outside the sphere; in this case $\vec p$ and the intersection are always on the same ray from the origin. If the origin lies inside the sphere, the intersection could be in the direction away from $\vec p$.
- | {"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9378890991210938, "perplexity": 219.41441094447092}, "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-2015-27/segments/1435375096706.9/warc/CC-MAIN-20150627031816-00275-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://brahma.tcs.tifr.res.in/events/finite-time-analysis-q-learning-linear-function-approximation?mini=2021-05 | # Finite-Time Analysis of Q-Learning with Linear Function Approximation
## Speaker:
Siva Theja Maguluri
## Affiliation:
Georgia Tech
United States of America
## Time:
Tuesday, 23 July 2019, 14:30 to 15:30
## Venue:
• A-201 (STCS Seminar Room)
## Organisers:
Abstract: We consider the model-free reinforcement learning problem and study the popular Q-learning algorithm with linear function approximation for finding the optimal policy. We provide a finite-time error bounds for the convergence of Q-learning with linear function approximation under an assumption on the sampling policy. Unlike some prior work in the literature, we do not need to make the unnatural assumption that the samples are i.i.d. (since they are Markovian), and do not require an additional projection step in the algorithm. To show this result, we first consider a more general nonlinear stochastic approximation algorithm under Markovian noise, and derive a finite-time bound on the mean-square error, which we believe is of independent interest. The key idea of our proof is to use Lyapunov drift arguments and exploit the geometric mixing property of the underlying Markov chain.
Bio: Siva Theja Maguluri is an Assistant Professor in the School of Industrial and Systems Engineering at Georgia Tech. Before that, he was a Research Staff Member in the Mathematical Sciences Department at IBM T. J. Watson Research Center. He obtained his Ph.D. and MS in ECE as well as MS in Applied Math from UIUC, and B.Tech in Electrical Engineering from IIT Madras. His research interests are broadly in Applied Probability, Optimization and Reinforcement Learning, and include Scheduling, Resource Allocation and Revenue Optimization in a variety of systems including Data Centers, Cloud Computing, Wireless Networks, Block Chains, Ride hailing systems etc. He is a co-recipient of the “Best Publication in Applied Probability” award, presented by INFORMS Applied probability society every two years. | {"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": 0.8822343349456787, "perplexity": 655.585606198746}, "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/1620243991553.4/warc/CC-MAIN-20210510235021-20210511025021-00082.warc.gz"} |
http://openstudy.com/updates/55d4897ee4b09ad8b74c3973 | • 1018
The magnitude of the velocity of a projectile when it is at its maximum height above ground level is 19 m/s. (a) What is the magnitude of the velocity of the projectile 1.7 s before it achieves its maximum height? (b) What is the magnitude of the velocity of the projectile 1.7 s after it achieves its maximum height? If we take x = 0 and y = 0 to be at the point of maximum height and positive x to be in the direction of the velocity there, what are the (c) x coordinate and (d) y coordinate of the projectile 1.7 s before it reaches its maximum height and the (e) x coordinate and (f) y coordinate
Mathematics
Looking for something else?
Not the answer you are looking for? Search for more explanations. | {"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": 0.85335773229599, "perplexity": 153.30182814689093}, "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-2017-13/segments/1490218189903.83/warc/CC-MAIN-20170322212949-00525-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://link.springer.com/chapter/10.1007/978-1-4612-3698-6_11 | # The Exact Hausdorff Measure of Brownian Multiple Points, II
• Jean-François Le Gall
Chapter
Part of the Progress in Probability book series (PRPR, volume 17)
## Abstract
The purpose of this note is to sharpen a result established in [5] concerning the Hausdorff measure of the set of multiple points of a d-dimensiohal Brownian motion. Let X = (Xt, t ≥ 0) denote a standard two-dimensional Brownian motion and, for every integer k ≥ 1, let Mk, denote the set of k-multiple points of X (a point z is said to be k-multiple if there exist k distinct times $$0 \leqslant t_1 < \ldots < t_k$$ such that $$X_{t_1 } = \ldots = X_{t_k } = z$$). A canonical measure on Mk, can be constructed as follows. Set: The intersection local time of X with itself, at the order k, is the Radon measure on J k formally defined by:
$${\alpha _{\text{k}}}({\text{d}}{{\text{t}}_1}...{\text{d}}{{\text{t}}_{\text{k}}}) = {\delta _{(0)}}({{\text{X}}_{{{\text{t}}_1}}} - {{\text{X}}_{{{\text{t}}_2}}})...{\delta _{(0)}}({{\text{X}}_{{{\text{t}}_{{\text{k}} - 1}}}} - {{\text{X}}_{{{\text{t}}_{\text{k}}}}})\;{\text{d}}{{\text{t}}_1}...{\text{d}}{{\text{t}}_{\text{k}}}$$
where δ(0) denotes the Dirac measure at 0 in ℝ2. A precise definition of α k may be found in Rosen [7] or Dynkin [2]. As the previous formal definition suggests, the measure α k is supported on the set $$\left\{ {({{\text{t}}_{{1}}},...,{{\text{t}}_{\text{k}}});{{\text{X}}_{{{{\text{t}}_{{1}}}}}} = ... = {{\text{X}}_{{{{\text{t}}_{\text{k}}}}}}} \right\}$$ of k-multiple times. Let ℓk denote the image measure of αk by the mapping $$({{\text{t}}_{{1}}},...,{{\text{t}}_{\text{k}}}) \to {{\text{X}}_{{{{\text{t}}_{{1}}}}}}$$. It follows that ℓk is supported on Mk. Notice that ℓ is not a Radon measure, but is a countable sum of finite measures.
## Preview
### References
1. [1]
Ciesielski,Z. Taylor,S.J.: First passage times and sojourn times for Brownian motion in space and the exact Hausdorff measure of the sample path. Trans. Amer. Math. Soc. 103, 434–450 (1962)
2. [2]
Dynkin,E.B.: Random fields associated with multiple points of the Brownian motion. J. Funct. Anal. 62, 397–434 (1985)Google Scholar
3. [3]
Federer,H.: Geometric Measure Theory. Springer-Verlag, Berlin Heidelberg New-York 1969.
4. [4]
Le Gall, J.F.: Le comportement du mouvement brownien entre les deux instants où il passe par un point double. J. Funct. Anal. 71, 246–262 (1987)
5. [5]
Le Gall,J.F.: The exact Hausdorff measure of Brownian multiple points. Seminar on Stochastic Processes 1986, 107–137. Birkhäuser Boston 1987.Google Scholar
6. [6]
Perkins,E.A.: The exact Hausdorff measure of the level sets of Brownian motion. Z. Wahrsch. verw. Gebiete 58, 373–388 (1981)
7. [7]
Rosen,J.: Self-intersections of random fields. Ann. Probab. 12, 108–119 (1984)
8. [8]
Taylor,S.J.: The exact Hausdorff measure of the sample path for planar Brownian motion. Proc. Camb. Philos. Soc. 60,253–258 (1964) | {"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": 2, "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": 0.9932315349578857, "perplexity": 1003.6076977485292}, "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-2018-09/segments/1518891812959.48/warc/CC-MAIN-20180220125836-20180220145836-00371.warc.gz"} |
http://mathhelpforum.com/new-users/215293-hi-having-problems-complex-number-multiplication.html | # Thread: Hi, having problems with a complex number multiplication
1. ## Hi, having problems with a complex number multiplication
Hi everyone, I'm Joanne and currently studying to become a maths teacher (1 year in to studying).
I'm having problems trying to work out the below multiplication.
I've worked out that the polar form of (2-2i)^12 is ( sorry about the ?'s)
But I am unsure of what to do next.
Do I work out the polar form of , then multiply them together, or am I doing this wrong to begin with?
Thanks
2. ## Re: Hi, having problems with a complex number multiplication
Originally Posted by Jojo55
Hi everyone, I'm Joanne and currently studying to become a maths teacher (1 year in to studying).
I'm having problems trying to work out the below multiplication.
I've worked out that the polar form of (2-2i)^12 is ( sorry about the ?'s)
$(2-2i)=2\sqrt 2 \exp \left( {\frac{{ -i \pi }}{4}} \right)$.
thus $(2-2i)^{12}=\left(2\sqrt 2\right)^{12} \exp \left( -3i\pi \right)$.
But $\left(2\sqrt 2\right)^{12}=2^{18}$.
Can you finish?
3. ## Re: Hi, having problems with a complex number multiplication
Are you familiar with the Binomial Theorem?
4. ## Re: Hi, having problems with a complex number multiplication
Originally Posted by jpritch422
Are you familiar with the Binomial Theorem?
What does that have to do with the OP?
5. ## Re: Hi, having problems with a complex number multiplication
Originally Posted by Plato
What does that have to do with the OP?
I think jpritch is suggesting that the problem be done without DeMoivre/Polar form.
I disagree with that suggestion, but I'm fairly certain that's where he's going with that.
6. ## Re: Hi, having problems with a complex number multiplication
Originally Posted by Henderson
I think jpritch is suggesting that the problem be done without DeMoivre/Polar form.
I disagree with that suggestion, but I'm fairly certain that's where he's going with that.
Actually, I understood what the post meant. I want to see why jpritch422 wanted to use that.
The irony is that DeMoivre's Rule is used for many proofs about binomial coefficients.
7. ## Re: Hi, having problems with a complex number multiplication
Originally Posted by Plato
$(2-2i)=2\sqrt 2 \exp \left( {\frac{{ -i \pi }}{4}} \right)$.
thus $(2-2i)^{12}=\left(2\sqrt 2\right)^{12} \exp \left( -3i\pi \right)$.
But $\left(2\sqrt 2\right)^{12}=2^{18}$.
Can you finish?
Sorry for the late reply. I managed to solve to get the answer of -1
Thanks for the help on this | {"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": 6, "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": 0.8162732720375061, "perplexity": 1588.6441292903069}, "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-2016-36/segments/1471983077957.84/warc/CC-MAIN-20160823201117-00043-ip-10-153-172-175.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/3796845/ideal-on-mathbbn-with-certain-property | # Ideal on $\mathbb{N}$ with certain property
Let $$\mathcal{I}$$ be an ideal on $$\mathbb{N}$$ that contains all finite sets and at least one infinite set. Define a filter
$$\mathcal{F}:=\{D\subseteq\mathbb{N}\mid \forall A\in\mathcal{I},A\cap D^{c}\text{ is finite, or equivalently} A\subseteq^{*}D\}$$.
$$\mathcal{F}$$ contains the cofinite filter, and it seems that if $$\mathcal{I}$$ is prime then $$\mathcal{F}$$ does not contain anything else. Does the converse hold? In other words, let us say an ideal has property P if the corresponding filter is the cofinite filter. Is P the same as being prime? Or is there simple characterization of P?
Someone suggested that this is same as asking for $$\mathcal{E}\subseteq(\mathcal{P}_{coinf}(\mathbb{N}),\subseteq^{*})$$ which is unbounded under $$\subseteq^{*}$$ and generates a proper non-prime ideal. I found that I know nothing about this poset. What is its cofinal type? What is its relation with other posets such as $$(\mathbb{N}^{\mathbb{N}},<^{*})$$?
Background: I was thinking if we define a topology on $$\mathbb{N}\cup\{\infty\}$$ by requiring certain sequences converge to $$\infty$$, will there be more (and which) sequences converging to $$\infty$$ than we expected. Also see this question.
• Ideal with your property P are called tall ideals. They've been extensively studied. An early source is Adrian Mathias's paper "Happy families"; a fairly recent survey of this and lots of other properties of ideals is Michael Hrusak's "Combinatorics of filters and ideals". Aug 20, 2020 at 2:22
• @AndreasBlass Thanks so much. Actually I noticed the second paper but didn't even scan through it carefully...Could you make this an answer so that I can accept it? Aug 20, 2020 at 2:41
Given $$P_1,P_2$$ non-principal prime ideals on $$\mathbb{N}$$ with $$P_1\neq P_2$$, let $$\mathcal{I}= P_1\cap P_2$$. Then $$\mathcal{I}$$ is an ideal containing all finite sets, but not prime (as there must be some $$A\subseteq \mathbb{N}$$ with $$A\notin P_1, A^c\notin P_2$$).
However $$\mathcal{I}$$ satisfies property P: Given any $$D$$ not cofinite, we may partition $$D^c$$ into $$4$$ infinite pieces: $$D_{11,}D_{12},D_{21},D_{22}$$. Then $$D_{i1}\cup D_{i2}\in P_1$$ for some $$i$$ and $$D_{1j}\cup D_{2j}\in P_2$$ for some $$j$$. Thus $$D_{ij}\in \mathcal{I}$$ and $$D_{ij}\cap D^c=D_{ij}$$ is infinite.
• $\mathcal{I}$ is required to contain all finite sets. Aug 20, 2020 at 0:07
• @1830rbc03 Thanks, good point - I have fixed this by replacing elements of $\mathbb{N}$ with non-principal ultrafilters on $\mathbb{N}$.The same argument works, but now $\mathcal{I}$ contains all finite sets.
Let $$X$$ be a maximal almost disjoint family of subsets of $$\mathbb{N}$$, and let $$\mathcal{I}$$ be the ideal generated by $$X$$. Then $$\mathcal{F}$$ will be the cofinite filter: if $$D\in\mathcal{F}$$ then $$D^c$$ is almost disjoint from every element of $$X$$, and thus must be finite by maximality of $$X$$. However, $$\mathcal{I}$$ is not prime. For instance, if you take two disjoint countably infinite subfamilies $$Y,Z\subset X$$, then by a simple diagonalization argument you can construct $$A\subset\mathbb{N}$$ which almost contains every element of $$Y$$ and is almost disjoint from every element of $$Z$$. Then $$A\not\in\mathcal{I}$$ since every element of $$\mathcal{I}$$ has infinite intersection with only finitely many elements of $$X$$, and $$A^c\not\in\mathcal{I}$$ for the same reason. | {"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": 48, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9717358350753784, "perplexity": 156.431670739254}, "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/1664030337516.13/warc/CC-MAIN-20221004152839-20221004182839-00490.warc.gz"} |
https://iitutor.com/index-notation/ | # Index Notation
A convenient way to write a product of $\textit{identical factors}$ is to use $\textbf{exponential}$ or $\textbf{index notation}$.
Rather than writing $5 \times 5 \times 5 \times 5$, we can write this product as $5^4$.
The small $4$ is called the $\textbf{exponent}$ or $\textbf{index}$, and the $5$ is called the $\textbf{base}$.
If $n$ is a positive integer, then $a^n$ is the product of $n$ factors of $a$.
$$\large a^n=\overbrace {a \times a \times a \times \cdots \times a}^{n}$$
We say that $a$ is the $\textbf{base}$, and $n$ is the $\textbf{exponent}$ or $\textbf{index}$.
The following table shows the first four powers of $2$.
$$\large \begin{array}{|c|c|c|c|} \hline \textit{Natural number} & \textit{Factorised form} & \textit{Exponent form} & \textit{Spoken form} \\ \hline 2 & 2 & 2^1 & \text{two} \\ \hline 4 & 2 \times 2 & 2^2 & \text{two squared} \\ \hline 8 & 2 \times 2 \times 2 & 2^3 & \text{two cubed} \\ \hline 16 & 2 \times 2 \times 2 \times 2 & 2^4 & \text{two to the fourth} \\ \hline \end{array}$$
Any non-zero number raised to the power zero is equal to $1$.
$$\large a^0 = 1, a \ne 0$$
$0^0$ is undefined.
$\textbf{Negative Bases}$
$\begin{eqnarray} (-1)^1 &=& -1 \\ (-1)^2 &=& -1 \times -1 = 1 \\ (-1)^3 &=& -1 \times -1 \times -1 = -1 \\ (-1)^4 &=& -1 \times -1 \times -1 \times -1 = 1 \\ (-2)^1 &=& -2 \\ (-2)^2 &=& -2 \times -2 = 4 \\ (-2)^3 &=& -2 \times -2 \times -2 = -8 \\ (-2)^4 &=& -2 \times -2 \times -2 \times -2 = 16 \\ \end{eqnarray}$
From the patterns above, we can see that:
$\textbf{negative}$ base raised to an $\textbf{even}$ exponent is $\textbf{positive}$.
$\textbf{negative}$ base raised to an $\textbf{odd}$ exponent is $\textbf{negative}$.
## Example 1
List the first four powers of 3.
$3^1 = 3$
$3^2 = 3 \times 3 = 9$
$3^3 = 3 \times 3 \times 3 = 27$
$3^4 = 3 \times 3 \times 2 \times 3 = 81$
## Example 2
Simplify $(-1)^{17}$.
$(-1)^{17} = -1$
## Example 3
Simplify $(-1)^{18}$.
$(-1)^{18} = 1$
## Example 4
Simplify $5^0$.
$5^0 = 1$ | {"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": 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": 0.9969161152839661, "perplexity": 315.44040346986174}, "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-2023-14/segments/1679296949644.27/warc/CC-MAIN-20230331144941-20230331174941-00700.warc.gz"} |
https://nemeth.aphtech.org/lesson11.15 | - Use 6 Dot Entry Switch to UEB Math Tutorial
# Lesson 11.15: Type Faces
## Explanation
A variety of fonts may be used to represent mathematics in print. To represent a modification in the print font, the following braille indicators are placed before the letter, number, or symbol that is to be shown in the modified type-form. Type-form indicators have no print equivalent.
boldface type indicator, dots four five six
italic type indicator, dots four six
script indicator, dot four
sanserif indicator, dots six, four six
Dots four six and dots four five six may have different meanings when used in braille mathematics, depending upon placement of these symbols with respect to other symbols, and context.
## Guidelines for using type-form indicators
Material displayed in alternative fonts does not always require the use of type-form indicators. If a particular font is consistently used throughout a text for letters, numerals, or other mathematical symbols, then the font is considered to be regular, not modified, and the type-form indicators are not used. For example, when variables in formulas are uniformly printed in an alternative font, such as boldface or italics, throughout a text, type-form indicators are not used. However, when an alternative font is used to convey a distinct mathematical meaning, then type-form indicators must be used. An example would be when different fonts are used to distinguish between two or more different meanings of the same letter, numeral, or symbol, or because the alternative font has mathematical significance.
## Type-form indicators used with numerals
The numeric indicator is placed between a type-form indicator and a numeral or decimal point. The type-form indicator precedes the numeral being modified. When a sign of operation appears before a numeral and it is not in a different font, the type-form indicator appears after the sign and before the numeric indicator. If the sign of operation and the numeral are being modified in the same font, then the type-form indicator precedes the sign of operation.
## Influence of type-form indicators with numerals
The type-form indicator's influence extends to the space following a numeral, or to a different type-form indicator representing another change in font.
## Compound expressions
A compound expression contains a numeral joined to a word or to an abbreviation by a hyphen. The following rules apply when brailling a compound expression.
Rule 1: If an entire expression is in a non-regular type-form, the appropriate type-form indicator must be used before the numeral; its influence extends through the entire compound expression.
Rule 2: If a numeral in an alternative font is followed by a hyphen and a word or abbreviation in regular font, the hyphen must be preceded by the literary termination sign, dot six, three, to indicate the change in font.
If a numeral is in a regular font and there is a change after the hyphen to an alternative font, place the appropriate type-form indicator between the hyphen and the following symbol.
If a numeral in an alternative font is followed by a word or abbreviation in a different alternative font after the hyphen, the change occurs after the hyphen. Appropriate type-form indicators must be used before each part of the expression.
The use of the numeric indicator within a number indicates a change of font. When numerals or expressions contain some digits that are in an alternative form of type, or when there is more than one form of type within an expression, the appropriate type-form indicator and the numeric indicator must precede each change in type. When an alternative font, such as boldface, italics, script, or sanserif, is changed to a regular font within an expression, the numeric indicator precedes the numerals which are displayed in regular font.
The sanserif type-form indicator might be used, infrequently, to make a distinction between two letters. This distinction has mathematical significance; thus, the type-form indicator must be used.
## Guidelines for using type-form indicators with letters
The type-form indicator must always be followed by an alphabetic indicator. An English letter is preceded by the English letter indicator, dots five six. If a letter is capitalized, the capitalization indicator is brailled after the letter indicator.
The script type-form indicator is used to denote letters which represent, for example, the set of real numbers, the set of rational numbers, or the set of integers. The Nemeth code uses the script indicator to denote these characters.
The influence of a type-form indicator extends only to the letter that immediately follows it. In a sequence of unspaced letters, a type-form indicator must precede each letter that is displayed in an alternative font.
## Type-form indicators with labeled mathematical statements, words, and phrases
The following type-form indicators are used for labeled mathematical statements, words, and phrases.
• opening boldface type-form indicator, dots six, three, four five six
• closing boldface type-form indicator, dots four five six, six, three
• opening italic type-form indicator, dots six, three, four six
• closing italic type-form indicator, dots four six, six, three
• all capitals, dots six, six
These modifications make it possible to change the font of words and phrases by enclosing them within a set of opening and closing type-form indicators. A blank cell is inserted after the opening indicator and before the closing indicator.
previous - next (This lesson contains no exercises) | {"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": 0.8028526306152344, "perplexity": 3650.848104583596}, "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/1600400245109.69/warc/CC-MAIN-20200926200523-20200926230523-00469.warc.gz"} |
https://www.physicsforums.com/threads/projectiles-initial-speed.321543/ | # Projectile's initial speed?
1. Jun 23, 2009
A projectile launched vertically from the surface of the Moon rises to an altitude of 270 km.
What was the projectile's initial speed in m/s?
okay so I keep getting this answer wrong but Im pretty sure Im doing it correctly.....
this is what I am doing:
2*6.67*7.35*270/3.02 and then all of that multiplied by 10^2 and then that answer square rooted and I get 936.27 m/s .....but that is not correct...HELP! what am I missing??
2. Jun 23, 2009
### CompuChip
Can you maybe explain where you got all those numbers from?
What is 6.67, what is 7.35, what is 3.02, where do the 2 and 10^2 come from and why square-root it?
i.e. post your formula and identify the variables. Now it's just a string of numbers without physical meaning.
3. Jun 23, 2009
Vi- square root 2GMmH/(1.74*10^6)2
7.35 *10^22 kg is the mass of the moon Mm
g= 6/67*10^-11
height reached by the projectile h= 260km = 270* 10^3
I plugged all of that in to the equation above and got the answer previously stated but it is wrong.
4. Jun 23, 2009
sorry Vintial = **
5. Jun 23, 2009
### MattRSK
Sounds like a kinematic equation problem to me.
#### Attached Files:
• ###### qxnyfl.gif
File size:
1.6 KB
Views:
11
6. Jun 23, 2009
### rl.bhat
Apply the conservation of energy theorem. When the projectile reaches the maximum height, the KE of projectile is equal to the change in PE.
PE on the surface of the earth = GMm/R. When it reaches the maximum height, the PE = GMm/(R+h)
Similar Discussions: Projectile's initial speed? | {"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": 0.9167433977127075, "perplexity": 2376.605680887883}, "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/1510934808935.79/warc/CC-MAIN-20171124195442-20171124215442-00618.warc.gz"} |
http://clay6.com/qa/4895/if-a-begin-1-2-3-end-and-b-begin-2-1-4-end-verify-that- | # If $A = \begin{bmatrix} -1 \\ 2 \\ 3 \end{bmatrix} \: and \: B = \begin{bmatrix} -2 & -1 & -4 \end{bmatrix}$verify that $$(AB)^T=B^TA^T$$
Toolbox:
• If A_{i,j} be a matrix m*n matrix , then the matrix obtained by interchanging the rows and column of A is called as transpose of A.
• If A is an m-by-n matrix and B is an n-by-p matrix, then their matrix product AB is the m-by-p matrix whose entries are given by dot product of the corresponding row of A and the corresponding column of B: $\begin{bmatrix}AB\end{bmatrix}_{i,j} = A_{i,1}B_{1,j} + A_{i,2}B_{2,j} + A_{i,3}B_{3,j} ... A_{i,n}B_{n,j}$
Step1:
Given
A=$\begin{bmatrix}-1\\2\\3\end{bmatrix}\$
B=$\begin{bmatrix}-2 & -1& -4\end{bmatrix}$
AB=$\begin{bmatrix}-1\\2\\3\end{bmatrix}\begin{bmatrix}-2 & -1& -4\end{bmatrix}$
$\;\;\;=\begin{bmatrix}(-1)(-2) &-1(-1) & -1(-4)\\2(-2) & 2(-1)&2(-4)\\3(-2) &3(-1) &3(-4)\end{bmatrix}$
$\;\;\;=\begin{bmatrix}2 &1 & 4\\-4 & -2&-8\\-6 &-3 &-12\end{bmatrix}$
Transpose of a matrix can be obtained by changing the rows and the column.
$(AB)'=\begin{bmatrix}2 & -4 & 6\\1 & -2 & -3\\4 & -8 & -12\end{bmatrix}$-------(1)
Step2:
$B'=\begin{bmatrix}-2\\-1\\-4\end{bmatrix}$
$A'=\begin{bmatrix}-1&2&3\end{bmatrix}$
$B'A'=\begin{bmatrix}-2\\-1\\-4\end{bmatrix}\begin{bmatrix}-1&2&3\end{bmatrix}$
$B'A'=\begin{bmatrix}-2(-1)&-2(2)&(3)(-2)\\-1(-1) & -1(2) & -1(3)\\-4(-1)& -4(2) &-4(3)\end{bmatrix}$
$\;\;\;\;\;=\begin{bmatrix}2 & -4 & 6\\1 & -2 & -3\\4 & -8 & -12\end{bmatrix}$-------(2)
Hence equ(1)=equ(2)
$(AB)^T=B^TA^T$ | {"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": 0.9663060307502747, "perplexity": 398.5334275572717}, "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-2017-47/segments/1510934806388.64/warc/CC-MAIN-20171121132158-20171121152158-00276.warc.gz"} |
http://mathhelpforum.com/discrete-math/23249-probability-eventual-return-random-walk.html | # Thread: Probability of Eventual Return in Random Walk
1. ## Probability of Eventual Return in Random Walk
The probability of eventual return is given by:
$f_{2} + f_{4} + f_{6} + ...+ f_{\infty} = 1$
where $f_{n}$ = Probability of return at Time Period n.
Note that returns must be in even numbers, as a +1 needs -1 to cancel each other out.
Ok, I understand the theory, but I cannot find a suitable proof.
Edit: Proof found. Problem solved.
$f_{n}$ is given by $f_{2n}= u_{2n-2} - u_{2n}$ where $u_{2n}={2n \choose n}2^{-2n}$
So, $f_{2} + f_{4} + f_{6} + ...+ f_{\infty} = u_{0} - u_{2} + u_{2} - u_{4} + ..... = u_{0} = 1$
Still, I'll be very grateful if anyone can explain this Theorem:
$f_{2n}= u_{2n-2} - u_{2n}$ | {"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": 7, "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": 0.9200865030288696, "perplexity": 947.9991396657898}, "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/1487501171632.91/warc/CC-MAIN-20170219104611-00407-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://leimao.github.io/blog/Quantum-Entanglement/ | ### Lei Mao
Machine Learning, Artificial Intelligence, Computer Science.
# Quantum Entanglement
### Introduction
Quantum entanglement has attracted some attention from the public that this mysterious process might be useful for lots of future applications, such as quantum computing and teleportation.
In this blog post, I would like to discuss quantum entanglement superficially using mathematics.
### Quantum Entanglement
Assume we have two independent quantum systems $Q$ and $Q^{\prime}$, represented respectively by the vector spaces $\mathbb{V}$ and $\mathbb{V}^{\prime}$. The quantum system obtained by merging $Q$ and $Q^{\prime}$ will have the tensor product $\mathbb{V} \otimes \mathbb{V}^{\prime}$ as a state space.
If $\mathbb{V} \in \mathbb{C}^n$ with basic states $| x_0 \rangle, | x_1 \rangle, \cdots, | x_{n-1} \rangle$ and $\mathbb{V}^{\prime} \in \mathbb{C}^m$ with basic states $| y_0 \rangle, | y_1 \rangle, \cdots, | y_{m-1} \rangle$, the tensor product state space would be $\mathbb{V} \otimes \mathbb{V}^{\prime} \in \mathbb{C}^{n \times m}$ with basic states $| x_i \rangle \otimes | y_j \rangle$ for $0 \leq i \leq n-1$ and $0 \leq j \leq m-1$. Here, the basic state $| x_i \rangle \otimes | y_j \rangle$ means the first quantum systems $Q$ is in the state $| x_i \rangle$ and the second quantum system $Q^{\prime}$ is in the state $| y_j \rangle$.
More independent quantum systems $Q_0, Q_1, \cdots, Q_{k-1}$ could be merged together and the state space of the merged quantum system would be $\mathbb{V}_0 \otimes \mathbb{V}_1 \otimes \cdots\ \otimes \mathbb{V}_{k-1}$.
The system state of the merged quantum system from two independent quantum systems $Q$ and $Q^{\prime}$ could be expressed using basic states.
$| \psi \rangle = \sum_{i=0}^{n-1} \sum_{j=0}^{m-1} c_{i,j} | x_i \rangle \otimes | y_j \rangle$
The probability of the system being in the state $| x_i \rangle \otimes | y_j \rangle$ after measurement, according to quantum mechanics, would be
$P(| x_i \rangle \otimes | y_j \rangle) = \frac{|c_{i,j}|^2}{\sum_{s=0}^{n-1} \sum_{t=0}^{m-1} |c_{s,t}|^2 }$
If $c_{i,j} = 0$, then $P(| x_i \rangle \otimes | y_j \rangle) = 0$
We further consider the merged system whose $n = 2$ and $m = 2$.
$| \psi \rangle = c_{0,0} | x_0 \rangle \otimes | y_0 \rangle + c_{0,1} | x_0 \rangle \otimes | y_1 \rangle + c_{1,0} | x_1 \rangle \otimes | y_0 \rangle + c_{1,1} | x_1 \rangle \otimes | y_1 \rangle$
Suppose $c_{0,0} = 0$, $c_{0,1} = 1$, $c_{1,0} = 1$, $c_{1,1} = 0$, i.e.,
$| \psi \rangle = | x_0 \rangle \otimes | y_1 \rangle + | x_1 \rangle \otimes | y_0 \rangle$
When we measure the state of the first quantum system $Q$, there are two possible outcomes, either the system was in the state $| x_0 \rangle$ or $| x_1 \rangle$. Similarly, when we measure the state of the first quantum system $Q^{\prime}$, there are two possible outcomes, either the system was in the state $| y_0 \rangle$ or $| y_1 \rangle$.
If we saw the system state of $Q$ is $| x_0 \rangle$, the system state of $Q^{\prime}$ must be $| y_1 \rangle$ even without measurement. Similarly, if we saw the system state of $Q$ is $| x_1 \rangle$, the system state of $Q^{\prime}$ must be $| y_0 \rangle$ even without measurement. This is because the probability of observing $| x_0 \rangle \otimes | y_0 \rangle$ or $| x_1 \rangle \otimes | y_1 \rangle$ is 0.
This is called quantum entanglement.
In this case, no matter how far the two subsystems in the entangled system is, we know the system states of both subsystems by just observing one single subsystem.
The quantum entanglement is simultaneous and instantaneous. If we describe this process using “velocity”, we would find the “velocity” is infinitely large, faster than light speed, which is the fastest “velocity” we are currently using for information transmission. However, we prefer not to describe this process using velocity, since it is not a conventional physical “travel” process.
Formally, if a merged system state $| \psi \rangle$ can be broken into the tensor product of states from the constituent subsystems, i.e.,
\begin{align} | \psi \rangle &= \sum_{i=0}^{n-1} \sum_{j=0}^{m-1} c_{i,j} | x_i \rangle \otimes | y_j \rangle \\ &= \Big(\sum_{i=0}^{n-1} c_{x, i} | x_i \rangle \Big) \otimes \Big(\sum_{j=0}^{m-1} c_{y, j} | y_j \rangle \Big) \\ &= \sum_{i=0}^{n-1} \sum_{j=0}^{m-1} c_{x, i} c_{y, j} | x_i \rangle \otimes | y_j \rangle \\ \end{align}
We call this merged system state $| \psi \rangle$ separable state. Otherwise we call it entangled state, as we would find there is no solution to solve the above equation for an entangled state.
### Conclusions
Some people who did not study physics sometimes described the process of quantum entanglement as if there is a causation relationship, which means that it is the state of one subsystem affecting the other subsystem. However, from our mathematics analysis, we know this causation relationship does not exist. | {"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9978739619255066, "perplexity": 310.8163971435064}, "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/1596439738727.76/warc/CC-MAIN-20200811025355-20200811055355-00347.warc.gz"} |
https://expeditionweather.info/blog/how-to-read-a-meteogram | Blog
Infos & Tutorials on how to read our Weatherdata
Weather charts & diagrams for alpinists and climbers
A meteogram is probably the most complex piece of information you're going to encounter on this site or in our forecasts. Meteograms require some help (therefore this section) and training to understand, but they deliver a lot of meteorological information in just one picture.
Basically, a meteogram is the vertical profile of the atmosphere for a given point and it's development over the forecast-time.
Informations about the point (2) and the starting time ("init")(1) of the forecast is given in the title above the chart.The vertical axis (3) represents the atmospheric altitude. It's labeled "Pressure", because as usual in meteorology, the altitude is given in pressure levels. That's why the labels on vertical axis seem a bit strange and are decreasing from bottom to top. However, you can find the altitudes in meters above sea level as well, they are the fine solid grey lines and numbered labels in the chart itself. On the horizontal axis (4) is the timeline. It begins with the timestamp mentioned in the title and goes on for 2-7 days, depending on the model you're looking at. The times marked in the timelines refer always to the UTC-Timezone. For use in the Himalayas, you typically have to substract 5-6 hours from UTC.
Then, there is a second, smaller plot-field (6) below the main chart (5). Again, the horizontal axis (4)is the timeline. The vertical axis represents precipitaion (7). The scale is fixed and ranges from 0 to 5 mm/h. Green bars in this field (8) indicate, that the model predicts precipitation for your mountain at the given time. The main plot itself is stuffed with solid and dotted lines, coloured areas and windbarbs. Let's go through them step by step.
The most eye-catching feature are probably the coloured, green areas. Basically, these areas represent humidity. When the relative humidity of an air parcel is above 70 %, it gets a greenish colour in the meteogram. If you take a closer look, you can see that there are three diffrent shades of green. A very light shade of green (1) indicates a relative humidity between 70 and 80 %, the somewhat darker geen (2) areas mean 80 - 90 % and the strong, brighter green (3) indicates relative humidity above 90 %. You can take the green areas as a quite good indicator for clouds. If relative humidity remains below 70 %, cloud formation is quite unlikely, so you can expect clear air and good visibilty in the white areas (4). Between 70 and 90 %, the cloud cover increases steadily. Cloud coverage is usually measured in octas and descibes the fraction of thy sky which is covered by clouds (4/8 means that 50 % of the sky is cloud-covered), and from 70 to 90 % you can expect 2 to 6/8 cloud coverage. Above 90 % means usually cloud coverage from 7 to 8/8 which translates into mostly overcast/dull or heavy fog.
Next feature are the red lines. They are temperature-isothermes (5). The 0-degree-isotherme (freezing level)(6) is slightly thicker than the others and they appear in an interval of 10 degrees. The interpretation of these lines is quite straight-forward, if they are climbing up, tempeatures are on the rise and if they sink, it's getting cooler. The warmest isotherme in the plot is always the lowest and it forms usually a wave-like pattern, due to the diurnal heating in layers close to the ground.
The grey lines (7) we already mentioned earlier, it's the altitude in meters above sea level (or in scientifc terms: geopotential height) corresponding to the pressure levels on the vertical axis. You can expect these lines to remain more or less horizontal, unless there's a significant high- or low-pressure-system coming in.
Then, there are the wind barbs (8). Basically, they are easy to read: they show the forecasted wind speed at a given altitude, at a given time. As often, the devil lies in the detail. First, let's take a look at how to interpret a windbarb. A windbarb can be seen as an arrow. It has a "pointy end" and an end with some barbs attached. While the "pointy end" is fixed to the altitude and time the information is valid for, the direction of the -abstracted- arrow represents the wind direction and the numbers, length and form of the barbs indicates the wind speed. The barbs can be long bars, short bars and triangles. A long bar corresponds to 10 knots, a short bar to 5 knots and a triangle to 50 knots. The predicted wind speed is then the sum of all the bars and triangles on a specific windbarb, e.g. 2 long and 1 short bars mean 25 kt; a triangle, 1 long and 1 short bar mean 65kt. Note that the direction of the "arrow" represents the direction of the wind, so if a barb is pointed vertically down, it means north-wind, if it's horizontal with the pointy end to the left, it's east-wind. In our meteograms, the windbarbs appear in an interval of 9 hours.
And finally, there are the dashed, blue or purple lines (1) which appear sometimes more, sometimes less pronounced in the meteograms. These lines represent vertical updraft velocity of an airparcel. In areas (or more precise: times and altitudes) where you find these lines, you can expect raising airmasses. Often, this raising airmasses go along with cloud formation and precipitation, except the lifted airmass is very dry - which often happens in arid or semi-arid climates. Usually, the combination of humidity (green fields) and lifting air (dashed lines) leads to precipitation signals in the lower plot (2). Vertical updraft velocity (or physically speaking: omega) can occur due to thermal heating in the lower layers (convection) or can have synoptic forcings such as troughs or frontal systems, sometimes it's also a combination of synoptic and convective forcing. In general, the stronger and widespread the omega is, the worse the weather likely will be. | {"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": 0.8494899868965149, "perplexity": 1339.82036167425}, "config": {"markdown_headings": false, "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-2019-04/segments/1547584334618.80/warc/CC-MAIN-20190123151455-20190123173455-00120.warc.gz"} |
https://physics.stackexchange.com/questions/43410/does-the-volume-of-a-thermodynamic-system-always-have-to-change-for-it-to-do-wor | # Does the volume of a thermodynamic system always have to change for it to do work?
Does the volume of a thermodynamic system always have to change for it to do work? If yes,could you explain why? And if no, could you provide the example of a system, where it is not neccesary.
It depends on how you define work. Work is sometimes defined as pressure times a change in volume ($p\Delta V$, or $\int p dV$ if the pressure is not constant), which is equivalent to force times distance, as John Rennie defines it in his answer. In this case it's necessary for the volume to change, purely from the definition.
However, another way to define work is something along the lines of "a change in energy that is not due to the transfer of heat or thermal radiation." In this case it is not necessary for the volume to change. A particular example where the word "work" is used in this way is in electronics, when one calculates the work involved in charging a capacitor as $\int V dQ$, where $V$ here is the voltage rather than the volume, and Q is the charge. In this case neither the volume of the capacitor nor the battery charging it changes, but work is said to be done because the internal energy of the capacitor has changed reversibly, without a transfer of heat.
To put it more mathematically, consider the fundamental equation of thermodynamics: $$d U = T dS - pdV + \sum_i \mu_i dN_i + \dots$$ (where the "$\dots$" can include many other optional terms, including a $V dQ$ one for a capacitor). The right-hand side of this equation represents all the ways in which a system's energy can change. The first term ($T dS$) represents a transfer of heat. Some people define "work" as just the second term ($-p dV$), whereas others define it as the sum of all the other terms apart from the first one. Thus, with the second definition you can have work that's associated with a change in volume, but you can also have work that's associated with a change in the chemical composition, charge, or any other conserved quantity.
• The additional terms require either interchange of molecules with some other system (or non equilibrium for the to be not zero. Nov 4, 2012 at 10:42
• (sorry) for them to be not zero. So adding/subtracting species while in thermal equlibrium (or not) is another way of doing work on the system. Nov 4, 2012 at 10:52
• @Eduardo this is true. Note that this can in principle be done without a change in volume, however. For example, you could remove molecules of some species $A$ while adding molecules of some other species $B$ that happen to occupy the same volume as $A$ molecules, but have a different chemical potential. Then you've done $\mu d N$ work without a change in volume. Nov 4, 2012 at 11:22
• Yes, I only wanted to add some to your correct answer (I gave the point). Note too, that electric currents, macrowave oven and any other energy transfer with no volume change or species interchange, enters the equation in the Tds term and thus, is considered heat transfer. Nov 4, 2012 at 11:49
• Kelvin would have loved a microwave oven as a present... Nov 4, 2012 at 11:51
Mechanical work $dW_\mathrm{mech} = -pdV$ is due to a volume change for a pressure $p$. But other kind of thermodynamic works exist:
• Chemical work $dW_\mathrm{chem} = \mu dN$ involves change in composition $N$ for a chemical potential $\mu$.
• Electrical work $dW_\mathrm{elect} = -E dP$ involves change in electric dipole moment $P$ in presence of an electric field $E$.
• Magnetic work $dW_\mathrm{mag} = -B dM$ involves change in magnetic dipole moment $M$ in presence of a magnetic field $B$.
• Etcetera.
Yes, because work is force times distance moved. It's not immediately obvious that this means work can only be done if the volume changes, but have a look at How much work is needed to compress a certain volume of gas? where I went into this in some detail. If any parts of this aren't clear comment here and I can go into them in more detail.
• Nathanial and Juanrga make good points. I must admit that I was only thinking about mechanical work. Nov 4, 2012 at 14:06
• John Rennie then can I say, "If a thermodynamic system consists of charges, and has an electric/magnetic field, then it is not necessary for the volume to change. But in the absence of charge, by the very definition of work (PdV), then yes, the volume MUST change." Nov 4, 2012 at 14:52
• @AdwaitKumar: possibly. The trouble is that if you accept a broad definition of work then it's hard to be sure you've excluded all the possibilities except for volume change. Nov 4, 2012 at 15:06 | {"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": 0.9050149321556091, "perplexity": 242.22518995294573}, "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-2022-27/segments/1656104240553.67/warc/CC-MAIN-20220703104037-20220703134037-00593.warc.gz"} |
https://wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2019&number=2605 | WIAS Preprint No. 2605, (2019)
# Generalized Scharfetter--Gummel schemes for electro-thermal transport in degenerate semiconductors using the Kelvin formula for the Seebeck coefficient
Authors
• Kantner, Markus
ORCID: 0000-0003-4576-3135
2010 Mathematics Subject Classification
• 35K57 35Q79 65N08 80A20
Keywords
• Finite volume Scharfetter--Gummel method, semiconductor device simulation, electro-thermal transport, non-isothermal drift-diffusion system, degenerate semiconductors, Fermi--Dirac statistics, Seebeck coefficient
DOI
10.20347/WIAS.PREPRINT.2605
Abstract
Many challenges faced in today's semiconductor devices are related to self-heating phenomena. The optimization of device designs can be assisted by numerical simulations using the non-isothermal drift-diffusion system, where the magnitude of the thermoelectric cross effects is controlled by the Seebeck coefficient. We show that the model equations take a remarkably simple form when assuming the so-called Kelvin formula for the Seebeck coefficient. The corresponding heat generation rate involves exactly the three classically known self-heating effects, namely Joule, recombination and Thomson--Peltier heating, without any further (transient) contributions. Moreover, the thermal driving force in the electrical current density expressions can be entirely absorbed in the (nonlinear) diffusion coefficient via a generalized Einstein relation. The efficient numerical simulation relies on an accurate and robust discretization technique for the fluxes (finite volume Scharfetter--Gummel method), which allows to cope with the typically stiff solutions of the semiconductor device equations. We derive two non-isothermal generalizations of the Scharfetter--Gummel scheme for degenerate semiconductors (Fermi--Dirac statistics) obeying the Kelvin formula. The approaches differ in the treatment of degeneration effects: The first is based on an approximation of the discrete generalized Einstein relation implying a specifically modified thermal voltage, whereas the second scheme follows the conventionally used approach employing a modified electric field. We present a detailed analysis and comparison of both schemes, indicating a superior performance of the modified thermal voltage scheme.
Appeared in | {"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": 0.9055793285369873, "perplexity": 2247.5319651519176}, "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/1669446710926.23/warc/CC-MAIN-20221203075717-20221203105717-00212.warc.gz"} |
http://mathhelpforum.com/trigonometry/169355-easy-angle-thing.html | # Math Help - easy angle thing
1. ## easy angle thing
ok so i have this list of questions like this one:
find the least positive value of B for which sin(A-B)=cos(A+B)
using translation, odd, periodic properties, etc.
the problem is i totally forgot how to work these out! i know there is a simple method to work this out without staring continually at the sin and cos graphs, i just need a little reminder. thanks
2. Originally Posted by furor celtica
ok so i have this list of questions like this one:
find the least positive value of B for which sin(A-B)=cos(A+B)
using translation, odd, periodic properties, etc.
the problem is i totally forgot how to work these out! i know there is a simple method to work this out without staring continually at the sin and cos graphs, i just need a little reminder. thanks
Dear furor celtica,
$\sin(A-B)=\cos(A+B)$
$\cos\left(\frac{\pi}{2}-(A-B)\right)=\cos(A+B)$
$\frac{\pi}{2}-(A-B)=2n\pi\pm(A+B)\mbox{ where }n\in Z$
$A=\frac{\pi}{4}-n\pi\mbox{ or }B=n\pi-\frac{\pi}{4}\mbox{ where }n\in Z$
Therefore the smallest positive value for B would be,
$n=1\Rightarrow{B=\pi-\dfrac{\pi}{4}=\dfrac{3\pi}{4}}$
Hope you understood.
3. umm i got most of it but at the level i'm at the n is not really appropriate, could you kinda simplify that?
4. Originally Posted by furor celtica
umm i got most of it but at the level i'm at the n is not really appropriate, could you kinda simplify that?
Dear furor celtica,
Do you mean that you do not understand how we got the n into the equation? | {"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": 5, "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": 0.9050926566123962, "perplexity": 842.7545163918886}, "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-2015-11/segments/1424936462762.87/warc/CC-MAIN-20150226074102-00239-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://maths.anu.edu.au/news-events/events/time-dependent-schrodinger-equation-microlocal-analysis-and-fredholm-theory-0 | The PDE & Analysis seminar covers topics in PDE and analysis.
schedule Date & time
Date/time
7 Oct 2022 | 12 - 1pm
person Speaker
Speakers
Andrew Hassell, ANU
next_week Event series
Contact
contact_support Contact
Contact name
Rong Wang
Contact email
Description
Abstract:
We consider at the time-dependent Schrodinger operator $P$ on $\mathbb{R}^{n+1}$, with fixed metric and potential that are flat/trivial outside a compact set in spacetime. Considering first the inhomogeneous equation
$Pu = f,$
in spacetime, we find Hilbert spaces of functions $P : X \to Y$ between which $P$ maps invertibly. This is done by proving microlocal propagation estimates, following Melrose and Vasy, near the characteristic variety of $P$, and assembling them into a global Fredholm estimate. Using this, we can solve the “final state problem”, which is to find a global solution to $Pu = 0$ where $u(x,t)$ has the asymptotic
$u(x, t) \sim t^{-n/2} e^{i|x|^2/4t} f_+(x/t), \quad t \to +\infty,$
for a prescribed function $f_+$.
Our framework leads to some precise results in linear scattering, which seem to be new. More significantly it suggests an entirely new approach to nonlinear scattering. I’ll mention a small data nonlinear scattering result which can be proved using this approach.
Location
Seminar Room 1.33
Hanna Neumann Building 145 | {"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": 0.8050287365913391, "perplexity": 1550.8867855863148}, "config": {"markdown_headings": false, "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-2023-14/segments/1679296950247.65/warc/CC-MAIN-20230401191131-20230401221131-00235.warc.gz"} |
https://direct.mit.edu/coli/article/37/1/231/2088/Grammar-Factorization-by-Tree-Decomposition | We describe the application of the graph-theoretic property known as treewidth to the problem of finding efficient parsing algorithms. This method, similar to the junction tree algorithm used in graphical models for machine learning, allows automatic discovery of efficient algorithms such as the O(n4) algorithm for bilexical grammars of Eisner and Satta. We examine the complexity of applying this method to parsing algorithms for general Linear Context-Free Rewriting Systems. We show that any polynomial-time algorithm for this problem would imply an improved approximation algorithm for the well-studied treewidth problem on general graphs.
This content is only available as a PDF.
## Author notes
*
Computer Science Department, University of Rochester, Rochester NY 14627. E-mail: [email protected]. | {"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": 0.9684628844261169, "perplexity": 886.0003308870992}, "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-2022-27/segments/1656103626162.35/warc/CC-MAIN-20220629084939-20220629114939-00142.warc.gz"} |
http://topdrawer.aamt.edu.au/Fractions/Big-ideas/Fractions-as-operators | Home > Fractions > Big ideas > Fractions as operators
# Fractions as operators
A fraction can be used to 'operate' on a quantity. In other words, the fraction acts as a function.
For example, to find $$\frac{3}{4}$$ of something, several combinations of operations could occur. You could:
• divide by 4, then multiply by 3
• multiply by 3, then divide by 4.
The outcome would be a smaller quantity than the original quantity. For example, $$\frac{3}{4} \times$$ 12 = 9.
When an improper fraction is the operator, the outcome will be a larger quantity than the original. For example, $$\frac{7}{4} \times$$ 12 = 21.
## Using the operator model
Using arrays to model fractions as operators provides a bridge between modelling the operations with groups and with area diagrams. | {"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": 0.923345148563385, "perplexity": 1121.3373221056017}, "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/1510934805708.41/warc/CC-MAIN-20171119172232-20171119192232-00675.warc.gz"} |
http://www-old.newton.ac.uk/programmes/ALT/seminars/2009032610001.html | Skip to content
# ALT
## Seminar
### Affine Gelfand-Tsetlin bases and affine Laumon spaces
Finkelberg, M (State, Moscow)
Thursday 26 March 2009, 10:00-11:00
Seminar Room 1, Newton Institute
#### Abstract
Affine Laumon space P is the moduli space of parabolic sheaves of rank n on the product of 2 projective lines. The natural correspondences give rise to the action of affine Yangian of sl(n) on the equivariant cohomology of P. The resulting module M is isomorphic to the universal Verma module over the affine gl(n). The classes of torus fixed points form a basis of M which is an affine analogue of the classical Gelfand-Tsetlin basis. The Chern classes of tautological vector bundles on P can be computed in terms of the affine Yangian action on M. This is a joint work with B.Feigin, A.Negut, and L.Rybnikov.
#### Video
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
Back to top ∧ | {"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": 0.8455777168273926, "perplexity": 1023.8208044567846}, "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-2015-35/segments/1440645359523.89/warc/CC-MAIN-20150827031559-00074-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://www.bradford-delong.com/2019/11/alan-m-turing-1950-_computing-machinery-and-intelligencehttpswwwscottaaronsoncompapersphilospdf_-the-vi.html | Alan M. Turing (1950): Computing Machinery and Intelligence: "The view that machines cannot give rise to surprises is due, I believe, to a fallacy to which philosophers and mathematicians are particularly subject. This is the assumption that as soon as a fact is presented to a mind all consequences of that fact spring into the mind simultaneously with it. It is a very useful assumption under many circumstances, but one too easily forgets that it is false...
#noted #2019-11-22 | {"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": 0.9680836796760559, "perplexity": 1240.153210183442}, "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-2022-05/segments/1642320301063.81/warc/CC-MAIN-20220118213028-20220119003028-00467.warc.gz"} |
https://cdsweb.cern.ch/collection/CMS%20Papers?ln=es | # CMS Papers
2016-07-29
17:26
Measurement of the ZZ production cross section and $\mathrm{ Z } \to {\ell^+\ell^-\ell^{\prime+}\ell^{\prime-}}$ branching fraction in pp collisions at $\sqrt{s} =$ 13 TeV Four-lepton production in proton-proton collisions, ${\mathrm{ p }\mathrm{ p }} \to \left(\mathrm{Z} / \gamma^*\right)\left(\mathrm{Z}/ \gamma^*\right) \to {\ell^+\ell^-\ell^{\prime+}\ell^{\prime-}}$, where $\ell, \ell' = \mathrm{ e }$ or $\mu$, is studied at a center-of-mass energy of 13 TeV with the CMS detector at the LHC. [...] CERN-EP-2016-174 ; CMS-SMP-16-001-003. - 2016. Additional information for the analysis - CMS AuthorList - Fulltext
2016-07-24
00:48
Measurement of electroweak production of a W boson and two forward jets in proton-proton collisions at $\sqrt{s} =$ 8 TeV / CMS Collaboration A measurement is presented of the cross section for the electroweak production of a W boson in association with two jets in proton-proton collisions at a center-of-mass energy of 8 TeV. [...] CERN-EP-2016-093 ; CMS-SMP-13-012-003 ; arXiv:1607.06975. - 2016. Additional information for the analysis - CMS AuthorList - Full text - Full text
2016-07-23
22:19
Measurement of the WZ production cross section in pp collisions at $\sqrt{s} =$ 13 TeV / CMS Collaboration The WZ production cross section in proton-proton collisions at $\sqrt{s} =$ 13 TeV is measured with the CMS experiment at the LHC using a data sample corresponding to an integrated luminosity of 2.3 fb$^{-1}$. [...] CERN-EP-2016-169 ; CMS-SMP-16-002-003 ; arXiv:1607.06943. - 2016. Additional information for the analysis - CMS AuthorList - Full text - Full text
2016-07-20
20:21
Search for dark matter in proton-proton collisions at 8 TeV with missing transverse momentum and vector boson tagged jets / CMS Collaboration A search is presented for an excess of events with large missing transverse momentum in association with at least one highly energetic jet, in a data sample of proton-proton collisions at a centre-of-mass energy of 8 TeV. [...] CERN-EP-2016-178 ; CMS-EXO-12-055-003 ; arXiv:1607.05764. - 2016. Additional information for the analysis - CMS AuthorList - Full text - Full text
2016-07-13
13:36
Search for lepton flavour violating decays of the Higgs boson to $\mathrm{ e }\tau$ and $\mathrm{ e }\mu$ in proton-proton collisions at $\sqrt{s}=$ 8 TeV / CMS Collaboration A direct search for lepton flavour violating decays of the Higgs boson (H) in the $\mathrm{ H } \to \mathrm{ e } \tau$ and $\mathrm{ H } \to \mathrm{ e } \mu$ channels is described. [...] CERN-EP-2016-112 ; CMS-HIG-14-040-003 ; arXiv:1607.03561. - 2016. Additional information for the analysis - CMS AuthorList - Full text - Full text
2016-07-13
12:58
Jet energy scale and resolution in the CMS experiment in pp collisions at 8 TeV / CMS Collaboration Improved jet energy scale corrections, based on a data sample corresponding to an integrated luminosity of 19.7 fb$^{-1}$ collected by the CMS experiment in proton-proton collisions at a center-of-mass energy of 8 TeV, are presented. [...] CERN-PH-EP-2015-305 ; CMS-JME-13-004-003 ; arXiv:1607.03663. - 2016. Additional information for the analysis - CMS AuthorList - Full text - Full text
2016-07-10
11:11
Observation of the decay $\mathrm{B}^{+} \to \psi ( 2 \mathrm{S} ) \phi ( 1020 ) \mathrm{ K }^{+}$ in pp collisions at $\sqrt{s} =$ 8 TeV / CMS Collaboration The decay $\mathrm{B}^{+} \to \psi( 2 \mathrm{S} ) \phi(1020) \mathrm{ K }^{+}$ is observed for the first time using data collected from pp collisions at $\sqrt{s} =$ 8 TeV by the CMS experiment at the LHC, corresponding to an integrated luminosity of 19.6 fb$^{-1}$. [...] arXiv:1607.02638 ; CERN-EP-2016-161 ; CMS-BPH-13-009. - 2016. - 28 p. Preprint - Full text
2016-07-05
08:37
Measurement of the differential cross sections for top quark pair production as a function of kinematic event variables in pp collisions at $\sqrt{s}$ = 7 and 8 TeV / CMS Collaboration Measurements are reported of the normalized differential cross sections for top quark pair production with respect to four kinematic event variables: the missing transverse energy; the scalar sum of the jet transverse momentum (pT); the scalar sum of the pT of all objects in the event; and the pT of leptonically decaying W bosons from top quark decays. [...] arXiv:1607.00837 ; CMS-TOP-12-042 ; CERN-EP-2016-139. - 2016. - 40 p. Preprint - Full text
2016-07-04
18:32
Search for new physics in final states with two opposite-sign, same-flavor leptons, jets, and missing transverse momentum in pp collisions at $\sqrt{s}=$ 13 TeV / CMS Collaboration A search is presented for physics beyond the standard model in final states with two opposite-sign, same-flavor leptons, jets, and missing transverse momentum. [...] arXiv:1607.00915 ; CERN-EP-2016-132 ; CMS-SUS-15-011. - 2016. - 36 p. Preprint - Full text
2016-06-27
17:30
Searches for $R$-parity-violating supersymmetry in pp collisions at $\sqrt{s}=$ 8 TeV in final states with 0-4 leptons / CMS Collaboration Results are presented from searches for $R$-parity-violating supersymmetry in events produced in pp collisions at $\sqrt{s}=$ 8 TeV at the LHC. [...] CERN-EP-2016-097 ; CMS-SUS-14-003-003 ; arXiv:1606.08076. - 2016. Additional information for the analysis - CMS AuthorList - Full text - Full text | {"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": 0.9991048574447632, "perplexity": 1651.140971856039}, "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/1469258943366.87/warc/CC-MAIN-20160723072903-00198-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://support.google.com/docs/answer/9366440?hl=en&ref_topic=3105395 | # IMSECH function
The IMSECH function returns the hyperbolic secant of the given complex number. For example, a given complex number "x+yi" returns "sech(x+yi)."
## Parts of an IMSECH function
`IMSECH(number) `
Part Description Notes `number` The complex number for which you want the hyperbolic secant. This can be either the result of the COMPLEX function, a real number interpreted as a complex number with imaginary parts equal to 0, or a string in the format “x+yi” where x and y are numeric.
## Sample formulas
`IMSECH(COMPLEX(4,6))`
`IMSECH(4)`
`IMSECH("2+3i")`
## Notes
The `IMSECH` function returns an error if the given number isn't a valid complex number.
## Examples
A B 1 Formula Result 2 `=IMSECH(COMPLEX(4,1))` 0.0198041304666168-0.0308224192896954i 3 `=IMSECH(3.5)` 0.0603397441201677 4 `=IMSECH("3+2i")` -0.0416749644111443-0.0906111371962376i
## Related functions
IMCOSH: The IMCOSH function returns the hyperbolic cosine of the given complex number.
IMSECH: The IMSECH function returns the hyperbolic secant of the given complex number.
COMPLEX: The COMPLEX function creates a complex number, given real and imaginary coefficients. | {"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": 0.906046450138092, "perplexity": 1648.0405614932897}, "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/1659882571847.45/warc/CC-MAIN-20220812230927-20220813020927-00436.warc.gz"} |
https://worldwidescience.org/topicpages/h/high-speed+solar+wind.html | #### Sample records for high-speed solar wind
1. Verification of high-speed solar wind stream forecasts using operational solar wind models
DEFF Research Database (Denmark)
Reiss, Martin A.; Temmer, Manuela; Veronig, Astrid M.
2016-01-01
and the background solar wind conditions. We found that both solar wind models are capable of predicting the large-scale features of the observed solar wind speed (root-mean-square error, RMSE ≈100 km/s) but tend to either overestimate (ESWF) or underestimate (WSA) the number of high-speed solar wind streams (threat......High-speed solar wind streams emanating from coronal holes are frequently impinging on the Earth's magnetosphere causing recurrent, medium-level geomagnetic storm activity. Modeling high-speed solar wind streams is thus an essential element of successful space weather forecasting. Here we evaluate...... high-speed stream forecasts made by the empirical solar wind forecast (ESWF) and the semiempirical Wang-Sheeley-Arge (WSA) model based on the in situ plasma measurements from the Advanced Composition Explorer (ACE) spacecraft for the years 2011 to 2014. While the ESWF makes use of an empirical relation...
2. High-speed solar wind flow parameters at 1 AU
International Nuclear Information System (INIS)
Feldman, W.C.; Asbridge, J.R.; Bame, S.J.; Gosling, J.T.
1976-01-01
To develop a set of constraints for theories of solar wind high-speed streams, a detailed study was made of the fastest streams observed at 1 AU during the time period spanning March 1971 through July 1974. Streams were accepted for study only if (1) the maximum speed exceeded 650 km s -1 ; (2) effects of stream-stream dynamical interaction on the flow parameters could be safely separated from the intrinsic characteristics of the high-speed regions; (3) the full width at half maximum (FWHM) of the stream when mapped back to 20 solar radii by using a constant speed approximation was greater than 45degree in Carrington longitude; and (4) there were no obvious solar-activity-induced contaminating effects. Nineteen streams during this time interval satisfied these criteria. Average parameters at 1 AU for those portions of these streams above V=650 km s -1 are given.Not only is it not presently known why electrons are significantly cooler than the protons within high-speed regions, but also observed particle fluxes and convected energy fluxes for speed greater than 650 km s -1 are substantially larger than those values predicted by any of the existing theories of solar wind high-speed streams. More work is therefore needed in refining present solar wind models to see whether suitable modifications and/or combinations of existing theories based on reasonable coronal conditions can accommodate the above high-speed flow parameters
3. Distant Tail Behavior During High Speed Solar Wind Streams and Magnetic Storms
Science.gov (United States)
Ho, C. M.; Tsurutani, B. T.
1997-01-01
We have examined the ISEE 3 distant tail data during three intense magnetic storms and have identified the tail response to high-speed solar wind streams, interplanetary magnetic clouds, and near-Earth storms.
4. (abstract) The Distant Tail Behavior During High Speed Solar Wind Streams and Magnetic Storms
Science.gov (United States)
Ho, C. M.; Tsurutani, B. T.
1996-01-01
We have examined the ISEE-3 distant tail data during three intense magnetic storms and have identified the tail response to high speed solar wind streams, interplanetary magnetic clouds, and near-Earth storms.
5. The Distant Tail Behavior During High Speed Solar Wind Streams and Magnetic Storms
Science.gov (United States)
Ho, C. M.; Tsurutani, B. T.
1996-01-01
We have examined the ISEE-3 distant tail data during three intense (Dststorms and have identified the tail response to high speed solar wind streams, interplanetary magnetic clouds, and near-Earth storms. The three storms have a peak Dst ranging from -150 to -220 nT, and occur on Jan. 9, Feb. 4, and Aug. 8, 1993.
6. Geosynchronous Relativistic Electron Events Associated with High-Speed Solar Wind Streams in 2006
Directory of Open Access Journals (Sweden)
Sungeun Lee
2009-12-01
Full Text Available Recurrent enhancements of relativistic electron events at geosynchronous orbit (GREEs were observed in 2006. These GREE enhancements were associated with high-speed solar wind streams coming from the same coronal hole. For the first six months of 2006, the occurrence of GREEs has 27 day periodicity and the GREEs were enhanced with various flux levels. Several factors have been studied to be related to GREEs: (1 High speed stream, (2 Pc5 ULF wave activity, (3 Southward IMF Bz, (4 substorm occurrence, (5 Whistler mode chorus wave, and (6 Dynamic pressure. In this paper, we have examined the effectiveness about those parameters in selected periods.
7. Source of proton anisotrophy in the high-speed solar wind
International Nuclear Information System (INIS)
Schwartz, S.J.; Feldman, W.C.; Gary, S.P.
1981-01-01
Two factors which can contribute to proton anisotropy in the high-speed solar wind are investigated. We present evidence that observed proton Tperpendicular< Tparallel anisotropies are maintained locally by plasma instabilities driven by proton and helium beams. The transfer of beam energy to T/sub perpendicular/ by means of these instabilities is shown to be sufficient to account for the aforementioned proton temperature anisotropy
8. The large scale and long term evolution of the solar wind speed distribution and high speed streams
International Nuclear Information System (INIS)
Intriligator, D.S.
1977-01-01
The spatial and temporal evolution of the solar wind speed distribution and of high speed streams in the solar wind are examined. Comparisons of the solar wind streaming speeds measured at Earth, Pioneer 11, and Pioneer 10 indicate that between 1 AU and 6.4 AU the solar wind speed distributions are narrower (i.e. the 95% value minus the 5% value of the solar wind streaming speed is less) at extended heliocentric distances. These observations are consistent with one exchange of momentum in the solar wind between high speed streams and low speed streams as they propagate outward from the Sun. Analyses of solar wind observations at 1 AU from mid 1964 through 1973 confirm the earlier results reported by Intriligator (1974) that there are statistically significant variations in the solar wind in 1968 and 1969, years of solar maximum. High speed stream parameters show that the number of high speed streams in the solar wind in 1968 and 1969 is considerably more than the predicted yearly average, and in 1965 and 1972 less. Histograms of solar wind speed from 1964 through 1973 indicate that in 1968 there was the highest percentage of elevated solar wind speeds and in 1965 and 1972 the lowest. Studies by others also confirm these results although the respective authors did not indicate this fact. The duration of the streams and the histograms for 1973 imply a shifting in the primary stream source. (Auth.)
9. The most intense current sheets in the high-speed solar wind near 1 AU
Science.gov (United States)
Podesta, John J.
2017-03-01
Electric currents in the solar wind plasma are investigated using 92 ms fluxgate magnetometer data acquired in a high-speed stream near 1 AU. The minimum resolvable scale is roughly 0.18 s in the spacecraft frame or, using Taylor's "frozen turbulence" approximation, one proton inertial length di in the plasma frame. A new way of identifying current sheets is developed that utilizes a proxy for the current density J obtained from the derivatives of the three orthogonal components of the observed magnetic field B. The most intense currents are identified as 5σ events, where σ is the standard deviation of the current density. The observed 5σ events are characterized by an average scale size of approximately 3di along the flow direction of the solar wind, a median separation of around 50di or 100di along the flow direction of the solar wind, and a peak current density on the order of 0.5 pA/cm2. The associated current-carrying structures are consistent with current sheets; however, the planar geometry of these structures cannot be confirmed using single-point, single-spacecraft measurements. If Taylor's hypothesis continues to hold for the energetically dominant fluctuations at kinetic scales 1high-speed wind occur at electron scales, although the peak current densities at kinetic and electron scales are predicted to be nearly the same as those found in this study.
10. Internal plasma state of the high speed solar wind at 1 AU
International Nuclear Information System (INIS)
Feldman, W.C.; Abraham--Shrauner, B.; Asbridge, J.R.; Bame, S.J.
1976-01-01
The character of particle velocity distributions in the high speed solar wind is presented. It is found that electron distribution shapes differ from simple bi-Maxwellians in that a hot, strongly beamed, high energy electron component is always present and is observed to move relative to a distinct low energy electron component along the magnetic field direction, B, away from the sun. The velocity difference between hot and cold electron components appears, at times, to be strongly correlated with the local Alfven speed. This correlation suggests that the solar wind heat flux is being limited some of the time in the neighborhood of 1 AU. Proton velocity distributions are also best described in terms of two relatively convecting, unresolved components. The velocity of the lower density proton beam component is generally larger than that of the main component and the temperature of the main component perpendicular to B is typically 2 to 3 times larger than its parallel temperature. Alpha particles as a whole generally move faster than the protons along B and have a temperature which is, on the average, 6 times higher than the temperature of the total proton population. Evidence is presented which supports the idea that the two-component proton structure observed in high speed regions is intimately related to fine scale velocity variations at 1 AU, and hence by inference, to prominent spatial and/or temporal structures present throughout that part of the corona from which the solar wind evolves
11. Cosmic ray nucleonic intensity in low-amplitude days during the passage of high-speed solar wind streams
International Nuclear Information System (INIS)
Agarwal, R.; Mishra, R.K.; Tiwari, S.; or [email protected]
2008-01-01
One of the most striking features of solar wind is its organization into high- and low- speed streams. It is now well established that the passage over the Earth of high-speed solar wind streams leads to geomagnetic disturbances. The high-speed plasma streams are thus a key element in the complex chain of events that link geomagnetic activity to the solar activity and are therefore of great interest to the solar terrestrial physics. Two types of high-speed solar wind streams - coronal-hole-associated (or corotating) and flare-generated - were studied based on magnetic field and solar wind plasma parameters. In the work, the dependence was obtained for cosmic ray (CR) depressions due to high-speed solar wind streams during low-amplitude days. The CR nucleonic intensity data were subjected to the superposed epoch analysis with respect to the start time of high-speed solar wind streams. It was found that streams of both types produce significant deviations in the CR intensity during low-amplitude anisotropic wave train events. At the onset of such streams the CR intensity reaches its minimum during low-amplitude events and then increases statistically. (Authors)
12. The most intense electric currents in turbulent high speed solar wind
Science.gov (United States)
Podesta, J. J.
2017-12-01
Theory and simulations suggest that dissipation of turbulent energy in collisionless astrophysical plasmas occurs most rapidly in spatial regions where the current density is most intense. To advance understanding of plasma heating by turbulent dissipation in the solar corona and solar wind, it is of interest to characterize the properties of plasma regions where the current density takes exceptionally large values and to identify the operative dissipation processes. In the solar wind, the curl of the magnetic field cannot be measured using data from a single spacecraft, however, a suitable proxy for this quantity can be constructed from the spatial derivative of the magnetic field along the flow direction of the plasma. This new approach is used to study the properties of the most intense current carrying structures in a high speed solar wind stream near 1 AU. In this study, based on 11 Hz magnetometer data from the WIND spacecraft, the spatial resolution of the proxy technique is approximately equal to the proton inertial length. Intense current sheets or current carrying structures were identified as events where the magnitude of the current density exceeds μ+5σ, where μ and σ are the mean and standard deviation of the magnitude of the current density (or its proxy), respectively. Statistical studies show (1) the average size of these 5σ events is close to the smallest resolvable scale in the data set, the proton inertial length; (2) the linear distance between neighboring events follows a power law distribution; and (3) the average peak current density of 5σ events is around 1 pA/cm2. The analysis techniques used in these studies have been validated using simulated spacecraft data from three dimensional hybrid simulations which show that results based on the analysis of the proxy are qualitatively and quantitatively similar to results based on the analysis of the true current density.
13. On the Relationship Between High Speed Solar Wind Streams and Radiation Belt Electron Fluxes
Science.gov (United States)
Zheng, Yihua
2011-01-01
Both past and recent research results indicate that solar wind speed has a close connection to radiation belt electron fluxes [e.g., Paulikas and Blake, 1979; Reeves et aI., 2011]: a higher solar wind speed is often associated with a higher level of radiation electron fluxes. But the relationship can be very complex [Reeves et aI., 2011]. The study presented here provides further corroboration of this viewpoint by emphasizing the importance of a global perspective and time history. We find that all the events during years 2010 and 2011 where the >0.8 MeV integral electron flux exceeds 10(exp 5) particles/sq cm/sr/s (pfu) at GEO orbit are associated with the high speed streams (HSS) following the onset of the Stream Interaction Region (SIR), with most of them belonging to the long-lasting Corotating Interaction Region (CIR). Our preliminary results indicate that during HSS events, a maximum speed of 700 km/s and above is a sufficient but not necessary condition for the > 0.8 MeV electron flux to reach 10(exp 5) pfu. But in the exception cases of HSS events where the electron flux level exceeds the 10(exp 5) pfu value but the maximum solar wind speed is less than 700 km/s, a prior impact can be noted either from a CME or a transient SIR within 3-4 days before the arrival of the HSS - stressing the importance of time history. Through superposed epoch analysis and studies providing comparisons with the CME events and the HSS events where the flux level fails to reach the 10(exp 5) pfu, we will present the quantitative assessment of behaviors and relationships of various quantities, such as the time it takes to reach the flux threshold value from the stream interface and its dependence on different physical parameters (e.g., duration of the HSS event, its maximum or average of the solar wind speed, IMF Bz, Kp). The ultimate goal is to apply what is derived to space weather forecasting.
14. High-speed solar wind streams and polar mesosphere winter echoes at Troll, Antarctica
Directory of Open Access Journals (Sweden)
S. Kirkwood
2015-06-01
Full Text Available A small, 54 MHz wind-profiler radar, MARA, was operated at Troll, Antarctica (72° S, 2.5° E, continuously from November 2011 to January 2014, covering two complete Antarctic winters. Despite very low power, MARA observed echoes from heights of 55–80 km (polar mesosphere winter echoes, PMWE on 60% of all winter days (from March to October. This contrasts with previous reports from radars at high northern latitudes, where PWME have been reported only by very high power radars or during rare periods of unusually high electron density at PMWE heights, such as during solar proton events. Analysis shows that PWME at Troll were not related to solar proton events but were often closely related to the arrival of high-speed solar wind streams (HSS at the Earth, with PWME appearing at heights as low as 56 km and persisting for up to 15 days following HSS arrival. This demonstrates that HSS effects penetrate directly to below 60 km height in the polar atmosphere. Using local observations of cosmic-noise absorption (CNA, a theoretical ionization/ion-chemistry model and a statistical model of precipitating energetic electrons associated with HSS, the electron density conditions during the HSS events are estimated. We find that PMWE detectability cannot be explained by these variations in electron density and molecular-ion chemistry alone. PWME become detectable at different thresholds depending on solar illumination and height. In darkness, PWME are detected only when the modelled electron density is above a threshold of about 1000 cm−3, and only above 75 km height, where negative ions are few. In daylight, the electron density threshold falls by at least 2 orders of magnitude and PWME are found primarily below 75 km height, even in conditions when a large proportion of negative ions is expected. There is also a strong dawn–dusk asymmetry with PWME detected very rarely during morning twilight but often during evening twilight. This behaviour cannot be
15. High-speed solar wind streams and polar mesosphere winter echoes at Troll, Antarctica
Energy Technology Data Exchange (ETDEWEB)
Kirkwood, S.; Belova, E. [Swedish Institute of Space Physics, Kiruna (Sweden). Polar Atmospheric Research; Osepian, A. [Polar Geophysical Institute, Murmansk (Russian Federation); Lee, Y.S. [Korea Astronomy and Space Science Institute, Daejeon (Korea, Republic of)
2015-10-01
A small, 54 MHz wind-profiler radar, MARA, was operated at Troll, Antarctica (72 S, 2.5 E), continuously from November 2011 to January 2014, covering two complete Antarctic winters. Despite very low power, MARA observed echoes from heights of 55-80 km (polar mesosphere winter echoes, PMWE) on 60% of all winter days (from March to October). This contrasts with previous reports from radars at high northern latitudes, where PWME have been reported only by very high power radars or during rare periods of unusually high electron density at PMWE heights, such as during solar proton events. Analysis shows that PWME at Troll were not related to solar proton events but were often closely related to the arrival of high-speed solar wind streams (HSS) at the Earth, with PWME appearing at heights as low as 56 km and persisting for up to 15 days following HSS arrival. This demonstrates that HSS effects penetrate directly to below 60 km height in the polar atmosphere. Using local observations of cosmic-noise absorption (CNA), a theoretical ionization/ion-chemistry model and a statistical model of precipitating energetic electrons associated with HSS, the electron density conditions during the HSS events are estimated. We find that PMWE detectability cannot be explained by these variations in electron density and molecular-ion chemistry alone. PWME become detectable at different thresholds depending on solar illumination and height. In darkness, PWME are detected only when the modelled electron density is above a threshold of about 1000 cm{sup -3}, and only above 75 km height, where negative ions are few. In daylight, the electron density threshold falls by at least 2 orders of magnitude and PWME are found primarily below 75 km height, even in conditions when a large proportion of negative ions is expected. There is also a strong dawn-dusk asymmetry with PWME detected very rarely during morning twilight but often during evening twilight. This behaviour cannot be explained if PMWE
16. Influence of coronal mass ejections on parameters of high-speed solar wind: a case study
Science.gov (United States)
Shugay, Yulia; Slemzin, Vladimir; Rodkin, Denis; Yermolaev, Yuri; Veselovsky, Igor
2018-05-01
We investigate the case of disagreement between predicted and observed in-situ parameters of the recurrent high-speed solar wind streams (HSSs) existing for Carrington rotation (CR) 2118 (December 2011) in comparison with CRs 2117 and 2119. The HSSs originated at the Sun from a recurrent polar coronal hole (CH) expanding to mid-latitudes, and its area in the central part of the solar disk increased with the rotation number. This part of the CH was responsible for the equatorial flank of the HSS directed to the Earth. The time and speed of arrival for this part of the HSS to the Earth were predicted by the hierarchical empirical model based on EUV-imaging and the Wang-Sheeley-Arge ENLIL semi-empirical replace model and compared with the parameters measured in-situ by model. The predicted parameters were compared with those measured in-situ. It was found, that for CR 2117 and CR 2119, the predicted HSS speed values agreed with the measured ones within the typical accuracy of ±100 km s-1. During CR 2118, the measured speed was on 217 km s-1 less than the value predicted in accordance with the increased area of the CH. We suppose that at CR 2118, the HSS overtook and interacted with complex ejecta formed from three merged coronal mass ejections (CMEs) with a mean speed about 400 km s-1. According to simulations of the Drag-based model, this complex ejecta might be created by several CMEs starting from the Sun in the period between 25 and 27 December 2011 and arriving to the Earth simultaneously with the HSS. Due to its higher density and magnetic field strength, the complex ejecta became an obstacle for the equatorial flank of the HSS and slowed it down. During CR 2117 and CR 2119, the CMEs appeared before the arrival of the HSSs, so the CMEs did not influence on the HSSs kinematics.
17. Dawn- Dusk Auroral Oval Oscillations Associated with High- Speed Solar Wind
Science.gov (United States)
Liou, Kan; Sibeck, David G.
2018-01-01
We report evidence of global-scale auroral oval oscillations in the millihertz range, using global auroral images acquired from the Ultraviolet Imager on board the decommissioned Polar satellite and concurrent solar wind measurements. On the basis of two events (15 January 1999 and 6 January 2000) studied, it is found that (1) quasi-periodic auroral oval oscillations (approximately 3 megahertz) can occur when solar wind speeds are high at northward or southward interplanetary magnetic field turning, (2) the oscillation amplitudes range from a few to more than 10 degrees in latitudes, (3) the oscillation frequency is the same for each event irrespective of local time and without any azimuthal phase shift (i.e., propagation), (4) the auroral oscillations occur in phase within both the dawn and dusk sectors but 180 degrees out of phase between the dawn and dusk sectors, and (5) no micropulsations on the ground match the auroral oscillation periods. While solar wind conditions favor the growth of the Kelvin-Helmholtz (K-H) instability on the magnetopause as often suggested, the observed wave characteristics are not consistent with predictions for K-H waves. The in-phase and out-of-phase features found in the dawn-dusk auroral oval oscillations suggest that wiggling motions of the magnetotail associated with fast solar winds might be the direct cause of the global-scale millihertz auroral oval oscillations. Plain Language Summary: We utilize global auroral image data to infer the motion of the magnetosphere and show, for the first time, the entire magnetospheric tail can move east-west in harmony like a windsock flapping in wind. The characteristic period of the flapping motion may be a major source of global long-period ULF (Ultra Low Frequency) waves, adding an extra source of the global mode ULF waves.
18. Mini-magnetospheric plasma propulsion (M2P2): High speed propulsion sailing the solar wind
International Nuclear Information System (INIS)
Winglee, Robert; Slough, John; Ziemba, Tim; Goodson, Anthony
2000-01-01
Mini-Magnetospheric Plasma Propulsion (M2P2) seeks the creation of a magnetic wall or bubble (i.e. a magnetosphere) that will intercept the supersonic solar wind which is moving at 300-800 km/s. In so doing, a force of about 1 N will be exerted on the spacecraft by the spacecraft while only requiring a few mN of force to sustain the mini-magnetosphere. Equivalently, the incident solar wind power is about 1 MW while about 1 kW electrical power is required to sustain the system, with about 0.25-0.5 kg being expended per day. This nominal configuration utilizing only solar electric cells for power, the M2P2 will produce a magnetic barrier approximately 15-20 km in radius, which would accelerate a 70-140 kg payload to speeds of about 50-80 km/s. At this speed, missions to the heliopause and beyond can be achieved in under 10 yrs. Design characteristics for a prototype are also described
19. Ulysses observations of a 'density hole' in the high-speed solar wind
International Nuclear Information System (INIS)
Riley, P.; Gosling, J.T.; McComas, D.J.; Forsyth, R.J.
1998-01-01
Ulysses observations at mid and high heliographic latitudes have revealed a solar wind devoid of the large variations in density, temperature, and speed that are commonly observed at low latitudes. One event, however, observed on May 1, 1996, while Ulysses was located at ∼3.7AU and 38.5 degree, stands out in the plasma data set. The structure, which is unique in the Ulysses high-latitude data set, is seen as a drop in proton density of almost an order of magnitude and a comparable rise in proton temperature. The event lasts ∼3(1)/(2) hours giving the structure a size of ∼9.6x10 6 km (0.06 AU) along the spacecraft trajectory. Minimum variance analysis of this interval indicates that the angle between the average magnetic field direction and the minimum variance direction is ∼92 degree, suggesting that the 'density hole' may be approximated by a series of planar slabs separated by several tangential discontinuities. We discuss several possible explanations for the origin of this structure, but ultimately the origin of the density hole remains unknown. copyright 1998 American Geophysical Union
20. On forecasting ionospheric total electron content responses to high-speed solar wind streams
Directory of Open Access Journals (Sweden)
Meng Xing
2016-01-01
Full Text Available Conditions in the ionosphere have become increasingly important to forecast, since more and more spaceborne and ground-based technological systems rely on ionospheric weather. Here we explore the feasibility of ionospheric forecasts with the current generation of physics-based models. In particular, we focus on total electron content (TEC predictions using the Global Ionosphere-Thermosphere Model (GITM. Simulations are configured in a forecast mode and performed for four typical high-speed-stream events during 2007–2012. The simulated TECs are quantified through a metric, which divides the globe into a number of local regions and robustly differentiates between quiet and disturbed periods. Proposed forecast products are hourly global maps color-coded by the TEC disturbance level of each local region. To assess the forecasts, we compare the simulated TEC disturbances with global TEC maps derived from Global Positioning System (GPS satellite observations. The forecast performance is found to be merely acceptable, with a large number of regions where the observed variations are not captured by the simulations. Examples of model-data agreements and disagreements are investigated in detail, aiming to understand the model behavior and improve future forecasts. For one event, we identify two adjacent regions with similar TEC observations but significant differences in how local chemistry versus plasma transport contribute to electron density changes in the simulation. Suggestions for further analysis are described.
1. Two-dimensional, time-dependent MHD description of interplanetary disturbances: simulation of high speed solar wind interactions
International Nuclear Information System (INIS)
Wu, S.T.; Han, S.M.; Dryer, M.
1979-01-01
A two-dimensional, time-dependent, magnetohydrodynamic, numerical model is used to investigate multiple, transient solar wind flows which start close to the Sun and then extend into interplanetary space. The initial conditions are assumed to be appropriate for steady, homogeneous solar wind conditions with an average, spiral magnetic field configuration. Because both radial and azimuthal dimensions are included, it is possible to place two or more temporally-developing streams side-by-side at the same time. Thus, the evolution of the ensuing stream interaction is simulated by this numerical code. Advantages of the present method are as follows: (1) the development and decay of asymmetric MHD shocks and their interactions are clearly indicated; and (2) the model allows flexibility in the specification of evolutionary initial conditions in the azimuthal direction, thereby making it possible to gain insight concerning the interplanetary consequences of real physical situations more accurately than by use of the one-dimensional approach. Examples of such situations are the occurrence of near-simultaneous solar flares in adjacent active regions and the sudden appearance of enlargement of coronal holes as a result of a transient re-arrangement from a closed to an open magnetic field topology. (author)
2. The Dependence of the Peak Velocity of High-Speed Solar Wind Streams as Measured in the Ecliptic by ACE and the STEREO satellites on the Area and Co-latitude of Their Solar Source Coronal Holes.
Science.gov (United States)
Hofmeister, Stefan J; Veronig, Astrid; Temmer, Manuela; Vennerstrom, Susanne; Heber, Bernd; Vršnak, Bojan
2018-03-01
We study the properties of 115 coronal holes in the time range from August 2010 to March 2017, the peak velocities of the corresponding high-speed streams as measured in the ecliptic at 1 AU, and the corresponding changes of the Kp index as marker of their geoeffectiveness. We find that the peak velocities of high-speed streams depend strongly on both the areas and the co-latitudes of their solar source coronal holes with regard to the heliospheric latitude of the satellites. Therefore, the co-latitude of their source coronal hole is an important parameter for the prediction of the high-speed stream properties near the Earth. We derive the largest solar wind peak velocities normalized to the coronal hole areas for coronal holes located near the solar equator and that they linearly decrease with increasing latitudes of the coronal holes. For coronal holes located at latitudes ≳ 60°, they turn statistically to zero, indicating that the associated high-speed streams have a high chance to miss the Earth. Similarly, the Kp index per coronal hole area is highest for the coronal holes located near the solar equator and strongly decreases with increasing latitudes of the coronal holes. We interpret these results as an effect of the three-dimensional propagation of high-speed streams in the heliosphere; that is, high-speed streams arising from coronal holes near the solar equator propagate in direction toward and directly hit the Earth, whereas solar wind streams arising from coronal holes at higher solar latitudes only graze or even miss the Earth.
3. Coronal holes and high-speed wind streams
International Nuclear Information System (INIS)
Zirker, J.B.
1977-01-01
Coronal holes low have been identified as Bartel's M regions, i.e., sources of high-speed wind streams that produce recurrent geomagnetic variations. Throughout the Skylab period the polar caps of the Sun were coronal holes, and at lower latitudes the most persistent and recurrent holes were equatorial extensions of the polar caps. The holes rotated 'rigidly' at the equatorial synodic rate. They formed in regions of unipolar photospheric magnetic field, and their internal magnetic fields diverged rapidly with increasing distance from the sun. The geometry of the magnetic field in the inner corona seems to control both the physical properties of the holes and the global distribution of high-speed wind streams in the heliosphere. The latitude variation of the divergence of the coronal magnetic field lines produces corresponding variations in wind speed.During the years of declining solar activity the global field of the corona approximates a perturbed dipole. The divergence of field lines in each hemisphere produces a high-speed wind near the poles and low-speed wind in a narrow belt that coincides with the magnetic neutral sheet. The analysis of electron density measurements within a polar hole indicates that solar wind is accelerated principally in the region between 2 and 5 R/sub s/ and that mechanical wave pressure (possibly Alfven wave) may be responsible for the accleration of the wind. Phenomenological models for the birth and decay of coronal holes have been proposed. Attempts to explain the birth and rigid rotation of holes through dynamo action have been only partially successful. The 11-year variation of cosmic ray intensities at the earth may result from cyclic variation of open field regions associated with coronal holes
4. Ionization and NO production in the polar mesosphere during high-speed solar wind streams. Model validation and comparison with NO enhancements observed by Odin-SMR
Energy Technology Data Exchange (ETDEWEB)
Kirkwood, S.; Belova, E. [Swedish Institute of Space Physics, Kiruna (Sweden). Polar Atmospheric Research; Osepian, A. [Polar Geophysical Institute, Murmansk (Russian Federation); Urban, J.; Perot, K. [Chalmers Univ. of Technology, Gothenburg (Sweden). Dept. of Radio and Space Science; Sinha, A.K. [Indian Institute of Geomagnetism, Navi Mumbai (India)
2015-09-01
Precipitation of high-energy electrons (EEP) into the polar middle atmosphere is a potential source of significant production of odd nitrogen, which may play a role in stratospheric ozone destruction and in perturbing large-scale atmospheric circulation patterns. High-speed streams of solar wind (HSS) are a major source of energization and precipitation of electrons from the Earth's radiation belts, but it remains to be determined whether these electrons make a significant contribution to the odd-nitrogen budget in the middle atmosphere when compared to production by solar protons or by lower-energy (auroral) electrons at higher altitudes, with subsequent downward transport. Satellite observations of EEP are available, but their accuracy is not well established. Studies of the ionization of the atmosphere in response to EEP, in terms of cosmic-noise absorption (CNA), have indicated an unexplained seasonal variation in HSS-related effects and have suggested possible order-of-magnitude underestimates of the EEP fluxes by the satellite observations in some circumstances. Here we use a model of ionization by EEP coupled with an ion chemistry model to show that published average EEP fluxes, during HSS events, from satellite measurements (Meredith et al., 2011), are fully consistent with the published average CNA response (Kavanagh et al., 2012). The seasonal variation of CNA response can be explained by ion chemistry with no need for any seasonal variation in EEP. Average EEP fluxes are used to estimate production rate profiles of nitric oxide between 60 and 100 km heights over Antarctica for a series of unusually well separated HSS events in austral winter 2010. These are compared to observations of changes in nitric oxide during the events, made by the sub-millimetre microwave radiometer on the Odin spacecraft. The observations show strong increases of nitric oxide amounts between 75 and 90 km heights, at all latitudes poleward of 60 S, about 10 days after the
5. Ionization and NO production in the polar mesosphere during high-speed solar wind streams. Model validation and comparison with NO enhancements observed by Odin-SMR
International Nuclear Information System (INIS)
Kirkwood, S.; Belova, E.; Urban, J.; Perot, K.
2015-01-01
Precipitation of high-energy electrons (EEP) into the polar middle atmosphere is a potential source of significant production of odd nitrogen, which may play a role in stratospheric ozone destruction and in perturbing large-scale atmospheric circulation patterns. High-speed streams of solar wind (HSS) are a major source of energization and precipitation of electrons from the Earth's radiation belts, but it remains to be determined whether these electrons make a significant contribution to the odd-nitrogen budget in the middle atmosphere when compared to production by solar protons or by lower-energy (auroral) electrons at higher altitudes, with subsequent downward transport. Satellite observations of EEP are available, but their accuracy is not well established. Studies of the ionization of the atmosphere in response to EEP, in terms of cosmic-noise absorption (CNA), have indicated an unexplained seasonal variation in HSS-related effects and have suggested possible order-of-magnitude underestimates of the EEP fluxes by the satellite observations in some circumstances. Here we use a model of ionization by EEP coupled with an ion chemistry model to show that published average EEP fluxes, during HSS events, from satellite measurements (Meredith et al., 2011), are fully consistent with the published average CNA response (Kavanagh et al., 2012). The seasonal variation of CNA response can be explained by ion chemistry with no need for any seasonal variation in EEP. Average EEP fluxes are used to estimate production rate profiles of nitric oxide between 60 and 100 km heights over Antarctica for a series of unusually well separated HSS events in austral winter 2010. These are compared to observations of changes in nitric oxide during the events, made by the sub-millimetre microwave radiometer on the Odin spacecraft. The observations show strong increases of nitric oxide amounts between 75 and 90 km heights, at all latitudes poleward of 60 S, about 10 days after the
6. Observation of atomic oxygen O(1S) green-line emission in the summer polar upper mesosphere associated with high-energy (≥30 keV) electron precipitation during high-speed solar wind streams
Science.gov (United States)
Lee, Young-Sook; Kwak, Young-Sil; Kim, Kyung-Chan; Solheim, Brian; Lee, Regina; Lee, Jaejin
2017-01-01
The auroral green-line emission at 557.7 nm wavelength as arising from the atomic oxygen O(1S → 1D) transition typically peaks at an altitude of 100 km specifically in the nightside oval, induced by auroral electrons within an energy range of 100 eV-30 keV. Intense aurora is known as being suppressed by sunlight in summer daytime but usually occurs in low electrical background conductivity. However, in the present study in summer (July) sunlit condition, enhancements of O(1S) emission rates observed by using the Wind Imaging Interferometer/UARS were frequently observed at low altitudes below 90 km, where ice particles are created initially as subvisible and detected as polar mesosphere summer echoes, emerging to be an optical phenomenon of polar mesospheric clouds. The intense O(1S) emission occurring in summer exceeds those occurring in the daytime in other seasons both in occurrence and in intensity, frequently accompanied by occurrences of supersonic neutral velocity (300-1500 m s-1). In the mesosphere, ion motion is controlled by electric field and the momentum is transferred to neutrals. The intense O(1S) emission is well associated with high-energy electron precipitation as observed during an event of high-speed solar wind streams. Meanwhile, since the minimum occurrences of O(1S) emission and supersonic velocity are maintained even in the low precipitation flux, the mechanism responsible is not only related to high-energy electron precipitation but also presumably to the local conditions, including the composition of meteoric-charged ice particles and charge separation expected in extremely low temperatures (<150 K).
7. Some design aspects of high-speed vertical-axis wind turbines
National Research Council Canada - National Science Library
Templin, R. J; South, P
1977-01-01
... (rotor height to diameter ratio, solidity, number of blades, etc.) for high-speed vertical-axis wind turbines from kilowatt to megawatt sizes and shows that very large turbines are theoretically feasible...
8. Aerodynamic Characteristics of High Speed Trains under Cross Wind Conditions
Science.gov (United States)
Chen, W.; Wu, S. P.; Zhang, Y.
2011-09-01
Numerical simulation for the two models in cross-wind was carried out in this paper. The three-dimensional compressible Reynolds-averaged Navier-Stokes equations(RANS), combined with the standard k-ɛ turbulence model, were solved on multi-block hybrid grids by second order upwind finite volume technique. The impact of fairing on aerodynamic characteristics of the train models was analyzed. It is shown that, the flow separates on the fairing and a strong vortex is generated, the pressure on the upper middle car decreases dramatically, which leads to a large lift force. The fairing changes the basic patterns around the trains. In addition, formulas of the coefficient of aerodynamic force at small yaw angles up to 24° were expressed.
9. The Dependence of the Peak Velocity of High-Speed Solar Wind Streams as Measured in the Ecliptic by ACE and the STEREO satellites on the Area and Co-Latitude of their Solar Source Coronal Holes
DEFF Research Database (Denmark)
Hofmeister, Stefan J.; Veronig, Astrid; Temmer, Manuela
2018-01-01
We study the properties of 115 coronal holes in the time‐range from 2010/08 to 2017/03, the peak velocities of the corresponding high‐speed streams as measured in the ecliptic at 1AU, and the corresponding changes of the Kp index as marker of their geo‐effectiveness. We find that the peak...... statistically to zero, indicating that the associated high‐speed streams have a high chance to miss the Earth. Similar, the Kp index per coronal hole area is highest for the coronal holes located near the solar equator and strongly decreases with increasing latitudes of the coronal holes. We interpret...
10. Pose Measurement Method and Experiments for High-Speed Rolling Targets in a Wind Tunnel
Directory of Open Access Journals (Sweden)
Zhenyuan Jia
2014-12-01
Full Text Available High-precision wind tunnel simulation tests play an important role in aircraft design and manufacture. In this study, a high-speed pose vision measurement method is proposed for high-speed and rolling targets in a supersonic wind tunnel. To obtain images with high signal-to-noise ratio and avoid impacts on the aerodynamic shape of the rolling targets, a high-speed image acquisition method based on ultrathin retro-reflection markers is presented. Since markers are small-sized and some of them may be lost when the target is rolling, a novel markers layout with which markers are distributed evenly on the surface is proposed based on a spatial coding method to achieve highly accurate pose information. Additionally, a pose acquisition is carried out according to the mentioned markers layout after removing mismatching points by Case Deletion Diagnostics. Finally, experiments on measuring the pose parameters of high-speed targets in the laboratory and in a supersonic wind tunnel are conducted to verify the feasibility and effectiveness of the proposed method. Experimental results indicate that the position measurement precision is less than 0.16 mm, the pitching and yaw angle precision less than 0.132° and the roll angle precision 0.712°.
11. Pose measurement method and experiments for high-speed rolling targets in a wind tunnel.
Science.gov (United States)
Jia, Zhenyuan; Ma, Xin; Liu, Wei; Lu, Wenbo; Li, Xiao; Chen, Ling; Wang, Zhengqu; Cui, Xiaochun
2014-12-12
High-precision wind tunnel simulation tests play an important role in aircraft design and manufacture. In this study, a high-speed pose vision measurement method is proposed for high-speed and rolling targets in a supersonic wind tunnel. To obtain images with high signal-to-noise ratio and avoid impacts on the aerodynamic shape of the rolling targets, a high-speed image acquisition method based on ultrathin retro-reflection markers is presented. Since markers are small-sized and some of them may be lost when the target is rolling, a novel markers layout with which markers are distributed evenly on the surface is proposed based on a spatial coding method to achieve highly accurate pose information. Additionally, a pose acquisition is carried out according to the mentioned markers layout after removing mismatching points by Case Deletion Diagnostics. Finally, experiments on measuring the pose parameters of high-speed targets in the laboratory and in a supersonic wind tunnel are conducted to verify the feasibility and effectiveness of the proposed method. Experimental results indicate that the position measurement precision is less than 0.16 mm, the pitching and yaw angle precision less than 0.132° and the roll angle precision 0.712°.
12. A study on high speed coupling design for wind turbine using a finite element analysis
Energy Technology Data Exchange (ETDEWEB)
Lee, Hyoung Woo; Kang, Jong Hun [Dept. of Mechatronics Engineering, Jungwon University, Geosan (Korea, Republic of); Han, Jeong Young [Pusan Educational Center for Computer Aided Machine Design, Pusan University, Busan (Korea, Republic of)
2016-08-15
The purpose of this study is to design a high speed coupling for 3 MW wind turbines and evaluate its structural stability. A basic analysis was performed to assess the structural stability of two materials, SPS6 steel plate and a composite material (Glass7628, Glass/Epoxy), in relation to misalignment in the axial and radial directions. The entire model was analyzed for a high speed coupling based on the SPS6 steel plate, which was found to have higher stability among the two materials, and safety factors were estimated for various levels of power delivery. To test the proposed high speed coupling design, a performance test was carried out to verify the stability of the final product.
13. A study on high speed coupling design for wind turbine using a finite element analysis
International Nuclear Information System (INIS)
Lee, Hyoung Woo; Kang, Jong Hun; Han, Jeong Young
2016-01-01
The purpose of this study is to design a high speed coupling for 3 MW wind turbines and evaluate its structural stability. A basic analysis was performed to assess the structural stability of two materials, SPS6 steel plate and a composite material (Glass7628, Glass/Epoxy), in relation to misalignment in the axial and radial directions. The entire model was analyzed for a high speed coupling based on the SPS6 steel plate, which was found to have higher stability among the two materials, and safety factors were estimated for various levels of power delivery. To test the proposed high speed coupling design, a performance test was carried out to verify the stability of the final product
14. Anechoic wind tunnel tests on high-speed train bogie aerodynamic noise
OpenAIRE
Latorre Iglesias, E.; Thompson, D.; Smith, M.; Kitagawa, T.; Yamazaki, N.
2016-01-01
Aerodynamic noise becomes a significant noise source at speeds normally reached by high-speed trains. The train bogies are identified as important sources of aerodynamic noise. Due to the difficulty to assess this noise source carrying out field tests, wind tunnel tests offer many advantages. Tests were performed in the large-scale low-noise anechoic wind tunnel at Maibara, Japan, using a 1/7 scale train car and bogie model for a range of flow speeds between 50, 76, 89 and 100 m/s. The depend...
15. Solar wind stream interfaces
International Nuclear Information System (INIS)
Gosling, J.T.; Asbridge, J.R.; Bame, S.J.; Feldman, W.C.
1978-01-01
Measurements aboard Imp 6, 7, and 8 reveal that approximately one third of all high-speed solar wind streams observed at 1 AU contain a sharp boundary (of thickness less than approx.4 x 10 4 km) near their leading edge, called a stream interface, which separates plasma of distinctly different properties and origins. Identified as discontinuities across which the density drops abruptly, the proton temperature increases abruptly, and the speed rises, stream interfaces are remarkably similar in character from one stream to the next. A superposed epoch analysis of plasma data has been performed for 23 discontinuous stream interfaces observed during the interval March 1971 through August 1974. Among the results of this analysis are the following: (1) a stream interface separates what was originally thick (i.e., dense) slow gas from what was originally thin (i.e., rare) fast gas; (2) the interface is the site of a discontinuous shear in the solar wind flow in a frame of reference corotating with the sun; (3) stream interfaces occur at speeds less than 450 km s - 1 and close to or at the maximum of the pressure ridge at the leading edges of high-speed streams; (4) a discontinuous rise by approx.40% in electron temperature occurs at the interface; and (5) discontinuous changes (usually rises) in alpha particle abundance and flow speed relative to the protons occur at the interface. Stream interfaces do not generally recur on successive solar rotations, even though the streams in which they are embedded often do. At distances beyond several astronomical units, stream interfaces should be bounded by forward-reverse shock pairs; three of four reverse shocks observed at 1 AU during 1971--1974 were preceded within approx.1 day by stream interfaces. Our observations suggest that many streams close to the sun are bounded on all sides by large radial velocity shears separating rapidly expanding plasma from more slowly expanding plasma
16. WINDING METHOD SELECTION FOR TECHNICAL IMPLEMENTATION OF FIBER OPTIC COMMUNICATION LINE FOR HIGH-SPEED OBJECT
Directory of Open Access Journals (Sweden)
Vyacheslav A. Loparev
2017-07-01
Full Text Available The paper deals with fiber-optical cable winding methods for realization of fiber-optic communication line with high-speed object. We consider possible options of coils for optical cable winding providing mobility of one of the cable ends on an object. It is shown that the choice of a winding process is caused by the need of ensuring the minimum deformation of fiber-optical micro cable in case of separation from a winding body. It is revealed that the minimum tension value and its unevenness are observed when reeling from coils with a rocket form. Design ratios for determination of winding parameters are given. It is shown that reduction of tension unevenness reduces the jumps of internal tension and probability of break and emergence of optical signal local attenuation. Decrease in internal stresses occurs due to the absence of overlapping of the coils of the underlying layers with the overlying ones. To confirm the operability and the possibility of constructive implementation of the selected winding scheme, experiments were carried out to perform rocket and other types of winding with the use of a specially designed machine model. It is shown that the application of line rocket winding enables to achieve stability when reeling a cable during the movement and excludes breaks. Attenuation of optical signal decreases due to the increase in the bend minimum radius. This phenomenon is explained by reduction of the internal stresses causing optical signal attenuation in the place of cable separation from the coil.
17. Pulse-burst PIV in a high-speed wind tunnel
International Nuclear Information System (INIS)
Beresh, Steven; Kearney, Sean; Wagner, Justin; Guildenbecher, Daniel; Henfling, John; Spillers, Russell; Pruett, Brian; Jiang, Naibo; Slipchenko, Mikhail; Mance, Jason; Roy, Sukesh
2015-01-01
Time-resolved particle image velocimetry (TR-PIV) has been achieved in a high-speed wind tunnel, providing velocity field movies of compressible turbulence events. The requirements of high-speed flows demand greater energy at faster pulse rates than possible with the TR-PIV systems developed for low-speed flows. This has been realized using a pulse-burst laser to obtain movies at up to 50 kHz, with higher speeds possible at the cost of spatial resolution. The constraints imposed by use of a pulse-burst laser are limited burst duration of 10.2 ms and a low duty cycle for data acquisition. Pulse-burst PIV has been demonstrated in a supersonic jet exhausting into a transonic crossflow and in transonic flow over a rectangular cavity. The velocity field sequences reveal the passage of turbulent structures and can be used to find velocity power spectra at every point in the field, providing spatial distributions of acoustic modes. The present work represents the first use of TR-PIV in a high-speed ground-test facility. (paper)
18. Global Sensitivity Analysis of High Speed Shaft Subsystem of a Wind Turbine Drive Train
Directory of Open Access Journals (Sweden)
2018-01-01
Full Text Available The wind turbine dynamics are complex and critical area of study for the wind industry. Quantification of the effective factors to wind turbine performance is valuable for making improvements to both power performance and turbine health. In this paper, the global sensitivity analysis of validated mathematical model for high speed shaft drive train test rig has been developed in order to evaluate the contribution of systems input parameters to the specified objective functions. The drive train in this study consists of a 3-phase induction motor, flexible shafts, shafts’ coupling, bearing housing, and disk with an eccentric mass. The governing equations were derived by using the Lagrangian formalism and were solved numerically by Newmark method. The variance based global sensitivity indices are introduced to evaluate the contribution of input structural parameters correlated to the objective functions. The conclusion from the current research provides informative beneficial data in terms of design and optimization of a drive train setup and also can provide better understanding of wind turbine drive train system dynamics with respect to different structural parameters, ultimately designing more efficient drive trains. Finally, the proposed global sensitivity analysis (GSA methodology demonstrates the detectability of faults in different components.
19. Manifestation of solar activity in solar wind particle flux density
International Nuclear Information System (INIS)
Kovalenko, V.A.
1988-01-01
An analysis has been made of the origin of long-term variations in flux density of solar wind particles (nv) for different velocity regimes. The study revealed a relationship of these variations to the area of the polar coronal holes (CH). It is shown that within the framework of the model under development, the main longterm variations of nv are a result of the latitude redistribution of the solar wind mass flux in the heliosphere and are due to changes in the large-scale geometry of the solar plasma flow in the corona. A study has been made of the variations of nv for high speed solar wind streams. It is found that nv in high speed streams which are formed in CH, decreases from minimum to maximum solar activity. The analysis indicates that this decrease is attributable to the magnetic field strength increase in coronal holes. It has been found that periods of rapid global changes of background magnetic fields on the Sun are accompanied by a reconfiguration of coronal magnetic fields, rapid changes in the length of quiescent filaments, and by an increase in the density of the particle flux of a high speed solar wind. It has been established that these periods precede the formation of CH, corresponding to the increase in solar wind velocity near the Earth and to enhancement of the level of geomagnetic disturbance. (author)
20. Application of Rapid Prototyping Methods to High-Speed Wind Tunnel Testing
Science.gov (United States)
Springer, A. M.
1998-01-01
This study was undertaken in MSFC's 14-Inch Trisonic Wind Tunnel to determine if rapid prototyping methods could be used in the design and manufacturing of high speed wind tunnel models in direct testing applications, and if these methods would reduce model design/fabrication time and cost while providing models of high enough fidelity to provide adequate aerodynamic data, and of sufficient strength to survive the test environment. Rapid prototyping methods utilized to construct wind tunnel models in a wing-body-tail configuration were: fused deposition method using both ABS plastic and PEEK as building materials, stereolithography using the photopolymer SL-5170, selective laser sintering using glass reinforced nylon, and laminated object manufacturing using plastic reinforced with glass and 'paper'. This study revealed good agreement between the SLA model, the metal model with an FDM-ABS nose, an SLA nose, and the metal model for most operating conditions, while the FDM-ABS data diverged at higher loading conditions. Data from the initial SLS model showed poor agreement due to problems in post-processing, resulting in a different configuration. A second SLS model was tested and showed relatively good agreement. It can be concluded that rapid prototyping models show promise in preliminary aerodynamic development studies at subsonic, transonic, and supersonic speeds.
1. Assessing trophic linkages in and around offshore wind farms using two high-speed optical sensors
Science.gov (United States)
Dudeck, Tim; Hufnagl, Marc; Auch, Dominik; Eckhardt, André; Möller, Klas-Ove; van Beusekom, Justus; Walter, Bettina; Möllmann, Christian; Floeter, Jens
2016-04-01
In search for clean, renewable energy sources European countries have built and planned numerous Offshore Wind Farms (OWF) in the North Sea region. While some research has been carried out on their influence on marine mammals and bottom-dwelling organisms, less is known about fish and lower trophic levels in these areas. Yet, marine mammals purposely seek these structures and there are indications that there are higher chances of fish encounters. However, the local bottom-up effects probably driving these aggregations of higher trophic level organisms are poorly understood. In this study we show preliminary results of primary and secondary production in and around German OWFs in the North Sea using a Laser Optical Particle Counter and a Video Plankton Recorder. With the two sensors working simultaneously on the TRIAXUS system at high speed, we were able to investigate and ground-truth size-spectrum changes on a very high spatial resolution making it possible to detect OWF effects from local to larger scales. Our results show new possibilities in OWF research and the necessity to collect highly resolved field data for meaningful results in these dynamic environments. Furthermore, the use of size spectra simplifies the integration of energy flow through low and medium trophic levels into biogeochemical models by using only a single automatically measurable variable such as size.
2. Solar wind acceleration in coronal holes
International Nuclear Information System (INIS)
Kopp, R.A.
1978-01-01
Past attempts to explain the large solar wind velocities in high speed streams by theoretical models of the expansion have invoked either extended nonthermal heating of the corona, heat flux inhibition, or direct addition of momentum to the expanding coronal plasma. Several workers have shown that inhibiting the heat flux at low coronal densities is probably not adequate to explain quantitatively the observed plasma velocities in high speed streams. It stressed that, in order to account for both these large plasma velocities and the low densities found in coronal holes (from which most high speed streams are believed to emanate), extended heating by itself will not suffice. One needs a nonthermal mechanism to provide the bulk acceleration of the high wind plasma close to the sun, and the most likely candidate at present is direct addition of the momentum carried by outward-propagating waves to the expanding corona. Some form of momentum addition appears to be absolutely necessary if one hopes to build quantitatively self-consistent models of coronal holes and high speed solar wind streams
3. The influence of solar active region evolution on solar wind streams, coronal hole boundaries and geomagnetic storms
International Nuclear Information System (INIS)
Gold, R.E.; Dodson-Prince, H.W.; Hedeman, E.R.; Roelof, E.C.
1982-01-01
We have studied solar and interplanetary data by identification of the heliographic longitudes of the coronal source regions of high speed solar wind streams and by mapping the velocities measured near earth back to the sun using the approximation of constant radial velocity. Interplay of active regions and solar wind were studied
4. Small Horizontal Axis Wind Turbine under High Speed Operation: Study of Power Evaluation
Science.gov (United States)
Moh. M. Saad, Magedi; Mohd, Sofian Bin; Zulkafli, Mohd Fadhli Bin; Abdullah, Aslam Bin; Rahim, Mohammad Zulafif Bin; Subari, Zulkhairi Bin; Rosly, Nurhayati Binti
2017-10-01
Mechanical energy is produced through the rotation of wind turbine blades by air that convert the mechanical energy into electrical energy. Wind turbines are usually designed to be use for particular applications and design characteristics may vary depending on the area of use. The variety of applications is reflected on the size of turbines and their infrastructures, however, performance enhancement of wind turbine may start by analyzing the small horizontal axis wind turbine (SHAWT) under high wind speed operation. This paper analyzes the implementations of SHAWT turbines and investigates their performance in both simulation and real life. Depending on the real structure of the rotor geometry and aerodynamic test, the power performance of the SHAWT was simulated using ANSYS-FLUENT software at different wind speed up to 33.33 m/s (120km/h) in order to numerically investigate the actual turbine operation. Dynamic mesh and user define function (UDF) was used for revolving the rotor turbine via wind. Simulation results were further validated by experimental data and hence good matching was yielded. And for reducing the energy producing cost, car alternator was formed to be used as a small horizontal wind turbine. As a result, alternator-based turbine system was found to be a low-cost solution for exploitation of wind energy.
5. CONSTRAINING HIGH-SPEED WINDS IN EXOPLANET ATMOSPHERES THROUGH OBSERVATIONS OF ANOMALOUS DOPPLER SHIFTS DURING TRANSIT
International Nuclear Information System (INIS)
Miller-Ricci Kempton, Eliza; Rauscher, Emily
2012-01-01
Three-dimensional (3D) dynamical models of hot Jupiter atmospheres predict very strong wind speeds. For tidally locked hot Jupiters, winds at high altitude in the planet's atmosphere advect heat from the day side to the cooler night side of the planet. Net wind speeds on the order of 1-10 km s –1 directed towards the night side of the planet are predicted at mbar pressures, which is the approximate pressure level probed by transmission spectroscopy. These winds should result in an observed blueshift of spectral lines in transmission on the order of the wind speed. Indeed, Snellen et al. recently observed a 2 ± 1 km s –1 blueshift of CO transmission features for HD 209458b, which has been interpreted as a detection of the day-to-night (substellar to anti-stellar) winds that have been predicted by 3D atmospheric dynamics modeling. Here, we present the results of a coupled 3D atmospheric dynamics and transmission spectrum model, which predicts the Doppler-shifted spectrum of a hot Jupiter during transit resulting from winds in the planet's atmosphere. We explore four different models for the hot Jupiter atmosphere using different prescriptions for atmospheric drag via interaction with planetary magnetic fields. We find that models with no magnetic drag produce net Doppler blueshifts in the transmission spectrum of ∼2 km s –1 and that lower Doppler shifts of ∼1 km s –1 are found for the higher drag cases, results consistent with—but not yet strongly constrained by—the Snellen et al. measurement. We additionally explore the possibility of recovering the average terminator wind speed as a function of altitude by measuring Doppler shifts of individual spectral lines and spatially resolving wind speeds across the leading and trailing terminators during ingress and egress.
6. Solar-wind minor ions: recent observations
International Nuclear Information System (INIS)
Bame, S.J.
1982-01-01
During the years following the Solar Wind Four Conference at Burghausen our knowledge of the solar wind ion composition and dynamics has grown. There have been some surprises, and our understanding of the evolution of the solar wind has been improved. Systematic studies have shown that the minor ions generally travel with a common bulk speed and have temperatures roughly proportional to their masses. It has been determined that the 3 He ++ content varies greatly; 3 He ++ / 4 He ++ ranges from as high as 10 2 values to below 2 x 10 - 4 . In some solar wind flows which can be related to energetic coronal events, the minor ions are found in unusual ionization states containing Fe 16 + as a prominent ion, showing that the states were formed at unusually high temperatures. Unexpectedly, in a few flows substantial quantities of 4 He + have been detected, sometimes with ions identifiable as O 2 + and O 3 + . Surprisingly, in some of these examples the ionization state is mixed showing that part of the plasma escaped the corona without attaining the usual million-degree temperatures while other parts were heated more nearly in the normal manner. Additionally, detailed studies of the minor ions have increased our understanding of the coronal expansion. For example, such studies have contributed to identifying near equatorial coronal streamers as the source of solar wind flows between high speed streams
7. Fault Tolerant and Optimal Control of Wind Turbines with Distributed High-Speed Generators
Directory of Open Access Journals (Sweden)
Urs Giger
2017-01-01
Full Text Available In this paper, the control scheme of a distributed high-speed generator system with a total amount of 12 generators and nominal generator speed of 7000 min − 1 is studied. Specifically, a fault tolerant control (FTC scheme is proposed to keep the turbine in operation in the presence of up to four simultaneous generator faults. The proposed controller structure consists of two layers: The upper layer is the baseline controller, which is separated into a partial load region with the generator torque as an actuating signal and the full-load operation region with the collective pitch angle as the other actuating signal. In addition, the lower layer is responsible for the fault diagnosis and FTC characteristics of the distributed generator drive train. The fault reconstruction and fault tolerant control strategy are tested in simulations with several actuator faults of different types.
8. Electromagnetic Design and Losses Analysis of a High-Speed Permanent Magnet Synchronous Motor with Toroidal Windings for Pulsed Alternator
Directory of Open Access Journals (Sweden)
Yuan Wan
2018-03-01
Full Text Available The configuration of conventional high-speed Permanent Magnet Synchronous Motors (PMSMs is usually long and thin, with overlong axial end winding lengths, which is not suitable for those applications that place severe restrictions on the axial length, such as pulsed alternators. This paper first studied the key design aspects of a flat-structure high-speed PMSM. The toroidal-windings, low-conductivity material of the retaining sleeve, large airgap and segmentation of magnets were studied to reduce the axial length of the motor. The division of the stator and the employment of a non-magnetic outer stator were used to improve overall performance. Then the losses of the prototype were calculated and the factors having an influence on the losses were also investigated, after which, their effects on the total loss were evaluated. The total loss could be effectively reduced by the decrease of strand number of conductors and the division of stator, while only being slightly reduced by epoxy resin pole fillers. Metal-stack pole fillers have the same effect on the reduction of rotor loss as epoxy resin, while maintaining the good thermal-conductivity of metal. In addition, the influence of the carrier frequency of the inverter on the losses was analyzed, and it was found that high carrier frequency was helpful to reduce rotor losses. Finally, a small-scale prototype was manufactured and the experimental results were provided.
9. High speed video shooting with continuous-wave laser illumination in laboratory modeling of wind - wave interaction
Science.gov (United States)
Kandaurov, Alexander; Troitskaya, Yuliya; Caulliez, Guillemette; Sergeev, Daniil; Vdovin, Maxim
2014-05-01
Three examples of usage of high-speed video filming in investigation of wind-wave interaction in laboratory conditions is described. Experiments were carried out at the Wind - wave stratified flume of IAP RAS (length 10 m, cross section of air channel 0.4 x 0.4 m, wind velocity up to 24 m/s) and at the Large Air-Sea Interaction Facility (LASIF) - MIO/Luminy (length 40 m, cross section of air channel 3.2 x 1.6 m, wind velocity up to 10 m/s). A combination of PIV-measurements, optical measurements of water surface form and wave gages were used for detailed investigation of the characteristics of the wind flow over the water surface. The modified PIV-method is based on the use of continuous-wave (CW) laser illumination of the airflow seeded by particles and high-speed video. During the experiments on the Wind - wave stratified flume of IAP RAS Green (532 nm) CW laser with 1.5 Wt output power was used as a source for light sheet. High speed digital camera Videosprint (VS-Fast) was used for taking visualized air flow images with the frame rate 2000 Hz. Velocity air flow field was retrieved by PIV images processing with adaptive cross-correlation method on the curvilinear grid following surface wave profile. The mean wind velocity profiles were retrieved using conditional in phase averaging like in [1]. In the experiments on the LASIF more powerful Argon laser (4 Wt, CW) was used as well as high-speed camera with higher sensitivity and resolution: Optronics Camrecord CR3000x2, frame rate 3571 Hz, frame size 259×1696 px. In both series of experiments spherical 0.02 mm polyamide particles with inertial time 7 ms were used for seeding airflow. New particle seeding system based on utilization of air pressure is capable of injecting 2 g of particles per second for 1.3 - 2.4 s without flow disturbance. Used in LASIF this system provided high particle density on PIV-images. In combination with high-resolution camera it allowed us to obtain momentum fluxes directly from
10. Enigmatic Solar Wind Disappearance Events – Do We Understand ...
Solar wind disappearance—polar field reversals—transient ... unlike its high speed counterpart that emanates only from large open field regions ..... Sheeley, N. R. Jr., Swanson, E. T., Wang, Y.-M. 1991, Out of the ecliptic tests of the inverse.
11. A comparison of solar wind streams and coronal structure near solar minimum
Science.gov (United States)
Nolte, J. T.; Davis, J. M.; Gerassimenko, M.; Lazarus, A. J.; Sullivan, J. D.
1977-01-01
Solar wind data from the MIT detectors on the IMP 7 and 8 satellites and the SOLRAD 11B satellite for the solar-minimum period September-December, 1976, were compared with X-ray images of the solar corona taken by rocket-borne telescopes on September 16 and November 17, 1976. There was no compelling evidence that a coronal hole was the source of any high speed stream. Thus it is possible that either coronal holes were not the sources of all recurrent high-speed solar wind streams during the declining phase of the solar cycle, as might be inferred from the Skylab period, or there was a change in the appearance of some magnetic field regions near the time of solar minimum.
12. Electric solar wind sail mass budget model
Directory of Open Access Journals (Sweden)
P. Janhunen
2013-02-01
Full Text Available The electric solar wind sail (E-sail is a new type of propellantless propulsion system for Solar System transportation, which uses the natural solar wind to produce spacecraft propulsion. The E-sail consists of thin centrifugally stretched tethers that are kept charged by an onboard electron gun and, as such, experience Coulomb drag through the high-speed solar wind plasma stream. This paper discusses a mass breakdown and a performance model for an E-sail spacecraft that hosts a mission-specific payload of prescribed mass. In particular, the model is able to estimate the total spacecraft mass and its propulsive acceleration as a function of various design parameters such as the number of tethers and their length. A number of subsystem masses are calculated assuming existing or near-term E-sail technology. In light of the obtained performance estimates, an E-sail represents a promising propulsion system for a variety of transportation needs in the Solar System.
13. Solar wind stagnation near comets
International Nuclear Information System (INIS)
Galeev, A.A.; Cravens, T.E.; Gombosi, T.I.
1983-03-01
The nature of the solar wind flow near comets is examined analytically. In particular, the typical values for the stagnation pressure and magnetic barrier strength are estimated, taking into account the magnetic field line tension and the charge exchange cooling of the mass loaded solar wind. Knowledge of the strength of the magnetic barrier is required in order to determine the location of the contact discontinuity which separates the contaminated solar wind plasma and the outflowing plasma of the cometary ionosphere. (author)
14. Development of a guiding system and visual feedback real-time controller for the high-speed self-align optical cable winding
International Nuclear Information System (INIS)
Lee, Chang Woo; Kang, Hyun Kyoo; Shin, Kee Hyun
2008-01-01
Recently, the demand for the optical cable has been rapidly growing because of the increasing number of internet users and the high speed internet data transmission required. But the present optical cable winding systems have some serious problems such as pile-up and collapse of cables usually near the flange of the bobbin in the process of cables winding. To reduce the pile-up collapse in cable winding systems, a new guiding system is developed for a high-speed self-align cable winding. First, mathematical models for the winding process and bobbin shape fault compensation were proposed, the winding mechanism was analyzed and synchronization logics for the motions of winding, traversing, and the guiding were created. A prototype cable winding systems was manufactured to validate the new guiding system and the suggested logic. Experiment results showed that the winding system with the developed guiding system outperformed the system without the guiding system in reducing pile-up and collapse in high-speed winding
15. Validation of the solar heating and cooling high speed performance (HISPER) computer code
Science.gov (United States)
Wallace, D. B.
1980-01-01
Developed to give a quick and accurate predictions HISPER, a simplification of the TRNSYS program, achieves its computational speed by not simulating detailed system operations or performing detailed load computations. In order to validate the HISPER computer for air systems the simulation was compared to the actual performance of an operational test site. Solar insolation, ambient temperature, water usage rate, and water main temperatures from the data tapes for an office building in Huntsville, Alabama were used as input. The HISPER program was found to predict the heating loads and solar fraction of the loads with errors of less than ten percent. Good correlation was found on both a seasonal basis and a monthly basis. Several parameters (such as infiltration rate and the outside ambient temperature above which heating is not required) were found to require careful selection for accurate simulation.
16. Wave-trains in the solar wind. III
International Nuclear Information System (INIS)
Richter, A.K.
1975-01-01
Applying an Alfven-Wave-Extended-QRH-approximation and the method of characteristics, the equations of motion for outwardly propagating Alfven waves are solved analytically for three different cases of an azimuthal dependence of the background solar wind, (a) for a pure fast-slow stream configuration, (b) for the situation where the high-speed stream originates from a diverging magnetic field, and (c) for the case of (b) and an initially decreasing density configuration ('coronal hole'). The reaction of these waves on the background state as well as mode-mode coupling effects are neglected. These three solar wind models are discussed shortly. For the superimposed Alfven waves it is found, on an average, that there is a strong azimuthal dependence of all relevant parameters which, correlated with the azimuthal distributions of the solar wind variables, leads to good agreements with observations. The signature of high-speed streams and these correlations could clearly indicate solar wind streams originating from 'coronal holes'. Contrary to the purely radial solar wind, where outwardly propagating Alfven waves are exclusively refracted towards the radial direction, a refraction nearly perpendicular to the direction of the interplanetary magnetic field in the compression region and closely towards the magnetic field direction down the trailing edge and in the low-speed regime is found. (Auth.)
17. Solar wind velocity and daily variation of cosmic rays
International Nuclear Information System (INIS)
Ahluwalia, H.S.; Riker, J.F.
1985-01-01
Recently parameters applicable to the solar wind and the interplanetary magnetic field (IMF) have become much better defined. Superior quality of data bases that are now available, particularly for the post-1971 period, make it possible to believe the long-term trends in the data. These data are correlated with the secular changes observed in the diurnal variation parameters obtained from neutron monitor data at Deep River and underground muon telescope data at Embudo (30 MEW) and Socorro (82 MWE). The annual mean amplitudes appear to have large values during the epochs of high speed solar wind streams. Results are discussed
18. Signature of open magnetic field lines in the extended solar corona and of solar wind acceleration
Science.gov (United States)
Antonucci, E.; Giordano, S.; Benna, C.; Kohl, J. L.; Noci, G.; Michels, J.; Fineschi, S.
1997-01-01
The observations carried out with the ultraviolet coronagraph spectrometer onboard the Solar and Heliospheric Observatory (SOHO) are discussed. The purpose of the observations was to determine the line of sight and radial velocity fields in coronal regions with different magnetic topology. The results showed that the regions where the high speed solar wind flows along open field lines are characterized by O VI 1032 and HI Lyman alpha 1216 lines. The global coronal maps of the line of sight velocity were reconstructed. The corona height, where the solar wind reaches 100 km/s, was determined.
19. Wind in the Solar System
Science.gov (United States)
McIntosh, Gordon
2010-01-01
As an astronomy instructor I am always looking for commonly experienced Earthly phenomena to help my students and me understand and appreciate similar occurrences elsewhere in the solar system. Recently I wrote short "TPT" articles on frost and precipitation. The present article is on winds in the solar system. A windy day or storm might…
20. PHOTOIONIZATION IN THE SOLAR WIND
Energy Technology Data Exchange (ETDEWEB)
Landi, E.; Lepri, S. T., E-mail: [email protected] [Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, MI 48109 (United States)
2015-10-20
In this work we investigate the effects of photoionization on the charge state composition of the solar wind. Using measured solar EUV and X-ray irradiance, the Michigan Ionization Code and a model for the fast and slow solar wind, we calculate the evolution of the charge state distribution of He, C, N, O, Ne, Mg, Si, S, and Fe with and without including photoionization for both types of wind. We find that the solar radiation has significant effects on the charge state distribution of C, N, and O, causing the ionization levels of these elements to be higher than without photoionization; differences are largest for oxygen. The ions commonly observed for elements heavier than O are much less affected, except in ICMEs where Fe ions more ionized than 16+ can also be affected by the solar radiation. We also show that the commonly used O{sup 7+}/O{sup 6+} density ratio is the most sensitive to photoionization; this sensitivity also causes the value of this ratio to depend on the phase of the solar cycle. We show that the O{sup 7+}/O{sup 6+} ratio needs to be used with caution for solar wind classification and coronal temperature estimates, and recommend the C{sup 6+}/C{sup 4+} ratio for these purposes.
1. Observations of micro-turbulence in the solar wind near the sun with interplanetary scintillation
Science.gov (United States)
Yamauchi, Y.; Misawa, H.; Kojima, M.; Mori, H.; Tanaka, T.; Takaba, H.; Kondo, T.; Tokumaru, M.; Manoharan, P. K.
1995-01-01
Velocity and density turbulence of solar wind were inferred from interplanetary scintillation (IPS) observations at 2.3 GHz and 8.5 GHz using a single-antenna. The observations were made during September and October in 1992 - 1994. They covered the distance range between 5 and 76 solar radii (Rs). We applied the spectrum fitting method to obtain a velocity, an axial ratio, an inner scale and a power-law spectrum index. We examined the difference of the turbulence properties near the Sun between low-speed solar wind and high-speed solar wind. Both of solar winds showed acceleration at the distance range of 10 - 30 Rs. The radial dependence of anisotropy and spectrum index did not have significant difference between low-speed and high-speed solar winds. Near the sun, the radial dependence of the inner scale showed the separation from the linear relation as reported by previous works. We found that the inner scale of high-speed solar wind is larger than that of low-speed wind.
2. Ulysses solar wind plasma observations at high southerly latitudes.
Science.gov (United States)
Phillips, J L; Bame, S J; Feldman, W C; Gosling, J T; Hammond, C M; McComas, D J; Goldstein, B E; Neugebauer, M; Scime, E E; Suess, S T
1995-05-19
Solar wind plasma observations made by the Ulysses spacecraft through -80.2 degrees solar latitude and continuing equatorward to -40.1 degrees are summarized. Recurrent high-speed streams and corotating interaction regions dominated at middle latitudes. The speed of the solar wind was typically 700 to 800 kilometers per second poleward of -35 degrees . Corotating reverse shocks persisted farther south than did forward shocks because of the tilt of the heliomagnetic streamer belt. Sporadic coronal mass ejections were seen as far south as -60.5 degrees . Proton temperature was higher and the electron strahl was broader at higher latitudes. The high-latitude wind contained compressional, pressure-balanced, and Alfvénic structures.
3. Average properties of cosmic ray diffusion in solar wind streams
International Nuclear Information System (INIS)
Morfill, G.; Richter, A.K.; Scholer, M.
1979-01-01
Applying a superposed epoch analysis to the Mariner 5 plasma and magnetic field observations of 13 corotating high speed solar wind streams, we obtain the average azimuthal distribution of all relevant parameters of the background interplanetary medium, as well as those of superimposed Alfven waves. Using these measurements in model calculations allows us to determine the radial and azimuthal variation of the background and fluctuation parameters between 1 and 5 AU, and thus to calculate the cosmic ray diffusion coefficient kappa from the plasma and field properties. The calculation of kappa assumes that quasi-linear wave-particle interaction theory is applicable, and that the Alfven waves responsible for the scattering are propagating in the azimuthally varying solar wind according to geometrical optics. The consequences of these calculations regarding the occurrence of solar wind stream associated Forbush decreases are discussed
4. THREE-DIMENSIONAL EVOLUTION OF SOLAR WIND DURING SOLAR CYCLES 22–24
International Nuclear Information System (INIS)
Manoharan, P. K.
2012-01-01
This paper presents an analysis of three-dimensional evolution of solar wind density turbulence and speed at various levels of solar activity between solar cycles 22 and 24. The solar wind data used in this study have been obtained from the interplanetary scintillation (IPS) measurements made at the Ooty Radio Telescope, operating at 327 MHz. Results show that (1) on average, there was a downward trend in density turbulence from the maximum of cycle 22 to the deep minimum phase of cycle 23; (2) the scattering diameter of the corona around the Sun shrunk steadily toward the Sun, starting from 2003 to the smallest size at the deepest minimum, and it corresponded to a reduction of ∼50% in the density turbulence between the maximum and minimum phases of cycle 23; (3) the latitudinal distribution of the solar wind speed was significantly different between the minima of cycles 22 and 23. At the minimum phase of solar cycle 22, when the underlying solar magnetic field was simple and nearly dipole in nature, the high-speed streams were observed from the poles to ∼30° latitudes in both hemispheres. In contrast, in the long-decay phase of cycle 23, the sources of the high-speed wind at both poles, in accordance with the weak polar fields, occupied narrow latitude belts from poles to ∼60° latitudes. Moreover, in agreement with the large amplitude of the heliospheric current sheet, the low-speed wind prevailed in the low- and mid-latitude regions of the heliosphere. (4) At the transition phase between cycles 23 and 24, the high levels of density and density turbulence were observed close to the heliospheric equator and the low-speed solar wind extended from the equatorial-to-mid-latitude regions. The above results in comparison with Ulysses and other in situ measurements suggest that the source of the solar wind has changed globally, with the important implication that the supply of mass and energy from the Sun to the interplanetary space has been significantly reduced
5. Non-linear vehicle-bridge-wind interaction model for running safety assessment of high-speed trains over a high-pier viaduct
Science.gov (United States)
Olmos, José M.; Astiz, Miguel Á.
2018-04-01
In order to properly study the high-speed traffic safety on a high-pier viaduct subject to episodes of lateral turbulent winds, an efficient dynamic interaction train-bridge-wind model has been developed and experimentally validated. This model considers the full wheel and rail profiles, the friction between these two bodies in contact, and the piers P-Delta effect. The model has been used to determine the critical train and wind velocities from which the trains cannot travel safely over the O'Eixo Bridge. The dynamic simulations carried out and the results obtained in the time domain show that traffic safety rates exceed the allowed limits for turbulent winds with mean velocities at the deck higher than 25 m/s.
6. A survey of solar wind conditions at 5 AU: A tool for interpreting solar wind-magnetosphere interactions at Jupiter
Directory of Open Access Journals (Sweden)
Robert Wilkes Ebert
2014-09-01
Full Text Available We examine Ulysses solar wind and interplanetary magnetic field (IMF observations at 5 AU for two ~13 month intervals during the rising and declining phases of solar cycle 23 and the predicted response of the Jovian magnetosphere during these times. The declining phase solar wind, composed primarily of corotating interaction regions and high-speed streams, was, on average, faster, hotter, less dense, and more Alfvénic relative to the rising phase solar wind, composed mainly of slow wind and interplanetary coronal mass ejections. Interestingly, none of solar wind and IMF distributions reported here were bimodal, a feature used to explain the bimodal distribution of bow shock and magnetopause standoff distances observed at Jupiter. Instead, many of these distributions had extended, non-Gaussian tails that resulted in large standard deviations and much larger mean over median values. The distribution of predicted Jupiter bow shock and magnetopause standoff distances during these intervals were also not bimodal, the mean/median values being larger during the declining phase by ~1 – 4%. These results provide data-derived solar wind and IMF boundary conditions at 5 AU for models aimed at studying solar wind-magnetosphere interactions at Jupiter and can support the science investigations of upcoming Jupiter system missions. Here, we provide expectations for Juno, which is scheduled to arrive at Jupiter in July 2016. Accounting for the long-term decline in solar wind dynamic pressure reported by McComas et al. (2013, Jupiter’s bow shock and magnetopause is expected to be at least 8 – 12% further from Jupiter, if these trends continue.
7. A survey of solar wind conditions at 5 AU: a tool for interpreting solar wind-magnetosphere interactions at Jupiter
Energy Technology Data Exchange (ETDEWEB)
Ebert, Robert W. [Space Science and Engineering Division, Southwest Research Institute, San Antonio, TX (United States); Bagenal, Fran [Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO (United States); McComas, David J. [Space Science and Engineering Division, Southwest Research Institute, San Antonio, TX (United States); Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, TX (United States); Fowler, Christopher M., E-mail: [email protected] [Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO (United States)
2014-09-19
We examine Ulysses solar wind and interplanetary magnetic field (IMF) observations at 5 AU for two ~13 month intervals during the rising and declining phases of solar cycle 23 and the predicted response of the Jovian magnetosphere during these times. The declining phase solar wind, composed primarily of corotating interaction regions and high-speed streams, was, on average, faster, hotter, less dense, and more Alfvénic relative to the rising phase solar wind, composed mainly of slow wind and interplanetary coronal mass ejections. Interestingly, none of solar wind and IMF distributions reported here were bimodal, a feature used to explain the bimodal distribution of bow shock and magnetopause standoff distances observed at Jupiter. Instead, many of these distributions had extended, non-Gaussian tails that resulted in large standard deviations and much larger mean over median values. The distribution of predicted Jupiter bow shock and magnetopause standoff distances during these intervals were also not bimodal, the mean/median values being larger during the declining phase by ~1–4%. These results provide data-derived solar wind and IMF boundary conditions at 5 AU for models aimed at studying solar wind-magnetosphere interactions at Jupiter and can support the science investigations of upcoming Jupiter system missions. Here, we provide expectations for Juno, which is scheduled to arrive at Jupiter in July 2016. Accounting for the long-term decline in solar wind dynamic pressure reported by McComas et al. (2013a), Jupiter's bow shock and magnetopause is expected to be at least 8–12% further from Jupiter, if these trends continue.
8. Global aspects of stream evolution in the solar wind
International Nuclear Information System (INIS)
Gosling, J.T.
1984-01-01
A spatially variable coronal expansion, when coupled with solar rotation, leads to the formation of high speed solar wind streams which evolve considerably with increasing heliocentric distance. Initially the streams steepen for simple kinematic reasons, but this steepening is resisted by pressure forces, leading eventually to the formation of forward-reverse shock pairs in the distant heliosphere. The basic physical processes responsible for stream steepening an evolution are explored and model calculations are compared with actual spacecraft observations of the process. The solar wind stream evolution problem is relatively well understood both observationally and theoretically. Tools developed in achieving this understanding should be applicable to other astrophysical systems where a spatially or temporally variable outflow is associated with a rotating object. 27 references, 13 figures
9. Variation of the solar wind velocity following solar flares
International Nuclear Information System (INIS)
Huang, Y.; Lee, Y.
1975-01-01
By use of the superposed epoch method, changes in the solar wind velocity following solar flares have been investigated by using the solar wind velocity data obtained by Pioneer 6 and 7 and Vela 3, 4, and 5 satellites. A significant increase of the solar wind velocity has been found on the second day following importance 3 solar flares and on the third day following importance 2 solar flares. No significant increase of the solar wind velocity has been found for limb flares. (auth)
10. [Comfort of crew and passengers and atmospheric pressure, noise, wind speed in high-speed train of Shijiazhuang-Taiyuan passenger dedicated line].
Science.gov (United States)
Zhai, Yi-biao; Huo, Wei; Liu, Qiao-ying; Chen, Bao-shan; Zhang, Jin-long; Shi, Lei
2012-11-01
To explore the crew and passengers' comfort on the Shijiazhuang-Taiyuan passenger dedicated line and physical factors, such as air pressure, noise, wind speed. Comfort investigation of all the crew (n = 244) and passengers (n = 377) on the Shijiazhuang-Taiyuan passenger dedicated line at speed of 250 km/h and 200 km/h and the detection of the air pressure, noise and wind speed were performed in 2011. Significantly higher ratio of comfortable feeling, lower ratio of seriously discomfortable feeling were observed in crew and passengers at 200 km/h compared with those at 250 km/h (P noise in passengers at 200 km/h. No significant difference was observed in ear discomfort induced by air pressure and noise among crew, and the duration of disappearance of discomfortable feeling among passengers between 200 km/h and 250 km/h. The noise in carriages exceeded the related standard when the high-speed train passing through the tunnels. The individuals feel more comfortable at 200 km/h than 250 km/h in this line., which may be related with rapid variation of wind speed and noise when the train passes through the tunnels with high speed.
11. Heat-flux gage measurements on a flat plate at a Mach number of 4.6 in the VSD high speed wind tunnel, a feasibility test (LA28). [wind tunnel tests of measuring instruments for boundary layer flow
Science.gov (United States)
1975-01-01
The feasibility of employing thin-film heat-flux gages was studied as a method of defining boundary layer characteristics at supersonic speeds in a high speed blowdown wind tunnel. Flow visualization techniques (using oil) were employed. Tabulated data (computer printouts), a test facility description, and photographs of test equipment are given.
12. The influence of solar active region evolution on solar wind streams, coronal hole boundaries and geomagnetic storms
Science.gov (United States)
Gold, R. E.; Dodson-Prince, H. W.; Hedeman, E. R.; Roelof, E. C.
1982-01-01
Solar and interplanetary data are examined, taking into account the identification of the heliographic longitudes of the coronal source regions of high speed solar wind (SW) streams by Nolte and Roelof (1973). Nolte and Roelof have 'mapped' the velocities measured near earth back to the sun using the approximation of constant radial velocity. The 'Carrington carpet' for rotations 1597-1616 is shown in a graph. Coronal sources of high speed streams appear in the form of solid black areas. The contours of the stream sources are laid on 'evolutionary charts' of solar active region histories for the Southern and Northern Hemispheres. Questions regarding the interplay of active regions and solar wind are investigated, giving attention to developments during the years 1973, 1974, and 1975.
13. Synoptic maps of solar wind parameters from in situ spacecraft observations
Science.gov (United States)
Gazis, P. R.
1995-01-01
Solar wind observations from the Interplanetary Monitoring Platform-8 (IMP-8) and Pioneer Venus Orbiter (PVO) spacecraft from 1982 until 1988 are combined to construct synoptic maps of solar wind parameters near 1 AU. Each map consists of 6 months of hourly averaged solar wind data, binned by heliographic latitude and Carrington longitude and projected back to the Sun. These maps show the structure and time evolution of solar wind streams near 1 AU in the heliographic latitudes of +/- 7.25 deg and provide and explicit picture of several phenomena, such as gradients, changes in the inclination of the heliospheric current sheet, and the relative positions of various structures in the inner heliosphere, that is difficult to obtain from single-spacecraft observations. The stream structure varied significantly during the last solar cycle. Between 1982 and early 1985, solar wind parameters did not depend strongly on heliographic latitude. During the last solar minimum, the solar wind developed significant latitudinal structure, and high-speed streams were excluded from the vicinity of the solar equator. The interplanetary magnetic field was strongly correlated with the coronal field, and the current sheet tended to coincide with the coronal neutral line. The solar wind speed showed the expected correlations with temperature, interplanetary magnetic field, and distance from the current sheet. The solar wind speed was anticorrelated with density, but the regions of highest density occurred east of the heliospheric current sheet and the regions of lowest solar wind speed. This is consistent with compression at the leading edge of high-speed streams.
14. Turbulence in the solar wind
CERN Document Server
Bruno, Roberto
2016-01-01
This book provides an overview of solar wind turbulence from both the theoretical and observational perspective. It argues that the interplanetary medium offers the best opportunity to directly study turbulent fluctuations in collisionless plasmas. In fact, during expansion, the solar wind evolves towards a state characterized by large-amplitude fluctuations in all observed parameters, which resembles, at least at large scales, the well-known hydrodynamic turbulence. This text starts with historical references to past observations and experiments on turbulent flows. It then introduces the Navier-Stokes equations for a magnetized plasma whose low-frequency turbulence evolution is described within the framework of the MHD approximation. It also considers the scaling of plasma and magnetic field fluctuations and the study of nonlinear energy cascades within the same framework. It reports observations of turbulence in the ecliptic and at high latitude, treating Alfvénic and compressive fluctuations separately in...
15. Acoustic Modifications of the Ames 40x80 Foot Wind Tunnel and Test Techniques for High-Speed Research Model Testing
Science.gov (United States)
Soderman, Paul T.; Olson, Larry (Technical Monitor)
1995-01-01
The NFAC 40- by 80- Foot Wind Tunnel at Ames is being refurbished with a new, deep acoustic lining in the test section which will make the facility nearly anechoic over a large frequency range. The modification history, key elements, and schedule will be discussed. Design features and expected performance gains will be described. Background noise reductions will be summarized. Improvements in aeroacoustic research techniques have been developed and used recently at NFAC on several wind tunnel tests of High Speed Research models. Research on quiet inflow microphones and struts will be described. The Acoustic Survey Apparatus in the 40x80 will be illustrated. A special intensity probe was tested for source localization. Multi-channel, high speed digital data acquisition is now used for acoustics. And most important, phased microphone arrays have been developed and tested which have proven to be very powerful for source identification and increased signal-to-noise ratio. Use of these tools for the HEAT model will be illustrated. In addition, an acoustically absorbent symmetry plane was built to satisfy the HEAT semispan aerodynamic and acoustic requirements. Acoustic performance of that symmetry plane will be shown.
16. Geometry of solar corona expansion and solar wind parameters
International Nuclear Information System (INIS)
Krajnev, M.B.
1980-01-01
The character of the parameter chanqe of solar wind plasma in the region of the Earth orbit is studied. The main regularities in the parametep behaviour of solar wind (plasma velocity and density) are qualitatively explained in the framework of a model according to which solar corona expansion stronqly differs from radial expansion, that is: the solar wind current lines are focused towards helioequator during the period of low solar activity with gradual transfer to radial expansion during the years of high solar activity. It is shown that the geometry of the solar wind current tubes and its change with the solar activity cycle can not serve an explanation of the observed change of the solar wind parameters
17. Polarization state of hydromagnetic fluctuations in the solar wind
International Nuclear Information System (INIS)
Bavassano, B.; Dobrowolny, M.; Mariani, F.; Ness, N.F.
1981-01-01
From presently available observations one can infer that the Alfvenic turbulence measured in the solar wind, predominantly on trailing edges of high-speed streams, is a mixture of modes with two different polarizations, namely. Alfvenic modes and modes which are the incompressible limit of slow magnetosonic waves. Using Helios 2 magnetic data and a variance analysis, we have separated parallel (to the mean field) and perpendicular components of the fluctuations and studied the possible correlation between such components which would be predicted as a consequence of the imcompressible character of the turbulence. Correlations between eigenvalues of the variance matrix are also investigated and discussed
18. Theoretical contributions to solar wind research - a review
International Nuclear Information System (INIS)
Cuperman, S.
1977-01-01
The theoretical work on the solar wind phenomena done since 1958 can be divided into two main parts: Part I - development and refinement of Parker's initial macroscopic model, the emphasis being placed upon steady state, spherically symmetric flow and the identification of the structure-less background solar wind plasma with the low speed flow. It is in this part that much progress in understanding the solar wind phenomenon has been achieved; Part II - generalization of Parker's initial model such as to include microscopic (kinetic) aspects, temporal variations, deviations from spherically symmetric conditions, complex local magnetic configurations, etc. The last two aspects, in particular, have received considerable attention with the discovery of the coronal holes, their association with high-speed flows and the tentative identification of these flows with the structure-less background solar wind plasma. This review is confined to Part I, as defined above. However, for completeness, several important aspects connected with the subjects enumerated under Part II and which represent the objects of the most recent investigation are also briefly reviewed. (Auth.)
19. 77 FR 61597 - Avalon Wind, LLC; Avalon Wind 2, LLC; Catalina Solar, LLC; Catalina Solar 2, LLC; Pacific Wind...
Science.gov (United States)
2012-10-10
... DEPARTMENT OF ENERGY Federal Energy Regulatory Commission [Docket No. EL12-109-000] Avalon Wind, LLC; Avalon Wind 2, LLC; Catalina Solar, LLC; Catalina Solar 2, LLC; Pacific Wind Lessee, LLC; Pacific Wind 2, LLC; Valentine Solar, LLC; EDF Renewable Development, Inc.; Notice of Petition for Declaratory...
20. Distributed Wind Cost Reduction: Learning from Solar
Energy Technology Data Exchange (ETDEWEB)
Tegen, Suzanne
2016-02-23
The distributed wind energy industry can learn several lessons from the solar industry regarding reducing soft costs. Suzanne Tegen presented this overview at the 2016 Distributed Wind Energy Association Business Conference in Washington, D.C., on February 23, 2016.
1. Astrospheres and Solar-like Stellar Winds
Directory of Open Access Journals (Sweden)
Wood Brian E.
2004-07-01
Full Text Available Stellar analogs for the solar wind have proven to be frustratingly difficult to detect directly. However, these stellar winds can be studied indirectly by observing the interaction regions carved out by the collisions between these winds and the interstellar medium (ISM. These interaction regions are called "astrospheres", analogous to the "heliosphere" surrounding the Sun. The heliosphere and astrospheres contain a population of hydrogen heated by charge exchange processes that can produce enough H I Ly alpha absorption to be detectable in UV spectra of nearby stars from the Hubble Space Telescope (HST. The amount of astrospheric absorption is a diagnostic for the strength of the stellar wind, so these observations have provided the first measurements of solar-like stellar winds. Results from these stellar wind studies and their implications for our understanding of the solar wind are reviewed here. Of particular interest are results concerning the past history of the solar wind and its impact on planetary atmospheres.
2. Solar Wind Earth Exchange Project (SWEEP)
Science.gov (United States)
2016-10-28
highly charged ions of the solar wind. The main challenge in predicting the resultant photon flux in the X-ray energy bands is due to the...Newton, an X-ray astronomical observatory. We use OMNI solar wind conditions, heavy ion composition data from ACE, the Hodges neutral hydrogen model...of SWEEP was to compare theoretical models of X-ray emission in the terrestrial magnetosphere caused by the Solar Wind Charge Exchange
3. Effect of vanadium carbide on dry sliding wear behavior of powder metallurgy AISI M2 high speed steel processed by concentrated solar energy
Energy Technology Data Exchange (ETDEWEB)
García, C. [Materials Engineering. E.I.I., Universidad de Valladolid. C/Paseo del cauce 59, 47011 Valladolid (Spain); Romero, A. [E.T.S. Ingenieros Industriales. Instituto de Investigaciones Energéticas y Aplicaciones Industriales (INEI). Universidad de Castilla-La Mancha, Edificio Politécnico, Avda. Camilo José Cela s/n, 13071 Ciudad Real (Spain); Herranz, G., E-mail: [email protected] [E.T.S. Ingenieros Industriales. Instituto de Investigaciones Energéticas y Aplicaciones Industriales (INEI). Universidad de Castilla-La Mancha, Edificio Politécnico, Avda. Camilo José Cela s/n, 13071 Ciudad Real (Spain); Blanco, Y.; Martin, F. [Materials Engineering. E.I.I., Universidad de Valladolid. C/Paseo del cauce 59, 47011 Valladolid (Spain)
2016-11-15
Mixtures of AISI M2 high speed steel and vanadium carbide (3, 6 or 10 wt.%) were prepared by powder metallurgy and sintered by concentrated solar energy (CSE). Two different powerful solar furnaces were employed to sinter the parts and the results were compared with those obtained by conventional powder metallurgy using a tubular electric furnace. CSE allowed significant reduction of processing times and high heating rates. The wear resistance of compacts was studied by using rotating pin-on-disk and linearly reciprocating ball-on-flat methods. Wear mechanisms were investigated by means of scanning electron microscopy (SEM) observations and chemical inspections of the microstructures of the samples. Better wear properties than those obtained by conventional powder metallurgy were achieved. The refinement of the microstructure and the formation of carbonitrides were the reasons for this. - Highlights: •Powder metallurgy of mixtures of M2 high speed steel and VC are studied. •Some sintering is done by concentrated solar energy. •Rotating pin-on-disk and linearly reciprocating ball-on-flat methods are used. •The tribological properties and wear mechanisms, under dry sliding, are studied.
4. Solar wind radiation damage in lunar dust grains and the characteristics of the ancient solar wind
International Nuclear Information System (INIS)
Borg, J.; Chaumont, J.
1980-01-01
Current understanding of the exposure history of lunar dust grains to the ancient solar wind is reviewed, the work being based mostly on a Monte Carlo statistical code, describing the 'gardening' effects of the meteorite bombardment in the lunar regolith, and on analytical models, yielding the lifetimes of the grains against various types of destruction processes. Families of lunar dust grains are identified, and evidence is presented showing that lunar dust grains were not partially shielded from solar wind ions. Results of solar wind simulation experiments are used to interpret the thickness distribution of the amorphous coatings of solar wind radiation-damaged material observed on 1-micron lunar dust grains. It is argued that such distributions reflect the speed distribution of the ancient solar wind as averaged over periods of approximately 5000 years in duration, and that the ancient solar wind is less energetic than the present day solar wind
5. Limitation of solar energy and wind energy
International Nuclear Information System (INIS)
White, R. S.
2008-01-01
Wind turbines, solar energy collectors and photovoltaic cells have been popular sources of electricity since the oil crisis in the late seventies, and they are increasingly favored by many scientists and much of the public as methods for reducing global warming. The older wind farms in California are outdated. New wind turbines have not followed, primarily because of competition from lower-cost natural gas. The Times urges increased federal and state subsidies for the wind and solar industries. The primary reason that wind and solar energies have not made inroads in the past, and will never supply more than a few percentage points of the world's electrical energy, is their unpredictable variations in time and their constant need for back-ups. The only non-carbon-dioxide-emitting generator capable of backing up wind and solar energy and replacing coal and gas generators is nuclear fission. Nuclear power may be the practical solution to global warming, after all.
6. Evolution of the solar wind acceleration region during 1990-1994
International Nuclear Information System (INIS)
Tokumaru, Munetoshi; Kondo, Tetsuro; Takaba, Hiroshi; Mori, Hirotaka; Tanaka, Takashi
1996-01-01
The single-station measurements of interplanetary scintillation (IPS) at 2GHz and 8GHz using the Kashima radio telescope are used to study the distribution of the solar wind velocity and density fluctuations near the sun. Wind velocities derived from our IPS data with the IPS co-spectrum method show a radial increase in the distance range between 10 and 30 Rs (solar radii). From the scintillation index analysis, it is found that the radial fall of density fluctuations in the solar wind is described by the power-law function. A series of Kashima IPS observations reveals that a pronounced change in velocity and turbulence level occurs at the polar region of the sun during 1990-1994. That is, the high-speed wind and the reduced-turbulence region develop there as the solar activity declines. This fact is consistent with the long-term evolution of the coronal magnetic structure inferred from He1083nm observations
7. Solar energy system with wind vane
Science.gov (United States)
Grip, Robert E
2015-11-03
A solar energy system including a pedestal defining a longitudinal axis, a frame that is supported by the pedestal and that is rotateable relative to the pedestal about the longitudinal axis, the frame including at least one solar device, and a wind vane operatively connected to the frame to urge the frame relative to the pedestal about the longitudinal axis in response to wind acting on the wind vane.
8. Solar winds along curved magnetic field lines
OpenAIRE
Li, Bo; Xia, Li-Dong; Chen, Yao
2011-01-01
Both remote-sensing measurements using the interplanetary scintillation (IPS) technique and in situ measurements by the Ulysses spacecraft show a bimodal structure for the solar wind at solar minimum conditions. At present what makes the fast wind fast and the slow wind slow still remains to be answered. While a robust empirical correlation exists between the coronal expansion rate $f_c$ of the flow tubes and the speeds $v$ measured in situ, further data analysis suggests that $v$ depends on ...
9. Theoretical models for MHD turbulence in the solar wind
International Nuclear Information System (INIS)
Veltri, P.; Malara, F.
1997-01-01
The in situ measurements of velocity, magnetic field, density and temperature fluctuations performed in the solar wind have greatly improved our knowledge of MDH turbulence not only from the point of view of space physics but also from the more general point of view of plasma physics. These fluctuations which extend over a wide range of frequencies (about 5 decades), a fact which seems to be the signature of turbulent nonlinear energy cascade, display, mainly in the trailing edge of high-speed streams, a number of features characteristic of a self-organized situation: i) a high degree of correlation between magnetic and velocity field fluctuations, ii) a very low level of fluctuations in mass density and magnetic-field intensity, iii) a considerable anisotropy revealed by minimum variance analysis of the magnetic-field correlation tensor. Many fundamental processes in plasma physics, which were largely unknown or not understood before their observations in the solar wind, have been explained, by building up analytical models or performing numerical simulations. We discuss the most recent analytical theories and numerical simulations and outline the limits implicit in any analysis which consider the low-frequency solar-wind fluctuations as a superposition of linear modes. The characterization of low-frequency fluctuations during Alfvenic periods, which results from the models discussed, is finally presented
10. Solar wind heavy ions from energetic coronal events
International Nuclear Information System (INIS)
Bame, S.J.
1978-01-01
Ions heavier than those of He can be resolved in the solar wind with electrostatic E/q analyzers when the local thermal temperatures are low. Ordinarily this condition prevails in the low speed solar wind found between high speed streams, i.e. the interstream, IS, solar wind. Various ions of O, Si and Fe are resolved in IS heavy ion spectra. Relative ion peak intensities indicate that the O ionization state is established in the IS coronal source regions at approx. 2.1 x 10 6 K while the state of Fe is frozen in at approx. 1.5 x 10 6 K farther out. Occasionally, anomalous spectra are observed in which the usually third most prominent ion peak, O 8+ , is depressed as are the Fe peaks ranging from Fe 12+ to Fe 7+ . A prominent peak in the usual Si 8+ position of IS spectra is self-consistently shown to be Fe 16+ . These features demonstrate that the ionization states were frozen in at higher than usual coronal temperatures. The source regions of these hot heavy ion spectra are identified as energetic coronal events including flares and nonflare coronal mass ejections. 24 references
11. Solar wind classification from a machine learning perspective
Science.gov (United States)
Heidrich-Meisner, V.; Wimmer-Schweingruber, R. F.
2017-12-01
It is a very well known fact that the ubiquitous solar wind comes in at least two varieties, the slow solar wind and the coronal hole wind. The simplified view of two solar wind types has been frequently challenged. Existing solar wind categorization schemes rely mainly on different combinations of the solar wind proton speed, the O and C charge state ratios, the Alfvén speed, the expected proton temperature and the specific proton entropy. In available solar wind classification schemes, solar wind from stream interaction regimes is often considered either as coronal hole wind or slow solar wind, although their plasma properties are different compared to "pure" coronal hole or slow solar wind. As shown in Neugebauer et al. (2016), even if only two solar wind types are assumed, available solar wind categorization schemes differ considerably for intermediate solar wind speeds. Thus, the decision boundary between the coronal hole and the slow solar wind is so far not well defined.In this situation, a machine learning approach to solar wind classification can provide an additional perspective.We apply a well-known machine learning method, k-means, to the task of solar wind classification in order to answer the following questions: (1) How many solar wind types can reliably be identified in our data set comprised of ten years of solar wind observations from the Advanced Composition Explorer (ACE)? (2) Which combinations of solar wind parameters are particularly useful for solar wind classification?Potential subtypes of slow solar wind are of particular interest because they can provide hints of respective different source regions or release mechanisms of slow solar wind.
12. High-latitude Conic Current Sheets in the Solar Wind
Energy Technology Data Exchange (ETDEWEB)
Khabarova, Olga V.; Obridko, Vladimir N.; Kharshiladze, Alexander F. [Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of the Russian Academy of Sciences (IZMIRAN), Moscow (Russian Federation); Malova, Helmi V. [Scobeltsyn Nuclear Physics Institute of Lomonosov Moscow State University, Moscow (Russian Federation); Kislov, Roman A.; Zelenyi, Lev M. [Space Research Centre of the Polish Academy of Sciences (CBK PAN), Warsaw (Poland); Tokumaru, Munetoshi; Fujiki, Ken’ichi [Institute for Space-Earth Environmental Research, Nagoya University (Japan); Sokół, Justyna M.; Grzedzielski, Stan [Space Research Centre of the Polish Academy of Sciences (CBK), Warsaw (Poland)
2017-02-10
We provide observational evidence for the existence of large-scale cylindrical (or conic-like) current sheets (CCSs) at high heliolatitudes. Long-lived CCSs were detected by Ulysses during its passages over the South Solar Pole in 1994 and 2007. The characteristic scale of these tornado-like structures is several times less than a typical width of coronal holes within which the CCSs are observed. CCS crossings are characterized by a dramatic decrease in the solar wind speed and plasma beta typical for predicted profiles of CCSs. Ulysses crossed the same CCS at different heliolatitudes at 2–3 au several times in 1994, as the CCS was declined from the rotation axis and corotated with the Sun. In 2007, a CCS was detected directly over the South Pole, and its structure was strongly highlighted by the interaction with comet McNaught. Restorations of solar coronal magnetic field lines reveal the occurrence of conic-like magnetic separators over the solar poles in both 1994 and 2007. Such separators exist only during solar minima. Interplanetary scintillation data analysis confirms the presence of long-lived low-speed regions surrounded by the typical polar high-speed solar wind in solar minima. Energetic particle flux enhancements up to several MeV/ nuc are observed at edges of the CCSs. We built simple MHD models of a CCS to illustrate its key features. The CCSs may be formed as a result of nonaxiality of the solar rotation axis and magnetic axis, as predicted by the Fisk–Parker hybrid heliospheric magnetic field model in the modification of Burger and coworkers.
13. Diagnostics of high-speed streams and coronal holes using geomagnetic pulsations
International Nuclear Information System (INIS)
Bol'shakova, O.V.; Troitskaya, V.A.
1980-01-01
In order to study the relations of high-speed solar wind streams and coronal holes analyzed are the parameters of geomagnetic pulsations of the Rs3 type and of high-speed streams at the decrease branch and in the minimum of solar activity. On the basis of the analysis of exciting pulsation regime determined are the differences in characteristics of high-speed stream properties. Presented are the graphical distributions of a number of occurrances of high-speed streams, coronal holes and pure regimes of Rs3R pulsations in several sections of 1973 in the Sun rotations of N1903-1919 and of the change of solar wind velocity while passing through the high-speed streams. It is found that Rs3R occurrance can serve an indicator of the high-speed flux connection with the large equatorial coronal hole. On the basis of the analysis of exciting pulsation properties determined are the differences in the stream characteristics. However the preliminary estimates permit to adopt neither the first nor the second of the existing hypotheses on the sourse of formation of high-speed streams
14. Solar Rotational Periodicities and the Semiannual Variation in the Solar Wind, Radiation Belt, and Aurora
Science.gov (United States)
Emery, Barbara A.; Richardson, Ian G.; Evans, David S.; Rich, Frederick J.; Wilson, Gordon R.
2011-01-01
The behavior of a number of solar wind, radiation belt, auroral and geomagnetic parameters is examined during the recent extended solar minimum and previous solar cycles, covering the period from January 1972 to July 2010. This period includes most of the solar minimum between Cycles 23 and 24, which was more extended than recent solar minima, with historically low values of most of these parameters in 2009. Solar rotational periodicities from S to 27 days were found from daily averages over 81 days for the parameters. There were very strong 9-day periodicities in many variables in 2005 -2008, triggered by recurring corotating high-speed streams (HSS). All rotational amplitudes were relatively large in the descending and early minimum phases of the solar cycle, when HSS are the predominant solar wind structures. There were minima in the amplitudes of all solar rotational periodicities near the end of each solar minimum, as well as at the start of the reversal of the solar magnetic field polarity at solar maximum (approx.1980, approx.1990, and approx. 2001) when the occurrence frequency of HSS is relatively low. Semiannual equinoctial periodicities, which were relatively strong in the 1995-1997 solar minimum, were found to be primarily the result of the changing amplitudes of the 13.5- and 27-day periodicities, where 13.5-day amplitudes were better correlated with heliospheric daily observations and 27-day amplitudes correlated better with Earth-based daily observations. The equinoctial rotational amplitudes of the Earth-based parameters were probably enhanced by a combination of the Russell-McPherron effect and a reduction in the solar wind-magnetosphere coupling efficiency during solstices. The rotational amplitudes were cross-correlated with each other, where the 27 -day amplitudes showed some of the weakest cross-correlations. The rotational amplitudes of the > 2 MeV radiation belt electron number fluxes were progressively weaker from 27- to 5-day periods
15. Experimental study of high-speed counter-rotation propeller on low speed wind range; Dojiku hantengata kosoku propeller no teisokuiki ni okeru fudo jikken
Energy Technology Data Exchange (ETDEWEB)
NONE
1997-03-01
Collaborative research was conducted by National Aerospace Laboratory and Japan Aircraft Development Company in the period of fiscal 1988-1992 into methods for testing aircraft with advanced propeller in low-speed wind tunnel. The propulsion efficiency of the currently available high-bypass turbofan engine is approximately 60% in the vicinity of Mach number 0.85. Propeller-driven aircraft, whose propulsion efficiency is as high as 80% in the low Mach number domain, are scarcely in practical use in the domain of Mach number 0.75 or higher. There are studies reported abroad as well as in Japan for the propeller-driven aircraft to enjoy higher propeller propulsion efficiency even in the vicinity of Mach number 0.8 by modifying the propeller diameter, number of blades, and blade sections, etc. This paper describes the experimental research into the high-speed counter-rotation propeller. A counter-rotation propeller 0.3m in diameter and provided with coaxially arranged 8times2 SR-2 blades is evaluated for pitch angles during the takeoff and landing modes, for thrust characteristics at the pitch angle for the cruising mode, and for propeller backwash and noise. 15 refs., 72 figs., 9 tabs.
16. Tropospheric weather influenced by solar wind through atmospheric vertical coupling downward control
Science.gov (United States)
Prikryl, Paul; Bruntz, Robert; Tsukijihara, Takumi; Iwao, Koki; Muldrew, Donald B.; Rušin, Vojto; Rybanský, Milan; Turňa, Maroš; Šťastný, Pavel
2018-06-01
Occurrence of severe weather in the context of solar wind coupling to the magnetosphere-ionosphere-atmosphere (MIA) system is investigated. It is observed that significant snowfall, wind and heavy rain, particularly if caused by low pressure systems in winter, tend to follow arrivals of high-speed solar wind. Previously published statistical evidence that explosive extratropical cyclones in the northern hemisphere tend to occur within a few days after arrivals of high-speed solar wind streams from coronal holes (Prikryl et al., 2009, 2016) is corroborated for the southern hemisphere. Cases of severe weather events are examined in the context of the magnetosphere-ionosphere-atmosphere (MIA) coupling. Physical mechanism to explain these observations is proposed. The leading edge of high-speed solar wind streams is a locus of large-amplitude magneto-hydrodynamic waves that modulate Joule heating and/or Lorentz forcing of the high-latitude lower thermosphere generating medium-scale atmospheric gravity waves that propagate upward and downward through the atmosphere. Simulations of gravity wave propagation in a model atmosphere using the Transfer Function Model (Mayr et al., 1990) reveal that propagating waves originating in the lower thermosphere can excite a spectrum of gravity waves in the lower atmosphere. In spite of significantly reduced amplitudes but subject to amplification upon reflection in the upper troposphere, these gravity waves can provide a lift of unstable air to release instabilities in the troposphere and initiate convection to form cloud/precipitation bands. It is primarily the energy provided by release of latent heat that leads to intensification of storms. These results indicate that vertical coupling in the atmosphere exerts downward control from solar wind to the lower atmospheric levels influencing tropospheric weather development.
17. Wind and solar resource data sets
DEFF Research Database (Denmark)
Clifton, Andrew; Hodge, Bri-Mathias; Draxl, Caroline
2017-01-01
The range of resource data sets spans from static cartography showing the mean annual wind speed or solar irradiance across a region to high temporal and high spatial resolution products that provide detailed information at a potential wind or solar energy facility. These data sets are used...... to support continental-scale, national, or regional renewable energy development; facilitate prospecting by developers; and enable grid integration studies. This review first provides an introduction to the wind and solar resource data sets, then provides an overview of the common methods used...... for their creation and validation. A brief history of wind and solar resource data sets is then presented, followed by areas for future research. For further resources related to this article, please visit the WIREs website....
18. Solar and Wind Site Screening Decision Trees
Science.gov (United States)
EPA and NREL created a decision tree to guide state and local governments and other stakeholders through a process for screening sites for their suitability for future redevelopment with solar photovoltaic (PV) energy and wind energy.
19. Electrostatic Solitary Waves in the Solar Wind: Evidence for Instability at Solar Wind Current Sheets
Science.gov (United States)
Malaspina, David M.; Newman, David L.; Wilson, Lynn Bruce; Goetz, Keith; Kellogg, Paul J.; Kerstin, Kris
2013-01-01
A strong spatial association between bipolar electrostatic solitary waves (ESWs) and magnetic current sheets (CSs) in the solar wind is reported here for the first time. This association requires that the plasma instabilities (e.g., Buneman, electron two stream) which generate ESWs are preferentially localized to solar wind CSs. Distributions of CS properties (including shear angle, thickness, solar wind speed, and vector magnetic field change) are examined for differences between CSs associated with ESWs and randomly chosen CSs. Possible mechanisms for producing ESW-generating instabilities at solar wind CSs are considered, including magnetic reconnection.
20. Wind loads on solar energy roofs
NARCIS (Netherlands)
Geurts, C.P.W.; Bentum, C.A. van
2007-01-01
This paper presents an overview of the wind loads on roofs, equipped with solar energy products, so called Active Roofs. Values given in this paper have been based on wind tunnel and full scale measurements, carried out at TNO, and on an interpretation of existing rules and guidelines. The results
1. Structure and sources of solar wind in the growing phase of 24th solar cycle
Science.gov (United States)
Slemzin, Vladimir; Goryaev, Farid; Shugay, Julia; Rodkin, Denis; Veselovsky, Igor
2015-04-01
We present analysis of the solar wind (SW) structure and its association with coronal sources during the minimum and rising phase of 24th solar cycle (2009-2011). The coronal sources prominent in this period - coronal holes, small areas of open magnetic fields near active regions and transient sources associated with small-scale solar activity have been investigated using EUV solar images and soft X-ray fluxes obtained by the CORONAS-Photon/TESIS/Sphinx, PROBA2/SWAP, Hinode/EIS and AIA/SDO instruments as well as the magnetograms obtained by HMI/SDO. It was found that at solar minimum (2009) velocity and magnetic field strength of high speed wind (HSW) and transient SW from small-scale flares did not differ significantly from those of the background slow speed wind (SSW). The major difference between parameters of different SW components was seen in the ion composition represented by the C6/C5, O7/O6, Fe/O ratios and the mean charge of Fe ions. With growing solar activity, the speed of HSW increased due to transformation of its sources - small-size low-latitude coronal holes into equatorial extensions of large polar holes. At that period, the ion composition of transient SW changed from low-temperature to high-temperature values, which was caused by variation of the source conditions and change of the recombination/ionization rates during passage of the plasma flow through the low corona. However, we conclude that criteria of separation of the SW components based on the ion ratios established earlier by Zhao&Fisk (2009) for higher solar activity are not applicable to the extremely weak beginning of 24th cycle. The research leading to these results has received funding from the European Commission's Seventh Framework Programme (FP7/2007-2013) under the grant agreement eHeroes (project n° 284461, www.eheroes.eu).
2. High-Speed Photography
International Nuclear Information System (INIS)
Paisley, D.L.; Schelev, M.Y.
1998-01-01
The applications of high-speed photography to a diverse set of subjects including inertial confinement fusion, laser surgical procedures, communications, automotive airbags, lightning etc. are briefly discussed. (AIP) copyright 1998 Society of Photo-Optical Instrumentation Engineers
3. High speed data acquisition
International Nuclear Information System (INIS)
Cooper, P.S.
1997-07-01
A general introduction to high speed data acquisition system techniques in modern particle physics experiments is given. Examples are drawn from the SELEX(E78 1) high statistics charmed baryon production and decay experiment now taking data at Fermilab
4. High speed heterostructure devices
CERN Document Server
Beer, Albert C; Willardson, R K; Kiehl, Richard A; Sollner, T C L Gerhard
1994-01-01
Volume 41 includes an in-depth review of the most important, high-speed switches made with heterojunction technology. This volume is aimed at the graduate student or working researcher who needs a broad overview andan introduction to current literature. Key Features * The first complete review of InP-based HFETs and complementary HFETs, which promise very low power and high speed * Offers a complete, three-chapter review of resonant tunneling * Provides an emphasis on circuits as well as devices.
5. The Solar Wind Environment in Time
Science.gov (United States)
Pognan, Quentin; Garraffo, Cecilia; Cohen, Ofer; Drake, Jeremy J.
2018-03-01
We use magnetograms of eight solar analogs of ages 30 Myr–3.6 Gyr obtained from Zeeman Doppler Imaging and taken from the literature, together with two solar magnetograms, to drive magnetohydrodynamical wind simulations and construct an evolutionary scenario of the solar wind environment and its angular momentum loss rate. With observed magnetograms of the radial field strength as the only variant in the wind model, we find that a power-law model fitted to the derived angular momentum loss rate against time, t, results in a spin-down relation Ω ∝ t ‑0.51, for angular speed Ω, which is remarkably consistent with the well-established Skumanich law Ω ∝ t ‑0.5. We use the model wind conditions to estimate the magnetospheric standoff distances for an Earth-like test planet situated at 1 au for each of the stellar cases, and to obtain trends of minimum and maximum wind ram pressure and average ram pressure in the solar system through time. The wind ram pressure declines with time as \\overline{{P}ram}}\\propto {t}2/3, amounting to a factor of 50 or so over the present lifetime of the solar system.
6. Wind and solar energy incentives in Iran
International Nuclear Information System (INIS)
Taleghani, G.; Kazemi Karegar, H.
2006-01-01
Incentive have yet been viewed as a means of supporting technological developments until a new technology becomes cost competitive wind based electricity is not jet generally competitive with alternate sources of electricity such as fossil fuels. This paper presents the potential for wind and solar in Iran and shows how much electric energy is now produced by renewable power plants compared to steam and gas. The importance of renewable energy effects on Iran environment and economy is also discussed and the issue of the contribution of renewable energy for producing electricity in the future will be shown. Also this paper highlights the ability of Iran to manufacture the components of the wind turbine and solar system locally, and its effect on the price of wind turbine and solar energy
7. ON THE NATURE OF THE SOLAR WIND FROM CORONAL PSEUDOSTREAMERS
International Nuclear Information System (INIS)
Wang, Y.-M.; Sheeley, N. R. J.R.; Grappin, R.; Robbrecht, E.
2012-01-01
Coronal pseudostreamers, which separate like-polarity coronal holes, do not have current sheet extensions, unlike the familiar helmet streamers that separate opposite-polarity holes. Both types of streamers taper into narrow plasma sheets that are maintained by continual interchange reconnection with the adjacent open magnetic field lines. White-light observations show that pseudostreamers do not emit plasma blobs; this important difference from helmet streamers is due to the convergence of like-polarity field lines above the X-point, which prevents the underlying loops from expanding outward and pinching off. The main component of the pseudostreamer wind has the form of steady outflow along the open field lines rooted just inside the boundaries of the adjacent coronal holes. These flux tubes are characterized by very rapid expansion below the X-point, followed by reconvergence at greater heights. Analysis of an idealized pseudostreamer configuration shows that, as the separation between the underlying holes increases, the X-point rises and the expansion factor f ss at the source surface increases. In situ observations of pseudostreamer crossings indicate wind speeds v ranging from ∼350 to ∼550 km s –1 , with O 7+ /O 6+ ratios that are enhanced compared with those in high-speed streams but substantially lower than in the slow solar wind. Hydrodynamic energy-balance models show that the empirical v-f ss relation overestimates the wind speeds from nonmonotonically expanding flux tubes, particularly when the X-point is located at low heights and f ss is small. We conclude that pseudostreamers produce a 'hybrid' type of outflow that is intermediate between classical slow and fast solar wind.
8. Clouds blown by the solar wind
International Nuclear Information System (INIS)
Voiculescu, M; Condurache-Bota, S; Usoskin, I
2013-01-01
In this letter we investigate possible relationships between the cloud cover (CC) and the interplanetary electric field (IEF), which is modulated by the solar wind speed and the interplanetary magnetic field. We show that CC at mid–high latitudes systematically correlates with positive IEF, which has a clear energetic input into the atmosphere, but not with negative IEF, in general agreement with predictions of the global electric circuit (GEC)-related mechanism. Thus, our results suggest that mid–high latitude clouds might be affected by the solar wind via the GEC. Since IEF responds differently to solar activity than, for instance, cosmic ray flux or solar irradiance, we also show that such a study allows distinguishing one solar-driven mechanism of cloud evolution, via the GEC, from others. (letter)
9. Ion acoustic waves in the solar wind
International Nuclear Information System (INIS)
Gurnett, D.A.; Frank, L.A.
1978-01-01
Plasma wave measurements on the Helios I and 2 spacecraft have revealed the occurrence of electric field turbulence in the solar wind at frequencies between the electron and ion plasma frequencies. Wavelength measurements with the Imp 6 spacecraft now provide strong evidence that these waves are short-wavelength ion acoustic waves which are Doppler-shifted upward in frequency by the motion of the solar wind. Comparison of the Helios results with measurements from the earth-orbiting Imp 6 and 8 spacecraft shows that the ion acoustic turbulence detected in interplanetary space has characteristics essentially identical to those of bursts of electrostatic turbulence generated by protons streaming into the solar wind from the earth's bow shock. In a few cases, enhanced ion acoustic wave intensities have been observed in direct association with abrupt increases in the anisotropy of the solar wind electron distribution. This relationship strongly suggests that the ion acoustic waves detected by Helios far from the earth are produced by an electron heat flux instability, as was suggested by Forslund. Possible related mechanisms which could explain the generation of ion acoustic waves by protons streaming into the solar wind from the earth's bow shock are also considered
10. Solar Illumination Control of the Polar Wind
Science.gov (United States)
Maes, L.; Maggiolo, R.; De Keyser, J.; André, M.; Eriksson, A. I.; Haaland, S.; Li, K.; Poedts, S.
2017-11-01
Polar wind outflow is an important process through which the ionosphere supplies plasma to the magnetosphere. The main source of energy driving the polar wind is solar illumination of the ionosphere. As a result, many studies have found a relation between polar wind flux densities and solar EUV intensity, but less is known about their relation to the solar zenith angle at the ionospheric origin, certainly at higher altitudes. The low energy of the outflowing particles and spacecraft charging means it is very difficult to measure the polar wind at high altitudes. We take advantage of an alternative method that allows estimations of the polar wind flux densities far in the lobes. We analyze measurements made by the Cluster spacecraft at altitudes from 4 up to 20 RE. We observe a strong dependence on the solar zenith angle in the ion flux density and see that both the ion velocity and density exhibit a solar zenith angle dependence as well. We also find a seasonal variation of the flux density.
11. Laboratory Facility for Simulating Solar Wind Sails
International Nuclear Information System (INIS)
Funaki, Ikkoh; Ueno, Kazuma; Oshio, Yuya; Ayabe, Tomohiro; Horisawa, Hideyuki; Yamakawa, Hiroshi
2008-01-01
Magnetic sail (MagSail) is a deep space propulsion system, in which an artificial magnetic cavity captures the energy of the solar wind to propel a spacecraft in the direction leaving the sun. For a scale-model experiment of the plasma flow of MagSail, we employed a magnetoplasmadynamic arcjet as a solar wind simulator. It is observed that a plasma flow from the solar wind simulator reaches a quasi-steady state of about 0.8 ms duration after a transient phase when initiating the discharge. During this initial phase of the discharge, a blast-wave was observed to develop radially in a vacuum chamber. When a solenoidal coil (MagSail scale model) is immersed into the quasi-steady flow where the velocity is 45 km/s, and the number density is 10 19 m-3, a bow shock as well as a magnetic cavity were formed in front of the coil. As a result of the interaction between the plasma flow and the magnetic cavity, the momentum of the simulated solar wind is decreased, and it is found from the thrust measurement that the solar wind momentum is transferred to the coil simulating MagSail.
12. ENERGY DISSIPATION PROCESSES IN SOLAR WIND TURBULENCE
Energy Technology Data Exchange (ETDEWEB)
Wang, Y.; Wei, F. S.; Feng, X. S.; Sun, T. R.; Zuo, P. B. [SIGMA Weather Group, State Key Laboratory for Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing 100190 (China); Xu, X. J. [Space Science Institute, Macau University of Science and Technology, Macao (China); Zhang, J., E-mail: [email protected] [School of Physics, Astronomy and Computational Sciences, George Mason University, 4400 University Drive, MSN 3F3, Fairfax, Virginia 22030 (United States)
2015-12-15
Turbulence is a chaotic flow regime filled by irregular flows. The dissipation of turbulence is a fundamental problem in the realm of physics. Theoretically, dissipation ultimately cannot be achieved without collisions, and so how turbulent kinetic energy is dissipated in the nearly collisionless solar wind is a challenging problem. Wave particle interactions and magnetic reconnection (MR) are two possible dissipation mechanisms, but which mechanism dominates is still a controversial topic. Here we analyze the dissipation region scaling around a solar wind MR region. We find that the MR region shows unique multifractal scaling in the dissipation range, while the ambient solar wind turbulence reveals a monofractal dissipation process for most of the time. These results provide the first observational evidences for intermittent multifractal dissipation region scaling around a MR site, and they also have significant implications for the fundamental energy dissipation process.
13. Solar wind controlled pulsations: A review
International Nuclear Information System (INIS)
Odera, T.J.
1986-01-01
Studies of the solar wind controlled Pc 3, 4 pulsations by early and recent researchers are highlighted. The review focuses on the recent observations, which cover the time during the International Magnetospheric Study (IMS). Results from early and recent observations agree on one point, that is, that the Pc 3, 4 pulsations are influenced by three main solar wind parameters, namely, the solar wind velocity V/sub 5w/, the IMF orientation theta/sub x/B, and magnitude B. The results can be interpreted, preferably, in terms of an external origin for Pc 3, 4 pulsations. This implies, essentially, the signal model, which means that the pulsations originate in the upstream waves (in the interplanetary medium) and are transported by convection to the magnetopause, where they couple to oscillations of the magnetospheric field lines
14. Diagnostics of the solar wind transition region
International Nuclear Information System (INIS)
Lotova, N.A.; Nagelis, Ya.V.; Rudnitskij, G.M.; Smirnova, T.V.; AN Latvijskoj SSR, Riga. Radioastrofizicheskaya Observatoriya; Moskovskij Gosudarstvennyj Univ.; AN SSSR, Moscow. Fizicheskij Inst.)
1988-01-01
Possibilities are discussed of a more complete study of hardly observable regions of the interplanetary medium, in the zone of the solar wind formation, where transition from subsonic to supersonic flow occurs at R sun . It is shown that an investigation of fine structure of the extended transonic region of the solar wind and of the sequence of changes in the parameters of the interplanetary plasma in the region of the solar wind formation with the changing distance from the Sun can be effectuated by using jointly different modifications of the occupation method. Combination of two or more modifications of this method supposes using compact radio sources of different classes and observations in two different wavelength ranges, namely at short centimeter and at meter waves
15. WIND observations of coherent electrostatic waves in the solar wind
Directory of Open Access Journals (Sweden)
A. Mangeney
1999-03-01
Full Text Available The time domain sampler (TDS experiment on WIND measures electric and magnetic wave forms with a sampling rate which reaches 120 000 points per second. We analyse here observations made in the solar wind near the Lagrange point L1. In the range of frequencies above the proton plasma frequency fpi and smaller than or of the order of the electron plasma frequency fpe, TDS observed three kinds of electrostatic (e.s. waves: coherent wave packets of Langmuir waves with frequencies f ~ fpe, coherent wave packets with frequencies in the ion acoustic range fpi < f < fpe, and more or less isolated non-sinusoidal spikes lasting less than 1 ms. We confirm that the observed frequency of the low frequency (LF ion acoustic wave packets is dominated by the Doppler effect: the wavelengths are short, 10 to 50 electron Debye lengths λD. The electric field in the isolated electrostatic structures (IES and in the LF wave packets is more or less aligned with the solar wind magnetic field. Across the IES, which have a spatial width of the order of ~ 25λD, there is a small but finite electric potential drop, implying an average electric field generally directed away from the Sun. The IES wave forms, which have not been previously reported in the solar wind, are similar, although with a smaller amplitude, to the weak double layers observed in the auroral regions, and to the electrostatic solitary waves observed in other regions in the magnetosphere. We have also studied the solar wind conditions which favour the occurrence of the three kinds of waves: all these e.s. waves are observed more or less continuously in the whole solar wind (except in the densest regions where a parasite prevents the TDS observations. The type (wave packet or IES of the observed LF waves is mainly determined by the proton temperature and by the direction of the magnetic field, which themselves depend on the latitude of WIND with respect to the heliospheric current sheet.Key words
16. WIND observations of coherent electrostatic waves in the solar wind
Directory of Open Access Journals (Sweden)
A. Mangeney
Full Text Available The time domain sampler (TDS experiment on WIND measures electric and magnetic wave forms with a sampling rate which reaches 120 000 points per second. We analyse here observations made in the solar wind near the Lagrange point L1. In the range of frequencies above the proton plasma frequency fpi and smaller than or of the order of the electron plasma frequency fpe, TDS observed three kinds of electrostatic (e.s. waves: coherent wave packets of Langmuir waves with frequencies f ~ fpe, coherent wave packets with frequencies in the ion acoustic range fpi < f < fpe, and more or less isolated non-sinusoidal spikes lasting less than 1 ms. We confirm that the observed frequency of the low frequency (LF ion acoustic wave packets is dominated by the Doppler effect: the wavelengths are short, 10 to 50 electron Debye lengths λD. The electric field in the isolated electrostatic structures (IES and in the LF wave packets is more or less aligned with the solar wind magnetic field. Across the IES, which have a spatial width of the order of ~ 25λD, there is a small but finite electric potential drop, implying an average electric field generally directed away from the Sun. The IES wave forms, which have not been previously reported in the solar wind, are similar, although with a smaller amplitude, to the weak double layers observed in the auroral regions, and to the electrostatic solitary waves observed in other regions in the magnetosphere. We have also studied the solar wind conditions which favour the occurrence of the three kinds of waves: all these e.s. waves are observed more or less continuously in the whole solar wind (except in the densest regions where a parasite prevents the TDS observations. The type (wave packet or IES of the observed LF waves is mainly determined
17. Statistics of counter-streaming solar wind suprathermal electrons at solar minimum: STEREO observations
Directory of Open Access Journals (Sweden)
B. Lavraud
2010-01-01
Full Text Available Previous work has shown that solar wind suprathermal electrons can display a number of features in terms of their anisotropy. Of importance is the occurrence of counter-streaming electron patterns, i.e., with "beams" both parallel and anti-parallel to the local magnetic field, which is believed to shed light on the heliospheric magnetic field topology. In the present study, we use STEREO data to obtain the statistical properties of counter-streaming suprathermal electrons (CSEs in the vicinity of corotating interaction regions (CIRs during the period March–December 2007. Because this period corresponds to a minimum of solar activity, the results are unrelated to the sampling of large-scale coronal mass ejections, which can lead to CSE owing to their closed magnetic field topology. The present study statistically confirms that CSEs are primarily the result of suprathermal electron leakage from the compressed CIR into the upstream regions with the combined occurrence of halo depletion at 90° pitch angle. The occurrence rate of CSE is found to be about 15–20% on average during the period analyzed (depending on the criteria used, but superposed epoch analysis demonstrates that CSEs are preferentially observed both before and after the passage of the stream interface (with peak occurrence rate >35% in the trailing high speed stream, as well as both inside and outside CIRs. The results quantitatively show that CSEs are common in the solar wind during solar minimum, but yet they suggest that such distributions would be much more common if pitch angle scattering were absent. We further argue that (1 the formation of shocks contributes to the occurrence of enhanced counter-streaming sunward-directed fluxes, but does not appear to be a necessary condition, and (2 that the presence of small-scale transients with closed-field topologies likely also contributes to the occurrence of counter-streaming patterns, but only in the slow solar wind prior to
18. High speed atom source
International Nuclear Information System (INIS)
Hoshino, Hitoshi.
1990-01-01
In a high speed atom source, since the speed is not identical between ions and electrons, no sufficient neutralizing effect for ionic rays due to the mixing of the ionic rays and the electron rays can be obtained failing to obtain high speed atomic rays at high density. In view of the above, a speed control means is disposed for equalizing the speed of ions forming ionic rays and the speed of electrons forming electron rays. Further, incident angle of the electron rays and/or ionic rays to a magnet or an electrode is made variable. As a result, the relative speed between the ions and the electrons to the processing direction is reduced to zero, in which the probability of association between the ions and the electrons due to the coulomb force is increased to improve the neutralizing efficiency to easily obtain fine and high density high speed electron rays. Further, by varying the incident angle, a track capable of obtaining an ideal mixing depending on the energy of the neutralized ionic rays is formed. Since the high speed electron rays has such high density, they can be irradiated easily to the minute region of the specimen. (N.H.)
19. Solar wind drivers of geomagnetic storms during more than four solar cycles
Directory of Open Access Journals (Sweden)
Richardson Ian G.
2012-05-01
Full Text Available Using a classification of the near-Earth solar wind into three basic flow types: (1 High-speed streams associated with coronal holes at the Sun; (2 Slow, interstream solar wind; and (3 Transient flows originating with coronal mass ejections (CMEs at the Sun, including interplanetary CMEs and the associated upstream shocks and post-shock regions, we determine the drivers of geomagnetic storms of various size ranges based on the Kp index and the NOAA “G” criteria since 1964, close to the beginning of the space era, to 2011, encompassing more than four solar cycles (20–23. We also briefly discuss the occurrence of storms since the beginning of the Kp index in 1932, in the minimum before cycle 17. We note that the extended low level of storm activity during the minimum following cycle 23 is without precedent in this 80-year interval. Furthermore, the “typical” numbers of storm days/cycle quoted in the standard NOAA G storm table appear to be significantly higher than those obtained from our analysis, except for the strongest (G5 storms, suggesting that they should be revised downward.
20. Combined wind and solar feed-in to the grid
CSIR Research Space (South Africa)
Mushwana, Crescent
2018-05-01
Full Text Available This presentation highlights South African wind and solar resources and presents a case study on wind and solar PV combination. It also distinguishes between traditional and new philosophies regarding energy system design and the changes...
1. Wind/solar resource in Texas
Energy Technology Data Exchange (ETDEWEB)
Nelson, V.; Starcher, K.; Gaines, H. [West Texas A& M Univ., Canyon, TX (United States)
1997-12-31
Data are being collected at 17 sites to delineate a baseline for the wind and solar resource across Texas. Wind data are being collected at 10, 25, and 40 m (in some cases at 50 m) to determine wind shear and power at hub heights of large turbines. Many of the sites are located in areas of predicted terrain enhancement. The typical day in a month for power and wind turbine output was calculated for selected sites and combination of sites; distributed systems. Major result to date is that there is the possibility of load matching in South Texas during the summer months, even though the average values by month indicate a low wind potential.
2. Numerical simulation of wind loads on solar panels
Science.gov (United States)
Su, Kao-Chun; Chung, Kung-Ming; Hsu, Shu-Tsung
2018-05-01
Solar panels mounted on the roof of a building or ground are often vulnerable to strong wind loads. This study aims to investigate wind loads on solar panels using computational fluid dynamic (CFD). The results show good agreement with wind tunnel data, e.g. the streamwise distribution of mean surface pressure coefficient of a solar panel. Wind uplift for solar panels with four aspect ratios is evaluated. The effect of inclined angle and clearance (or height) of a solar panel is addressed. It is found that wind uplift of a solar panel increases when there is an increase in inclined angle and the clearance above ground shows an opposite effect.
3. Solar wind structure suggested by bimodal correlations of solar wind speed and density between the spacecraft SOHO and Wind
Science.gov (United States)
Ogilvie, K. W.; Coplan, M. A.; Roberts, D. A.; Ipavich, F.
2007-08-01
We calculate the cross-spacecraft maximum lagged-cross-correlation coefficients for 2-hour intervals of solar wind speed and density measurements made by the plasma instruments on the Solar and Heliospheric Observatory (SOHO) and Wind spacecraft over the period from 1996, the minimum of solar cycle 23, through the end of 2005. During this period, SOHO was located at L1, about 200 R E upstream from the Earth, while Wind spent most of the time in the interplanetary medium at distances of more than 100 R E from the Earth. Yearly histograms of the maximum, time-lagged correlation coefficients for both the speed and density are bimodal in shape, suggesting the existence of two distinct solar wind regimes. The larger correlation coefficients we suggest are due to structured solar wind, including discontinuities and shocks, while the smaller are likely due to Alfvénic turbulence. While further work will be required to firmly establish the physical nature of the two populations, the results of the analysis are consistent with a solar wind that consists of turbulence from quiet regions of the Sun interspersed with highly filamentary structures largely convected from regions in the inner solar corona. The bimodal appearance of the distributions is less evident in the solar wind speed than in the density correlations, consistent with the observation that the filamentary structures are convected with nearly constant speed by the time they reach 1 AU. We also find that at solar minimum the fits for the density correlations have smaller high-correlation components than at solar maximum. We interpret this as due to the presence of more relatively uniform Alfvénic regions at solar minimum than at solar maximum.
4. The Solar Wind as a Turbulence Laboratory
Directory of Open Access Journals (Sweden)
Vincenzo Carbone
2013-05-01
Full Text Available In this review we will focus on a topic of fundamental importance for both astrophysics and plasma physics, namely the occurrence of large-amplitude low-frequency fluctuations of the fields that describe the plasma state. This subject will be treated within the context of the expanding solar wind and the most meaningful advances in this research field will be reported emphasizing the results obtained in the past decade or so. As a matter of fact, Helios inner heliosphere and Ulysses' high latitude observations, recent multi-spacecrafts measurements in the solar wind (Cluster four satellites and new numerical approaches to the problem, based on the dynamics of complex systems, brought new important insights which helped to better understand how turbulent fluctuations behave in the solar wind. In particular, numerical simulations within the realm of magnetohydrodynamic (MHD turbulence theory unraveled what kind of physical mechanisms are at the basis of turbulence generation and energy transfer across the spectral domain of the fluctuations. In other words, the advances reached in these past years in the investigation of solar wind turbulence now offer a rather complete picture of the phenomenological aspect of the problem to be tentatively presented in a rather organic way.
5. Energy Primer: Solar, Water, Wind, and Biofuels.
Science.gov (United States)
Portola Inst., Inc., Menlo Park, CA.
This is a comprehensive, fairly technical book about renewable forms of energy--solar, water, wind, and biofuels. The biofuels section covers biomass energy, agriculture, aquaculture, alcohol, methane, and wood. The focus is on small-scale systems which can be applied to the needs of the individual, small group, or community. More than one-fourth…
6. Identifying Wind and Solar Ramping Events: Preprint
Energy Technology Data Exchange (ETDEWEB)
Florita, A.; Hodge, B. M.; Orwig, K.
2013-01-01
Wind and solar power are playing an increasing role in the electrical grid, but their inherent power variability can augment uncertainties in power system operations. One solution to help mitigate the impacts and provide more flexibility is enhanced wind and solar power forecasting; however, its relative utility is also uncertain. Within the variability of solar and wind power, repercussions from large ramping events are of primary concern. At the same time, there is no clear definition of what constitutes a ramping event, with various criteria used in different operational areas. Here the Swinging Door Algorithm, originally used for data compression in trend logging, is applied to identify variable generation ramping events from historic operational data. The identification of ramps in a simple and automated fashion is a critical task that feeds into a larger work of 1) defining novel metrics for wind and solar power forecasting that attempt to capture the true impact of forecast errors on system operations and economics, and 2) informing various power system models in a data-driven manner for superior exploratory simulation research. Both allow inference on sensitivities and meaningful correlations, as well as the ability to quantify the value of probabilistic approaches for future use in practice.
7. Classification of solar wind with machine learning
NARCIS (Netherlands)
E. Camporeale (Enrico); A. Carè (Algo); J.E. Borovsky (Joseph)
2017-01-01
htmlabstractWe present a four-category classification algorithm for the solar wind, based on Gaussian Process. The four categories are the ones previously adopted in Xu and Borovsky (2015): ejecta, coronal hole origin plasma, streamer belt origin plasma, and sector reversal origin plasma. The
8. Mirror Instability in the Turbulent Solar Wind
Czech Academy of Sciences Publication Activity Database
Hellinger, Petr; Landi, S.; Matteini, L.; Verdini, A.; Franci, L.
2017-01-01
Roč. 838, č. 2 (2017), 158/1-158/7 ISSN 0004-637X Institutional support: RVO:67985815 Keywords : instabilities * solar wind * waves Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics OBOR OECD: Astronomy (including astrophysics,space science) Impact factor: 5.533, year: 2016
9. Solar wind conditions for a quiet magnetosphere
International Nuclear Information System (INIS)
Kerns, K.J.; Gussenhoven, M.S.
1990-01-01
The conditions of the solar wind that lead to a quiet magnetosphere are determined under the assumption that the quiet or baseline magnetosphere can be identified by prolonged periods of low values of the am index. The authors analyzed solar wind data from 1978 to 1984 (7 years) during periods in which am ≤ 3 nT to identify those solar wind parameters that deviate significantly from average values. Parallel studies were also performed for prolonged periods of Kp = 0, 0+ and AE z ) show distinctive variations from average values. They independently varied these solar wind parameters and the length of time the conditions must persist to minimize am. This was done with the additional requirement that the conditions yield a reasonable number of occurrences (5% of the data set). The resulting baseline conditions are V ≤ 390 km/s; 180 degree - arctan |B y /B z | ≤ 101 degree, when b z ≤ 0 (no restriction on B z positive); B ≤ 6.5 nT; and persistence of these conditions for at least 5 hours. Minimizing the am index does not require a clear upper limit on the value of B z as might be anticipated from the work of Gussenhoven (1988) and Berthelier (1980). Apparently, this is a result of the requirement that the conditions must occur 5% of the time. When the requirement is lowered to 1% occurrence, an upper limit to B z emerges
10. Modeling 3-D solar wind structure
Czech Academy of Sciences Publication Activity Database
Odstrčil, Dušan
2003-01-01
Roč. 32, č. 4 (2003), s. 497-506 ISSN 0273-1177 R&D Projects: GA AV ČR IAA3003003; GA AV ČR IBS1003006 Institutional research plan: CEZ:AV0Z1003909 Keywords : solar wind * modeling Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 0.483, year: 2003
11. Wind and solar resource data sets: Wind and solar resource data sets
Energy Technology Data Exchange (ETDEWEB)
Clifton, Andrew [National Renewable Energy Laboratory, Golden CO USA; Hodge, Bri-Mathias [National Renewable Energy Laboratory, Golden CO USA; Power Systems Engineering Center, National Renewable Energy Laboratory, Golden CO USA; Draxl, Caroline [National Renewable Energy Laboratory, Golden CO USA; National Wind Technology Center, National Renewable Energy Laboratory, Golden CO USA; Badger, Jake [Department of Wind Energy, Danish Technical University, Copenhagen Denmark; Habte, Aron [National Renewable Energy Laboratory, Golden CO USA; Power Systems Engineering Center, National Renewable Energy Laboratory, Golden CO USA
2017-12-05
The range of resource data sets spans from static cartography showing the mean annual wind speed or solar irradiance across a region to high temporal and high spatial resolution products that provide detailed information at a potential wind or solar energy facility. These data sets are used to support continental-scale, national, or regional renewable energy development; facilitate prospecting by developers; and enable grid integration studies. This review first provides an introduction to the wind and solar resource data sets, then provides an overview of the common methods used for their creation and validation. A brief history of wind and solar resource data sets is then presented, followed by areas for future research.
12. Kinetic Physics of the Solar Corona and Solar Wind
Directory of Open Access Journals (Sweden)
Marsch Eckart
2006-07-01
Full Text Available Kinetic plasma physics of the solar corona and solar wind are reviewed with emphasis on the theoretical understanding of the in situ measurements of solar wind particles and waves, as well as on the remote-sensing observations of the solar corona made by means of ultraviolet spectroscopy and imaging. In order to explain coronal and interplanetary heating, the microphysics of the dissipation of various forms of mechanical, electric and magnetic energy at small scales (e.g., contained in plasma waves, turbulences or non-uniform flows must be addressed. We therefore scrutinise the basic assumptions underlying the classical transport theory and the related collisional heating rates, and also describe alternatives associated with wave-particle interactions. We elucidate the kinetic aspects of heating the solar corona and interplanetary plasma through Landau- and cyclotron-resonant damping of plasma waves, and analyse in detail wave absorption and micro instabilities. Important aspects (virtues and limitations of fluid models, either single- and multi-species or magnetohydrodynamic and multi-moment models, for coronal heating and solar wind acceleration are critically discussed. Also, kinetic model results which were recently obtained by numerically solving the Vlasov–Boltzmann equation in a coronal funnel and hole are presented. Promising areas and perspectives for future research are outlined finally.
13. Intermittency Statistics in the Expanding Solar Wind
Science.gov (United States)
Cuesta, M. E.; Parashar, T. N.; Matthaeus, W. H.
2017-12-01
The solar wind is observed to be turbulent. One of the open questions in solar wind research is how the turbulence evolves as the solar wind expands to great distances. Some studies have focused on evolution of the outer scale but not much has been done to understand how intermittency evolves in the expanding wind beyond 1 AU (see [1,2]). We use magnetic field data from Voyager I spacecraft from 1 to 10AU to study the evolution of statistics of magnetic discontinuities. We perform various statistical tests on these discontinuities and make connections to the physical processes occurring in the expanding wind.[1] Tsurutani, Bruce T., and Edward J. Smith. "Interplanetary discontinuities: Temporal variations and the radial gradient from 1 to 8.5 AU." Journal of Geophysical Research: Space Physics 84.A6 (1979): 2773-2787.[2] Greco, A., et al. "Evidence for nonlinear development of magnetohydrodynamic scale intermittency in the inner heliosphere." The Astrophysical Journal 749.2 (2012): 105.
14. High speed network sampling
OpenAIRE
Rindalsholt, Ole Arild
2005-01-01
Master i nettverks- og systemadministrasjon Classical Sampling methods play an important role in the current practice of Internet measurement. With today’s high speed networks, routers cannot manage to generate complete Netflow data for every packet. They have to perform restricted sampling. This thesis summarizes some of the most important sampling schemes and their applications before diving into an analysis on the effect of sampling Netflow records.
15. Proceedings of the Flat-plate Solar Array Project Research Forum on the High-speed Growth and Characterization of Crystals for Solar Cells
Science.gov (United States)
Dumas, K. A. (Editor)
1984-01-01
Theoretical and experimental phenomena, applications, and characterization including stress/strain and other problem areas that limit the rate of growth of crystals suitable for processing into efficient, cost-effective solar cells are discussed. Melt spinning, ribbon growth, rapid solidification, laser recrystallization, and ignot growth of silicon and metals are also discussed.
16. Solar Wind Features Responsible for Magnetic Storms and Substorms During the Declining Phase of the Solar Cycle: 197
Science.gov (United States)
Tsurutani, B.; Arballo, J.
1994-01-01
We examine interplanetary data and geomagnetic activity indices during 1974 when two long-lasting solar wind corotating streams existed. We find that only 3 major storms occurred during 1974, and all were associated with coronal mass ejections. Each high speed stream was led by a shock, so the three storms had sudden commencements. Two of the 1974 major storms were associated with shock compression of preexisting southward fields and one was caused by southward fields within a magnetic cloud. Corotating streams were responsible for recurring moderate to weak magnetic storms.
17. Wind and IMP 8 Solar Wind, Magnetosheath and Shock Data
Science.gov (United States)
2004-01-01
The purpose of this project was to provide the community access to magnetosheath data near Earth. We provided 27 years of IMP 8 magnetosheath proton velocities, densities, and temperatures with our best (usually 1-min.) time resolution. IMP 8 crosses the magnetosheath twice each 125 day orbit, and we provided magnetosheath data for the roughly 27 years of data for which magnetometer data are also available (which are needed to reliably pick boundaries). We provided this 27 years of IMP 8 magnetosheath data to the NSSDC; this data is now integrated with the IMP 8 solar wind data with flags indicating whether each data point is in the solar wind, magnetosheath, or at the boundary between the two regions. The plasma speed, density, and temperature are provided for each magnetosheath point. These data are also available on the MIT web site ftp://space .mit.edu/pub/plasma/imp/www/imp.html. We provide ASCII time-ordered rows of data giving the observation time, the spacecraft position in GSE, the velocity is GSE, the density and temperature for protons. We also have analyzed and archived on our web site the Wind magnetosheath plasma parameters. These consist of ascii files of the proton and alpha densities, speeds, and thermal speeds. These data are available at ftp://space.mit.edu/pub/plasma/wind/sheath These are the two products promised in the work statement and they have been completed in full.
18. Is tropospheric weather influenced by solar wind through atmospheric vertical coupling downward control?
Science.gov (United States)
Prikryl, Paul; Tsukijihara, Takumi; Iwao, Koki; Muldrew, Donald B.; Bruntz, Robert; Rušin, Vojto; Rybanský, Milan; Turňa, Maroš; Šťastný, Pavel; Pastirčák, Vladimír
2017-04-01
More than four decades have passed since a link between solar wind magnetic sector boundary structure and mid-latitude upper tropospheric vorticity was discovered (Wilcox et al., Science, 180, 185-186, 1973). The link has been later confirmed and various physical mechanisms proposed but apart from controversy, little attention has been drawn to these results. To further emphasize their importance we investigate the occurrence of mid-latitude severe weather in the context of solar wind coupling to the magnetosphere-ionosphere-atmosphere (MIA) system. It is observed that significant snowstorms, windstorms and heavy rain, particularly if caused by low pressure systems in winter, tend to follow arrivals of high-speed solar wind. Previously published statistical evidence that explosive extratropical cyclones in the northern hemisphere tend to occur after arrivals of high-speed solar wind streams from coronal holes (Prikryl et al., Ann. Geophys., 27, 1-30, 2009; Prikryl et al., J. Atmos. Sol.-Terr. Phys., 149, 219-231, 2016) is corroborated for the southern hemisphere. A physical mechanism to explain these observations is proposed. The leading edge of high-speed solar wind streams is a locus of large-amplitude magneto-hydrodynamic waves that modulate Joule heating and/or Lorentz forcing of the high-latitude lower thermosphere generating medium-scale atmospheric gravity waves that propagate upward and downward through the atmosphere. Simulations of gravity wave propagation in a model atmosphere using the Transfer Function Model (Mayr et al., Space Sci. Rev., 54, 297-375, 1990) show that propagating waves originating in the thermosphere can excite a spectrum of gravity waves in the lower atmosphere. In spite of significantly reduced amplitudes but subject to amplification upon reflection in the upper troposphere, these gravity waves can provide a lift of unstable air to release instabilities in the troposphere thus initiating convection to form cloud/precipitation bands
19. High Speed Photomicrography
Science.gov (United States)
Hyzer, William G.
1983-03-01
One of the most challenging areas in applying high-speed photography and videography in the plant and laboratory is in the recording of rapid events at macro and microscopic scales. Depth of field, exposure efficiency, working distance, and required exposure time are all reduced as optical magnification is increased, which severely taxes the skill and ingenuity of workers interested in recording any fast moving phenomena through the microscope or with magnifying lenses. This paper defines the problems inherent in photographing within macro and microscopic ranges and offers a systematic approach to optimizing the selection of equipment and choice of applicable techniques.
20. High speed rotary drum
Energy Technology Data Exchange (ETDEWEB)
Sagara, H
1970-03-25
A high speed rotary drum is disclosed in which the rotor vessel is a double-wall structure comprising an inner wave-shaped pipe inserted coaxially within an outer straight pipe, the object being to provide a strengthened composite light-weight structure. Since force induced axial deformation of the straight pipe and radial deformation of the corrugated pipe are small, the composite effectively resists external forces and, if the waves of the inner pipe are given a sufficient amplitude, the thickness of both pipes may be reduced to lower the overall weight. Thus high angular velocities can be obtained to separate U/sup 235/ from gaseous UF/sub 6/.
1. Solar and wind exergy potentials for Mars
International Nuclear Information System (INIS)
Delgado-Bonal, Alfonso; Martín-Torres, F. Javier; Vázquez-Martín, Sandra; Zorzano, María-Paz
2016-01-01
The energy requirements of the planetary exploration spacecrafts constrain the lifetime of the missions, their mobility and capabilities, and the number of instruments onboard. They are limiting factors in planetary exploration. Several missions to the surface of Mars have proven the feasibility and success of solar panels as energy source. The analysis of the exergy efficiency of the solar radiation has been carried out successfully on Earth, however, to date, there is not an extensive research regarding the thermodynamic exergy efficiency of in-situ renewable energy sources on Mars. In this paper, we analyse the obtainable energy (exergy) from solar radiation under Martian conditions. For this analysis we have used the surface environmental variables on Mars measured in-situ by the Rover Environmental Monitoring Station onboard the Curiosity rover and from satellite by the Thermal Emission Spectrometer instrument onboard the Mars Global Surveyor satellite mission. We evaluate the exergy efficiency from solar radiation on a global spatial scale using orbital data for a Martian year; and in a one single location in Mars (the Gale crater) but with an appreciable temporal resolution (1 h). Also, we analyse the wind energy as an alternative source of energy for Mars exploration and compare the results with those obtained on Earth. We study the viability of solar and wind energy station for the future exploration of Mars, showing that a small square solar cell of 0.30 m length could maintain a meteorological station on Mars. We conclude that the low density of the atmosphere of Mars is responsible of the low thermal exergy efficiency of solar panels. It also makes the use of wind energy uneffective. Finally, we provide insights for the development of new solar cells on Mars. - Highlights: • We analyse the exergy of solar radiation under Martian environment • Real data from in-situ instruments is used to determine the maximum efficiency of radiation • Wind
2. Solar wind velocity and geomagnetic moment variations
International Nuclear Information System (INIS)
Kalinin, Yu.D.; Rozanova, T.S.
1982-01-01
The mean year values of the solar wind velocity have been calculated from the mean-year values of a geomagnetic activity index am according to the Svalgard equation of regression for the pe-- riod from 1930 to 1960. For the same years the values of the geomagnetic moment M and separately of its ''inner'' (causes of which'' are inside the Earth) and ''external'' (causes of which are outside the Earth) parts have been calculated from the mean year data of 12 magnetic observatories. The proof of the presence of the 11-year variation in the moment M has been obtained. It is concluded that the 11-year variations in M result from the variations of the solar wind velocity
3. Mirror Instability in the Turbulent Solar Wind
Czech Academy of Sciences Publication Activity Database
Hellinger, Petr; Landi, S.; Matteini, L.; Verdini, A.; Franci, L.
2017-01-01
Roč. 838, č. 2 (2017), č. článku 158. ISSN 0004-637X Institutional support: RVO:68378289 Keywords : instabilities * solar wind * turbulence * waves Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 5.533, year: 2016 http://iopscience.iop.org/article/10.3847/1538-4357/aa67e0
4. The Solar Wind as a Turbulence Laboratory
Directory of Open Access Journals (Sweden)
Bruno Roberto
2005-09-01
Full Text Available In this review we will focus on a topic of fundamental importance for both plasma physics and astrophysics, namely the occurrence of large-amplitude low-frequency fluctuations of the fields that describe the plasma state. This subject will be treated within the context of the expanding solar wind and the most meaningful advances in this research field will be reported emphasizing the results obtained in the past decade or so. As a matter of fact, Ulysses’ high latitude observations and new numerical approaches to the problem, based on the dynamics of complex systems, brought new important insights which helped to better understand how turbulent fluctuations behave in the solar wind. In particular, numerical simulations within the realm of magnetohydrodynamic (MHD turbulence theory unraveled what kind of physical mechanisms are at the basis of turbulence generation and energy transfer across the spectral domain of the fluctuations. In other words, the advances reached in these past years in the investigation of solar wind turbulence now offer a rather complete picture of the phenomenological aspect of the problem to be tentatively presented in a rather organic way.
5. Kinetic Properties of the Neutral Solar Wind
International Nuclear Information System (INIS)
Florinski, V.; Heerikhuisen, J.
2017-01-01
Charge-exchange collisions between the solar wind protons and interstellar hydrogen produce a distinctive population of neutral hydrogen streaming radially at nearly the solar-wind speed. This tenuous population, known as the neutral solar wind (NSW) is thought to play a key role in the appearance of the Interplanetary Boundary EXplorer ribbon, a bright circular band in the sky that is the source of neutral hydrogen with energies near 1 keV. According to the leading model of the ribbon, the velocity distribution of NSW hydrogen is imparted on the pickup ions (PUIs) generated via charge exchange with the interstellar protons beyond the heliopause, and in this way controls the stability of the resulting ring distribution of PUIs against hydromagnetic wave generation. In this paper, we examine the velocity distributions of the NSW atoms in the heliosphere and the outer heliosheath regions by following the phase-space trajectories of the Boltzmann equation. It is demonstrated that these distributions are highly anisotropic, with the parallel (radial) temperature greatly exceeding the perpendicular temperature. Ions picked up near 90° from the anisotropic NSW would form a stable ring distribution capable of generating the ribbon flux. We also discuss a second population of neutrals born in charge transfer collisions with interstellar PUIs, the so-called neutralized pickup ion (NPI) component. Their high thermal velocities translate into large parallel velocity spread of the daughter ribbon PUIs, which would adversely affect plasma stability in local interstellar space.
6. Kinetic Properties of the Neutral Solar Wind
Science.gov (United States)
Florinski, V.; Heerikhuisen, J.
2017-03-01
Charge-exchange collisions between the solar wind protons and interstellar hydrogen produce a distinctive population of neutral hydrogen streaming radially at nearly the solar-wind speed. This tenuous population, known as the neutral solar wind (NSW) is thought to play a key role in the appearance of the Interplanetary Boundary EXplorer ribbon, a bright circular band in the sky that is the source of neutral hydrogen with energies near 1 keV. According to the leading model of the ribbon, the velocity distribution of NSW hydrogen is imparted on the pickup ions (PUIs) generated via charge exchange with the interstellar protons beyond the heliopause, and in this way controls the stability of the resulting ring distribution of PUIs against hydromagnetic wave generation. In this paper, we examine the velocity distributions of the NSW atoms in the heliosphere and the outer heliosheath regions by following the phase-space trajectories of the Boltzmann equation. It is demonstrated that these distributions are highly anisotropic, with the parallel (radial) temperature greatly exceeding the perpendicular temperature. Ions picked up near 90° from the anisotropic NSW would form a stable ring distribution capable of generating the ribbon flux. We also discuss a second population of neutrals born in charge transfer collisions with interstellar PUIs, the so-called neutralized pickup ion (NPI) component. Their high thermal velocities translate into large parallel velocity spread of the daughter ribbon PUIs, which would adversely affect plasma stability in local interstellar space.
7. Solar Wind Charge Exchange During Geomagnetic Storms
Science.gov (United States)
Robertson, Ina P.; Cravens, Thomas E.; Sibeck, David G.; Collier, Michael R.; Kuntz, K. D.
2012-01-01
On March 31st. 2001, a coronal mass ejection pushed the subsolar magnetopause to the vicinity of geosynchronous orbit at 6.6 RE. The NASA/GSFC Community Coordinated Modeling Center (CCMe) employed a global magnetohydrodynamic (MHD) model to simulate the solar wind-magnetosphere interaction during the peak of this geomagnetic storm. Robertson et aL then modeled the expected 50ft X-ray emission due to solar wind charge exchange with geocoronal neutrals in the dayside cusp and magnetosheath. The locations of the bow shock, magnetopause and cusps were clearly evident in their simulations. Another geomagnetic storm took place on July 14, 2000 (Bastille Day). We again modeled X-ray emission due to solar wind charge exchange, but this time as observed from a moving spacecraft. This paper discusses the impact of spacecraft location on observed X-ray emission and the degree to which the locations of the bow shock and magnetopause can be detected in images.
8. The southern high-speed stream: results from the SWICS instrument on Ulysses.
Science.gov (United States)
Geiss, J; Gloeckler, G; von Steiger, R; Balsiger, H; Fisk, L A; Galvin, A B; Ipavich, F M; Livi, S; McKenzie, J F; Ogilvie, K W
1995-05-19
The high-speed solar wind streaming from the southern coronal hole was remarkably uniform and steady and was confined by a sharp boundary that extended to the corona and chromosphere. Charge state measurements indicate that the electron temperature in this coronal hole reached a maximum of about 1.5 million kelvin within 3 solar radii of the sun. This result, combined with the observed lack of depletion of heavy elements, suggests that an additional source of momentum is required to accelerate the polar wind.
9. On the Origins of the Intercorrelations Between Solar Wind Variables
Science.gov (United States)
Borovsky, Joseph E.
2018-01-01
It is well known that the time variations of the diverse solar wind variables at 1 AU (e.g., solar wind speed, density, proton temperature, electron temperature, magnetic field strength, specific entropy, heavy-ion charge-state densities, and electron strahl intensity) are highly intercorrelated with each other. In correlation studies of the driving of the Earth's magnetosphere-ionosphere-thermosphere system by the solar wind, these solar wind intercorrelations make determining cause and effect very difficult. In this report analyses of solar wind spacecraft measurements and compressible-fluid computer simulations are used to study the origins of the solar wind intercorrelations. Two causes are found: (1) synchronized changes in the values of the solar wind variables as the plasma types of the solar wind are switched by solar rotation and (2) dynamic interactions (compressions and rarefactions) in the solar wind between the Sun and the Earth. These findings provide an incremental increase in the understanding of how the Sun-Earth system operates.
10. ISOTOPIC MASS FRACTIONATION OF SOLAR WIND: EVIDENCE FROM FAST AND SLOW SOLAR WIND COLLECTED BY THE GENESIS MISSION
International Nuclear Information System (INIS)
Heber, Veronika S.; Baur, Heinrich; Wieler, Rainer; Bochsler, Peter; McKeegan, Kevin D.; Neugebauer, Marcia; Reisenfeld, Daniel B.; Wiens, Roger C.
2012-01-01
NASA's Genesis space mission returned samples of solar wind collected over ∼2.3 years. We present elemental and isotopic compositions of He, Ne, and Ar analyzed in diamond-like carbon targets from the slow and fast solar wind collectors to investigate isotopic fractionation processes during solar wind formation. The solar wind provides information on the isotopic composition for most volatile elements for the solar atmosphere, the bulk Sun and hence, on the solar nebula from which it formed 4.6 Ga ago. Our data reveal a heavy isotope depletion in the slow solar wind compared to the fast wind composition by 63.1 ± 2.1 per mille for He, 4.2 ± 0.5 per mille amu –1 for Ne and 2.6 ± 0.5 per mille amu –1 for Ar. The three Ne isotopes suggest that isotopic fractionation processes between fast and slow solar wind are mass dependent. The He/H ratios of the collected slow and fast solar wind samples are 0.0344 and 0.0406, respectively. The inefficient Coulomb drag model reproduces the measured isotopic fractionation between fast and slow wind. Therefore, we apply this model to infer the photospheric isotopic composition of He, Ne, and Ar from our solar wind data. We also compare the isotopic composition of oxygen and nitrogen measured in the solar wind with values of early solar system condensates, probably representing solar nebula composition. We interpret the differences between these samples as being due to isotopic fractionation during solar wind formation. For both elements, the magnitude and sign of the observed differences are in good agreement with the values predicted by the inefficient Coulomb drag model.
11. ISOTOPIC MASS FRACTIONATION OF SOLAR WIND: EVIDENCE FROM FAST AND SLOW SOLAR WIND COLLECTED BY THE GENESIS MISSION
Energy Technology Data Exchange (ETDEWEB)
Heber, Veronika S.; Baur, Heinrich; Wieler, Rainer [Institute for Geochemistry and Petrology, ETH Zurich, Clausiusstrasse 25, CH-8092 Zurich (Switzerland); Bochsler, Peter [Physikalisches Institut, Universitaet Bern, Sidlerstasse 5, CH-3012 Bern (Switzerland); McKeegan, Kevin D. [Department of Earth and Space Sciences, University of California Los Angeles, 595 Charles Young Drive East, Box 951567, Los Angeles, CA 90095-1567 (United States); Neugebauer, Marcia [Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721-0092 (United States); Reisenfeld, Daniel B. [Department of Physics and Astronomy, University of Montana, Missoula, MT 59812 (United States); Wiens, Roger C., E-mail: [email protected] [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)
2012-11-10
NASA's Genesis space mission returned samples of solar wind collected over {approx}2.3 years. We present elemental and isotopic compositions of He, Ne, and Ar analyzed in diamond-like carbon targets from the slow and fast solar wind collectors to investigate isotopic fractionation processes during solar wind formation. The solar wind provides information on the isotopic composition for most volatile elements for the solar atmosphere, the bulk Sun and hence, on the solar nebula from which it formed 4.6 Ga ago. Our data reveal a heavy isotope depletion in the slow solar wind compared to the fast wind composition by 63.1 {+-} 2.1 per mille for He, 4.2 {+-} 0.5 per mille amu{sup -1} for Ne and 2.6 {+-} 0.5 per mille amu{sup -1} for Ar. The three Ne isotopes suggest that isotopic fractionation processes between fast and slow solar wind are mass dependent. The He/H ratios of the collected slow and fast solar wind samples are 0.0344 and 0.0406, respectively. The inefficient Coulomb drag model reproduces the measured isotopic fractionation between fast and slow wind. Therefore, we apply this model to infer the photospheric isotopic composition of He, Ne, and Ar from our solar wind data. We also compare the isotopic composition of oxygen and nitrogen measured in the solar wind with values of early solar system condensates, probably representing solar nebula composition. We interpret the differences between these samples as being due to isotopic fractionation during solar wind formation. For both elements, the magnitude and sign of the observed differences are in good agreement with the values predicted by the inefficient Coulomb drag model.
12. Turbulent Transport in a Three-dimensional Solar Wind
Energy Technology Data Exchange (ETDEWEB)
Shiota, D. [Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Aichi 464-8601 (Japan); Zank, G. P.; Adhikari, L.; Hunana, P. [Center for Space Plasma and Aeronomic Research (CSPAR), Department of Space Science, University of Alabama in Huntsville, Huntsville, AL 35805 (United States); Telloni, D. [INAF—Astrophysical Observatory of Torino, Via Osservatorio 20, I-10025 Pino Torinese (Italy); Bruno, R., E-mail: [email protected] [INAF-IAPS Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere 100, I-00133 Roma (Italy)
2017-03-01
Turbulence in the solar wind can play essential roles in the heating of coronal and solar wind plasma and the acceleration of the solar wind and energetic particles. Turbulence sources are not well understood and thought to be partly enhanced by interaction with the large-scale inhomogeneity of the solar wind and the interplanetary magnetic field and/or transported from the solar corona. To investigate the interaction with background inhomogeneity and the turbulence sources, we have developed a new 3D MHD model that includes the transport and dissipation of turbulence using the theoretical model of Zank et al. We solve for the temporal and spatial evolution of three moments or variables, the energy in the forward and backward fluctuating modes and the residual energy and their three corresponding correlation lengths. The transport model is coupled to our 3D model of the inhomogeneous solar wind. We present results of the coupled solar wind-turbulence model assuming a simple tilted dipole magnetic configuration that mimics solar minimum conditions, together with several comparative intermediate cases. By considering eight possible solar wind and turbulence source configurations, we show that the large-scale solar wind and IMF inhomogeneity and the strength of the turbulence sources significantly affect the distribution of turbulence in the heliosphere within 6 au. We compare the predicted turbulence distribution results from a complete solar minimum model with in situ measurements made by the Helios and Ulysses spacecraft, finding that the synthetic profiles of the turbulence intensities show reasonable agreement with observations.
13. Morphology of Pseudostreamers and Solar Wind Properties
Science.gov (United States)
Panasenco, Olga; Velli, Marco
2016-05-01
The solar dynamo and photospheric convection lead to three main types of structures extending from the solar surface into the corona - active regions, solar filaments (prominences when observed at the limb) and coronal holes. These structures exist over a wide range of scales, and are interlinked with each other in evolution and dynamics. Active regions can form clusters of magnetic activity and the strongest overlie sunspots. In the decay of active regions, the boundaries separating opposite magnetic polarities (neutral lines) develop the specific structures called filament channels above which filaments form. In the presence of flux imbalance decaying active regions can also give birth to lower latitude coronal holes. The accumulation of magnetic flux at coronal hole boundaries also creates the conditions for filament formation: polar crown filaments are permanently present at the boundaries of the polar coronal holes. Middle-latitude and equatorial coronal holes - the result of active region evolution - can create pseudostreamers (PSs) if other coronal holes of the same polarity are present. While helmet streamers form between open fields of opposite polarities, the pseudostreamer, characterized by a smaller coronal imprint, typically shows a more prominent straight ray or stalk extending from the corona. The pseudostreamer base at photospheric heights is multipolar; often one observes tripolar magnetic configurations with two neutral lines - where filaments can form - separating the coronal holes. Here we discuss the specific role of filament channels on pseudostreamer topology and on solar wind properties. 1D numerical analysis of PSs shows that the properties of the solar wind from around PSs depend on the presence/absence of filament channels, number of channels and chirality at the PS base low in the corona.
14. The sun, the solar wind, and the heliosphere
CERN Document Server
Miralles, Mari Paz
2011-01-01
This volume presents a concise, up-to-date overview of current research on the observations, theoretical interpretations, and empirical and physical descriptions of the Sun, the Solar Wind, and the Heliosphere, from the solar interior outward to the planets.
15. Coupled Solar Wind-Magnetosphere-Ionosphere-Thermosphere System by QFT
Science.gov (United States)
Chen, Shao-Guang
NM may be applied to the high-speed and the microscopic conditions. Because of the result of a test of GR with use of a hydrogen-maser frequency standard in a spacecraft launched nearly vertically upward to 10000 km (R. F. C. Vessot et.al., Phys. Rev. Lett. 45, 2081 (1980)), the isotropy of one-way velocity of light had been validated at the 1*10 (-10) level (D2.4-0030-12, H0.1-0009-12, H0.2-0008-12). Again from the Lorentz transformation (H01-0006-08) and the uncertainty principle (H05-0036-10) deduced from the metrical results of Doppler effects, SR and QM, thereby QFT and GR, all become the inferential theorems from generalized NM. Eq.(1) is as a bridge to join the modern physics and classical physics. In my paper ‘Basal electric and magnetic fields of celestial bodies come from positive-negative charge separation caused by gravitation of quasi-Casimir pressure in weak interaction’ (D31-0054-10): According to QFT the gravitation is the statistic average pressure collided by net virtual neutrinos nuν _{0} flux, the net nuν _{0} flux can press a part freedom electrons in plasma of ionosphere into the surface of celestial bodies, the static electric force of redundant positive ions prevents electrons further falling and till reach the equilibrium of stable spatial charge distribution, which is just the cause of the geomagnetic field and the geo-electric field. In the solar surface plasma add the negative charge from ionosphere electrons again rotate, thereby come into being the solar basal magnetic field. The solar surface plasma with additional electrons get the dynamic balance between the upwards force of stable positive charge distribution in the solar upside gas and the downwards force of the vacuum net nuν _{0} flux pressure (solar gravity). When the Jupiter enter into the connecting line of Sun and the center of Galaxy, the pressure (solar gravity) observed from earth will weaken because of the Jupiter stop (shield) the most net nuν _{0} flux which
16. Coulomb collisions in the solar wind
Science.gov (United States)
Klein, L. W.; Ogilvie, K. W.; Burlaga, L. F.
1985-01-01
A major improvement of the present investigation over previous studies of the subject is related to the use of helium temperatures obtained from helium ion measurements uncontaminated by the high-velocity tail of the proton distribution. More observations, covering a large parameter range, were employed, and the effects of interspecies drift were taken into account. It is shown in a more definite way than has been done previously, that Coulomb collisions provide the most important mechanism bringing about equilibrium between helium and protons in the solar wind. Other mechanisms may play some part in restricted regions, but Coulomb collisions are dominant on the macroscale.
17. Simulation experiments and solar wind sputtering
International Nuclear Information System (INIS)
Griffith, J.E.; Papanastassiou, D.A.; Russell, W.A.; Tombrello, T.A.; Weller, R.A.
1978-01-01
In order to isolate the role played by solar wind sputtering from other lunar surface phenomena a number of simulation experiments were performed, including isotope abundance measurements of Ca sputtered from terrestrial fluorite and plagioclase by 50-keV and 130-keV 14 N beams, measurement of the energy distribution of U atoms sputtered with 80-keV 40 Ar, and measurement of the fraction of sputtered U atoms which stick on the surfaces used to collect these atoms. 10 references
18. Genesis Solar Wind Science Canister Components Curated as Potential Solar Wind Collectors and Reference Contamination Sources
Science.gov (United States)
Allton, J. H.; Gonzalez, C. P.; Allums, K. K.
2016-01-01
The Genesis mission collected solar wind for 27 months at Earth-Sun L1 on both passive and active collectors carried inside of a Science Canister, which was cleaned and assembled in an ISO Class 4 cleanroom prior to launch. The primary passive collectors, 271 individual hexagons and 30 half-hexagons of semiconductor materials, are described in. Since the hard landing reduced the 301 passive collectors to many thousand smaller fragments, characterization and posting in the online catalog remains a work in progress, with about 19% of the total area characterized to date. Other passive collectors, surfaces of opportunity, have been added to the online catalog. For species needing to be concentrated for precise measurement (e.g. oxygen and nitrogen isotopes) an energy-independent parabolic ion mirror focused ions onto a 6.2 cm diameter target. The target materials, as recovered after landing, are described in. The online catalog of these solar wind collectors, a work in progress, can be found at: http://curator.jsc.nasa.gov/gencatalog/index.cfm This paper describes the next step, the cataloging of pieces of the Science Canister, which were surfaces exposed to the solar wind or component materials adjacent to solar wind collectors which may have contributed contamination.
19. DEPENDENCE OF SOLAR-WIND POWER SPECTRA ON THE DIRECTION OF THE LOCAL MEAN MAGNETIC FIELD
International Nuclear Information System (INIS)
Podesta, J. J.
2009-01-01
Wavelet analysis can be used to measure the power spectrum of solar-wind fluctuations along a line in any direction (θ, φ) with respect to the local mean magnetic field B 0 . This technique is applied to study solar-wind turbulence in high-speed streams in the ecliptic plane near solar minimum using magnetic field measurements with a cadence of eight vectors per second. The analysis of nine high-speed streams shows that the reduced spectrum of magnetic field fluctuations (trace power) is approximately azimuthally symmetric about B 0 in both the inertial range and dissipation range; in the inertial range the spectra are characterized by a power-law exponent that changes continuously from 1.6 ± 0.1 in the direction perpendicular to the mean field to 2.0 ± 0.1 in the direction parallel to the mean field. The large uncertainties suggest that the perpendicular power-law indices 3/2 and 5/3 are both consistent with the data. The results are similar to those found by Horbury et al. at high heliographic latitudes. Comparisons between solar-wind observations and the theories of strong incompressible MHD turbulence developed by Goldreich and Sridhar and Boldyrev are not rigorously justified because these theories only apply to turbulence with vanishing cross-helicity although the normalized cross-helicity of solar-wind turbulence is not negligible. Assuming these theories can be generalized in such a way that the three-dimensional wavevector spectra have similar functional forms when the cross-helicity is nonzero, then for the interval of Ulysses data analyzed by Horbury et al. the ratio of the spectra perpendicular and parallel to B 0 is more consistent with the Goldreich and Sridhar scaling P perpendicular /P || ∝ ν 1/3 than with the Boldyrev scaling ν 1/2 . The analysis of high-speed streams in the ecliptic plane does not yield a reliable measurement of this scaling law. The transition from a turbulent MHD-scale energy cascade to a kinetic Alfven wave (KAW
20. The solar wind and the earth
International Nuclear Information System (INIS)
Akasofu, I.; Kamide, Y.
1987-01-01
The sun constantly emits an enormous amount of radiation into space. This energy emission consists of three modes. Almost all the energy is emitted in the form of familiar sunlight but sun also emits X-rays, extreme ultraviolet (EUV), and UV radiation, which is absorbed above the earth's stratosphere, as a second mode of solar energy. The sun has made another important mode of energy emission in which the energy is carried out by charged particles. These particles have a bery wide range of energies, from less than 1 keV to more than 1 GeV. Because of this wide range, it is convenient to group them into two components: particles, with energies greater than 10 keV and the lower-energy particles. The former are generally referred to as solar portions or solar cosmic rays; their emission is associated with active features on the sun. Low-energy particles constitute plasma which is called the solar wind
1. The 3-D solar radioastronomy and the structure of the corona and the solar wind. [solar probes of solar activity
Science.gov (United States)
Steinberg, J. L.; Caroubalos, C.
1976-01-01
The mechanism causing solar radio bursts (1 and 111) is examined. It is proposed that a nonthermal energy source is responsible for the bursts; nonthermal energy is converted into electromagnetic energy. The advantages are examined for an out-of-the-ecliptic solar probe mission, which is proposed as a means of stereoscopically viewing solar radio bursts, solar magnetic fields, coronal structure, and the solar wind.
2. Solar wind structure out of the ecliptic plane over solar cycles
Science.gov (United States)
Sokol, J. M.; Bzowski, M.; Tokumaru, M.
2017-12-01
Sun constantly emits a stream of plasma known as solar wind. Ground-based observations of the solar wind speed through the interplanetary scintillations (IPS) of radio flux from distant point sources and in-situ measurements by Ulysses mission revealed that the solar wind flow has different characteristics depending on the latitude. This latitudinal structure evolves with the cycle of solar activity. The knowledge on the evolution of solar wind structure is important for understanding the interaction between the interstellar medium surrounding the Sun and the solar wind, which is responsible for creation of the heliosphere. The solar wind structure must be taken into account in interpretation of most of the observations of heliospheric energetic neutral atoms, interstellar neutral atoms, pickup ions, and heliospheric backscatter glow. The information on the solar wind structure is not any longer available from direct measurements after the termination of Ulysses mission and the only source of the solar wind out of the ecliptic plane is the IPS observations. However, the solar wind structure obtained from this method contains inevitable gaps in the time- and heliolatitude coverage. Sokół et al 2015 used the solar wind speed data out of the ecliptic plane retrieved from the IPS observations performed by Institute for Space-Earth Environmental Research (Nagoya University, Japan) and developed a methodology to construct a model of evolution of solar wind speed and density from 1985 to 2013 that fills the data gaps. In this paper we will present a refined model of the solar wind speed and density structure as a function of heliographic latitude updated by the most recent data from IPS observations. And we will discuss methods of extrapolation of the solar wind structure out of the ecliptic plane for the past solar cycles, when the data were not available, as well as forecasting for few years upward.
3. Solar wind velocity and temperature in the outer heliosphere
Science.gov (United States)
Gazis, P. R.; Barnes, A.; Mihalov, J. D.; Lazarus, A. J.
1994-01-01
At the end of 1992, the Pioneer 10, Pioneer 11, and Voyager 2 spacecraft were at heliocentric distances of 56.0, 37.3, and 39.0 AU and heliographic latitudes of 3.3 deg N, 17.4 deg N, and 8.6 deg S, respectively. Pioneer 11 and Voyager 2 are at similar celestial longitudes, while Pioneer 10 is on the opposite side of the Sun. All three spacecraft have working plasma analyzers, so intercomparison of data from these spacecraft provides important information about the global character of the solar wind in the outer heliosphere. The averaged solar wind speed continued to exhibit its well-known variation with solar cycle: Even at heliocentric distances greater than 50 AU, the average speed is highest during the declining phase of the solar cycle and lowest near solar minimum. There was a strong latitudinal gradient in solar wind speed between 3 deg and 17 deg N during the last solar minimum, but this gradient has since disappeared. The solar wind temperature declined with increasing heliocentric distance out to a heliocentric distance of at least 20 AU; this decline appeared to continue at larger heliocentric distances, but temperatures in the outer heliosphere were suprisingly high. While Pioneer 10 and Voyager 2 observed comparable solar wind temperatures, the temperature at Pioneer 11 was significantly higher, which suggests the existence of a large-scale variation of temperature with heliographic longitude. There was also some suggestion that solar wind temperatures were higher near solar minimum.
4. Characteristics of Solar Wind Density Depletions During Solar Cycles 23 and 24
Directory of Open Access Journals (Sweden)
Keunchan Park
2017-06-01
Full Text Available Solar wind density depletions are phenomena that solar wind density is rapidly decreased and keep the state. They are generally believed to be caused by the interplanetary (IP shocks. However, there are other cases that are hardly associated with IP shocks. We set up a hypothesis for this phenomenon and analyze this study. We have collected the solar wind parameters such as density, speed and interplanetary magnetic field (IMF data related to the solar wind density depletion events during the period from 1996 to 2013 that are obtained with the advanced composition explorer (ACE and the Wind satellite. We also calculate two pressures (magnetic, dynamic and analyze the relation with density depletion. As a result, we found total 53 events and the most these phenomena’s sources caused by IP shock are interplanetary coronal mass ejection (ICME. We also found that solar wind density depletions are scarcely related with IP shock’s parameters. The solar wind density is correlated with solar wind dynamic pressure within density depletion. However, the solar wind density has an little anti-correlation with IMF strength during all events of solar wind density depletion, regardless of the presence of IP shocks. Additionally, In 47 events of IP shocks, we find 6 events that show a feature of blast wave. The quantities of IP shocks are weaker than blast wave from the Sun, they are declined in a short time after increasing rapidly. We thus argue that IMF strength or dynamic pressure are an important factor in understanding the nature of solar wind density depletion. Since IMF strength and solar wind speed varies with solar cycle, we will also investigate the characteristics of solar wind density depletion events in different phases of solar cycle as an additional clue to their physical nature.
5. Relationship between coronal holes and high speed streams at L1: arrival times, durations, and intensities
Science.gov (United States)
Luo, B.; Bu, X.; Liu, S.; Gong, J.
2017-12-01
Coronal holes are sources of high-speed steams (HSS) of solar wind. When coronal holes appear at mid/low latitudes on the Sun, consequential HSSs may impact Earth and cause recurrent geospace environment disturbances, such as geomagnetic storms, relativistic electron enhancements at the geosynchronous orbit, and thermosphere density enhancements. Thus, it is of interests for space weather forecasters to predict when (arrival times), how long (time durations), and how severe (intensities) HSSs may impact Earth when they notice coronal holes on the sun and are anticipating their geoeffectiveness. In this study, relationship between coronal holes and high speed streams will be statistically investigated. Several coronal hole parameters, including passage times of solar central meridian, coronal hole longitudinal widths, intensities reflected by mean brightness, are derived using Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA) images for years 2011 to 2016. These parameters will be correlated with in-situ solar wind measurements measured at the L1 point by the ACE spacecraft, which can give some results that are useful for space weather forecaster in predicting the arrival times, durations, and intensities of coronal hole high-speed streams in about 3 days advance.
6. The solar wind in the third dimension
International Nuclear Information System (INIS)
Neugebauer, M.
1996-01-01
For many years, solar-wind physicists have been using plasma and field data acquired near the ecliptic plane together with data on the scintillation of radio sources and remote sensing of structures in the solar corona to estimate the properties of the high-latitude solar wind. Because of the highly successful Ulysses mission, the moment of truth is now here. This paper summarizes the principal agreements and differences between the Ulysses observations and expectations. The speed of the high-latitude solar wind was even greater than anticipated. The strength of the radial component of the interplanetary magnetic field was found to be independent of latitude. The tilt of the heliospheric current sheet caused reverse corotating shocks to be observed to higher latitudes than forward corotating shocks. The energetic particles accelerated in these shocks were detected well poleward of the latitudes at which Ulysses observed the interaction regions themselves. As anticipated, there was a strong flux of outward propagating Alfven waves throughout the polar flow. Those waves were probably largely responsible for the smaller-than-anticipated increase of galactic cosmic rays with increasing latitude. As expected, the charge state or ionization temperature of heavy ions was lower in the polar flow than in low-latitude interstream flows. What was not anticipated was the correlation of elemental abundances with ionization temperatures; the Ulysses data revealed a connection between the first ionization time in the upper chromosphere and the final ionization state in the corona. As expected, transient events were detected to ∼60 deg. latitude, but the properties of those high latitude transient flows held some surprises. At high latitudes, the speeds of the transient interplanetary plasma clouds were approximately the same as the speed of the ambient plasma and the expansion of the clouds drove forward and reverse shock pairs that had never been seen at low latitudes. At high
7. Hardware and software for automating the process of studying high-speed gas flows in wind tunnels of short-term action
Science.gov (United States)
Yakovlev, V. V.; Shakirov, S. R.; Gilyov, V. M.; Shpak, S. I.
2017-10-01
In this paper, we propose a variant of constructing automation systems for aerodynamic experiments on the basis of modern hardware-software means of domestic development. The structure of the universal control and data collection system for performing experiments in wind tunnels of continuous, periodic or short-term action is proposed. The proposed hardware and software development tools for ICT SB RAS and ITAM SB RAS, as well as subsystems based on them, can be widely applied to any scientific and experimental installations, as well as to the automation of technological processes in production.
8. Ion acoustic waves and related plasma observations in the solar wind
International Nuclear Information System (INIS)
Gurnett, D.A.; Marsch, E.; Pilipp, W.; Schwenn, R.; Rosenbauer, H.
1979-01-01
This paper presents an investigation of solar wind ion acoustic waves and their relationship to the macroscopic and microscopic characteristics of the solar wind plasma. Comparisons with the overall solar wind corotational structure show that the most intense ion acoustic waves usually occur in the low-velocity regions ahead of high-speed solar wind streams. Of the detailed plasma parameters investigated, the ion acoustic wave intensities are found to be most closely correlated with the electron to proton temperature ratio T/sub e//T/sub p/ and with the electron heat flux. Investigations of the detailed electron and proton distribution functions also show that the ion acoustic waves usually occur in regions with highly non-Maxwellian distributions characteristic of double-proton streams. The distribution functions for the double-proton streams are usually not resolved into two clearly defined peaks, but rather they appear as a broad shoulder on the main proton distribution. Two main mechanisms, an electron heat flux instability and a double-ion beam instability, are considered for generating the ion-acoustic-like waves observed in the solar wind. Both mechanisms have favorable and unfavorable features. The electron heat flux mechanism can account for the observed waves at moderate to large ratios of T/sub e//T/sub p/ but has problems when T/sub e//T/sub p/ is small, as sometimes occurs. The ion beam instability appears to provide more flexibility on the T/sub e//T/sub p/ ratio; however detailed comparisons using observed distribution functions indicate that the ion beam mode is usually stable. Possible resolutions of these difficulties are discussed
9. Substorm Occurrence and Intensity Associated With Three Types of Solar Wind Structure
Science.gov (United States)
Liou, Kan; Sotirelis, Thomas; Richardson, Ian
2018-01-01
This paper presents the results of a study of the characteristics of substorms that occurred during three distinct types of solar wind: coronal mass ejection (CME) associated, high-speed streams (HSS), and slow solar wind (SSW). A total number of 53,468 geomagnetic substorm onsets from 1983 to 2009 is used and sorted by the three solar wind types. It is found that the probability density function (PDF) of the intersubstorm time can be fitted by the combination of a dominant power law with an exponential cutoff component and a minor lognormal component, implying that substorms are associated with two distinctly different dynamical processes corresponding, perhaps, to the "externally driven" and "internally driven" processes, respectively. We compare substorm frequency and intensity associated with the three types of solar wind. It is found that the intersubstorm time is the longest during SSW and shortest during CME intervals. The averaged intersubstorm time for the internally driven substorms is 3.13, 3.15, and 7.96 h for CME, HSS, and SSW, respectively. The substorm intensity PDFs, as represented by the peak value of |SML| (the generalization of AL), can be fitted by two lognormal distribution functions. The averaged substorm intensity for either component is largest for CME (292 and 674 nT) and smallest for SSW (265 and 434 nT). We argue that the externally driven substorms are more intense than those driven internally. We conclude that the dynamical process of substorms is controlled mainly by the direct solar wind-magnetosphere coupling, whereas the internally driven process only plays a very modest minor role.
10. Were chondrites magnetized by the early solar wind?
Science.gov (United States)
Oran, Rona; Weiss, Benjamin P.; Cohen, Ofer
2018-06-01
Chondritic meteorites have been traditionally thought to be samples of undifferentiated bodies that never experienced large-scale melting. This view has been challenged by the existence of post-accretional, unidirectional natural remanent magnetization (NRM) in CV carbonaceous chondrites. The relatively young inferred NRM age [∼10 million years (My) after solar system formation] and long duration of NRM acquisition (1-106 y) have been interpreted as evidence that the magnetizing field was that of a core dynamo within the CV parent body. This would imply that CV chondrites represent the primitive crust of a partially differentiated body. However, an alternative hypothesis is that the NRM was imparted by the early solar wind. Here we demonstrate that the solar wind scenario is unlikely due to three main factors: 1) the magnitude of the early solar wind magnetic field is estimated to be limits field amplification due to pile-up of the solar wind to less than a factor of 3.5 times that of the instantaneous solar wind field, and 3) the solar wind field likely changed over timescales orders of magnitude shorter than the timescale of NRM acquisition. Using analytical arguments, numerical simulations and astronomical observations of the present-day solar wind and magnetic fields of young stars, we show that the maximum mean field the ancient solar wind could have imparted on an undifferentiated CV parent body is <3.5 nT, which is 3-4 and 3 orders of magnitude weaker than the paleointensities recorded by the CV chondrites Allende and Kaba, respectively. Therefore, the solar wind is highly unlikely to be the source of the NRM in CV chondrites. Nevertheless, future high sensitivity paleomagnetic studies of rapidly-cooled meteorites with high magnetic recording fidelity could potentially trace the evolution of the solar wind field in time.
11. Solar Wind Associated with Near Equatorial Coronal Hole M ...
2015-05-25
May 25, 2015 ... coronal hole and solar wind. For both the wavelength bands, we also com- pute coronal hole radiative energy near the earth and it is found to be of similar order as that of solar wind energy. However, for the wavelength. 193 Å, owing to almost similar magnitudes of energy emitted by coronal hole and ...
12. Alfvénic fluctuations in "newborn"' polar solar wind
Directory of Open Access Journals (Sweden)
B. Bavassano
2005-06-01
Full Text Available The 3-D structure of the solar wind is strongly dependent upon the Sun's activity cycle. At low solar activity a bimodal structure is dominant, with a fast and uniform flow at the high latitudes, and slow and variable flows at low latitudes. Around solar maximum, in sharp contrast, variable flows are observed at all latitudes. This last kind of pattern, however, is a relatively short-lived feature, and quite soon after solar maximum the polar wind tends to regain its role. The plasma parameter distributions for these newborn polar flows appear very similar to those typically observed in polar wind at low solar activity. The point addressed here is about polar wind fluctuations. As is well known, the low-solar-activity polar wind is characterized by a strong flow of Alfvénic fluctuations. Does this hold for the new polar flows too? An answer to this question is given here through a comparative statistical analysis on parameters such as total energy, cross helicity, and residual energy, that are of general use to describe the Alfvénic character of fluctuations. Our results indicate that the main features of the Alfvénic fluctuations observed in low-solar-activity polar wind have been quickly recovered in the new polar flows developed shortly after solar maximum. Keywords. Interplanetary physics (MHD waves and turbulence; Sources of the solar wind – Space plasma physics (Turbulence
13. Correlation of Pc5 wave power inside and outside themagnetosphere during high speed streams
Directory of Open Access Journals (Sweden)
R. L. Kessel
2004-01-01
Full Text Available We show a clear correlation between the ULF wave power (Pc5 range inside and outside the Earth's magnetosphere during high speed streams in 1995. We trace fluctuations beginning 200RE upstream using Wind data, to fluctuations just upstream from Earth's bow shock and in the magnetosheath using Geotail data and compare to pulsations on the ground at the Kilpisjarvi ground station. With our 5-month data set we draw the following conclusions. ULF fluctuations in the Pc5 range are found in high speed streams; they are non-Alfvénic at the leading edge and Alfvénic in the central region. Compressional and Alfvénic fluctuations are modulated at the bow shock, some features of the waveforms are preserved in the magnetosheath, but overall turbulence and wave power is enhanced by about a factor of 10. Parallel (compressional and perpendicular (transverse power are at comparable levels in the solar wind and magnetosheath, both in the compression region and in the central region of high speed streams. Both the total parallel and perpendicular Pc5 power in the solar wind (and to a lesser extent in the magnetosheath correlate well with the total Pc5 power of the ground-based H-component magnetic field. ULF fluctuations in the magnetosheath during high speed streams are common at frequencies from 1–4mHz and can coincide with the cavity eigenfrequencies of 1.3, 1.9, 2.6, and 3.4mHz, though other discrete frequencies are also often seen.
Key words. Interplanetary physics (MHD waves and turbulence – Magnetospheric physics (solar wind-magnetosphere interactions; MHD waves and instabilities
14. The Western Wind and Solar Integration Study Phase 2
Energy Technology Data Exchange (ETDEWEB)
Lew, Debra [National Renewable Energy Lab. (NREL), Golden, CO (United States); Brinkman, Greg [National Renewable Energy Lab. (NREL), Golden, CO (United States); Ibanez, E. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Florita, A. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Heaney, M. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Hodge, B. -M. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Hummon, M. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Stark, G. [National Renewable Energy Lab. (NREL), Golden, CO (United States); King, J. [RePPAE; Lefton, S. A. [Intertek-APTECH, Houston, TX (United States); Kumar, N. [Intertek-APTECH, Houston, TX (United States); Agan, D. [Intertek-APTECH, Houston, TX (United States); Jordan, G. [GE Energy, Fairfield, CT (United States); Venkataraman, S. [GE Energy, Fairfield, CT (United States)
2013-09-01
The electric grid is a highly complex, interconnected machine, and changing one part of the grid can have consequences elsewhere. Adding wind and solar affects the operation of the other power plants and adding high penetrations can induce cycling of fossil-fueled generators. Cycling leads to wear-and-tear costs and changes in emissions. Phase 2 of the Western Wind and Solar Integration Study (WWSIS-2) evaluated these costs and emissions and simulated grid operations for a year to investigate the detailed impact of wind and solar on the fossil-fueled fleet. This built on Phase 1, one of the largest wind and solar integration studies ever conducted, which examined operational impacts of high wind and solar penetrations in the West(GE Energy 2010).
15. The Western Wind and Solar Integration Study Phase 2
Energy Technology Data Exchange (ETDEWEB)
Lew, D.; Brinkman, G.; Ibanez, E.; Hodge, B. M.; Hummon, M.; Florita, A.; Heaney, M.
2013-09-01
The electric grid is a highly complex, interconnected machine, and changing one part of the grid can have consequences elsewhere. Adding wind and solar affects the operation of the other power plants and adding high penetrations can induce cycling of fossil-fueled generators. Cycling leads to wear-and-tear costs and changes in emissions. Phase 2 of the Western Wind and Solar Integration Study (WWSIS-2) evaluated these costs and emissions and simulated grid operations for a year to investigate the detailed impact of wind and solar on the fossil-fueled fleet. This built on Phase 1, one of the largest wind and solar integration studies ever conducted, which examined operational impacts of high wind and solar penetrations in the West.
16. The model of unshocked deceleration of the solar wind
International Nuclear Information System (INIS)
Gidalevich, E.Ya.
1977-01-01
The motion of the Sun relative to the interstellar gas is considered as an hydrodynamic flow in a point-source field. Interstellar gas has been found to undergo considerable compaction as it is braked in the solar gravitational field. Solar-wind braking due to ion charge exchange processes on interstellar hydrogen atoms is discussed. It is shown that tangible solar-wind braking occurs at a distance of about 3x1O 14 cm from the Sun in the apex direction. In the opposite direction solar wind propagates freely
17. 双馈风电机组与高速永磁风电机组对比分析﹡%Comparison of Doubly-fed Induction Generator and High Speed Permanent Magnet Wind Power Generator
Institute of Scientific and Technical Information of China (English)
2013-01-01
is paper compared two main wind turbines. One is doubly-fed induction generator, the other is high speed permanent magnet wind power generator. It calculated the efficiency and annual electric energy production in different IEC wind classes, and compared the cost based on the market value. A er analyzing the reliability, e ciency and power grid adaptability, it came to the conclusion that two types of wind turbines have di erent advantages and meet di erent requirements from customers. erefore, development of two types of wind turbines will be be er adapted to the market competition.% 本文从风电机组角度对两种主流的发电方式，即双馈式发电机组和高速永磁发电机组，进行了对比分析。计算了两种发电方式的效率及在不同风区的年发电量，根据市场价格对各部件进行成本对比。在综合考虑了可靠性、效率、电网适应性等方面后指出，两种方式各有特点，适合客户的不同需求。因此，作为风电机组开发商，同时开发两种机型方能更好地适应市场的竞争。
18. Innovations in Wind and Solar PV Financing
Energy Technology Data Exchange (ETDEWEB)
Cory, K.; Coughlin, J.; Jenkin, T.; Pater, J.; Swezey, B.
2008-02-01
There is growing national interest in renewable energy development based on the economic, environmental, and security benefits that these resources provide. Historically, greater development of our domestic renewable energy resources has faced a number of hurdles, primarily related to cost, regulation, and financing. With the recent sustained increase in the costs and associated volatility of fossil fuels, the economics of renewable energy technologies have become increasingly attractive to investors, both large and small. As a result, new entrants are investing in renewable energy and new business models are emerging. This study surveys some of the current issues related to wind and solar photovoltaic (PV) energy project financing in the electric power industry, and identifies both barriers to and opportunities for increased investment.
19. Suprathermal protons in the interplanetary solar wind
Science.gov (United States)
Goodrich, C. C.; Lazarus, A. J.
1976-01-01
Using the Mariner 5 solar wind plasma and magnetic field data, we present observations of field-aligned suprathermal proton velocity distributions having pronounced high-energy shoulders. These observations, similar to the interpenetrating stream observations of Feldman et al. (1974), are clear evidence that such proton distributions are interplanetary rather than bow shock associated phenomena. Large Alfven speed is found to be a requirement for the occurrence of suprathermal proton distribution; further, we find the proportion of particles in the shoulder to be limited by the magnitude of the Alfven speed. It is suggested that this last result could indicate that the proton thermal anisotropy is limited at times by wave-particle interactions
20. Relationships between the solar wind and the polar cap magnetic activity
International Nuclear Information System (INIS)
Berthelier, A.
1981-01-01
The influence of solar wind conditions on magnetic activity is described in order to delineate the differences in the response of the magnetic activity to the arrival on the magnetopause of different typical solar wind variations. By determining a new index of local magnetic activity free from seasonal and diurnal effects we put in evidence the dependence of the various effects upon the invariant latitude. Most important results are: (1) the main increase of the magnetic activity does not occur at the same invariant latitude for different interplanetary variations, e.g. peaks of Bz tend to increase magnetic activity mainly in the auroral zones while peaks of B correspond to a uniform increase in magnetic activity over the polar cap and auroral zone; (2) there is a two steps response of magnetic activity to the high speed plasma streams; (3) an increase of magnetic activity is observed for large and northward Bz, which probably indicates that the solar wind-magnetosphere coupling is efficient under these circumstances. The specific influences of the IMF polarity are also briefly reviewed. (orig.)
1. Dst Prediction Based on Solar Wind Parameters
Directory of Open Access Journals (Sweden)
Yoon-Kyung Park
2009-12-01
Full Text Available We reevaluate the Burton equation (Burton et al. 1975 of predicting Dst index using high quality hourly solar wind data supplied by the ACE satellite for the period from 1998 to 2006. Sixty magnetic storms with monotonously decreasing main phase are selected. In order to determine the injection term (Q and the decay time (tau of the equation, we examine the relationships between Dst* and VB_s, Delta Dst* and VB_s, and Delta Dst* and Dst* during the magnetic storms. For this analysis, we take into account one hour of the propagation time from the ACE satellite to the magnetopause, and a half hour of the response time of the magnetosphere/ring current to the solar wind forcing. The injection term is found to be Q({nT}/h=-3.56VB_s for VB_s>0.5mV/m and Q({nT}/h=0 for VB_s leq0.5mV/m. The tau (hour is estimated as 0.060 Dst* + 16.65 for Dst*>-175nT and 6.15 hours for Dst* leq -175nT. Based on these empirical relationships, we predict the 60 magnetic storms and find that the correlation coefficient between the observed and predicted Dst* is 0.88. To evaluate the performance of our prediction scheme, the 60 magnetic storms are predicted again using the models by Burton et al. (1975 and O'Brien & McPherron (2000a. The correlation coefficients thus obtained are 0.85, the same value for both of the two models. In this respect, our model is slightly improved over the other two models as far as the correlation coefficients is concerned. Particularly our model does a better job than the other two models in predicting intense magnetic storms (Dst* lesssim -200nT.
2. Extended neutral atmosphere effect on solar wind interaction with nonmagnetic bodies of the solar system
International Nuclear Information System (INIS)
Breus, T.K.; Krymskij, A.M.; Mitnitskij, V.Ya.
1987-01-01
Numeric modelling of the Venus flow-around by the solar wind with regard to stream loading by heavy ions, produced under photoionization of the Venus neutral oxygen corona, is conducted. It is shown, that this effect can account for a whole number of peculiarities related to the solar wind interaction with the planet which have not been clearly explained yet, namely, shock wave position, solar wind stream and magnetic field characteristics behind the front
3. Wind tunnel and CFD modelling of wind pressures on solar energy systems on flat roofs
NARCIS (Netherlands)
Bronkhorst, A.J.; Franke, J.; Geurts, C.P.W.; Bentum, van C.A.; Grepinet, F.
2010-01-01
Design of solar energy mounting systems requires more knowledge on the wind patterns around these systems. To obtain more insight in the flow patterns, which cause the pressure distributions on the solar energy systems, a wind tunnel test and Computational Fluid Dynamics analysis have been
4. Electrifying Greece with solar and wind energy
Directory of Open Access Journals (Sweden)
Mentis Dimitris
2014-01-01
Full Text Available Ensuring energy security, reducing GHG emissions and boosting the competitiveness of a country’s economy by attracting investments and technical knowhow are of paramount importance considering the targets of “20-20-20” set by the European community. Being the cradle of civilization, Greece appears today as a country caught in a prolonged hard economic and social crisis, the way out of which its citizens are looking forward as well as the entire European Union. Establishment of the leading renewable energy sources like solar and wind in Greece will not only increase the independence of its own electrification but will also provide with a foundation for developing the market of international trade of “green” energy. This paper initially highlights the current status of photovoltaics and wind turbines in Greece. Furthermore, this study evaluates whether a higher penetration of the above mentioned green energy sources would have positive impact in the economy of the country or not and in what extent they could decline the CO2 emissions until 2020, comparing to the corresponding levels in 2010.
5. CONDITIONED ANALYSIS OF HIGH-LATITUDE SOLAR WIND INTERMITTENCY
International Nuclear Information System (INIS)
D'Amicis, R.; Consolini, G.; Bavassano, B.; Bruno, R.
2012-01-01
The solar wind is a turbulent medium displaying intermittency. Its intermittent features have been widely documented and studied, showing how the intermittent character is different in fast and slow wind. In this paper, a statistical conditioned analysis of the solar wind intermittency for a period of high-latitude fast solar wind is presented. In particular, the intermittent features are investigated as a function of the Alfvénic degree of fluctuations at a given scale. The results show that the main contribution to solar wind intermittency is due to non-Alfvénic structures, while Alfvénic increments are found to be characterized by a smaller level of intermittency than the previous ones. Furthermore, the lifetime statistics of Alfvénic periods are discussed in terms of a multiscale texture of randomly oriented flux tubes.
6. Charge States of Krypton and Xenon in the Solar Wind
Science.gov (United States)
Bochsler, Peter; Fludra, Andrzej; Giunta, Alessandra
2017-09-01
We calculate charge state distributions of Kr and Xe in a model for two different types of solar wind using the effective ionization and recombination rates provided from the OPEN_ADAS data base. The charge states of heavy elements in the solar wind are essential for estimating the efficiency of Coulomb drag in the inner corona. We find that xenon ions experience particularly low Coulomb drag from protons in the inner corona, comparable to the notoriously weak drag of protons on helium ions. It has been found long ago that helium in the solar wind can be strongly depleted near interplanetary current sheets, whereas coronal mass ejecta are sometimes strongly enriched in helium. We argue that if the extraordinary variability of the helium abundance in the solar wind is due to inefficient Coulomb drag, the xenon abundance must vary strongly. In fact, a secular decrease of the solar wind xenon abundance relative to the other heavier noble gases (Ne, Ar, Kr) has been postulated based on a comparison of noble gases in recently irradiated and ancient samples of ilmenite in the lunar regolith. We conclude that decreasing solar activity and decreasing frequency of coronal mass ejections over the solar lifetime might be responsible for a secularly decreasing abundance of xenon in the solar wind.
7. Latitude dependence of long-term geomagnetic activity and its solar wind drivers
Energy Technology Data Exchange (ETDEWEB)
Myllys, M. [Helsinki Univ. (Finland). Dept. of Physics; Partamies, N. [Finnish Meteorological Institute, Helsinki (Finland); University Centre in Svalbard, Longyearbyen (Norway). Dept. of Arctic Geophysics; Juusola, L. [Finnish Meteorological Institute, Helsinki (Finland)
2015-09-01
To validate the usage of global indices in studies of geomagnetic activity, we have examined the latitude dependence of geomagnetic variations in Fennoscandia and Svalbard from 1994 to 2010. Daily standard deviation (SD) values of the horizontal magnetic field have been used as a measure of the ground magnetic disturbance level.We found that the timing of the geomagnetic minimum depends on the latitude region: corresponding to the minimum of sunspot cycle 22 (in 1996), the geomagnetic minimum occurred between the geomagnetic latitudes 57-61 in 1996 and at the latitudes 64-67 in 1997, which are the average auroral oval latitudes. During sunspot cycle 23, all latitude regions experienced the minimum in 2009, a year after the sunspot minimum. These timing differences are due to the latitude dependence of the 10 s daily SD on the different solar wind drivers. In the latitude region of 64-67 , the impact of the high-speed solar wind streams (HSSs) on the geomagnetic activity is the most pronounced compared to the other latitude groups, while in the latitude region of 57-61 , the importance of the coronal mass ejections (CMEs) dominates. The geomagnetic activity maxima during ascending solar cycle phases are typically caused by CME activity and occur especially in the oval and sub-auroral regions. The strongest geomagnetic activity occurs during the descending solar cycle phases due to a mixture of CME and HSS activity. Closer to the solar minimum, less severe geomagnetic activity is driven by HSSs and mainly visible in the poleward part of the auroral region. According to our study, however, the timing of the geomagnetic activity minima (and maxima) in different latitude bands is different, due to the relative importance of different solar wind drivers at different latitudes.
8. Latitude dependence of long-term geomagnetic activity and its solar wind drivers
International Nuclear Information System (INIS)
Myllys, M.
2015-01-01
To validate the usage of global indices in studies of geomagnetic activity, we have examined the latitude dependence of geomagnetic variations in Fennoscandia and Svalbard from 1994 to 2010. Daily standard deviation (SD) values of the horizontal magnetic field have been used as a measure of the ground magnetic disturbance level.We found that the timing of the geomagnetic minimum depends on the latitude region: corresponding to the minimum of sunspot cycle 22 (in 1996), the geomagnetic minimum occurred between the geomagnetic latitudes 57-61 in 1996 and at the latitudes 64-67 in 1997, which are the average auroral oval latitudes. During sunspot cycle 23, all latitude regions experienced the minimum in 2009, a year after the sunspot minimum. These timing differences are due to the latitude dependence of the 10 s daily SD on the different solar wind drivers. In the latitude region of 64-67 , the impact of the high-speed solar wind streams (HSSs) on the geomagnetic activity is the most pronounced compared to the other latitude groups, while in the latitude region of 57-61 , the importance of the coronal mass ejections (CMEs) dominates. The geomagnetic activity maxima during ascending solar cycle phases are typically caused by CME activity and occur especially in the oval and sub-auroral regions. The strongest geomagnetic activity occurs during the descending solar cycle phases due to a mixture of CME and HSS activity. Closer to the solar minimum, less severe geomagnetic activity is driven by HSSs and mainly visible in the poleward part of the auroral region. According to our study, however, the timing of the geomagnetic activity minima (and maxima) in different latitude bands is different, due to the relative importance of different solar wind drivers at different latitudes.
9. Weather-power station. Solar energy, wind energy, water energy
Energy Technology Data Exchange (ETDEWEB)
Schatta, M
1975-10-02
A combined power station is described, which enables one to convert solar energy and wind energy into other forms of energy. The plant consists of a water-filled boiler, in which solar energy heats the water by concentration, solar cells, and finally wind rotors, which transform wind energy into electrical energy. The transformed energy is partly available as steam heat, partly as mechanical or electrical energy. The plant can be used for supplying heating systems or electrolysis equipment. Finally, by incorporating suitable motors, a mobile version of the system can be produced.
10. Wind and Solar Curtailment: International Experience and Practices
DEFF Research Database (Denmark)
Lew, Debra; Bird, Lori; Milligan, Michael
2013-01-01
High penetrations of wind and solar generation on power systems are resulting in increasing curtailment. Wind and solar integration studies predict increased curtailment as penetration levels grow. This paper examines experiences with curtailment on bulk power systems internationally. It discusses...... how much curtailment is occurring, how it is occurring, why it is occurring, and what is being done to reduce curtailment. This summary is produced as part of the International Energy Agency Wind Task 25 on Design and Operation of Power Systems with Large Amounts of Wind Power....
11. Different magnetospheric modes: solar wind driving and coupling efficiency
Directory of Open Access Journals (Sweden)
N. Partamies
2009-11-01
Full Text Available This study describes a systematic statistical comparison of isolated non-storm substorms, steady magnetospheric convection (SMC intervals and sawtooth events. The number of events is approximately the same in each group and the data are taken from about the same years to avoid biasing by different solar cycle phase. The very same superposed epoch analysis is performed for each event group to show the characteristics of ground-based indices (AL, PCN, PC potential, particle injection at the geostationary orbit and the solar wind and IMF parameters. We show that the monthly occurrence of sawtooth events and isolated non-stormtime substorms closely follows maxima of the geomagnetic activity at (or close to the equinoxes. The most strongly solar wind driven event type, sawtooth events, is the least efficient in coupling the solar wind energy to the auroral ionosphere, while SMC periods are associated with the highest coupling ratio (AL/EY. Furthermore, solar wind speed seems to play a key role in determining the type of activity in the magnetosphere. Slow solar wind is capable of maintaining steady convection. During fast solar wind streams the magnetosphere responds with loading–unloading cycles, represented by substorms during moderately active conditions and sawtooth events (or other storm-time activations during geomagnetically active conditions.
12. Transient flows of the solar wind associated with small-scale solar activity in solar minimum
Science.gov (United States)
Slemzin, Vladimir; Veselovsky, Igor; Kuzin, Sergey; Gburek, Szymon; Ulyanov, Artyom; Kirichenko, Alexey; Shugay, Yulia; Goryaev, Farid
The data obtained by the modern high sensitive EUV-XUV telescopes and photometers such as CORONAS-Photon/TESIS and SPHINX, STEREO/EUVI, PROBA2/SWAP, SDO/AIA provide good possibilities for studying small-scale solar activity (SSA), which is supposed to play an important role in heating of the corona and producing transient flows of the solar wind. During the recent unusually weak solar minimum, a large number of SSA events, such as week solar flares, small CMEs and CME-like flows were observed and recorded in the databases of flares (STEREO, SWAP, SPHINX) and CMEs (LASCO, CACTUS). On the other hand, the solar wind data obtained in this period by ACE, Wind, STEREO contain signatures of transient ICME-like structures which have shorter duration (<10h), weaker magnetic field strength (<10 nT) and lower proton temperature than usual ICMEs. To verify the assumption that ICME-like transients may be associated with the SSA events we investigated the number of weak flares of C-class and lower detected by SPHINX in 2009 and STEREO/EUVI in 2010. The flares were classified on temperature and emission measure using the diagnostic means of SPHINX and Hinode/EIS and were confronted with the parameters of the solar wind (velocity, density, ion composition and temperature, magnetic field, pitch angle distribution of the suprathermal electrons). The outflows of plasma associated with the flares were identified by their coronal signatures - CMEs (only in few cases) and dimmings. It was found that the mean parameters of the solar wind projected to the source surface for the times of the studied flares were typical for the ICME-like transients. The results support the suggestion that weak flares can be indicators of sources of transient plasma flows contributing to the slow solar wind at solar minimum, although these flows may be too weak to be considered as separate CMEs and ICMEs. The research leading to these results has received funding from the European Union’s Seventh Programme
13. Correlation of Magnetic Fields with Solar Wind Plasma Parameters at 1AU
Science.gov (United States)
Shen, F.
2017-12-01
The physical parameters of the solar wind observed in-situ near 1AU have been studied for several decades, and relationships between them, such as the positive correlation between the solar wind plasma temperature T and velocity V, and the negative correlation between density N and velocity V, are well known. However, the magnetic field intensity does not appear to be well correlated with any individual plasma parameter. In this paper, we discuss previously under-reported correlations between B and the combined plasma parameters √NV2 as well as between B and √NT. These two correlations are strong during the periods of corotating interaction regions and high speed streams, moderate during intervals of slow solar wind, and rather poor during the passage of interplanetary coronal mass ejections. The results indicate that the magnetic pressure in the solar wind is well correlated both with the plasma dynamic pressure and the thermal pressure. Then, we employ a 3D MHD model to simulate the formation of the relationships between the magnetic strength B and √NV2 as well as √NT observed at 1AU. The inner boundary condition is derived by empirical models, with the magnetic field and density are optional. Five kinds of boundary conditions at the inner boundary of heliosphere are tested. In the cases that the magnetic field is related to speed at the inner boundary, the correlation coefficients between B and √NV2 as well as between B and √NT are even higher than that in the observational results. At 1AU the simulated radial magnetic field shows little latitude dependence, which matches the observation of Ulysses. Most of the modeled characters in these cases are closer to observation than others. This inner boundary condition may more accurately characterize Sun's magnetic influence on the heliosphere. The new input may be able to improve the simulation of CME propagation in the inner heliosphere and the space weather forecasting.
14. ROLE OF THE CORONAL ALFVÉN SPEED IN MODULATING THE SOLAR-WIND HELIUM ABUNDANCE
Energy Technology Data Exchange (ETDEWEB)
Wang, Y.-M., E-mail: [email protected] [Space Science Division, Naval Research Laboratory, Washington, DC 20375 (United States)
2016-12-20
The helium abundance He/H in the solar wind is relatively constant at ∼0.04 in high-speed streams, but varies in phase with the sunspot number in slow wind, from ∼0.01 at solar minimum to ∼0.04 at maximum. Suggested mechanisms for helium fractionation have included frictional coupling to protons and resonant interactions with high-frequency Alfvénic fluctuations. We compare He/H measurements during 1995–2015 with coronal parameters derived from source-surface extrapolations of photospheric field maps. We find that the near-Earth helium abundance is an increasing function of the magnetic field strength and Alfvén speed v {sub A} in the outer corona, while being only weakly correlated with the proton flux density. Throughout the solar cycle, fast wind is associated with short-term increases in v {sub A} near the source surface; resonance with Alfvén waves, with v {sub A} and the relative speed of α -particles and protons decreasing with increasing heliocentric distance, may then lead to enhanced He/H at 1 au. The modulation of helium in slow wind reflects the tendency for the associated coronal Alfvén speeds to rise steeply from sunspot minimum, when this wind is concentrated around the source-surface neutral line, to sunspot maximum, when the source-surface field attains its peak strengths. The helium abundance near the source surface may represent a balance between collisional decoupling from protons and Alfvén wave acceleration.
15. Small Footprint Solar/Wind-powered CASTNET System Dataset
Data.gov (United States)
U.S. Environmental Protection Agency — In this Research Effort “Small Footprint Solar/Wind-Powered CASTNET System” there are two data sets. One data set contains atmospheric concentration measurements, at...
16. Saturn radio emission and the solar wind - Voyager-2 studies
International Nuclear Information System (INIS)
Desch, M.D.; Rucker, H.O.; Observatorium Lustbuhel, Graz, Austria)
1985-01-01
Voyager 2 data from the Plasma Science experiment, the Magnetometer experiment and the Planetary Radio Astronomy experiment were used to analyze the relationship between parameters of the solar wind/interplanetary medium and the nonthermal Saturn radiation. Solar wind and interplanetary magnetic field properties were combined to form quantities known to be important in controlling terrestrial magnetospheric processes. The Voyager 2 data set used in this investigation consists of 237 days of Saturn preencounter measurements. However, due to the immersion of Saturn and the Voyager 2 spacecraft into the extended Jupiter magnetic tail, substantial periods of the time series were lacking solar wind data. To cope with this problem a superposed epoch method (CHREE analysis) was used. The results indicate the superiority of the quantities containing the solar wind density in stimulating the radio emission of Saturn - a result found earlier using Voyager 1 data - and the minor importance of quantities incorporating the interplanetary magnetic field. 10 references
17. Western Wind and Solar Integration Study: Phase 2 (Presentation)
Energy Technology Data Exchange (ETDEWEB)
Lew, D.; Brinkman, G.; Ibanez, E.; Lefton, S.; Kumar, N.; Venkataraman, S.; Jordan, G.
2013-09-01
This presentation summarizes the scope and results of the Western Wind and Solar Integration Study Phase 2, which examined operational impacts of high penetrations of variable renewable generation in the West.
18. Analysis of ISEE-3/ICE solar wind data
Science.gov (United States)
Coplan, Michael A.
1989-01-01
Under the grant that ended November 11, 1988 work was accomplished in a number of areas, as follows: (1) Analysis of solar wind data; (2) Analysis of Giacobini/Zinner encounter data; (3) Investigation of solar wind and magnetospheric electron velocity distributions; and (4) Experimental investigation of the electronic structure of clusters. Reprints and preprints of publications resulting from this work are included in the appendices.
19. Electron heat flux instabilities in the solar wind
International Nuclear Information System (INIS)
Gary, S.P.; Feldman, W.C.; Forslund, D.W.; Montgomery, M.D.
1975-01-01
There are at least three plasma instabilities associated with the electron heat flux in the solar wind. This letter reports the study of the unstable fast magnetosonic, Alfven and whistler modes via a computer code which solves the full electromagnetic, linear, Vlasov dispersion relation. Linear theory demonstrates that both the magnetosonic and Alfven instabilities are candidates for turbulent limitation of the heat flux in the solar wind at 1 A.U
20. Economic viability of wind and solar energy for industrial use
International Nuclear Information System (INIS)
Lashkari, Z.F.
1994-01-01
Non conventional energy sources have begun to move from fringes of technological possibility towards commercial viability. Out of the four sources, i e. solar, wind, biogas and minimicro hydel the first two viz. wind and solar energy are of relevance for industries in western region of India. This has to be seen in the context of developments in technology and hence economics both worldwide and in India. (author)
1. On Electron-Scale Whistler Turbulence in the Solar Wind
Science.gov (United States)
Narita, Y.; Nakamura, R.; Baumjohann, W.; Glassmeier, K.-H.; Motschmann, U.; Giles, B.; Magnes, W.; Fischer, D.; Torbert, R. B.; Russell, C. T.
2016-01-01
For the first time, the dispersion relation for turbulence magnetic field fluctuations in the solar wind is determined directly on small scales of the order of the electron inertial length, using four-point magnetometer observations from the Magnetospheric Multiscale mission. The data are analyzed using the high-resolution adaptive wave telescope technique. Small-scale solar wind turbulence is primarily composed of highly obliquely propagating waves, with dispersion consistent with that of the whistler mode.
2. Potential for Development of Solar and Wind Resource in Bhutan
Energy Technology Data Exchange (ETDEWEB)
Gilman, P.; Cowlin, S.; Heimiller, D.
2009-09-01
With support from the U.S. Agency for International Development (USAID), the U.S. Department of Energy's National Renewable Energy Laboratory (NREL) produced maps and data of the wind and solar resources in Bhutan. The solar resource data show that Bhutan has an adequate resource for flat-plate collectors, with annual average values of global horizontal solar radiation ranging from 4.0 to 5.5 kWh/m2-day (4.0 to 5.5 peak sun hours per day). The information provided in this report may be of use to energy planners in Bhutan involved in developing energy policy or planning wind and solar projects, and to energy analysts around the world interested in gaining an understanding of Bhutan's wind and solar energy potential.
3. The Character of the Solar Wind, Surface Interactions, and Water
Science.gov (United States)
Farrell, William M.
2011-01-01
We discuss the key characteristics of the proton-rich solar wind and describe how it may interact with the lunar surface. We suggest that solar wind can be both a source and loss of water/OH related volatiles, and review models showing both possibilities. Energy from the Sun in the form of radiation and solar wind plasma are in constant interaction with the lunar surface. As such, there is a solar-lunar energy connection, where solar energy and matter are continually bombarding the lunar surface, acting at the largest scale to erode the surface at 0.2 Angstroms per year via ion sputtering [1]. Figure 1 illustrates this dynamically Sun-Moon system.
4. Diamagnetic effect in the foremoon solar wind observed by Kaguya
Science.gov (United States)
Nishino, Masaki N.; Saito, Yoshifumi; Tsunakawa, Hideo; Miyake, Yohei; Harada, Yuki; Yokota, Shoichiro; Takahashi, Futoshi; Matsushima, Masaki; Shibuya, Hidetoshi; Shimizu, Hisayoshi
2017-04-01
Direct interaction between the lunar surface and incident solar wind is one of the crucial phenomena of the planetary plasma sciences. Recent observations by lunar orbiters revealed that strength of the interplanetary magnetic field (IMF) at spacecraft altitude often increases over crustal magnetic fields on the dayside. In addition, variations of the IMF on the lunar night side have been reported in the viewpoint of diamagnetic effect around the lunar wake. However, few studies have been performed for the IMF over non-magnetized regions on the dayside. Here we show an event where strength of the IMF decreases at 100 km altitude on the lunar dayside (i.e. in the foremoon solar wind) when the IMF is almost parallel to the incident solar wind flow, comparing the upstream solar wind data from ACE with Kaguya magnetometer data. The lunar surface below the Kaguya orbit is not magnetized (or very weakly magnetized), and the sunward-travelling protons show signatures of those back-scattered at the lunar surface. We find that the decrease in the magnetic pressure is compensated by the thermal pressure of the back-scattered protons. In other words, the IMF strength in the foremoon solar wind decreases by diamagnetic effect of sunward-travelling protons back-scattered at the lunar dayside surface. Such an effect would be prominent in the high-beta solar wind, and may be ubiquitous in the environment where planetary surface directly interacts with surrounding space plasma.
5. Recent Successes of Wave/Turbulence Driven Models of Solar Wind Acceleration
Science.gov (United States)
Cranmer, S. R.; Hollweg, J. V.; Chandran, B. D.; van Ballegooijen, A. A.
2010-12-01
A key obstacle in the way of producing realistic simulations of the Sun-heliosphere system is the lack of a first-principles understanding of coronal heating. Also, it is still unknown whether the solar wind is "fed" through flux tubes that remain open (and are energized by footpoint-driven wavelike fluctuations) or if mass and energy are input intermittently from closed loops into the open-field regions. In this presentation, we discuss self-consistent models that assume the energy comes from solar Alfven waves that are partially reflected, and then dissipated, by magnetohydrodynamic turbulence. These models have been found to reproduce many of the observed features of the fast and slow solar wind without the need for artificial "coronal heating functions" used by earlier models. For example, the models predict a variation with wind speed in commonly measured ratios of charge states and elemental abundances that agrees with observed trends. This contradicts a commonly held assertion that these ratios can only be produced by the injection of plasma from closed-field regions on the Sun. This presentation also reviews two recent comparisons between the models and empirical measurements: (1) The models successfully predict the amplitude and radial dependence of Faraday rotation fluctuations (FRFs) measured by the Helios probes for heliocentric distances between 2 and 15 solar radii. The FRFs are a particularly sensitive test of turbulence models because they depend not only on the plasma density and Alfven wave amplitude in the corona, but also on the turbulent correlation length. (2) The models predict the correct sense and magnitude of changes seen in the polar high-speed solar wind by Ulysses from the previous solar minimum (1996-1997) to the more recent peculiar minimum (2008-2009). By changing only the magnetic field along the polar magnetic flux tube, consistent with solar and heliospheric observations at the two epochs, the model correctly predicts that the
6. Implications of the Deep Minimum for Slow Solar Wind Origin
Science.gov (United States)
Antiochos, S. K.; Mikic, Z.; Lionello, R.; Titov, V. S.; Linker, J. A.
2009-12-01
The origin of the slow solar wind has long been one of the most important problems in solar/heliospheric physics. Two observational constraints make this problem especially challenging. First, the slow wind has the composition of the closed-field corona, unlike the fast wind that originates on open field lines. Second, the slow wind has substantial angular extent, of order 30 degrees, which is much larger than the widths observed for streamer stalks or the widths expected theoretically for a dynamic heliospheric current sheet. We propose that the slow wind originates from an intricate network of narrow (possibly singular) open-field corridors that emanate from the polar coronal hole regions. Using topological arguments, we show that these corridors must be ubiquitous in the solar corona. The total solar eclipse in August 2008, near the lowest point of the Deep Minimum, affords an ideal opportunity to test this theory by using the ultra-high resolution Predictive Science's (PSI) eclipse model for the corona and wind. Analysis of the PSI eclipse model demonstrates that the extent and scales of the open-field corridors can account for both the angular width of the slow wind and its closed-field composition. We discuss the implications of our slow wind theory for the structure of the corona and heliosphere at the Deep Minimum and describe further observational and theoretical tests. This work has been supported by the NASA HTP, SR&T, and LWS programs.
7. Solar wind temperature observations in the outer heliosphere
Science.gov (United States)
Gazis, P. R.; Barnes, A.; Mihalov, J. D.; Lazarus, A. J.
1992-01-01
The Pioneer 10, Pioneer 11, and Voyager 2 spacecraft are now at heliocentric distances of 50, 32 and 33 AU, and heliographic latitudes of 3.5 deg N, 17 deg N, and 0 deg N, respectively. Pioneer 11 and Voyager 2 are at similar celestial longitudes, while Pioneer l0 is on the opposite side of the sun. The baselines defined by these spacecraft make it possible to resolve radial, longitudinal, and latitudinal variations of solar wind parameters. The solar wind temperature decreases with increasing heliocentric distance out to a distance of 10-15 AU. At larger heliocentric distances, this gradient disappears. These high solar wind temperatures in the outer heliosphere have persisted for at least 10 years, which suggests that they are not a solar cycle effect. The solar wind temperature varied with heliographic latitude during the most recent solar minimum. The solar wind temperature at Pioneer 11 and Voyager 2 was higher than that seen at Pioneer 10 for an extended period of time, which suggests the existence of a large-scale variation of temperature with celestial longitude, but the contribution of transient phenomena is yet to be clarified.
8. Solar wind ion trends and signatures: STEREO PLASTIC observations approaching solar minimum
Directory of Open Access Journals (Sweden)
A. B. Galvin
2009-10-01
Full Text Available STEREO has now completed the first two years of its mission, moving from close proximity to Earth in 2006/2007 to more than 50 degrees longitudinal separation from Earth in 2009. During this time, several large-scale structures have been observed in situ. Given the prevailing solar minimum conditions, these structures have been predominantly coronal hole-associated solar wind, slow solar wind, their interfaces, and the occasional transient event. In this paper, we extend earlier solar wind composition studies into the current solar minimum using high-resolution (1-h sampling times for the charge state analysis. We examine 2-year trends for iron charge states and solar wind proton speeds, and present a case study of Carrington Rotation 2064 (December 2007 which includes minor ion (He, Fe, O kinetic and Fe composition parameters in comparison with proton and magnetic field signatures at large-scale structures observed during this interval.
9. SEAL FOR HIGH SPEED CENTRIFUGE
Science.gov (United States)
Skarstrom, C.W.
1957-12-17
A seal is described for a high speed centrifuge wherein the centrifugal force of rotation acts on the gasket to form a tight seal. The cylindrical rotating bowl of the centrifuge contains a closure member resting on a shoulder in the bowl wall having a lower surface containing bands of gasket material, parallel and adjacent to the cylinder wall. As the centrifuge speed increases, centrifugal force acts on the bands of gasket material forcing them in to a sealing contact against the cylinder wall. This arrangememt forms a simple and effective seal for high speed centrifuges, replacing more costly methods such as welding a closure in place.
10. The solar wind at solar maximum: comparisons of EISCAT IPS and in situ observations
Directory of Open Access Journals (Sweden)
A. R. Breen
Full Text Available The solar maximum solar wind is highly structured in latitude, longitude and in time. Coronal measurements show a very high degree of variability, with large variations that are less apparent within in situ spacecraft measurements. Interplanetary scintillation (IPS observations from EISCAT, covering distances from 20 to 100 solar radii (RS, are an ideal source of information on the inner solar wind and can be used, therefore, to cast light on its evolution with distance from the Sun. Earlier comparisons of in situ and IPS measurements under solar minimum conditions showed good large-scale agreement, particularly in the fast wind. In this study we attempt a quantitative comparison of measurements made over solar maximum by EISCAT (20–100 RS and the Wind and Ulysses spacecraft (at 215 RS and 300–1000 RS, respectively. The intervals studied were August–September 1999, May 2000, September 2000 and May 2001, the last-named being the period of the second Ulysses fast latitude scan. Both ballistic and – when possible – MHD/ballistic hybrid models were used to relate the data sets, and we compare the results obtained from these two mapping methods. The results of this study suggest that solar wind velocities measured in situ were less variable than those estimated from IPS measurements closer to the Sun, with the greatest divergence between IPS velocities and in situ measurements occurring in regions where steep longitudinal velocity gradients were seen in situ. We suggest that the interaction between streams of solar wind with different velocities leads to "smoothing" of solar wind velocities between 30–60 RS and 1 AU, and that this process continues at greater distances from the Sun.
Key words. Interplanetary physics (solar wind plasma; sources of the solar wind; instruments and techniques
11. Multicriteria GIS modeling of wind and solar farms in Colorado
Energy Technology Data Exchange (ETDEWEB)
Janke, Jason R. [Metropolitan State College of Denver, Department of Earth and Atmospheric Sciences, CB 22 P.O. Box 173362-22, Denver, CO 80217-3362 (United States)
2010-10-15
The majority of electricity and heat in Colorado comes from coal and natural gas; however, renewable energy sources will play an integral role in the state's energy future. Colorado is the 11th windiest state and has more than 250 sunny days per year. The objectives of this research are to: 1) determine which landcover classes are affiliated with high wind and solar potential; and 2) identify areas that are suitable for wind and solar farms using multicriteria GIS modelling techniques. Renewable potential (NREL wind speed measurements at 50 m above the ground and NREL annual insolation data), landcover, population density, federal lands, and distance to roads, transmission lines, and cities were reclassified according to their suitability. Each was assigned weights based on their relative importance to one another. Superb wind classes are located in high alpine areas. Unfortunately, these areas are not suitable for large-scale wind farm development due to their inaccessibility and location within a sensitive ecosystem. Federal lands have low wind potential. According to the GIS model, ideal areas for wind farm development are located in northeastern Colorado. About 41 850 km{sup 2} of the state has model scores that are in the 90-100% range. Although annual solar radiation varies slightly, inter-mountain areas receive the most insolation. As far as federal lands, Indian reservations have the greatest solar input. The GIS model indicates that ideal areas for solar development are located in northwestern Colorado and east of Denver. Only 191 km{sup 2} of the state had model scores that were in the 90-100% range. These results suggest that the variables used in this analysis have more of an effect at eliminating non-suitable areas for large-scale solar farms; a greater area exists for suitable wind farms. However, given the statewide high insolation values with minimal variance, solar projects may be better suited for small-scale residential or commercial
12. Observation of solar wind with radio-star scintillation
International Nuclear Information System (INIS)
Watanabe, Takashi
1974-01-01
Large solar flares occurred in groups in early August 1972, and many interesting phenomena were observed. The solar wind condition during this period, obtained by scintillation observation, is reviewed. The velocity of solar wind has been determined from the observation of interplanetary space scintillation at Toyokawa, Fujigamine and Sugadaira. Four to ten radio wave sources were observed for ten minutes at each southing every day. Strong earth magnetic storm and the Forbush decrease of cosmic ray were observed during the period from August 3rd to 7th. Pioneer 9 observed a solar wind having the maximum velocity as high as 1,100 km/sec, and HEOS-II observed a solar wind having the velocity close to 2,000 km/sec. On the other hand, according to the scintillation of 3C-48 and 3C-144, the velocity of solar wind passing in the interplanetary space on the westside of the earth was only 300 to 400 km/sec. Therefore it is considered that the condition of solar wind on the east side of the earth differs from that on the west side of the earth. Pioneer 9 observed the pass of a shock wave on August 9th. With all radio wave sources, high velocity solar wind was observed and Pioneer 6 positioned on the west side of the earth also observed it. The thickness of this shock wave is at least 0.3 AU. Discussion is made on the cause for the difference between the asymmetric shock wave in the direction of south-west and symmetrical shock wave. The former may be blast wave, and the latter may be piston driven shock wave and the like. (Iwakiri, K.)
13. The influence of solar wind on extratropical cyclones – Part 1: Wilcox effect revisited
Directory of Open Access Journals (Sweden)
M. Rybanský
2009-01-01
Full Text Available A sun-weather correlation, namely the link between solar magnetic sector boundary passage (SBP by the Earth and upper-level tropospheric vorticity area index (VAI, that was found by Wilcox et al. (1974 and shown to be statistically significant by Hines and Halevy (1977 is revisited. A minimum in the VAI one day after SBP followed by an increase a few days later was observed. Using the ECMWF ERA-40 re-analysis dataset for the original period from 1963 to 1973 and extending it to 2002, we have verified what has become known as the "Wilcox effect" for the Northern as well as the Southern Hemisphere winters. The effect persists through years of high and low volcanic aerosol loading except for the Northern Hemisphere at 500 mb, when the VAI minimum is weak during the low aerosol years after 1973, particularly for sector boundaries associated with south-to-north reversals of the interplanetary magnetic field (IMF BZ component. The "disappearance" of the Wilcox effect was found previously by Tinsley et al. (1994 who suggested that enhanced stratospheric volcanic aerosols and changes in air-earth current density are necessary conditions for the effect. The present results indicate that the Wilcox effect does not require high aerosol loading to be detected. The results are corroborated by a correlation with coronal holes where the fast solar wind originates. Ground-based measurements of the green coronal emission line (Fe XIV, 530.3 nm are used in the superposed epoch analysis keyed by the times of sector boundary passage to show a one-to-one correspondence between the mean VAI variations and coronal holes. The VAI is modulated by high-speed solar wind streams with a delay of 1–2 days. The Fourier spectra of VAI time series show peaks at periods similar to those found in the solar corona and solar wind time series. In the modulation of VAI by solar wind the IMF BZ seems to control the phase of the Wilcox effect and the depth of the VAI minimum. The
14. Simulation study of solar wind push on a charged wire: basis of solar wind electric sail propulsion
Directory of Open Access Journals (Sweden)
P. Janhunen
2007-03-01
Full Text Available One possibility for propellantless propulsion in space is to use the momentum flux of the solar wind. A way to set up a solar wind sail is to have a set of thin long wires which are kept at high positive potential by an onboard electron gun so that the wires repel and deflect incident solar wind protons. The efficiency of this so-called electric sail depends on how large force a given solar wind exerts on a wire segment and how large electron current the wire segment draws from the solar wind plasma when kept at a given potential. We use 1-D and 2-D electrostatic plasma simulations to calculate the force and present a semitheoretical formula which captures the simulation results. We find that under average solar wind conditions at 1 AU the force per unit length is (5±1×10−8 N/m for 15 kV potential and that the electron current is accurately given by the well-known orbital motion limited (OML theory cylindrical Langmuir probe formula. Although the force may appear small, an analysis shows that because of the very low weight of a thin wire per unit length, quite high final speeds (over 50 km/s could be achieved by an electric sailing spacecraft using today's flight-proved components. It is possible that artificial electron heating of the plasma in the interaction region could increase the propulsive effect even further.
15. Simulation study of solar wind push on a charged wire: basis of solar wind electric sail propulsion
Directory of Open Access Journals (Sweden)
P. Janhunen
2007-03-01
Full Text Available One possibility for propellantless propulsion in space is to use the momentum flux of the solar wind. A way to set up a solar wind sail is to have a set of thin long wires which are kept at high positive potential by an onboard electron gun so that the wires repel and deflect incident solar wind protons. The efficiency of this so-called electric sail depends on how large force a given solar wind exerts on a wire segment and how large electron current the wire segment draws from the solar wind plasma when kept at a given potential. We use 1-D and 2-D electrostatic plasma simulations to calculate the force and present a semitheoretical formula which captures the simulation results. We find that under average solar wind conditions at 1 AU the force per unit length is (5±1×10−8 N/m for 15 kV potential and that the electron current is accurately given by the well-known orbital motion limited (OML theory cylindrical Langmuir probe formula. Although the force may appear small, an analysis shows that because of the very low weight of a thin wire per unit length, quite high final speeds (over 50 km/s could be achieved by an electric sailing spacecraft using today's flight-proved components. It is possible that artificial electron heating of the plasma in the interaction region could increase the propulsive effect even further.
16. The Solar Wind Source Cycle: Relationship to Dynamo Behavior
Science.gov (United States)
Luhmann, J. G.; Li, Y.; Lee, C. O.; Jian, L. K.; Petrie, G. J. D.; Arge, C. N.
2017-12-01
Solar cycle trends of interest include the evolving properties of the solar wind, the heliospheric medium through which the Sun's plasmas and fields interact with Earth and the planets -including the evolution of CME/ICMEs enroute. Solar wind sources include the coronal holes-the open field regions that constantly evolve with solar magnetic fields as the cycle progresses, and the streamers between them. The recent cycle has been notably important in demonstrating that not all solar cycles are alike when it comes to contributions from these sources, including in the case of ecliptic solar wind. In particular, it has modified our appreciation of the low latitude coronal hole and streamer sources because of their relative prevalence. One way to understand the basic relationship between these source differences and what is happening inside the Sun and on its surface is to use observation-based models like the PFSS model to evaluate the evolution of the coronal field geometry. Although the accuracy of these models is compromised around solar maximum by lack of global surface field information and the sometimes non-potential evolution of the field related to more frequent and widespread emergence of active regions, they still approximate the character of the coronal field state. We use these models to compare the inferred recent cycle coronal holes and streamer belt sources of solar wind with past cycle counterparts. The results illustrate how (still) hemispherically asymmetric weak polar fields maintain a complex mix of low-to-mid latitude solar wind sources throughout the latest cycle, with a related marked asymmetry in the hemispheric distribution of the ecliptic wind sources. This is likely to be repeated until the polar field strength significantly increases relative to the fields at low latitudes, and the latter symmetrize.
17. High Speed SPM of Functional Materials
Energy Technology Data Exchange (ETDEWEB)
Huey, Bryan D. [Univ. of Connecticut, Storrs, CT (United States)
2015-08-14
The development and optimization of applications comprising functional materials necessitates a thorough understanding of their static and dynamic properties and performance at the nanoscale. Leveraging High Speed SPM and concepts enabled by it, efficient measurements and maps with nanoscale and nanosecond temporal resolution are uniquely feasible. This includes recent enhancements for topographic, conductivity, ferroelectric, and piezoelectric properties as originally proposed, as well as newly developed methods or improvements to AFM-based mechanical, friction, thermal, and photoconductivity measurements. The results of this work reveal fundamental mechanisms of operation, and suggest new approaches for improving the ultimate speed and/or efficiency, of data storage systems, magnetic-electric sensors, and solar cells.
18. High-speed holographic camera
International Nuclear Information System (INIS)
Novaro, Marc
The high-speed holographic camera is a disgnostic instrument using holography as an information storing support. It allows us to take 10 holograms, of an object, with exposures times of 1,5ns, separated in time by 1 or 2ns. In order to get these results easily, no mobile part is used in the set-up [fr
19. Preferred solar wind emitting longitudes on the sun
International Nuclear Information System (INIS)
Gosling, J.T.; Asbridge, J.R.; Bame, S.J.; Feldman, W.C.
1977-01-01
During the 11 1/2-year period from July 1964 through December 1975, high- and low-speed solar wind flows originated from preferred solar longitudes. The preferred longitude effect was most pronounced from 1970 onward but was also evident in the years preceding 1970. The most pronounced modulation in average solar wind speed with longitude (approximately 20%) was obtained when it was assumed that the synodic rotation period of the sun is 27.025 days. Some deep internal structure in the sun must ultmately be responsible for these long-lived longitudinal effects, which appear to rotate rigidly with the sun
20. Large-scale interaction of the solar wind with cometary plasma tails
International Nuclear Information System (INIS)
Niedner, M.B. Jr.
1979-01-01
The study of the behavior of plasma tails in the context of their interaction with the solar wind could have important implications for the structure of the interplanetary medium in three dimensions. Comet Kohoutek 1973f exhibited a broad range of plasma tail behavior. On 1974 January 20, the tail was in a highly disturbed condition. Comet Kohoutek was encountering the leading edge of a very strong high-speed stream at the time the plasma tail disturbance started to develop. Comparison of the observed tail geometry on January 20 with the theoretical position angles generated from the wind sock theory of plasma tails and the corotated satellite observations shows that the tail disturbance was probably caused by large gradients of the polar component of the solar-wind velocity. Within hours after the disturbance of January 20, the plasma tail of comet Kohoutek became disconnected from the cometary head, and was replaced by a new plasma tail. The comet was very near an interplanetary sector boundary at the time of disconnection. The disconnection event (DE) is suggested to have resulted from the magnetic reconnection of plasma tail field lines. A similar analysis of other DEs found in original plate material and in published photographs shows the most DEs occur near corotated sector boundaries. Thus, the sector boundary model is further supported, and the finding provides the only known method of probing sector structure to high latitudes. Sector boundaries can often extend to high latitudes in a nearly North-South orientation, and this property is not restricted to times away from solar minimum. Furthermore, the boundaries are inferred to be randomly tilted with respect to the polarity sequence across the boundary and to the magnetic signs of the solar poles
1. The Yaglom law in the expanding solar wind
International Nuclear Information System (INIS)
Gogoberidze, G.; Perri, S.; Carbone, V.
2013-01-01
We study the Yaglom law, which relates the mixed third-order structure function to the average dissipation rate of turbulence, in a uniformly expanding solar wind by using the two-scale expansion model of magnetohydrodynamic (MHD) turbulence. We show that due to the expansion of the solar wind, two new terms appear in the Yaglom law. The first term is related to the decay of the turbulent energy by nonlinear interactions, whereas the second term is related to the non-zero cross-correlation of the Elsässer fields. Using magnetic field and plasma data from WIND and Helios 2 spacecrafts, we show that at lower frequencies in the inertial range of MHD turbulence the new terms become comparable to Yaglom's third-order mixed moment, and therefore they cannot be neglected in the evaluation of the energy cascade rate in the solar wind.
2. The magnetosphere under weak solar wind forcing
Directory of Open Access Journals (Sweden)
C. J. Farrugia
2007-02-01
Full Text Available The Earth's magnetosphere was very strongly disturbed during the passage of the strong shock and the following interacting ejecta on 21–25 October 2001. These disturbances included two intense storms (Dst*≈−250 and −180 nT, respectively. The cessation of this activity at the start of 24 October ushered in a peculiar state of the magnetosphere which lasted for about 28 h and which we discuss in this paper. The interplanetary field was dominated by the sunward component [B=(4.29±0.77, −0.30±0.71, 0.49±0.45 nT]. We analyze global indicators of geomagnetic disturbances, polar cap precipitation, ground magnetometer records, and ionospheric convection as obtained from SuperDARN radars. The state of the magnetosphere is characterized by the following features: (i generally weak and patchy (in time low-latitude dayside reconnection or reconnection poleward of the cusps; (ii absence of substorms; (iii a monotonic recovery from the previous storm activity (Dst corrected for magnetopause currents decreasing from ~−65 to ~−35 nT, giving an unforced decreased of ~1.1 nT/h; (iv the probable absence of viscous-type interaction originating from the Kelvin-Helmholtz (KH instability; (v a cross-polar cap potential of just 20–30 kV; (vi a persistent, polar cap region containing (vii very weak, and sometimes absent, electron precipitation and no systematic inter-hemisphere asymmetry. Whereas we therefore infer the presence of a moderate amount of open flux, the convection is generally weak and patchy, which we ascribe to the lack of solar wind driver. This magnetospheric state approaches that predicted by Cowley and Lockwood (1992 but has never yet been observed.
3. A model for the origin of solar wind stream interfaces
International Nuclear Information System (INIS)
Hundhausen, A.J.; Burlaga, L.F.
1975-01-01
The basic variations in solar wind properties that have been observed at 'stream interfaces' near 1 AU are explained by a gas dynamic model in which a radially propagating stream, produced by a temperature variation in the solar envelope, steepens nonlinearly while moving through interplanetary space. The region thus identified with the stream interface separates the ambient solar wind from the fresh hot material originally in the stream. However, the interface regions given by the present model are thicker than most stream interfaces observed in the solar wind, a fact suggesting that some additional physical process may be important in determining that thickness. Variations in the density, speed, or Alfven pressure alone appear not to produce streams with such an interface
4. SOLAR WIND HEAVY IONS OVER SOLAR CYCLE 23: ACE/SWICS MEASUREMENTS
International Nuclear Information System (INIS)
Lepri, S. T.; Landi, E.; Zurbuchen, T. H.
2013-01-01
Solar wind plasma and compositional properties reflect the physical properties of the corona and its evolution over time. Studies comparing the previous solar minimum with the most recent, unusual solar minimum indicate that significant environmental changes are occurring globally on the Sun. For example, the magnetic field decreased 30% between the last two solar minima, and the ionic charge states of O have been reported to change toward lower values in the fast wind. In this work, we systematically and comprehensively analyze the compositional changes of the solar wind during cycle 23 from 2000 to 2010 while the Sun moved from solar maximum to solar minimum. We find a systematic change of C, O, Si, and Fe ionic charge states toward lower ionization distributions. We also discuss long-term changes in elemental abundances and show that there is a ∼50% decrease of heavy ion abundances (He, C, O, Si, and Fe) relative to H as the Sun went from solar maximum to solar minimum. During this time, the relative abundances in the slow wind remain organized by their first ionization potential. We discuss these results and their implications for models of the evolution of the solar atmosphere, and for the identification of the fast and slow wind themselves.
5. Conductive solar wind models in rapidly diverging flow geometries
International Nuclear Information System (INIS)
Holzer, T.E.; Leer, E.
1980-01-01
A detailed parameter study of conductive models of the solar wind has been carried out, extending the previous similar studies of Durney (1972) and Durney and Hundhausen (1974) by considering collisionless inhibition of thermal conduction, rapidly diverging flow geometries, and the structure of solutions for the entire n 0 -T 0 plane (n 0 and T 0 are the coronal base density and temperature). Primary emphasis is placed on understanding the complex effects of the physical processes operative in conductive solar wind models. There are five points of particular interest that have arisen from the study: (1) neither collisionless inhibition of thermal conduction nor rapidly diverging flow geometries can significantly increase the solar wind speed at 1 AU; (2) there exists a firm upper limit on the coronal base temperature consistent with observed values of the coronal base pressure and solar wind mass flux density; (3) the principal effect of rapidly diverging flow geometries is a decrease in the solar wind mass flux density at 1 AU and an increase in the mass flux density at the coronal base; (4) collisionless inhibition of thermal conduction can lead to a solar wind flow speed that either increases or decreases with increasing coronal base density (n 0 ) and temperature (T 0 , depending on the region of the n 0 -T 0 plane considered; (5) there is a region of the n 0 -T/sub o/ plane at high coronal base densities where low-speed, high-mass-flux, transonic solar wind flows exist: a region not previously considered
6. Meteoric ions in the corona and solar wind
International Nuclear Information System (INIS)
Lemaire, J.
1990-01-01
The total mass of refractory material of interplanetary origin penetrating and evaporated in the meltosphere surrounding the sun has been inferred from observations of meteoroids and fireballs falling in earth's atmosphere. The amount of iron atoms deposited this way in the solar corona is of the order of 3000 t/s or larger. The measured flux of outflowing solar wind iron ions is equal to 2200 t/s. The close agreement of both fluxes is evidence that a significant fraction of iron ions observed in the solar wind and in the corona must be of meteoric origin. A similar accord is also obtained for silicon ions. The mean velocity of meteoroid ions formed in the solar corona is equal to the free-fall velocity: i.e., independent of their atomic mass as the thermal speed of heavy ion measured in low-density solar wind streams at 1 AU. Furthermore, the heavy ions of meteoric origin escape out of the corona with a larger bulk velocity than the protons which are mainly of solar origin. These differences of heavy ion and proton bulk velocities are also observed in the solar wind. 52 refs
7. Solar-wind predictions for the Parker Solar Probe orbit. Near-Sun extrapolations derived from an empirical solar-wind model based on Helios and OMNI observations
Science.gov (United States)
Venzmer, M. S.; Bothmer, V.
2018-03-01
Context. The Parker Solar Probe (PSP; formerly Solar Probe Plus) mission will be humanitys first in situ exploration of the solar corona with closest perihelia at 9.86 solar radii (R⊙) distance to the Sun. It will help answer hitherto unresolved questions on the heating of the solar corona and the source and acceleration of the solar wind and solar energetic particles. The scope of this study is to model the solar-wind environment for PSPs unprecedented distances in its prime mission phase during the years 2018 to 2025. The study is performed within the Coronagraphic German And US SolarProbePlus Survey (CGAUSS) which is the German contribution to the PSP mission as part of the Wide-field Imager for Solar PRobe. Aim. We present an empirical solar-wind model for the inner heliosphere which is derived from OMNI and Helios data. The German-US space probes Helios 1 and Helios 2 flew in the 1970s and observed solar wind in the ecliptic within heliocentric distances of 0.29 au to 0.98 au. The OMNI database consists of multi-spacecraft intercalibrated in situ data obtained near 1 au over more than five solar cycles. The international sunspot number (SSN) and its predictions are used to derive dependencies of the major solar-wind parameters on solar activity and to forecast their properties for the PSP mission. Methods: The frequency distributions for the solar-wind key parameters, magnetic field strength, proton velocity, density, and temperature, are represented by lognormal functions. In addition, we consider the velocity distributions bi-componental shape, consisting of a slower and a faster part. Functional relations to solar activity are compiled with use of the OMNI data by correlating and fitting the frequency distributions with the SSN. Further, based on the combined data set from both Helios probes, the parameters frequency distributions are fitted with respect to solar distance to obtain power law dependencies. Thus an empirical solar-wind model for the inner
8. Solar wind and its interaction with the Earth magnetosphere
International Nuclear Information System (INIS)
Grib, S.A.
1978-01-01
A critical review is given regarding the research of the stationary and non-stationary interaction of the solar wind with the Earth magnetosphere. Highlighted is the significance of the interplanetary magnetic field in the non-stationary movement of the solar wind flux. The problem of the solar wind shock waves interaction with the ''bow wave-Earth's magnetosphere'' system is being solved. Considered are the secondary phenomena, as a result of which the depression-type wave occurs, that lowers the pressure on the Earth's maanetosphere. The law, governing the movement of the magnetosphere subsolar point during the abrupt start of a geomagnetic storm has been discovered. Stationary circumvention of the magnetosphere by the solar wind flux is well described by the gas dynamic theory of the hypersonic flux. Non-stationary interaction of the solar wind shock waves with the magnetosphere is magnetohydrodynamic. It is pointed out, that the problems under consideration are important for the forecasting of strong geomagnetic perturbations on the basis of cosmic observations
9. Effect of Alfvenic fluctuations on the solar wind
International Nuclear Information System (INIS)
Chien, T.H.
1974-01-01
The major source of microscale fluctuations in the interplanetary medium due to the outwardly propagating Alfven waves is considered. The effect of the Alfven waves on the supersonic expansion of the solar wind is studied under the assumption that the motion of the interplanetary medium can be resolved physically into a comparatively smooth and slowly varying mesoscale flow and field with very irregular disordered incompressible microscale Alfvenic fluctuations superposed on it. The important features of the solar wind such as heat conduction flux, spiral interplanetary magnetic field, and proton thermal anisotropy are included in the theory. For inviscid, steady state, spherically symmetrical model of the solar wind, the two-fluid formulation of the background mesoscale MHD equations is obtained. The results show that during the expansion process, fluctuation energy is converted into the kinetic energy of the solar wind. Due to the presence of the Alfvenic fluctuations, the velocity of the solar wind is about 5 percent higher than that without considering the fluctuations. (U.S.)
10. LONG-TERM TRENDS IN THE SOLAR WIND PROTON MEASUREMENTS
Energy Technology Data Exchange (ETDEWEB)
Elliott, Heather A.; McComas, David J. [Southwest Research Institute, San Antonio, TX (United States); DeForest, Craig E. [Southwest Research Institute, Boulder, CO (United States)
2016-11-20
We examine the long-term time evolution (1965–2015) of the relationships between solar wind proton temperature ( T {sub p}) and speed ( V {sub p}) and between the proton density ( n {sub p}) and speed using OMNI solar wind observations taken near Earth. We find a long-term decrease in the proton temperature–speed ( T {sub p}– V {sub p}) slope that lasted from 1972 to 2010, but has been trending upward since 2010. Since the solar wind proton density–speed ( n {sub p}– V {sub p}) relationship is not linear like the T {sub p}– V {sub p} relationship, we perform power-law fits for n {sub p}– V {sub p}. The exponent (steepness in the n {sub p}– V {sub p} relationship) is correlated with the solar cycle. This exponent has a stronger correlation with current sheet tilt angle than with sunspot number because the sunspot number maxima vary considerably from cycle to cycle and the tilt angle maxima do not. To understand this finding, we examined the average n {sub p} for different speed ranges, and found that for the slow wind n {sub p} is highly correlated with the sunspot number, with a lag of approximately four years. The fast wind n {sub p} variation was less, but in phase with the cycle. This phase difference may contribute to the n {sub p}– V {sub p} exponent correlation with the solar cycle. These long-term trends are important since empirical formulas based on fits to T {sub p} and V {sub p} data are commonly used to identify interplanetary coronal mass ejections, but these formulas do not include any time dependence. Changes in the solar wind density over a solar cycle will create corresponding changes in the near-Earth space environment and the overall extent of the heliosphere.
11. Dissipation and heating in solar wind turbulence: from the macro to the micro and back again.
Science.gov (United States)
Kiyani, Khurom H; Osman, Kareem T; Chapman, Sandra C
2015-05-13
The past decade has seen a flurry of research activity focused on discerning the physics of kinetic scale turbulence in high-speed astrophysical plasma flows. By 'kinetic' we mean spatial scales on the order of or, in particular, smaller than the ion inertial length or the ion gyro-radius--the spatial scales at which the ion and electron bulk velocities decouple and considerable change can be seen in the ion distribution functions. The motivation behind most of these studies is to find the ultimate fate of the energy cascade of plasma turbulence, and thereby the channels by which the energy in the system is dissipated. This brief Introduction motivates the case for a themed issue on this topic and introduces the topic of turbulent dissipation and heating in the solar wind. The theme issue covers the full breadth of studies: from theory and models, massive simulations of these models and observational studies from the highly rich and vast amount of data collected from scores of heliospheric space missions since the dawn of the space age. A synopsis of the theme issue is provided, where a brief description of all the contributions is discussed and how they fit together to provide an over-arching picture on the highly topical subject of dissipation and heating in turbulent collisionless plasmas in general and in the solar wind in particular. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
12. High-speed parallel counter
International Nuclear Information System (INIS)
Gus'kov, B.N.; Kalinnikov, V.A.; Krastev, V.R.; Maksimov, A.N.; Nikityuk, N.M.
1985-01-01
This paper describes a high-speed parallel counter that contains 31 inputs and 15 outputs and is implemented by integrated circuits of series 500. The counter is designed for fast sampling of events according to the number of particles that pass simultaneously through the hodoscopic plane of the detector. The minimum delay of the output signals relative to the input is 43 nsec. The duration of the output signals can be varied from 75 to 120 nsec
13. High-speed AC motors
Energy Technology Data Exchange (ETDEWEB)
Jokinen, T.; Arkkio, A. [Helsinki University of Technology Laboratory of Electromechanics, Otaniemi (Finland)
1997-12-31
The paper deals with various types of highspeed electric motors, and their limiting powers. Standard machines with laminated rotors can be utilised if the speed is moderate. The solid rotor construction makes it possible to reach higher power and speed levels than those of laminated rotors. The development work on high-speed motors done at Helsinki University of Technology is presented, too. (orig.) 12 refs.
14. A study of the solar wind deceleration in the Earth's foreshock region
Science.gov (United States)
Zhang, T.-L.; Schwingenschuh, K.; Russell, C. T.
1995-01-01
Previous observations have shown that the solar wind is decelerated and deflected in the earth's upstream region populated by long-period waves. This deceleration is corelated with the 'diffuse' but not with the 'reflected' ion population. The speed of the solar wind may decrease tens of km/s in the foreshock region. The solar wind dynamic pressure exerted on the magnetopause may vary due to the fluctuation of the solar wind speed and density in the foreshock region. In this study, we examine this solar wind deceleration and determine how the solar wind deceleration varies in the foreshock region.
15. A hybrid reconfigurable solar and wind energy system
Science.gov (United States)
We study the feasibility of a novel hybrid solar-wind hybrid system that shares most of its infrastructure and components. During periods of clear sunny days the system will generate electricity from the sun using a parabolic concentrator. The concentrator is formed by individual mirror elements and focuses the light onto high intensity vertical multi-junction (VMJ) cells. During periods of high wind speeds and at night, the same concentrator setup will be reconfigured to channel the wind into a wind turbine which will be used to harness wind energy. In this study we report on the feasibility of this type of solar/wind hybrid energy system. The key mechanisms; optics, cooling mechanism of VMJ cells and air flow through the system were investigated using simulation tools. The results from these simulations, along with a simple economic analysis giving the levelized cost of energy for such a system are presented. An iterative method of design refinement based on the simulation results was used to work towards a prototype design. The levelized cost of the system achieved in the economic analysis shows the system to be a good alternative for a grid isolated site and could be used as a standalone system in regions of lower demand. The new approach to solar wind hybrid system reported herein will pave way for newer generation of hybrid systems that share common infrastructure in addition to the storage and distribution of energy.
16. Weakest solar wind of the space age and the current 'MINI' solar maximum
International Nuclear Information System (INIS)
McComas, D. J.; Angold, N.; Elliott, H. A.; Livadiotis, G.; Schwadron, N. A.; Smith, C. W.; Skoug, R. M.
2013-01-01
The last solar minimum, which extended into 2009, was especially deep and prolonged. Since then, sunspot activity has gone through a very small peak while the heliospheric current sheet achieved large tilt angles similar to prior solar maxima. The solar wind fluid properties and interplanetary magnetic field (IMF) have declined through the prolonged solar minimum and continued to be low through the current mini solar maximum. Compared to values typically observed from the mid-1970s through the mid-1990s, the following proton parameters are lower on average from 2009 through day 79 of 2013: solar wind speed and beta (∼11%), temperature (∼40%), thermal pressure (∼55%), mass flux (∼34%), momentum flux or dynamic pressure (∼41%), energy flux (∼48%), IMF magnitude (∼31%), and radial component of the IMF (∼38%). These results have important implications for the solar wind's interaction with planetary magnetospheres and the heliosphere's interaction with the local interstellar medium, with the proton dynamic pressure remaining near the lowest values observed in the space age: ∼1.4 nPa, compared to ∼2.4 nPa typically observed from the mid-1970s through the mid-1990s. The combination of lower magnetic flux emergence from the Sun (carried out in the solar wind as the IMF) and associated low power in the solar wind points to the causal relationship between them. Our results indicate that the low solar wind output is driven by an internal trend in the Sun that is longer than the ∼11 yr solar cycle, and they suggest that this current weak solar maximum is driven by the same trend.
17. Understanding non-equilibrium collisional and expansion effects in the solar wind with Parker Solar Probe
Science.gov (United States)
Korreck, K. E.; Klein, K. G.; Maruca, B.; Alterman, B. L.
2017-12-01
The evolution of the solar wind from the corona to the Earth and throughout the heliosphere is a complex interplay between local micro kinetics and large scale expansion effects. These processes in the solar wind need to be separated in order to understand and distinguish the dominant mechanism for heating and acceleration of the solar wind. With the upcoming launch in 2018 of Parker Solar Probe and the launch of Solar Orbiter after, addressing the local and global phenomena will be enabled with in situ measurements. Parker Solar Probe will go closer to the Sun than any previous mission enabling the ability to examine the solar wind at an early expansion age. This work examines the predictions for what will be seen inside of the 0.25 AU (54 solar radii) where Parker Solar Probe will take measurements and lays the groundwork for disentangling the expansion and collisional effects. In addition, methods of thermal plasma data analysis to determine the stability of the plasma in the Parker Solar Probe measurements will be discussed.
18. A large-scale view of Space Technology 5 magnetometer response to solar wind drivers.
Science.gov (United States)
Knipp, D J; Kilcommons, L M; Gjerloev, J; Redmon, R J; Slavin, J; Le, G
2015-04-01
In this data report we discuss reprocessing of the Space Technology 5 (ST5) magnetometer database for inclusion in NASA's Coordinated Data Analysis Web (CDAWeb) virtual observatory. The mission consisted of three spacecraft flying in elliptical orbits, from 27 March to 27 June 2006. Reprocessing includes (1) transforming the data into the Modified Apex Coordinate System for projection to a common reference altitude of 110 km, (2) correcting gain jumps, and (3) validating the results. We display the averaged magnetic perturbations as a keogram, which allows direct comparison of the full-mission data with the solar wind values and geomagnetic indices. With the data referenced to a common altitude, we find the following: (1) Magnetic perturbations that track the passage of corotating interaction regions and high-speed solar wind; (2) unexpectedly strong dayside perturbations during a solstice magnetospheric sawtooth oscillation interval characterized by a radial interplanetary magnetic field (IMF) component that may have enhanced the accompanying modest southward IMF; and (3) intervals of reduced magnetic perturbations or "calms," associated with periods of slow solar wind, interspersed among variable-length episodic enhancements. These calms are most evident when the IMF is northward or projects with a northward component onto the geomagnetic dipole. The reprocessed ST5 data are in very good agreement with magnetic perturbations from the Defense Meteorological Satellite Program (DMSP) spacecraft, which we also map to 110 km. We briefly discuss the methods used to remap the ST5 data and the means of validating the results against DMSP. Our methods form the basis for future intermission comparisons of space-based magnetometer data.
19. Distribution and solar wind control of compressional solar wind-magnetic anomaly interactions observed at the Moon by ARTEMIS
Science.gov (United States)
Halekas, J. S.; Poppe, A. R.; Lue, C.; Farrell, W. M.; McFadden, J. P.
2017-06-01
A statistical investigation of 5 years of observations from the two-probe Acceleration, Reconnection, Turbulence, and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) mission reveals that strong compressional interactions occur infrequently at high altitudes near the ecliptic but can form in a wide range of solar wind conditions and can occur up to two lunar radii downstream from the lunar limb. The compressional events, some of which may represent small-scale collisionless shocks ("limb shocks"), occur in both steady and variable interplanetary magnetic field (IMF) conditions, with those forming in steady IMF well organized by the location of lunar remanent crustal magnetization. The events observed by ARTEMIS have similarities to ion foreshock phenomena, and those observed in variable IMF conditions may result from either local lunar interactions or distant terrestrial foreshock interactions. Observed velocity deflections associated with compressional events are always outward from the lunar wake, regardless of location and solar wind conditions. However, events for which the observed velocity deflection is parallel to the upstream motional electric field form in distinctly different solar wind conditions and locations than events with antiparallel deflections. Consideration of the momentum transfer between incoming and reflected solar wind populations helps explain the observed characteristics of the different groups of events.Plain Language SummaryWe survey the environment around the Moon to determine when and where strong amplifications in the charged particle density and magnetic field strength occur. These structures may be some of the smallest shock waves in the solar system, and learning about their formation informs us about the interaction of charged particles with small-scale magnetic fields throughout the solar system and beyond. We find that these compressions occur in an extended region downstream from the lunar dawn and dusk regions and
20. Coupling of the solar wind to measures of magnetic activity
International Nuclear Information System (INIS)
McPherron, R.L.; Fay, R.A.; Garrity, C.R.; Bargatze, L.F.; Baker, D.N.; Clauer, C.R.; Searls, C.
1984-01-01
The technique of linear prediction filtering has been used to generate empirical response functions relating the solar wind electric field to the most frequently used magnetic indices, AL, AU, Dst and ASYM. Two datasets, one from 1967-1968 and one from 1973-1974, provided the information needed to calculate the empirical response functions. These functions have been convolved with solar wind observations obtained during the IMS to predict the indices. These predictions are compared with the observed indices during two, three-day intervals studied extensively by participants in the CDAW-6 workshop. Differences between the observed and predicted indices are discussed in terms of the linear assumption and in terms of physical processes other than direct solar wind-magnetosphere interaction
1. Solar wind power electric plant on Vis (Croatia)
International Nuclear Information System (INIS)
1998-01-01
A project of a solar photovoltaic electric power plant presented by the Republic of Croatia at the meeting of the E.P.I.A. Mission for photovoltaic technology of the Mediterranean countries, aroused a great interest of the representatives of the invited countries. However, the interest within Croatia in the project has disappeared although E.P.I.A. offered a financing of two thirds of costs. There are attempts to construct 1800 kw wind-driven generators at the same location not taking into consideration a possibility of building a hybrid solar-wind-power electric plant. The chance that the solar part is completely of domestic origin is not accepted but the preference is given to the building of imported wind-driven generators. (orig.)
2. Effects of electrons on the solar wind proton temperature anisotropy
International Nuclear Information System (INIS)
Michno, M. J.; Lazar, M.; Schlickeiser, R.; Yoon, P. H.
2014-01-01
Among the kinetic microinstabilities, the firehose instability is one of the most efficient mechanisms to restrict the unlimited increase of temperature anisotropy in the direction of an ambient magnetic field as predicted by adiabatic expansion of collision-poor solar wind. Indeed, the solar wind proton temperature anisotropy detected near 1 AU shows that it is constrained by the marginal firehose condition. Of the two types of firehose instabilities, namely, parallel and oblique, the literature suggests that the solar wind data conform more closely to the marginal oblique firehose condition. In the present work, however, it is shown that the parallel firehose instability threshold is markedly influenced by the presence of anisotropic electrons, such that under some circumstances, the cumulative effects of both electron and proton anisotropies could describe the observation without considering the oblique firehose mode.
3. THE NEW HORIZONS SOLAR WIND AROUND PLUTO (SWAP) OBSERVATIONS OF THE SOLAR WIND FROM 11–33 au
Energy Technology Data Exchange (ETDEWEB)
Elliott, H. A.; McComas, D. J.; Valek, P.; Weidner, S.; Livadiotis, G. [Southwest Research Institute, 6220 Culebra Road, San Antonio, TX 78238 (United States); Nicolaou, G., E-mail: [email protected] [Swedish Institute of Space Physics, Box 812, SE-98128, Kiruna (Sweden)
2016-04-15
The Solar Wind Around Pluto (SWAP) instrument on National Aeronautics and Space Administration's New Horizons Pluto mission has collected solar wind observations en route from Earth to Pluto, and these observations continue beyond Pluto. Few missions have explored the solar wind in the outer heliosphere making this dataset a critical addition to the field. We created a forward model of SWAP count rates, which includes a comprehensive instrument response function based on laboratory and flight calibrations. By fitting the count rates with this model, the proton density (n), speed (V), and temperature (T) parameters are determined. Comparisons between SWAP parameters and both propagated 1 au observations and prior Voyager 2 observations indicate consistency in both the range and mean wind values. These comparisons as well as our additional findings confirm that small and midsized solar wind structures are worn down with increasing distance due to dynamic interaction of parcels of wind with different speed. For instance, the T–V relationship steepens, as the range in V is limited more than the range in T with distance. At times the T–V correlation clearly breaks down beyond 20 au, which may indicate wind currently expanding and cooling may have an elevated T reflecting prior heating and compression in the inner heliosphere. The power of wind parameters at shorter periodicities decreases with distance as the longer periodicities strengthen. The solar rotation periodicity is present in temperature beyond 20 au indicating the observed parcel temperature may reflect not only current heating or cooling, but also heating occurring closer to the Sun.
4. THE NEW HORIZONS SOLAR WIND AROUND PLUTO (SWAP) OBSERVATIONS OF THE SOLAR WIND FROM 11–33 au
International Nuclear Information System (INIS)
Elliott, H. A.; McComas, D. J.; Valek, P.; Weidner, S.; Livadiotis, G.; Nicolaou, G.
2016-01-01
The Solar Wind Around Pluto (SWAP) instrument on National Aeronautics and Space Administration's New Horizons Pluto mission has collected solar wind observations en route from Earth to Pluto, and these observations continue beyond Pluto. Few missions have explored the solar wind in the outer heliosphere making this dataset a critical addition to the field. We created a forward model of SWAP count rates, which includes a comprehensive instrument response function based on laboratory and flight calibrations. By fitting the count rates with this model, the proton density (n), speed (V), and temperature (T) parameters are determined. Comparisons between SWAP parameters and both propagated 1 au observations and prior Voyager 2 observations indicate consistency in both the range and mean wind values. These comparisons as well as our additional findings confirm that small and midsized solar wind structures are worn down with increasing distance due to dynamic interaction of parcels of wind with different speed. For instance, the T–V relationship steepens, as the range in V is limited more than the range in T with distance. At times the T–V correlation clearly breaks down beyond 20 au, which may indicate wind currently expanding and cooling may have an elevated T reflecting prior heating and compression in the inner heliosphere. The power of wind parameters at shorter periodicities decreases with distance as the longer periodicities strengthen. The solar rotation periodicity is present in temperature beyond 20 au indicating the observed parcel temperature may reflect not only current heating or cooling, but also heating occurring closer to the Sun
5. Magnetic fields in the solar system planets, moons and solar wind interactions
CERN Document Server
Wicht, Johannes; Gilder, Stuart; Holschneider, Matthias
2018-01-01
This book addresses and reviews many of the still little understood questions related to the processes underlying planetary magnetic fields and their interaction with the solar wind. With focus on research carried out within the German Priority Program ”PlanetMag”, it also provides an overview of the most recent research in the field. Magnetic fields play an important role in making a planet habitable by protecting the environment from the solar wind. Without the geomagnetic field, for example, life on Earth as we know it would not be possible. And results from recent space missions to Mars and Venus strongly indicate that planetary magnetic fields play a vital role in preventing atmospheric erosion by the solar wind. However, very little is known about the underlying interaction between the solar wind and a planet’s magnetic field. The book takes a synergistic interdisciplinary approach that combines newly developed tools for data acquisition and analysis, computer simulations of planetary interiors an...
6. The turbulent cascade and proton heating in the solar wind during solar minimum
International Nuclear Information System (INIS)
Coburn, Jesse T.; Smith, Charles W.; Vasquez, Bernard J.; Stawarz, Joshua E.; Forman, Miriam A.
2013-01-01
Solar wind measurements at 1 AU during the recent solar minimum and previous studies of solar maximum provide an opportunity to study the effects of the changing solar cycle on in situ heating. Our interest is to compare the levels of activity associated with turbulence and proton heating. Large-scale shears in the flow caused by transient activity are a source that drives turbulence that heats the solar wind, but as the solar cycle progresses the dynamics that drive the turbulence and heat the medium are likely to change. The application of third-moment theory to Advanced Composition Explorer (ACE) data gives the turbulent energy cascade rate which is not seen to vary with the solar cycle. Likewise, an empirical heating rate shows no significan changes in proton heating over the cycle.
7. Agua Caliente Wind/Solar Project at Whitewater Ranch
Energy Technology Data Exchange (ETDEWEB)
Hooks, Todd [Agua Caliente Band of Cahuilla Indians, Palm Springs, CA (United States); Stewart, Royce [Red Mountain Energy Partners, Sante Fe, NM (United States)
2014-12-16
Agua Caliente Band of Cahuilla Indians (ACBCI) was awarded a grant by the Department of Energy (DOE) to study the feasibility of a wind and/or solar renewable energy project at the Whitewater Ranch (WWR) property of ACBCI. Red Mountain Energy Partners (RMEP) was engaged to conduct the study. The ACBCI tribal lands in the Coachella Valley have very rich renewable energy resources. The tribe has undertaken several studies to more fully understand the options available to them if they were to move forward with one or more renewable energy projects. With respect to the resources, the WWR property clearly has excellent wind and solar resources. The DOE National Renewable Energy Laboratory (NREL) has continued to upgrade and refine their library of resource maps. The newer, more precise maps quantify the resources as among the best in the world. The wind and solar technology available for deployment is also being improved. Both are reducing their costs to the point of being at or below the costs of fossil fuels. Technologies for energy storage and microgrids are also improving quickly and present additional ways to increase the wind and/or solar energy retained for later use with the network management flexibility to provide power to the appropriate locations when needed. As a result, renewable resources continue to gain more market share. The transitioning to renewables as the major resources for power will take some time as the conversion is complex and can have negative impacts if not managed well. While the economics for wind and solar systems continue to improve, the robustness of the WWR site was validated by the repeated queries of developers to place wind and/or solar there. The robust resources and improving technologies portends toward WWR land as a renewable energy site. The business case, however, is not so clear, especially when the potential investment portfolio for ACBCI has several very beneficial and profitable alternatives.
8. Kinetic Properties of Solar Wind Silicon and Iron Ions
Science.gov (United States)
Janitzek, N. P.; Berger, L.; Drews, C.; Wimmer-Schweingruber, R. F.
2017-12-01
Heavy ions with atomic numbers Z>2 account for less than one percent of the solar wind ions. However, serving as test particles with differing mass and charge, they provide a unique experimental approach to major questions of solar and fundamental plasma physics such as coronal heating, the origin and acceleration of the solar wind and wave-particle interaction in magnetized plasma. Yet the low relative abundances of the heavy ions pose substantial challenges to the instrumentation measuring these species with reliable statistics and sufficient time resolution. As a consequence the numbers of independent measurements and studies are small. The Charge Time-Of-Flight (CTOF) mass spectrometer as part of the Charge, ELement and Isotope Analysis System (CELIAS) onboard the SOlar and Heliospheric Observatory (SOHO) is a linear time-of-flight mass spectrometer which was operated at Lagrangian point L1 in 1996 for a few months only, before it suffered an instrument failure. Despite its short operation time, the CTOF sensor measured solar wind heavy ions with excellent charge state separation, an unprecedented cadence of 5 minutes and very high counting statistics, exceeding similar state-of-the-art instruments by a factor of ten. In contrast to earlier CTOF studies which were based on reduced onboard post-processed data, in our current studies we use raw Pulse Height Analysis (PHA) data providing a significantly increased mass, mass-per-charge and velocity resolution. Focussing on silicon and iron ion measurements, we present an overview of our findings on (1) short time behavior of heavy ion 1D radial velocity distribution functions, (2) differential streaming between heavy ions and solar wind bulk protons, (3) kinetic temperatures of heavy ions. Finally, we compare the CTOF results with measurements of the Solar Wind Ion Composition Spectrometer (SWICS) instrument onboard the Advanced Composition Explorer (ACE).
9. Laboratory Simulations of CME-Solar Wind Interactions Using a Coaxial Gun and Background Plasma
Science.gov (United States)
Wallace, B. H.; Zhang, Y.; Fisher, D.; Gilmore, M.
2016-12-01
Understanding and predicting solar coronal mass ejections (CMEs) is of critical importance for mitigating their disruptive behavior on ground- and space-based technologies. While predictive models of CME propagation and evolution have relied primarily on sparse in-situ data along with ground and satellite images for validation purposes, emerging laboratory efforts have shown that CME-like events can be created with parameters applicable to the solar regime that may likewise aid in predictive modeling. A modified version of the coaxial plasma gun from the Plasma Bubble Expansion Experiment (PBEX) [A. G. Lynn, Y. Zhang, S. C. Hsu, H. Li, W. Liu, M. Gilmore, and C. Watts, Bull. Amer. Phys. Soc. 52, 53 (2007)] will be used in conjunction with the Helicon-Cathode (HelCat) basic plasma science device in order to observe the magnetic characteristics of CMEs as they propagate through the solar wind. The evolution of these interactions will be analyzed using a multi-tip Langmuir probe array, a 33-position B-dot probe array, and a high speed camera. The results of this investigation will be used alongside the University of Michigan's BATS-R-US 3-D MHD numerical code, which will be used to perform simulations of the coaxial plasma gun experiment. The results of these two approaches will be compared in order to validate the capabilities of the BATS-R-US code as well as to further our understanding of magnetic reconnection and other processes that take place as CMEs propagate through the solar wind. The details of the experimental setup as well as the analytical approach are discussed.
10. Formation of Heliospheric Arcs of Slow Solar Wind
Energy Technology Data Exchange (ETDEWEB)
Higginson, A. K.; Zurbuchen, T. H. [Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, MI 48109 (United States); Antiochos, S. K.; DeVore, C. R. [Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Wyper, P. F., E-mail: [email protected] [Department of Mathematical Sciences, Durham University, Durham DH1 3LE (United Kingdom)
2017-05-01
A major challenge in solar and heliospheric physics is understanding the origin and nature of the so-called slow solar wind. The Sun’s atmosphere is divided into magnetically open regions, known as coronal holes, where the plasma streams out freely and fills the solar system, and closed regions, where the plasma is confined to coronal loops. The boundary between these regions extends outward as the heliospheric current sheet (HCS). Measurements of plasma composition strongly imply that much of the slow wind consists of plasma from the closed corona that escapes onto open field lines, presumably by field-line opening or by interchange reconnection. Both of these processes are expected to release closed-field plasma into the solar wind within and immediately adjacent to the HCS. Mysteriously, however, slow wind with closed-field plasma composition is often observed in situ far from the HCS. We use high-resolution, three-dimensional, magnetohydrodynamic simulations to calculate the dynamics of a coronal hole with a geometry that includes a narrow corridor flanked by closed field and is driven by supergranule-like flows at the coronal-hole boundary. These dynamics produce giant arcs of closed-field plasma that originate at the open-closed boundary in the corona, but extend far from the HCS and span tens of degrees in latitude and longitude at Earth. We conclude that such structures can account for the long-puzzling slow-wind observations.
11. Flank solar wind interaction. Annual report, June 1991-July 1992
International Nuclear Information System (INIS)
1992-08-01
This report summarizes the results of the first 12 months of our program to study the interaction of the Earth's magnetosphere with the solar wind on the far flanks of the bow shock. This study employs data from the ISEE-3 spacecraft during its traversals of the Earth's magnetotail and correlative data from spacecraft monitoring the solar wind upstream. Our main effort to date has involved assembling data sets and developing new plotting programs. Two talks were given at the Spring Meeting of the American Geophysical Union describing our initial results from analyzing data from the far flank foreshock and magnetosheath. The following sections summarize our results
12. ANALYSING SOLAR-WIND HYBRID POWER GENERATING SYSTEM
Directory of Open Access Journals (Sweden)
Mustafa ENGİN
2005-02-01
Full Text Available In this paper, a solar-wind hybrid power generating, system that will be used for security lighting was designed. Hybrid system was installed and solar cells, wind turbine, battery bank, charge regulators and inverter performance values were measured through the whole year. Using measured values of overall system efficiency, reliability, demanded energy cost per kWh were calculated, and percentage of generated energy according to resources were defined. We also include in the paper a discussion of new strategies to improve hybrid power generating system performance and demanded energy cost per kWh.
13. Dependence of Substorm Evolution on Solar Wind Condition: Simulation Study
Science.gov (United States)
Kamiyoshikawa, N.; Ebihara, Y.; Tanaka, T.
2017-12-01
A substorm is one of the remarkable disturbances occurring in the magnetosphere. It is known that the substorm occurs frequently when IMF is southward and solar wind speed is high. However, the physical process to determine substorm scale is not well understood. We reproduced substorms by using global MHD simulation, calculated auroral electrojet (ionospheric Hall current) flowing in the ionosphere to investigate the dependence of substorm evolution on solar wind condition. Solar wind speed of 372.4 km/s and IMF Bz of 5.0 nT were imposed to, obtain the quasi-stationary state of the magnetosphere. Then the solar wind parameters were changed as a step function. For the solar wind speed, we assumed 300 km/s, 500 km/s and 700 km/s. For IMF, we assumed -1.0 nT, -3.0 nT, -5.0 nT, -7.0 nT and -9.0 nT. In total, 15 simulation runs were performed. In order to objectively evaluate the substorm, the onset was identified with the method based on the one proposed by Newell et al. (2011). This method uses the SME index that is an extension of the AE index. In this study, the geomagnetic variation induced by the ionospheric Hall current was obtained every 1 degree from the magnetic latitude 40 degrees to 80 degrees and in every 0.5 hours in the magnetic region direction. The upper and the lower envelopes of the geomagnetic variation are regarded as SMU index and SML index, respectively. The larger the solar wind speed, the larger the southward IMF, the more the onset tends to be faster. This tendency is consistent with the onset occurrence probability indicated by Newell et al. (2016). Moreover, the minimum value of the SML index within 30 minutes from the beginning of the onset tends to decrease with the solar wind speed and the magnitude of the southward IMF. A rapid decrease of the SML index can be explained by a rapid increase in the field-aligned currents flowing in and out of the nightside ionosphere. This means that electromagnetic energies flowing into the ionosphere
14. Solar wind plasma structure near a 'HELIOS-Perihelion'
International Nuclear Information System (INIS)
Kikuchi, H.
1979-01-01
The purpose of this paper is to introduce a couple of preliminary but important results obtained from HELIOS observation concerning solar wind plasma structure near a ''HELIOS-Perihelion'' among the data analyses in progress, partly in relation to laboratory plasma. Idealized profiles of the bulk velocity, density and temperature of solar wind near 0.3 AU as deduced from HELIOS A data and correlated K-coronal contours were obtained. During 1974 - 1976, the sun was in the period of declining cycle, and the coronal holes expanded to lower latitudes from northern and southern holes. There is general tendency that the northern coronal hole is somewhat larger than the southern coronal hole. In regards to solar wind velocity, there are two fast stream regions with velocity as high as 800 Km/sec. An electron spectrum measured near a HELIOS-Perihelion (0.3 AU) approximately in the solar direction is shown. Three regions can be distinguished in velocity distribution. The density contours of solar wind electrons in velocity space exhibit a narrow beam of electrons in the magnetic field direction close to the plane of observation. (Kato, T.)
15. Harmonic analysis and suppression in hybrid wind & PV solar system
Science.gov (United States)
Gupta, Tripti; Namekar, Swapnil
2018-04-01
The growing demand of electricity has led to produce power through non-conventional source of energy such as solar energy, wind energy, hydro power, energy through biogas and biomass etc. Hybrid system is taken to complement the shortcoming of either sources of energy. The proposed system is grid connected hybrid wind and solar system. A 2.1 MW Doubly fed Induction Generator (DFIG) has been taken for analysis of wind farm whose rotor part is connected to two back-to-back converters. A 250 KW Photovoltaic (PV) array taken to analyze solar farm where inverter is required to convert power from DC to AC since electricity generated through solar PV is in the form of DC. Stability and reliability of the system is very important when the system is grid connected. Harmonics is the major Power quality issue which degrades the quality of power at load side. Harmonics in hybrid system arise through the use of power conversion unit. The other causes of harmonics are fluctuation in wind speed and solar irradiance. The power delivered to grid must be free from harmonics and within the limits specified by Indian grid codes. In proposed work, harmonic analysis of the hybrid system is performed in Electrical Transient Analysis program (ETAP) and single tuned harmonic filter is designed to maintain the utility grid harmonics within limits.
16. CHARACTERIZATION OF TRANSITIONS IN THE SOLAR WIND PARAMETERS
International Nuclear Information System (INIS)
Perri, S.; Balogh, A.
2010-01-01
The distinction between fast and slow solar wind streams and the dynamically evolved interaction regions is reflected in the characteristic fluctuations of both the solar wind and the embedded magnetic field. High-resolution magnetic field data from the Ulysses spacecraft have been analyzed. The observations show rapid variations in the magnetic field components and in the magnetic field strength, suggesting a structured nature of the solar wind at small scales. The typical sizes of fluctuations cover a broad range. If translated to the solar surface, the scales span from the size of granules (∼10 3 km) and supergranules (∼10 4 km) on the Sun down to ∼10 2 km and less. The properties of the short time structures change in the different types of solar wind. While fluctuations in fast streams are more homogeneous, slow streams present a bursty behavior in the magnetic field variances, and the regions of transition are characterized by high levels of power in narrow structures around the transitions. The probability density functions of the magnetic field increments at several scales reveal a higher level of intermittency in the mixed streams, which is related to the presence of well localized features. It is concluded that, apart from the differences in the nature of fluctuations in flows of different coronal origin, there is a small-scale structuring that depends on the origin of streams themselves but it is also related to a bursty generation of the fluctuations.
17. High speed computer assisted tomography
International Nuclear Information System (INIS)
Maydan, D.; Shepp, L.A.
1980-01-01
X-ray generation and detection apparatus for use in a computer assisted tomography system which permits relatively high speed scanning. A large x-ray tube having a circular anode (3) surrounds the patient area. A movable electron gun (8) orbits adjacent to the anode. The anode directs into the patient area xrays which are delimited into a fan beam by a pair of collimating rings (21). After passing through the patient, x-rays are detected by an array (22) of movable detectors. Detector subarrays (23) are synchronously movable out of the x-ray plane to permit the passage of the fan beam
18. GPP Webinar: Market Outlook and Innovations in Wind and Solar Power
Science.gov (United States)
Green Power Partnership webinar reviewing the state of the renewable energy industry as a whole, with a focus on wind and solar power and exploring recent marketplace innovations in wind and solar power and renewable energy purchases.
19. Power generation from wind turbines in a solar chimney
Energy Technology Data Exchange (ETDEWEB)
Foote, Tudor [Graduate Student, Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, Jolley Hall, Campus Box 1185, One Brookings Drive, St. Louis, Missouri, 63130 (United States); Agarwal, Ramesh K. [William Palm Professor, Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, Jolley Hall, Campus Box 1185, One Brookings Drive, St. Louis, Missouri, 63130 (United States)
2013-07-01
Recent studies have shown that shrouded wind turbines can generate greater power compared to bare turbines. A solar chimney generates an upward draft of wind inside a tower and a shroud around the wind turbine. There are numerous empty silos on farms in the U.S. that can be converted to solar chimneys with minor modifications at modest cost. The objective of this study is to determine the potential of these silos/chimneys for generating wind power. The study is conducted through analytical/computational approach by employing the commercial Computational Fluid Dynamics (CFD) software. Computations are performed for five different geometric configurations consisting of a turbine, a cylindrical silo, and/or a venturi and/or a diffuser using the dimensions of typical silos and assuming Class 3 wind velocity. The incompressible Navier-Stokes equations with the Boussinesq approximation and a two equation realizable {kappa}-{epsilon} model are employed in the calculations, and the turbine is modeled as an actuator disk. The power coefficient (Cp) and generated power are calculated for the five cases. Consistent with recent literature, it was found that the silos with diffusers increase the Cp beyond Betz’s limit significantly and thus the generated power. It should be noted that Cp is calculated by normalizing it by the turbine area swept by the wind. This study shows the potential of using abandoned silos in the mid-west and other parts of the country for localized wind power generation.
20. Magnetosheath for almost-aligned solar wind magnetic field and flow vectors: Wind observations across the dawnside magnetosheath at X = -12 Re
Science.gov (United States)
Farrugia, C. J.; Erkaev, N. V.; Torbert, R. B.; Biernat, H. K.; Gratton, F. T.; Szabo, A.; Kucharek, H.; Matsui, H.; Lin, R. P.; Ogilvie, K. W.; Lepping, R. P.; Smith, C. W.
2010-08-01
While there are many approximations describing the flow of the solar wind past the magnetosphere in the magnetosheath, the case of perfectly aligned (parallel or anti-parallel) interplanetary magnetic field (IMF) and solar wind flow vectors can be treated exactly in a magnetohydrodynamic (MHD) approach. In this work we examine a case of nearly-opposed (to within 15°) interplanetary field and flow vectors, which occurred on October 24-25, 2001 during passage of the last interplanetary coronal mass ejection in an ejecta merger. Interplanetary data are from the ACE spacecraft. Simultaneously Wind was crossing the near-Earth (X ˜ -13 Re) geomagnetic tail and subsequently made an approximately 5-hour-long magnetosheath crossing close to the ecliptic plane (Z = -0.7 Re). Geomagnetic activity was returning steadily to quiet, “ground” conditions. We first compare the predictions of the Spreiter and Rizzi theory with the Wind magnetosheath observations and find fair agreement, in particular as regards the proportionality of the magnetic field strength and the product of the plasma density and bulk speed. We then carry out a small-perturbation analysis of the Spreiter and Rizzi solution to account for the small IMF components perpendicular to the flow vector. The resulting expression is compared to the time series of the observations and satisfactory agreement is obtained. We also present and discuss observations in the dawnside boundary layer of pulsed, high-speed (v ˜ 600 km/s) flows exceeding the solar wind flow speeds. We examine various generating mechanisms and suggest that the most likely cause is a wave of frequency 3.2 mHz excited at the inner edge of the boundary layer by the Kelvin-Helmholtz instability.
1. A Model fot the Sources of the Slow Solar Wind
Science.gov (United States)
Antiochos, S. K.; Mikic, Z.; Titov, V. S.; Lionello, R.; Linker, J. A.
2011-01-01
Models for the origin of the slow solar wind must account for two seemingly contradictory observations: the slow wind has the composition of the closed-field corona, implying that it originates from the continuous opening and closing of flux at the boundary between open and closed field. On the other hand, the slow wind also has large angular width, up to approx.60deg, suggesting that its source extends far from the open-closed boundary. We propose a model that can explain both observations. The key idea is that the source of the slow wind at the Sun is a network of narrow (possibly singular) open-field corridors that map to a web of separatrices and quasi-separatrix layers in the heliosphere. We compute analytically the topology of an open-field corridor and show that it produces a quasi-separatrix layer in the heliosphere that extends to angles far from the heliospheric current sheet. We then use an MHD code and MDI/SOHO observations of the photospheric magnetic field to calculate numerically, with high spatial resolution, the quasi-steady solar wind, and magnetic field for a time period preceding the 2008 August 1 total solar eclipse. Our numerical results imply that, at least for this time period, a web of separatrices (which we term an S-web) forms with sufficient density and extent in the heliosphere to account for the observed properties of the slow wind. We discuss the implications of our S-web model for the structure and dynamics of the corona and heliosphere and propose further tests of the model. Key words: solar wind - Sun: corona - Sun: magnetic topology
2. Turbulence and Waves as Sources for the Solar Wind
Science.gov (United States)
Cranmer, S. R.
2008-05-01
Gene Parker's insights from 50 years ago provided the key causal link between energy deposition in the solar corona and the acceleration of solar wind streams. However, the community is still far from agreement concerning the actual physical processes that give rise to this energy. It is still unknown whether the solar wind is fed by flux tubes that remain open (and are energized by footpoint-driven wavelike fluctuations) or if mass and energy is input more intermittently from closed loops into the open-field regions. No matter the relative importance of reconnections and loop-openings, though, we do know that waves and turbulent motions are present everywhere from the photosphere to the heliosphere, and it is important to determine how they affect the mean state of the plasma. In this presentation, I will give a summary of wave/turbulence models that seem to succeed in explaining the time-steady properties of the corona (and the fast and slow solar wind). The coronal heating and solar wind acceleration in these models comes from anisotropic turbulent cascade, which is driven by the partial reflection of low-frequency Alfven waves propagating along the open magnetic flux tubes. Specifically, a 2D model of coronal holes and streamers at solar minimum reproduces the latitudinal bifurcation of slow and fast streams seen by Ulysses. The radial gradient of the Alfven speed affects where the waves are reflected and damped, and thus whether energy is deposited below or above Parker's critical point. As predicted by earlier studies, a larger coronal expansion factor gives rise to a slower and denser wind, higher temperature at the coronal base, less intense Alfven waves at 1 AU, and correlative trends for commonly measured ratios of ion charge states and FIP-sensitive abundances that are in general agreement with observations. Finally, I will outline the types of future observations that would be most able to test and refine these ideas.
3. Elemental composition and ionization state of the solar atmosphere and solar wind
International Nuclear Information System (INIS)
Joselyn, J.A.C.
1978-01-01
Abundance measurements have always proved useful in generating and refining astrophysical theories. Some of the classical problems of astrophysics involve determining the relative abundances of elements in the atmosphere of a star from observations of its line spectrum, and then synthesizing the physical processes which would produce such abundances. Theories of the formation of the solar system are critically tested by their ability to explain observed abundances, and, elemental abundances can serve as tracers, helping to determine the origin and transport of ions. Since the solar wind originates at the sun, it can act as a diagnostic probe of solar conditions. In particular, measurements of the composition of the solar wind should be related to the solar composition. And, assuming ionization equilibrium, measurements of the relative abundances of the ionization states in the solar wind should infer coronal temperatures and temperature gradients. However, most spherically symmetric models of the solar wind are unable to explain the relationship between the composition estimated from solar observations and as measured at 1 AU; and, recent observations of significant flow speeds in the transition region raise doubts about the validity of the assumption of ionization equilibrium
4. High-speed Maglev studies in Canada
International Nuclear Information System (INIS)
Atherton, D.L.; Eastham, A.R.
1974-01-01
This paper reports on Canadian studies of superconducting magnetic levitation and variable-speed linear synchronous motor propulsion for high-speed inter-city guided ground transport. Levitation is obtained by the interaction of vehicle-mounted superconducting magnets and the eddy currents induced in aluminium strip conductors on the guideway. Non-contact propulsion by linear synchronous motor (LSM) is obtained by using vehicle-borne superconducting magnets and powered guideway coils. A suggested guidance scheme uses a flat guideway with 'null-flux' loops overlying the LSM windings. The propulsion magnets interact with the loops and the edges of the levitation strips to provide lateral stabilization. The test facility is a 7.6m wheel, rotating with a peripheral speed of 33m/s. (author)
5. Origin of the Wang-Sheeley-Arge solar wind model
Science.gov (United States)
Sheeley, Neil R., Jr.
2017-03-01
A correlation between solar wind speed at Earth and the amount of magnetic field line expansion in the corona was verified in 1989 using 22 years of solar and interplanetary observations. We trace the evolution of this relationship from its birth 15 years earlier in the Skylab era to its current use as a space weather forecasting technique. This paper is the transcript of an invited talk at the joint session of the Historical Astronomy Division and the Solar Physics Division of the American Astronomical Society during its 224th meeting in Boston, MA, on 3 June 2014.
6. Solar wind flows associated with hot heavy ions
International Nuclear Information System (INIS)
Fenimore, E.E.
1980-05-01
Solar wind heavy ion spectra measured with the Vela instrumentation have been studied with the goal of determining the solar origins of various solar wind structures which contain anomalously high ionization states. Since the ionization states freeze-in close to the sun they are good indicators of the plasma conditions in the low and intermediate corona. Heavy ion spectra from three different periods throughout the solar cycle have been analyzed. These data are consistent with freezing-in temperatures ranging from approx. 1.5 x 10 6 K to higher than 9 x 10 6 . The spectra indicating hot coronal conditions occur in roughly 1/7 of all measurements and almost exclusively in postshock flows (PSFs), nonshock related helium abundance enhancements (HAEs), or noncompressive density enhancements (NCDEs). The PSFs and HAEs are both probably interplanetary manifestations of solar flares. The observation of several flare-related HAEs which were not preceded by an interplanetary shock suggests that the flare-heated plasma can evolve into the solar wind without producing a noticeable shock at 1 AU. The NCDEs with hot heavy ions differ from the PSF-HAEs in several ways implying that they evolve from events or places with lower temperatures and less energy than those associated with the flares, but with higher temperatures and densities than the quiet corona. Active regions, coronal mass ejections, and equatorial streamers are possible sources for the NCDEs with spectra indicating hot coronal conditions. These events owe their enhanced densities to coronal processes as opposed to interplanetary dynamical processes. Models of the solar wind expansion demonstrate how some NCDEs can have extreme, nonequilibrium ionization distributions
7. The "FIP Effect" and the Origins of Solar Energetic Particles and of the Solar Wind
OpenAIRE
Reames, Donald V.
2018-01-01
We find that the element abundances in solar energetic particles (SEPs) and in the slow solar wind (SSW), relative to those in the photosphere, show different patterns as a function of the first ionization potential (FIP) of the elements. Generally, the SEP and SSW abundances reflect abundance samples of the solar corona, where low-FIP elements, ionized in the chromosphere, are more efficiently conveyed upward to the corona than high-FIP elements that are initially neutral atoms. Abundances o...
8. EVOLUTION OF THE RELATIONSHIPS BETWEEN HELIUM ABUNDANCE, MINOR ION CHARGE STATE, AND SOLAR WIND SPEED OVER THE SOLAR CYCLE
International Nuclear Information System (INIS)
Kasper, J. C.; Stevens, M. L.; Korreck, K. E.; Maruca, B. A.; Kiefer, K. K.; Schwadron, N. A.; Lepri, S. T.
2012-01-01
The changing relationships between solar wind speed, helium abundance, and minor ion charge state are examined over solar cycle 23. Observations of the abundance of helium relative to hydrogen (A He ≡ 100 × n He /n H ) by the Wind spacecraft are used to examine the dependence of A He on solar wind speed and solar activity between 1994 and 2010. This work updates an earlier study of A He from 1994 to 2004 to include the recent extreme solar minimum and broadly confirms our previous result that A He in slow wind is strongly correlated with sunspot number, reaching its lowest values in each solar minima. During the last minimum, as sunspot numbers reached their lowest levels in recent history, A He continued to decrease, falling to half the levels observed in slow wind during the previous minimum and, for the first time observed, decreasing even in the fastest solar wind. We have also extended our previous analysis by adding measurements of the mean carbon and oxygen charge states observed with the Advanced Composition Explorer spacecraft since 1998. We find that as solar activity decreased, the mean charge states of oxygen and carbon for solar wind of a given speed also fell, implying that the wind was formed in cooler regions in the corona during the recent solar minimum. The physical processes in the coronal responsible for establishing the mean charge state and speed of the solar wind have evolved with solar activity and time.
9. Wind and solar energy curtailment: A review of international experience
DEFF Research Database (Denmark)
Bird, Lori; Lew, Debra; Milligan, Michael
2016-01-01
Greater penetrations of variable renewable generation on some electric grids have resulted in increased levels of curtailment in recent years. Studies of renewable energy grid integration have found that curtailment levels may grow as the penetration of wind and solar energy generation increases....
10. NEMO 2 - Be aware: Wind and solar are coming
Energy Technology Data Exchange (ETDEWEB)
Lund, P. [Helsinki Univ. of Technology, Otaniemi (Finland)
1996-12-31
Finnish research and development is well placed with respect to new renewable energy technologies in that there exists considerable expertise in specialized areas. For example, over 20 % of all power transmission equipment and generators used in wind energy systems world-wide are manufactured in Finland, while advanced instruments for monitoring wind speed are also highly regarded internationally. Moreover, unique wind technology for complex windy and freezing conditions have been developed. Finland has a 10 % share in the European photovoltaic market, and has competitive advantages in photovoltaic systems and applications, thin film solar cells, and automated electronic controlling systems. A unique solar energy storage system based on hydrogen technology demonstrates skills on overcoming the summer-winter syndrome of large-scale solar energy utilization. The annual turnover of the Finnish industries on solar and wind energy has increased from 5 million ECU in 1988 to almost 50 million ECU in 1996. The national R and D and D from 1988 onwards has played an important role in this context. Most of the research and development into new and renewable energy technologies in Finland has been carried out through the Advanced New Energy Systems and Technologies Research Programme (NEMO2) of Tekes
11. Signatures of kinetic instabilities in the solar wind
Czech Academy of Sciences Publication Activity Database
Matteini, L.; Hellinger, Petr; Goldstein, B. E.; Landi, S.; Velli, M.; Neugebauer, M.
2013-01-01
Roč. 118, č. 6 (2013), s. 2771-2782 ISSN 2169-9380 R&D Projects: GA ČR GAP209/12/2023 Grant - others:EU(XE) SHOCK Project No. 284515 Institutional support: RVO:67985815 Keywords : solar wind ions * numerical simulations * kinetic instabities Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 3.440, year: 2013
12. Imprint of the Sun on the Solar Wind
Science.gov (United States)
Woo, R.; Habbal, S. R.
1998-01-01
Observations of the inner corona in polarized brightness by the Mauna Loa MkIII K-coronameter and soft X-ray by Yohkoh of the inner corona are combined with Ulysses radio occultation measurements of the solar wind to demonstrate that the signature of active regions and bright points is present in the heliocentric distance range of 10-30 Ro.
13. Kinetic instabilities in the solar wind driven by temperature anisotropies
Science.gov (United States)
Yoon, Peter H.
2017-12-01
The present paper comprises a review of kinetic instabilities that may be operative in the solar wind, and how they influence the dynamics thereof. The review is limited to collective plasma instabilities driven by the temperature anisotropies. To limit the scope even further, the discussion is restricted to the temperature anisotropy-driven instabilities within the model of bi-Maxwellian plasma velocity distribution function. The effects of multiple particle species or the influence of field-aligned drift will not be included. The field-aligned drift or beam is particularly prominent for the solar wind electrons, and thus ignoring its effect leaves out a vast portion of important physics. Nevertheless, for the sake of limiting the scope, this effect will not be discussed. The exposition is within the context of linear and quasilinear Vlasov kinetic theories. The discussion does not cover either computer simulations or data analyses of observations, in any systematic manner, although references will be made to published works pertaining to these methods. The scientific rationale for the present analysis is that the anisotropic temperatures associated with charged particles are pervasively detected in the solar wind, and it is one of the key contemporary scientific research topics to correctly characterize how such anisotropies are generated, maintained, and regulated in the solar wind. The present article aims to provide an up-to-date theoretical development on this research topic, largely based on the author's own work.
14. A Review of Hybrid Solar PV and Wind Energy System
Directory of Open Access Journals (Sweden)
2015-07-01
Full Text Available Due to the fact that solar and wind power is intermittent and unpredictable in nature, higher penetration of their types in existing power system could cause and create high technical challenges especially to weak grids or stand-alone systems without proper and enough storage capacity. By integrating the two renewable resources into an optimum combination, the impact of the variable nature of solar and wind resources can be partially resolved and the overall system becomes more reliable and economical to run. This paper provides a review of challenges and opportunities / solutions of hybrid solar PV and wind energy integration systems. Voltage and frequency fluctuation, and harmonics are major power quality issues for both grid-connected and stand-alone systems with bigger impact in case of weak grid. This can be resolved to a large extent by having proper design, advanced fast response control facilities, and good optimization of the hybrid systems. The paper gives a review of the main research work reported in the literature with regard to optimal sizing design, power electronics topologies and control. The paper presents a review of the state of the art of both grid-connected and stand-alone hybrid solar and wind systems.
15. Solar Wind Monitor--A School Geophysics Project
Science.gov (United States)
Robinson, Ian
2018-01-01
Described is an established geophysics project to construct a solar wind monitor based on a nT resolution fluxgate magnetometer. Low-cost and appropriate from school to university level it incorporates elements of astrophysics, geophysics, electronics, programming, computer networking and signal processing. The system monitors the earth's field in…
16. Review Space Weather and Solar Wind Studies with OWFA
In this paper, we review the results of interplanetary scintillation (IPS) observations made with the legacy .... complex flow of solar wind at different time and spa- ..... in a step of ∼20 .... observing program with the legacy system of the ORT.
17. Solar wind reconstruction from magnetosheath data using an adjoint approach
International Nuclear Information System (INIS)
Nabert, C.; Othmer, C.
2015-01-01
We present a new method to reconstruct solar wind conditions from spacecraft data taken during magnetosheath passages, which can be used to support, e.g., magnetospheric models. The unknown parameters of the solar wind are used as boundary conditions of an MHD (magnetohydrodynamics) magnetosheath model. The boundary conditions are varied until the spacecraft data matches the model predictions. The matching process is performed using a gradient-based minimization of the misfit between data and model. To achieve this time-consuming procedure, we introduce the adjoint of the magnetosheath model, which allows efficient calculation of the gradients. An automatic differentiation tool is used to generate the adjoint source code of the model. The reconstruction method is applied to THEMIS (Time History of Events and Macroscale Interactions during Substorms) data to calculate the solar wind conditions during spacecraft magnetosheath transitions. The results are compared to actual solar wind data. This allows validation of our reconstruction method and indicates the limitations of the MHD magnetosheath model used.
18. Solar wind reconstruction from magnetosheath data using an adjoint approach
Energy Technology Data Exchange (ETDEWEB)
Nabert, C.; Othmer, C. [Technische Univ. Braunschweig (Germany). Inst. fuer Geophysik und extraterrestrische Physik; Glassmeier, K.H. [Technische Univ. Braunschweig (Germany). Inst. fuer Geophysik und extraterrestrische Physik; Max Planck Institute for Solar System Research, Goettingen (Germany)
2015-07-01
We present a new method to reconstruct solar wind conditions from spacecraft data taken during magnetosheath passages, which can be used to support, e.g., magnetospheric models. The unknown parameters of the solar wind are used as boundary conditions of an MHD (magnetohydrodynamics) magnetosheath model. The boundary conditions are varied until the spacecraft data matches the model predictions. The matching process is performed using a gradient-based minimization of the misfit between data and model. To achieve this time-consuming procedure, we introduce the adjoint of the magnetosheath model, which allows efficient calculation of the gradients. An automatic differentiation tool is used to generate the adjoint source code of the model. The reconstruction method is applied to THEMIS (Time History of Events and Macroscale Interactions during Substorms) data to calculate the solar wind conditions during spacecraft magnetosheath transitions. The results are compared to actual solar wind data. This allows validation of our reconstruction method and indicates the limitations of the MHD magnetosheath model used.
19. Magnetosheath Propagation Time of Solar Wind Directional Discontinuities
Science.gov (United States)
Samsonov, A. A.; Sibeck, D. G.; Dmitrieva, N. P.; Semenov, V. S.; Slivka, K. Yu.; Å afránkova, J.; Němeček, Z.
2018-05-01
Observed delays in the ground response to solar wind directional discontinuities have been explained as the result of larger than expected magnetosheath propagation times. Recently, Samsonov et al. (2017, https://doi.org/10.1002/2017GL075020) showed that the typical time for a southward interplanetary magnetic field (IMF) turning to propagate across the magnetosheath is 14 min. Here by using a combination of magnetohydrodynamic simulations, spacecraft observations, and analytic calculations, we study the dependence of the propagation time on solar wind parameters and near-magnetopause cutoff speed. Increases in the solar wind speed result in greater magnetosheath plasma flow velocities, decreases in the magnetosheath thickness and, as a result, decreases in the propagation time. Increases in the IMF strength result in increases in the magnetosheath thickness and increases in the propagation time. Both magnetohydrodynamic simulations and observations suggest that propagation times are slightly smaller for northward IMF turnings. Magnetosheath flow deceleration must be taken into account when predicting the arrival times of solar wind structures at the dayside magnetopause.
20. Air emissions due to wind and solar power.
Science.gov (United States)
Katzenstein, Warren; Apt, Jay
2009-01-15
Renewables portfolio standards (RPS) encourage large-scale deployment of wind and solar electric power. Their power output varies rapidly, even when several sites are added together. In many locations, natural gas generators are the lowest cost resource available to compensate for this variability, and must ramp up and down quickly to keep the grid stable, affecting their emissions of NOx and CO2. We model a wind or solar photovoltaic plus gas system using measured 1-min time-resolved emissions and heat rate data from two types of natural gas generators, and power data from four wind plants and one solar plant. Over a wide range of renewable penetration, we find CO2 emissions achieve approximately 80% of the emissions reductions expected if the power fluctuations caused no additional emissions. Using steam injection, gas generators achieve only 30-50% of expected NOx emissions reductions, and with dry control NOx emissions increase substantially. We quantify the interaction between state RPSs and NOx constraints, finding that states with substantial RPSs could see significant upward pressure on NOx permit prices, if the gas turbines we modeled are representative of the plants used to mitigate wind and solar power variability.
1. Solar wind oscillations with a 1.3 year period
Science.gov (United States)
Richardson, John D.; Paularena, Karolen I.; Belcher, John W.; Lazarus, Alan J.
1994-01-01
The Interplanetary Monitoring Platform 8 (IMP-8) and Voyager 2 spacecraft have recently detected a very strong modulation in the solar wind speed with an approximately 1.3 year period. Combined with evidence from long-term auroral and magnetometer studies, this suggests that fundamental changes in the Sun occur on a roughly 1.3 year time scale.
2. Electron energetics in the expanding solar wind via Helios observations
Czech Academy of Sciences Publication Activity Database
Štverák, Štěpán; Trávníček, Pavel M.; Hellinger, Petr
2015-01-01
Roč. 120, č. 10 (2015), s. 8177-8193 ISSN 2169-9380 Institutional support: RVO:68378289 Keywords : solar wind plasma * plasma energization * transport processes Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 3.318, year: 2015 http://onlinelibrary.wiley.com/doi/10.1002/2015JA021368/abstract
3. Electron energetics in the expanding solar wind via Helios observations
Czech Academy of Sciences Publication Activity Database
Štverák, Štěpán; Trávníček, Pavel M.; Hellinger, Petr
2015-01-01
Roč. 120, č. 10 (2015), s. 8177-8193 ISSN 2169-9380 R&D Projects: GA ČR GAP209/12/2041; GA ČR GA15-17490S Institutional support: RVO:67985815 Keywords : solar wind * electrons energetics * transport processes Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 3.318, year: 2015
4. Depletion of solar wind plasma near a planetary boundary
International Nuclear Information System (INIS)
Zwan, B.J.; Wolf, R.A.
1976-01-01
A mathematical model is presented that describes the squeezing of solar wind plasma out along interplanetary magnetic field lines in the region between the bow shock and the effective planetary boundary (in the case of the earth, the magnetopause). In the absence of local magnetic merging the squeezing process should create a 'depletion layer,' a region of very low plasma density just outside the magnetopause. Numerical solutions are obtained for the dimensionless magnetohydrodynamic equations describing this depletion process for the case where the solar wind magnetic field is perpendicular to the solar wind flow direction. For the case of the earth with a magnetopause standoff distance of 10 R/subE/, the theory predicts that the density should be reduced by a factor > or =2 in a layer about 700--1300 km thick if M/subA/, the Alfven Mach number in the solar wind, is equal to 8. The layer thickness should vary as M/subA/ -2 and should be approximately uniform for a large area of the magnetopause around the subsolar point. Computed layer thicknesses are somewhat smaller than those derived from Lees' axisymmetric model. Depletion layers should develop fully only where magnetic merging is locally unimportant. Scaling of the model calculations to Venus and Mars suggest layer thicknesses about 1/10 and 1/15 those of the earth, respectively, neglecting diffusion and ionospheric effects
5. Solar wind heat flux regulation by the whistler instability
International Nuclear Information System (INIS)
Gary, S.P.; Feldman, W.C.
1977-01-01
This paper studies the role of the whistler instability in the regulation of the solar wind heat flux near 1 AU. A comparison of linear and second-order theory with experimental results provides strong evidence that the whistler may at times contribute to the limitation of this heat flux
6. Proton thermal energetics in the solar wind: Helios reloaded
Czech Academy of Sciences Publication Activity Database
Hellinger, Petr; Trávníček, P.; Štverák, Štěpán; Matteini, L.; Velli, M.
2013-01-01
Roč. 118, č. 4 (2013), s. 1351-1365 ISSN 2169-9380 Institutional support: RVO:68378289 Keywords : solar wind * proton energetics * turbulent heating Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 3.440, year: 2013 http://onlinelibrary.wiley.com/doi/10.1002/jgra.50107/abstract
7. Solar wind dynamic pressure variations and transient magnetospheric signatures
International Nuclear Information System (INIS)
Sibeck, D.G.; Baumjohann, W.
1989-01-01
Contrary to the prevailing popular view, we find some transient ground events with bipolar north-south signatures are related to variations in solar wind dynamic pressure and not necessarily to magnetic merging. We present simultaneous solar wind plasma observations for two previously reported transient ground events observed at dayside auroral latitudes. During the first event, originally reported by Lanzerotti et al. [1987], conjugate ground magnetometers recorded north-south magetic field deflections in the east-west and vertical directions. The second event was reported by Todd et al. [1986], we noted ground rader observations indicating strong northward then southward ionospheric flows. The events were associated with the postulated signatures of patchy, sporadic, merging of magnetosheath and magnetospheric magnetic field lines at the dayside magnetospause, known as flux transfer events. Conversely, we demonstrate that the event reported by Lanzerotti et al. was accompanied by a sharp increase in solar wind dynamic pressure, a magnetospheric compression, and a consequent ringing of the magnetospheric magnetic field. The event reported by Todd et al. was associated with a brief but sharp increase in the solar wind dynamic pressure. copyright American Geophysical Union 1989
8. Remote Sensing of the Heliospheric Solar Wind using Radio ...
tribpo
Astr. (2000) 21, 439–444. Remote Sensing of the Heliospheric Solar Wind using Radio. Astronomy Methods and Numerical Simulations. S. Ananthakrishnan, National Center for Radio Astrophysics, Tata Institute of. Fundamental Research, Pune, India. Abstract. The ground-based radio astronomy method of interplanetary.
9. Solar wind charge exchange observed through the lunar exosphere
Czech Academy of Sciences Publication Activity Database
Robertson, I. P.; Sembay, S.; Stubbs, T. J.; Kuntz, K. D.; Collier, M. R.; Cravens, T. E.; Snowden, S. L.; Hills, H. K.; Porter, F. S.; Trávníček, Pavel M.; Carter, J. A.; Read, A. M.
2009-01-01
Roč. 36, - (2009), L21102/1-L21102/5 ISSN 0094-8276 Institutional research plan: CEZ:AV0Z30420517 Keywords : lunar exosphere * solar wind * X-rays Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 3.204, year: 2009
10. Study on Pyroelectric Harvesters Integrating Solar Radiation with Wind Power
Directory of Open Access Journals (Sweden)
Chun-Ching Hsiao
2015-07-01
11. 3D Anisotropy of Solar Wind Turbulence, Tubes, or Ribbons?
Science.gov (United States)
Verdini, Andrea; Grappin, Roland; Alexandrova, Olga; Lion, Sonny
2018-01-01
We study the anisotropy with respect to the local magnetic field of turbulent magnetic fluctuations at magnetofluid scales in the solar wind. Previous measurements in the fast solar wind obtained axisymmetric anisotropy, despite that the analysis method allows nonaxisymmetric structures. These results are probably contaminated by the wind expansion that introduces another symmetry axis, namely, the radial direction, as indicated by recent numerical simulations. These simulations also show that while the expansion is strong, the principal fluctuations are in the plane perpendicular to the radial direction. Using this property, we separate 11 yr of Wind spacecraft data into two subsets characterized by strong and weak expansion and determine the corresponding turbulence anisotropy. Under strong expansion, the small-scale anisotropy is consistent with the Goldreich & Sridhar critical balance. As in previous works, when the radial symmetry axis is not eliminated, the turbulent structures are field-aligned tubes. Under weak expansion, we find 3D anisotropy predicted by the Boldyrev model, that is, turbulent structures are ribbons and not tubes. However, the very basis of the Boldyrev phenomenology, namely, a cross-helicity increasing at small scales, is not observed in the solar wind: the origin of the ribbon formation is unknown.
12. Solar-wind krypton and solid/gas fractionation in the early solar nebula
Science.gov (United States)
Wiens, Roger C.; Burnett, D. S.; Neugebauer, M.; Pepin, R. O.
1991-01-01
The solar-system Kr abundance is calculated from solar-wind noble-gas ratios, determined previously by low-temperature oxidations of lunar ilmenite grains, normalized to Si by spacecraft solar-wind measurements. The estimated Kr-83 abundance of 4.1 + or - 1.5 per million Si atoms is within uncertainty of estimates assuming no fractionation, determined from CI-chondrite abundances of surrounding elements. This is significant because it is the first such constraint on solid/gas fractionation, though the large uncertainty only confines it to somewhat less than a factor of two.
13. Solar origins of solar wind properties during the cycle 23 solar minimum and rising phase of cycle 24
Science.gov (United States)
Luhmann, Janet G.; Petrie, Gordon; Riley, Pete
2012-01-01
The solar wind was originally envisioned using a simple dipolar corona/polar coronal hole sources picture, but modern observations and models, together with the recent unusual solar cycle minimum, have demonstrated the limitations of this picture. The solar surface fields in both polar and low-to-mid-latitude active region zones routinely produce coronal magnetic fields and related solar wind sources much more complex than a dipole. This makes low-to-mid latitude coronal holes and their associated streamer boundaries major contributors to what is observed in the ecliptic and affects the Earth. In this paper we use magnetogram-based coronal field models to describe the conditions that prevailed in the corona from the decline of cycle 23 into the rising phase of cycle 24. The results emphasize the need for adopting new views of what is ‘typical’ solar wind, even when the Sun is relatively inactive. PMID:25685422
14. Solar-wind system powers mountain clean-up
Energy Technology Data Exchange (ETDEWEB)
NONE
2001-03-01
By using a hybrid solar-wind system, the Japanese have tackled the problem of human excrement left by tourists in mountain lodges and in natural parks by installing flush toilets and wastewater treatment plants. The solar array (4.9 kW{sub p}) consists of 76 panels of single-crystal photovoltaic cells each with an output of 64 Wp. The wind turbines (total capacity 2.1 kW) operate whatever the wind strength or direction. Storage batteries prevent any dip in power which would result from low ambient temperatures. The system can still function at temperatures as low as minus 25{sup o}C. Between November and April when the lodge is closed, the waste is decomposed biologically. A block diagram shows the elements of the system, and details of cost are given. The system won the 1999 New Energy Award.
15. HEMISPHERIC ASYMMETRIES IN THE POLAR SOLAR WIND OBSERVED BY ULYSSES NEAR THE MINIMA OF SOLAR CYCLES 22 AND 23
International Nuclear Information System (INIS)
Ebert, R. W.; Dayeh, M. A.; Desai, M. I.; McComas, D. J.; Pogorelov, N. V.
2013-01-01
We examined solar wind plasma and interplanetary magnetic field (IMF) observations from Ulysses' first and third orbits to study hemispheric differences in the properties of the solar wind and IMF originating from the Sun's large polar coronal holes (PCHs) during the declining and minimum phase of solar cycles 22 and 23. We identified hemispheric asymmetries in several parameters, most notably ∼15%-30% south-to-north differences in averages for the solar wind density, mass flux, dynamic pressure, and energy flux and the radial and total IMF magnitudes. These differences were driven by relatively larger, more variable solar wind density and radial IMF between ∼36°S-60°S during the declining phase of solar cycles 22 and 23. These observations indicate either a hemispheric asymmetry in the PCH output during the declining and minimum phase of solar cycles 22 and 23 with the southern hemisphere being more active than its northern counterpart, or a solar cycle effect where the PCH output in both hemispheres is enhanced during periods of higher solar activity. We also report a strong linear correlation between these solar wind and IMF parameters, including the periods of enhanced PCH output, that highlight the connection between the solar wind mass and energy output and the Sun's magnetic field. That these enhancements were not matched by similar sized variations in solar wind speed points to the mass and energy responsible for these increases being added to the solar wind while its flow was subsonic.
16. ESTABLISHING A CONNECTION BETWEEN ACTIVE REGION OUTFLOWS AND THE SOLAR WIND: ABUNDANCE MEASUREMENTS WITH EIS/HINODE
International Nuclear Information System (INIS)
Brooks, David H.; Warren, Harry P.
2011-01-01
One of the most interesting discoveries from Hinode is the presence of persistent high-temperature high-speed outflows from the edges of active regions (ARs). EUV imaging spectrometer (EIS) measurements indicate that the outflows reach velocities of 50 km s -1 with spectral line asymmetries approaching 200 km s -1 . It has been suggested that these outflows may lie on open field lines that connect to the heliosphere, and that they could potentially be a significant source of the slow speed solar wind. A direct link has been difficult to establish, however. We use EIS measurements of spectral line intensities that are sensitive to changes in the relative abundance of Si and S as a result of the first ionization potential (FIP) effect, to measure the chemical composition in the outflow regions of AR 10978 over a 5 day period in 2007 December. We find that Si is always enhanced over S by a factor of 3-4. This is generally consistent with the enhancement factor of low FIP elements measured in situ in the slow solar wind by non-spectroscopic methods. Plasma with a slow wind-like composition was therefore flowing from the edge of the AR for at least 5 days. Furthermore, on December 10 and 11, when the outflow from the western side was favorably oriented in the Earth direction, the Si/S ratio was found to match the value measured a few days later by the Advanced Composition Explorer/Solar Wind Ion Composition Spectrometer. These results provide strong observational evidence for a direct connection between the solar wind, and the coronal plasma in the outflow regions.
17. High-speed data search
Science.gov (United States)
Driscoll, James N.
1994-01-01
The high-speed data search system developed for KSC incorporates existing and emerging information retrieval technology to help a user intelligently and rapidly locate information found in large textual databases. This technology includes: natural language input; statistical ranking of retrieved information; an artificial intelligence concept called semantics, where 'surface level' knowledge found in text is used to improve the ranking of retrieved information; and relevance feedback, where user judgements about viewed information are used to automatically modify the search for further information. Semantics and relevance feedback are features of the system which are not available commercially. The system further demonstrates focus on paragraphs of information to decide relevance; and it can be used (without modification) to intelligently search all kinds of document collections, such as collections of legal documents medical documents, news stories, patents, and so forth. The purpose of this paper is to demonstrate the usefulness of statistical ranking, our semantic improvement, and relevance feedback.
18. High speed laser tomography system
Science.gov (United States)
Samsonov, D.; Elsaesser, A.; Edwards, A.; Thomas, H. M.; Morfill, G. E.
2008-03-01
A high speed laser tomography system was developed capable of acquiring three-dimensional (3D) images of optically thin clouds of moving micron-sized particles. It operates by parallel-shifting an illuminating laser sheet with a pair of galvanometer-driven mirrors and synchronously recording two-dimensional (2D) images of thin slices of the imaged volume. The maximum scanning speed achieved was 120000slices/s, sequences of 24 volume scans (up to 256 slices each) have been obtained. The 2D slices were stacked to form 3D images of the volume, then the positions of the particles were identified and followed in the consecutive scans. The system was used to image a complex plasma with particles moving at speeds up to cm/s.
19. Sustainable business models for wind and solar energy in Romania
Directory of Open Access Journals (Sweden)
Nichifor Maria Alexandra
2015-06-01
20. Data Assimilation in the Solar Wind: Challenges and First Results.
Science.gov (United States)
Lang, Matthew; Browne, Philip; van Leeuwen, Peter Jan; Owens, Mathew
2017-11-01
Data assimilation (DA) is used extensively in numerical weather prediction (NWP) to improve forecast skill. Indeed, improvements in forecast skill in NWP models over the past 30 years have directly coincided with improvements in DA schemes. At present, due to data availability and technical challenges, DA is underused in space weather applications, particularly for solar wind prediction. This paper investigates the potential of advanced DA methods currently used in operational NWP centers to improve solar wind prediction. To develop the technical capability, as well as quantify the potential benefit, twin experiments are conducted to assess the performance of the Local Ensemble Transform Kalman Filter (LETKF) in the solar wind model ENLIL. Boundary conditions are provided by the Wang-Sheeley-Arge coronal model and synthetic observations of density, temperature, and momentum generated every 4.5 h at 0.6 AU. While in situ spacecraft observations are unlikely to be routinely available at 0.6 AU, these techniques can be applied to remote sensing of the solar wind, such as with Heliospheric Imagers or interplanetary scintillation. The LETKF can be seen to improve the state at the observation location and advect that improvement toward the Earth, leading to an improvement in forecast skill in near-Earth space for both the observed and unobserved variables. However, sharp gradients caused by the analysis of a single observation in space resulted in artificial wavelike structures being advected toward Earth. This paper is the first attempt to apply DA to solar wind prediction and provides the first in-depth analysis of the challenges and potential solutions.
1. Solar wind stream interaction regions throughout the heliosphere
Science.gov (United States)
Richardson, Ian G.
2018-01-01
This paper focuses on the interactions between the fast solar wind from coronal holes and the intervening slower solar wind, leading to the creation of stream interaction regions that corotate with the Sun and may persist for many solar rotations. Stream interaction regions have been observed near 1 AU, in the inner heliosphere (at ˜ 0.3-1 AU) by the Helios spacecraft, in the outer and distant heliosphere by the Pioneer 10 and 11 and Voyager 1 and 2 spacecraft, and out of the ecliptic by Ulysses, and these observations are reviewed. Stream interaction regions accelerate energetic particles, modulate the intensity of Galactic cosmic rays and generate enhanced geomagnetic activity. The remote detection of interaction regions using interplanetary scintillation and white-light imaging, and MHD modeling of interaction regions will also be discussed.
2. Resistive instabilities of current sheets in the solar wind
Energy Technology Data Exchange (ETDEWEB)
Dobrowolny, M [CNR, Laboratorio per il Plasma nello Spazio, Frascati, Italy; Trussoni, E [CNR, Laboratorio di Cosmo-Geofisica, Turin, Italy
1979-03-01
Resistive magnetohydrodynamic instabilities are investigated numerically for non-antisymmetric magnetic field profiles similar to those indicated in spacecraft data on solar wind discontinuities. The eigenvalue problem derived for the growth rate of possible instabilities from dimensionless equations for velocity and magnetic field perturbations is solved starting from the outer regions where the plasma is frozen to the magnetic field. For an antisymmetric magnetic profile, calculations show only tearing modes to be present, with instabilities occurring only at long wavelengths, while for a non-antisymmetric magnetic profile resembling the observed solar wind, calculations indicate the presence of rippling modes driven by resistivity gradients, in addition to the tearing modes. Calculations of the scale lengths of variation of the reversing component based on a scaling law relating the maximum growth rate to the magnetic Reynolds number are found to agree with observed solar current sheet scale lengths.
3. Transport of transient solar wind particles in Earth's cusps
International Nuclear Information System (INIS)
Parks, G. K.; Lee, E.; Teste, A.; Wilber, M.; Lin, N.; Canu, P.; Dandouras, I.; Reme, H.; Fu, S. Y.; Goldstein, M. L.
2008-01-01
An important problem in space physics still not understood well is how the solar wind enters the Earth's magnetosphere. Evidence is presented that transient solar wind particles produced by solar disturbances can appear in the Earth's mid-altitude (∼5 R E geocentric) cusps with densities nearly equal to those in the magnetosheath. That these are magnetosheath particles is established by showing they have the same ''flattop'' electron distributions as magnetosheath electrons behind the bow shock. The transient ions are moving parallel to the magnetic field (B) toward Earth and often coexist with ionospheric particles that are flowing out. The accompanying waves include electromagnetic and broadband electrostatic noise emissions and Bernstein mode waves. Phase-space distributions show a mixture of hot and cold electrons and multiple ion species including field-aligned ionospheric O + beams
4. Applying Nyquist's method for stability determination to solar wind observations
Science.gov (United States)
Klein, Kristopher G.; Kasper, Justin C.; Korreck, K. E.; Stevens, Michael L.
2017-10-01
The role instabilities play in governing the evolution of solar and astrophysical plasmas is a matter of considerable scientific interest. The large number of sources of free energy accessible to such nearly collisionless plasmas makes general modeling of unstable behavior, accounting for the temperatures, densities, anisotropies, and relative drifts of a large number of populations, analytically difficult. We therefore seek a general method of stability determination that may be automated for future analysis of solar wind observations. This work describes an efficient application of the Nyquist instability method to the Vlasov dispersion relation appropriate for hot, collisionless, magnetized plasmas, including the solar wind. The algorithm recovers the familiar proton temperature anisotropy instabilities, as well as instabilities that had been previously identified using fits extracted from in situ observations in Gary et al. (2016). Future proposed applications of this method are discussed.
5. Solar wind fluctuations at large scale: A comparison between low and high solar activity conditions
International Nuclear Information System (INIS)
Bavassano, B.; Bruno, R.
1991-01-01
The influence of the Sun's activity cycle on the solar wind fluctuations at time scales from 1 hour to 3 days in the inner heliosphere (0.3 to 1 AU) is investigated. Hourly averages of plasma and magnetic field data by Helios spacecraft are used. Since fluctuations behave quite differently with changing scale, the analysis is performed separately for two different ranges in time scale. Between 1 and 6 hours Alfvenic fluctuations and pressure-balanced structures are extensively observed. At low solar activity and close to 0.3 AU, Alfvenic fluctuations are more frequent than pressure-balanced structures. This predominance, however, weakens for rising solar activity and radial distance, to the point that a role exchange, in terms of occurrence rate, is found at the maximum of the cycle close to 1 AU. On the other hand, in all cases Alfvenic fluctuations have a larger amplitude than pressure-balanced structures. On the whole, the Alfvenic contribution to the solar wind energy spectrum comes out to be dominant at all solar activity conditions. At scales from 0.5 to 3 days the most important feature is the growth, as the solar wind expansion develops, of strong positive correlations between magnetic and thermal pressures. These structures are progressively built up by the interaction between different wind flows. This effect is more pronounced at low than at high activity. Our findings support the conclusion that the solar cycle evolution of the large-scale velocity pattern is the factor governing the observed variations
6. THE CONTRIBUTION OF CORONAL JETS TO THE SOLAR WIND
Energy Technology Data Exchange (ETDEWEB)
Lionello, R.; Török, T.; Titov, V. S.; Mikić, Z.; Linker, J. A. [Predictive Science Inc., 9990 Mesa Rim Road, Suite 170, San Diego, CA 92121 (United States); Leake, J. E.; Linton, M. G., E-mail: [email protected] [US Naval Research Laboratory 4555 Overlook Avenue, SW Washington, DC 20375 (United States)
2016-11-01
Transient collimated plasma eruptions in the solar corona, commonly known as coronal (or X-ray) jets, are among the most interesting manifestations of solar activity. It has been suggested that these events contribute to the mass and energy content of the corona and solar wind, but the extent of these contributions remains uncertain. We have recently modeled the formation and evolution of coronal jets using a three-dimensional (3D) magnetohydrodynamic (MHD) code with thermodynamics in a large spherical domain that includes the solar wind. Our model is coupled to 3D MHD flux-emergence simulations, i.e., we use boundary conditions provided by such simulations to drive a time-dependent coronal evolution. The model includes parametric coronal heating, radiative losses, and thermal conduction, which enables us to simulate the dynamics and plasma properties of coronal jets in a more realistic manner than done so far. Here, we employ these simulations to calculate the amount of mass and energy transported by coronal jets into the outer corona and inner heliosphere. Based on observed jet-occurrence rates, we then estimate the total contribution of coronal jets to the mass and energy content of the solar wind to (0.4–3.0)% and (0.3–1.0)%, respectively. Our results are largely consistent with the few previous rough estimates obtained from observations, supporting the conjecture that coronal jets provide only a small amount of mass and energy to the solar wind. We emphasize, however, that more advanced observations and simulations (including parametric studies) are needed to substantiate this conjecture.
7. WSA-Enlil Solar Wind Prediction
Data.gov (United States)
National Oceanic and Atmospheric Administration, Department of Commerce — WSA-Enlil is a large-scale, physics-based prediction model of the heliosphere, used by the Space Weather Forecast Office to provide 1-4 day advance warning of solar...
8. Predicting Atmospheric Ionization and Excitation by Precipitating SEP and Solar Wind Protons Measured By MAVEN
Science.gov (United States)
Jolitz, Rebecca; Dong, Chuanfei; Lee, Christina; Lillis, Rob; Brain, David; Curry, Shannon; Halekas, Jasper; Bougher, Stephen W.; Jakosky, Bruce
2017-10-01
Precipitating energetic particles ionize and excite planetary atmospheres, increasing electron content and producing aurora. At Mars, the solar wind and solar energetic particles (SEPs) can precipitate directly into the atmosphere because solar wind protons can charge exchange to become neutral and pass the magnetosheath, and SEPs are sufficiently energetic to cross the magnetosheath unchanged. We will compare ionization and Lyman alpha emission rates for solar wind and SEP protons during nominal solar activity and a CME shock front impact event on May 16 2016. We will use the Atmospheric Scattering of Protons and Energetic Neutrals (ASPEN) model to compare excitation and ionization rates by SEPs and solar wind protons currently measured by the SWIA (Solar Wind Ion Analyzer) and SEP instruments aboard the MAVEN spacecraft. Results will help quantify how SEP and solar wind protons influence atmospheric energy deposition during solar minimum.
9. Solar Panel Buffeted by Wind at Phoenix Site
Science.gov (United States)
2008-01-01
Winds were strong enough to cause about a half a centimeter (.19 inch) of motion of a solar panel on NASA's Phoenix Mars lander when the lander's Surface Stereo Imager took this picture on Aug. 31, 2008, during the 96th Martian day since landing. The lander's telltale wind gauge has been indicating wind speeds of about 4 meters per second (9 miles per hour) during late mornings at the site. These conditions were anticipated and the wind is not expected to do any harm to the lander. The Phoenix Mission is led by the University of Arizona, Tucson, on behalf of NASA. Project management of the mission is by NASA's Jet Propulsion Laboratory, Pasadena, Calif. Spacecraft development is by Lockheed Martin Space Systems, Denver.
10. The solar wind in time: a change in the behaviour of older winds?
Science.gov (United States)
O'Fionnagáin, D.; Vidotto, A. A.
2018-05-01
In this paper, we model the wind of solar analogues at different ages to investigate the evolution of the solar wind. Recently, it has been suggested that winds of solar type stars might undergo a change in properties at old ages, whereby stars older than the Sun would be less efficient in carrying away angular momentum than what was traditionally believed. Adding to this, recent observations suggest that old solar-type stars show a break in coronal properties, with a steeper decay in X-ray luminosities and temperatures at older ages. We use these X-ray observations to constrain the thermal acceleration of winds of solar analogues. Our sample is based on the stars from the Sun in Time' project with ages between 120 and 7000 Myr. The break in X-ray properties leads to a break in wind mass-loss rates (\\dot{M}) at roughly 2 Gyr, with \\dot{M} (t 2 Gyr) ∝ t-3.9. This steep decay in \\dot{M} at older ages could be the reason why older stars are less efficient at carrying away angular momentum, which would explain the anomalously rapid rotation observed in older stars. We also show that none of the stars in our sample would have winds dense enough to produce thermal emission above 1-2 GHz, explaining why their radio emissions have not yet been detected. Combining our models with dynamo evolution models for the magnetic field of the Earth, we find that, at early ages (≈100 Myr), our Earth had a magnetosphere that was three or more times smaller than its current size.
11. High speed operation of permanent magnet machines
Science.gov (United States)
El-Refaie, Ayman M.
This work proposes methods to extend the high-speed operating capabilities of both the interior PM (IPM) and surface PM (SPM) machines. For interior PM machines, this research has developed and presented the first thorough analysis of how a new bi-state magnetic material can be usefully applied to the design of IPM machines. Key elements of this contribution include identifying how the unique properties of the bi-state magnetic material can be applied most effectively in the rotor design of an IPM machine by "unmagnetizing" the magnet cavity center posts rather than the outer bridges. The importance of elevated rotor speed in making the best use of the bi-state magnetic material while recognizing its limitations has been identified. For surface PM machines, this research has provided, for the first time, a clear explanation of how fractional-slot concentrated windings can be applied to SPM machines in order to achieve the necessary conditions for optimal flux weakening. A closed-form analytical procedure for analyzing SPM machines designed with concentrated windings has been developed. Guidelines for designing SPM machines using concentrated windings in order to achieve optimum flux weakening are provided. Analytical and numerical finite element analysis (FEA) results have provided promising evidence of the scalability of the concentrated winding technique with respect to the number of poles, machine aspect ratio, and output power rating. Useful comparisons between the predicted performance characteristics of SPM machines equipped with concentrated windings and both SPM and IPM machines designed with distributed windings are included. Analytical techniques have been used to evaluate the impact of the high pole number on various converter performance metrics. Both analytical techniques and FEA have been used for evaluating the eddy-current losses in the surface magnets due to the stator winding subharmonics. Techniques for reducing these losses have been
12. Solar-wind interactions with the Moon: role of oxygen ions
International Nuclear Information System (INIS)
Mukherjee, N.R.
1979-01-01
The solar-wind interacts directly with the lunar surface due to tenuous atmosphere and magnetic field. The interaction results in an almost complete absorption of the solar-wind corpuscles producing no upstream bowshock but a cavity downstream. The solar-wind oxygen ionic species induce and undergo a complex set of reactions with the elements of the lunar minerals and the solar-wind derived trapped gases. In this paper, the long-term concentration and the role of oxygen derived from the solar-wind is discussed. (Auth.)
13. Heating of Solar Wind Ions via Cyclotron Resonance
Science.gov (United States)
Navarro, R.; Moya, P. S.; Figueroa-Vinas, A.; Munoz, V.; Valdivia, J. A.
2017-12-01
Remote and in situ observations in the solar wind show that ion and electron velocity distributions persistently deviate from thermal equilibrium in the form of relative streaming between species components, temperature anisotropy, etc. These non-thermal features represent a source of free energy for the excitation of kinetic instabilities and fluctuations in the plasma. In this regard, it is believed that plasma particles can be heated, through a second order Fermi acceleration process, by multiple resonances with unstable counter-propagating field-aligned Ion-cyclotron waves. For multi-species plasmas, several collective wave modes participate in this process. In this work, we test this model by studying the percentage of ions that resonate with the waves modes described by the proper kinetic multi-species dispersion relation in a solar-wind-like plasma composed of electrons, protons, and alpha particles. Numerical results are compared with WIND spacecraft data to test its relevance for the existence of thresholds for the preferential perpendicular heating of He+2 ions as observed in the solar wind fast streams.
14. Canadian high speed magnetically levitated vehicle system
Energy Technology Data Exchange (ETDEWEB)
Atherton, D L [Queen' s Univ., Kingston, Ont.; Belanger, P R; Burke, P E; Dawson, G E; Eastham, A R; Hayes, W F; Ooi, B T; Silvester, P; Slemon, G R
1978-04-01
A technically feasible high speed (400 to 480 km/h) guided ground transportation system, based on the use of the vehicle-borne superconducting magnets for electrodynamic suspension and guidance and for linear synchronous motor propulsion was defined as a future modal option for Canadian application. Analysis and design proposals were validated by large-scale tests on a rotating wheel facility and by modelling system components and their interactions. Thirty ton vehicles carrying 100 passengers operate over a flat-topped elevated guideway, which minimizes system down-time due to ice and snow accumulation and facilitates the design of turn-outs. A clearance of up to 15 cm is produced by the electrodynamic interaction between the vehicle-borne superconducting magnets and aluminum guideway strips. Propulsion and automatic system control is provided by the superconducting linear synchronous motor which operates at good efficiency (0.74) and high power factor (0.95). The vehicle is guided primarily by the interaction between the LSM field magnet array and flat null-flux loops overlying the stator windings in the guideway. The linear synchronous motor, electrodynamic suspension as well as levitation strip joints, parasitic LSM winding losses and limitations to the use of ferromagnetic guideway reinforcement were investigated experimentally on the test wheel facility. The use of a secondary suspension assures adequate dynamic stability, and good ride quality is achieved by optimized passive components with respect to lateral modes and by an actively controlled secondary suspension with respect to vertical motion.
15. The "FIP Effect" and the Origins of Solar Energetic Particles and of the Solar Wind
Science.gov (United States)
Reames, Donald V.
2018-03-01
We find that the element abundances in solar energetic particles (SEPs) and in the slow solar wind (SSW), relative to those in the photosphere, show different patterns as a function of the first ionization potential (FIP) of the elements. Generally, the SEP and SSW abundances reflect abundance samples of the solar corona, where low-FIP elements, ionized in the chromosphere, are more efficiently conveyed upward to the corona than high-FIP elements that are initially neutral atoms. Abundances of the elements, especially C, P, and S, show a crossover from low to high FIP at {≈} 10 eV in the SEPs but {≈} 14 eV for the solar wind. Naively, this seems to suggest cooler plasma from sunspots beneath active regions. More likely, if the ponderomotive force of Alfvén waves preferentially conveys low-FIP ions into the corona, the source plasma that eventually will be shock-accelerated as SEPs originates in magnetic structures where Alfvén waves resonate with the loop length on closed magnetic field lines. This concentrates FIP fractionation near the top of the chromosphere. Meanwhile, the source of the SSW may lie near the base of diverging open-field lines surrounding, but outside of, active regions, where such resonance does not exist, allowing fractionation throughout the chromosphere. We also find that energetic particles accelerated from the solar wind itself by shock waves at corotating interaction regions, generally beyond 1 AU, confirm the FIP pattern of the solar wind.
16. Detection of fast nanoparticles in the solar wind
International Nuclear Information System (INIS)
Meyer-Vernet, N.; Maksimovic, M.; Lecacheux, A.; Le Chat, G.; Czechowski, A.; Mann, I.; Goetz, K.; Kaiser, M. L.; Cyr, O. C. St.; Bale, S. D.
2010-01-01
Dust grains in the nanometer range bridge the gap between atoms and larger grains made of bulk material. Their small size embodies them with special properties. Due to their high relative surface area, they have a high charge-to-mass ratio, so that the Lorentz force in the solar wind magnetic field exceeds the gravitational force and other forces by a large amount, and they are accelerated to a speed of the order of magnitude of the solar wind speed. When such fast nanoparticles impact a spacecraft, they produce craters whose matter vaporises and ionises, yielding transient voltages as high as do much larger grains of smaller speed. These properties are at the origin of their recent detection at 1 AU in the solar wind. We discuss the detection of fast nanoparticles by wave instruments of different configurations, with applications to the recent detections on STEREO/WAVES and CASSINI/RPWS. Finally we discuss the opportunities for nanoparticle detection by wave instruments on future missions and/or projects in the inner heliosphere such as Bepi-Colombo and Solar Orbiter.
17. Invited article: Electric solar wind sail: toward test missions.
Science.gov (United States)
Janhunen, P; Toivanen, P K; Polkko, J; Merikallio, S; Salminen, P; Haeggström, E; Seppänen, H; Kurppa, R; Ukkonen, J; Kiprich, S; Thornell, G; Kratz, H; Richter, L; Krömer, O; Rosta, R; Noorma, M; Envall, J; Lätt, S; Mengali, G; Quarta, A A; Koivisto, H; Tarvainen, O; Kalvas, T; Kauppinen, J; Nuottajärvi, A; Obraztsov, A
2010-11-01
The electric solar wind sail (E-sail) is a space propulsion concept that uses the natural solar wind dynamic pressure for producing spacecraft thrust. In its baseline form, the E-sail consists of a number of long, thin, conducting, and centrifugally stretched tethers, which are kept in a high positive potential by an onboard electron gun. The concept gains its efficiency from the fact that the effective sail area, i.e., the potential structure of the tethers, can be millions of times larger than the physical area of the thin tethers wires, which offsets the fact that the dynamic pressure of the solar wind is very weak. Indeed, according to the most recent published estimates, an E-sail of 1 N thrust and 100 kg mass could be built in the rather near future, providing a revolutionary level of propulsive performance (specific acceleration) for travel in the solar system. Here we give a review of the ongoing technical development work of the E-sail, covering tether construction, overall mechanical design alternatives, guidance and navigation strategies, and dynamical and orbital simulations.
18. Geometry of the solar wind transition region during the 11-year solar cycle
International Nuclear Information System (INIS)
Lotova, N.A.; Blums, D.F.
1986-01-01
Geometry of the solar wind transition region and its dynamics during the 11-year solar cycle is investigated. It is shown that the space geometry of the transition region suffers considerable changes. In the years of minimum of solar activity (1975-1977) the transition region has a form close to elliptical, shifts nearer to the Sun, while its width decreases. During the years of maximum of Solar activity (1979-1981) the form of the transition region becomes close to spherically symmetric, is located further from the Sun and its width is increased
19. On the relation between ionospheric winter anomalies and solar wind
International Nuclear Information System (INIS)
Rumi, G.C.
2001-01-01
There are two different winter anomalies. A small one that appears in connection with ionization at relatively low latitudes in the bottom of the D-region of the ionosphere. There, the electron densities in the winter happen to be less than should be expected. On the other hand, the classic winter anomaly is present when in the winter the upper D-region, again at relatively low latitudes, has more ionization than should be expected. Both these effects are due to the slant compression of the geomagnetic field produced by the solar wind in the wind in the winter season (which is, of course, the summer season when reference is made to events in the other hemisphere). It is shown that the small winter anomaly is a consequence of a hemispheric imbalance in the flux of galactic cosmic rays determined by the obliquely distorted geomagnetic field. It is shown that the standard winter anomaly can be ascribed to the influx of a super solar wind, which penetrates into the Earth's polar atmosphere down to E-region, heights and, duly concentrated through a funneling action at the winter pole of the distorted geomagnetic field, slows down the winter polar vortex. An equatorward motion of the polar air with its content of nitric oxide brings about the excess of ionization in the upper D-region at lower latitudes. The experimentally observed rhythmic recurrence of the upper winter anomaly is correlated to a possible rhythmic recurrence of the super solar wind. The actual detection of the upper winter anomaly could yield some information on the velocity of the basic solar wind. A by-product of the present analysis, the determination of Γ, the coefficient of collisional detachment of the electrons from the O 2 - ions, is presented in the Appendix
20. On the relation between ionospheric winter anomalies and solar wind
Energy Technology Data Exchange (ETDEWEB)
Rumi, G.C. [Lecco, (Italy)
2001-06-01
There are two different winter anomalies. A small one that appears in connection with ionization at relatively low latitudes in the bottom of the D-region of the ionosphere. There, the electron densities in the winter happen to be less than should be expected. On the other hand, the classic winter anomaly is present when in the winter the upper D-region, again at relatively low latitudes, has more ionization than should be expected. Both these effects are due to the slant compression of the geomagnetic field produced by the solar wind in the wind in the winter season (which is, of course, the summer season when reference is made to events in the other hemisphere). It is shown that the small winter anomaly is a consequence of a hemispheric imbalance in the flux of galactic cosmic rays determined by the obliquely distorted geomagnetic field. It is shown that the standard winter anomaly can be ascribed to the influx of a super solar wind, which penetrates into the Earth's polar atmosphere down to E-region, heights and, duly concentrated through a funneling action at the winter pole of the distorted geomagnetic field, slows down the winter polar vortex. An equatorward motion of the polar air with its content of nitric oxide brings about the excess of ionization in the upper D-region at lower latitudes. The experimentally observed rhythmic recurrence of the upper winter anomaly is correlated to a possible rhythmic recurrence of the super solar wind. The actual detection of the upper winter anomaly could yield some information on the velocity of the basic solar wind. A by-product of the present analysis, the determination of {gamma}, the coefficient of collisional detachment of the electrons from the O{sub 2} {sup -} ions, is presented in the Appendix.
1. A Generalized Equatorial Model for the Accelerating Solar Wind
Science.gov (United States)
Tasnim, S.; Cairns, Iver H.; Wheatland, M. S.
2018-02-01
A new theoretical model for the solar wind is developed that includes the wind's acceleration, conservation of angular momentum, deviations from corotation, and nonradial velocity and magnetic field components from an inner boundary (corresponding to the onset of the solar wind) to beyond 1 AU. The model uses a solution of the time-steady isothermal equation of motion to describe the acceleration and analytically predicts the Alfvénic critical radius. We fit the model to near-Earth observations of the Wind spacecraft during the solar rotation period of 1-27 August 2010. The resulting data-driven model demonstrates the existence of noncorotating, nonradial flows and fields from the inner boundary (r = rs) outward and predicts the magnetic field B = (Br,Bϕ), velocity v = (vr,vϕ), and density n(r,ϕ,t), which vary with heliocentric distance r, heliolatitude ϕ, and time t in a Sun-centered standard inertial plane. The description applies formally only in the equatorial plane. In a frame corotating with the Sun, the transformed velocity v' and a field B' are not parallel, resulting in an electric field with a component Ez' along the z axis. The resulting E'×B'=E'×B drift lies in the equatorial plane, while the ∇B and curvature drifts are out of the plane. Together these may lead to enhanced scattering/heating of sufficiently energetic particles. The model predicts that deviations δvϕ from corotation at the inner boundary are common, with δvϕ(rs,ϕs,ts) comparable to the transverse velocities due to granulation and supergranulation motions. Abrupt changes in δvϕ(rs,ϕs,ts) are interpreted in terms of converging and diverging flows at the cell boundaries and centers, respectively. Large-scale variations in the predicted angular momentum demonstrate that the solar wind can drive vorticity and turbulence from near the Sun to 1 AU and beyond.
2. Western Wind and Solar Integration Study: Hydropower Analysis
Energy Technology Data Exchange (ETDEWEB)
Acker, T.; Pete, C.
2012-03-01
The U.S. Department of Energy's (DOE) study of 20% Wind Energy by 2030 was conducted to consider the benefits, challenges, and costs associated with sourcing 20% of U.S. energy consumption from wind power by 2030. This study found that with proactive measures, no insurmountable barriers were identified to meet the 20% goal. Following this study, DOE and the National Renewable Energy Laboratory (NREL) conducted two more studies: the Eastern Wind Integration and Transmission Study (EWITS) covering the eastern portion of the U.S., and the Western Wind and Solar Integration Study (WWSIS) covering the western portion of the United States. The WWSIS was conducted by NREL and research partner General Electric (GE) in order to provide insight into the costs, technical or physical barriers, and operational impacts caused by the variability and uncertainty of wind, photovoltaic, and concentrated solar power when employed to serve up to 35% of the load energy in the WestConnect region (Arizona, Colorado, Nevada, New Mexico, and Wyoming). WestConnect is composed of several utility companies working collaboratively to assess stakeholder and market needs to and develop cost-effective improvements to the western wholesale electricity market. Participants include the Arizona Public Service, El Paso Electric Company, NV Energy, Public Service of New Mexico, Salt River Project, Tri-State Generation and Transmission Cooperative, Tucson Electric Power, Xcel Energy and the Western Area Power Administration.
3. Solar and wind potentialities in Mauritania. Presentation of pumping
International Nuclear Information System (INIS)
1996-01-01
The programs of rural hydraulics based upon the use of renewable energies, either solar or wind, have gained in importance in Africa during the last decade; particularly in Mauritania, a Sahelian country, which is extending widely beyond the western edge of Sahara. This country has been hardly affected by the prolonged droughts which have recently struck this region. Water is a major problem here. Important projects appeared concerning the pumping of water with the help of solar photovoltaic systems and wind mechanical pumps; other processes are being studied: pumping with aero-generators, sea water desalinating... Today Mauritania is at the top of countries of the subregion concerning the number of installations of wind mechanical pumps. The meteorological conditions are in fact favourable to such realizations. A technical and economic comparative study of the results of functioning obtained on the field with a photovoltaic pumping installation and a wind pumping installation, is presented: better technical performances and greater reliability for the photovoltaic pump, lower cost and technological mastery for the wind pump. (author). 9 refs., 8 figs
4. An extended structure-function model and its application to the analysis of solar wind intermittency properties
Directory of Open Access Journals (Sweden)
C.-Y. Tu
Full Text Available An extended structure-function model is developed by including the new effect in the p-model of Meneveau and Sreenivasan which shows that the averaged energy cascade rate changes with scale, a situation which has been found to prevail in non-fully-developed turbulence in the inner solar wind. This model is useful for the small-scale fluctuations in the inner heliosphere, where the turbulence is not fully developed and cannot be explained quantitatively by any of the previous intermittency turbulence models. With two model parameters, the intrinsic index of the energy spectrum α, and the fragmentation fraction P1, the model can fit, for the first time, all the observed scaling exponents of the structure functions, which are calculated for time lags ranging from 81 s to 0.7 h from the Helios solar wind data. From the cases we studied we cannot establish for P1 either a clear radial evolution trend, or a solar-wind-speed or stream-structure dependence or a systematic anisotropy for both the flow velocity and magnetic field component fluctuations. Generally, P1 has values between 0.7 and 0.8. However, in some cases in low-speed wind P1 has somewhat higher values for the magnetic components, especially for the radial component. In high-speed wind, the inferred intrinsic spectral indices α of the velocity and magnetic field components are about equal, while the experimental spectral indices derived from the observed power spectra differ. The magnetic index is somewhat larger than the index of the velocity spectrum. For magnetic fluctuations in both high- and low-speed winds, the intrinsic exponent α has values which are near 1.5, while the observed spectral exponent has much higher values. In the solar wind with considerable density fluctuations near the interplanetary current sheet near 1 AU, it is found that P1 has a comparatively high value of 0
5. A Model for the Sources of the Slow Solar Wind
Science.gov (United States)
Antiochos, S. K.; Mikić, Z.; Titov, V. S.; Lionello, R.; Linker, J. A.
2011-04-01
Models for the origin of the slow solar wind must account for two seemingly contradictory observations: the slow wind has the composition of the closed-field corona, implying that it originates from the continuous opening and closing of flux at the boundary between open and closed field. On the other hand, the slow wind also has large angular width, up to ~60°, suggesting that its source extends far from the open-closed boundary. We propose a model that can explain both observations. The key idea is that the source of the slow wind at the Sun is a network of narrow (possibly singular) open-field corridors that map to a web of separatrices and quasi-separatrix layers in the heliosphere. We compute analytically the topology of an open-field corridor and show that it produces a quasi-separatrix layer in the heliosphere that extends to angles far from the heliospheric current sheet. We then use an MHD code and MDI/SOHO observations of the photospheric magnetic field to calculate numerically, with high spatial resolution, the quasi-steady solar wind, and magnetic field for a time period preceding the 2008 August 1 total solar eclipse. Our numerical results imply that, at least for this time period, a web of separatrices (which we term an S-web) forms with sufficient density and extent in the heliosphere to account for the observed properties of the slow wind. We discuss the implications of our S-web model for the structure and dynamics of the corona and heliosphere and propose further tests of the model.
6. Observations of the solar wind speed near the sun
International Nuclear Information System (INIS)
Grall, R. R.; Coles, Wm. A.; Klinglesmith, M. T.
1996-01-01
Two-antenna scintillation (IPS) observations can provide accurate measurements of the velocity with which electron density fluctuations drift past the line of sight. These fluctuations can be used as tracers for the solar plasma and allow us to estimate the solar wind velocity near the Sun where spacecraft have not yet penetrated. We present recent IPS measurements made with the EISCAT and VLBA arrays. We have found that by using baselines which are several times the scale size of the diffraction pattern we are able to partially deconvolve the line of sight integration which affects remote sensing data. The long baselines allow the fast and slow components of the solar wind to be separated and their velocities estimated individually. In modeling IPS it is important that the scattering be 'weak' because the model then requires only 1 spatial parameter instead of 3. EISCAT can only operate near 933MHz which limits the observation to outside of 18R · , however the VLBA has higher frequency receivers which allow it to observe inside of 15R · . The density variance δN e 2 in the fast wind is a factor of 10-15 less than in the slow (Coles et al., 1995) making it necessary to consider the entire line of sight, particularly when the fast wind occupies the center portion. Using the point of closest approach and the average velocity to characterize the observation can lead to an incorrect interpretation of the data. We have compared our IPS observations with maps made from the Yohkoh soft X ray, HAO's white-light electron density, and Stanford magnetic field measurements as well as with the IMP8 and Ulysses spacecraft data to assist in placing the fast and slow wind. Here we have selected those observation from 1994 which were dominated by the southern coronal hole and have estimated a velocity acceleration profile for the fast solar wind between 7 and 100R · which is presented in Figure 1. The observations suggest that the fast solar wind is fully developed by ≅7R
7. Perturbation of the solar wind in a model terrestrial foreshock
International Nuclear Information System (INIS)
Skadron, G.; Holdaway, R.D.; Scholer, M.
1986-01-01
We analyze the perturbation of the solar wind in the earth's foreshock. The foreshock is modulated as a planar magnetic flux tube having a 15 R/sub E/ half width. Within the flux tube the upstream energetic particle pressure is assumed to fall monotonically to zero at the flux tube boundary and decline in the upstream direction with a scale length of 8 R/sub E/. The incident solar wind is assumed to flow uniformly with a velocity of 400 km s -1 , a density of 8 cm -3 , a pressure of 50 eV cm -3 , and a magnetic field of 4γ directed parallel to the flow. The solar wind density, velocity, and magnetic field within the foreshock are described by the steady state ideal MHD equations. We find that (1) the vector solar wind velocity perturbation rotates from the sunward to the transverse direction with increasing distance from the axis of the flux tube, (2) the peak solar wind deflection is located --3R/sub E/ within the flux tube boundary, (3) a central upstream pressure of 200 eV cm -3 produces a maxium deceleration of 6 km s -1 and a maximum deflection of 1.3 0 , (4) a central upstream pressure of 600 eV cm -3 produces a maximum deceleration of 19 km s -1 and a maximum deflection of 3.6 0 , and (5) the deflection and deceleration are accompanied by perturbations of the solar wind density and magnetic field. These perturbations are largest near the flux tube boundary where both form spikes having a width of --2R/sub E/. For a 600 eV cm -3 central pressure those spikes have amplitudes of 2 cm -3 and lγ, respectively. We have analyzed the linearized flow problem analytically and reduced the solutions to quadrature. These solutions are found to be good approximations to the numerical nonlinear solutions for moderate values of the upstream particle pressure
8. Implementation Strategy for a Global Solar and Wind Atlas
Energy Technology Data Exchange (ETDEWEB)
NONE
2012-01-15
In July 2009, Major Economies Forum leaders met to prepare for the COP 15 Copenhagen Conference that took place later that year. At this occasion the Major Economies Forum Global Partnership f or low carbon and climate-friendly technology was founded and Technology Action Plans (TAPs) for ten key low-carbon technologies were drafted. At that juncture Denmark, Germany and Spain took on the responsibility for drafting TAPs for Solar and Wind Energy Technologies. The TAPs were then consolidated and presented at COP 15 that would later take place in December in Copenhagen. Since then, countries that led the development of the Action Plans have started their implementation. During a first Clean Energy Ministerial (CEM) in July 2010 in Washington on the invitation of Steven Chu, US Secretary of Energy, several initiatives were launched. Denmark, Germany and Spain took the lead in the implementation of the TAPs for Solar and Wind Technologies and initiated the Multilateral Working Group on Solar and Wind Energy Technologies (MWGSW). Several countries joined the working group in Washington and afterwards. In two international workshops in Bonn (June 2010) and Madrid (November 2010) and in meetings during the first CEM in Washington (July 2010) and the second CEM in Abu Dhabi (April 2011) the Multilateral Working Group made substantial progress in the two initial fields of action: (1) the Development of a Global Solar and Wind Atlas; and (2) the Development of a Long-term Strategy on Joint Capacity Building. Discussion papers on the respective topics were elaborated involving the Working Group's member countries as well as various international institutions. This led to concrete proposals for several pilot activities in both fields of action. After further specifying key elements of the suggested projects in two expert workshops in spring 2011, the Multilateral Working Group convened for a third international workshop in Copenhagen, Denmark, to discuss the project
9. Single ICMEs and Complex Transient Structures in the Solar Wind in 2010 - 2011
Science.gov (United States)
Rodkin, D.; Slemzin, V.; Zhukov, A. N.; Goryaev, F.; Shugay, Y.; Veselovsky, I.
2018-05-01
We analyze the statistics, solar sources, and properties of interplanetary coronal mass ejections (ICMEs) in the solar wind. The total number of coronal mass ejections (CMEs) registered in the Coordinated Data Analysis Workshops catalog (CDAW) during the first eight years of Cycle 24 was 61% larger than in the same period of Cycle 23, but the number of X-ray flares registered by the Geostationary Operational Environmental Satellite (GOES) was 20 % smaller because the solar activity was lower. The total number of ICMEs in the given period of Cycle 24 in the Richardson and Cane list was 29% smaller than in Cycle 23, which may be explained by a noticeable number of non-classified ICME-like events in the beginning of Cycle 24. For the period January 2010 - August 2011, we identify solar sources of the ICMEs that are included in the Richardson and Cane list. The solar sources of ICME were determined from coronagraph observations of the Earth-directed CMEs, supplemented by modeling of their propagation in the heliosphere using kinematic models (a ballistic and drag-based model). A detailed analysis of the ICME solar sources in the period under study showed that in 11 cases out of 23 (48%), the observed ICME could be associated with two or more sources. For multiple-source events, the resulting solar wind disturbances can be described as complex (merged) structures that are caused by stream interactions, with properties depending on the type of the participating streams. As a reliable marker to identify interacting streams and their sources, we used the plasma ion composition because it freezes in the low corona and remains unchanged in the heliosphere. According to the ion composition signatures, we classify these cases into three types: complex ejecta originating from weak and strong CME-CME interactions, as well as merged interaction regions (MIRs) originating from the CME high-speed stream (HSS) interactions. We describe temporal profiles of the ion composition for
10. The genesis solar-wind sample return mission
International Nuclear Information System (INIS)
Wiens, Roger C.
2009-01-01
The compositions of the Earth's crust and mantle, and those of the Moon and Mars, are relatively well known both isotopically and elementally. The same is true of our knowledge of the asteroid belt composition, based on meteorite analyses. Remote measurements of Venus, the Jovian atmosphere, and the outer planet moons, have provided some estimates of their compositions. The Sun constitutes a large majority, > 99%, of all the matter in the solar system. The elemental composition of the photosphere, the visible 'surface' of the Sun, is constrained by absorption lines produced by particles above the surface. Abundances for many elements are reported to the ±10 or 20% accuracy level. However, the abundances of other important elements, such as neon, cannot be determined in this way due to a relative lack of atomic states at low excitation energies. Additionally and most importantly, the isotopic composition of the Sun cannot be determined astronomically except for a few species which form molecules above sunspots, and estimates derived from these sources lack the accuracy desired for comparison with meteoritic and planetary surface samples measured on the Earth. The solar wind spreads a sample of solar particles throughout the heliosphere, though the sample is very rarified: collecting a nanogram of oxygen, the third most abundant element, in a square centimeter cross section at the Earth's distance from the Sun takes five years. Nevertheless, foil collectors exposed to the solar wind for periods of hours on the surface of the Moon during the Apollo missions were used to determine the helium and neon solar-wind compositions sufficiently to show that the Earth's atmospheric neon was significantly evolved relative to the Sun. Spacecraft instruments developed subsequently have provided many insights into the composition of the solar wind, mostly in terms of elemental composition. These instruments have the advantage of observing a number of parameters simultaneously
11. Coronal hole evolution from multi-viewpoint data as input for a STEREO solar wind speed persistence model
Science.gov (United States)
Temmer, Manuela; Hinterreiter, Jürgen; Reiss, Martin A.
2018-03-01
We present a concept study of a solar wind forecasting method for Earth, based on persistence modeling from STEREO in situ measurements combined with multi-viewpoint EUV observational data. By comparing the fractional areas of coronal holes (CHs) extracted from EUV data of STEREO and SoHO/SDO, we perform an uncertainty assessment derived from changes in the CHs and apply those changes to the predicted solar wind speed profile at 1 AU. We evaluate the method for the time period 2008-2012, and compare the results to a persistence model based on ACE in situ measurements and to the STEREO persistence model without implementing the information on CH evolution. Compared to an ACE based persistence model, the performance of the STEREO persistence model which takes into account the evolution of CHs, is able to increase the number of correctly predicted high-speed streams by about 12%, and to decrease the number of missed streams by about 23%, and the number of false alarms by about 19%. However, the added information on CH evolution is not able to deliver more accurate speed values for the forecast than using the STEREO persistence model without CH information which performs better than an ACE based persistence model. Investigating the CH evolution between STEREO and Earth view for varying separation angles over ˜25-140° East of Earth, we derive some relation between expanding CHs and increasing solar wind speed, but a less clear relation for decaying CHs and decreasing solar wind speed. This fact most likely prevents the method from making more precise forecasts. The obtained results support a future L5 mission and show the importance and valuable contribution using multi-viewpoint data.
12. Coronal hole evolution from multi-viewpoint data as input for a STEREO solar wind speed persistence model
Directory of Open Access Journals (Sweden)
Temmer Manuela
2018-01-01
Full Text Available We present a concept study of a solar wind forecasting method for Earth, based on persistence modeling from STEREO in situ measurements combined with multi-viewpoint EUV observational data. By comparing the fractional areas of coronal holes (CHs extracted from EUV data of STEREO and SoHO/SDO, we perform an uncertainty assessment derived from changes in the CHs and apply those changes to the predicted solar wind speed profile at 1 AU. We evaluate the method for the time period 2008–2012, and compare the results to a persistence model based on ACE in situ measurements and to the STEREO persistence model without implementing the information on CH evolution. Compared to an ACE based persistence model, the performance of the STEREO persistence model which takes into account the evolution of CHs, is able to increase the number of correctly predicted high-speed streams by about 12%, and to decrease the number of missed streams by about 23%, and the number of false alarms by about 19%. However, the added information on CH evolution is not able to deliver more accurate speed values for the forecast than using the STEREO persistence model without CH information which performs better than an ACE based persistence model. Investigating the CH evolution between STEREO and Earth view for varying separation angles over ∼25–140° East of Earth, we derive some relation between expanding CHs and increasing solar wind speed, but a less clear relation for decaying CHs and decreasing solar wind speed. This fact most likely prevents the method from making more precise forecasts. The obtained results support a future L5 mission and show the importance and valuable contribution using multi-viewpoint data.
13. Role of the Coronal Alfvén Speed in Modulating the Solar-wind Helium Abundance
Science.gov (United States)
Wang, Y.-M.
2016-12-01
The helium abundance He/H in the solar wind is relatively constant at ˜0.04 in high-speed streams, but varies in phase with the sunspot number in slow wind, from ˜0.01 at solar minimum to ˜0.04 at maximum. Suggested mechanisms for helium fractionation have included frictional coupling to protons and resonant interactions with high-frequency Alfvénic fluctuations. We compare He/H measurements during 1995-2015 with coronal parameters derived from source-surface extrapolations of photospheric field maps. We find that the near-Earth helium abundance is an increasing function of the magnetic field strength and Alfvén speed v A in the outer corona, while being only weakly correlated with the proton flux density. Throughout the solar cycle, fast wind is associated with short-term increases in v A near the source surface; resonance with Alfvén waves, with v A and the relative speed of α-particles and protons decreasing with increasing heliocentric distance, may then lead to enhanced He/H at 1 au. The modulation of helium in slow wind reflects the tendency for the associated coronal Alfvén speeds to rise steeply from sunspot minimum, when this wind is concentrated around the source-surface neutral line, to sunspot maximum, when the source-surface field attains its peak strengths. The helium abundance near the source surface may represent a balance between collisional decoupling from protons and Alfvén wave acceleration.
14. Self consistent MHD modeling of the solar wind from coronal holes with distinct geometries
Science.gov (United States)
Stewart, G. A.; Bravo, S.
1995-01-01
Utilizing an iterative scheme, a self-consistent axisymmetric MHD model for the solar wind has been developed. We use this model to evaluate the properties of the solar wind issuing from the open polar coronal hole regions of the Sun, during solar minimum. We explore the variation of solar wind parameters across the extent of the hole and we investigate how these variations are affected by the geometry of the hole and the strength of the field at the coronal base.
15. Predicting Ionization Rates from SEP and Solar Wind Proton Precipitation into the Martian Atmosphere
Science.gov (United States)
Jolitz, R.; Dong, C.; Lee, C. O.; Curry, S.; Lillis, R. J.; Brain, D.; Halekas, J. S.; Larson, D. E.; Bougher, S. W.; Jakosky, B. M.
2017-12-01
Precipitating energetic particles ionize planetary atmospheres and increase total electron content. At Mars, the solar wind and solar energetic particles (SEPs) can precipitate directly into the atmosphere because solar wind protons can charge exchange to become neutrals and pass through the magnetosheath, while SEPs are sufficiently energetic to cross the magnetosheath unchanged. In this study we will present predicted ionization rates and resulting electron densities produced by solar wind and SEP proton ionization during nominal solar activity and a CME shock front impact event on May 16 2016. We will use the Atmospheric Scattering of Protons and Energetic Neutrals (ASPEN) model to compare ionization by SEP and solar wind protons currently measured by the SWIA (Solar Wind Ion Analyzer) and SEP instruments aboard the MAVEN spacecraft. Results will help to quantify how the ionosphere responds to extreme solar events during solar minimum.
16. MHD effects of the solar wind flow around planets
Directory of Open Access Journals (Sweden)
H. K. Biernat
2000-01-01
Full Text Available The study of the interaction of the solar wind with magnetized and unmagnetized planets forms a central topic of space research. Focussing on planetary magnetosheaths, we review some major developments in this field. Magnetosheath structures depend crucially on the orientation of the interplanetary magnetic field, the solar wind Alfvén Mach number, the shape of the obstacle (axisymmetric/non-axisymmetric, etc., the boundary conditions at the magnetopause (low/high magnetic shear, and the degree of thermal anisotropy of the plasma. We illustrate the cases of Earth, Jupiter and Venus. The terrestrial magnetosphere is axisymmetric and has been probed in-situ by many spacecraft. Jupiter's magnetosphere is highly non-axisymmetric. Furthermore, we study magnetohydrodynamic effects in the Venus magnetosheath.
17. Spacecraft observations of solar wind turbulence: an overview
International Nuclear Information System (INIS)
Horbury, T S; Forman, M A; Oughton, S
2005-01-01
Spacecraft measurements in the solar wind offer the opportunity to study magnetohydrodynamic (MHD) turbulence in a collisionless plasma in great detail. We review some of the key results of the study of this medium: the presence of large amplitude Alfven waves propagating predominantly away from the Sun; the existence of an active turbulent cascade; and the presence of intermittency similar to that in neutral fluids. We also discuss the presence of anisotropy in wavevector space relative to the local magnetic field direction. Some models suggest that MHD turbulence can evolve to a state with power predominantly in wavevectors either parallel to the magnetic field ('slab' fluctuations) or approximately perpendicular to it ('2D'). We review the existing evidence for such anisotropy, which has important consequences for the transport of energetic particles. Finally, we present the first results of a new analysis which provides the most accurate measurements to date of the wave-vector anisotropy of wavevector power in solar wind MHD turbulence
18. Solar wind acceleration in a prescribed flow geometry
International Nuclear Information System (INIS)
Biernat, H.; Koemle, N.; Lichtenegger, H.
1985-01-01
It is known that the flow tubes above coronal holes diverge stronger than radial and that the magnetic field lines may be considerably curved near the border of the holes. The authors investigate the consequences of such a magnetic field geometry on the flow of the solar wind plasma in the vicinity of the Sun. For this purpose the one-dimensional conservation equations are solved along prescribed flow tubes. A temperature profile based on observational data (EUV rocket-observations) is used in the calculations. In an alternative approach the temperature is determined by a polytropic index, which is assumed to be variable. The authors study how both curvature and non-radial divergence of the flow tubes modify the velocity, the density, and the energy balance of the solar wind plasma. (Auth.)
19. Counterstreaming solar wind halo electron events on open field lines?
Science.gov (United States)
Gosling, J. T.; Mccomas, D. J.; Phillips, J. L.
1992-01-01
Counterstreaming solar wind halo electron events have been identified as a common 1 AU signature of coronal mass ejection events, and have generally been interpreted as indicative of closed magnetic field topologies, i.e., magnetic loops or flux ropes rooted at both ends in the Sun, or detached plasmoids. In this paper we examine the possibility that these events may instead occur preferentially on open field lines, and that counterstreaming results from reflection or injection behind interplanetary shocks or from mirroring from regions of compressed magnetic field farther out in the heliosphere. We conclude that neither of these suggested sources of counterstreaming electron beams is viable and that the best interpretation of observed counterstreaming electron events in the solar wind remains that of passage of closed field structures.
20. On the penetration of solar wind inhomogeneities into the magnetosphere
International Nuclear Information System (INIS)
Maksimov, V.P.; Senatorov, V.N.
1980-01-01
Laboratory experiments were used as a basis to study the process of interaction between solar wind inhomogeneities and the Earth's magnetosphere. The given inhomogeneity represents a lump of plasma characterized by an increased concentration of particles (nsub(e) approximately 20-30 cm -3 ), a discrete form (characteristic dimensions of the lump are inferior to the magnetosphere diameter) and the velocity v approximately 350 km/s. It is shown that there is the possibility of penetration of solar wind inhomogeneities inside the Earth's magnetosphere because of the appearance in the inhomogeneity of an electric field of transverse polarization. The said process is a possible mechanism of the formation of the magnetopshere entrance layer
1. Control of particle precipitation by energy transfer from solar wind
Science.gov (United States)
Bremer, J.; Gernandt, H.
1985-12-01
The energy transfer function (epsilon), introduced by Perreault and Akasofu (1978), appears to be well suited for the description of the long-term control of the particle precipitation by interplanetary parameters. An investigation was conducted with the objective to test this control in more detail. This investigation included the calculation of hourly epsilon values on the basis of satellite-measured solar wind and IMF (interplanetary magnetic field) data. The results were compared with corresponding geomagnetic and ionospheric data. The ionospheric data had been obtained by three GDR (German Democratic Republic) teams during the 21st, 22nd, and 23rd Soviet Antarctic Expeditions in the time period from 1976 to 1979. It was found that, in high latitudes, the properties of the solar wind exercise a pronounced degree of control on the precipitation of energetic particles into the atmosphere, taking into account a time delay of about one hour due to the occurrence of magnetospheric storage processes.
2. Nearly incompressible MHD turbulence in the solar wind
International Nuclear Information System (INIS)
Matthaeus, W.H.; Zhou, Y.
1989-01-01
Observational studies indicate that solar wind plasma and magnetic field fluctuations may be meaningfully viewed as an example of magnetohydrodynamic turbulence. This paper presents a brief summary of some relevant results of turbulence theory and reviews a turbulence style description of 'typical' solar wind conditions. Recent results, particularly those regarding the radial evolution of inertial range cross helicity, support the viewpoint that interplanetary turbulence is active and evolving with heliocentric distance. A number of observed properties can be understood by appeal to incompressible turbulence mechanisms. This connection may be understood by appeal to incompressible turbulence mechanisms. This connection may be understood in terms of theories of pseudosound density fluctuations and nearly incompressible magnetohydrodynamics, which are also reviewed here. Finally, we summarize a recent two-scale dynamical theory of the radial and temporal evolution of the turbulence, which may provide an additional framework for understanding the observations. (author). 49 refs
3. Save with Solar and Wind, Summer 2002 (Newsletter)
Energy Technology Data Exchange (ETDEWEB)
2002-07-01
This newsletter is published by the Department of Energy's Federal Energy Management Program. It is intended for facility managers, contracting officials, energy specialists, and others involved in helping Federal agencies increase their use of cost-effective solar and wind energy systems at their facilities. Renewable energy systems ultimately save agencies money by reducing utility costs; they also help to lower the emissions associated with the use of fossil fuels. This issue describes a new strategy to achieve the Federal goal for renewable energy, as well as some new solar and wind systems installed at facilities of the Department of Defense, the U.S. Geological Survey, the U.S. Postal Service, the National Park Service, and other agencies.
4. A desalination plant with solar and wind energy
International Nuclear Information System (INIS)
Chen, H; Ye, Z; Gao, W
2013-01-01
The shortage of freshwater resources has become a worldwide problem. China has a water shortage, although the total amount of water resources is the sixth in the world, the per capita water capacity is the 121th (a quarter of the world's per capita water capacity), and the United Nations considers China one of the poorest 13 countries in the world in terms of water. In order to increase the supply of fresh water, a realistic way is to make full use of China's long and narrow coastline for seawater desalination. This paper discusses a sea water desalination device, the device adopts distillation, uses the greenhouse effect principle and wind power heating principle, and the two-type start is used to solve the problem of vertical axis wind turbine self-starting. Thrust bearings are used to ensure the stability of the device, and to ensure absorbtion of wind energy and solar energy, and to collect evaporation of water to achieve desalination. The device can absorb solar and wind energy instead of input energy, so it can be used in ship, island and many kinds of environment. Due to the comprehensive utilization of wind power and solar power, the efficiency of the device is more than other passive sea water desalting plants, the initial investment and maintenance cost is lower than active sea water desalting plant. The main part of the device cannot only be used in offshore work, but can also be used in deep sea floating work, so the device can utilise deep sea energy. In order to prove the practicability of the device, the author has carried out theory of water production calculations. According to the principle of conservation of energy, the device ais bsorbing solar and wind power, except loose lost part which is used for water temperature rise and phase transition. Assume the inflow water temperature is 20 °C, outflow water temperature is 70 °C, the energy utilization is 60%, we can know that the water production quantity is 8 kg/ m 2 per hour. Comparing
5. Small Coronal Holes Near Active Regions as Sources of Slow Solar Wind
Energy Technology Data Exchange (ETDEWEB)
Wang, Y.-M., E-mail: [email protected] [Space Science Division, Naval Research Laboratory, Washington, DC 20375 (United States)
2017-06-01
We discuss the nature of the small areas of rapidly diverging, open magnetic flux that form in the strong unipolar fields at the peripheries of active regions (ARs), according to coronal extrapolations of photospheric field measurements. Because such regions usually have dark counterparts in extreme-ultraviolet (EUV) images, we refer to them as coronal holes, even when they appear as narrow lanes or contain sunspots. Revisiting previously identified “AR sources” of slow solar wind from 1998 and 1999, we find that they are all associated with EUV coronal holes; the absence of well-defined He i 1083.0 nm counterparts to some of these holes is attributed to the large flux of photoionizing radiation from neighboring AR loops. Examining a number of AR-associated EUV holes during the 2014 activity maximum, we confirm that they are characterized by wind speeds of ∼300–450 km s{sup −1}, O{sup 7+}/O{sup 6+} ratios of ∼0.05–0.4, and footpoint field strengths typically of order 30 G. The close spacing between ARs at sunspot maximum limits the widths of unipolar regions and their embedded holes, while the continual emergence of new flux leads to rapid changes in the hole boundaries. Because of the highly nonradial nature of AR fields, the smaller EUV holes are often masked by the overlying canopy of loops, and may be more visible toward one solar limb than at central meridian. As sunspot activity declines, the AR remnants merge to form much larger, weaker, and longer-lived unipolar regions, which harbor the “classical” coronal holes that produce recurrent high-speed streams.
6. Velocity fluctuations in polar solar wind: a comparison between different solar cycles
Directory of Open Access Journals (Sweden)
B. Bavassano
2009-02-01
Full Text Available The polar solar wind is a fast, tenuous and steady flow that, with the exception of a relatively short phase around the Sun's activity maximum, fills the high-latitude heliosphere. The polar wind properties have been extensively investigated by Ulysses, the first spacecraft able to perform in-situ measurements in the high-latitude heliosphere. The out-of-ecliptic phases of Ulysses cover about seventeen years. This makes possible to study heliospheric properties at high latitudes in different solar cycles. In the present investigation we focus on hourly- to daily-scale fluctuations of the polar wind velocity. Though the polar wind is a quite uniform flow, fluctuations in its velocity do not appear negligible. A simple way to characterize wind velocity variations is that of performing a multi-scale statistical analysis of the wind velocity differences. Our analysis is based on the computation of velocity differences at different time lags and the evaluation of statistical quantities (mean, standard deviation, skewness, and kurtosis for the different ensembles. The results clearly show that, though differences exist in the three-dimensional structure of the heliosphere between the investigated solar cycles, the velocity fluctuations in the core of polar coronal holes exhibit essentially unchanged statistical properties.
7. Velocity fluctuations in polar solar wind: a comparison between different solar cycles
Directory of Open Access Journals (Sweden)
B. Bavassano
2009-02-01
Full Text Available The polar solar wind is a fast, tenuous and steady flow that, with the exception of a relatively short phase around the Sun's activity maximum, fills the high-latitude heliosphere. The polar wind properties have been extensively investigated by Ulysses, the first spacecraft able to perform in-situ measurements in the high-latitude heliosphere. The out-of-ecliptic phases of Ulysses cover about seventeen years. This makes possible to study heliospheric properties at high latitudes in different solar cycles. In the present investigation we focus on hourly- to daily-scale fluctuations of the polar wind velocity. Though the polar wind is a quite uniform flow, fluctuations in its velocity do not appear negligible. A simple way to characterize wind velocity variations is that of performing a multi-scale statistical analysis of the wind velocity differences. Our analysis is based on the computation of velocity differences at different time lags and the evaluation of statistical quantities (mean, standard deviation, skewness, and kurtosis for the different ensembles. The results clearly show that, though differences exist in the three-dimensional structure of the heliosphere between the investigated solar cycles, the velocity fluctuations in the core of polar coronal holes exhibit essentially unchanged statistical properties.
8. Magnetic dips in the solar wind
International Nuclear Information System (INIS)
Dobrowolny, M.; Bavassano, B.; Mariani, F.; Ness, N.; Burlaga, L.
1978-09-01
With the help of magnetic data from the HELIOS 1 fluxgate magnetometer, with a 0.2 sec resolution, the structures of several interplanetary discontinuities involving magnetic dips and rotations of the magnetic field vector were investigated. A minimum variance analysis illustrates the behavior of the magnetic field through the transition in the plane of its maximum variation. By means of this analysis, quite different structures have been individuated, in particular, narrow transitions resembling almost one-dimensional reconnected neutral sheets. For the thinner cases (scale lengths of the magnetic rotation of the order or smaller than 1,000 km), results show the observed structures could be the nonlinear effect of a resistive tearing mode instability having developed on an originally one-dimensional neutral sheet at the solar corona
9. Mars, solar wind, and supernova - implications of the Viking data
International Nuclear Information System (INIS)
Shimizu, M.
1977-01-01
A scenario for the evolution of the Martian atmosphere consistent with various data of the Viking 1 and 2 and the Mariner 9 has been presented: Mars was formed from Renazzo-type meteorites polluted by the products of supernova explosion. A dense ancient Martian atmosphere has been swept away by the solar wind and the present tenuous atmosphere was supplied recently by the volcanic gas from the Tharsis region, after the occurrence of the magnetic field. (Auth.)
10. Electron temperature anisotropy constraints in the solar wind
Czech Academy of Sciences Publication Activity Database
Štverák, Štěpán; Trávníček, Pavel M.; Maksimovic, M.; Marsch, E.; Fazakerley, A.; Scime, E. E.
2008-01-01
Roč. 113, A3 /2008/ (2008), A03103/1-A03103/10 ISSN 0148-0227 R&D Projects: GA AV ČR IAA300420602 Grant - others:EU(XE) ESA-PECS project No. 98024 Institutional research plan: CEZ:AV0Z10030501; CEZ:AV0Z30420517 Keywords : solar wind electrons * temperature anisotropy * radial Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 3.147, year: 2008
11. Optimization criteria for solar and wind power systems
Energy Technology Data Exchange (ETDEWEB)
Salieva, R B
1976-01-01
It is shown that the design of solar and wind power systems requires both the specification of the target function and the optimization of the system with respect to two criteria, namely, the system must be economical (minimum cost to the economy) and it must be reliable (the probability of failure-free operation of the system must be not less than a standard value).
12. Statistical Properties of Geomagnetic Activity Indices and Solar Wind Parameters
Directory of Open Access Journals (Sweden)
Jung-Hee Kim
2014-06-01
Full Text Available As the prediction of geomagnetic storms is becoming an important and practical problem, conditions in the Earth’s magnetosphere have been studied rigorously in terms of those in the interplanetary space. Another approach to space weather forecast is to deal with it as a probabilistic geomagnetic storm forecasting problem. In this study, we carry out detailed statistical analysis of solar wind parameters and geomagnetic indices examining the dependence of the distribution on the solar cycle and annual variations. Our main findings are as follows: (1 The distribution of parameters obtained via the superimposed epoch method follows the Gaussian distribution. (2 When solar activity is at its maximum the mean value of the distribution is shifted to the direction indicating the intense environment. Furthermore, the width of the distribution becomes wider at its maximum than at its minimum so that more extreme case can be expected. (3 The distribution of some certain heliospheric parameters is less sensitive to the phase of the solar cycle and annual variations. (4 The distribution of the eastward component of the interplanetary electric field BV and the solar wind driving function BV2, however, appears to be all dependent on the solar maximum/minimum, the descending/ascending phases of the solar cycle and the equinoxes/solstices. (5 The distribution of the AE index and the Dst index shares statistical features closely with BV and BV2 compared with other heliospheric parameters. In this sense, BV and BV2 are more robust proxies of the geomagnetic storm. We conclude by pointing out that our results allow us to step forward in providing the occurrence probability of geomagnetic storms for space weather and physical modeling.
13. High-Speed Wind-Tunnel Investigation of the Lateral Stability Characteristics of a 0.10-Scale Model of the Grumman XF9F-2 Airplane, TED No. NACA DE 301
Science.gov (United States)
Polhamus, Edward C.; King, Thomas J., Jr.
1949-01-01
An investigation was made in the Langley high-speed 7- by 10-foot tunnel to determine the high-speed lateral and directional stability characteristics of a 0.10-scale model of the Grumman XF9F-2 airplane in the Mach number range from 0.40 to 0.85. The results indicate that static lateral and directional stability is present throughout the Mach number range investigated although in the Mach number range from 0.75 to 0.85 there is an appreciable decrease in rolling moment due to sideslip. Calculations of the dynamic stability indicate that according to current flying-quality requirements the damping of the lateral oscillation, although probably satisfactory for the sea-level condition, may not be satisfactory for the majority of the altitude conditions investigated
14. Interaction of the solar wind with comets: a Rosetta perspective.
Science.gov (United States)
Glassmeier, Karl-Heinz
2017-07-13
The Rosetta mission provides an unprecedented possibility to study the interaction of comets with the solar wind. As the spacecraft accompanies comet 67P/Churyumov-Gerasimenko from its very low-activity stage through its perihelion phase, the physics of mass loading is witnessed for various activity levels of the nucleus. While observations at other comets provided snapshots of the interaction region and its various plasma boundaries, Rosetta observations allow a detailed study of the temporal evolution of the innermost cometary magnetosphere. Owing to the short passage time of the solar wind through the interaction region, plasma instabilities such as ring--beam and non-gyrotropic instabilities are of less importance during the early life of the magnetosphere. Large-amplitude ultra-low-frequency (ULF) waves, the 'singing' of the comet, is probably due to a modified ion Weibel instability. This instability drives a cross-field current of implanted cometary ions unstable. The initial pick-up of these ions causes a major deflection of the solar wind protons. Proton deflection, cross-field current and the instability induce a threefold structure of the innermost interaction region with the characteristic Mach cone and Whistler wings as stationary interaction signatures as well as the ULF waves representing the dynamic aspect of the interaction.This article is part of the themed issue 'Cometary science after Rosetta'. © 2017 The Authors.
15. Kinetic instabilities in the solar wind: A short review
Energy Technology Data Exchange (ETDEWEB)
Matteini, Lorenzo, E-mail: [email protected] [Imperial College London, London SW7 2AZ (United Kingdom)
2016-03-25
We know from in situ measurements that solar wind plasma is far from thermal equilibrium. Distribution functions of its main constituents -electrons, protons, and alpha particles-show several departures from Maxwellian, including temperature anisotropy, relative drifts and secondary populations streaming along the local magnetic field. We present a short review of recent solar wind observations of these non-thermal features and associated signatures of wave-particle interactions. Several kinetic instabilities are expected to be at work in the solar wind during its expansion, playing a role in the continuous shaping of particle distributions with distance, and regulating the macroscopic behavior of the plasma. Over the past years, modeling of these processes by means of numerical simulations has been successful in reproducing and explaining the observations; these include the evolution of the plasma due to radial expansion and the response of individual species to different kinetic instabilities. Finally, the impact of local inhomogeneities, like current sheets and turbulence, on the development of kinetic instabilities is also discussed.
16. Dynamics of Intense Currents in the Solar Wind
Science.gov (United States)
Artemyev, Anton V.; Angelopoulos, Vassilis; Halekas, Jasper S.; Vinogradov, Alexander A.; Vasko, Ivan Y.; Zelenyi, Lev M.
2018-06-01
Transient currents in the solar wind are carried by various magnetic field discontinuities that contribute significantly to the magnetic field fluctuation spectrum. Internal instabilities and dynamics of these discontinuities are believed to be responsible for magnetic field energy dissipation and corresponding charged particle acceleration and heating. Accurate modeling of these phenomena requires detailed investigation of transient current formation and evolution. By examining such evolution using a unique data set compiled from observations of the same solar wind flow by two spacecraft at Earth’s and Mars’s orbits, we show that it consists of several processes: discontinuity thinning (decrease in thickness normalized by the ion inertial length), intensification of currents normalized to the proton thermal current (i.e., the product of proton charge, density, and thermal velocity), and increase in the compressional component of magnetic field variations across discontinuities. The significant proton temperature variation around most observed discontinuities indicates possible proton heating. Plasma velocity jumps across the discontinuities are well correlated with Alfvén velocity changes. We discuss possible explanations of the observed discontinuity evolution. We also compare the observed evolution with predictions of models describing discontinuity formation due to Alfvén wave steepening. Our results show that discontinuity modeling likely requires taking into account both the effects of nonlinear Alfvén wave dynamics and solar wind expansion.
17. On WKB expansions for Alfven waves in the solar wind
International Nuclear Information System (INIS)
Hollweg, J.V.
1990-01-01
The author reexamines the WKB expansion for toroidal Alfven waves in the solar wind, as described by equations (9) of Heinemann and Olbert (1980). His principal conclusions are as follows: (1) The WKB expansion used by Belcher (1971) and Hollweg (1973) is nonuniformly convergent. (2) Using the method of multiple scales (Nayfeh, 1981), he obtains an expansion which is uniform. (3) The uniform expansion takes into account the small modification to the Alfven wave phase speed due to spatial gradients of the background. (4) Both the uniform and nonuniform expansions reveal that each normal mode has both Elsaesser variables δz + ≠ 0 and δz - ≠ 0. Thus if δz - corresponds to the outgoing mode in a homogeneous background, an observation of δz + ≠ 0 does not necessarily imply the presence of the inward propagating mode, as is commonly assumed. (5) Even at the Alfven critical point (where V = υ A ) he finds that δz + ≠ 0. Thus incompressible MHD turbulence, which requires both δz + ≠ 0 and δz - ≠ 0, can proceed at the Alfven critical point (cf. Roberts, 1989). (6) With very few exceptions, the predictions of these calculations do not agree with recent observations (Marsch and Tu, 1990) of the power spectra of δz + and δz - in the solar wind. Thus the evolution of Alfven waves in the solar wind is governed by dynamics not included in the Heinemann and Olbert equations
18. Construction of Solar-Wind-Like Magnetic Fields
Science.gov (United States)
Roberts, Dana Aaron
2012-01-01
Fluctuations in the solar wind fields tend to not only have velocities and magnetic fields correlated in the sense consistent with Alfven waves traveling from the Sun, but they also have the magnitude of the magnetic field remarkably constant despite their being broadband. This paper provides, for the first time, a method for constructing fields with nearly constant magnetic field, zero divergence, and with any specified power spectrum for the fluctuations of the components of the field. Every wave vector, k, is associated with two polarizations the relative phases of these can be chosen to minimize the variance of the field magnitude while retaining the\\random character of the fields. The method is applied to a case with one spatial coordinate that demonstrates good agreement with observed time series and power spectra of the magnetic field in the solar wind, as well as with the distribution of the angles of rapid changes (discontinuities), thus showing a deep connection between two seemingly unrelated issues. It is suggested that using this construction will lead to more realistic simulations of solar wind turbulence and of the propagation of energetic particles.
19. Analysis of the solar/wind resources in Southern Spain for optimal sizing of hybrid solar-wind power generation systems
Science.gov (United States)
Quesada-Ruiz, S.; Pozo-Vazquez, D.; Santos-Alamillos, F. J.; Lara-Fanego, V.; Ruiz-Arias, J. A.; Tovar-Pescador, J.
2010-09-01
A drawback common to the solar and wind energy systems is their unpredictable nature and dependence on weather and climate on a wide range of time scales. In addition, the variation of the energy output may not match with the time distribution of the load demand. This can partially be solved by the use of batteries for energy storage in stand-alone systems. The problem caused by the variable nature of the solar and wind resources can be partially overcome by the use of energy systems that uses both renewable resources in a combined manner, that is, hybrid wind-solar systems. Since both resources can show complementary characteristics in certain location, the independent use of solar or wind systems results in considerable over sizing of the batteries system compared to the use of hybrid solar-wind systems. Nevertheless, to the day, there is no single recognized method for properly sizing these hybrid wind-solar systems. In this work, we present a method for sizing wind-solar hybrid systems in southern Spain. The method is based on the analysis of the wind and solar resources on daily scale, particularly, its temporal complementary characteristics. The method aims to minimize the size of the energy storage systems, trying to provide the most reliable supply.
20. The northern edge of the band of solar wind variability: Ulysses at ∼4.5AU
International Nuclear Information System (INIS)
Gosling, J.T.; Bame, S.J.; Feldman, W.C.; McComas, D.J.; Riley, P.; Goldstein, B.E.; Neugebauer, M.
1997-01-01
Ulysses observations reveal that the northern edge of the low-latitude band of solar wind variability at ∼4.5AU was located at N30 degree in the latter part of 1996 when solar activity was at a minimum. This edge latitude is intermediate between edge latitudes found during previous encounters with the band edge along different portions of Ulysses close-quote polar orbit about the Sun. Corotating interaction regions, CIRs, near the northern edge of the band were tilted in such a manner that the forward and reverse shocks bounding the CIRs were propagating equatorward and poleward, respectively, providing definite confirmation that CIRs have opposed tilts in the opposite solar hemispheres. No shocks or coronal mass ejections, CMEs, were detected during the ∼1.5y traverse of the northern, high-latitude northern hemisphere; however, at the northern edge of the band of variability an expanding CME was observed that was driving a shock into the high-speed wind.copyright 1997 American Geophysical Union
1. Solar wind modulation of the Martian ionosphere observed by Mars Global Surveyor
Directory of Open Access Journals (Sweden)
J.-S. Wang
2004-06-01
Full Text Available Electron density profiles in the Martian ionosphere observed by the radio occultation experiment on board Mars Global Surveyor have been analyzed to determine if the densities are influenced by the solar wind. Evidence is presented that the altitude of the maximum ionospheric electron density shows a positive correlation to the energetic proton flux in the solar wind. The solar wind modulation of the Martian ionosphere can be attributed to heating of the neutral atmosphere by the solar wind energetic proton precipitation. The modulation is observed to be most prominent at high solar zenith angles. It is argued that this is consistent with the proposed modulation mechanism.
2. Analysis of off-grid hybrid wind turbine/solar PV water pumping systems
Science.gov (United States)
While many remote water pumping systems exist (e.g. mechanical windmills, solar photovoltaic , wind-electric, diesel powered), very few combine both the wind and solar energy resources to possibly improve the reliability and the performance of the system. In this paper, off-grid wind turbine (WT) a...
3. SOLAR WIND STRAHL BROADENING BY SELF-GENERATED PLASMA WAVES
Energy Technology Data Exchange (ETDEWEB)
Pavan, J.; Gaelzer, R. [UFPEL, Pelotas (Brazil); Vinas, A. F. [NASA GSFC, Greenbelt, MD 20771 (United States); Yoon, P. H. [IPST, UMD, College Park, MD (United States); Ziebell, L. F., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [UFRGS, Porto Alegre (Brazil)
2013-06-01
This Letter reports on the results of numerical simulations which may provide a possible explanation for the strahl broadening during quiet solar conditions. The relevant processes involved in the broadening are due to kinetic quasi-linear wave-particle interaction. Making use of static analytical electron distribution in an inhomogeneous field, it is found that self-generated electrostatic waves at the plasma frequency, i.e., Langmuir waves, are capable of scattering the strahl component, resulting in energy and pitch-angle diffusion that broadens its velocity distribution significantly. The present theoretical results provide an alternative or complementary explanation to the usual whistler diffusion scenario, suggesting that self-induced electrostatic waves at the plasma frequency might play a key role in broadening the solar wind strahl during quiet solar conditions.
4. Cometary X-rays : solar wind charge exchange in cometary atmospheres
NARCIS (Netherlands)
Bodewits, Dennis
2007-01-01
The interaction of the solar wind with the planets and the interstellar medium is of key importance for the evolution of our solar system. The interaction with Earth's atmosphere is best known for the northern light. In case of Mars, the interaction with the solar wind might have lead to the erosion
5. Solar cycle variation of cosmic ray intensity along with interplanetary and solar wind plasma parameters
International Nuclear Information System (INIS)
Mishra, R.K.; Tiwari, S.; Agarwal, R.
2008-01-01
Galactic cosmic rays are modulated at their propagation in the heliosphere by the effect of the large-scale structure of the interplanetary medium. A comparison of the variations in the cosmic ray intensity data obtained by neutron monitoring stations with those in geomagnetic disturbance, solar wind velocity (V), interplanetary magnetic field (B), and their product (V , B) near the Earth for the period 1964-2004 has been presented so as to establish a possible correlation between them. We used the hourly averaged cosmic ray counts observed with the neutron monitor in Moscow. It is noteworthy that a significant negative correlation has been observed between the interplanetary magnetic field, product (V , B) and cosmic ray intensity during the solar cycles 21 and 22. The solar wind velocity has a good positive correlation with cosmic ray intensity during solar cycle 21, whereas it shows a weak correlation during cycles 20, 22 and 23. The interplanetary magnetic field shows a weak negative correlation with cosmic rays for solar cycle 20, and a good anti-correlation for solar cycles 21-23 with the cosmic ray intensity, which, in turn, shows a good positive correlation with disturbance time index (Dst) during solar cycles 21 and 22, and a weak correlation for cycles 20 and 23. (Authors)
6. Three-dimensional structure of the coronal magnetic field and the solar wind speed distribution projected on the photosphere in 1974
International Nuclear Information System (INIS)
1987-01-01
Since the solar wind and coronal holes were relatively steady in 1974, the average distribution of the solar wind speed on the source surface and that of the line-of-sight component of the photospheric magnetic fields (B 1 ) can be constructed, with fair accuracy, by the superposed epoch analysis. The three-dimensional structure of the coronal magnetic fields is then computed from this average map of B 1 based on the potential model. The average distribution of the solar wind speed on the source surface, obtained from interplanetary scintillation observations, is then projected onto the photosphere along the open field lines in the corona. The high-speed regions thus projected are compared with the He I (1083 nm) coronal holes and are found to have a similar geometry. The results are also suggestive that the solar wind does not blow out uniformly from the vicinity of a coronal hole and that the speed is higher at the east side in that region than at the west side. The slower speed regions on the source surface have a sinusoidal structure in heliographic latitude-longitude coordinates and are similar to the brightness distribution of the K corona and the structure of closed field line regions projected onto the photosphere. copyrightAmerican Geophysical Union 1987
7. High Speed On-Wafer Characterization Laboratory
Data.gov (United States)
Federal Laboratory Consortium — At the High Speed On-Wafer Characterization Laboratory, researchers characterize and model devices operating at terahertz (THz) and millimeter-wave frequencies. The...
8. Estimation of wind and solar resources in Mali
Energy Technology Data Exchange (ETDEWEB)
Badger, J.; Kamissoko, F.; Olander Rasmussen, M.; Larsen, Soeren; Guidon, N.; Boye Hansen, L.; Dewilde, L.; Alhousseini, M.; Noergaard, P.; Nygaard, I.
2012-11-15
The wind resource has been estimated for all of Mali at 7.5 km resolution using the KAMM/WAsP numerical wind atlas methodology. Three domains were used to cover entire country and three sets of wind classes used to capture change in large scale forcing over country. The final output includes generalized climate statistics for any location in Mali, giving wind direction and wind speed distribution. The modelled generalized climate statistics can be used directly in the WAsP software. The preliminary results show a wind resource, which is relatively low, but which under certain conditions may be economically feasible, i.e. at favourably exposed sites, giving enhanced winds, and where practical utilization is possible, given consideration to grid connection or replacement or augmentation of diesel-based electricity systems. The solar energy resource for Mali was assessed for the period between July 2008 and June 2011 using a remote sensing based estimate of the down-welling surface shortwave flux. The remote sensing estimates were adjusted on a month-by-month basis to account for seasonal differences between the remote sensing estimates and in situ data. Calibration was found to improve the coefficient of determination as well as decreasing the mean error both for the calibration and validation data. Compared to the results presented in the ''Renewable energy resources in Mali - preliminary mapping''-report that showed a tendency for underestimation compared to data from the NASA PPOWER/SSE database, the presented results show a very good agreement with the in situ data (after calibration) with no significant bias. Unfortunately, the NASA-database only contains data up until 2005, so a similar comparison could not be done for the time period analyzed in this study, although the agreement with the historic NASA data is still useful as reference. (LN)
9. The influence of solar wind variability on magnetospheric ULF wave power
International Nuclear Information System (INIS)
Pokhotelov, D.; Rae, I.J.; Mann, I.R.
2015-01-01
Magnetospheric ultra-low frequency (ULF) oscillations in the Pc 4-5 frequency range play an important role in the dynamics of Earth's radiation belts, both by enhancing the radial diffusion through incoherent interactions and through the coherent drift-resonant interactions with trapped radiation belt electrons. The statistical distributions of magnetospheric ULF wave power are known to be strongly dependent on solar wind parameters such as solar wind speed and interplanetary magnetic field (IMF) orientation. Statistical characterisation of ULF wave power in the magnetosphere traditionally relies on average solar wind-IMF conditions over a specific time period. In this brief report, we perform an alternative characterisation of the solar wind influence on magnetospheric ULF wave activity through the characterisation of the solar wind driver by its variability using the standard deviation of solar wind parameters rather than a simple time average. We present a statistical study of nearly one solar cycle (1996-2004) of geosynchronous observations of magnetic ULF wave power and find that there is significant variation in ULF wave powers as a function of the dynamic properties of the solar wind. In particular, we find that the variability in IMF vector, rather than variabilities in other parameters (solar wind density, bulk velocity and ion temperature), plays the strongest role in controlling geosynchronous ULF power. We conclude that, although time-averaged bulk properties of the solar wind are a key factor in driving ULF powers in the magnetosphere, the solar wind variability can be an important contributor as well. This highlights the potential importance of including solar wind variability especially in studies of ULF wave dynamics in order to assess the efficiency of solar wind-magnetosphere coupling.
10. Relationship between velocity gradients and magnetic turbulence in the solar wind
International Nuclear Information System (INIS)
Garrett, H.B.
1974-01-01
The correlations among the time derivative of the solar-wind velocity, the magnitude of the interplanetary magnetic field (IMF), and the IMF turbulence level are examined to test the idea that interaction between two colliding solar-wind streams can generate turbulence in the solar wind and the IMF. Data obtained by Explorer 33 on the solar wind and IMF are described, and the analysis techniques are outlined. The results indicate that the IMF turbulence level, as measured by the variance, is correlated with the existence of positive velocity gradients in the solar wind. It is noted that while the variance is an increasing function of the field magnitude, it is also independently correlated with the solar-wind velocity gradient
11. Solar wind proton temperature anisotropy: Linear theory and WIND/SWE observations
Czech Academy of Sciences Publication Activity Database
Hellinger, Petr; Trávníček, Pavel; Kasper, J. C.; Lazarus, A. J.
2006-01-01
Roč. 33, č. 9 (2006), L09101/1-L09101/4 ISSN 0094-8276 R&D Projects: GA AV ČR(CZ) IAA3042403 Grant - others:ESA(XE) PECS 98024; NASA (US) NAG-10915 Institutional research plan: CEZ:AV0Z30420517 Keywords : proton temperature anisotropy * solar wind * in situ observations Subject RIV: DG - Athmosphere Sciences, Meteorology Impact factor: 2.602, year: 2006
12. Dynamics of large-scale solar wind streams obtained by the double superposed epoch analysis
Science.gov (United States)
Yermolaev, Yu. I.; Lodkina, I. G.; Nikolaeva, N. S.; Yermolaev, M. Yu.
2015-09-01
Using the OMNI data for period 1976-2000, we investigate the temporal profiles of 20 plasma and field parameters in the disturbed large-scale types of solar wind (SW): corotating interaction regions (CIR), interplanetary coronal mass ejections (ICME) (both magnetic cloud (MC) and Ejecta), and Sheath as well as the interplanetary shock (IS). To take into account the different durations of SW types, we use the double superposed epoch analysis (DSEA) method: rescaling the duration of the interval for all types in such a manner that, respectively, beginning and end for all intervals of selected type coincide. As the analyzed SW types can interact with each other and change parameters as a result of such interaction, we investigate separately eights sequences of SW types: (1) CIR, (2) IS/CIR, (3) Ejecta, (4) Sheath/Ejecta, (5) IS/Sheath/Ejecta, (6) MC, (7) Sheath/MC, and (8) IS/Sheath/MC. The main conclusion is that the behavior of parameters in Sheath and in CIR are very similar both qualitatively and quantitatively. Both the high-speed stream (HSS) and the fast ICME play a role of pistons which push the plasma located ahead them. The increase of speed in HSS and ICME leads at first to formation of compression regions (CIR and Sheath, respectively) and then to IS. The occurrence of compression regions and IS increases the probability of growth of magnetospheric activity.
13. The spiral field inhibition of thermal conduction in two-fluid solar wind models
Science.gov (United States)
Nerney, S.; Barnes, A.
1978-01-01
The paper reports on two-field models which include the inhibition of thermal conduction by the spiraling interplanetary field to determine whether any of the major conclusions obtained by Nerney and Barnes (1977) needs to be modified. Comparisons with straight field line models reveal that for most base conditions, the primary effect of the inhibition of thermal conduction is the bottling-up of heat in the electrons as well as the quite different temperature profiles at a large heliocentric radius. The spiral field solutions show that coronal hole boundary conditions do not correspond to states of high-speed streams as observed at 1 AU. The two-fluid models suggest that the spiral field inhibition of thermal conduction in the equatorial plane will generate higher gas pressures in comparison with flows along the solar rotation axis (between 1 and 10 AU). In particular, massive outflows of stellar winds, such as outflow from T Tauri stars, cannot be driven by thermal conduction. The conclusions of Nerney and Barnes remain essentially unchanged.
14. Anisotropic Behaviour of Magnetic Power Spectra in Solar Wind Turbulence.
Science.gov (United States)
Banerjee, S.; Saur, J.; Gerick, F.; von Papen, M.
2017-12-01
Introduction:High altitude fast solar wind turbulence (SWT) shows different spectral properties as a function of the angle between the flow direction and the scale dependent mean magnetic field (Horbury et al., PRL, 2008). The average magnetic power contained in the near perpendicular direction (80º-90º) was found to be approximately 5 times larger than the average power in the parallel direction (0º- 10º). In addition, the parallel power spectra was found to give a steeper (-2) power law than the perpendicular power spectral density (PSD) which followed a near Kolmogorov slope (-5/3). Similar anisotropic behaviour has also been observed (Chen et al., MNRAS, 2011) for slow solar wind (SSW), but using a different method exploiting multi-spacecraft data of Cluster. Purpose:In the current study, using Ulysses data, we investigate (i) the anisotropic behaviour of near ecliptic slow solar wind using the same methodology (described below) as that of Horbury et al. (2008) and (ii) the dependence of the anisotropic behaviour of SWT as a function of the heliospheric latitude.Method:We apply the wavelet method to calculate the turbulent power spectra of the magnetic field fluctuations parallel and perpendicular to the local mean magnetic field (LMF). According to Horbury et al., LMF for a given scale (or size) is obtained using an envelope of the envelope of that size. Results:(i) SSW intervals always show near -5/3 perpendicular spectra. Unlike the fast solar wind (FSW) intervals, for SSW, we often find intervals where power parallel to the mean field is not observed. For a few intervals with sufficient power in parallel direction, slow wind turbulence also exhibit -2 parallel spectra similar to FSW.(ii) The behaviours of parallel and perpendicular power spectra are found to be independent of the heliospheric latitude. Conclusion:In the current study we do not find significant influence of the heliospheric latitude on the spectral slopes of parallel and perpendicular
15. Wind Tunnel Tests of Parabolic Trough Solar Collectors: March 2001--August 2003
Energy Technology Data Exchange (ETDEWEB)
Hosoya, N.; Peterka, J. A.; Gee, R. C.; Kearney, D.
2008-05-01
Conducted extensive wind-tunnel tests on parabolic trough solar collectors to determine practical wind loads applicable to structural design for stress and deformation, and local component design for concentrator reflectors.
16. Voyager microwave scintillation measurements of solar wind plasma parameters
International Nuclear Information System (INIS)
Martin, J.M.
1985-01-01
During the solar conjunctions of Voyager 1 and 2 spacecraft in August 1979, September 1980, and November 1982, temporal variations of intensity and frequency of the dual-wavelength (3.6 and 13 cm) radio transmissions from the spacecraft were observed and subsequently analyzed to infer characteristics of the solar wind plasma flow. Measurements of the temporal wave structure function were used to estimate the spectral index of the power law spatial spectrum of irregularities. Theoretical-intensity scintillation spectra were compared with measured intensity spectra to obtain least-squares estimates of (1) mean velocity, (2) random velocity, (3) axial ratio, and (4) electron density standard deviation. Uncertainties in parameter estimates were calculated by standard propagation of errors techniques. Mean velocity and electron density standard deviations in 1979-1980 show little dependence on solar latitude. Density standard deviation estimates were 3-10% of the background mean density and mean velocity estimates ranged from approx.200 km/s inside 17 solar radii to approx.300 km/s at 25 solar radii. 1982 density standard deviation estimates increased rapidly with latitude near 45 0 N, then sharply decreased north of that latitude, indicating the existence of a polar region of reduced fluctuations surrounded by a thin cone of strong density irregularities
17. Intercalibration and Cross-Correlation of Ace and Wind Solar Wind Data
Science.gov (United States)
2003-01-01
This report covers activities funded from October 1, 1998 through September 30, 2002. Two yearly status reports have been filed on this grant, and they are included as Appendix 1. The purpose of this grant was to compare ACE and Wind solar wind parameters when the two spacecraft were near to one another and then to use the intercalibrated parameters to carry out scientific investigations. In September, 2001 a request for a one-year, no-cost extension until September 30, 2002 was submitted and approved. The statement of work for that extension included adjustment of ACE densities below wind speeds of 350 km/s, a study of shock normal orientations using travel time delays between the two spacecraft, comparison of density jumps at shocks, and a study of temperature anisotropies and double streaming to see if such features evolved between the spacecraft.
18. A study on evaluating the power generation of solar-wind hybrid systems in Izmir, Turkey
Energy Technology Data Exchange (ETDEWEB)
Ulgen, K. [Ege Univ., Solar Energy Inst., Izmir (Turkey); Hepbasli, A. [Ege Univ., Dept. of Mechanical Engineering, Izmir (Turkey)
2003-03-15
Turkey is abundant in terms of renewable energy resources. Residential and industrial utilization of solar energy started in the 1980s, while the first Build-Operate-Transfer (BOT) windmill park, located at Alacati, Izmir, was commissioned in 1998. Additionally, power generation through solar-wind hybrid systems has recently appeared on the Turkish market. This study investigates the wind and solar thermal power availability in Izmir, located in the western part of Turkey. Simple models were developed to determine wind, solar, and hybrid power resources per unit area. Experimental data, consisting of hourly records over a 5 yr period, 1995-1999, were measured in the Solar/Wind Meteorological Station of the Solar Energy Institute at Ege University. Correlations between solar and wind power data were carried out on an hourly, a daily, and a monthly basis. It can be concluded that possible applications of hybrid systems could be considered for the efficient utilization of these resources. (Author)
19. HEMISPHERIC ASYMMETRIES IN THE POLAR SOLAR WIND OBSERVED BY ULYSSES NEAR THE MINIMA OF SOLAR CYCLES 22 AND 23
Energy Technology Data Exchange (ETDEWEB)
Ebert, R. W.; Dayeh, M. A.; Desai, M. I.; McComas, D. J. [Southwest Research Institute, P.O. Drawer 28510, San Antonio, TX 78228 (United States); Pogorelov, N. V. [Physics Department, University of Alabama in Huntsville, Huntsville, AL 35899 (United States)
2013-05-10
We examined solar wind plasma and interplanetary magnetic field (IMF) observations from Ulysses' first and third orbits to study hemispheric differences in the properties of the solar wind and IMF originating from the Sun's large polar coronal holes (PCHs) during the declining and minimum phase of solar cycles 22 and 23. We identified hemispheric asymmetries in several parameters, most notably {approx}15%-30% south-to-north differences in averages for the solar wind density, mass flux, dynamic pressure, and energy flux and the radial and total IMF magnitudes. These differences were driven by relatively larger, more variable solar wind density and radial IMF between {approx}36 Degree-Sign S-60 Degree-Sign S during the declining phase of solar cycles 22 and 23. These observations indicate either a hemispheric asymmetry in the PCH output during the declining and minimum phase of solar cycles 22 and 23 with the southern hemisphere being more active than its northern counterpart, or a solar cycle effect where the PCH output in both hemispheres is enhanced during periods of higher solar activity. We also report a strong linear correlation between these solar wind and IMF parameters, including the periods of enhanced PCH output, that highlight the connection between the solar wind mass and energy output and the Sun's magnetic field. That these enhancements were not matched by similar sized variations in solar wind speed points to the mass and energy responsible for these increases being added to the solar wind while its flow was subsonic.
20. Ensemble downscaling in coupled solar wind-magnetosphere modeling for space weather forecasting.
Science.gov (United States)
Owens, M J; Horbury, T S; Wicks, R T; McGregor, S L; Savani, N P; Xiong, M
2014-06-01
Advanced forecasting of space weather requires simulation of the whole Sun-to-Earth system, which necessitates driving magnetospheric models with the outputs from solar wind models. This presents a fundamental difficulty, as the magnetosphere is sensitive to both large-scale solar wind structures, which can be captured by solar wind models, and small-scale solar wind "noise," which is far below typical solar wind model resolution and results primarily from stochastic processes. Following similar approaches in terrestrial climate modeling, we propose statistical "downscaling" of solar wind model results prior to their use as input to a magnetospheric model. As magnetospheric response can be highly nonlinear, this is preferable to downscaling the results of magnetospheric modeling. To demonstrate the benefit of this approach, we first approximate solar wind model output by smoothing solar wind observations with an 8 h filter, then add small-scale structure back in through the addition of random noise with the observed spectral characteristics. Here we use a very simple parameterization of noise based upon the observed probability distribution functions of solar wind parameters, but more sophisticated methods will be developed in the future. An ensemble of results from the simple downscaling scheme are tested using a model-independent method and shown to add value to the magnetospheric forecast, both improving the best estimate and quantifying the uncertainty. We suggest a number of features desirable in an operational solar wind downscaling scheme. Solar wind models must be downscaled in order to drive magnetospheric models Ensemble downscaling is more effective than deterministic downscaling The magnetosphere responds nonlinearly to small-scale solar wind fluctuations.
1. Investigating the Correlation Between Wind and Solar Power Forecast Errors in the Western Interconnection: Preprint
Energy Technology Data Exchange (ETDEWEB)
Zhang, J.; Hodge, B. M.; Florita, A.
2013-05-01
Wind and solar power generations differ from conventional energy generation because of the variable and uncertain nature of their power output. This variability and uncertainty can have significant impacts on grid operations. Thus, short-term forecasting of wind and solar generation is uniquely helpful for power system operations to balance supply and demand in an electricity system. This paper investigates the correlation between wind and solar power forecasting errors.
2. Application of Power Systems Economics to Wind and Solar Power Integration
OpenAIRE
Mills, Andrew David
2015-01-01
The focus of this dissertation is the economic implications of the technical challenges of integrating variable generation, namely wind and solar, into the electric power system. The research is organized around three topics: short-term variability of wind and solar generation, changes in the economic value of wind and solar with increasing penetration, and the effectiveness of different measures at mitigating changes in economic value with increasing penetration levels. Early studies of PV g...
3. The Solar Wind from Pseudostreamers and their Environs: Opportunities for Observations with Parker Solar Probe and Solar Orbiter
Science.gov (United States)
Panasenco, O.; Velli, M.; Panasenco, A.; Lionello, R.
2017-12-01
The solar dynamo and photospheric convection lead to three main types of structures extending from the solar surface into the corona - active regions, solar filaments (prominences when observed at the limb) and coronal holes. These structures exist over a wide range of scales, and are interlinked with each other in evolution and dynamics. Active regions can form clusters of magnetic activity and the strongest overlie sunspots. In the decay of active regions, the boundaries separating opposite magnetic polarities (neutral lines) develop specific structures called filament channels above which filaments form. In the presence of flux imbalance decaying active regions can also give birth to lower latitude coronal holes. The accumulation of magnetic flux at coronal hole boundaries also creates conditions for filament formation: polar crown filaments are permanently present at the boundaries of the polar coronal holes. Mid-latitude and equatorial coronal holes - the result of active region evolution - can create pseudostreamers if other coronal holes of the same polarity are present. While helmet streamers form between open fields of opposite polarities, the pseudostreamer, characterized by a smaller coronal imprint, typically shows a more prominent straight ray or stalk extending from the corona. The pseudostreamer base at photospheric heights is multipolar; often one observes tripolar magnetic configurations with two neutral lines - where filaments can form - separating the coronal holes. Here we discuss the specific role of filament channels on pseudostreamer topology and on solar wind properties. 1D numerical analysis of pseudostreamers shows that the properties of the solar wind from around PSs depend on the presence/absence of filament channels, number of channels and chirality at thepseudostreamer base low in the corona. We review and model possible coronal magnetic configurations and solar wind plasma properties at different distances from the solar surface that
4. Solar and wind energy utilization at Sarawak Southern national parks
International Nuclear Information System (INIS)
Abdul Rahman, N.; Kolot, A.
2006-01-01
The intentions of renewable energy utilization in Sarawak national parks were to reduce the environmental impacts to the protected surrounding and to overcome fuel transportation problem, as most national parks in Sarawak are not viable for the state electricity grid connection. The study was conducted at three national parks in southern Sarawak; viz. Samusan, Tanjung Datu and Pulau Talang-Talang Besar National Park. The study focused on the effectiveness of the system implementation, energy load and associated problems. Both Samusan and Tanjung Datu National systems are hybrids, which consist of solar photovoltaic panels, wind turbine and diesel generators, whereas, Pulau Talang-Talang Besar National Park is a stand alone system of solar photovoltaic panels only. In addition, the inefficient energy usage was observed at Samusan National Park. The study have identified that lack of local expertise, spare parts availability, transportation and inefficient energy management as the major problems associated to the solar and wind energy system in all national parks studied. Albeit the problems mentioned, the study discovered that the systems were acceptably reliable and satisfactorily supply fraction of the energy requirements to the national parks communities
5. Coronal mass ejections and disturbances in solar wind plasma parameters in relation with geomagnetic storms
International Nuclear Information System (INIS)
Verma, P L; Singh, Puspraj; Singh, Preetam
2014-01-01
Coronal Mass Ejections (CMEs) are the drastic solar events in which huge amount of solar plasma materials are ejected into the heliosphere from the sun and are mainly responsible to generate large disturbances in solar wind plasma parameters and geomagnetic storms in geomagnetic field. We have studied geomagnetic storms, (Dst ≤-75 nT) observed during the period of 1997-2007 with Coronal Mass Ejections and disturbances in solar wind plasma parameters (solar wind temperature, velocity, density and interplanetary magnetic field) .We have inferred that most of the geomagnetic storms are associated with halo and partial halo Coronal Mass Ejections (CMEs).The association rate of halo and partial halo coronal mass ejections are found 72.37 % and 27.63 % respectively. Further we have concluded that geomagnetic storms are closely associated with the disturbances in solar wind plasma parameters. We have determined positive co-relation between magnitudes of geomagnetic storms and magnitude of jump in solar wind plasma temperature, jump in solar wind plasma density, jump in solar wind plasma velocity and jump in average interplanetary magnetic field with co-relation co-efficient 0 .35 between magnitude of geomagnetic storms and magnitude of jump in solar wind plasma temperature, 0.19 between magnitude of geomagnetic storms and magnitude of jump in solar wind density, 0.34 between magnitude of geomagnetic storms and magnitude of jump in solar wind plasma velocity, 0.66 between magnitude of geomagnetic storms and magnitude of jump in average interplanetary magnetic field respectively. We have concluded that geomagnetic storms are mainly caused by Coronal Mass Ejections and disturbances in solar wind plasma parameters that they generate.
6. Solar wind fluctuations at large scale - A comparison between low and high solar activity conditions
Science.gov (United States)
Bavassano, B.; Bruno, R.
1991-02-01
The influence of the sun's activity cycle on the solar wind fluctuations at time scales from 1 hour to 3 days in the inner heliosphere (0.3 to 1 AU) is investigated. Hourly averages of plasma and magnetic field data by Helios spacecraft are used. Since fluctuations behave quite differently with changing scale, the analysis is performed separately for two different ranges in time scale. Between 1 and 6 hours Alfvenic fluctuations and pressure-balanced structures are extensively observed. At low solar activity and close to 0.3 AU Alfvenic fluctuations are more frequent than pressure-balanced structures. This predominance, however, weakens for rising solar activity and radial distance, to the point that a role-exchange, in terms of occurrence rate, is found at the maximum of the cycle close to 1 AU. On the other hand, in all cases Alfvenic fluctuations have a larger amplitude than pressure-balanced structures. The Alfvenic contribution to the solar wind energy spectrum comes out to be dominant at all solar activity conditions. These findings support the conclusion that the solar cycle evolution of the large-scale velocity pattern is the factor governing the observed variations.
7. Reducing Heating In High-Speed Cinematography
Science.gov (United States)
Slater, Howard A.
1989-01-01
Infrared-absorbing and infrared-reflecting glass filters simple and effective means for reducing rise in temperature during high-speed motion-picture photography. "Hot-mirror" and "cold-mirror" configurations, employed in projection of images, helps prevent excessive heating of scenes by powerful lamps used in high-speed photography.
8. The AMPTE program's contribution to studies of the solar wind-magnetosphere-ionosphere interaction
International Nuclear Information System (INIS)
Sibeck, D.G.
1990-01-01
The Active Magnetospheric Particle Tracer Explorers (AMPTE) program provided important information on the behavior of clouds of plasma artificially injected into the solar wind and the earth's magnetosphere. Now that the releases are over, data from the satellites are being analyzed to investigate the processes by which the ambient solar wind mass, momentum, and energy are transferred to the magnetosphere. Work in progress at APL indicates that the solar wind is much more inhomogeneous than previously believed, that the solar wind constantly buffets the magnetosphere, and that ground observers may remotely sense these interactions as geomagnetic pulsations. 8 refs
9. Global solar magetic field organization in the extended corona: influence on the solar wind speed and density over the cycle.
Science.gov (United States)
Réville, V.; Velli, M.; Brun, S.
2017-12-01
The dynamics of the solar wind depends intrinsically on the structure of the global solar magnetic field, which undergoes fundamental changes over the 11yr solar cycle. For instance, the wind terminal velocity is thought to be anti-correlated with the expansion factor, a measure of how the magnetic field varies with height in the solar corona, usually computed at a fixed height (≈ 2.5 Rȯ, the source surface radius which approximates the distance at which all magnetic field lines become open). However, the magnetic field expansion affects the solar wind in a more detailed way, its influence on the solar wind properties remaining significant well beyond the source surface: we demonstrate this using 3D global MHD simulations of the solar corona, constrained by surface magnetograms over half a solar cycle (1989-2001). For models to comply with the constraints provided by observed characteristics of the solar wind, namely, that the radial magnetic field intensity becomes latitude independent at some distance from the Sun (Ulysses observations beyond 1 AU), and that the terminal wind speed is anti-correlated with the mass flux, they must accurately describe expansion beyond the solar wind critical point (even up to 10Rȯ and higher in our model). We also show that near activity minimum, expansion in the higher corona beyond 2.5 Rȯ is actually the dominant process affecting the wind speed. We discuss the consequences of this result on the necessary acceleration profile of the solar wind, the location of the sonic point and of the energy deposition by Alfvén waves.
10. 78 FR 77447 - California Wind Energy Association, First Solar, Inc. v. California Independent System Operator...
Science.gov (United States)
2013-12-23
... Energy Association, First Solar, Inc. v. California Independent System Operator Corporation, Southern...), California Wind Energy Association and First Solar, Inc. (collectively, Complainants) filed a formal complaint against the California Independent System Operator Corporation (CAISO) and Southern California...
11. Line Ratios for Solar Wind Charge Exchange with Comets
Energy Technology Data Exchange (ETDEWEB)
Mullen, P. D.; Cumbee, R. S.; Lyons, D.; Shelton, R. L.; Stancil, P. C. [Department of Physics and Astronomy and the Center for Simulational Physics, University of Georgia, Athens, GA 30602 (United States); Gu, L.; Kaastra, J., E-mail: [email protected] [SRON Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA Utrecht (Netherlands)
2017-07-20
Charge exchange (CX) has emerged in X-ray emission modeling as a significant process that must be considered in many astrophysical environments—particularly comets. Comets host an interaction between solar wind ions and cometary neutrals to promote solar wind charge exchange (SWCX). X-ray observatories provide astronomers and astrophysicists with data for many X-ray emitting comets that are impossible to accurately model without reliable CX data. Here, we utilize a streamlined set of computer programs that incorporate the multi-channel Landau–Zener theory and a cascade model for X-ray emission to generate cross sections and X-ray line ratios for a variety of bare and non-bare ion single electron capture (SEC) collisions. Namely, we consider collisions between the solar wind constituent bare and H-like ions of C, N, O, Ne, Na, Mg, Al, and Si and the cometary neutrals H{sub 2}O, CO, CO{sub 2}, OH, and O. To exemplify the application of this data, we model the X-ray emission of Comet C/2000 WM1 (linear) using the CX package in SPEX and find excellent agreement with observations made with the XMM-Newton RGS detector. Our analyses show that the X-ray intensity is dominated by SWCX with H, while H{sub 2}O plays a secondary role. This is the first time, to our knowledge, that CX cross sections have been implemented into a X-ray spectral fitting package to determine the H to H{sub 2}O ratio in cometary atmospheres. The CX data sets are incorporated into the modeling packages SPEX and Kronos .
12. The Solar Wind-Mars Interaction Boundaries in Three Dimensions
Science.gov (United States)
Gruesbeck, J.; Espley, J. R.; Connerney, J. E. P.; DiBraccio, G. A.; Soobiah, Y. I. J.
2017-12-01
The Martian magnetosphere is a product of the interaction of Mars with the interplanetary magnetic field and the supersonic solar wind. A bow shock forms upstream of the planet as the solar wind is diverted around the planet. Closer to the planet another boundary is located that separates the shock-heated solar wind plasma from the planetary plasma in the Martian magnetosphere. The Martian magnetosphere is induced by the pile-up of the interplanetary magnetic field. This induced magnetospheric boundary (IMB) has been referred to by different names, in part due to the observations available at the time. The location of these boundaries have been previously analyzed using data from Phobos 2, Mars Global Surveyor, and Mars Express resulting in models describing their average shapes. Observations of individual transitions demonstrate that it is a boundary with a finite thickness. The MAVEN spacecraft has been in orbit about Mars since November 2014 resulting in many encounters of the spacecraft with the boundaries. Using data from the Particle and Fields Package (PFP), we identify over 1000 bow shock crossings and over 4000 IMB crossings that we use to model the average locations. We model the boundaries as a 3-dimensional surface allowing observations of asymmetry. The average location of the bow shock and IMB lies further from the planet in the southern hemisphere, where stronger crustal fields are present. The MAVEN PFP dataset allows concurrent observations of the magnetic field and plasma environment to investigate the nature of the IMB and the relationship of the boundary to the different plasma signatures. Finally, we model the upstream and downstream encounters of the boundaries separately to produce shell models that quantify the finite thicknesses of the boundaries.
13. Solar wind control of stratospheric temperatures in Jupiter's auroral regions?
Science.gov (United States)
Sinclair, James Andrew; Orton, Glenn; Kasaba, Yasumasa; Sato, Takao M.; Tao, Chihiro; Waite, J. Hunter; Cravens, Thomas; Houston, Stephen; Fletcher, Leigh; Irwin, Patrick; Greathouse, Thomas K.
2017-10-01
Auroral emissions are the process through which the interaction of a planet’s atmosphere and its external magnetosphere can be studied. Jupiter exhibits auroral emission at a multitude of wavelengths including the X-ray, ultraviolet and near-infrared. Enhanced emission of CH4 and other stratospheric hydrocarbons is also observed coincident with Jupiter’s shorter-wavelength auroral emission (e.g. Caldwell et al., 1980, Icarus 44, 667-675, Kostiuk et al., 1993, JGR 98, 18823). This indicates that auroral processes modify the thermal structure and composition of the auroral stratosphere. The exact mechanism responsible for this auroral-related heating of the stratosphere has however remained elusive (Sinclair et al., 2017a, Icarus 292, 182-207, Sinclair et al., 2017b, GRL, 44, 5345-5354). We will present an analysis of 7.8-μm images of Jupiter measured by COMICS (Cooled Mid-Infrared Camera and Spectrograph, Kataza et al., 2000, Proc. SPIE(4008), 1144-1152) on the Subaru telescope. These images were acquired on January 11th, 12th, 13th, 14th, February 4, 5th and May 17th, 18th, 19th and 20th in 2017, allowing the daily variability of Jupiter’s auroral-related stratospheric heating to be tracked. Preliminary results suggest lower stratospheric temperatures are directly forced by the solar wind dynamical pressure. The southern auroral hotspot exhibited a significant increase in brightness temperature over a 24-hour period. Over the same time period, a solar wind propagation model (Tao et al. 2005, JGR 110, A11208) predicts a strong increase in the solar wind dynamical pressure at Jupiter.
14. A Deeper Understanding of Stability in the Solar Wind: Applying Nyquist's Instability Criterion to Wind Faraday Cup Data
Science.gov (United States)
Alterman, B. L.; Klein, K. G.; Verscharen, D.; Stevens, M. L.; Kasper, J. C.
2017-12-01
Long duration, in situ data sets enable large-scale statistical analysis of free-energy-driven instabilities in the solar wind. The plasma beta and temperature anisotropy plane provides a well-defined parameter space in which a single-fluid plasma's stability can be represented. Because this reduced parameter space can only represent instability thresholds due to the free energy of one ion species - typically the bulk protons - the true impact of instabilities on the solar wind is under estimated. Nyquist's instability criterion allows us to systematically account for other sources of free energy including beams, drifts, and additional temperature anisotropies. Utilizing over 20 years of Wind Faraday cup and magnetic field observations, we have resolved the bulk parameters for three ion populations: the bulk protons, beam protons, and alpha particles. Applying Nyquist's criterion, we calculate the number of linearly growing modes supported by each spectrum and provide a more nuanced consideration of solar wind stability. Using collisional age measurements, we predict the stability of the solar wind close to the sun. Accounting for the free-energy from the three most common ion populations in the solar wind, our approach provides a more complete characterization of solar wind stability.
15. A study of density modulation index in the inner heliospheric solar wind during solar cycle 23
International Nuclear Information System (INIS)
Bisoi, Susanta Kumar; Janardhan, P.; Ingale, M.; Subramanian, P.; Ananthakrishnan, S.; Tokumaru, M.; Fujiki, K.
2014-01-01
The ratio of the rms electron density fluctuations to the background density in the solar wind (density modulation index, ε N ≡ ΔN/N) is of vital importance for understanding several problems in heliospheric physics related to solar wind turbulence. In this paper, we have investigated the behavior of ε N in the inner heliosphere from 0.26 to 0.82 AU. The density fluctuations ΔN have been deduced using extensive ground-based observations of interplanetary scintillation at 327 MHz, which probe spatial scales of a few hundred kilometers. The background densities (N) have been derived using near-Earth observations from the Advanced Composition Explorer. Our analysis reveals that 0.001 ≲ ε N ≲ 0.02 and does not vary appreciably with heliocentric distance. We also find that ε N declines by 8% from 1998 to 2008. We discuss the impact of these findings on problems ranging from our understanding of Forbush decreases to the behavior of the solar wind dynamic pressure over the recent peculiar solar minimum at the end of cycle 23.
16. Current system of the solar wind: results of numerical calculation
International Nuclear Information System (INIS)
Pisanko, Yu.V.
1985-01-01
Results of numerical calculations of surface current in the interplanetary current layer and steady volume current in the solar wind for heliocentric distances (1-10)Rsub(s) (Rsub(s) is the Sun radius) are given. The strength of current dependence on spatial coordinates is considered. Stationary nondissipative magnetohydrodynamic corona expansion (SNMCE) in the reference system rotating with the Sun is studied. Calculations show that three-dimensional current system of nonaxial-symmetric and nonsymmetric relatively to helioequator plane of SNMCE is more complicated than the zonal ring current around the Sun, which is the only component of the current system in spatial symmetric case
17. Effects in atmospheric electricity daily variation controlled by solar wind
International Nuclear Information System (INIS)
Ptitsyna, N.G.; Tyasto, M.I.; Levitin, A.E.; Gromova, L.A.; Tuomi, T.; AN SSSR, Moscow
1995-01-01
An analysis of fair weather atmospheric electricity, one of the environmental factors which affects the biosphere, is conducted. A distinct difference in the diurnal variation of atmospheric electric field at Helsinki is found between disturbed and extremely quiet conditions in the magnetosphere in winter before midnight. The comparison with the numerical model of the ionospheric electric field based on the solar wind parameters reveals that the maximum contribution of the magnetospheric-ionospheric generator to atmospheric electric field is about 100-150 v/m which assumes values of about 30% of the surface field. 8 refs.; 2 figs
18. Simulation of transcontinental wind and solar PV generation time series
DEFF Research Database (Denmark)
Nuño Martinez, Edgar; Maule, Petr; Hahmann, Andrea N.
2018-01-01
to the technical characteristics of individual installations spread across large regions. The proposed methodology is validated using actual power data in Europe and can be applied to represent intermittent generation in network development plans, reliability and market studies, as well as operational guidelines.......The deployment of Renewable Energy Sources (RES) is driving modern power systems towards a fundamental green transition. In this regard, there is a need to develop models to accurately capture the variability of wind and solar photovoltaic (PV) power, at different geographical and temporal scales...
19. Solar wind monitor—a school geophysics project
Science.gov (United States)
Robinson, Ian
2018-05-01
Described is an established geophysics project to construct a solar wind monitor based on a nT resolution fluxgate magnetometer. Low-cost and appropriate from school to university level it incorporates elements of astrophysics, geophysics, electronics, programming, computer networking and signal processing. The system monitors the earth’s field in real-time uploading data and graphs to a website every few minutes. Modular design encourages construction and testing by teams of students as well as expansion and refinement. The system has been tested running unattended for months at a time. Both the hardware design and software is published as open-source [1, 10].
20. Proton fire hose instabilities in the expanding solar wind
Czech Academy of Sciences Publication Activity Database
Hellinger, Petr
2017-01-01
Roč. 83, č. 1 (2017), č. článku 705830105. ISSN 0022-3778 Institutional support: RVO:68378289 Keywords : astrophysicals plasmas * plasma expansion * plasma simulation Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.160, year: 2016 https://www.cambridge.org/ core /journals/journal-of-plasma-physics/article/proton-fire-hose-instabilities-in-the-expanding-solar-wind/6BA70378B25728533588A1A68073AC2F
1. Assessing temporal complementarity of solar, wind and hydrokinetic energy
Directory of Open Access Journals (Sweden)
Jurasz Jakub
2016-01-01
Full Text Available Renewable energy sources (RES exhibit various characteristics when it comes to their availability in time and space domain. Some are characterised by significant variability and limited predictability. This makes their integration to the power grid a complicated task. Temporal and spatial complementarity of RES is perceived as one of the possible ways to facilitate the process of integration. This paper investigates the concept of temporal complementarity of solar wind and hydrokinetic energy in case of two sites in Poland. Obtained results indicate existence of some beneficial complementarity on inter-annual and annual time scale. Combination of those three RES in one hybrid system makes power source more reliable.
2. Three Sides Billboard Wind-Solar Hybrid System Design
Directory of Open Access Journals (Sweden)
Bai Xuefeng
2015-01-01
Full Text Available With the high development of world economy, the demand of energy is increasing all the time, As energy shortage and environment problem are increasing outstanding, Renewable energy has been attracting more and more attention. A kind of three sides billboard supply by wind-Solar hybrid system has been designed in this paper, the overall structure of the system, components, working principle and control strategy has been analyzed from the system perspective. The software and hardware of the system are debugged together and the result is acquired. System function is better and has achieved the expected results.
3. Solar Wind Interaction and Impact on the Venus Atmosphere
Science.gov (United States)
Futaana, Yoshifumi; Stenberg Wieser, Gabriella; Barabash, Stas; Luhmann, Janet G.
2017-11-01
Venus has intrigued planetary scientists for decades because of its huge contrasts to Earth, in spite of its nickname of "Earth's Twin". Its invisible upper atmosphere and space environment are also part of the larger story of Venus and its evolution. In 60s to 70s, several missions (Venera and Mariner series) explored Venus-solar wind interaction regions. They identified the basic structure of the near-Venus space environment, for example, existence of the bow shock, magnetotail, ionosphere, as well as the lack of the intrinsic magnetic field. A huge leap in knowledge about the solar wind interaction with Venus was made possible by the 14-year long mission, Pioneer Venus Orbiter (PVO), launched in 1978. More recently, ESA's probe, Venus Express (VEX), was inserted into orbit in 2006, operated for 8 years. Owing to its different orbit from that of PVO, VEX made unique measurements in the polar and terminator regions, and probed the near-Venus tail for the first time. The near-tail hosts dynamic processes that lead to plasma energization. These processes in turn lead to the loss of ionospheric ions to space, slowly eroding the Venusian atmosphere. VEX carried an ion spectrometer with a moderate mass-separation capability and the observed ratio of the escaping hydrogen and oxygen ions in the wake indicates the stoichiometric loss of water from Venus. The structure and dynamics of the induced magnetosphere depends on the prevailing solar wind conditions. VEX studied the response of the magnetospheric system on different time scales. A plethora of waves was identified by the magnetometer on VEX; some of them were not previously observed by PVO. Proton cyclotron waves were seen far upstream of the bow shock, mirror mode waves were observed in magnetosheath and whistler mode waves, possibly generated by lightning discharges were frequently seen. VEX also encouraged renewed numerical modeling efforts, including fluid-type of models and particle-fluid hybrid type of models
4. Energy coupling function and solar wind-magnetosphere dynamo
International Nuclear Information System (INIS)
Kan, J.R.; Lee, L.C.
1979-01-01
The power delivered by the solar wind dynamo to the open magnetosphere is calculated based on the concept of field line reconnection, independent of the MHD steady reconnection theories. By recognizing a previously overlooked geometrical relationship between the reconnection electric field and the magnetic field, the calculated power is shown to be approximately proportional to the Akasofu-Perreault energy coupling function for the magnetospheric substorm. In addition to the polar cap potential, field line reconnection also gives rise to parallel electric fields on open field lines in the high-latitude cusp and the polar cap reions
5. Proton thermal energetics in the solar wind: Helios reloaded
Czech Academy of Sciences Publication Activity Database
Hellinger, Petr; Trávníček, Pavel M.; Štverák, Štěpán; Matteini, L.; Velli, M.
2013-01-01
Roč. 118, č. 4 (2013), s. 3151-3165 ISSN 2169-9380 R&D Projects: GA ČR GAP209/12/2041; GA ČR GAP209/12/2023 EU Projects: European Commission(XE) 263340 - SWIFF Grant - others:EU(XE) SHOCK Project No. 284515 Institutional support: RVO:67985815 ; RVO:68378289 Keywords : solar wind * proton energetics * turbulent heating Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics; BL - Plasma and Gas Discharge Physics (UFA-U) Impact factor: 3.440, year: 2013
6. Cause of solar wind speed variations observed at 1 a.u
International Nuclear Information System (INIS)
1981-01-01
An attempt is made to interpret solar wind variations observed at the earth's distance, namely the solar cycle variations, the semi-annual variations, and the 27-day variations, as well as the polarity changes of the interplanetary magnetic field, mainly in terms of two effects, a positive latitudinal gradient of the solar wind speed and a wobbling solar dipole, combined with the annual (heliospheric) latitudinal excursion of the earth. It is shown that a significant part of the solar wind variations observed at the earth's distance and the changes of polarity pattern of the interplanetary magnetic field can be reasonably well reproduced by the two effects
International Nuclear Information System (INIS)
Harmon, J.K.; Coles, W.A.
1983-01-01
The microturbulence spectrum of the solar wind is estimated using the spectral broadening of planetary radar signals. Observations were made with the two radars (12.6 cm and 70 cm) at Arecibo Observatory during the 1979 and 1981 superior conjunctions of Venus. These observations, which span the solar distance range of 5.4 to 25.5 R/sub sun/, are the first of their type to be reported. The data are consistent with earlier observations where comparisons can be made. The flattening of the high-frequency portion of the spectrum near the Sun reported by Woo and Armstrong is confirmed. In one case clear evidence for an inner scale in the vicinity of 2 km is found. Two transients, 1979 August 15 and 1981 April 24-25, with rather different characteristics were observed
8. The influence of solar wind variability on magnetospheric ULF wave power
Directory of Open Access Journals (Sweden)
D. Pokhotelov
2015-06-01
Full Text Available Magnetospheric ultra-low frequency (ULF oscillations in the Pc 4–5 frequency range play an important role in the dynamics of Earth's radiation belts, both by enhancing the radial diffusion through incoherent interactions and through the coherent drift-resonant interactions with trapped radiation belt electrons. The statistical distributions of magnetospheric ULF wave power are known to be strongly dependent on solar wind parameters such as solar wind speed and interplanetary magnetic field (IMF orientation. Statistical characterisation of ULF wave power in the magnetosphere traditionally relies on average solar wind–IMF conditions over a specific time period. In this brief report, we perform an alternative characterisation of the solar wind influence on magnetospheric ULF wave activity through the characterisation of the solar wind driver by its variability using the standard deviation of solar wind parameters rather than a simple time average. We present a statistical study of nearly one solar cycle (1996–2004 of geosynchronous observations of magnetic ULF wave power and find that there is significant variation in ULF wave powers as a function of the dynamic properties of the solar wind. In particular, we find that the variability in IMF vector, rather than variabilities in other parameters (solar wind density, bulk velocity and ion temperature, plays the strongest role in controlling geosynchronous ULF power. We conclude that, although time-averaged bulk properties of the solar wind are a key factor in driving ULF powers in the magnetosphere, the solar wind variability can be an important contributor as well. This highlights the potential importance of including solar wind variability especially in studies of ULF wave dynamics in order to assess the efficiency of solar wind–magnetosphere coupling.
9. A 15N-poor isotopic composition for the solar system as shown by Genesis solar wind samples.
Science.gov (United States)
Marty, B; Chaussidon, M; Wiens, R C; Jurewicz, A J G; Burnett, D S
2011-06-24
The Genesis mission sampled solar wind ions to document the elemental and isotopic compositions of the Sun and, by inference, of the protosolar nebula. Nitrogen was a key target element because the extent and origin of its isotopic variations in solar system materials remain unknown. Isotopic analysis of a Genesis Solar Wind Concentrator target material shows that implanted solar wind nitrogen has a (15)N/(14)N ratio of 2.18 ± 0.02 × 10(-3) (that is, ≈40% poorer in (15)N relative to terrestrial atmosphere). The (15)N/(14)N ratio of the protosolar nebula was 2.27 ± 0.03 × 10(-3), which is the lowest (15)N/(14)N ratio known for solar system objects. This result demonstrates the extreme nitrogen isotopic heterogeneity of the nascent solar system and accounts for the (15)N-depleted components observed in solar system reservoirs.
10. Solar minimum Lyman alpha sky background observations from Pioneer Venus orbiter ultraviolet spectrometer - Solar wind latitude variation
Science.gov (United States)
Ajello, J. M.
1990-01-01
Measurements of interplanetary H I Lyman alpha over a large portion of the celestial sphere were made at the recent solar minimum by the Pioneer Venus orbiter ultraviolet spectrometer. These measurements were performed during a series of spacecraft maneuvers conducted to observe Halley's comet in early 1986. Analysis of these data using a model of the passage of interstellar wind hydrogen through the solar system shows that the rate of charge exchange with solar wind protons is 30 percent less over the solar poles than in the ecliptic. This result is in agreement with a similar experiment performed with Mariner 10 at the previous solar minimum.
11. Spectral Analysis of Geomagnetic Activity Indices and Solar Wind Parameters
Directory of Open Access Journals (Sweden)
Jung-Hee Kim
2014-06-01
Full Text Available Solar variability is widely known to affect the interplanetary space and in turn the Earth’s electromagnetical environment on the basis of common periodicities in the solar and geomagnetic activity indices. The goal of this study is twofold. Firstly, we attempt to associate modes by comparing a temporal behavior of the power of geomagnetic activity parameters since it is barely sufficient searching for common peaks with a similar periodicity in order to causally correlate geomagnetic activity parameters. As a result of the wavelet transform analysis we are able to obtain information on the temporal behavior of the power in the velocity of the solar wind, the number density of protons in the solar wind, the AE index, the Dst index, the interplanetary magnetic field, B and its three components of the GSM coordinate system, BX, BY, BZ. Secondly, we also attempt to search for any signatures of influence on the space environment near the Earth by inner planets orbiting around the Sun. Our main findings are as follows: (1 Parameters we have investigated show periodicities of ~ 27 days, ~ 13.5 days, ~ 9 days. (2 The peaks in the power spectrum of BZ appear to be split due to an unknown agent. (3 For some modes powers are not present all the time and intervals showing high powers do not always coincide. (4 Noticeable peaks do not emerge at those frequencies corresponding to the synodic and/or sidereal periods of Mercury and Venus, which leads us to conclude that the Earth’s space environment is not subject to the shadow of the inner planets as suggested earlier.
12. Scale Dependence of Magnetic Helicity in the Solar Wind
Science.gov (United States)
Brandenburg, Axel; Subramanian, Kandaswamy; Balogh, Andre; Goldstein, Melvyn L.
2011-01-01
We determine the magnetic helicity, along with the magnetic energy, at high latitudes using data from the Ulysses mission. The data set spans the time period from 1993 to 1996. The basic assumption of the analysis is that the solar wind is homogeneous. Because the solar wind speed is high, we follow the approach first pioneered by Matthaeus et al. by which, under the assumption of spatial homogeneity, one can use Fourier transforms of the magnetic field time series to construct one-dimensional spectra of the magnetic energy and magnetic helicity under the assumption that the Taylor frozen-in-flow hypothesis is valid. That is a well-satisfied assumption for the data used in this study. The magnetic helicity derives from the skew-symmetric terms of the three-dimensional magnetic correlation tensor, while the symmetric terms of the tensor are used to determine the magnetic energy spectrum. Our results show a sign change of magnetic helicity at wavenumber k approximately equal to 2AU(sup -1) (or frequency nu approximately equal to 2 microHz) at distances below 2.8AU and at k approximately equal to 30AU(sup -1) (or nu approximately equal to 25 microHz) at larger distances. At small scales the magnetic helicity is positive at northern heliographic latitudes and negative at southern latitudes. The positive magnetic helicity at small scales is argued to be the result of turbulent diffusion reversing the sign relative to what is seen at small scales at the solar surface. Furthermore, the magnetic helicity declines toward solar minimum in 1996. The magnetic helicity flux integrated separately over one hemisphere amounts to about 10(sup 45) Mx(sup 2) cycle(sup -1) at large scales and to a three times lower value at smaller scales.
13. Solar Wind Proton Temperature Anisotropy: Linear Theory and WIND/SWE Observations
Science.gov (United States)
Hellinger, P.; Travnicek, P.; Kasper, J. C.; Lazarus, A. J.
2006-01-01
We present a comparison between WIND/SWE observations (Kasper et al., 2006) of beta parallel to p and T perpendicular to p/T parallel to p (where beta parallel to p is the proton parallel beta and T perpendicular to p and T parallel to p are the perpendicular and parallel proton are the perpendicular and parallel proton temperatures, respectively; here parallel and perpendicular indicate directions with respect to the ambient magnetic field) and predictions of the Vlasov linear theory. In the slow solar wind, the observed proton temperature anisotropy seems to be constrained by oblique instabilities, by the mirror one and the oblique fire hose, contrary to the results of the linear theory which predicts a dominance of the proton cyclotron instability and the parallel fire hose. The fast solar wind core protons exhibit an anticorrelation between beta parallel to c and T perpendicular to c/T parallel to c (where beta parallel to c is the core proton parallel beta and T perpendicular to c and T parallel to c are the perpendicular and parallel core proton temperatures, respectively) similar to that observed in the HELIOS data (Marsch et al., 2004).
14. High - speed steel for precise cased tools
International Nuclear Information System (INIS)
Karwiarz, J.; Mazur, A.
2001-01-01
The test results of high-vanadium high - speed steel (SWV9) for precise casted tools are presented. The face -milling cutters of NFCa80A type have been tested in industrial operating conditions. An average life - time of SWV9 steel tools was 3-10 times longer compare to the conventional high - speed milling cutters. Metallography of SWB9 precise casted steel revealed beneficial for tool properties distribution of primary vanadium carbides in the steel matrix. Presented results should be a good argument for wide application of high - vanadium high - speed steel for precise casted tools. (author)
15. Extended MHD Turbulence and Its Applications to the Solar Wind
Science.gov (United States)
Abdelhamid, Hamdi M.; Lingam, Manasvi; Mahajan, Swadesh M.
2016-10-01
Extended MHD is a one-fluid model that incorporates two-fluid effects such as electron inertia and the Hall drift. This model is used to construct fully nonlinear Alfvénic wave solutions, and thereby derive the kinetic and magnetic spectra by resorting to a Kolmogorov-like hypothesis based on the constant cascading rates of the energy and generalized helicities of this model. The magnetic and kinetic spectra are derived in the ideal (k\\lt 1/{λ }I), Hall (1/{λ }I\\lt k\\lt 1/{λ }e), and electron inertia (k\\gt 1/{λ }e) regimes; k is the wavenumber and {λ }s=c/{ω }{ps} is the skin depth of species “s.” In the Hall regime, it is shown that the emergent results are fully consistent with previous numerical and analytical studies, especially in the context of the solar wind. The focus is primarily on the electron inertia regime, where magnetic energy spectra with power-law indexes of -11/3 and -13/3 are always recovered. The latter, in particular, is quite close to recent observational evidence from the solar wind with a potential slope of approximately -4 in this regime. It is thus plausible that these spectra may constitute a part of the (extended) inertial range, as opposed to the standard “dissipation” range paradigm.
16. Reevaluation of the Solar Wind 36Ar/38Ar Ratio
Science.gov (United States)
Becker, R. H.; Schlutter, D. J.; Rider, P. E.; Pepin, R. O.
1996-03-01
The isotopic composition of solar wind (SW) argon is an important parameter in the modeling of the evolution of the terrestrial planet atmospheres. Anders and Grevesse assumed a 36Ar/38Ar ratio for SW of 5.31, essentially equal to that of air. Considerable evidence has since developed which indicates that this ratio is too low. Benkert et al. have reported their best estimate for the recent SW as 5.48 +/- 0.05, determined from measurements of lunar soil 71501. Based on Ar data obtained from surface oxidation of a metal separate from the Weston meteorite and from an uncontrolled etch of lunar sample 67701, reported by our group previously, we consider even this value to be too low. Since values of 5.75 to 5.85 were reported by Black for initial low temperature (fairly high SW 36Ar/38Ar ratio (in the range of ~5.6 to ~5.7), we decided to analyze Kapoeta for its light solar wind gases using the acid-etching techniques developed in our laboratory based on the CSSE procedure of Benkert et al.
17. MHD turbulence in the solar wind: evolution and anisotropy
International Nuclear Information System (INIS)
Horbury, T. S.; Forman, M. A.; Oughton, S.
2005-01-01
Spacecraft measurements in the solar wind offer the opportunity to study magnetohydrodynamic turbulence in a collisionless plasma in great detail. We review some of the key results of the study of this medium: the presence of large amplitude Alfven waves propagating predominantly away from the Sun; the existence of an active turbulent cascade; and intermittency similar to that in neutral fluids. The presence of a magnetic field leads to anisotropy of the fluctuations, which are predominantly perpendicular to this direction, as well as anisotropy of the spectrum. Some models suggest that MHD turbulence can evolve to a state with power predominantly in wave vectors either parallel to the magnetic field (slab fluctuations) or approximately perpendicular to it (2D). We present results of a new, wavelet-based analysis of magnetic field fluctuations in the solar wind, and demonstrate that the 2D component has a spectral index near the Kolmogorov value of 5/3, while slab fluctuations have a spectral index near 2. We also estimate the relative power levels in slab and 2D fluctuations, as well as the level of compressive fluctuations. Deviations of the data from the simple slab/2D model suggest the presence of power in intermediate directions and we compare our data with critical balance models. (Author)
18. LANGMUIR WAVE DECAY IN INHOMOGENEOUS SOLAR WIND PLASMAS: SIMULATION RESULTS
Energy Technology Data Exchange (ETDEWEB)
Krafft, C. [Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex (France); Volokitin, A. S. [IZMIRAN, Troitsk, 142190, Moscow (Russian Federation); Krasnoselskikh, V. V., E-mail: [email protected] [Laboratoire de Physique et Chimie de l’Environnement et de l’Espace, 3A Av. de la Recherche Scientifique, F-45071 Orléans Cedex 2 (France)
2015-08-20
Langmuir turbulence excited by electron flows in solar wind plasmas is studied on the basis of numerical simulations. In particular, nonlinear wave decay processes involving ion-sound (IS) waves are considered in order to understand their dependence on external long-wavelength plasma density fluctuations. In the presence of inhomogeneities, it is shown that the decay processes are localized in space and, due to the differences between the group velocities of Langmuir and IS waves, their duration is limited so that a full nonlinear saturation cannot be achieved. The reflection and the scattering of Langmuir wave packets on the ambient and randomly varying density fluctuations lead to crucial effects impacting the development of the IS wave spectrum. Notably, beatings between forward propagating Langmuir waves and reflected ones result in the parametric generation of waves of noticeable amplitudes and in the amplification of IS waves. These processes, repeated at different space locations, form a series of cascades of wave energy transfer, similar to those studied in the frame of weak turbulence theory. The dynamics of such a cascading mechanism and its influence on the acceleration of the most energetic part of the electron beam are studied. Finally, the role of the decay processes in the shaping of the profiles of the Langmuir wave packets is discussed, and the waveforms calculated are compared with those observed recently on board the spacecraft Solar TErrestrial RElations Observatory and WIND.
19. Corotating pressure waves without streams in the solar wind
International Nuclear Information System (INIS)
Burlaga, L.F.
1983-01-01
Voyager 1 and 2 magnetic field and plasma data are presented which demonstrate the existence of large scale, corotating, non-linear pressure waves between 2 AU and 4 AU that are not accompanied by fast streams. The pressure waves are presumed to be generated by corotating streams near the Sun. For two of the three pressure waves that are discussed, the absence of a stream is probably a real, physical effect, viz., a consequence of deceleration of the stream by the associated compression wave. For the third pressure wave, the apparent absence of a stream may be a geometrical effect it is likely that the stream was at latitudes just above those of the spacecraft, while the associated shocks and compression wave extended over a broader range of latitudes so that they could be observed by the spacecraft. It is suggested that the development of large-scale non-linear pressure waves at the expense of the kinetic energy of streams produces a qualitative change in the solar wind in the outer heliosphere. Within a few AU the quasi-stationary solar wind structure is determined by corotating streams whose structure is determined by the boundary conditions near the Sun
20. Observations & modeling of solar-wind/magnetospheric interactions
Science.gov (United States)
Hoilijoki, Sanni; Von Alfthan, Sebastian; Pfau-Kempf, Yann; Palmroth, Minna; Ganse, Urs
2016-07-01
The majority of the global magnetospheric dynamics is driven by magnetic reconnection, indicating the need to understand and predict reconnection processes and their global consequences. So far, global magnetospheric dynamics has been simulated using mainly magnetohydrodynamic (MHD) models, which are approximate but fast enough to be executed in real time or near-real time. Due to their fast computation times, MHD models are currently the only possible frameworks for space weather predictions. However, in MHD models reconnection is not treated kinetically. In this presentation we will compare the results from global kinetic (hybrid-Vlasov) and global MHD simulations. Both simulations are compared with in-situ measurements. We will show that the kinetic processes at the bow shock, in the magnetosheath and at the magnetopause affect global dynamics even during steady solar wind conditions. Foreshock processes cause an asymmetry in the magnetosheath plasma, indicating that the plasma entering the magnetosphere is not symmetrical on different sides of the magnetosphere. Behind the bow shock in the magnetosheath kinetic wave modes appear. Some of these waves propagate to the magnetopause and have an effect on the magnetopause reconnection. Therefore we find that kinetic phenomena have a significant role in the interaction between the solar wind and the magnetosphere. While kinetic models cannot be executed in real time currently, they could be used to extract heuristics to be added in the faster MHD models.
1. Kappa-Electrons Downstream of the Solar Wind Termination Shock
Science.gov (United States)
Fahr, H. J.
2017-12-01
A theoretical description of the solar wind electron distribution function downstream of the termination shock under the influence of the shock-induced injection of overshooting KeV-energetic electrons will be presented. A kinetic phasespace transport equation in the bulk frame of the heliosheath plasma flow is developed for the solar wind electrons, taking into account shock-induced electron injection, convective changes, magnetic cooling processes and whistler wave-induced energy diffusion. Assuming that the local electron distribution under the prevailing Non-LTE conditions can be represented by a local kappa function with a local kappa parameter that varies with the streamline coordinates, we determine the parameters of the resulting, initial kappa distribution for the downstream electrons. From this initial function spectral electron fluxes can be derived and can be compared with those measured by the VOYAGER-1 spacecraft in the range between 40 to 70 KeV. It can then be shown that with kappa values around kappa = 6 one can in fact fit these data very satisfactorily. In addition it is shown that for isentropic electron flows kappa-distributed electrons have to undergo simultaneous changes of both parameters, i.e. kappa and theta, of the electron kappa function. It is also shown then that under the influence of energy sinks and sources the electron flux becomes non-isentropic with electron entropies changing along the streamline.
2. 3D Electric Waveforms of Solar Wind Turbulence
Science.gov (United States)
Kellogg, P. J.; Goetz, K.; Monson, S. J.
2018-01-01
Electric fields provide the major coupling between the turbulence of the solar wind and particles. A large part of the turbulent spectrum of fluctuations in the solar wind is thought to be kinetic Alfvén waves; however, whistlers have recently been found to be important. In this article, we attempt to determine the mode identification of individual waveforms using the three-dimensional antenna system of the SWaves experiments on the STEREO spacecraft. Samples are chosen using waveforms with an apparent periodic structure, selected visually. The short antennas of STEREO respond to density fluctuations and to electric fields. Measurement of four quantities using only three antennas presents a problem. Methods to overcome or to ignore this difficulty are presented. We attempt to decide whether the waveforms correspond to the whistler mode or the Alfvén mode by using the direction of rotation of the signal. Most of the waveforms are so oblique—nearly linearly polarized—that the direction cannot be determined. However, about one third of the waveforms can be identified, and whistlers and Alfvén waves are present in roughly equal numbers. The selected waveforms are very intense but intermittent and are orders of magnitude stronger than the average, yet their accumulated signal accounts for a large fraction of the average. The average, however, is supposed to be the result of a turbulent mixture of many waves, not short coherent events. This presents a puzzle for future work.
3. On the nature of obstacles braking solar wind near Mars and Venera planets and on specific features of the interaction between solar wind and atmospheres of these planets
International Nuclear Information System (INIS)
Breus, T.K.; Gringauz, K.I.
1980-01-01
Discussed is the nature of obstacles braking solar wind near Mars and Venera according to the data of soviet measurements at ''Mars'' and ''Venera'' series automatic interplanetary stations. It is shown that alongside with essential similarity there exist differences among the zones of flow-around of Venera and Mars by solar wind. Such differences include, particularly, smaller dimensions of the obstacle of Venera as compared with Mars, and correspondingly less remote position of the shock wave front from the planet, different peculiarities of property changes of day-time ionosphere depending on the Sun zenith angle and other. The analysis of the experimental data permits to conclude that ionosphere and correspondingly the induced magnetic field of Venera play a determining role in the formation of the shock wave and the picture of planet flow-around by solar wind, while the determining role in the obstacle formation braking solar wind of Mars is played by the eigen planet field
4. Magnetic reconnection physics in the solar wind with Voyager 2
Science.gov (United States)
Stevens, Michael L.
2009-08-01
Magnetic reconnection is the process by which the magnetic topology evolves in collisionless plasmas. This phenomenon is fundamental to a broad range of astrophysical processes such as stellar flares, magnetospheric substorms, and plasma accretion, yet it is poorly understood and difficult to observe in situ . In this thesis, the solar wind plasma permeating interplanetary space is treated as a laboratory for reconnection physics. I present an exhaustive statistical approach to the identification of reconnection outflow jets in turbulent plasma and magnetic field time series data. This approach has been automated and characterized so that the resulting reconnection survey can be put in context with other related studies. The algorithm is shown to perform similarly to ad hoc studies in the inner heliosphere. Based on this technique, I present a survey of 138 outflow jets for the Voyager 2 spacecraft mission, including the most distant in situ evidence of reconnection discovered to date. Reconnection in the solar wind is shown to be strongly correlated with stream interactions and with solar activity. The solar wind magnetic field is found to be reconnecting via large, quasi-steady slow- mode magnetohydrodynamic structures as far out as the orbit of Neptune. The role of slow-mode shocks is explored and, in one instance, a well-developed reconnection structure is shown to be in good agreement with the Petschek theory for fast reconnection. This is the first reported example of a reconnection exhaust that satisfies the full jump conditions for a stationary slow-mode shock pair. A complete investigation into corotating stream interactions over the Voyager 2 mission has revealed that detectable reconnection structure occurs in about 23% of forced, global-scale current sheets. Contrary to previous studies, I find that signatures of this kind are most likely to be observed for current sheets where the magnetic field shear and the plasma-b are high. Evidence has been found
5. Autonomous wind/solar power systems with battery storage
Energy Technology Data Exchange (ETDEWEB)
Protogeropoulos, C I
1993-12-31
The performance of an autonomous hybrid renewable energy system consisting of combined photovoltaic/wind power generation with battery storage is under evaluation in this thesis. Detailed mathematical analysis of the renewable components and the battery was necessary in order to establish the theoretical background for accurate simulation results. Model validation was achieved through experimentation. The lack of a sizing method to combine both hybrid system total cost and long-term reliability level was the result of an extended literature survey. The new achievements which are described in this research work refer to: - simplified modelling for the performance of amorphous-silicon photovoltaic panels for all solar irradiance levels. -development of a new current-voltage expression with respect to wind speed for wind turbine performance simulation. -establishment of the battery storage state of voltage, SOV, simulation algorithm for long-term dynamic operational conditions. The proposed methodology takes into account 8 distinct cases covering steady state and transient effects and can be used for autonomous system reliability calculations. -techno-economic evaluation of the size of the hybrid system components by considering both reliability and economic criteria as design parameters. Two sizing scenarios for the renewable components are examined : the average year method and the worst renewable` month method. (Author)
6. High-Speed Sealift Technology Development Plan
National Research Council Canada - National Science Library
2002-01-01
.... The purpose of the project was to define the technology investments required to enable development of the high-speed commercial and military ships needed to provide realistic future mission capabilities...
7. Lubrication and cooling for high speed gears
Science.gov (United States)
Townsend, D. P.
1985-01-01
The problems and failures occurring with the operation of high speed gears are discussed. The gearing losses associated with high speed gearing such as tooth mesh friction, bearing friction, churning, and windage are discussed with various ways shown to help reduce these losses and thereby improve efficiency. Several different methods of oil jet lubrication for high speed gearing are given such as into mesh, out of mesh, and radial jet lubrication. The experiments and analytical results for the various methods of oil jet lubrication are shown with the strengths and weaknesses of each method discussed. The analytical and experimental results of gear lubrication and cooling at various test conditions are presented. These results show the very definite need of improved methods of gear cooling at high speed and high load conditions.
8. The solar wind neon abundance observed with ACE/SWICS and ULYSSES/SWICS
International Nuclear Information System (INIS)
Shearer, Paul; Raines, Jim M.; Lepri, Susan T.; Thomas, Jonathan W.; Gilbert, Jason A.; Landi, Enrico; Zurbuchen, Thomas H.; Von Steiger, Rudolf
2014-01-01
Using in situ ion spectrometry data from ACE/SWICS, we determine the solar wind Ne/O elemental abundance ratio and examine its dependence on wind speed and evolution with the solar cycle. We find that Ne/O is inversely correlated with wind speed, is nearly constant in the fast wind, and correlates strongly with solar activity in the slow wind. In fast wind streams with speeds above 600 km s –1 , we find Ne/O = 0.10 ± 0.02, in good agreement with the extensive polar observations by Ulysses/SWICS. In slow wind streams with speeds below 400 km s –1 , Ne/O ranges from a low of 0.12 ± 0.02 at solar maximum to a high of 0.17 ± 0.03 at solar minimum. These measurements place new and significant empirical constraints on the fractionation mechanisms governing solar wind composition and have implications for the coronal and photospheric abundances of neon and oxygen. The results are made possible by a new data analysis method that robustly identifies rare elements in the measured ion spectra. The method is also applied to Ulysses/SWICS data, which confirms the ACE observations and extends our view of solar wind neon into the three-dimensional heliosphere.
9. The solar wind neon abundance observed with ACE/SWICS and ULYSSES/SWICS
Energy Technology Data Exchange (ETDEWEB)
Shearer, Paul; Raines, Jim M.; Lepri, Susan T.; Thomas, Jonathan W.; Gilbert, Jason A.; Landi, Enrico; Zurbuchen, Thomas H. [Department of Atmospheric, Oceanic, and Space Sciences, University of Michigan, Ann Arbor, MI 48109 (United States); Von Steiger, Rudolf [International Space Science Institute, Hallerstrasse 6, CH-3012 Bern (Switzerland)
2014-07-01
Using in situ ion spectrometry data from ACE/SWICS, we determine the solar wind Ne/O elemental abundance ratio and examine its dependence on wind speed and evolution with the solar cycle. We find that Ne/O is inversely correlated with wind speed, is nearly constant in the fast wind, and correlates strongly with solar activity in the slow wind. In fast wind streams with speeds above 600 km s{sup –1}, we find Ne/O = 0.10 ± 0.02, in good agreement with the extensive polar observations by Ulysses/SWICS. In slow wind streams with speeds below 400 km s{sup –1}, Ne/O ranges from a low of 0.12 ± 0.02 at solar maximum to a high of 0.17 ± 0.03 at solar minimum. These measurements place new and significant empirical constraints on the fractionation mechanisms governing solar wind composition and have implications for the coronal and photospheric abundances of neon and oxygen. The results are made possible by a new data analysis method that robustly identifies rare elements in the measured ion spectra. The method is also applied to Ulysses/SWICS data, which confirms the ACE observations and extends our view of solar wind neon into the three-dimensional heliosphere.
10. Transition region, coronal heating and the fast solar wind
Science.gov (United States)
Li, Xing
2003-07-01
It is assumed that magnetic flux tubes are strongly concentrated at the boundaries of supergranule convection cells. A power law spectrum of high frequency Alfvén waves with a spectral index -1 originating from the sun is assumed to supply all the energy needed to energize the plasma flowing in such magnetic flux tubes. At the high frequency end, the waves are eroded by ions due to ion cyclotron resonance. The magnetic flux concentration is essential since it allows a sufficiently strong energy flux to be carried by high frequency ion cyclotron waves and these waves can be readily released at the coronal base by cyclotron resonance. The main results are: 1. The waves are capable of creating a steep transition region, a hot corona and a fast solar wind if both the wave frequency is high enough and the magnetic flux concentration is sufficiently strong in the boundaries of the supergranule convection zone. 2. By primarily heating alpha particles only, it is possible to produce a steep transition region, a hot corona and a fast solar wind. Coulomb coupling plays a key role in transferring the thermal energy of alpha particles to protons and electrons at the corona base. The electron thermal conduction then does the remaining job to create a sharp transition region. 3. Plasma species (even ions) may already partially lose thermal equilibrium in the transition region, and minor ions may already be faster than protons at the very base of the corona. 4. The model predicts high temperature alpha particles (Talpha ~ 2 x 107 K) and low proton temperatures (Tp solar radii, suggesting that hydrogen Lyman lines observed by UVCS above coronal holes may be primarily broadened by Alfvén waves in this range.
11. Does the magnetic expansion factor (fs) play a role in solar wind acceleration?
Science.gov (United States)
Wallace, Samantha; Arge, Charles N.; Pihlstrom, Ylva
2017-08-01
For the past 25 years, magnetic expansion factor (fs) has been a key parameter used in the calculation of terminal solar wind speed (vsw) in both the Wang-Sheeley-Arge (WSA) model and its predecessor the Wang-Sheeley (WS) model. Since the discovery of an inverse relationship between fs and vsw, the physical role that magnetic expansion factor plays in the acceleration of the solar wind has been explored and debated. In this study, we investigate whether magnetic expansion factor plays a causal role in determining the terminal speed of the solar wind or merely serves as proxy. To do so, we explore how fs, as determined by WSA, relates to vsw for two different scenarios: 1) extended periods where the fast solar wind emerges from the centers of large coronal holes, and 2) periods where the solar wind emerges from pseudostreamers. For these same scenarios, we will also consider an alternative empirical relationship between solar wind speed and the minimum angular distance at the photosphere of a solar wind source to the nearest coronal hole boundary (i.e., DCHB, θb). We then compare these two different prediction techniques directly with heliospheric observations (i.e., ACE, STEREO-A & B, Ulysses) of solar wind speed to determine whether one clearly out performs the other.
12. ULF Wave Activity in the Magnetosphere: Resolving Solar Wind Interdependencies to Identify Driving Mechanisms
Science.gov (United States)
Bentley, S. N.; Watt, C. E. J.; Owens, M. J.; Rae, I. J.
2018-04-01
Ultralow frequency (ULF) waves in the magnetosphere are involved in the energization and transport of radiation belt particles and are strongly driven by the external solar wind. However, the interdependency of solar wind parameters and the variety of solar wind-magnetosphere coupling processes make it difficult to distinguish the effect of individual processes and to predict magnetospheric wave power using solar wind properties. We examine 15 years of dayside ground-based measurements at a single representative frequency (2.5 mHz) and a single magnetic latitude (corresponding to L ˜ 6.6RE). We determine the relative contribution to ULF wave power from instantaneous nonderived solar wind parameters, accounting for their interdependencies. The most influential parameters for ground-based ULF wave power are solar wind speed vsw, southward interplanetary magnetic field component Bzstill account for significant amounts of power. We suggest that these three parameters correspond to driving by the Kelvin-Helmholtz instability, formation, and/or propagation of flux transfer events and density perturbations from solar wind structures sweeping past the Earth. We anticipate that this new parameter reduction will aid comparisons of ULF generation mechanisms between magnetospheric sectors and will enable more sophisticated empirical models predicting magnetospheric ULF power using external solar wind driving parameters.
13. COMPLEX MAPPING OF ENERGY RESOURCES FOR ALLOCATION OF SOLAR AND WIND ENERGY OBJECTS
Directory of Open Access Journals (Sweden)
B. A. Novakovskiy
2016-01-01
Full Text Available The paper presents developed methodology of solar and wind energy resources complex mapping at the regional level, taking into account the environmental and socio-economic factors affecting the placement of renewable energy facilities. Methodology provides a reasonable search and allocation of areas, the most promising for the placement of wind and solar power plants.
14. Developing a hybrid solar/wind powered irrigation system for crops in the Great Plains
Science.gov (United States)
Some small scale irrigation systems (powered by wind or solar do not require subsidies, but this paper discusses ways to achieve an economical renewable energy powered center pivot irrigation system for crops in the Great Plains. By adding a solar-photovoltaic (PV) array together with a wind...
15. Solar PV resource for higher penetration through a combined spatial aggregation with wind
CSIR Research Space (South Africa)
Bischof-Niemz, ST
2016-06-01
Full Text Available between wind and solar PV and how these would be reflected in the power system. The benefits of spatial distribution of renewables are well understood, but the impact of the combined spatial aggregation of wind and solar PV is central to the design...
16. Analysis of Ion Charge States in Solar Wind and CMEs Arati ...
states of various elements observed in situ in the solar wind and CMEs. The competing processes of ionization and recombination lead to depar- tures from collision ionization equilibrium. The use of this as a diagnostic of acceleration and heating processes of the solar wind and CMEs is sensi- tive to the accuracy of the ...
17. Magnetosheath waves under very low solar wind dynamic pressure: Wind/Geotail observations
Directory of Open Access Journals (Sweden)
C. J. Farrugia
2005-06-01
Full Text Available The expanded bow shock on and around "the day the solar wind almost disappeared" (11 May 1999 allowed the Geotail spacecraft to make a practically uninterrupted 54-h-long magnetosheath pass near dusk (16:30-21:11 magnetic local time at a radial distance of 24 to 30 RE (Earth radii. During most of this period, interplanetary parameters varied gradually and in such a way as to give rise to two extreme magnetosheath structures, one dominated by magnetohydrodynamic (MHD effects and the other by gas dynamic effects. We focus attention on unusual features of electromagnetic ion wave activity in the former magnetosheath state, and compare these features with those in the latter. Magnetic fluctuations in the gas dynamic magnetosheath were dominated by compressional mirror mode waves, and left- and right-hand polarized electromagnetic ion cyclotron (EIC waves transverse to the background field. In contrast, the MHD magnetosheath, lasting for over one day, was devoid of mirror oscillations and permeated instead by EIC waves of weak intensity. The weak wave intensity is related to the prevailing low solar wind dynamic pressures. Left-hand polarized EIC waves were replaced by bursts of right-hand polarized waves, which remained for many hours the only ion wave activity present. This activity occurred when the magnetosheath proton temperature anisotropy (= became negative. This was because the weakened bow shock exposed the magnetosheath directly to the (negative temperature anisotropy of the solar wind. Unlike the normal case studied in the literature, these right-hand waves were not by-products of left-hand polarized waves but derived their energy source directly from the magnetosheath temperature anisotropy. Brief entries into the
18. Magnetosheath waves under very low solar wind dynamic pressure: Wind/Geotail observations
Directory of Open Access Journals (Sweden)
C. J. Farrugia
2005-06-01
Full Text Available The expanded bow shock on and around "the day the solar wind almost disappeared" (11 May 1999 allowed the Geotail spacecraft to make a practically uninterrupted 54-h-long magnetosheath pass near dusk (16:30-21:11 magnetic local time at a radial distance of 24 to 30 RE (Earth radii. During most of this period, interplanetary parameters varied gradually and in such a way as to give rise to two extreme magnetosheath structures, one dominated by magnetohydrodynamic (MHD effects and the other by gas dynamic effects. We focus attention on unusual features of electromagnetic ion wave activity in the former magnetosheath state, and compare these features with those in the latter. Magnetic fluctuations in the gas dynamic magnetosheath were dominated by compressional mirror mode waves, and left- and right-hand polarized electromagnetic ion cyclotron (EIC waves transverse to the background field. In contrast, the MHD magnetosheath, lasting for over one day, was devoid of mirror oscillations and permeated instead by EIC waves of weak intensity. The weak wave intensity is related to the prevailing low solar wind dynamic pressures. Left-hand polarized EIC waves were replaced by bursts of right-hand polarized waves, which remained for many hours the only ion wave activity present. This activity occurred when the magnetosheath proton temperature anisotropy (= became negative. This was because the weakened bow shock exposed the magnetosheath directly to the (negative temperature anisotropy of the solar wind. Unlike the normal case studied in the literature, these right-hand waves were not by-products of left-hand polarized waves but derived their energy source directly from the magnetosheath temperature anisotropy. Brief entries into the low latitude boundary layer (LLBL and duskside magnetosphere occurred under such inflated conditions that the magnetospheric magnetic pressure was insufficient to maintain pressure balance. In these crossings, the inner edge of
19. Elsaesser variable analysis of fluctuations in the ion foreshock and undisturbed solar wind
Science.gov (United States)
Labelle, James; Treumann, Rudolf A.; Marsch, Eckart
1994-01-01
Magnetohydrodynamics (MHD) fluctuations in the solar wind have been investigated previously by use of Elsaesser variables. In this paper, we present a comparison of the spectra of Elsaesser variables in the undisturbed solar wind at 1 AU and in the ion foreshock in front of the Earth. Both observations take place under relatively strong solar wind flow speed conditions (approximately equal 600 km/s). In the undisturbed solar wind we find that outward propagating Alfven waves dominate, as reported by other observers. In the ion foreshock the situation is more complex, with neither outward nor inward propagation dominating over the entire range investigated (1-10 mHz). Measurements of the Poynting vectors associated with the fluctuations are consistent with the Elsaesser variable analysis. These results generally support interpretations of the Elsaesser variables which have been made based strictly on solar wind data and provide additional insight into the nature of the ion foreshock turbulence.
20. Contribution of Strong Discontinuities to the Power Spectrum of the Solar Wind
International Nuclear Information System (INIS)
Borovsky, Joseph E.
2010-01-01
Eight and a half years of magnetic field measurements (2 22 samples) from the ACE spacecraft in the solar wind at 1 A.U. are analyzed. Strong (large-rotation-angle) discontinuities in the solar wind are collected and measured. An artificial time series is created that preserves the timing and amplitudes of the discontinuities. The power spectral density of the discontinuity series is calculated and compared with the power spectral density of the solar-wind magnetic field. The strong discontinuities produce a power-law spectrum in the ''inertial subrange'' with a spectral index near the Kolmogorov -5/3 index. The discontinuity spectrum contains about half of the power of the full solar-wind magnetic field over this ''inertial subrange.'' Warnings are issued about the significant contribution of discontinuities to the spectrum of the solar wind, complicating interpretation of spectral power and spectral indices.
1. AUTOMATIC DETECTION ALGORITHM OF DYNAMIC PRESSURE PULSES IN THE SOLAR WIND
International Nuclear Information System (INIS)
Zuo, Pingbing; Feng, Xueshang; Wang, Yi; Xie, Yanqiong; Li, Huijun; Xu, Xiaojun
2015-01-01
Dynamic pressure pulses (DPPs) in the solar wind are a significant phenomenon closely related to the solar-terrestrial connection and physical processes of solar wind dynamics. In order to automatically identify DPPs from solar wind measurements, we develop a procedure with a three-step detection algorithm that is able to rapidly select DPPs from the plasma data stream and simultaneously define the transition region where large dynamic pressure variations occur and demarcate the upstream and downstream region by selecting the relatively quiet status before and after the abrupt change in dynamic pressure. To demonstrate the usefulness, efficiency, and accuracy of this procedure, we have applied it to the Wind observations from 1996 to 2008 by successfully obtaining the DPPs. The procedure can also be applied to other solar wind spacecraft observation data sets with different time resolutions
2. The effect of asymmetric solar wind on the Lyman α sky background
International Nuclear Information System (INIS)
Joselyn, J.A.; Holzer, T.E.
1975-01-01
The Lyman α (Ly α) sky background arises from the scattering of solar Ly α from a spatial distribution of neutral hydrogen in interplanetary space. This distribution is partially determined by the solar wind proton flux, which provides the principal mechanism of loss by charge exchange of the neutral hydrogen. By generating isophotal maps of scattered Ly α for several choices of interstellar wind direction and solar wind proton flux distributions, the results show that latitudinal variations of the solar wind proton flux can have a significant effect on the observed location and shape of the Ly α intensity maximum. This fact should aid in the interpretation of Ly α maps and also indicates a possible method for inferring values for the average solar wind proton flux out of the ecliptic plane
3. Solar power. [comparison of costs to wind, nuclear, coal, oil and gas
Science.gov (United States)
Walton, A. L.; Hall, Darwin C.
1990-01-01
This paper describes categories of solar technologies and identifies those that are economic. It compares the private costs of power from solar, wind, nuclear, coal, oil, and gas generators. In the southern United States, the private costs of building and generating electricity from new solar and wind power plants are less than the private cost of electricity from a new nuclear power plant. Solar power is more valuable than nuclear power since all solar power is available during peak and midpeak periods. Half of the power from nuclear generators is off-peak power and therefore is less valuable. Reliability is important in determining the value of wind and nuclear power. Damage from air pollution, when factored into the cost of power from fossil fuels, alters the cost comparison in favor of solar and wind power. Some policies are more effective at encouraging alternative energy technologies that pollute less and improve national security.
4. Effect of solar wind plasma parameters on space weather
International Nuclear Information System (INIS)
Rathore, Balveer S.; Gupta, Dinesh C.; Kaushik, Subhash C.
2015-01-01
Today's challenge for space weather research is to quantitatively predict the dynamics of the magnetosphere from measured solar wind and interplanetary magnetic field (IMF) conditions. Correlative studies between geomagnetic storms (GMSs) and the various interplanetary (IP) field/plasma parameters have been performed to search for the causes of geomagnetic activity and develop models for predicting the occurrence of GMSs, which are important for space weather predictions. We find a possible relation between GMSs and solar wind and IMF parameters in three different situations and also derived the linear relation for all parameters in three situations. On the basis of the present statistical study, we develop an empirical model. With the help of this model, we can predict all categories of GMSs. This model is based on the following fact: the total IMF B total can be used to trigger an alarm for GMSs, when sudden changes in total magnetic field B total occur. This is the first alarm condition for a storm's arrival. It is observed in the present study that the southward B z component of the IMF is an important factor for describing GMSs. A result of the paper is that the magnitude of B z is maximum neither during the initial phase (at the instant of the IP shock) nor during the main phase (at the instant of Disturbance storm time (Dst) minimum). It is seen in this study that there is a time delay between the maximum value of southward B z and the Dst minimum, and this time delay can be used in the prediction of the intensity of a magnetic storm two-three hours before the main phase of a GMS. A linear relation has been derived between the maximum value of the southward component of B z and the Dst, which is Dst = (−0.06) + (7.65) B z +t. Some auxiliary conditions should be fulfilled with this, for example the speed of the solar wind should, on average, be 350 km s −1 to 750 km s −1 , plasma β should be low and, most importantly, plasma temperature
5. Three-fluid, three-dimensional magnetohydrodynamic solar wind model with eddy viscosity and turbulent resistivity
Energy Technology Data Exchange (ETDEWEB)
Usmanov, Arcadi V.; Matthaeus, William H. [Department of Physics and Astronomy, University of Delaware, Newark, DE 19716 (United States); Goldstein, Melvyn L., E-mail: [email protected] [Code 672, NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States)
2014-06-10
We have developed a three-fluid, three-dimensional magnetohydrodynamic solar wind model that incorporates turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating. The solar wind plasma is described as a system of co-moving solar wind protons, electrons, and interstellar pickup protons, with separate energy equations for each species. Numerical steady-state solutions of Reynolds-averaged solar wind equations coupled with turbulence transport equations for turbulence energy, cross helicity, and correlation length are obtained by the time relaxation method in the corotating with the Sun frame of reference in the region from 0.3 to 100 AU (but still inside the termination shock). The model equations include the effects of electron heat conduction, Coulomb collisions, photoionization of interstellar hydrogen atoms and their charge exchange with the solar wind protons, turbulence energy generation by pickup protons, and turbulent heating of solar wind protons and electrons. The turbulence transport model is based on the Reynolds decomposition and turbulence phenomenologies that describe the conversion of fluctuation energy into heat due to a turbulent cascade. In addition to using separate energy equations for the solar wind protons and electrons, a significant improvement over our previous work is that the turbulence model now uses an eddy viscosity approximation for the Reynolds stress tensor and the mean turbulent electric field. The approximation allows the turbulence model to account for driving of turbulence by large-scale velocity gradients. Using either a dipole approximation for the solar magnetic field or synoptic solar magnetograms from the Wilcox Solar Observatory for assigning boundary conditions at the coronal base, we apply the model to study the global structure of the solar wind and its three-dimensional properties, including embedded turbulence, heating, and acceleration throughout the heliosphere. The model results are
6. Regional variations in the health, environmental, and climate benefits of wind and solar generation
OpenAIRE
Siler-Evans, Kyle; Azevedo, Inês Lima; Morgan, M. Granger; Apt, Jay
2013-01-01
When wind or solar energy displace conventional generation, the reduction in emissions varies dramatically across the United States. Although the Southwest has the greatest solar resource, a solar panel in New Jersey displaces significantly more sulfur dioxide, nitrogen oxides, and particulate matter than a panel in Arizona, resulting in 15 times more health and environmental benefits. A wind turbine in West Virginia displaces twice as much carbon dioxide as the same turbine in California. De...
7. Techno-Economic Assessment of Concentrating Solar Power and Wind Hybridization in Jordan
Directory of Open Access Journals (Sweden)
2018-03-01
A strong complementarity between wind and direct normal solar radiation was observed in the selected location in Jordan, which emphasizes the attractiveness of the selected hybrid system. The optimal configuration of the CSP-wind hybrid system was obtained with a solar field of a 2.6 solar multiple and a 5 hours energy storage. The achieved capacity factor was 94%, and the LCOE is lower than those resulted for standalone CSP plants.
8. Self consistent MHD modeling of the solar wind from polar coronal holes
International Nuclear Information System (INIS)
Stewart, G. A.; Bravo, S.
1996-01-01
We have developed a 2D self consistent MHD model for solar wind flow from antisymmetric magnetic geometries. We present results in the case of a photospheric magnetic field which has a dipolar configuration, in order to investigate some of the general characteristics of the wind at solar minimum. As in previous studies, we find that the magnetic configuration is that of a closed field region (a coronal helmet belt) around the solar equator, extending up to about 1.6 R · , and two large open field regions centred over the poles (polar coronal holes), whose magnetic and plasma fluxes expand to fill both hemispheres in interplanetary space. In addition, we find that the different geometries of the magnetic field lines across each hole (from the almost radial central polar lines to the highly curved border equatorial lines) cause the solar wind to have greatly different properties depending on which region it flows from. We find that, even though our simplified model cannot produce realistic wind values, we can obtain a polar wind that is faster, less dense and hotter than equatorial wind, and found that, close to the Sun, there exists a sharp transition between the two wind types. As these characteristics coincide with observations we conclude that both fast and slow solar wind can originate from coronal holes, fast wind from the centre, slow wind from the border
9. Cost-covering remuneration - wind and solar energy skinned
International Nuclear Information System (INIS)
Niederhaeusern, A.
2008-01-01
In this article, the details of Switzerland's cost-covering remuneration scheme for electrical energy from renewable resources are discussed. Several experts from the renewable energies area express their opinions on the scheme's tariffs for the remuneration of electrical energy fed into the public mains. Wind energy is quoted as being 'skinned', with a lower tariff than before and solar energy is quoted as being promoted 'with the hand brake still on'. Geothermal energy and power from biomass power stations is quoted as being 'undamaged' by the new remuneration system. In general, the opinion is expressed that small investors and producers have, once more, been put at a disadvantage. The situation in Switzerland is briefly compared with that in Germany, France, Spain and Italy. An overview of the tariffs is presented in tabular form
10. Critical materials: wind industry and solar industry are battling
International Nuclear Information System (INIS)
Anon.
2015-01-01
Neodymium, dysprosium, tellurium, indium and gallium are materials whose shortage and price fluctuations could have an impact on the development of wind energy and solar energy as about a quarter of the production of rare earth elements is used for the fabrication of permanent magnets. Between 1966 and 1984 the United States were the first producer in the world, then the production of these materials has moved little by little towards China. In 2010 China produced 97% of rare earth elements and in the same year it reduced the quantities to export which led to a panic in the market. Now governments and the industry are facing the challenge. New production capacities have been opened particularly in the United-States and Australia, ancient mines have been re-opened, recycling policies have been developed and an optimization of the use of rare-earth elements has been favored. (A.C.)
11. Solar wind interaction with type-1 comet tails
International Nuclear Information System (INIS)
Ershkovich, A.I.
1977-01-01
A comet tail is considered as a plasma cylinder separated by a tangential discontinuity surface from the solar wind. Under typical conditions a comet tail boundary is shown to undergo the Kelvin-Helmholtz instability. With infinite amplitude the stabilizing effect of the magnetic field increases, and waves become stable. The proposed model supplies the detailed quantitative description of helical waves observed in type-1 comet tails. This theory enables the evaluation of the comet tail magnetic field by means of the observations of helical waves. The magnetic field in the comet tail turns out to be of the order of the interplanetary field. This conclusion seems to be in accordance with Alfven's idea that the magnetic field in type-1 comet tails is a captured interplanetary field. (Auth.)
12. Particle acceleration and reconnection in the solar wind
Energy Technology Data Exchange (ETDEWEB)
Zank, G. P.; Hunana, P.; Mostafavi, P.; Le Roux, J. A.; Webb, G. M. [Center for Space Plasma and Aeronomic Research (CSPAR), University of Alabama, Huntsville, AL 35805 (United States); Department of Space Science, University of Alabama, Huntsville, AL 35899 (United States); Khabarova, O. [Heliophysical Laboratory, IZMIRAN, Troitsk, Moscow 142190 (Russian Federation); Cummings, A. C.; Stone, E. C. [California Institute of Technology, Mail Code 290-17, Pasadena, CA 91125 (United States); Decker, R. B. [Johns Hopkins University/Applied Physics Lab., Laurel, MD 20723-6099 (United States)
2016-03-25
An emerging paradigm for the dissipation of magnetic turbulence in the supersonic solar wind is via localized quasi-2D small-scale magnetic island reconnection processes. An advection-diffusion transport equation for a nearly isotropic particle distribution describes particle transport and energization in a region of interacting magnetic islands [1; 2]. The dominant charged particle energization processes are 1) the electric field induced by quasi-2D magnetic island merging, and 2) magnetic island contraction. The acceleration of charged particles in a “sea of magnetic islands” in a super-Alfvénic flow, and the energization of particles by combined diffusive shock acceleration (DSA) and downstream magnetic island reconnection processes are discussed.
13. From the Solar Wind to the Magnetospheric Substorm
Institute of Scientific and Technical Information of China (English)
E.A. Ponomarev; P.A. Sedykh; O.V. Mager
2005-01-01
This paper gives a brief outline of the progression from the first substorm model developed in Ref.[4] and [8] based on Kennel's ideas[3], to the present views about the mechanism by which solar wind kinetic energy is converted to electromagnetic energy at the Bow Shock and by which this energy is transferred to the magnetosphere in the form of current; about the transformation of the energy of this current to gas kinetic energy of convecting plasma tubes, and, finally, the back transformation of gas kinetic energy to electromagnetic energy in secondary magnetospheric MHD generators. The questions of the formation of the magnetospheric convection system, the nature of substorm break-up, and of the matching of currents in the magnetosphere-ionosphere system are discussed.
14. Western Wind and Solar Integration Study Phase 2 (Presentation)
Energy Technology Data Exchange (ETDEWEB)
Lew, D.; Brinkman, G.; Ibanez, E.; Kumar, N.; Lefton, S.; Jordan, G.; Venkataraman, S.; King, J.
2013-06-01
This presentation accompanies Phase 2 of the Western Wind and Solar Integration Study, a follow-on to Phase 1, which examined the operational impacts of high penetrations of variable renewable generation on the electric power system in the West and was one of the largest variable generation studies to date. High penetrations of variable generation can induce cycling of fossil-fueled generators. Cycling leads to wear-and-tear costs and changes in emissions. Phase 2 calculated these costs and emissions, and simulated grid operations for a year to investigate the detailed impact of variable generation on the fossil-fueled fleet. The presentation highlights the scope of the study and results.
15. New Model of a Solar Wind Airplane for Geomatic Operations
Science.gov (United States)
Achachi, A.; Benatia, D.
2015-08-01
The ability for an aircraft to fly during a much extended period of time has become a key issue and a target of research, both in the domain of civilian aviation and unmanned aerial vehicles. This paper describes a new design and evaluating of solar wind aircraft with the objective to assess the impact of a new system design on overall flight crew performance. The required endurance is in the range of some hours in the case of law enforcement, border surveillance, forest fire fighting or power line inspection. However, other applications at high altitudes, such as geomatic operations for delivering geographic information, weather research and forecast, environmental monitoring, would require remaining airborne during days, weeks or even months. The design of GNSS non precision approach procedure for different airports is based on geomatic data.
16. The structure of rotational discontinuities. [in solar wind
Science.gov (United States)
Neugebauer, M.
1989-01-01
This study examines the structures of a set of rotational discontinuities detected in the solar wind by the ISEE-3 spacecraft. It is found that the complexity of the structure increases as the angle theta between the propagation vector k and the magnetic field decreases. For rotational discontinuities that propagate at a large angle to the field with an ion (left-hand) sense of rotation, the magnetic hodograms tend to be flattened, in agreement with prior numerical simulations. When theta is large, angular 'overshoots' are often observed at one or both ends of the discontinuity. When the propagation is nearly parallel to the field (when theta is small), many different types of structure are seen, ranging from straight lines, to S-shaped curves, to complex, disorganized shapes.
17. NEW MODEL OF A SOLAR WIND AIRPLANE FOR GEOMATIC OPERATIONS
Directory of Open Access Journals (Sweden)
A. Achachi
2015-08-01
Full Text Available The ability for an aircraft to fly during a much extended period of time has become a key issue and a target of research, both in the domain of civilian aviation and unmanned aerial vehicles. This paper describes a new design and evaluating of solar wind aircraft with the objective to assess the impact of a new system design on overall flight crew performance. The required endurance is in the range of some hours in the case of law enforcement, border surveillance, forest fire fighting or power line inspection. However, other applications at high altitudes, such as geomatic operations for delivering geographic information, weather research and forecast, environmental monitoring, would require remaining airborne during days, weeks or even months. The design of GNSS non precision approach procedure for different airports is based on geomatic data.
18. Moving an asteroid with electric solar wind sail
Science.gov (United States)
Merikallio, S.; Janhunen, P.
2010-12-01
The electric solar wind sail (E-Sail) is a new propulsion method for interplanetary travel which was invented in 2006 and is currently under development. The E-Sail uses charged tethers to extract momentum from the solar wind particles to obtain propulsive thrust. According to current estimates, the E-Sail is 2-3 orders of magnitude better than traditional propulsion methods (chemical rockets and ion engines) in terms of produced lifetime-integrated impulse per propulsion system mass. Here we analyze the problem of using the E-Sail for directly deflecting an Earth-threatening asteroid. The problem then culminates into how to attach the E-Sail device to the asteroid. We assess alternative attachment strategies, namely straightforward direct towing with a cable and the gravity tractor method which works for a wider variety of situations. We also consider possible techniques to scale up the E-Sail force beyond the baseline one Newton level to deal with more imminent or larger asteroid or cometary threats. As a baseline case we consider an asteroid of effective diameter of 140 m and mass of 3 million tons, which can be deflected with a baseline 1 N E-Sail within 10 years. With a 5 N E-Sail the deflection could be achieved in 5 years. Once developed, the E-Sail would appear to provide a safe and reasonably low-cost way of deflecting dangerous asteroids and other heavenly bodies in cases where the collision threat becomes known several years in advance.
19. Particle acceleration via reconnection processes in the supersonic solar wind
International Nuclear Information System (INIS)
Zank, G. P.; Le Roux, J. A.; Webb, G. M.; Dosch, A.; Khabarova, O.
2014-01-01
An emerging paradigm for the dissipation of magnetic turbulence in the supersonic solar wind is via localized small-scale reconnection processes, essentially between quasi-2D interacting magnetic islands. Charged particles trapped in merging magnetic islands can be accelerated by the electric field generated by magnetic island merging and the contraction of magnetic islands. We derive a gyrophase-averaged transport equation for particles experiencing pitch-angle scattering and energization in a super-Alfvénic flowing plasma experiencing multiple small-scale reconnection events. A simpler advection-diffusion transport equation for a nearly isotropic particle distribution is derived. The dominant charged particle energization processes are (1) the electric field induced by quasi-2D magnetic island merging and (2) magnetic island contraction. The magnetic island topology ensures that charged particles are trapped in regions where they experience repeated interactions with the induced electric field or contracting magnetic islands. Steady-state solutions of the isotropic transport equation with only the induced electric field and a fixed source yield a power-law spectrum for the accelerated particles with index α = –(3 + M A )/2, where M A is the Alfvén Mach number. Considering only magnetic island contraction yields power-law-like solutions with index –3(1 + τ c /(8τ diff )), where τ c /τ diff is the ratio of timescales between magnetic island contraction and charged particle diffusion. The general solution is a power-law-like solution with an index that depends on the Alfvén Mach number and the timescale ratio τ diff /τ c . Observed power-law distributions of energetic particles observed in the quiet supersonic solar wind at 1 AU may be a consequence of particle acceleration associated with dissipative small-scale reconnection processes in a turbulent plasma, including the widely reported c –5 (c particle speed) spectra observed by Fisk and Gloeckler
20. Non-Gaussian probability distributions of solar wind fluctuations
Directory of Open Access Journals (Sweden)
E. Marsch
Full Text Available The probability distributions of field differences ∆x(τ=x(t+τ-x(t, where the variable x(t may denote any solar wind scalar field or vector field component at time t, have been calculated from time series of Helios data obtained in 1976 at heliocentric distances near 0.3 AU. It is found that for comparatively long time lag τ, ranging from a few hours to 1 day, the differences are normally distributed according to a Gaussian. For shorter time lags, of less than ten minutes, significant changes in shape are observed. The distributions are often spikier and narrower than the equivalent Gaussian distribution with the same standard deviation, and they are enhanced for large, reduced for intermediate and enhanced for very small values of ∆x. This result is in accordance with fluid observations and numerical simulations. Hence statistical properties are dominated at small scale τ by large fluctuation amplitudes that are sparsely distributed, which is direct evidence for spatial intermittency of the fluctuations. This is in agreement with results from earlier analyses of the structure functions of ∆x. The non-Gaussian features are differently developed for the various types of fluctuations. The relevance of these observations to the interpretation and understanding of the nature of solar wind magnetohydrodynamic (MHD turbulence is pointed out, and contact is made with existing theoretical concepts of intermittency in fluid turbulence.
1. Radiation Belt Transport Driven by Solar Wind Dynamic Pressure Fluctuations
Science.gov (United States)
Kress, B. T.; Hudson, M. K.; Ukhorskiy, A. Y.; Mueller, H.
2012-12-01
2. Solar wind heating by an embedded quasi-isothermal pick-up ion fluid
Directory of Open Access Journals (Sweden)
H. J. Fahr
Full Text Available It is well known that the solar wind plasma consists of primary ions of solar coronal origin and secondary ions of interstellar origin. Interstellar H-atoms penetrate into the inner heliosphere and when ionized there are converted into secondary ions. These are implanted into the magnetized solar wind flow and are essentially enforced to co-move with this flow. By nonlinear interactions with wind-entrained Alfvén waves the latter are processed in the co-moving velocity space. This pick-up process, however, also causes actions back upon the original solar wind flow, leading to a deceleration, as well as a heating of the solar wind plasma. The resulting deceleration is not only due to the loading effect, but also due to the action of the pressure gradient. To calculate the latter, it is important to take into account the stochastic acceleration that suffers at their convection out of the inner heliosphere by the quasi-linear interactions with MHD turbulences. Only then can the presently reported VOYAGER observations of solar wind decelerations and heatings in the outer heliosphere be understood in terms of the current, most likely values of interstellar gas parameters. In a consistent view of the thermodynamics of the solar wind plasma, which is composed of secondary ions and solar wind protons, we also derive that the latter are globally heated at their motion to larger solar distances. The arising heat transfer is due to the action of suprathermal ions which drive MHD waves that are partially absorbed by solar wind protons and thereby establish their observed quasi-polytropy. We obtain a quantitative expression for the solar wind proton pressure as a function of solar distance. This expression clearly shows the change from an adiabatic to a quasi-polytropic behaviour with a decreasing polytropic index at increasing distances, as has been observed by the VOYAGERS. This also allows one to calculate the average percentage of the intitial energy
3. Solar wind heating by an embedded quasi-isothermal pick-up ion fluid
Directory of Open Access Journals (Sweden)
H. J. Fahr
2002-10-01
Full Text Available It is well known that the solar wind plasma consists of primary ions of solar coronal origin and secondary ions of interstellar origin. Interstellar H-atoms penetrate into the inner heliosphere and when ionized there are converted into secondary ions. These are implanted into the magnetized solar wind flow and are essentially enforced to co-move with this flow. By nonlinear interactions with wind-entrained Alfvén waves the latter are processed in the co-moving velocity space. This pick-up process, however, also causes actions back upon the original solar wind flow, leading to a deceleration, as well as a heating of the solar wind plasma. The resulting deceleration is not only due to the loading effect, but also due to the action of the pressure gradient. To calculate the latter, it is important to take into account the stochastic acceleration that suffers at their convection out of the inner heliosphere by the quasi-linear interactions with MHD turbulences. Only then can the presently reported VOYAGER observations of solar wind decelerations and heatings in the outer heliosphere be understood in terms of the current, most likely values of interstellar gas parameters. In a consistent view of the thermodynamics of the solar wind plasma, which is composed of secondary ions and solar wind protons, we also derive that the latter are globally heated at their motion to larger solar distances. The arising heat transfer is due to the action of suprathermal ions which drive MHD waves that are partially absorbed by solar wind protons and thereby establish their observed quasi-polytropy. We obtain a quantitative expression for the solar wind proton pressure as a function of solar distance. This expression clearly shows the change from an adiabatic to a quasi-polytropic behaviour with a decreasing polytropic index at increasing distances, as has been observed by the VOYAGERS. This also allows one to calculate the average percentage of the intitial energy
4. Polar and equatorial coronal hole winds at solar minima: From the heliosphere to the inner corona
Energy Technology Data Exchange (ETDEWEB)
Zhao, L.; Landi, E., E-mail: [email protected] [Department of Atmospheric, Oceanic, and Space Sciences, University of Michigan, Ann Arbor, MI 48105 (United States)
2014-02-01
Fast solar wind can be accelerated from at least two different sources: polar coronal holes and equatorial coronal holes. Little is known about the relationship between the wind coming from these two different latitudes and whether these two subcategories of fast wind evolve in the same way during the solar cycle. Nineteen years of Ulysses observations, from 1990 to 2009, combined with ACE observations from 1998 to the present provide us with in situ measurements of solar wind properties that span two entire solar cycles. These missions provide an ideal data set to study the properties and evolution of the fast solar wind originating from equatorial and polar holes. In this work, we focus on these two types of fast solar wind during the minima between solar cycles 22 and 23 and 23 and 24. We use data from SWICS, SWOOPS, and VHM/FGM on board Ulysses and SWICS, SWEPAM, and MAG on board ACE to analyze the proton kinetic, thermal, and dynamic characteristics, heavy ion composition, and magnetic field properties of these two fast winds. The comparison shows that: (1) their kinetic, thermal, compositional, and magnetic properties are significantly different at any time during the two minima and (2) they respond differently to the changes in solar activity from cycle 23 to 24. These results indicate that equatorial and polar fast solar wind are two separate subcategories of fast wind. We discuss the implications of these results and relate them to remote-sensing measurements of the properties of polar and equatorial coronal holes carried out in the inner corona during these two solar minima.
5. Polar and equatorial coronal hole winds at solar minima: From the heliosphere to the inner corona
International Nuclear Information System (INIS)
Zhao, L.; Landi, E.
2014-01-01
Fast solar wind can be accelerated from at least two different sources: polar coronal holes and equatorial coronal holes. Little is known about the relationship between the wind coming from these two different latitudes and whether these two subcategories of fast wind evolve in the same way during the solar cycle. Nineteen years of Ulysses observations, from 1990 to 2009, combined with ACE observations from 1998 to the present provide us with in situ measurements of solar wind properties that span two entire solar cycles. These missions provide an ideal data set to study the properties and evolution of the fast solar wind originating from equatorial and polar holes. In this work, we focus on these two types of fast solar wind during the minima between solar cycles 22 and 23 and 23 and 24. We use data from SWICS, SWOOPS, and VHM/FGM on board Ulysses and SWICS, SWEPAM, and MAG on board ACE to analyze the proton kinetic, thermal, and dynamic characteristics, heavy ion composition, and magnetic field properties of these two fast winds. The comparison shows that: (1) their kinetic, thermal, compositional, and magnetic properties are significantly different at any time during the two minima and (2) they respond differently to the changes in solar activity from cycle 23 to 24. These results indicate that equatorial and polar fast solar wind are two separate subcategories of fast wind. We discuss the implications of these results and relate them to remote-sensing measurements of the properties of polar and equatorial coronal holes carried out in the inner corona during these two solar minima.
6. RECONSTRUCTING THE SOLAR WIND FROM ITS EARLY HISTORY TO CURRENT EPOCH
Energy Technology Data Exchange (ETDEWEB)
Airapetian, Vladimir S.; Usmanov, Arcadi V., E-mail: [email protected], E-mail: [email protected] [NASA Goddard Space Flight Center, Greenbelt, MD (United States)
2016-02-01
Stellar winds from active solar-type stars can play a crucial role in removal of stellar angular momentum and erosion of planetary atmospheres. However, major wind properties except for mass-loss rates cannot be directly derived from observations. We employed a three-dimensional magnetohydrodynamic Alfvén wave driven solar wind model, ALF3D, to reconstruct the solar wind parameters including the mass-loss rate, terminal velocity, and wind temperature at 0.7, 2, and 4.65 Gyr. Our model treats the wind thermal electrons, protons, and pickup protons as separate fluids and incorporates turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating to properly describe proton and electron temperatures of the solar wind. To study the evolution of the solar wind, we specified three input model parameters, the plasma density, Alfvén wave amplitude, and the strength of the dipole magnetic field at the wind base for each of three solar wind evolution models that are consistent with observational constrains. Our model results show that the velocity of the paleo solar wind was twice as fast, ∼50 times denser and 2 times hotter at 1 AU in the Sun's early history at 0.7 Gyr. The theoretical calculations of mass-loss rate appear to be in agreement with the empirically derived values for stars of various ages. These results can provide realistic constraints for wind dynamic pressures on magnetospheres of (exo)planets around the young Sun and other active stars, which is crucial in realistic assessment of the Joule heating of their ionospheres and corresponding effects of atmospheric erosion.
7. RECONSTRUCTING THE SOLAR WIND FROM ITS EARLY HISTORY TO CURRENT EPOCH
International Nuclear Information System (INIS)
2016-01-01
Stellar winds from active solar-type stars can play a crucial role in removal of stellar angular momentum and erosion of planetary atmospheres. However, major wind properties except for mass-loss rates cannot be directly derived from observations. We employed a three-dimensional magnetohydrodynamic Alfvén wave driven solar wind model, ALF3D, to reconstruct the solar wind parameters including the mass-loss rate, terminal velocity, and wind temperature at 0.7, 2, and 4.65 Gyr. Our model treats the wind thermal electrons, protons, and pickup protons as separate fluids and incorporates turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating to properly describe proton and electron temperatures of the solar wind. To study the evolution of the solar wind, we specified three input model parameters, the plasma density, Alfvén wave amplitude, and the strength of the dipole magnetic field at the wind base for each of three solar wind evolution models that are consistent with observational constrains. Our model results show that the velocity of the paleo solar wind was twice as fast, ∼50 times denser and 2 times hotter at 1 AU in the Sun's early history at 0.7 Gyr. The theoretical calculations of mass-loss rate appear to be in agreement with the empirically derived values for stars of various ages. These results can provide realistic constraints for wind dynamic pressures on magnetospheres of (exo)planets around the young Sun and other active stars, which is crucial in realistic assessment of the Joule heating of their ionospheres and corresponding effects of atmospheric erosion
8. On Lunar Exospheric Column Densities and Solar Wind Access Beyond the Terminator from ROSAT Soft X-Ray Observations of Solar Wind Charge Exchange
Science.gov (United States)
Collier, Michael R.; Snowden, S. L.; Sarantos, M.; Benna, M.; Carter, J. A.; Cravens, T. E.; Farrell, W. M.; Fatemi, S.; Hills, H. Kent; Hodges, R. R.;
2014-01-01
We analyze the Rontgen satellite (ROSAT) position sensitive proportional counter soft X-ray image of the Moon taken on 29 June 1990 by examining the radial profile of the surface brightness in three wedges: two 19 deg wedges (one north and one south) 13-32 deg off the terminator toward the dark side and one wedge 38 deg wide centered on the antisolar direction. The radial profiles of both the north and the south wedges show significant limb brightening that is absent in the 38 deg wide antisolar wedge. An analysis of the soft X-ray intensity increase associated with the limb brightening shows that its magnitude is consistent with that expected due to solar wind charge exchange (SWCX) with the tenuous lunar atmosphere based on lunar exospheric models and hybrid simulation results of solar wind access beyond the terminator. Soft X-ray imaging thus can independently infer the total lunar limb column density including all species, a property that before now has not been measured, and provide a large-scale picture of the solar wind-lunar interaction. Because the SWCX signal appears to be dominated by exospheric species arising from solar wind implantation, this technique can also determine how the exosphere varies with solar wind conditions. Now, along with Mars, Venus, and Earth, the Moon represents another solar system body at which SWCX has been observed.
9. Energy Technology Data Exchange (ETDEWEB)
Pitňa, Alexander; Šafránková, Jana; Němeček, Zdeněk [Charles University, Faculty of Mathematics and Physics, V Holesovickach 2, Prague, CZ-18000 (Czech Republic); Franci, Luca, E-mail: [email protected] [Dipartimento di Fisica e Astronomia, Universita degli Studi di Firenze, I-50125 Firenze (Italy)
2017-07-20
We investigate the decay of magnetic and kinetic energies behind IP shocks with motivation to find a relaxation time when downstream turbulence reaches a usual solar wind value. We start with a case study that introduces computation techniques and quantifies a contribution of kinetic fluctuations to the general energy balance. This part of the study is based on high-time (31 ms) resolution plasma data provided by the Spektr-R spacecraft. On the other hand, a statistical part is based on 92 s Wind plasma and magnetic data and its results confirm theoretically established decay laws for kinetic and magnetic energies. We observe the power-law behavior of the energy decay profiles and we estimated the power-law exponents of both kinetic and magnetic energy decay rates as −1.2. We found that the decay of MHD turbulence does not start immediately after the IP shock ramp and we suggest that the proper decay of turbulence begins when a contribution of the kinetic processes becomes negligible. We support this suggestion with a detailed analysis of the decay of turbulence at the kinetic scale.
10. Majority of Solar Wind Intervals Support Ion-Driven Instabilities
Science.gov (United States)
Klein, K. G.; Alterman, B. L.; Stevens, M. L.; Vech, D.; Kasper, J. C.
2018-05-01
We perform a statistical assessment of solar wind stability at 1 AU against ion sources of free energy using Nyquist's instability criterion. In contrast to typically employed threshold models which consider a single free-energy source, this method includes the effects of proton and He2 + temperature anisotropy with respect to the background magnetic field as well as relative drifts between the proton core, proton beam, and He2 + components on stability. Of 309 randomly selected spectra from the Wind spacecraft, 53.7% are unstable when the ion components are modeled as drifting bi-Maxwellians; only 4.5% of the spectra are unstable to long-wavelength instabilities. A majority of the instabilities occur for spectra where a proton beam is resolved. Nearly all observed instabilities have growth rates γ slower than instrumental and ion-kinetic-scale timescales. Unstable spectra are associated with relatively large He2 + drift speeds and/or a departure of the core proton temperature from isotropy; other parametric dependencies of unstable spectra are also identified.
11. Decay of Solar Wind Turbulence behind Interplanetary Shocks
International Nuclear Information System (INIS)
Pitňa, Alexander; Šafránková, Jana; Němeček, Zdeněk; Franci, Luca
2017-01-01
We investigate the decay of magnetic and kinetic energies behind IP shocks with motivation to find a relaxation time when downstream turbulence reaches a usual solar wind value. We start with a case study that introduces computation techniques and quantifies a contribution of kinetic fluctuations to the general energy balance. This part of the study is based on high-time (31 ms) resolution plasma data provided by the Spektr-R spacecraft. On the other hand, a statistical part is based on 92 s Wind plasma and magnetic data and its results confirm theoretically established decay laws for kinetic and magnetic energies. We observe the power-law behavior of the energy decay profiles and we estimated the power-law exponents of both kinetic and magnetic energy decay rates as −1.2. We found that the decay of MHD turbulence does not start immediately after the IP shock ramp and we suggest that the proper decay of turbulence begins when a contribution of the kinetic processes becomes negligible. We support this suggestion with a detailed analysis of the decay of turbulence at the kinetic scale.
12. INFLUENCE OF THE AMBIENT SOLAR WIND FLOW ON THE PROPAGATION BEHAVIOR OF INTERPLANETARY CORONAL MASS EJECTIONS
Energy Technology Data Exchange (ETDEWEB)
Temmer, Manuela; Rollett, Tanja; Moestl, Christian; Veronig, Astrid M. [Kanzelhoehe Observatory-IGAM, Institute of Physics, University of Graz, Universitaetsplatz 5, A-8010 Graz (Austria); Vrsnak, Bojan [Hvar Observatory, Faculty of Geodesy, University of Zagreb, Kaciceva 26, HR-10000 Zagreb (Croatia); Odstrcil, Dusan [Cooperative Institute for Research in Environmental Sciences, University of Colorado at Boulder, Boulder, CO (United States)
2011-12-20
We study three coronal mass ejection (CME)/interplanetary coronal mass ejection (ICME) events (2008 June 1-6, 2009 February 13-18, and 2010 April 3-5) tracked from Sun to 1 AU in remote-sensing observations of Solar Terrestrial Relations Observatory Heliospheric Imagers and in situ plasma and magnetic field measurements. We focus on the ICME propagation in interplanetary (IP) space that is governed by two forces: the propelling Lorentz force and the drag force. We address the question: which heliospheric distance range does the drag become dominant and the CME adjust to the solar wind flow. To this end, we analyze speed differences between ICMEs and the ambient solar wind flow as a function of distance. The evolution of the ambient solar wind flow is derived from ENLIL three-dimensional MHD model runs using different solar wind models, namely, Wang-Sheeley-Arge and MHD-Around-A-Sphere. Comparing the measured CME kinematics with the solar wind models, we find that the CME speed becomes adjusted to the solar wind speed at very different heliospheric distances in the three events under study: from below 30 R{sub Sun }, to beyond 1 AU, depending on the CME and ambient solar wind characteristics. ENLIL can be used to derive important information about the overall structure of the background solar wind, providing more reliable results during times of low solar activity than during times of high solar activity. The results from this study enable us to obtain greater insight into the forces acting on CMEs over the IP space distance range, which is an important prerequisite for predicting their 1 AU transit times.
13. INFLUENCE OF THE AMBIENT SOLAR WIND FLOW ON THE PROPAGATION BEHAVIOR OF INTERPLANETARY CORONAL MASS EJECTIONS
International Nuclear Information System (INIS)
Temmer, Manuela; Rollett, Tanja; Möstl, Christian; Veronig, Astrid M.; Vršnak, Bojan; Odstrčil, Dusan
2011-01-01
We study three coronal mass ejection (CME)/interplanetary coronal mass ejection (ICME) events (2008 June 1-6, 2009 February 13-18, and 2010 April 3-5) tracked from Sun to 1 AU in remote-sensing observations of Solar Terrestrial Relations Observatory Heliospheric Imagers and in situ plasma and magnetic field measurements. We focus on the ICME propagation in interplanetary (IP) space that is governed by two forces: the propelling Lorentz force and the drag force. We address the question: which heliospheric distance range does the drag become dominant and the CME adjust to the solar wind flow. To this end, we analyze speed differences between ICMEs and the ambient solar wind flow as a function of distance. The evolution of the ambient solar wind flow is derived from ENLIL three-dimensional MHD model runs using different solar wind models, namely, Wang-Sheeley-Arge and MHD-Around-A-Sphere. Comparing the measured CME kinematics with the solar wind models, we find that the CME speed becomes adjusted to the solar wind speed at very different heliospheric distances in the three events under study: from below 30 R ☉ , to beyond 1 AU, depending on the CME and ambient solar wind characteristics. ENLIL can be used to derive important information about the overall structure of the background solar wind, providing more reliable results during times of low solar activity than during times of high solar activity. The results from this study enable us to obtain greater insight into the forces acting on CMEs over the IP space distance range, which is an important prerequisite for predicting their 1 AU transit times.
14. INERTIAL RANGE TURBULENCE OF FAST AND SLOW SOLAR WIND AT 0.72 AU AND SOLAR MINIMUM
Energy Technology Data Exchange (ETDEWEB)
Teodorescu, Eliza; Echim, Marius; Munteanu, Costel [Institute for Space Sciences, Măgurele (Romania); Zhang, Tielong [Space Research Institute, Graz (Austria); Bruno, Roberto [INAF-IAPS, Istituto di Astrofizica e Planetologia Spaziali, Rome (Italy); Kovacs, Peter, E-mail: [email protected] [Geological and Geophysical Institute of Hungary, Budapest (Hungary)
2015-05-10
We investigate Venus Express observations of magnetic field fluctuations performed systematically in the solar wind at 0.72 Astronomical Units (AU), between 2007 and 2009, during the deep minimum of solar cycle 24. The power spectral densities (PSDs) of the magnetic field components have been computed for time intervals that satisfy the data integrity criteria and have been grouped according to the type of wind, fast and slow, defined for speeds larger and smaller, respectively, than 450 km s{sup −1}. The PSDs show higher levels of power for the fast wind than for the slow. The spectral slopes estimated for all PSDs in the frequency range 0.005–0.1 Hz exhibit a normal distribution. The average value of the trace of the spectral matrix is −1.60 for fast solar wind and −1.65 for slow wind. Compared to the corresponding average slopes at 1 AU, the PSDs are shallower at 0.72 AU for slow wind conditions suggesting a steepening of the solar wind spectra between Venus and Earth. No significant time variation trend is observed for the spectral behavior of both the slow and fast wind.
15. Costs of solar and wind power variability for reducing CO2 emissions.
Science.gov (United States)
Lueken, Colleen; Cohen, Gilbert E; Apt, Jay
2012-09-04
We compare the power output from a year of electricity generation data from one solar thermal plant, two solar photovoltaic (PV) arrays, and twenty Electric Reliability Council of Texas (ERCOT) wind farms. The analysis shows that solar PV electricity generation is approximately one hundred times more variable at frequencies on the order of 10(-3) Hz than solar thermal electricity generation, and the variability of wind generation lies between that of solar PV and solar thermal. We calculate the cost of variability of the different solar power sources and wind by using the costs of ancillary services and the energy required to compensate for its variability and intermittency, and the cost of variability per unit of displaced CO(2) emissions. We show the costs of variability are highly dependent on both technology type and capacity factor. California emissions data were used to calculate the cost of variability per unit of displaced CO(2) emissions. Variability cost is greatest for solar PV generation at $8-11 per MWh. The cost of variability for solar thermal generation is$5 per MWh, while that of wind generation in ERCOT was found to be on average $4 per MWh. Variability adds ~$15/tonne CO(2) to the cost of abatement for solar thermal power, $25 for wind, and$33-$40 for PV. 16. Miniature high speed compressor having embedded permanent magnet motor Science.gov (United States) Zhou, Lei (Inventor); Zheng, Liping (Inventor); Chow, Louis (Inventor); Kapat, Jayanta S. (Inventor); Wu, Thomas X. (Inventor); Kota, Krishna M. (Inventor); Li, Xiaoyi (Inventor); Acharya, Dipjyoti (Inventor) 2011-01-01 A high speed centrifugal compressor for compressing fluids includes a permanent magnet synchronous motor (PMSM) having a hollow shaft, the being supported on its ends by ball bearing supports. A permanent magnet core is embedded inside the shaft. A stator with a winding is located radially outward of the shaft. The PMSM includes a rotor including at least one impeller secured to the shaft or integrated with the shaft as a single piece. The rotor is a high rigidity rotor providing a bending mode speed of at least 100,000 RPM which advantageously permits implementation of relatively low-cost ball bearing supports. 17. Acceleration of the Fast Solar Wind through Minor Ions Science.gov (United States) Li, X. 2004-01-01 It is assumed that the magnetic flux tubes are strongly concentrated at the boundaries of the supergranule convection cells. A power law spectrum of high frequency Alfvén waves with a spectral index -1 originating from the sun is assumed to supply all the energy needed to energize the plasma flowing in such magnetic flux tubes. At the high frequency end, the waves are eroded by ions due to ion cyclotron resonance. The magnetic flux concentration is essential since it allows a sufficiently strong energy flux to be carried by high frequency ion cyclotron waves and these waves can be readily released at the coronal base by cyclotron resonance. The main results are: 1. By primarily heating alpha particles only, it is possible to produce a steep transition region, a hot corona and a fast solar wind. Coulomb coupling plays a key role in transferring the thermal energy of alpha particles to protons and electrons at the corona base. The electron thermal conduction then does the remaining job to create a sharp transition region. 2. Plasma species may already partially lose thermal equilibrium in the transition region, minor ions may already be faster than protons at the very bottom of the corona. 3. The model predicts high temperature alpha particles (T 2 × 107 K) and low proton temperatures (Tp solar radii, suggests that hydrogen Lyman lines observed by UVCS above coronal holes may be primarily broadened by Alfvén waves in this range. 18. Regional variations in the health, environmental, and climate benefits of wind and solar generation. Science.gov (United States) Siler-Evans, Kyle; Azevedo, Inês Lima; Morgan, M Granger; Apt, Jay 2013-07-16 When wind or solar energy displace conventional generation, the reduction in emissions varies dramatically across the United States. Although the Southwest has the greatest solar resource, a solar panel in New Jersey displaces significantly more sulfur dioxide, nitrogen oxides, and particulate matter than a panel in Arizona, resulting in 15 times more health and environmental benefits. A wind turbine in West Virginia displaces twice as much carbon dioxide as the same turbine in California. Depending on location, we estimate that the combined health, environmental, and climate benefits from wind or solar range from$10/MWh to \$100/MWh, and the sites with the highest energy output do not yield the greatest social benefits in many cases. We estimate that the social benefits from existing wind farms are roughly 60% higher than the cost of the Production Tax Credit, an important federal subsidy for wind energy. However, that same investment could achieve greater health, environmental, and climate benefits if it were differentiated by region.
19. Latitudinal distribution of the solar wind properties in the low- and high-pressure regimes: Wind observations
Directory of Open Access Journals (Sweden)
C. Lacombe
Full Text Available The solar wind properties depend on λ, the heliomagnetic latitude with respect to the heliospheric current sheet (HCS, more than on the heliographic latitude. We analyse the wind properties observed by Wind at 1 AU during about 2.5 solar rotations in 1995, a period close to the last minimum of solar activity. To determine λ, we use a model of the HCS which we fit to the magnetic sector boundary crossings observed by Wind. We find that the solar wind properties mainly depend on the modulus |λ|. But they also depend on a local parameter, the total pressure (magnetic pressure plus electron and proton thermal pressure. Furthermore, whatever the total pressure, we observe that the plasma properties also depend on the time: the latitudinal gradients of the wind speed and of the proton temperature are not the same before and after the closest HCS crossing. This is a consequence of the dynamical stream interactions. In the low pressure wind, at low |λ|, we find a clear maximum of the density, a clear minimum of the wind speed and of the proton temperature, a weak minimum of the average magnetic field strength, a weak maximum of the average thermal pressure, and a weak maximum of the average β factor. This overdense sheet is embedded in a density halo. The latitudinal thickness is about 5° for the overdense sheet, and 20° for the density halo. The HCS is thus wrapped in an overdense sheet surrounded by a halo, even in the non-compressed solar wind. In the high-pressure wind, the plasma properties are less well ordered as functions of the latitude than in the low-pressure wind; the minimum of the average speed is seen before the HCS crossing. The latitudinal thickness of the high-pressure region is about 20°. Our observations are qualitatively consistent with the numerical model of Pizzo for the deformation of the heliospheric current sheet and plasma sheet.
Key words: Interplanetary physics (solar wind
20. Wind and Solar Energy Role in the Achievement of EU Climate Policy After 2020
International Nuclear Information System (INIS)
Knezevic, S.
2016-01-01
This paper grades the possible role of solar and wind energy in the generation of electricity after 2020. The development of those energy sources will be defined by the climate policy implemented based on the last year's Paris Climate Agreement, but also by the existing initiatives of the European Commission (2030 climate and energy framework and 2050 low-carbon economy). Additionally, electricity generation from RES is observed through the decrease of dependency on the import of fossil fuels outside of the EU. According to the report of the International Renewable Energy Agency (IRENA), the biggest share of RES power plants, after hydro power plants, in EU are wind and solar power plants. Both wind and sun are constantly available resources, but with variable specific power, which makes the maximal generation dependent on the time of day and/or weather (wind, clouds). Future increase of wind and solar energy has to be observed from various perspectives as to properly grade it for the next period, until 2020. Therefore, this paper considers the following, intertwined aspects: Maturity of wind and solar technologies and future trends, Price of electricity generation from wind and solar power plants, with an analysis of price decreasing trends; Possibilities of power energy system and measures for the acceptance of wind and solar power plants; Integrative approach to all forms and transformations of electricity; Market integration of RES - aspirations towards free trade(author).
1. Solar-wind interactions with the Moon: nature and composition of nitrogen compounds
International Nuclear Information System (INIS)
Mukherjee, N.R.
1981-01-01
The lunar atmosphere and magnetic field are very tenuous. The solar wind, therefore, interacts directly with the lunar surface material and the dominant nature of interaction is essentially complete absorption of solar-wind particles by the surface material resulting in no upstream bowshock, but a cavity downstream. The solar-wind nitrogen ion species induce and undergo a complex set of reactions with the elements of lunar material and the solar-wind-derived trapped elements. The nitrogen concentration indigeneous to the lunar surface material is practically nil. Therefore any nitrogen and nitrogen compounds found in the lunar surface material are due to the solar-wind implantation of nitrogen ions. The flux of the solar-wind nitrogen ion species is about 6 X 10 3 cm -2 s -1 . Since there is no evidence for accumulation of nitrogen species in the lunar surface material, the outflux of nitrogen species from the lunar material to the atmosphere is the same as the solar-wind nitrogen ion flux. The species of the outflux are primarily NO and NH 3 , and their respective concentrations in the near surface lunar atmosphere are found to be 327 and 295 cm -3 . (Auth.)
2. Signatures of Slow Solar Wind Streams from Active Regions in the Inner Corona
Science.gov (United States)
Slemzin, V.; Harra, L.; Urnov, A.; Kuzin, S.; Goryaev, F.; Berghmans, D.
2013-08-01
The identification of solar-wind sources is an important question in solar physics. The existing solar-wind models ( e.g., the Wang-Sheeley-Arge model) provide the approximate locations of the solar wind sources based on magnetic field extrapolations. It has been suggested recently that plasma outflows observed at the edges of active regions may be a source of the slow solar wind. To explore this we analyze an isolated active region (AR) adjacent to small coronal hole (CH) in July/August 2009. On 1 August, Hinode/EUV Imaging Spectrometer observations showed two compact outflow regions in the corona. Coronal rays were observed above the active-region coronal hole (ARCH) region on the eastern limb on 31 July by STEREO-A/EUVI and at the western limb on 7 August by CORONAS- Photon/TESIS telescopes. In both cases the coronal rays were co-aligned with open magnetic-field lines given by the potential field source surface model, which expanded into the streamer. The solar-wind parameters measured by STEREO-B, ACE, Wind, and STEREO-A confirmed the identification of the ARCH as a source region of the slow solar wind. The results of the study support the suggestion that coronal rays can represent signatures of outflows from ARs propagating in the inner corona along open field lines into the heliosphere.
3. An illustrative note on the system price effect of wind and solar power. The German case
International Nuclear Information System (INIS)
Jaegemann, Cosima
2014-01-01
Exposing wind and solar power to the market price signal allows for cost-efficient investment decisions, as it incentivizes investors to account for the marginal value (MV el ) of renewable energy technologies. As shown by Lamont (2008), the MV el of wind and solar power units depends on their penetration level. More specifically, the MV el of wind and solar power units is a function of the respective unit's capacity factor and the covariance between its generation profile and the system marginal costs. The latter component of the MV el (i.e., the covariance) is found to decline as the wind and solar power penetration increases, displacing dispatchable power plants with higher short-run marginal costs of power production and thus reducing the system marginal costs in all generation hours. This so called 'system price effect' is analyzed in more detail in this paper. The analysis complements the work Lamont (2008) in two regards. First of all, an alternative expression for the MV el of wind and solar power units is derived, which shows that the MV el of fluctuating renewable energy technologies depends not only on their own penetration level but also on a variety of other parameters that are specific to the electricity system. Second, based on historical wholesale prices and wind and solar power generation data for Germany, a numerical 'ceteris paribus' example for Germany is presented which illustrates that the system price effect is already highly relevant for both wind and solar power generation in Germany.
4. Solar wind and coronal structure near sunspot minimum - Pioneer and SMM observations from 1985-1987
Science.gov (United States)
Mihalov, J. D.; Barnes, A.; Hundhausen, A. J.; Smith, E. J.
1990-01-01
Changes in solar wind speed and magnetic polarity observed at the Pioneer spacecraft are discussed here in terms of the changing magnetic geometry implied by SMM coronagraph observations over the period 1985-1987. The pattern of recurrent solar wind streams, the long-term average speed, and the sector polarity of the interplanetary magnetic field all changed in a manner suggesting both a temporal variation, and a changing dependence on heliographic latitude. Coronal observations during this epoch show a systematic variation in coronal structure and the magnetic structure imposed on the expanding solar wind. These observations suggest interpretation of the solar wind speed variations in terms of the familiar model where the speed increases with distance from a nearly flat interplanetary current sheet, and where this current sheet becomes aligned with the solar equatorial plane as sunspot minimum approaches, but deviates rapidly from that orientation after minimum.
5. Thermodynamic characteristics of a novel wind-solar-liquid air energy storage system
Science.gov (United States)
Ji, W.; Zhou, Y.; Sun, Y.; Zhang, W.; Pan, C. Z.; Wang, J. J.
2017-12-01
Due to the nature of fluctuation and intermittency, the utilization of wind and solar power will bring a huge impact to the power grid management. Therefore a novel hybrid wind-solar-liquid air energy storage (WS-LAES) system was proposed. In this system, wind and solar power are stored in the form of liquid air by cryogenic liquefaction technology and thermal energy by solar thermal collector, respectively. Owing to the high density of liquid air, the system has a large storage capacity and no geographic constraints. The WS-LAES system can store unstable wind and solar power for a stable output of electric energy and hot water. Moreover, a thermodynamic analysis was carried out to investigate the best system performance. The result shows that the increases of compressor adiabatic efficiency, turbine inlet pressure and inlet temperature all have a beneficial effect.
6. Assessment of solar and wind energy potentials for three free economic and industrial zones of Iran
International Nuclear Information System (INIS)
Mohammadi, Kasra; Mostafaeipour, Ali; Sabzpooshani, Majid
2014-01-01
This paper aims to evaluate the potential of renewable energy sources of solar and wind in three free economic and industrial zones of Chabahar, Kish and Salafchegan in Iran. Feasibility of harnessing solar energy was investigated by using key solar parameters like monthly mean global, beam and diffuse solar radiation as well as clearness index. It was found that all locations had great potentials for utilizing different solar | {"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": 0.8979652523994446, "perplexity": 2448.174278920793}, "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/1531676589757.30/warc/CC-MAIN-20180717164437-20180717184437-00079.warc.gz"} |
http://www.nag.com/numeric/cl/nagdoc_cl23/html/G08/g08cjc.html | nag_anderson_darling_uniform_prob (g08cjc) (PDF version)
g08 Chapter Contents
g08 Chapter Introduction
NAG C Library Manual
# NAG Library Function Documentnag_anderson_darling_uniform_prob (g08cjc)
## 1 Purpose
nag_anderson_darling_uniform_prob (g08cjc) calculates the Anderson–Darling goodness-of-fit test statistic and its probability for the case of standard uniformly distributed data.
## 2 Specification
#include #include
void nag_anderson_darling_uniform_prob (Integer n, Nag_Boolean issort, double y[], double *a2, double *p, NagError *fail)
## 3 Description
Calculates the Anderson–Darling test statistic ${A}^{2}$ (see nag_anderson_darling_stat (g08chc)) and its upper tail probability by using the approximation method of Marsaglia and Marsaglia (2004) for the case of uniformly distributed data.
## 4 References
Anderson T W and Darling D A (1952) Asymptotic theory of certain ‘goodness-of-fit’ criteria based on stochastic processes Annals of Mathematical Statistics 23 193–212
Marsaglia G and Marsaglia J (2004) Evaluating the Anderson–Darling distribution J. Statist. Software 9(2)
## 5 Arguments
1: nIntegerInput
On entry: $n$, the number of observations.
Constraint: ${\mathbf{n}}>1$.
2: issortNag_BooleanInput
On entry: set ${\mathbf{issort}}=\mathrm{Nag_TRUE}$ if the observations are sorted in ascending order; otherwise the function will sort the observations.
3: y[n]doubleInput/Output
On entry: ${y}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$, the $n$ observations.
On exit: if ${\mathbf{issort}}=\mathrm{Nag_FALSE}$, the data sorted in ascending order; otherwise the array is unchanged.
Constraint: if ${\mathbf{issort}}=\mathrm{Nag_TRUE}$, the values must be sorted in ascending order. Each ${y}_{i}$ must lie in the interval $\left(0,1\right)$.
4: a2double *Output
On exit: ${A}^{2}$, the Anderson–Darling test statistic.
5: pdouble *Output
On exit: $p$, the upper tail probability for ${A}^{2}$.
6: failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).
## 6 Error Indicators and Warnings
NE_BAD_PARAM
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_BOUND
The data in y must lie in the interval $\left(0,1\right)$.
NE_INT
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}>1$.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_NOT_INCREASING
${\mathbf{issort}}=\mathrm{Nag_TRUE}$ and the data in y is not sorted in ascending order.
## 7 Accuracy
Probabilities greater than approximately $0.09$ are accurate to five decimal places; lower value probabilities are accurate to six decimal places.
None.
## 9 Example
This example calculates the ${A}^{2}$ statistic and its $p$-value for uniform data obtained by transforming exponential variates.
### 9.1 Program Text
Program Text (g08cjce.c)
### 9.2 Program Data
Program Data (g08cjce.d)
### 9.3 Program Results
Program Results (g08cjce.r)
nag_anderson_darling_uniform_prob (g08cjc) (PDF version)
g08 Chapter Contents
g08 Chapter Introduction
NAG C Library Manual | {"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": 0.9843617677688599, "perplexity": 4983.425911724022}, "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-2015-11/segments/1424936464123.82/warc/CC-MAIN-20150226074104-00322-ip-10-28-5-156.ec2.internal.warc.gz"} |
http://matrixmaths.blogspot.com/ | ## Thursday, March 5, 2009
### QS 026 Permutation & Combination : Combinations
A general concept about combination is counting a number of possibility without replacing and most importantly, the arrangements don't matter.
Let's watch this useful video, may it helps you perceive combination better...
## Friday, February 27, 2009
### QS026 Permutation & Combination : Factorial
This is another basic principle a student must possess before going deeper into the Permutations and Combination chapter. View this video for further explanation.
After understanding this fundamental, we will learn better about Permutation & Combination
## Sunday, February 8, 2009
### QS026 Numerical Method - Newton Raphson Method
This method is used to approximate a certain root of an equation. This is done by find it's derivative and putting it in
Technically this is a tedious method with repetition of numerical computation. Students tends to make mistake. However with the usage of "Calculate" option in today's scientific calculator, mistakes can be minimize.
Basically we need to approximate the initial value and hope that the value will be reduced to the root instead of converging.
Please see this useful video on Newton-Raphson Method...
### QS026 Numerical Method - Trapezium Rule
In this first sub-topic of Chapter 7, basically matriculation students are exposed to an alternative numerical method to find the area under a certain graph. Normally we would use integration as the fastest and more accurate way of finding area under the graph.
Trapezium rule however, introduce an alternative where we actually break the area under the graph into several trapezium. Instead of integrating, we add all those trapezium areas together to sums up the equivalent area under the graph.
Remember the value gained does not necessarily be the same as trapezium rule actually gets the approximate area under the graph only. Interesting method nonetheless and the easier way for some functions that has difficult integrations.
This video will give you better step-by-step explanation.
## Saturday, February 7, 2009
### QS026 Differential Equations - Integrating Factor
If a First Order Linear Equation can't be separated, then comes the Differential using the Integrating Factor:
• Identify the integrating factor.
• Multiply both sides of the equation with the integrating factor, then;
• Integrate both sides of the equation.
Observe the video for better explanation.
There you have it, two noticable techniques in Differential Equation in Chapter 6 of QS026 Matriculation Mathematics.
### QS026 Differential Equations - Separable Variable
Basic Concept of Separable Variable is:
• The equations should be able to be separated to two different sides then,
• Integrate...
It's that simple...
See? Very easy...
Good Luck
## Thursday, December 25, 2008
### Vector Project
I am currently working on a project involving the topic Vector. I am working on a teaching aid that will help students visualize plane equations in vector.
I am well aware that Hayat students have difficulty in visualizing the problems involving planes in vector thus making me more determine to come up with this universal teaching aid that can be manipulated to help students visualize vector better.
I am afraid I can't reveal as yet as it is still under development stage. I hope as soon as it finishes and I will have the opportunity to present this innovative creation then I will share them here. For the time being...enjoy this comprehensive video about Vector.
Nice presentation by the way. Should help student understand vector better. | {"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": 0.8310647010803223, "perplexity": 1480.1417740087256}, "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/1469258943369.84/warc/CC-MAIN-20160723072903-00275-ip-10-185-27-174.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/116684/maintaining-the-line-with-the-2d-iterands | Maintaining the line with the 2D iterands
Suppose a linear system is given $$AX=B,$$ where $A\in\mathbb{R}^{n\times n}$ is a symmetric strictly diagonal matrix, and $X, B\in\mathbb{R}^{n\times 2}$. Therefore, the 2D Jacobi iterative solver is applicable here, $$X_{k+1}=D^{-1}(B-RX_k),$$ where the splitting corresponds to $A=D+R$, with $D$ containing only the diagonal entries of $A$. Could it be proved that the iterands $X_0, X_1, X_2, \dots$ are maintaining the line per each row of $X$, meaning that, for $x^i\in\mathbb{R}^2$ being the $i-$th row of $X$, the rows in sequence $x^i_0, x^i_1, x^i_2, \dots$, are colinear (on one line)?
-
This was cross posted at scicomp: http://scicomp.stackexchange.com/questions/1558/2d-jacobi-line-maintenance – Victor Liu Mar 7 '12 at 20:12
Yes; I thought about migrating it, but did not manage to do so. Perhaps certain linking by moderators? – user506901 Mar 8 '12 at 7:47 | {"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": 0.96468186378479, "perplexity": 523.5147080280318}, "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-2014-52/segments/1418802765678.46/warc/CC-MAIN-20141217075245-00024-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://www.lessonplanet.com/teachers/batty-the-bat | # Batty the Bat
Young readers read a short paragraph about Batty the bat. They then answer four fill in the blank statements, and write a sentence about a bat before drawing a picture of a bat. | {"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": 0.8257136940956116, "perplexity": 2252.0952065428846}, "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/1500549424247.30/warc/CC-MAIN-20170723042657-20170723062657-00077.warc.gz"} |
https://fr.maplesoft.com/support/help/maple/view.aspx?path=StudyGuides%2FMultivariateCalculus%2FChapter8%2FExamples%2FSection8-1%2FExample8-1-25 | Example 8-1-25 - Maple Help
Chapter 8: Applications of Triple Integration
Section 8.1: Volume
Example 8.1.25
Use an iterated triple integral to obtain the volume of $R$, the region bounded above by the sphere ${x}^{2}+{y}^{2}+{z}^{2}=6$, and below by the paraboloid $z={x}^{2}+{y}^{2}$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 98, "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": 0.9631304740905762, "perplexity": 563.4579608969991}, "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/1664030334992.20/warc/CC-MAIN-20220927064738-20220927094738-00250.warc.gz"} |
http://www.mathisfunforum.com/post.php?tid=16391&qid=189861 | Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
You are not logged in.
|
Options
bobbym
2011-09-13 07:22:34
Hi;
I can use it a lot easier than explain it. Here is the site that taught me.
http://2000clicks.com/MathHelp/IneqMuir … ality.aspx
anonimnystefy
2011-09-13 06:47:58
bobbym
2011-09-13 03:41:43
Hi all;
bobbym
2011-09-12 06:46:21
Hi;
why not?
Try a = 2, b = 2, c = 1.
I think this is where your error is.
You are okay after A)
It was a pretty good idea though.
anonimnystefy
2011-09-12 06:43:28
why not?
bobbym
2011-09-12 06:42:03
Hi;
This statement is not true under the conditions of the problem.
anonimnystefy
2011-09-12 06:31:20
hi guys
is this correct for (3):
bobbym
2011-09-12 06:06:04
It is okay. I am not sure about the problem either.
bob bundy
2011-09-12 05:15:52
Ok, my mistake.
Bob
bobbym
2011-09-12 04:38:06
Hi Bob;
Positive numbers a,b, and c satisfy the inequality a+b+c>= abc. Prove that a^2+b^2+c^2>=(abc)^2
because that is do-able.
Not if you have
a = 2, b = 5 / 4, c = 2
a = 3, b = 1, c = 2
I am fairly sure the original problem #3 is true.
bob bundy
2011-09-12 04:29:28
This is for grade 9 and the other two were fairly straight forward. Could the question be:
Positive numbers a,b, and c satisfy the inequality a+b+c>= abc. Prove that a^2+b^2+c^2>=(abc)^2
because that is do-able.
Bob
bobbym
2011-09-11 22:13:11
Hi;
A little help.
3) Positive numbers a,b, and c satisfy the inequality a+b+c>= abc. Prove that a^2+b^2+c^2>=abc
Therefore it is not mandatory that this can be done by the AMGM.
bob bundy
2011-09-10 18:22:38
hi again,
(2) Like this:
and
So put these together and you get what you wanted.
Now for (3). edit: Many hours later. I cannot do this one yet. I've put out a general request for more brains.
Bob
bob bundy
2011-09-10 18:09:06
hi fromwoodhouse,
Here's my proof for (1)
Consider the case m ≥ 0
In that case treat |m| as just m
but we know from the case that m and 1 + m > 0 so
Now consider the alternative case that m < 0
That means we can replace |m| with -m
this time we know 1 - m > 0 as m < 0 so
If a product is negative then one factor must be + and one must be - so
either m > 0 and (m + 1) < 0 but this contradicts the assumption that m < 0
or m < 0 and (m + 1) > 0 which leads to -1 < m < 0
Now to look at number (2). See next post.
Hope that helps
Bob
2011-09-10 02:22:03
#### fromwodehouse wrote:
1) Prove: if n<0 and |m|= m-n/m+n , -1<m<0 or m>1
2) Given m = 4-x/3, n = x+3/4, p = 2-3x/5 , and m>n>p
Prove that the possible value of x is {-7/17<x<1}
fromwodehouse,
because of the Order of Operations,
you must use grouping symbols for these: | {"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": 0.8757134079933167, "perplexity": 3878.1866888383993}, "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-2014-15/segments/1397609538423.10/warc/CC-MAIN-20140416005218-00197-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/sunny-morning-eld-atmospheric-pressure-10n-m-temperature-279-k-lm-crew-lled-balloon-1000m3-q2605161 | On a sunny morning in a ?eld, the atmospheric pressure is 10N/m and the
temperature is 279 K. The ?lm crew has ?lled a balloon with 1000m3 of preheated
air at atmospheric pressure and a temperature of 300 K. The mass of the empty
balloon and its load is 240 Kg. Under these conditions, the balloon rises above its
burden, but the airship remains grounded. To begin the ascent, the air within the
balloon is brought to a higher temperature. It expands but remains at the pressure
of 105 N/m2 . No air enters or leaves the balloon. How much heat must be added to
the air in the balloon to initiate the ?ight? | {"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": 0.8358411192893982, "perplexity": 1670.0338388140444}, "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-2016-22/segments/1464050960463.61/warc/CC-MAIN-20160524004920-00150-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://www.semanticscholar.org/paper/Two-Connected-Spanning-Subgraphs-with-at-Most-Edges-Heeger-Vygen/c8399fc9ba40789d03cf32a5f79f5f35f5221a39 | # Two-Connected Spanning Subgraphs with at Most $\frac{10}{7}{OPT}$ Edges
@article{Heeger2017TwoConnectedSS,
title={Two-Connected Spanning Subgraphs with at Most \$\frac\{10\}\{7\}\{OPT\}\$ Edges},
author={Klaus Heeger and Jens Vygen},
journal={SIAM J. Discret. Math.},
year={2017},
volume={31},
pages={1820-1835}
}
• Published 1 September 2016
• Mathematics
• SIAM J. Discret. Math.
We present a $\frac{10}{7}$-approximation algorithm for the minimum two-vertex-connected spanning subgraph problem.
3 Citations
## Figures from this paper
A 4/3-Approximation Algorithm for the Minimum 2-Edge Connected Subgraph Problem
• Mathematics, Computer Science
ACM Trans. Algorithms
• 2019
A factor 4/3 approximation algorithm for the problem of finding a minimum 2-edge connected spanning subgraph of a given undirected multigraph, based upon a reduction to a restricted class of graphs.
An Upper Bound of 7n/6 for the Minimum Size 2EC on Cubic 3-Edge Connected Graphs
It is shown that every 3-edge connected cubic graph G=(V, E), with n=|V| allows a 2EC solution for G of size at most 7n/6, which improves upon Boyd, Iwata and Takazawa's guarantee of 6n/5.
Beating the Integrality Ratio for s-t-Tours in Graphs
• Computer Science
2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
• 2018
This paper devise a polynomial-time algorithm for the s-t-path graph TSP with approximation ratio 1.497 and introduces several completely new techniques, including a new type of ear-decomposition, an enhanced ear induction that reveals a novel connection to matroid union, a stronger lower bound, and a reduction of general instances to instances in which s and t have small distance.
## References
SHOWING 1-10 OF 19 REFERENCES
Improving on the 1.5-Approximation of a Smallest 2-Edge Connected Spanning Subgraph
• Mathematics, Computer Science
SIAM J. Discret. Math.
• 2001
We give a $\frac{17}{12}$-approximation algorithm for the following NP-hard problem: Given a simple undirected graph, find a 2-edge connected spanning subgraph that has the minimum number of edges.
Approximation Algorithms for the Minimum Cardinality Two-Connected Spanning Subgraph Problem
• Computer Science, Mathematics
IPCO
• 2005
The minimum cardinality 2-connected spanning subgraph problem is considered. An approximation algorithm with a performance ratio of 9/7 ≈ 1.286 is presented. This improves the previous best ratio of
A 5/4-approximation algorithm for minimum 2-edge-connectivity
• Computer Science
SODA '03
• 2003
A 5/4-approximation algorithm is presented for the minimum cardinality 2-edge-connected spanning subgraph problem in undirected graphs and is shown that the ratio is tight with respect to current lower bounds, and any further improvement is possible only if new lower bounds are discovered.
Improved approximation algorithms for biconnected subgraphs via better lower bounding techniques
• Computer Science, Mathematics
SODA '93
• 1993
Better techniques to lower bound the size of the minimum subgraphs are provided, which allows us to achieve approximation factors of a and \$ respectively, thereby improving on existing algorithms that achieve NP-hard results.
Improving biconnectivity approximation via local optimization
• Computer Science
SODA '96
• 1996
This paper presents a new technique which can be used to further improve parallel approximation factors to 5/3 + {epsilon}, and reveals an algorithm with a factor of {alpha} + 1/5, where a is the approximation factor of any 2-edge connectivity approximation algorithm.
Approximating minimum-size k-connected spanning subgraphs via matching
• Mathematics
Proceedings of 37th Conference on Foundations of Computer Science
• 1996
An efficient heuristic is presented for the problem of finding a minimum-size k-connected spanning subgraph of a given graph G=(V,E), which is simple, deterministic, and runs in time O(k|E|/sup 2/).
Shorter tours by nicer ears: 7/5-approximation for the graph-TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs
• Computer Science, Mathematics
ArXiv
• 2012
The key new ingredient of all algorithms is a special kind of ear-decomposition optimized using forest representations of hypergraphs that provides the lower bounds that are used to deduce the approximation ratios.
On approximability of the minimum-cost k-connected spanning subgraph problem
• Mathematics
SODA '99
• 1999
This work provides the first proof that Vfnhing a PTAS for the k-vertex-connectivitv nroblem in unweiehted graphs is NP-hard even for k = 2 aid for graphs of bocnded degree, and shows that the algorithmic results for Euclidean graphs cannot be extended to arbitrarily high dimensions.
Problems in graph connectivity
• Mathematics, Computer Science
• 2006
This thesis presents different approximation algorithms for edge connectivity and vertex connectivity problems and discusses the average- k-VCSS problem and average-k-ECSS problem, which deal with finding k-connected spanning subgraphs of minimum average weight.
Biconnectivity approximations and graph carvings
• Computer Science, Mathematics
STOC '92
• 1992
This work considers the problem of finding an approximation to the smallest 2-connected subgraph, by an efficient algorithm, and shows that an approximation factor of 2 is possible in polynomial time for finding a k-edge connected spanning subgraph. | {"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": 0.88430255651474, "perplexity": 2251.6972105092304}, "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-2022-21/segments/1652663016853.88/warc/CC-MAIN-20220528123744-20220528153744-00408.warc.gz"} |
http://math.stackexchange.com/questions/251225/find-correlation-of-x-and-y-given-eyx-and-exy | # Find correlation of x and y, given E(Y|X) and E(X|Y)
Suppose that X and Y are random variables such that E(Y | X) = 7 - (1/4)x and E(X | Y) = 10 - Y . Determine the correlation of X and Y .
Edit:
So far I've got
E(x)=4 E(y)=6
Now I'm trying to find
E(xy) to use in cov(x,y)=E(xy)-E(x)E(y)
V(x)
V(y)
all to use in cor(x,y)=cov(x,y)/(v(x)v(y))^.5
-
Correlation as measured by...? – Xodarap Dec 5 '12 at 3:15
cor(x,y) = cov(x,y) / (v(x)v(y))^.5 ...Im not sure I understand your question though – Dan Dec 5 '12 at 3:20
Pearson's is a fine way to define correlation; it's just not the only way. – Xodarap Dec 5 '12 at 3:22
Hint: $E[Y\mid X]$ is the minimum-mean-square-error estimator of $Y$ given the value of $X$. The linear minimum-mean-square-error estimator of $Y$ given the value of $X$ is
$$\hat{Y} = \mu_Y + \frac{\rho\sigma_Y}{\sigma_X}(X-\mu_X).$$
Similar statements apply to $E[X\mid Y]$ etc. Just interchange $X$ and $Y$ in the above formulas.
Now, if $E[Y\mid X]$ is a linear function of $X$ and $E[X\mid Y]$ is a linear function of $Y$, can you use the known forms of the linear minimum-mean-square-error estimators to deduce the value of $\rho$?
-
yeah Ive found E(y)=6. Any other hints? – Dan Dec 5 '12 at 3:28
You don't need to find $E[Y]$ or $E[X]$. Hint: show that the coefficients of $X$ and $Y$ in the equations given to you are $\rho\sigma_Y/\sigma_X$ and $\rho\sigma_X/\sigma_Y$ and use the information given to you to deduce that $\rho=0.5$ without needing to find $E[X]$ or $E[Y]$ or $\text{var}(X)$ or $\text{var}(Y)$ or $\text{cov}(X,Y)$ or $E[XY]$. – Dilip Sarwate Dec 5 '12 at 3:35
@DilipSarwate (+1), but I think you meant to write $\rho = -1/2$ in your comment. – r.e.s. Dec 5 '12 at 4:16
@r.e.s. Yes, you are correct. I realized that I had neglected to take the sign of $\rho$ into account after it was too late to edit the comment and was going to write a further comment. Thanks for the upvote. – Dilip Sarwate Dec 5 '12 at 11:25 | {"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": 0.8745031952857971, "perplexity": 330.07036898890624}, "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-2014-52/segments/1418802768497.135/warc/CC-MAIN-20141217075248-00129-ip-10-231-17-201.ec2.internal.warc.gz"} |
http://deboragemin.it/wxlj/volume-of-a-trapezoid-calculator.html | So to calculate the volume of trapezoidal footing we need to calculate the volume of a cuboid and a truncated pyramid. Mathematical Handbook of Formulas and Tables. 6 m3 CSTRs are usually used for liquid-phase rxns. If the box has internal measurements of 6" high*18" wide*12" deep then the volume of the box is 1296/1728=. Calculated Volume of Trapezoid = (1/3) *(4+1+√(4 x1)) = 2. 333 Cubic Meters. Read it carefully for a better understanding of calculation. The volume calculator supports numeric but also literal expressions. Use this volume of a trapezoidal prism calculator to find the volume by providing the prism area, length of top, height of the prism and trapezoidal. Required angular riprap size, D50, per Searcy (1967) Required angular riprap size, D50, per Searcy (1967). Property #1) The angles on the same side of a leg are called adjacent angles and are supplementary ( more ) Property #2) Area of a Trapezoid =. A rhombus refers to a quadrilateral having two simultaneous characteristics: sides are all equal AND the opposite sides are parallel. (2) Its length equals half the sum of the base lengths. The Isosceles Trapezoids is a quadrilateral with two non parallel sides equal and two parallel sides unequal. The final number is represented as a squared number. If the prism length is L,trapezoid base width B, trapezoid top width A, and trapezoid height H, then the volume of the prism is given by the four-variable formula: V(L, B, A, H) = LH(A + B)/2. Example: Calculate volume to achieve 80 % conversion in CSTR. Volume Calculator Enter the approximate length and width of the shape you want to cover, then the desired depth (standard depth for mulch is 3"), then click Calculate. Area Calculation results are then considered for Volume Computation (Quantity Takeoff). 8 ⎛ ⎞ − = 3 3 0 0. The trapezoids hug the curve better than left- or right- hand rule rectangles and so gives you a better estimate of the area. Show Instructions In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. In this formula, b 1 and b 2 are the base of the trapezoid. Volume of a cylinder formula. To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then. volume of trapezoidal prism and unit conversion of answer - Duration: 7:00. Maximize Area of Trapezoid Date: 07/28/2003 at 09:35:34 From: Jupe Subject: Find d so that the area is maximum Given an isosceles trapezoid with three of its sides of length 10 cm: d cm +-----+ \ / 10 cm \ / 10 cm \ / \ / +-----+ 10 cm find d so that the area is maximum. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Hydraulic radius of a trapezoidal channel:. While the left-hand rule, the right-hand rule and the midpoint rule use rectangles, The trapezoid rule uses trapezoids. Hello, I'm preparing for a presentation about solids of revolution. The weir opening has a flat bottom and sides that have a particular slope. That detention pond would be a good example of a trapezoidal prism: V = H/2 * h(a + b) where H is the height of the prism, h is the height of the trapezoid and a and b are the two bases of the trapezoid. 5)(15)= 787. we have been written the java code in three to four different formats. 99 USD per year until cancelled $19. diagonals, lateral side (height) and angle between the diagonals 4. Calculators Caltrans AVSF Volumes Channel - Grass Lining Channel - Riprap Lining Channel - Trapezoidal Circular Pipe Culvert Inlet Control HEC-14 Riprap Apron HEC-22 Gutter Spread HEC-22 Inlet Interception Capacity Sphere Trapezoidal Basin Volume. So, plug in the area and the height to the equation for A and H and then multiply these two together. Using this calculator, we will understand methods of how to find the surface area and volume of the hemisphere. Find the area of just the trapezoidal face A = 1 2h(b1+b2), then multiply it by the length of the entire prism. This python program allows the user to enter both sides of the Trapezoid and height. As we mentioned earlier in the article, it is the height of the trapezoid. A shape known as a Trapezoid in North America or a Trapezium in the rest of the English speaking world, can come in many shapes, but has to have at least one pair of parallel running sides. 1st method: Spreadsheet calculations. Four cylinder volume calculators based on radius or diameter in metres and centimetres. Using height, angles at the base and sides 4. We can find the median length of a trapezoid by using this below formula:. The following formula calculates the circumference of a circle using a cell named diameter: =diameter*PI() The diameter of a circle is the radius times 2. This trapezoid calculator will compute the area of a trapezoid for you. Trapezoidal prism-surface area and volume youtube. This method is mainly applicable to estimate the area under a curve by splitting the entire area into a number of. Knowing that the trapezoid is half the height of the triangle, calculate the area of the trapezoid. a table of area formulas and perimeter formulas used to calculate the area and perimeter of two-dimensional geometrical shapes: square, rectangle. Its volume is the area of the trapezoid ABCD times the length. Using the trapezoidal rule with four function values, estimate the volume of the cone. 2) Calculate the volume of composite shapes. Thus the volume of the ditch is. Math Calculators. To understand how to calculate square footage we must first begin with the definition of area. The area of the trapezoid is calculated using the formula from the upper base and lower base and height. State your answer in cubic units. Geometry/Plane. How To Calculate Concrete Volume For Retaining Wall: Retaining wall is a masonry wall constructed to resist the pressure of liquid, earth filling, sand or other granular material filled behind it. This article contains a collection of calculators for calculating geometric figures volume. You also can create a Volume Surface and read the volumes from the Statistics Tab in the surface propoerties. Alternatively, I can find the area of the entire shape (16 x 12) then subtract the missing piece (in pink) from the larger piece. Example #2. The volume and surface area – these are typically what need calculating when a triangular prism is concerned. Our calculators are simple to use, enter the input values and click calculate button to get the answer instantly. The SI unit for volume is the cubic meter, or m3. 5* h * (a + b) How to use the calculator Enter the sides a and b and the height h of the trapezoid as positive real numbers and press "calculate". Therefore, the other two angles must total 180 degrees as well. Free Trapezoid Sides & Angles Calculator - Calculate sides, angles of an trapezoid step-by-step This website uses cookies to ensure you get the best experience. The formula for the volume of trapezoidal prism is volume=Hh(b1+b2)/2. Formula for Volume of a Trapezoidal Prism. Then multiply that by the length l=26. Good Study Habits. The calculation essentially relies on the fact a trapezoid's area can be equated to that of a rectangle: (base 1 + base 2) / 2 is actually the width of a rectangle with an equivalent area. Find the volume of the prism if its length is 10 inches. Cipolletti (Trapezoidal) Weir. For example, in a fish tank, it's the number of gallons of water the tank holds. A trapezoid is defined as having 4 sides and at least one pair of parallel sides. 5 5 1 91% of 32 84 pshp. For example, if we have an acre pond with an average depth of 5 feet, and an overflow rate of 10 gallons per minute, our residence time would be: 226 (5) / (10) = 113 days. Trapezoidal Rule integration works by approximating the region under the graph of a function as a trapezoid, and it calculates the area. Surface area of rhombus Knowing the angle a : Rhombus. You want to know the volume for certain surface ond/or area in Autodesk® AutoCAD® Civil 3D®. To find the area of a compound shape, follow these simple steps: Step 1: Work out the. Supporters: Online Education - comprehensive directory of online education programs and college degrees. And I wondered if I can find any practical applications in the real world for this. This calculator determines the flow rate for a Cipolletti weir, which is a commonly used weir in many irrigation districts. Four cylinder volume calculators based on radius or diameter in metres and centimetres. Trapezoidal Volume Calculation Formula. Let the lengths of the both parallel sides of a trapezoid be a and b and the distance between them is h (the trapezoid altitude). Lower case h is the height of the trapezoid, and upper case H is. (A + B = 18 feet). You can use these calculations to determine that here. parallelogram, trapezoid (trapezium), triangle, rhombus, kite, regular polygon, circle, and ellipse. Enter value and select a conversion from the buttons below and result will be displayed. Take the volume of that cone and subtract the volume of the cone that is part of the "trapezoidal cylinder". Numerical Evaluation of. The trapezoidal footing formula is used to determine the volume of a trapezoidal footing from the respective drawing specifications. A trapezoid is a 4-sided figure with one pair of parallel sides. printable worksheets > measurement worksheets. Typical values for density are provided, but may be changed to accommodate more specific materials. diagonals, lateral side (height) and angle between the diagonals 4. Calculate the volume, height, length, or base of a partially filled trapezoid shaped tank. Surface Area of a Trapezoidal Prism Calculator. a more detailed explanation (in text and video) of each area formula. The below formula has used for calculating the volume of the trapezoidal footing. A general formula is volume = length * base_area; the one parameter you always need to have given is the prism length, and there are four ways to calculate the base - triangle area. Enter radiuses and height and choose the number of decimal places. The depth of the hole is to be 4. Fish Tank Calculator for Volume. Math Calculators Use our free online math calculators to evaluate, convert, verify and solve your math questions easily. You can use these calculations to determine that here. volume of trapezoidal prism and unit conversion of answer - Duration: 7:00. The formula for finding the area of a trapezoid is 1/2(a+b)h, or the length of the top added to the length of the bottom, divided in half and then multiplied by the height of the trapezoid. There are a great many physical quantities subject to measurement for which there most certainly is an underlying well-defined function. If we consider one of the trapezoid side walls as base, the height of the prism would be 22 cm. A 2 - Cross section area of second side. The Egyptian Triumph: The Volume of an Incomplete Pyramid. A trapezoid is a geometric figure with 4 sides that has 2 parallel sides. The most basic two equations are as followed: Volume = 0. Surface Areas. I know how to find volume and I know how to use trapezoid rule but I have no idea how to combine them. The methodology for the flume calculations follows that of ISO 9826 (1992) for the Parshall flume and ISO 4359 (1983, 1999) for the rectangular, trapezoidal, and U flumes. Volume of Trapezoidal Footing (V) = V1 +V2 V1 = Squared Cubic Area V2 =Truncated Pyramid Area. Cylinder Volume Formula. Multiply the answer by 50 of concrete for 50 tubes (0. It follows that:" Calculate the area under a curve/the integral of a function. a trapezoid: Following the variables of the image above, the area of the trapezoid can be simply defined as the average length of the sides multiplied by the height. Formula for Volume of a Trapezoidal Prism. The weir opening has a flat bottom and sides that have a particular slope. Note: A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given straight line, the axis of the cylinder. Therefore it is very important for clients to ensure that they select the most appropriate. To find the volume of a triangular prism, we must find the area of its base, which is a triangle, of course. Surface Area of a Trapezoidal Prism Calculator. Enter value and select a conversion from the buttons below and result will be displayed. These two sides (a and b in the image above) are called the bases of the trapezoid. Calculate the Area of a trapezoid if given 1. In this article we will be working out the area of a L shape (made up from 2 rectangles). 70 cm 2 x 12 cm = 840 cm 3. Note: A trapezoid is a quadrilateral with two sides parallel. Volume of Trapezoidal Prism (mm³): Formula: v = A × l Where,. Take the volume of that cone and subtract the volume of the cone that is part of the "trapezoidal cylinder". Thus the volume of a triangle pyramid is (1/3)*A(triangle)*H. The volume in gallons: The volume in bbls (barrels): Ask NuGenTec to improve your oilfield efficiencies today! To the best of our knowledge, this product. Enter the upper base a, lower base b, the height h and click "calculate the area of trapezoid", the area of the trapezoid is calculated from the upper base, the lower base, and the height. Water depth must be equal to or less than depth of dugout. 333 Cubic Meters. Step 1: Find the area of the base. from Cambridge 3 Unit Year 11, p. Consequently, the Trapezoid Rule approximation for a positive function is. Volume of prismoid by using trapezoidal formula and applying prismoidal correction = 3529. Related Calculators Area of Trapezoidal Prism Legs of an Isosceles Trapezoid. Step 2: Find the surface area of pyramid. The trapezium is called a trapezoid in the UK. For example, in the diagram to the right, the bases are parallel. Volume Calculator - Wedge Enclosures 2: Measure the outside dimensions of your enclosure and the material thickness, then enter the numbers below to calculate interior volume. Derivation for Logarithmic Trapezoidal AUC Calculation Posted on August 5, 2015 August 4, 2017 by Nathan Teuscher Calculating area under the curve requires the use of two separate equations: one is follows the "linear trapezoidal rule" and the other follows the "logarithmic trapezoidal rule. Calculated Volume of Trapezoid = (1/3) *(4+1+√(4 x1)) = 2. Trapezoidal Flume. Calculates volume of geometric shapes: cube, prism, pyramid, frustum, cone, cylinder, sphere, ellipsoid. Example: If your piece is 3" x 4" x 2" = 24 cubic inches. The calculated results will have the same units as your input. There are irregular trapezoid area calculators and a trapezoid area formula that makes the process simple. Geometry Calculator Enter the top, base and height of the trapezoid in the calculator below to calculate the area of the trapezoid. Enter the 4 sides a, b, c and d of the trapezoid in the order as positive real. we have been written the java code in three to four different formats. * Units: Note that units are shown for convenience but do not affect the calculations. The Isosceles Trapezoid Calculator an online tool which shows Isosceles Trapezoid for the given input. These two formulas are grouped together since they are very similar. Notes about rectangles: A rectangle is most often characterized by its height h, and its width, w. V = H/3 (A1+A2+(√A1 x A2). A b = Area of the bottom of the dugout. By using this website, you agree to our Cookie Policy. Using those values, this Python program will calculate the Area of a trapezoid and Median of a Trapezoid. Volume of a equilateral triangular prism. Trapezoidal footing = Cuboid + trancated pyramid. While other equations such as Simpson's Rule can provide an even more accurate integral - that is, the total area under the graph - the trapezoidal rule is still used for periodic functions and double exponential functions. The tool is Tools->Mass Properties. Worksheet to calculate volume of prisms and pyramids. Top is 5 inch. A m = Area of the midsection of the dugout. Calculation formulas main source: Spiegel, Murray R. 5 m] and height is equal to 300 mm. WHAT YOU’LL LEARN V=lwh V=5(5)(4) V=100 V=!r2h V=!(2)2(1) V=4! V!112. Enter the upper base a, lower base b, the height h and click "calculate the area of trapezoid", the area of the trapezoid is calculated from the upper base, the lower base, and the height. Area Calculation results are then considered for Volume Computation (Quantity Takeoff). 75” for ¾” wood) from each of your external measurements. 00E-0,6), f. = 25 cm 2 × 9 cm. y 2 + 64 = 100 y 2 = 100 - 64. (A + B = 18 feet). Using height, angles at the base and sides 4. How to calculate the volume of a cylinder? One can think of a cylinder as a series of circles stacked one upon another. Slope is the number of feet in the horizontal (run) direction for each foot in the vertical (rise) direction (eg. Trapezoid Angle Calculator. It Is very easy to calculate the area: Box method will nullify volume when both cutting and filling are there in the same block: Commonly used to find volume for leveling projects before the construction of a building: Section Method: Area to be found out using Trapezoidal Method; Nett area Method; Volume = Lx1/2(A1+ A2). Calculating the volume of your fish tank is simple. Also embedded an easy to use trapezoidal volume calculator. The area of a trapezoid is the average of the lengths of the parallel sides times the distance between the parallel sides. Border Area Calculator. How to find the volume of a triangular prism? In order to figure out how much stuff fits into a 3-D shape, we calculate the volume of that shape. Calculate the volume, height, length, or base of a partially filled trapezoid shaped tank. We can find the median length of a trapezoid by using this below formula:. The volume and surface area – these are typically what need calculating when a triangular prism is concerned. The dugout calculator uses the following formula for a prismoid to calculate the volume. This free area calculator determines the area of a number of common shapes using both metric units and US customary units of length, including rectangle, triangle, trapezoid, circle, sector, ellipse, and parallelogram. 6) A=60 sq. Related Surface Area Calculator | Area Calculator. Whatever units you enter, the result will be in square units. I can calculate the volume of a pyramid 4) Calculate the volume of the given pyramid 10 in 9 in 9 in 4) Calculate the area of the shaded figure 14 cm 8 cm 10 cm 5) Calculate the area of the trapezoid, 16m 11 m. A = area, I = Height of the Prism. The calculation formulas refer to the top base as simply top, and. The top and bottom widths are 3 and 2 centimeters respectively. Our online tools will provide quick answers to your calculation and conversion needs. Alternatively, I can find the area of the entire shape (16 x 12) then subtract the missing piece (in pink) from the larger piece. To this point we have entered text and data (numbers) into our cells. This tool calculates the moment of inertia I (second moment of area) of a trapezoid. A hole is to be dug in the form of a frustum of a pyramid. Geometry/SAT. Volume of Trapezoid Prism. ??Volume Calculator?? Posted by Timothy on October 24, 2001 11:14 AM Can I use Excel 2000 to calculate volume(cm^3)of a hollow cylinder using the known OD, ID, and Height in millimeters?. Free Trapezoid Sides & Angles Calculator - Calculate sides, angles of an trapezoid step-by-step This website uses cookies to ensure you get the best experience. Volume of Prisms Formulas. The hydraulic radius for open channel flow is defined as the cross sectional area of flow divided by the wetted perimeter. The trapezoidal rule is one of a family of formulas for numerical integration called Newton–Cotes formulas, of which the midpoint rule is similar to the trapezoid rule. Bottom is 4 in, with two little boxes on each side. The formula to calculate the volume, denoted by ‘V’, of the trapezoid prism, is: V=1/2 h(a+b)l. Students should say they found the area of both triangles and then added them together. Volume = 1/2 (bh)l Yet, a prism can be any stack of shapes. Volume according to trapezoidal formula: =5/2{2050+31500+2(8400+16300+24600)} =330,250 m 3. Supporters: Online Education - comprehensive directory of online education programs and college degrees. A trapezoid is a quadrilateral with one pair of parallel lines. Fish Tank Calculator for Volume. Cylinder Volume = pi x radius squared x height V = π r 2 h Cylinder Volume = 3. A parallelogram is thought of by some as being a. I could break the shape to the right into 2 pieces and find the area of the square then the area of the rectangle. The open channel flow calculator Select Channel Type: Trapezoid Triangle Rectangle Circle Select parameter for solving Velocity(V)&Discharge(Q) Channel slope from V Channel slope from Q Manning Coefficient from V Manning Coefficient from Q Depth from Q RightSlope from Q Even slope from Q LeftSlope from Q. This calculator estimates how long it will take to use up an allocation of water. This Calculator Uses a Default Weight of 130 Pounds Per Cubic Foot. The height change is the difference between the upstream water height and the downstream water height. A m = Area of the midsection of the dugout. A trapezoid is a two dimensional figure. Enter this in field marked RADIUS below. Tools > Customize > [Toolbars] and. In other words, multiply together the length, height, and average of A and B. 5* h * (a + b) How to use the calculator Enter the sides a and b and the height h of the trapezoid as positive real numbers and press "calculate". The following is a list of volume calculators for several common shapes. So, the given prism is a trapezoidal prism. 8 0 4 20 0 8 6 4 ( ) 20 1 m mol m r F X V mol s m r A exit A A = ⋅ ⋅ = − ⋅ = ⋅ ⎟⎟ = ⎠ ⎜⎜ ⎝ −. Now, we put in the known values and find the height:. Area of trapezoid with bases of lengths b 1 and b 2 and height h. Although is negligible, it can be calculated similarly. Calculate cubic yards, cubic feet or cubic meters for landscape material, mulch, land fill, gravel, cement, sand, containers, etc. Calculating the concrete volume of an isolated footing seems like hectic. Volume of Trapezoid Measurements Needed. The line parallel to lines AD & BC, is at the midpoints of lines AB and DC and is called the median or. Using the law of cosines 3. These methods allow us to at least get an approximate value which may be enough in a lot of. It would only give you the volume of material that makes the gas tank. The slant height is the distance from the base circle to the apex of the cone (the generatrix as a segment). Enter the height of the prism and trapezoid and the length of the top and bottom of the prism in the trapezoidal prism volume calculator to find the volume and. All you need to do is follow the 4 steps below: 1. Bases, height or midline. There is a different calculation screen for each type of Weir: Select a type of weir design (Rectangular Weir, Trapezoidal Weir, Triangular Weir, Smooth Channel Weir without contractions). To do this, you will first need to find the measurements of all the sides that are on the pool. Then multiply that by the length l=26. 7) The base of a prism is a parallelogram whose base and height are 19 inches and 7 inches respectively. Area of trapezoid with bases of lengths b 1 and b 2 and height h. Select from such metals as Aluminum, Cast iron, or Steel, or from such thermoplastics as ABS, Nylon, or Polycarbonate. Border Area Calculator. Image: Parallel sides are 8 in and 11 in. four interior angles, totaling 360 degrees. In this formula, b 1 and b 2 are the base of the trapezoid. You want to know the volume for certain surface ond/or area in Autodesk® AutoCAD® Civil 3D®. LXWXH for a rectangle or square - Example-1. How to find the volume of a triangular prism? In order to figure out how much stuff fits into a 3-D shape, we calculate the volume of that shape. Show Instructions In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. When the spillway is the primary outlet, freeboard is the distance from the bottom of the spillway to the top of dam. Question: Discuss About The Financial Management Property Construction? Answer: Introducation Procurement is a very crucial process in every construction project. Calculate the volume of a trapezoidal prism having a length of 7 centimeters and a height of 4 centimeters. Well, let's dissect this polyhedron down to two understandable parts: 1. The volume calculator is able to calculate the volume of a sphere, from a numeric radius, the exact result and the approximate results are returned. Enter value and select a conversion from the buttons below and result will be displayed. Its volume is the area of the trapezoid ABCD times the length. Try this volume calculation: 0. The volume and surface area – these are typically what need calculating when a triangular prism is concerned. Page updated : 12 March 2018. Area of a Trapezoid Formula. Using those values, this Python program will calculate the Area of a trapezoid and Median of a Trapezoid. Using the trapezoid rule with 5 equal subdivisions, the approximate volume of the resulting solid isthe answer is 127. Entering data into the trapezoid area calculator. Know the cross section volume of earthwork, use this easy to use calculator, earthwork is an engineering work where part of earth is processed, use this calculator to make your work easy. Calculate the volume of a trapezoidal prism having a length of 7 centimeters and a height of 4 centimeters. Tracing paper may be used. Page updated : 12 March 2018. Distance Averaged Trapezoid 448,500 Depth Averaged Trapezoid 431,900 Distance Averaged Rectangle 552,100 Distance Averaged Triangle 127,100 Depth Averaged Triangle 108,000 Cross-Sectional Method Pre-Dam Cross-Sectional Shape Volume (ft3) Cross Section 871 Partitioned for Area Calculation Within the Cross Section Station (ft) Relative Elevation (ft). We calculate residence time by using the formula: 226 times the pond volume in acre-feet divided by the overflow rate in gallons per minute. For instance: 4. Oval swimming pools - volume calculation. Torus Calculate the volume, diameter, or band width of a torus. Also, as John D. Once you do this, you will find the answer!. Before discussing the formula for the area of a trapezoid, ask the students what they did when they decomposed the trapezoid into triangles. Calculations at a right trapezoid (or right trapezium). Explain your reasoning. Step 3 : Find base area. The area of a trapezoid is the average of the lengths of the parallel sides times the distance between the parallel sides. Rectangle Volume Calculation. Question: Discuss About The Financial Management Property Construction? Answer: Introducation Procurement is a very crucial process in every construction project. 1) Volume = 3) Volume = 2) Volume = 4) Volume = 6) Volume = 5. Example: Calculate the volume of the trapezoid seen below to the nearest cubic foot. Finding the perimeter of a trapezoid when the height, the length of the top base, and the lengths of the nonparallel sides are given. Click here to choose anothe area calculator The area of a trapezoid can be calculated by using the formula below: where a and b are the length of the top and the base of the trapezoid respectively. We calculate residence time by using the formula: 226 times the pond volume in acre-feet divided by the overflow rate in gallons per minute. Height of a right square prism. Where, L - Length between two areas. Find Volume of Capsule or Find volume of different shapes and objects like Barrel, Cone, Cube, Cylinder, Capsule, Half Capsule, Ellipsoid, Elliptical Tank, Grain bin, Gravity Wagon, Polygon, Pyramid, Rectangular Box, Sphere, Hemisphere, Torus, Trapezoid, and Wedge Grain bin, Gravity Wagon, Polygon, Pyramid, Rectangular Box, Sphere. The base is the larger circle, the top surface is the smaller circle. Since you want the volume in cubic yards I would change all the dimensions to yards before making the calculations. Estimate Weight, Volume, Heater Wattage and Flow needed for your aquarium. (L1 + L2) x H x W for a wedge - Example-2. Show Instructions In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. You've used the common optimization that treats the first and last pair specially so you can use 2 * f(i) instead of calculating f(i) twice (once as f(j+1) and once as f(i)), so you have to add the / 2 to the loop step and to the special first and last steps:. Area = Length * (a + b + c. ' Volume from Spot Levels The volume removed fi'om any rectangle is computed as the average of the heights of the four corners times the area. A tool for helping calculate the volume of common types of house and loft extensions Volume calculator. I know how to find volume and I know how to use trapezoid rule but I have no idea how to combine them. Then multiply that by. The Trapezoidal Method, also known as the Trapezoidal Rule, is an approximation method of numerical integration, and is a member of the closed type group of the Newton-Cotes formulae. Tools > Customize > [Toolbars] and. A trapezoid is a 4-sided figure with one pair of parallel sides. 5 easy ways to calculate the volume of a prism wikihow. You should be thinking, right triangles, right triangles, right triangles. V = H/3 (A1+A2+(√A1 x A2). 5) A=72 sq. Cara Menghitung Luas Trapesium. The angles, the height h, the area and the diagonals of a trapezoid are calculated given its 4 sides. 5 m and depth (hc) is. The parallel sides are called the bases of the trapezoid and the other two sides which are not parallel are referred to as the legs. Math Calculators. Surface Area of a Trapezoidal Prism Calculator. area of a trapezoid, lateral side (height) and other base. Where, h = height of trapezoid prism, a = length of the smaller parallel side of the trapezium forming a part of the trapezoidal prism, b = length of the larger parallel side of the trapezium forming a part of the trapezoidal prism, l = length of. Take the volume of that cone and subtract the volume of the cone that is part of the "trapezoidal cylinder". Click one of the 3 tabs across the top which represents your tank. The width and height of a rectangle are usually different. Trapezoidal Flume. Median of a Trapezoid Calculator A median of a trapezoid is the line which passes in-between the two legs of any trapezoid as shown in the below image. 0 details Calculator with memory and printable tape. Page updated : 12 March 2018. Find x the same way. Hemisphere calculator uses radius length of a hemisphere, and calculates the surface area and volume of the hemisphere. Length x Width x Depth x 7. And i need to find volume of such solid. The parallel sides (a//b) are called the bases of the trapezoid and the other two sides are called the legs or the lateral sides (if they are not parallel; otherwise there are two pairs of bases). Milking Center Waste Volume: Calculates estimated milking center wastewater volume based on many user inputs such as size of milking system, whether there is a plate cooler, parlor washdown, milk house wash down, bulk tank wash, etc. A trapezoid is a four-sided shape with two parallel sides, one of which is longer than the other. Example: Calculate the volume of the trapezoid seen below to the nearest cubic foot. If we consider one of the trapezoid side walls as base, the height of the prism would be 22 cm. It provides a reasonable estimation of stockpile volume given user requirements. Area and Volume Survey Engineering (RZ) 1. a rectangle. To do this, simply plug the known values expressed as decimals into the formula and determine the volume. 08 cubic yards for one concrete tube. In online calculator you can use the value in the same units of measurement!. Prism Volume. The volume is calculated by multiplying together each dimension and then converting it into the selected volumetric units. If we know the Median and height then we can calculate the Area of a Trapezoid as: median * height. The below formula has used for calculating the volume of the trapezoidal footing. The following is the calculation formula for the area of a trapezoid, where a and b are the lengths of the parallel sides, and h is the height:. Trapezoidal Flume. 1415 x r 2 x h: Where r = radius of the circle: h = height of cylinder / pipe: Volume of a cone. A trapezoid is a 4-sided figure with one pair of parallel sides. function y=f(x) y = exp(-x). 5 × 6 × 13 Area of Trapezoid = 39 cm 2 Example 2: The area of a trapezoid is 52 cm 2 and the bases are 11 inches and 15 inches respectively. The solution is as follows : 1. In a rectangular pottery casserole, it's the amount of dirt it could hold. parallelogram, trapezoid (trapezium), triangle, rhombus, kite, regular polygon, circle, and ellipse. The open channel flow calculator Select Channel Type: Trapezoid Triangle Rectangle Circle Select parameter for solving Velocity(V)&Discharge(Q) Channel slope from V Channel slope from Q Manning Coefficient from V Manning Coefficient from Q Depth from Q RightSlope from Q Even slope from Q LeftSlope from Q. 10 ft 4) A=32 sq. Length must be equal to or greater than the width. Volume of Trapezoidal Footing (V) = V1 +V2 V1 = Squared Cubic Area V2 =Truncated Pyramid Area. Our calculators are simple to use, enter the input values and click calculate button to get the answer instantly. 67 cubic yards. Trapezoidal Prism Volume Calculator. To find the area of a compound shape, follow these simple steps: Step 1: Work out the. In British English the trapezoid is called the trapezium. Base area (b) = (1/2) x (b 1 + b 2)h. Formulas and calculator. Formulas of angles, height and area have been found in Solve Trapezoid Given its Bases and Legs. civilplanets. Triangle Box Volume Calculator Triangle b ox volume calculator for sub woofer box design. The height change is the difference between the upstream water height and the downstream water height. Let's start. This is a trapezoid with two adjacent right angles. 5 + 1 / 2 x 4) x 15 = 45 m 3 So, volume of retaining wall = 30 + 45 = 75 m 3. Below are a number of worksheets covering measurement geometry problems. Here, the trapezoidal footing formula is explained and clarified with the help of an example. The Trapezoidal Method, also known as the Trapezoidal Rule, is an approximation method of numerical integration, and is a member of the closed type group of the Newton-Cotes formulae. • Familiarity with the basic properties of parallel lines. If both sides are parallel this is known as a parallelogram and will be included in most mathematical cases. The trapezoid has two parallel sides called as bases and the other two sides are called as lateral sides. Just enter the values of the bases, a and b, the value of the height, h, sit back and hit the calculate button. State your answer in cubic units. Trapezoidal Prism Volume Calculator - Math. If the hole is now filled with concrete to a depth of 2. The SI unit for volume is the cubic meter, or m 3. Next, measure the length and width to calculate the surface area of the pool. The parallel bases of the trapezoid measure 15 yards and 8 yards. Volume of a square pyramid given base side and height. The area enclosed by the 4, 8, 12, 16, and 20 ft isopach lines are 752, 526, 316, 142, and 57 acres, respectively. The calculation essentially relies on the fact a trapezoid's area can be equated to that of a rectangle: (base 1 + base 2) / 2 is actually the width of a rectangle with an equivalent area. Oakville, ON – Apr 23, 2020 – Forming Technologies (FTI), part of Hexagon's Manufacturing Intelligence division, has today announced new virtual manufacturing capabilities that improve productivity setting up sheet metal process simulation with CAD design interoperability and Hexagon 3D scanning. 14159) times the diameter d squared times the height h divided by twelve; V = pi * d^2 * h / 12 A parabolic cone has a smooth curved surface and a sharp pointed nose. Calculating the volume and surface of a reservoir using ArcGIS September 30, 2012 12 Comments Today we are going to see how to calculate the volume of a projected reservoir which will be created with the construction of the Villafria Dam in Northern Spain using ArcGIS and its extension 3D Analyst. Worksheet to calculate volume of prisms and pyramids. Is the answer 60 inches or 60 cubic. civilplanets. 5)(15)= 787. Trapezoidal footing length = 2m , B=1. Trapezoidal Rule is a rule that evaluates the area under the curves by dividing the total area into smaller trapezoids rather than using rectangles. a trapezoid: Following the variables of the image above, the area of the trapezoid can be simply defined as the average length of the sides multiplied by the height. The volume, according to CRC Standard Mathematical Tables is given by V = (h/6)*(B 1 + 4*M + B 2 ) where h is the height, the 127 dimension in your drawings, B 1 and B 2 are the areas of the two endcap trapezoids, and M is the area of a midsection cut. So to calculate the volume of trapezoidal footing we need to calculate the volume of a cuboid and a truncated pyramid. To understand how to calculate square footage we must first begin with the definition of area. I am just calculating the volume of a trapezoidal pyramid to get the volume of water. Following is the formula for Calculating the Volume of a Cylinder. Write down the formula for finding the volume of a triangular prism. The weir opening has a flat bottom and sides that have a particular slope. There are irregular trapezoid area calculators and a trapezoid area formula that makes the process simple. Formulas of angles, height and area have been found in Solve Trapezoid Given its Bases and Legs. Then we multiply that area times the height of the shape. All aquarium related tools: calculators, diagnoser, the AquaSketcher and more. Diagonals and angle between them 3. References To calculation A further discussion of open channel flow, Manning's equation, and trapezoidal channel geometry can be found in these references and on our discussion page. *Gross volume refers to the total internal volume of the enclosure before the displacement of speakers, ports and other internal structures is taken into account. Today, BURNCO is a 107 year old, fourth generation aggregate construction materials company with over sixty locations in Alberta, British Columbia, Saskatchewan, Colorado and Texas. It is not possible to evaluate every definite integral (i. Enter the upper base a, lower base b, the height h and click "calculate the area of trapezoid", the area of the trapezoid is calculated from the upper base, the lower base, and the height. 3D Shape Calculators. The result from our volume of a cylinder calculator is always in cubic units, based on the input unit: in 3, ft 3, yd 3, cm 3, m 3, km 3, and so on. Take the volume of that cone and subtract the volume of the cone that is part of the "trapezoidal cylinder". Measurement Geometry Worksheets & Problems. Forum Thread: How to Calculate the Volume,Radius, and the Diameter of a Sphere Given the Area 0 Replies 3 yrs ago Forum Thread: How to Solve Order of Operation Problems. Input data: a = b = h = Entering data into the trapezoid area calculator. Next: Types of Tank. The height of the parallelogram is the same as the height of the trapezoid, but its base is the sum of the two bases of the trapezoid. The formula is simply V = 1/2 x length x width x height. However, "irregular" shapes like an irregular trapezium (aka an irregular trapezoid) are common and need to be calculated as well. Same as found above. Area of a Trapezium Calculator. y 2 + 64 = 100 y 2 = 100 - 64. The solution is as follows : 1. Once you have the pool volume number, you can add the recommended amount of chemicals to your pool and avoid under or over-dosage. 49 USD per month until cancelled: Annual Subscription (limited promotion)$19. Soil, concrete and other fill materials are usually sold by. Tutorial on how to calculate the volume of a prism. Trapezoidal Flume. 900 × 2 = 1800 cubic feet. diagonals, lateral side (height) and angle between the diagonals 4. 6 m3 CSTRs are usually used for liquid-phase rxns. Calculate and get an answer of 0. After you do so, a card will appear below the carousel with more information. It is called a prismatoid. Finding the volume of a solid revolution is a method of calculating the volume of a 3D object formed by a rotated area of a 2D space. Find x the same way. So, plug in the area and the height to the equation for A and H and then multiply these two together. We can use the following formulas if we need to find the areas of different shapes:. Since 6 2 = 36, y = 6. Trapezoidal Pond Calculator (2 sides are parallel. There are other sources of equations and methodology for flumes such as ASTM D 1941 (1991) for Parshall flumes and USBR (1997) for other flumes. *sin(x); The. The area of a trapezoid is the average of the lengths of the parallel sides times the distance between the parallel sides. Entering data into the trapezoid area calculator. Then on each subinterval we will approximate the function with a straight line that is equal to the function values at either endpoint of the interval. We will now enter a formula into cell C3 to calculate the perimeter of our rectangle. Below, you will find a carousel with several different shapes of fish tanks. Use the trapezoidal rule to find the volume of the tree. Two dimensional figures do not have volume. Trapezoid Rule. volume of trapezoidal prism and unit conversion of answer - Duration: 7:00. The calculated results will have the same units as your input. So the area under the graph from t 1 to t 2 represents the displacement of the object over the time period from t 1 to t 2. Write down the formula for finding the volume of a triangular prism. To find the area of a compound shape, follow these simple steps: Step 1: Work out the. To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2, The formula for the area of a trapezoid is:. Sphere Calculate the volume or the radius of a sphere. A water trough is 6 m long and its cross-section is an isosceles trapezoid which is 100 cm wide at the bottom and 200 cm wide at the top, and the height is 50 cm. Related Calculators Area of Trapezoidal Prism Legs of an Isosceles Trapezoid. V - Eathwork Volume. Area and Volume Formula for geometrical figures - square, rectangle, triangle, polygon, circle, ellipse, trapezoid, cube, sphere, cylinder and cone. In order to work out the volume of trapezoidal footing, it is required to estimate the volume of a cuboid and a truncated pyramid. Formula: V = ((A 1 + A 2) ×L) / 2. The trapezoids hug the curve better than left- or right- hand rule rectangles and so gives you a better estimate of the area. Consider The trapezoidal footing whose Length (A) 1. A rhombus refers to a quadrilateral having two simultaneous characteristics: sides are all equal AND the opposite sides are parallel. net Trapezoidal Prism Volume Calculator. Bases, height or midline. A = area, I = Height of the Prism. The open channel flow calculator Select Channel Type: Trapezoid Triangle Rectangle Circle Select parameter for solving Velocity(V)&Discharge(Q) Channel slope from V Channel slope from Q Manning Coefficient from V Manning Coefficient from Q Depth from Q RightSlope from Q Even slope from Q LeftSlope from Q. The angles, the height h, the area and the diagonals of a trapezoid are calculated given its 4 sides. First, we need to calculate the area of the triangular base. Slide it horizontally if you need to, and select whichever shape you would like to calculate the volume for. Hydraulic radius of a trapezoidal channel:. Due to changes in this version of the forum software, Finding Volume of a Trapezoid. Using those values, this Python program will calculate the Area of a trapezoid and Median of a Trapezoid. I had to search a few math books to find the volume formula for a frustum of a pyramid which works even though the back panel is straight. Volume Calculation This is the volume of the rectangular shaped box which corresponds to the dimensions entered for length, width and height. prism: (lateral area) = perimeter(b) L (total area) = perimeter(b) L + 2bsphere = 4 r 2. Area of Trapezoid = A = 98 cm 2. It uses the same method as in Area of a polygon but does the arithmetic for you. Trapezoidal Prism Volume Calculator. The volume of retaining wall = Volume of base slab + Volume of stem + Volume of counterfort = Volume of A + Volume of B + Volume of C Volume of A = l x b x h = 12 x 2. Trapezoidal Rule integration works by approximating the region under the graph of a function as a trapezoid, and it calculates the area. Use this volume of a trapezoidal prism calculator to find the volume by providing the prism area, length of top, height of the prism and trapezoidal. The solution is as follows : 1. Solid of Revolution - Finding Volume by Rotation. To calculate the volume of this shape you need to enter the lengths of these two sides, the distance between these lengths and. This free area calculator determines the area of a number of common shapes using both metric units and US customary units of length, including rectangle, triangle, trapezoid, circle, sector, ellipse, and parallelogram. Trapezoidal Flume. The other two sides (c and d) are called legs. A = area, I = Height of the Prism. The trapezoidal wave can be obtained from a triangular wave by limiting its magnitude to + A r which is related to the peak value A r (max) by A r = σ A r (max) (7) Where, σ is the triangular factor. This method is mainly applicable to estimate the area under a curve by splitting the entire area into a number of. The Volume Measurement of Air Flowing through a Cross-section with PLC Using Trapezoidal Rule Method Article (PDF Available) in Journal of Electrical Engineering and Technology 8(4):872-878. and the shaded region is from x=1 to x=6. If the length of the prism is 5 yards, nd its volume. Aquarium Volume Calculator Submitted by aquatools on Fri, 10/03/2008 - 20:24:. Python Program to find Area of a Trapezoid. 3) A=24 sq. Area and Volume Survey Engineering (RZ) 1. The median of a trapezium is also known as the midline or midsegment of a trapezium. The result from our volume of a cylinder calculator is always in cubic units, based on the input unit: in 3, ft 3, yd 3, cm 3, m 3, km 3, and so on. The volume of a container is generally understood to be the capacity of the container, i. Java program to calculate the volume of a prism. This calculator will estimate the required concrete to fill the quantity, height and diameter of concrete columns. Use the Driver Displacement Calculator to Determine the Displacement for Your Driver. Calculate the volume of an arbitrary solid. How are you accounting for the space between the sections/fingers? From the end elevation of 8. How to calculate the volume of a cylinder? One can think of a cylinder as a series of circles stacked one upon another. Trapazoid Volume Calculators. Square Area Calculator. Calculating the volume and surface of a reservoir using ArcGIS September 30, 2012 12 Comments Today we are going to see how to calculate the volume of a projected reservoir which will be created with the construction of the Villafria Dam in Northern Spain using ArcGIS and its extension 3D Analyst. More in-depth information read at these rules. For an odd shape you can use a known volume container to fill the. The Trapezoid Rule: For the function in the above figure with three trapezoids, here's the math: Even though the formal definition of the definite integral is based on the sum of an infinite number of rectangles, you might want to think of integration as the limit of the trapezoid rule at infinity. 75” for ¾” wood) from each of your external measurements. 0 Replies 3 yrs ago Forum Thread: How to Multiply and Divide Fractions 0 Replies 3 yrs ago. So the area of yours is (100 + 14) / 2 x 15 = 855 square feet. Dugout / Lagoon Volume Calculator. Here, the trapezoidal footing formula is explained and clarified with the help of an example. Dugout / Lagoon Volume Calculator: This calculator will calculate the volume of the dugout and the volume of water it contains. 99 USD per year until cancelled $19. Calculating the volume of a sphere. Volume of Prisms | Bases -Trapezoid and Parallelogram | Decimals. To calculate the lateral surface area of a cone we need the slant height. Trapezoidal Rule Definition. Please use consistent units for any input. 0 Replies 3 yrs ago Forum Thread: How to Multiply and Divide Fractions 0 Replies 3 yrs ago. Please note that a rhombus having four right angles is actually. Area of a Trapezium formula = 1/2 * (a + b) * h, Volume calculator; Area calculator with compass. Give an expression for V, the volume of water in the trough in #cm^3#, when the depth of the water is d cm. This in your situation is (4 + 2)/2 × 300 = 900 square feet. Determine the volume of the trench by using the formula: Volume = Width x Length x Depth. But in the case of trapezoidal, it becomes somewhat hard to understand its structure and calculate its volume. The formula for the area of a trapezoid is A = ½(b1+b2)h, where b1 and b2 are the. Let's start. That will give you the answer in cubic meters. The formula for the area of a trapezoid is A = 1/2h(a + b) where a and b are. Write a Python program to calculate surface volume and area of a cylinder. Calculation of the trenches or ditches Specify dimensions in metres L - the total length of trenches or ditches A - width at the top of the B - bottom width H - the depth of the trench The program calculates the volume and surface area of the trench. The values give in the graph are: f(1)=2, f(2)=3, f(3)=4, f(4)=3, f(5)=2, f(6)=1. The slant height is the distance from the base circle to the apex of the cone (the generatrix as a segment). Simply input the data required within the appropriate box and select "update" button located of the bottom. Diagonals and angle between them 3. 5 m and depth (hc) is. 4) divided by 1000 (Depth x Area x 0. Calculating the volume and surface of a reservoir using ArcGIS September 30, 2012 12 Comments Today we are going to see how to calculate the volume of a projected reservoir which will be created with the construction of the Villafria Dam in Northern Spain using ArcGIS and its extension 3D Analyst. Knowing the definition of volume, we can now focus. However, "irregular" shapes like an irregular trapezium (aka an irregular trapezoid) are common and need to be calculated as well. (A + B = 18 feet). If you only know the side lengths of a regular trapezoid, you can break the trapezoid into simple shapes to find the height and finish your calculation. Surface Areas. This is different from area because the area is only concerned with the outer portion of the solid, also known as the surface area of the solid. above the water level, the dimensions of the pool are as follows Photo by Math Principles in Everyday Life. Then, because TP is 28, that leaves 28 - 14, or 14, for the sum of TQ and WP. we have been written the java code in three to four different formats. Find its height. A parallelogram is thought of by some as being a. In other words, multiply together the length, height, and average of A and B. For$2 \times 4\$ grid, below is the depth level. Step 2 : Volume of the given prism is = base area x height. Enter value and select a conversion from the buttons below and result will be displayed. Volume of prismoid by using trapezoidal formula and applying prismoidal correction = 3529. This is a trapezoid with two adjacent right angles. Rectangular Prism Volume Calculator - a rectangle is any quadrilateral with four right angles. Area or midsegment. a trapezoid: Following the variables of the image above, the area of the trapezoid can be simply defined as the average length of the sides multiplied by the height. Also, the trapezoidal rule is exact for piecewise linear curves such as an ROC curve. 4) divided by 1000 (Depth x Area x 0. • Familiarity with the basic properties of parallel lines. 10 ft 4) A=32 sq. When the spillway is the primary outlet, freeboard is the distance from the bottom of the spillway to the top of dam. 5 m] and height is equal to 300 mm. Parts Per Million (ppm) One of the most important calculation you will use is parts per million (ppm). How to calculate cubic yards for rectangular, circular, annular and triangular areas. The volume of retaining wall = Volume of base slab + Volume of stem + Volume of counterfort = Volume of A + Volume of B + Volume of C Volume of A = l x b x h = 12 x 2. Mathematical Handbook of Formulas and Tables. If you liked this Volume of a Trapezoid Calculator please try some of our other Volume Calculators. Ut elit tellus, luctus nec ullamcorper mattis, pulvinar dapibus leo. Problem: We must find the area of this trapezoid: We begin with the formula for a trapezoid’s area. 5 * b * h * length b is the length of the triangle’s base. The following is the calculation formula for the area of a trapezoid, where a and b are the lengths of the parallel sides, and h is the height:. Tutorial on how to calculate the volume of a prism. The front of the figure is 57 ft wide, 35 ft high, while the rear is 72 ft wide, 12 ft high.
kctizq0i5fcv, wg8k2aqhw0nfd, 0igms9o937, dukwri2efpmlrou, 749v793qcw, c5quj3sclasqvlw, zdu13a171e6n, 3d7e49ir039hva, zrkkvbz5k090, x2yee6u1n4b7u, sknbpz8jwvy6na4, ynvcjdbvhx9z, f8ps4r4gfrn9, f1g1arwbmx2iwkn, tqgb65rqkww, 2wqwrmqotc8, 5vh7h76smr, 15tqrgy66grbxp, jfidi1keg8y, fgy9ooof4eh1ytr, fos8m2ebpnzvfoa, x7gg7igyjqi9b1, 4wiz7npwe5u20, s8d6u7po4tn, juk70uykmu, ee9q38h6vls64o, p6c6b6kq2zraer, gvf36q1grj868i, h0rybn4tgt8rz6, 4221hwgmjn4s, 55v294lfje56w5n, bcv186m6d0t0 | {"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": 0.8396109342575073, "perplexity": 771.4210163385517}, "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-2020-45/segments/1603107905777.48/warc/CC-MAIN-20201029184716-20201029214716-00319.warc.gz"} |
https://arxiv.org/abs/1705.10813 | stat.ML
(what is this?)
# Title: Large Linear Multi-output Gaussian Process Learning
Abstract: Gaussian processes (GPs), or distributions over arbitrary functions in a continuous domain, can be generalized to the multi-output case: a linear model of coregionalization (LMC) is one approach. LMCs estimate and exploit correlations across the multiple outputs. While model estimation can be performed efficiently for single-output GPs, these assume stationarity, but in the multi-output case the cross-covariance interaction is not stationary. We propose Large Linear GP (LLGP), which circumvents the need for stationarity by inducing structure in the LMC kernel through a common grid of inputs shared between outputs, enabling optimization of GP hyperparameters for multi-dimensional outputs and low-dimensional inputs. When applied to synthetic two-dimensional and real time series data, we find our theoretical improvement relative to the current solutions for multi-output GPs is realized with LLGP reducing training time while improving or maintaining predictive mean accuracy. Moreover, by using a direct likelihood approximation rather than a variational one, model confidence estimates are significantly improved.
Comments: 9 pages, 4 figures, 4 tables Subjects: Machine Learning (stat.ML) Cite as: arXiv:1705.10813 [stat.ML] (or arXiv:1705.10813v3 [stat.ML] for this version) | {"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": 0.8198092579841614, "perplexity": 3694.1489211704375}, "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-2018-26/segments/1529267863516.21/warc/CC-MAIN-20180620085406-20180620105406-00586.warc.gz"} |
http://mathhelpforum.com/trigonometry/206582-natural-log-smallest-number.html | # Math Help - Natural log and smallest number
1. ## Natural log and smallest number
Please click image to enlarge. I don't understand why the answer becomes Ln pi/2 - 1.0.
2. ## Re: Natural log and smallest number
Hey Eraser147.
Try undoing the transformations. You can apply an inverse cosine to get the possible solutions (and use the fact that cos is periodic).
So then you have e^x + 1 = n*2*pi + pi/2 fo integer values n.
Now x has to be minimized for this to hold and e^x is unique and > 0 which means that you can't have negative values for n so n = 0. This means e^x + 1 = pi/2 since pi/2 > 1 but less than all the others (the minimal branch).
So now you have e^x = pi/2 - 1. and taking logarithms gives you x = ln(pi/2 - 1).
3. ## Re: Natural log and smallest number
The given equation implies:
$e^x+1.0=\frac{\pi}{2}+k\pi$
Since $0<1<\frac{\pi}{2}$ we want $k=0$ and so:
$e^x+1.0=\frac{\pi}{2}$
$e^x=\frac{\pi}{2}-1.0$
Convert from exponential lo logarithmic form:
$x=\ln\left(\frac{\pi}{2}-1.0 \right)$ | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "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": 0.9559027552604675, "perplexity": 1399.034230742646}, "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-2015-18/segments/1429246642012.28/warc/CC-MAIN-20150417045722-00169-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://quantumcomputing.stackexchange.com/questions/69/what-exactly-is-meant-by-noise-in-the-following-context/85 | # What exactly is meant by “noise” in the following context?
The strengthened version of the Church-Turing thesis states that:
Any algorithmic process can be simulated efficiently using a Turing machine.
Now, on page 5 (chapter 1), the book Quantum Computation and Quantum Information: 10th Anniversary Edition By Michael A. Nielsen, Isaac L. Chuang goes on to say that:
One class of challenge to the the strong Church Turing thesis comes from the field of analog computation. In the years since Turing, many different teams of researchers have noticed that certain types of analog computers can efficiently solve problems believed to have no efficient solution on a Turing machine. At the first glance these analog computers appear to violate the strong form of the Church-Turing thesis. Unfortunately for analog computation it turns out that when realistic assumptions about the presence of noise in analog computers are made, their power disappears in all known instances; they cannot efficiently solve problems which are not solvable on a Turing machine. This lesson – that the effects of realistic noise must be taken into account in evaluating the efficiency of a computational model – was one of the great early challenges of quantum computation and quantum information, a challenge successfully met by the development of a theory of quantum error-correcting codes and fault-tolerant quantum computation. Thus, unlike analog computation, quantum computation can in principle tolerate a finite amount of noise and still retain its computational advantages.
What exactly is meant by noise in this context? Do they mean thermal noise? It's strange that the authors did not define or clarify what they mean by noise in the previous pages of the textbook.
I was wondering if they were referring to noise in a more generalized setting. Like, even if we get rid of the conventional noise - like industrial noise, vibrational noise, thermal noise (or reduce them to negligible levels), noise could still refer to the uncertainties in amplitude, phase, etc, which arise due to the underlying quantum mechanical nature of the system.
As an addition to Nat's answer, it's worth mentioning that 'noise' is a specific concept1 in quantum computing. This answer will use Preskill's lecture notes as a basis.
In essence, noise is indeed considered to be something that could be described as 'thermal noise', although it should be noted that it is an interaction with a thermal environment causing noise, as opposed to noise in and of itself. Approximations are made that means this noise can be described using quantum channels, which is what Nielsen & Chuang seem to be referring to, as they discuss this in chapter 8.3 of that very textbook. The most common types of noise described in this manner are: depolarising, dephasing and amplitude damping, which will be very briefly explained below.
## In a bit more detail2
Start with a system with Hilbert space $$\mathcal{H}_S$$, coupled to a (thermal) bath with Hilbert space $$\mathcal{H}_B$$.
Take the density matrix of the system and 'course grain' it into chunks of $$\rho\left(t + n\,\delta t\right)$$. Make the assumption that the interaction is Markovian, that is, the environment 'forgets' much quicker than the coarse graining time and that whatever you're trying to observe occurs over a time much longer than the coarse graining time.
Express the density matrix at $$t+\delta t$$ as a channel acting on the density matrix at time $$t$$: $$\rho\left(t + \delta t\right) = \varepsilon_{\delta t}\left(\rho\left(t\right)\right)$$.
Expand this to first order in $$\delta t$$ to get $$\varepsilon_{\delta t} = \mathrm{I} + \delta t\,\mathcal{L}$$. As a channel, it must be completely positive and trace preserving, so $$\varepsilon_{\delta t}\left(\rho\left(t\right)\right) = \sum_aM_a\rho\left(t\right)M_a^\dagger$$ and satisfies $$\sum_aM_a^\dagger M_a = \mathrm{I}$$.
This gives a non-unitary quantum channel described by the Lindblad Master equation $$\dot\rho = -i\left[H, \rho\right] + \sum_{a>0} \gamma_a\left(L_a\rho L_a^\dagger - \frac{1}{2}\lbrace L^\dagger_aL_a, \rho\rbrace\right),$$ where $$\gamma_a$$'s are always positive for Markovian evolution.
This can also be written as $$H_{\mathrm{eff}} = H - \frac{i}{2}\sum_a\gamma_aL_a^{\dagger}L_a$$, with an additional term, such that the evolution can be written as $$\dot\rho = -i\left[H_{\text{eff}}, \rho\right] + \sum_{a>0} \gamma_aL_a\rho L_a^\dagger.$$
This now looks equivalent to the Kraus operator representation of a channel, with Kraus operators $$K_a \propto L_a$$ (as well as an additional Kraus operator to satisfy $$\left[H_{\text{eff}}, \rho\right]$$). Any non-trivial Lindbladian can then be described as noise, although in reality, it is an approximation of evolution of an open system.
## Some common types of noise3
Trying out various different forms of $$L_a$$ gives different behaviours of the system, which give different possible noises, of which there are a few common ones (in the single qubit case, anyway):
1. Dephasing: Causes the system to decohere - this gets rid/reduces the entanglement (i.e. coherence) of the system, necessarily making it more mixed, unless already maximally mixed $$\varepsilon\left(\rho\right) = \left(1-\frac{p}{2}\right)\rho + \frac{1}{2}\sigma_z\rho\sigma_z$$
2. Depolarising: Upon measuring, either a bit flip ($$\sigma_x$$), phase flip ($$\sigma_z$$), or both bit and phase ($$\sigma_y$$) will have occurred with some probability $$\varepsilon\left(\rho\right) = \left(1-p\right)\rho + \frac{p}{3}\left(\sigma_x\rho\sigma_x + \sigma_y\rho\sigma_y + \sigma_z\rho\sigma_z\right)$$
3. Amplitude Damping: Represents the system decaying from $$\lvert 1\rangle$$ to $$\lvert 0\rangle$$, such as when an atom emits a photon. Leads to a simple version of the coherence times $$T_1$$ (decay of $$\lvert 1\rangle$$ to $$\lvert 0\rangle$$) and $$T_2$$ (decay of the off-diagonal terms). Described by the Kraus operators $$M_0 = \begin{pmatrix}1 & 0 \\ 0 & \sqrt{1-p}\end{pmatrix} \text{ and } M_1 = \begin{pmatrix}0 & \sqrt{p} \\ 0 & 0\end{pmatrix},$$ giving $$\varepsilon\left(\rho\right) = M_0\rho M_0^\dagger + M_1\rho M_1^\dagger$$
1 Or rather, several very broad concepts resulting from the same fundamental idea
2 I wouldn't go around calling this rigorous or anything
3 Within this context, naturally
Unfortunately for analog computation it turns out that when realistic assumptions about the presence of noise in analog computers are made, their power disappears in all known instances; they cannot efficiently solve problems which are not solvable on a Turing machine.
"Noise" appears to be used in the general sense of non-idealities in a signal:
In signal processing, noise is a general term for unwanted (and, in general, unknown) modifications that a signal may suffer during capture, storage, transmission, processing, or conversion.[1]
Sometimes the word is also used to mean signals that are random (unpredictable) and carry no useful information; even if they are not interfering with other signals or may have been introduced intentionally, as in comfort noise.
-"Noise (signal processing)", Wikipedia
For an example of what they're talking about, let's consider a simple circuit:
$$\require{enclose} \def\place#1#2#3{\smash{\rlap{\hskip{#1pt}\raise{#2pt}{#3}}}} % \bbox[10pt]{\enclose{box}{\phantom{\Rule{250pt}{75pt}{0pt}}}} % \place{-275}{70}{\enclose{box}{\bbox[5pt,lightblue]{ \begin{array}{c} \text{resistor} \\ \text{set resistance:}~R \end{array} }}} % \place{-270}{0}{ \enclose{box}{\bbox[5pt,lightblue]{ \begin{array}{c} \text{power source} \\ \text{set voltage:}~V \end{array} }}} % \place{-55}{30}{ \enclose{box}{\bbox[5pt,lightblue]{ \begin{array}{c} \text{current meter} \\ \text{measured current:}~I \end{array} }}}$$
Since we can select both $V$ and $R$ and we know Ohm's law, $I=\frac{V}{R}$, we can use this circuit to divide numbers for us:
1. Select some division problem to perform, $\frac{a}{b}=?$.
2. Set the voltage source to $V=a~\mathrm{V}$.
3. Set the resistor to $R=b~\mathrm{\Omega}$.
4. Measure $I=?~\mathrm{A}$ to get the result!
This is a simple analog computer that can divide numbers without need for us to perform the math in some other manner, e.g. digital logic.
But what's really cool about this? If we're naive, we might believe that it can do real computation:
In computability theory, the theory of real computation deals with hypothetical computing machines using infinite-precision real numbers. They are given this name because they operate on the set of real numbers. Within this theory, it is possible to prove interesting statements such as "The complement of the Mandelbrot set is only partially decidable."
These hypothetical computing machines can be viewed as idealised analog computers which operate on real numbers, whereas digital computers are limited to computable numbers.
-"Real computation", Wikipedia
The thing's that Ohm's law uses real-number values, $\left\{V,I,R\right\}{\in}\mathbb{R}$. If we believe that these values actually have infinite precision, then we can perform multiplication or division with infinite precision in finite time; this is a feat that a Turing machine can't perform with finite-time operations.
Anyway, back to the original quote:
Unfortunately for analog computation it turns out that when realistic assumptions about the presence of noise in analog computers are made, their power disappears in all known instances; they cannot efficiently solve problems which are not solvable on a Turing machine.
They're basically saying that, whenever someone's come up with a scheme like this, the non-idealities of the situation (noise in the signals, design, etc.) tend to derail the idealistic expectations.
The quoted excerpt seems to use this as a jumping-off point to discuss how quantum computers aren't as limited by this problem as classical analog computers often seem to have been.
Asking the author to clarify would give you the exact answer you are looking for. However, based upon the context provided I believe this may be related to the problem quantum noise spectroscopy attempts to solve.
## Noise
According to a team of Dartmouth researchers led by Professor Lorenza Viola,
These quantum properties are essential for quantum computing, but they are easily lost through decoherence, when quantum systems are subject to "noise" in an external environment.
The quantum properties she is referring too are quantum system properties such as the ability to be in a superposition of two different states simultaneously as stated in the same article.
## My Conclusion
Therefore, based upon both the context provided in the question and the context provided by the team of Dartmouth researchers, I would conclude that the noise the book refers to is environmental noise. | {"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": 30, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8617869019508362, "perplexity": 526.3954974442428}, "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/1603107890028.58/warc/CC-MAIN-20201025212948-20201026002948-00271.warc.gz"} |
https://www.studyxapp.com/homework-help/a-a-2-kg-metal-plate-slides-down-a-21meter-high-slope-at-thebottom-its-speed-is-q1572565151601319938 | # Question Solved1 AnswerA) A 2 kg metal plate slides down a 21-meter high slope. At the bottom its speed is 7 m/s. To the nearest Joule, what was the magnitude of the work done by friction? B) If the slope in the above problem is 43 degrees, what is the coefficent of friction (to 2 decimal places)?
YUHKCZ The Asker · Physics
A) A 2 kg metal plate slides down a 21-meter high slope. At the bottom its speed is 7 m/s. To the nearest Joule, what was the magnitude of the work done by friction?
B) If the slope in the above problem is 43 degrees, what is the coefficent of friction (to 2 decimal places)?
Transcribed Image Text: A) A 2 kg metal plate slides down a 21-meter high slope. At the bottom its speed is 7 m/s. To the nearest Joule, what was the magnitude of the work done by friction? B) If the slope in the above problem is 43 degrees, what is the coefficent of friction (to 2 decimal places)?
More
Transcribed Image Text: A) A 2 kg metal plate slides down a 21-meter high slope. At the bottom its speed is 7 m/s. To the nearest Joule, what was the magnitude of the work done by friction? B) If the slope in the above problem is 43 degrees, what is the coefficent of friction (to 2 decimal places)?
See Answer
Add Answer +20 Points
Community Answer
Y7YEQN The First Answerer
See all the answers with 1 Unlock
Get 4 Free Unlocks by registration
a) from conservation of Enersy{:[mgh=(1)/(2)mv^(2)+w_(f)],[2xx9.8 xx21=(1)/(2)xx2xx7^(2)+w_(f)],[w_(f)=2xx9.8 xx21-7^(2)]:}Woik done ly w_(f)=362.6J fric ... See the full answer | {"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": 0.9339698553085327, "perplexity": 1052.0963314225164}, "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-2023-06/segments/1674764495001.99/warc/CC-MAIN-20230127164242-20230127194242-00867.warc.gz"} |
http://www.zora.uzh.ch/id/eprint/68356/ | # Physical impacts of climate change on landslide occurrence and related 8 adaptation
Huggel, Christian; Khabarov, Nikolay; Korup, Oliver; Obersteiner, Michael (2012). Physical impacts of climate change on landslide occurrence and related 8 adaptation. In: Clague, John J; Stead, Douglas. Landslides: Types, Mechanisms and Modeling. Cambridge: Cambridge University Press, 121-133.
## Abstract
This chapter provides a review on current understanding of different effects of climate change on landslides and debris flows in cold, temperate, and tropical mountains. We start with observed impacts of climate change on shallow landslides and debris flows, followed by discussions of rock-slope failures, and the physical processes that make climate an important cause and trigger of landslides. While an increase in extreme precipitation has been observed in many regions worldwide over the past decades, changes in frequency and magnitude of landslides are more difficult to identify. In high mountain regions with snow, glacier and permafrost slope stability is not only sensitive to changes in precipitation but also to changes in temperature. In the European Alps an increase of high alpine rock slope failures has been detected over the past decades and correlates to an increase in mean air temperature.
Future projections generally indicate a further increase of extreme precipitation events that are likely to go along with an increase of landslide occurrence. Seasonal variations of precipitation and earlier melt of snow imply changes of landslide seasonality. Changes in sediment supply can furthermore strongly condition debris flow frequency and magnitude as recent studies have shown. We conclude this chapter with a case study, based on a model of a landslide early warning system, that outlines the potential and limitations of adaptation to future changes in precipitation.
## Abstract
This chapter provides a review on current understanding of different effects of climate change on landslides and debris flows in cold, temperate, and tropical mountains. We start with observed impacts of climate change on shallow landslides and debris flows, followed by discussions of rock-slope failures, and the physical processes that make climate an important cause and trigger of landslides. While an increase in extreme precipitation has been observed in many regions worldwide over the past decades, changes in frequency and magnitude of landslides are more difficult to identify. In high mountain regions with snow, glacier and permafrost slope stability is not only sensitive to changes in precipitation but also to changes in temperature. In the European Alps an increase of high alpine rock slope failures has been detected over the past decades and correlates to an increase in mean air temperature.
Future projections generally indicate a further increase of extreme precipitation events that are likely to go along with an increase of landslide occurrence. Seasonal variations of precipitation and earlier melt of snow imply changes of landslide seasonality. Changes in sediment supply can furthermore strongly condition debris flow frequency and magnitude as recent studies have shown. We conclude this chapter with a case study, based on a model of a landslide early warning system, that outlines the potential and limitations of adaptation to future changes in precipitation.
## Statistics
### Altmetrics
87 downloads since deposited on 28 Dec 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": 0.847568690776825, "perplexity": 2539.776195954161}, "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-2017-43/segments/1508187823839.40/warc/CC-MAIN-20171020063725-20171020083725-00621.warc.gz"} |
https://hal-lirmm.ccsd.cnrs.fr/lirmm-02991855 | # A Relaxation of the Directed Disjoint Paths Problem: A Global Congestion Metric Helps
2 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : In the Directed Disjoint Paths problem, we are given a digraph D and a set of requests {(s1, t1),. .. , (s k , t k)}, and the task is to find a collection of pairwise vertex-disjoint paths {P1,. .. , P k } such that each Pi is a path from si to ti in D. This problem is NP-complete for fixed k = 2 and W[1]-hard with parameter k in DAGs. A few positive results are known under restrictions on the input digraph, such as being planar or having bounded directed tree-width, or under relaxations of the problem, such as allowing for vertex congestion. Good news are scarce, however, for general digraphs. In this article we propose a novel global congestion metric for the problem: we only require the paths to be "disjoint enough", in the sense that they must behave properly not in the whole graph, but in an unspecified large part of it. Namely, in the Disjoint Enough Directed Paths problem, given an n-vertex digraph D, a set of k requests, and non-negative integers d and s, the task is to find a collection of paths connecting the requests such that at least d vertices of D occur in at most s paths of the collection. We study the parameterized complexity of this problem for a number of choices of the parameter, including the directed tree-width of D. Among other results, we show that the problem is W[1]-hard in DAGs with parameter d and, on the positive side, we give an algorithm in time O(n d+2 · k d·s) and a kernel of size d · 2 k−s · k s + 2k in general digraphs. This latter result has consequences for the Steiner Network problem: we show that it is FPT parameterized by the number k of terminals and d, where d = n − c and c is the size of the solution.
Keywords :
Document type :
Conference papers
Domain :
Cited literature [26 references]
https://hal-lirmm.ccsd.cnrs.fr/lirmm-02991855
Contributor : Isabelle Gouat <>
Submitted on : Friday, November 6, 2020 - 10:45:03 AM
Last modification on : Monday, December 14, 2020 - 5:27:16 PM
Long-term archiving on: : Sunday, February 7, 2021 - 6:32:30 PM
### File
LIPIcs-MFCS-2020-68.pdf
Files produced by the author(s)
### Citation
Raul Lopes, Ignasi Sau Valls. A Relaxation of the Directed Disjoint Paths Problem: A Global Congestion Metric Helps. 45th International Symposium on Mathematical Foundations of Computer Science (MFCS), Aug 2020, Prague, Czech Republic. pp.68:1-68:15, ⟨10.4230/LIPIcs.MFCS.2020.68⟩. ⟨lirmm-02991855⟩
Record views | {"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": 0.8328111171722412, "perplexity": 1366.3059080902485}, "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-2021-39/segments/1631780057830.70/warc/CC-MAIN-20210926053229-20210926083229-00476.warc.gz"} |
https://theportal.wiki/wiki?title=The_Road_to_Reality_Study_Notes&diff=6065&oldid=6029 | # Difference between revisions of "The Road to Reality Study Notes"
Each week The Road to Reality Book Club tackles a chapter of Sir Roger Penrose's Epic Tome. We use these meetings as an opportunity to write down the major points to be taken from our reading. Here we attempt to sum up what we believe Penrose was trying to convey and why. The hope is that these community-generated reading notes will benefit people in the future as they go on the same journey.
Chapters 1-16 focus on mathematical concepts while the later chapters use this background to describe the physical world.
## Chapter 1 The Roots of Science
### 1.1 The quest for the forces that shape the world
Understanding natural processes has been a common pursuit since the dawn of humanity. After many millennia of chaos and frustration, it was discovered that the regular movement of celestial bodies, such as the sun and moon, could be described mathematically. It became apparent that mathematics unlocked deep truths about the universe. Many people in ancient times allowed their imaginations to be carried away by their fascination with the subject, leading to mystical associations with mathematical objects. One famous example from the ancient Greeks is the association between Platonic solids and the basic elementary states of matter.
### 1.2 Mathematical truth
There was a need to define a more rigorous method for differentiating truth claims. The Greek philosopher Thales of Miletus (c. 625-547 BC) and Pythagoras of Samos (c. 572-497 BC) are considered to be the first to introduce the concept of mathematical proof. Developing a rigorous mathematical framework was central to the development of science. Mathematical proof allowed for much stronger statements to be made about relationships between the arithmetic of numbers and the geometry of physical space.
A mathematical proof is essentially an argument in which one starts from a mathematical statement, which is taken to be true, and using only logical rules arrives at a new mathematical statement. If the mathematician hasn't broken any rules then the new statement is called a theorem. The most fundamental mathematical statements, from which all other proofs are built, are called axioms and their validity is taken to be self-evident. Mathematicians trust that the axioms, on which their theorems depend, are actually true. The Greek philosopher Plato (c.429-347 BC) believed that mathematical proofs referred not to actual physical objects but to certain idealized entities. Physical manifestations of geometric objects could come close to the Platonic world of mathematical forms, but they were always approximations. To Plato the idealized mathematical world of forms was a place of absolute truth, but inaccessible from the physical world.
### 1.3 Is Plato's mathematical world "real"?
Penrose asks us to consider if the world of mathematics in any sense real. He claims that objective truths are revealed through mathematics and that it is not a subjective matter of opinion. He uses Fermat's last theorem as a point to consider what it would mean for mathematical statements to be subjective. He shows that "the issue is the objectivity of the Fermat assertion itself, not whether anyone’s particular demonstration of it (or of its negation) might happen to be convincing to the mathematical community of any particular time". Penrose introduces a more complicated mathematical notion, the axiom of choice, which has been debated amongst mathematicians. He notes that "questions as to whether some particular proposal for a mathematical entity is or is not to be regarded as having objective existence can be delicate and sometimes technical". Finally he discusses the Mandelbrot set and claims that it exists in a place outside of time and space and was only uncovered by Mandelbrot. Any mathematical notion can be thought of as existing in that place. Penrose invites the reader to reconsider their notions of reality beyond the matter and stuff that makes up the physical world.
For further discussion from Penrose on this topic see Is Mathematics Invented or Discovered?
### 1.4 Three worlds and three deep mysteries
Figure 1.3: Penrose three worlds
Penrose outlines his conception of three worlds:
• The Platonic Mathematical
• The Physical
• The Mental
as show in figure 1.3. Connections between these worlds present a great number of mysteries. The main focus of the book is to explore the connection between mathematics and its use in describing the physical world. Note that only a small subset of the mathematical world us utilized in describing the physical world. The reason why mathematics can describe the physical world so accurately is unknown. Moving in the counter clockwise direction there is a mysterious connection between the physical world and that of the mind. He believes that there must be some basis of consciousness in physical reality, but it is still unknown. Finally there is the connection between the mental world and mathematics. Penrose believes that there is no mathematical notion beyond our mental construction. He highlights that this figure represents many of his prejudices and might upset some people. Maybe the connections from one world do not fully describe the other, or are incomplete. Penrose believes that not much progress can be made with respect to the mental world until we know much more about the physical world.
### 1.5 The Good, the True, and the Beautiful
The full conception of Plato's theory of forms was not limited to only mathematical notions. Mathematics was linked to the concept of Truth but Plato was also interested in the absolute idealized forms of Beauty and Good. Beauty plays an important role in many mathematical discoveries and is often used as a guide to the truth. Questions of morality are of less relevance in this context but are critical with respect to the mental world. Moral debates are outside of the scope of this book but must be considered as science and technology progress. Penrose notes that figure 1.3 has purposely been constructed to be paradoxical in the sense that each world is entirely encompassed by the next. He writes "There may be a sense in which the three worlds are not separate at all, but merely reflect, individually, aspects of a deeper truth about the world as a whole of which we have little conception at the present time."
## Chapter 2 An ancient theorem and a modern question
### 2.1 The Pythagorean theorem
To explore the process of pursuing mathematical truth, Penrose outlines a few proofs of the Pythagorean theorem. The theorem can be stated as such, "For any right-angled triangle, the squared length of the hypotenuse $$c$$ is the sum of the squared lengths of the other two sides $$a$$ and $$b$$ or in mathematical notation $$a^2 + b^2 = c^2.$$
There are hundreds of proofs of the Pythagorean theorem but Penrose chooses to focus on two. The first involves filling up a plane with squares of two different sizes. Then adding a second pattern on top of tiled squares connecting the centers of the larger original squares. By translating the tilted pattern to the corner of the large square and observing the areas covered by the pattern you can show that the square on the hypotenuse is equal to the sum of the squares on the other two sides. While the outlined proof appears reasonable there are some implicit assumptions made. For instance what do you mean when we say square? What is a right angle?
### 2.2 Euclid's postulates
Euclid of Alexandria, sometimes referred to as the "father of geometry", was one of the first people to attempt to outline and document the assumptions that went into his geometrical arguments. Euclid broke these assumptions into two categories, axioms which were self-evident, essentially definitions, and a set of five postulates which were less certain, but appeared true. Penrose outlines the first 4 postulates as:
1. There is a (unique) straight line segment connecting any two points.
2. There is an unlimited (continuous) extendibility of any straight line segment.
3. There existence a circle with any centre and with any value for its radius.
4. There is equality of all right angles.
Euclid was trying to establish the rules which govern his geometry. Some interesting ideas start to emerge such as the indefinitely extendible geometric plane and the concept of congruence. Penrose writes "In effect, the fourth postulate is asserting the isotropy and homogeneity of space, so that a figure in one place could have the ‘same’ (i.e. congruent) geometrical shape as a figure in some other place". Surprisingly Euclid's first four postulates still align well with our understanding of a two-dimensional metric space.
Euclid's fifth postulate, also known as the parallel postulate, was more troublesome. In Penrose words "it asserts that if two straight line segments $$a$$ and $$b$$ in a plane both intersect another straight line $$c$$ (so that $$c$$ is what is called a transversal of $$a$$ and $$b$$) such that the sum of the interior angles on the same side of $$c$$ is less than two right angles, then $$a$$ and $$b$$, when extended far enough on that side of $$c$$, will intersect somewhere". One can see that the formulation of the fifth postulate is more complicated than the rest which lead to speculation of it's validity. With the fifth postulate one can go on to properly build a square and begin to explore the world of Euclidean geometry.
### 2.3 Similar-areas proof of the Pythagorean theorem
Penrose revisits the Pythagorean theorem by outlining another proof. Starting with a right triangle, subdivide the shape into two smaller triangles by drawing a line perpendicular to the hypotenuse through the right angle. The two smaller triangles are said to be similar to one another meaning they have the same shape but are different sizes. This is true because each of the smaller triangles has a right angle and shares an angle with the larger triangle. The third angle known because the sum of the angles in any triangle is always the same. Knowing that the sum of the area of the two small triangles equals the area of the big triangle (by construction), we can square the sides and show that the pythagorean theorem holds.
Again Penrose asks us to revisit our assumptions and examine which of Euclid's postulates were needed. Particularly our claim that the sum of the angles in a triangle add up to the same value of 180° (or $$\pi$$ radians). One must use the parallel postulate to show that this is true. Penrose asks us to consider what would it mean for the parallel postulate to be false? What would that imply? Would that make any sense? With these questions in mind we begin to explore a different kind of geometry.
### 2.4 Hyperbolic geometry: conformal picture
M. C. Escher’s woodcut Circle Limit I, illustrating the conformal representation of the hyperbolic plane.
The topic of questioning fundamental assumptions is taken to a level deeper with the example of Euclid’s fifth postulate and hyperbolic geometry, illustrated with M.C. Escher’s Circle limit I. The notion that all the black and white fish near the boundary are equal in ‘size’ to the fish near the center starts the section with an interesting point of confusion between our visual perception of Euclidean geometry and the hyperbolic representation.
Within the hyperbolic plane, Euclid’s first four postulates hold true, however, the fifth parallel postulate is false. Penrose notes some interesting consequences of this are that the interior angles of a triangle do not add to π, the Pythagorean theorem fails to hold, and a given shape does not have a similar shape of a larger size. The idea of conformal representations is then introduced with the example that angular relations between lines in the Euclidean and this representation of the hyperbolic plane are precisely the same.
Penrose then gives us the relation between the interior angles of the hyperbolic triangle to its area and says that while there is a sense of ‘unpleasantness’ with the fact that the sum of the interior angles of a triangle within the hyperbolic frame do not add to π, there is something ‘elegant and remarkable’ in direct relation of these angles to the area of the triangle, which is impossible to show within the Euclidean framework. He then leaves us with the equation for hyperbolic distance and notes that with this, hyperbolic geometry has all the properties of Euclidean geometry apart from those that need the parallel postulate, and this allows us to form congruent shapes.
### 2.5 Other representations of hyperbolic geometry
Since hyperbolic geometry is a more abstract construct, the conformal representation presented in section 2.4 is not the only way to represent hyperbolic geometry in terms of Euclidean geometry. Projective representations are next presented, where the difference is that hyperbolic straight lines are now represented as Euclidean straight lines. The cost of this ‘simplification’ is that angles are no longer the same. Penrose gives the reader an equation which allows the projective geometry to be obtained from a radial expansion from the center of the conformal representation.
The geometer Eugenio Beltrami is introduced as having discovered a geometric method relating these different hyperbolic representations which involve projections from the plane to spherical surfaces and back. Imagine the hyperbolic plane cuts a sphere at the equator. Hemispheric representation is the hyperbolic geometry representation on the northern hemisphere of the Beltrami sphere, found from projecting the projective representation upward onto its surface. Straight Euclidean lines in the plane are now semicircles which meet the equator orthogonally. Stereographic projection is introduced with the example of projecting these semicircles back onto the plane but projecting from the point of the south pole. This beautifully gives us the conformal representation on the plane. Two important properties of stereographic projection are:
• Conformal, so angles are preserved
• Sends circles on the sphere to circles on the plane
It is then emphasized that each of these representations are merely ‘Euclidean models’ of hyperbolic geometry and are not to be taken as what the geometry actually ‘is’. In fact, there are more representations such as the Minkowskian geometry of special relativity. The idea of a generalized ‘square’ is then presented in conformal and projective hyperbolic representations to show an interesting generalization of the Euclidean square.
### 2.6 Historical aspects of hyperbolic geometry
A historical backdrop is painted for the discovery of hyperbolic geometry as well as the importance of the proof by contradiction. Girolamo Saccheri’s work in 1733 used the proof by contradiction in attempt to prove Euclid’s fifth, but failed to show a contradiction. He did however discover the nature of hyperbolic geometry.
Following Saccheri, Heinrich Lambert derived many results by using this same method, including the hyperbolic angle/area relation that was mentioned in section 2.4. His tentative reasoning for belief in a consistent geometry without the fifth postulate was thinking about geometry on a ‘sphere of imaginary radius’. To illustrate this, Thomas Hariot’s angle/area relation for a Euclidean spherical triangle is given and compared to Lamberts hyperbolic relation. Lambert’s formula is recovered by replacing R2 with -1/R2 , showing that the ‘pseudo-radius’ is in fact imaginary: -C-1/2 .
Penrose makes the point that there are many instances in mathematics where the name attached to a concept is not that of the original discoverer. Some examples given:
• It is typical to attribute the discovery and first full acceptance of this geometry differing from Euclid’s via the absence of the fifth postulate to Carl Friedrich Gauss, but because Gauss did not publish his work, Janos Bolyai and Nicolai Ivanoivich Lobachevsky are also named as having independently rediscovered this geometry a few decades later. Hyperbolic geometry is frequently referred to as Lobachevskian geometry.
• Eugenio Beltrami was mentioned in section 2.5 for the discovery of the relations between the projective and conformal, via the hemispherical realizations. The conformal representation is commonly referred to as the Poincare model and the projective representation as the ‘Klein’ representation after their rediscoveries later in the 19th century. Beltrami is however best known for his pseudo-sphere representation involving Newton’s tractrix curve.
### 2.7 Relation to physical space
Penrose ends chapter 2 with a short discussion on the applicability of hyperbolic geometry to physical space. He notes that the geometry works perfectly well in higher dimensions and asks the question about our universe on cosmological scale. Is it Euclidean? Hyperbolic?
There are three types of geometry that would satisfy isotropy and homogeneity: Euclidean, hyperbolic, and elliptic. Einstein’s general relativity shows that Euclidean, although very accurate, is only an approximation of the actual geometry. We do not yet know the answer to the above question. There is evidence and support for each of the three geometries, but Penrose is transparent in his preference of the hyperbolic argument.
Penrose states that ‘fortunately for those…who are attracted to the beauties of hyperbolic geometry’, the space of velocities, according to modern relativity theory, is certainly a three-dimensional hyperbolic geometry rather than Euclidean.
He ends the chapter by stating that the Pythagorean theorem remains vital. The ‘Riemannian’ geometries that generalize hyperbolic geometry depend on the theorem in the limit of small distances, even though it is superseded for ‘large’ distances.
## Chapter 3 Kinds of number in the physical world
### 3.1 A Pythagorean catastrophe?
We now switch over to the idea of ‘number’, and the layers of generality that lie beneath integers. The Pythagoreans solved the question, by using proof by contradiction, of attempting to find a rational number (fraction) whose square is precisely 2. There does not exist such a number within the confines are integers and rationals, which was troubling for them at the time since it was desired to have all of geometry be described by these types of physical numbers.
Penrose gives the proof by contradiction for the Pythagorean question above and explains the necessity of identifying the precise assumptions that go into a proof. He explains that there exist other generalities than that was originally used in the proof, whereby these precise assumptions must be used to judge the logic. The Pythagoreans used integers and rationals to explain the existence of the real numbers.
### 3.2 The real number system
Natural Numbers:
‘Counting’ numbers from 1 to $$\infty$$.
Whole Numbers:
All counting numbers including 0, cannot be a fraction.
Integers:
All natural numbers and their negative counterparts and 0. If and are integers, then their sum , their difference , and their product are all integers (that is, the integers are closed under addition and multiplication), but their quotient may or may not be an integer, depending on whether can be divided by with no remainder.
Rational Numbers:
A number that can be expressed as the ratio a/b of two integers (or whole numbers) a and b, with b non-zero. The decimal expansion is alyas ultimately periodic, at a certain point the infinite sequence of digits consists of some finite sequence repeated indefinitely.
Irrational Numbers:
A number that cannot be expressed as the ratio of two integers. When an irrational number is expressed in decimal notation it never terminates nor repeats.
Arise in the solution of a general quadratic equation:
$Ax^{2} + Bx + C = 0$
With A non-zero, the solutions being (derived from the quadratic formula):
$-\frac{B}{2A}\sqrt{\left(\frac{B}{2A}\right)^2}+\frac{C}{A}, \quad -\frac{B}{2A}\sqrt{\left(\frac{B}{2A}\right)^2}-\frac{C}{A}$
where, to keep within the realm of real numbers, be must have B2 greater than 4AC. When A, B, and C are integers or rational numbers, and where there is no rational solution to the equation, the solutions are quadratic irrationals.
Real Numbers:
A number in the set of all numbers above that falls on the real number line. It can have any value.
Algebraic Real Numbers:
Any number that is the solution to a polynomial with rational coefficients.
Transcendental Real Numbers
Any number that is not the solution to a polynomial with rational coefficients.
### 3.3 Real numbers in the physical world
Penrose states that while the historical driving force for mathematical ideas were to find constructs that mimic the behavior of the physical world, it is normally not possible to examine the physical world in such precise detail to abstract clear cut mathematics from it. Instead, the mathematics provides its own ‘momentum’ within the subject itself whereby it may seem to diverge from what it had been set up to achieve, but ultimately leads us to a deeper meaning of the world.
The real number system is given as an example of this since no direct evidence from Nature exists to show that the physical notion of ‘distance’ extends from arbitrarily large scales to the indefinitely tiny. Though, from cosmological scale to the quantum, to volumes and the metrics of spacetime, the ranges are increasing, and the fundamentals of calculus rely on the infinitesimal.
We may still ask whether the real number system is ‘correct’ for describing the physical universe or have we gotten lucky with extrapolation thus far. Penrose describes quantum mechanics as not implying any discreteness to Nature, nevertheless this idea may persist and echoes a quote from Einstein’s last published work where he suggested ‘discretely based algebraic theory’ might be the way forward for future physics. Penrose ends with stating that his idea of spin networks are both discrete and foundational in quantum gravity, led to his Twistor Theory, but real numbers are still fundamental in our understanding of the physical world.
### 3.4 Do natural numbers need the physical world?
Progressing this philosophical train of thought to the natural numbers, Penrose notes that the operations of addition and multiplication of natural numbers are independent of the nature of geometry of the world. Perhaps our notion of these numbers depends upon our universe specifically, but he stresses that it is hard to imagine that there would not be an important role for such fundamental entities.
To support this, Penrose introduces us to the idea of a set, which is an abstraction that does not appear to be tied to the specific structure of the universe. He then describes a method by which an empty or null set can be used to conjure the natural number system, out of nothing but the abstract idea of a set itself, and states that this technique can be used for the real number system as well.
Penrose ends by referring us back to Fig 1.3 (depiction of the mental, physical, and platonic worlds) and notes the mysterious nature of the fact that natural and real numbers having no reliance on the physical world for their existence, yet they seem to have direct relevance in describing the structure of the world.
### 3.5 Discrete numbers in the physical world
What might it mean to say that there are minus three cows in a field? An interesting question to start us thinking about the nature of discrete numbers and negatives in our world as defined as scalar quantities. Penrose states that only in the last hundred years that the integers in the negative seem to have direct physical relevance.
Electric charge is quantified in terms of integral multiples, positive, negative, or zero. Further, the three quarks within protons have charges 2/3, 2/3, -1/3. Is this the fundamental entity, and as such, the basic unit of charge is 1/3? This is just one example of an additive quantum number and Penrose notes that our present knowledge is that “all known additive quantum numbers are indeed quantified in terms of the system of integers…” Further, Dirac’s antiparticle theory shows us a physical and meaningful use for the negative numbers in which the additive quantum number of the antiparticle has precisely the negative of the value that it has for the original particle.
Penrose ends the chapter by stating that there are other kinds of number that appear to play a fundamental role in the universe, the most important and striking of which are the complex numbers. While they are fundamental to mathematics, “it is an even more striking instance of the convergence between mathematical ideas and the deeper workings of the physical universe”.
## Chapter 4 Magical Complex Numbers
Penrose introduced the complex numbers, extending addition, subtraction, multiplication, and division of the reals to the system obtained by adjoining i, the square root of -1. Polynomial equations can be solved by complex numbers, this property is called algebraic closure and follows from the Fundamental Theorem of Algebra.
Complex numbers can be visualized graphically as a plane, where the horizontal coordinate gives the real coordinate of the number and the vertical coordinate gives the imaginary part. This helps understand the behavior of power series; for example, the power series $$1-x^2+x^4+\cdots$$ converges to the function $$1/(1+x²)$$ only when $$|x|<1$$, despite the fact that the function doesn't seem to have "singular" behavior anywhere on the real line. This can be explained by switching to the complex number system using $$z=x+iy$$ whereby $$1/(1+z²)$$ can be examined to have singularities at $$x=i,-i$$.
With this, Penrose introduces us to the idea of the circle of convergence as a circle in the complex plane centered at 0 with poles/singularities of $$f(z)$$ defining the circle radius. The series is convergent for any point z inside of this circle.
Finally, the Mandelbrot set is defined as the set of all points $$c$$ in the complex plane so that repeated applications of the transformation mapping $$z$$ to $$z^2+c$$, starting with $$z=0$$, do not escape to infinity.
## Chapter 5 Geometry of logarithms, powers, and roots
### 5.1 Geometry of complex algebra
Penrose asks us to view complex addition and multiplication as transformations from the complex plane to itself, rather than just as simple addition and multiplication. The visual representations of these operations are given as the parallelogram and similar-triangle laws for addition and multiplication respectively.
Rather than just ‘adding’ and ‘multiplying’ these can be viewed as ‘translation’ and ‘rotation’ within the complex plane. For example, multiply a real number by the complex number $$i$$ rotates the point in the complex plane π/2 and viewing the parallelogram and similar-triangle laws as translation and rotation:
Penrose further introduces the concept of polar coordinates where $$r$$ is the distance from the origin and $$θ$$ is the angle made from the real axis in an anticlockwise direction.
### 5.2 The idea of the complex logarithm
Armed with both the cartesian and polar representations of complex numbers, it is now possible to show that the multiplication of two complex numbers leads to adding their arguments and multiplying the moduli. This, for the moduli, converts multiplication into addition.
This idea is fundamental in the use of logarithms. We first start with the expression $$b^{m+n} = b^m \times b^n$$, which represents the idea of exponentiation. This is easy to grasp for $$m$$ and $$n$$ being positive integers, as each side just represents $$m+n$$ instances of the number $$b$$, all multiplied together. If $$b$$ is positive, this law is then showed to hold for exponents that are positive integers, values of 0, negative, and fractions. If $$b$$ is negative, we require further expansion into the complex plane.
We would need a definition of $$b^p$$ for all complex numbers $$p,q,b$$ such that $$b^{p+q} = b^p \times b^q$$. If we then define the logarithm to the base b as the inverse of the function $$f(z) = b^z$$ such that $$z=log_bw$$ for $$w=b^z$$ then we should expect $$z=log_b(p \times q) = log_bp + log_bq$$. This would then convert multiplication into addition and allow for exponentiation in the complex plane.
### 5.3 Multiple valuedness, natural logarithms
We need to be careful with the above assertion of the logarithm, mainly since $$b^z$$ and $$log_bw$$ are ‘many valued’. Solving the equations would require a particular choice for $$b$$ to isolate the solution. With this, the ‘base of natural logarithms’ is introduced as the number e, whose definition is the power series $$1+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+…$$. This power series converges for all values of z which then makes for an interesting choice to solve the ambiguity problem above. Thus we can rephrase the problem above with the natural logarithm, $$z=logw$$ if $$w=e^z$$.
However, even with this natural logarithm we run into multi-valuedness ambiguity from above. Namely that $$z$$ still has many values that lead to the same solution with $$z+2πin$$, where $$n$$ is any integer we care to choose. This represents a full rotation of $$2π$$ in the complex plane with all multiples of $$n$$ achieving the same point, $$z$$.
Penrose goes further in representing $$z$$ with polar coordinates showing $$z=logr+iθ$$, then $$e^z=re^{iθ}$$. This formulation shows us that when we multiply two complex numbers, we take the product of their moduli and the sum of their arguments (using the addition to multiplication formula introduced in 5.2).
Rounding out the chapter, Penrose gives us another further representation of assuming $$r=1$$, such that we recover the ‘unit circle’ in the complex plane with $$w=e^{iθ}$$. We can 'encapsulate the essentials of trigonometry in the much simpler properties of complex exponential functions' on this circle by showing $$e^{iθ}=cos(θ) + isin(θ)$$.
• $$e^{i\theta}$$ is helpful notation for understanding rotating
• $$e^{i\theta} = cos \theta + i sin \theta$$
• (Worth looking into Taylor Series, which is related.)
### 5.4 Complex Powers
Returning to the ambiguity problem of multi-valuedness, it seems the best way to avoid issues is when a particular choice of $$logw$$ has been specified. As an example, $$w^z$$ with $$z=\frac{1}{2}$$. We can specify a rotation for $$logw$$ to achieve $$+w^\frac{1}{2}$$, then another rotation of $$logw$$ to achieve $$-w^\frac{1}{2}$$. The sign change is achieved because of the Euler formula $$e^{πi}=-1$$. Note the process$w^z=e^{zlogw}=e^{zre^{iθ}}=e^{ze^{iθ}}$, then specifying rotations for theta allows us to achieve either $$+w^\frac{1}{2}$$ or $$-w^\frac{1}{2}$$.
Penrose notes an interesting curiosity for the quantity $$i^i$$. We can specify $$logi=\frac{1}{2}πi$$ because of the general relationship $$logw=logr+iθ$$. If $$w=i$$, then its easy to see $$logi=\frac{1}{2}πi$$ from noting that y is on the vertical axis in the complex plane (rotation of $$\frac{π}{2}$$). This specification, and all rotations, amazingly achieve real number values for $$i^i$$.
We end the section with the idea of finite multiplicative groups, or cyclic groups Zn, which contain $$n$$ quantities (nth roots of unity if around the unit circle) with the property that any two can be multiplied together to get another member of the group. As an example, Penrose gives us $$w^z=e^{ze^{i(θ+2πin)}}$$ with $$n=3$$, leading to three elements $$1, ω, ω^2$$ with $$ω=e^\frac{2πi}{3}$$. Note $$ω^3=1$$ and $$ω^-1=ω^2$$. These form a cyclic group Z3 and in the complex plane, represent vertices of an equilateral triangle. Multiplication by ω rotates the triangle through $$\frac{2}{3}π$$ anticlockwise and multiplication by $$ω^2$$ turns it through $$\frac{2}{3}π$$ clockwise. The cyclic group is graphically shown below:
### 5.5 Some Relations To Modern Particle Physics
Penrose rounds out the chapter with some examples of complex concepts in the world of particle physics. Additive quantum numbers were briefly introduced in section 3.5, and here we are introduced to multiplicative quantum numbers, which are quantified in terms of nth roots of unity.
The notion of parity is introduced as approximately a multiplicative quantum number with n=2, and an example is the family of particles called bosons. Penrose notes that fermions could also be considered a parity group but it is not the normal convention. The distinction between these two particles are that bosons are completely restored to their original states under a $$2π$$ rotation, whereas fermions require $$4π$$ (two rotations). Thus a multiplicative quantum number of $$-1$$ can be assigned to a fermion and $$+1$$ to a boson.
An example of a multiplicative quantum number with $$n=3$$ relates to quarks, which have values for electric charge that are not integer multiples of the electron’s charge, but in fact $$\frac{1}{3}$$ multiples. If $$q$$ is the value of electric charge with respect to an electron ($$q=-1$$ for electron charge), then quarks have q=$$\frac{2}{3}$$ or $$-\frac{1}{3}$$ and antiquarks q=$$\frac{1}{3}$$ or $$-\frac{2}{3}$$. If we take the multiplicative quantum number $$e^{-2qπi}$$, then we find the values $$1,ω,ω^2$$ from section 5p4, which constitute the cyclic group Z3.
## Chapter 6 Real-number calculus
### 6.1 What makes an honest function?
Calculus is built from the two ingredients, differentiation and integration. Differentiation is a local phenomenon which concerns the rates that things change whereby integration is a more quantity that measures the totality. Incredibly, these two ingredients are the inverse of one another (fundamental theorem of calculus).
These two operate on ‘functions’ and Penrose notes that these can be thought of as ‘mappings’ from some array of numbers (domain) to another (target). Penrose gives the three examples below which will be used later in the chapter as mapping the real number system to itself:
### 6.2 Slopes of functions
Differentiation is concerned with and calculates the rates that things change, or ‘slopes’ of these things. For the curves given in section 6p1 above, two of the three do not have unique slopes at the origin and are said to be not differentiable at the origin, or not smooth there. Further, the curve of theta(x) has a jump at the origin which is to say that it is discontinuous there, whereas $$|x|$$ and $$x^2$$ were continuous everywhere.
Taking differentiation a step further, Penrose shows us two plots which look very similar, but are represented by different functions, $$x^3$$ and $$x|x|$$. Each are differentiable and continuous, but the difference has to do with the curvature (second derivative) at the origin. $$x|x|$$ does not have a well-defined curvature here and is said to not be twice differentiable.
### 6.3 Higher derivatives; $$C^\infty$$-smooth functions
Looking closer at the concept of two derivatives of the same function (second derivative, or curvature), Penrose shows us the functions from 6p2 and their first and second derivatives. Note that the first derivative of $$f(x)$$, written $$f’(x)$$, meets the x-axis at places of local minima or maxima and the second derivative of $$f(x)$$, written $$f’’(x)$$, meets the x-axis where the curvature goes to $$0$$ and is said to be a point of inflection.
In general, a function can be smooth for many derivatives and the mathematical terminology for general smoothness is to say that $$f(x)$$ is $$C^n$$-smooth. It can be seen that $$x|x|$$ is $$C^1$$-smooth but not $$C^2$$-smooth due to the discontinuity at the origin in the derivative. In general $$x^n|x|$$ is $$C^n$$-smooth but not $$C^{n+1}$$-smooth. In fact, a function can be $$C^\infty$$-smooth if it is smooth for every positive integer. Note that negative integers for $$x^n$$ immediately are not smooth for $$x^{-1}$$ (discontinuous at the origin).
Penrose notes that Euler would have required $$C^\infty$$-smooth functions to be defined as functions, and then gives the function: $h(x) = \begin{cases} 0, & \mbox{if } x \le 0 \\ e^{-\frac{1}{x}}, & \mbox{if } x > 0 \end{cases}$ as an example of a $$C^\infty$$-smooth function but one that Euler would still not be happy with since it is two functions stuck together.
### 6.4 The "Eulerian" notion of a function?
How, then do we define the notion of a ‘Eulerian’ function? This can be accomplished in two ways. The first using complex numbers and is incredibly simple. If we extend $$f(x)$$ to $$f(z)$$ in the complex plane, then all we require is for $$f(z)$$ to be once differentiable (a kind of $$C^1$$-smooth function). That’s it, magically. We will see that this can be stated with $$f(x)$$ being an analytic function.
The second method involves power series manipulations, and Penrose notes that ‘the fact that complex differentiability turns out to be equivalent to power series expansions is one of the truly great pieces of complex-number magic’.
For the second method, the power series of $$f(x)$$ is introduced, $$f(x) = a_0 + a_1x + a_2x^2 + a_3x^3 + …$$ For this series to exist then it must be $$C^\infty$$-smooth. We must take and evaluate derivatives $$f(x)$$ to find the coefficients, thus an infinite number of derivatives (positive integers) must exist for the power series to exist. If we evaluate $$f(x)$$ at the origin, we call this a power series expansion about the origin. About any other point $$p$$ would be considered a power series expansion about $$p$$. (Maclaurin Series about origin, see also Taylor Series for the general case)
The power series is considered analytic if it encompasses the power series about point $$p$$, and if it analytic at all points of its domain, we call it an analytic function, or equivalently a $$C^ω$$-smooth function. Euler would be pleased with this notion of an analytic function, which is ‘smoothier’ than the set of $$C^\infty$$-smooth functions ($$h(x)$$ from 6p3 is $$C^\infty$$-smooth but not $$C^ω$$-smooth).
• Physics in trying to understand reality by approximating it.
### 6.5 The rules of differentiation
• Armed with these few rules (and loads and loads of practice), one can become an "expert at differentiation" without needing to have much in the way of actual understanding of why the rules work!
### 6.6 Integration
As stated in section 6p1, integration is the inverse of differentiation as stated in the fundamental theorem of calculus. Penrose provides the following visual and explanation. If we start with the differentiated curve, the area underneath the derivative curve bounded by two points on the x-axis, and the x-axis itself is equal to the difference in heights of the original curve evaluated at the two points.
Integration is noted as making the function smoother and smoother, whereas differentiation continues to make things ‘worse’ until some functions reach a discontinuity and become ‘non-differentiable’.
Penrose ends the chapter noting that there are approaches which enable the process of differentiation to be continued indefinitely, even if the function is not differentiable. One example is the Dirac Delta Function which is of ‘considerable importance in quantum mechanics’. This extends our notion of $$C^n$$-functions into the negative integer space ($$C^{-1},C^{-2},...$$) and will be discussed later with complex numbers. Penrose notes that this leads us further away from the ‘Eulerian’ functions, but complex numbers provide us with an irony that expresses one of their finest magical feats of all.
• If we integrated then differentiate, we get the same answer back. Non-commutative the other way.
## Chapter 7 Complex-number calculus
### 7.1 Complex smoothness; holomorphic functions
An outline for section 7 is presented, in which calculus with complex numbers is introduced. The material in this chapter leads up to the explanation of holomorphic functions, which play a vital role in much of the mathematical as well as physics material later in the book.
To do so, the notion of a special type of integration along a contour in the complex plane is to be defined. This integration can then be used to solve for the coefficients of a Taylor series expression which allow for us to see that any complex function which is complex-smooth in the complex plane is necessarily analytic, or holomorphic.
As will be stated in 7.3, instead of directly providing the definition of holomorphic functions, Penrose chooses to demonstrate the argument with the ingredients in order to show a "wonderful example of the way that mathematicians can often obtain their results. Neither the premise ($$f(z)$$ is complex-smooth) nor the conclusion ($$f(z)$$ is analytic) contains a hint of the notion of contour integration or the multivaluedness of a complex logarithm. Yet these ingredients provide the essential clues to the true route to finding the answer".
### 7.2 Contour integration
In the real number sense, integrals are taken from a single point $$a$$ to another point $$b$$ along the real number line. Usually the horizontal axis, and there is only one way to travel along this line (moving positive and negative along the axis). However, in the complex plane points involve two dimensions, and therefore have many such routes that allow us to get from a complex point $$a$$ to $$b$$.
The Cauchy-Riemann equations (to be formally introduced later in chapter 10) allow us to narrow our focus to find a path-specific answer, where the value of the integral on this path is the same for any other path that can be formed from the first by continuous deformation in its domain. Note that the function $$\frac{1}{z}$$ has a hole in the domain at the origin, which can prevent a continuous deformation thereby allowing for different answers for the value of the integral depending on the path taken.
Continuous deformation in this sense is defined as homologous deformation, where parts of the path can cancel each other out if they are traversed in opposite directions. This contrasts with homotopic paths where you may not cancel parts. As a visualization we take the function of $$\frac{1}{z}$$ with a homologous path:
The amazing result here is that a general contour from $$a$$ to $$b$$ for the function $$\frac{1}{z}$$ has be rephrased and shown to be equal to the result for a closed contour that loops around the point of non-analyticity (the origin in this case), regardless of where the points $$a$$ and $$b$$ (or the point of non-analyticity) lie in the complex plane. Note that since $$logz$$ is multi-valued, we need to specify the actual closed contour being used (if we looped twice rather than once, then the answer is different).
### 7.3 Power series from complex smoothness
The example in section 7p2 is a particular case for the well-known Cauchy Integral Formula, which allows us to know what the function is doing at the origin (or another general point $$p$$) by what it is doing at a set of points surrounding the origin or the general point $$p$$.
$\frac{1}{2πi}\oint\frac{f(z)}{z-p}dz=f(p)$
A 'higher-order' version of this formula allows us to inspect $$n$$ number of derivatives with the same relationship.
$\frac{n!}{2πi}\oint\frac{f(z)}{(z-p)^{n+1}}dz=f^{(n)}(p)$
If we use this to provide the definition of a derivative at a point, we can then construct a Maclaurin formula (if using the origin, otherwise the more general Taylor series) for $$f(z)$$ using the derivatives in the coefficients of the terms.
$\sum_{n=0} ^ {\infty} \frac {f^{(n)}(p)}{n!} (z-p)^{n}$
This can be shown to sum to $$f(z)$$, thereby showing the function has an actual $$n$$th derivative at the origin or general point $$p$$. This concludes the argument showing that complex smoothness in a region surrounding the origin or point implies that the function is also holomorphic. Penrose notes that neither the premise ($$f(z)$$ is complex-smooth) nor the conclusion ($$f(z)$$ is analytic) contains contour integration or multivaluedness of a complex logarithm, yet these ingredients are essential for finding the route to the answer and that this is a ‘wonderful example of the way that mathematicians can often obtain their results’.
### 7.4 Analytic continuation
We now know that complex smoothness throughout a region is equivalent to the existence of a power series expansion about any point in the region. A region here is defined as a open region, where the boundary is not included in the domain.
For example, if there is no singularity in the function, the region can be thought of as a circle of infinite radius. Taking $$f(z)=\frac{1}{z}$$ however forces an infinite number of circles centered at any point with boundary radii passing through the origin (noting that an open region does not contain the boundary) to construct the domain.
Now we consider the question, given a function $$f(z)$$ holomorphic in domain $$D$$, can we extend the domain to a larger $$D’$$ so that $$f(z)$$ also extends holomorphically? A procedure is formed in which we use a succession of power series about a sequence of points, forming a path where the circles of convergence overlap. This then results in a function that is uniquely determined by the values in the initial region as well as the path along which it was continued. Penrose notes this analytic continuation as a remarkable ‘rigidity’ about holomorphic functions.
An example of this rigidity and path dependence is ‘our old friend’ $$logz$$. There is no power series expansion about the origin due to the singularity there but depending on the path chosen of points around the origin (clockwise or anti-clockwise) the function extends or subtracts in value by $$2πi$$. See chapter 5 and the euler formula ($$e^{πi}=-1$$) for a refresher. | {"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": 2, "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": 0.8827641010284424, "perplexity": 357.62877435652433}, "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-2020-34/segments/1596439738653.47/warc/CC-MAIN-20200810072511-20200810102511-00404.warc.gz"} |
http://texnicalstuff.blogspot.com/2009/08/natural-question-morphisms-of-functors.html | ## Monday, August 3, 2009
### Natural Question: Morphisms of Functors?
By now I hope the reader sees the waltz that goes on here: we introduced objects, then asked about mappings between them. We introduced categories, and morphisms between them (functors). We now ask "Well, what about functors, can we have morphisms between them?"
(The very clever reader who asks "Wait, what about morphisms of morphisms?" We may get to this, it's basically the notion of comma categories, or slice categories. If I recall correctly, the two are the same. We'll get into it some more before covering the notion of universal arrows.)
The recommended reading this time includes some Youtube lectures by the Catsters:
Now there are many different ways to present natural transformations, because it's not so simple as it seems. We introduced functors in two ways: as a way to encode a mathematical process, and as a generalization of assigning information to each object of the domain. We have thus two different ways to present morphisms of functors.
### Homotopy Analogy
How can we have a mapping of one process to another? This intuition is hard to grasp, personally I want to jump all over the idea of homotopy deformation. But recall a homotopy deformation takes two paths $\gamma_{1},\gamma_{2}:I\to\mathbb{C}$ where $I$ is an interval, and deforms one into the other. More precisely:
$H:I\times[0,1]\to\mathbb{C}$
The problem is that we need some category theoretic analog to: the product $\times$ and the unit interval. I'll cheat and give the answer: we have some notion of the product of categories, and the category theoretic interval is our beloved 2. We set up the diagram describing the product category $C\times\mathbf{2}$:
We treat the objects of this category as an ordered pair $(0,x)$ and $(1,x)$. For all practical purposes, $C\times\mathbf{2}$ behaves like two copies of $C$: $C\times{0}$ and $C\times{1}$. We have arrows joining the first to the second, as we have demonstrated in our diagram.
Here the functors $T_{0},T_{1}:C\to{C\times\mathbf{2}}$ ("bottom" and "top", respectively) are defined for each arrow $f$ of $C$ by $T_{0}(f)=(f,0)$ and $T_{1}(f)=(f,1)$.
Let $\downarrow$ denote the unique non-identity arrow $0\to{1}$ in 2. We can define a transformation between $T_0,T_1:C\to{C\times\mathbf{2}}$ by
$\mu:T_{0}\to{T_{1}},\quad \mu(c)=(c,\downarrow)$
for any object $c$. It maps "bottom" to "top" and is clearly "natural". This $\mu$ mapping is the skeleton of the "homotopy deformation" of processes. It's specifically something called a "universal natural transformation" from $C$. (Remark: the term "universal" means that we factor everything through it. We'll show what this means.)
Let $S,T:C\to{B}$ be functors. There is a unique functor $F:C\times\mathbf{2}\to B$ with $(F\circ{}\mu):C\to{B}$ identified as the "homotopy deformation" of $S\Rightarrow{T}$. (Notation: for our "homotopy deformation" of processes, we denote it with a special arrow $\Rightarrow{}$.)
Now what exactly is going on here? We basically identify acting on the "top" with $F$ as being "the same" as acting on $C$ by $S$; and we similarly identify acting on the "bottom" with $F$ as being "the same" as acting on $C$ by $T$. Now the question arises: what about acting on $(c,\downarrow)$? How does this behave?
$F$ acts on $(c,\downarrow)$ in precisely the homotopic way we envisioned. It "deforms" the "top" into the "bottom". Such a deformation is usually dubbed a "natural transformation" and denoted by the special arrow $S\Rightarrow{T}$. Note that the domain and codomain of natural transformations are functors. Specifically functors which have the same domain and codomain.
We see explicitly, for $f:c\to{c^{\prime}}$,
1. $F(f,0)=S(f)$,
2. $F(f,1)=T(f)$,
3. $F(f,\downarrow)=T(f)\circ[(F\circ\mu)(c)]=[(F\circ\mu)(c^{\prime})]\circ S(f)$.
This is precisely the behavior describing a natural transformation $(F\circ\mu)$.
The reader interested in this "homotopy" presentation of natural transformations can refer to
• The Catsters "Natural transformations 1" Youtube lecture (2007)
• Saunders Mac Lane, Categories for the Working Mathematician Graduate Texts in Mathematics (vol 5) Springer-Verlag, Second Edition (1998); specifically the end of the section on products of categories (page 39 of my copy)
Sadly I haven't seen any other material on this presentation of natural transformations in this "homotopic way".
### Morphisms of (Pre-)Sheaves
We have presented functors with the notion of generalizing vector fields to categories previously. A functor (presheaf really) "assigns" to each object of its domain some information, a mathematical object in the codomain, in a "consistent way".
The question that presents itself now is: we have assigned information in one way $S:C\to{B}$ and in another way $T:C\to{B}$. Is there a way to relate these two assignments?
Now there is a weakness with this motivation, consider the following situation: we have a vector and we can obtain a scalar (its norm). If we have the functor $S:C\to\mathbf{Vect}$ (where Vect is the category of vector spaces with morphisms be linear transformations) and $T:C\to\mathbf{Set}$, a "morphism" of these functors $\|\cdot\|:S\Rightarrow{T}$ done "in the obvious way" isn't a natural transformation. Why not? Because the codomains of $S$ and $T$ are different! But turning a vector into a scalar via the norm is really quite a natural thing to do!
But that's the wrong way to think of "naturally transforming $S$ into $T$". What we should instead do is consider the following situation, let $S,T:C\to\mathbf{Vect}$. They assign to each object of $C$ a vector space. Each morphism of $C$ becomes a linear transformation. However, the linear transformations are projections onto subspaces. This is the only way we could get the restriction morphism demand of the presheaf functor to work out.
The natural transformation then is subject to the condition that this morphism-of-sheaves is compatible with restrictions. In other words, we restrict then change the method of assigning information is the same as changing the method of assigning information then restricting. This is the same as demanding the following commutes:
In the immortal infallible words of wikipedia:
Heuristically speaking, a morphism of sheaves is analogous to a function between them. However, because sheaves contain data relative to every open set of a topological space, a morphism of sheaves is defined as a collection of functions, one for each open set, which satisfy a compatibility condition.
The interested reader can peruse a variety of references on the material:
### Formal Considerations
We've given two approaches motivating the notion of natural transformations (or "morphisms of functors"). We should, being good mathematicians, define what a natural transformation is precisely.
Definition 1. Given two functors $F,G:C\to{D}$, a "Natural Transformation" $\tau:F\Rightarrow{G}$ consists of
• a function $\tau$ mapping each object $x\in{C}$ to a morphism $\tau_{x}:F(x)\to{G(x)}$
such that
• for any morphism $f:x\to{y}$ in $C$, the following diagram commutes:
(Note the notation: we use $\Rightarrow$ instead of $\to$ to indicate we're working with a natural transformation!)
What this effectively does is it "compares" (well, "relates") two different ways of assigning information in a "natural way". This is what both the homotopy approach and presheaf approach tells us, just in a more intuitive way.
Since a natural transformation "is-a" morphism (sort of), we can have an isomorphism. But we don't call it just that. We give it the adjective "natural" to indicate it's really a natural transformation with an "inverse". More precisely:
Definition 2. Let $F,G:C\to{D}$ be functors, a "natural isomorphism" consists of
• a natural transformation $\alpha:F\Rightarrow{G}$
equipped with
• a unique natural transformation $\beta:G\Rightarrow{F}$
such that
• $\beta\circ\alpha=1_{F}$ and $\alpha\circ\beta=1_{G}$.
It's not uncommon to see this written as $\alpha:F\cong{G}$.
### We Can "Compose" Natural Transformations With Functors
It's important to make a note here that I haven't really seen in e.g. Mac Lane's Categories for the Working Mathematician, but it's used all the time. We can "compose" natural transformations with functors "in the obvious way".
The only place that I have actually seen explicitly spell this out, shockingly enough, is Wikipedia(!):
If η : F ⇒ G is a natural transformation between functors F, G : C → D, and H : D → E is another functor, then we can form the natural transformation Hη : H∘F ⇒ H∘G by defining
$(H \eta)_X = H_{\eta_X}.$
If on the other hand K : B → C is a functor, the natural transformation ηK : F∘K ⇒ G∘K is defined by
$(\eta K)_X = \eta_{K(X)}.\,$
Source: Wikipedia, Natural Transformations. | {"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": 0.9742568135261536, "perplexity": 484.32071859496676}, "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/1502886107065.72/warc/CC-MAIN-20170821003037-20170821023037-00475.warc.gz"} |
http://mathoverflow.net/questions/127961/a-question-about-primitive-recursive-functions?answertab=votes | # A question about primitive recursive functions
I have a question about primitive recursive functions. Maybe it's trivial, if it is I will move it into math.stackexchange.
Is there a primitive recursive function $f$ which is a bijection of $N$ onto $N$ such that $f^{-1}$ is not primitive recursive ?
-
Exercise 5.6 in this book claims that bijective primitive functions are a group, i.e. such a function $f$ exists: books.google.co.il/… – Denis Apr 18 '13 at 13:39
DK, you mean to say that they are not a group. Frank, the inverse of Ackermann is primitive recursive, but this is not a bijection. But you can fix it up via the even/odd trick as in my argument and also as in DK's link (and those arguments are fundamentally similar). – Joel David Hamkins Apr 18 '13 at 14:03
The answer is yes. First, let $g$ be a total computable function whose rate of growth is too fast for it to be primitive recursive, such as the diagonal Ackermann function. Now, define $f(k)=2n$, if $k$ is the number coding up (in some canonical way) the computation of $g(n)$. That is, $k$ should encode a list of the entire computation sequence for $g(n)$, including snapshots of the configuration of each stage of computation, what is on the tape, where the head is, the state and so on. Now, for numbers $k'$ that are not codes of computations, we let $f(k')$ be the smallest odd number not yet used. Thus, we have a bijection $f:\mathbb{N}\to\mathbb{N}$.
Furthermore, $f$ is primitive recursive, because for a given $k$, we can bound the length of time it takes to compute $f(k)$---the algorithm need only unpack $k$ and verify whether it is a proper code or not, and then do some easy computations on the side.
Meanwhile, the inverse function is not primitive recursive. The point here is that $k$ is far larger than $n$. We cannot get from $n$ or $2n$ to a code $k$ for the computation of $g(n)$, because we assumed that the growth rate of $g$ was too high for it to be primitive recursive. | {"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": 0.975306510925293, "perplexity": 168.66942627868434}, "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-2015-06/segments/1422115900160.86/warc/CC-MAIN-20150124161140-00141-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://www.inf.ufpr.br/vignatti/publication/2020-kdd/ | # Estimating the Percolation Centrality of Large Networks through Pseudo-dimension Theory
### Abstract
In this work we investigate the problem of estimating the percolation centrality of every vertex in a graph. This centrality measure quantifies the importance of each vertex in a graph going through a contagious process. It is an open problem whether the percolation centrality can be computed in $\mathcal{O}(n^{3-c})$ time, for any constant $c>0$. In this paper we present a $\tilde{\mathcal{O}}(m)$ randomized approximation algorithm for the percolation centrality for every vertex of $G$, generalizing techniques developed by Riondato, Upfal and Kornaropoulos. The estimation obtained by the algorithm is within $\epsilon$ of the exact value with probability $1- \delta$, for {\it fixed} constants $0 < \epsilon,\delta < 1$. In fact, we show in our experimental analysis that in the case of real-world complex networks, the output produced by our algorithm is significantly closer to the exact values than its guarantee in terms of theoretical worst case analysis.
Type
Publication
In ACM SIGKDD'20 - International Conference on Knowledge Discovery & Data Mining | {"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": 0.9691411256790161, "perplexity": 307.7805589179124}, "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/1631780057787.63/warc/CC-MAIN-20210925232725-20210926022725-00189.warc.gz"} |
http://link.springer.com/article/10.1023%2FA%3A1019191431273 | Numerical Algorithms
, Volume 20, Issue 1, pp 75–100
# Solving stable generalized Lyapunov equations with the matrix sign function
• Peter Benner
• Enrique S. Quintana-Ortí
Article
DOI: 10.1023/A:1019191431273
Benner, P. & Quintana-Ortí, E.S. Numerical Algorithms (1999) 20: 75. doi:10.1023/A:1019191431273
## Abstract
We investigate the numerical solution of the stable generalized Lyapunov equation via the sign function method. This approach has already been proposed to solve standard Lyapunov equations in several publications. The extension to the generalized case is straightforward. We consider some modifications and discuss how to solve generalized Lyapunov equations with semidefinite constant term for the Cholesky factor. The basic computational tools of the method are basic linear algebra operations that can be implemented efficiently on modern computer architectures and in particular on parallel computers. Hence, a considerable speed-up as compared to the Bartels–Stewart and Hammarling methods is to be expected. We compare the algorithms by performing a variety of numerical tests.
generalized Lyapunov equationsmathematical softwarematrix sign functionNewton iterationalgebraic Riccati equations65F1093B4093B51
## Authors and Affiliations
• Peter Benner
• 1
• Enrique S. Quintana-Ortí
• 2
1. 1.Zentrum für Technomathematik, Fachbereich 3/Mathematik und InformatikUniversität BremenBremenGermany
2. 2.Departamento de InformáticaUniversidad Jaime ICastellónSpain | {"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": 0.9489856958389282, "perplexity": 2410.3900148488074}, "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-2016-40/segments/1474738662321.90/warc/CC-MAIN-20160924173742-00126-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://open.library.ubc.ca/cIRcle/collections/48630/items/1.0394214 | # Open Collections
## BIRS Workshop Lecture Videos
### Stochastic Formalism and Simulation of Quantum Dissipative Dynamics Cao, Jianshu
#### Description
Our starting point is a stochastic decomposition scheme to study dissipative dynamics of an open system. In this scheme, any two-body interactions between constituents of the quantum system can be decoupled with a common white noise that acts on the two individual subsystems. \$\$ \$\$ (I) Using the decomposition scheme, we obtain a stochasticâ differential equation, which reduces to generalized hierarchical equations of motion (GHEOM) and thus represents a unified treatment of boson, fermion, and spin baths.[1] Applications of GHEOM to spin baths confirm the scaling relation that maps spin baths to boson baths and characterizes anharmonic effects often associated with low-frequency or strong coupling spin modes. [2] \$\$ \$\$ (II) The decomposition scheme also leads to the stochastic path integral approach, which directly simulates quantum dissipation with complex noise. The approach is applied successfully to obtain the equilibrium density matrix, multichomophoric spectra, and Forster energy transfer rate. [3] For real time propagation, we demonstrate the advantages of combining stochastic path integrals, deterministic quantum master equations [4], and possibly the transfer tensor method [5]. \$\$ \$\$ [1] A unified stochastic formalism of quantum dissipation: I. Generalized Hierarchical equation, Hsien and Cao, JCP 148, p014103 (2018) \$\$ \$\$ [2] A unified stochastic formalism of quantum dissipation: II. Beyond linear response of spin baths. Hsien and Cao, JCP 148, p014104 (2018) \$\$ \$\$ [3] Equilibrium-reduced density matrix formulation: Influence of noise, disorder, and temperature on localization in excitonic systems. J. Moix, Y. Zhao, and J. Cao, Phys. Rev. B 85, 115412 (2012) \$\$ \$\$ [4] A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems. J. M. Moix and J. Cao, J. Chem. Phys. 139, 134106 (2013) \$\$ \$\$ [5] Non-Markovian dynamical maps: Numerical processing of open quantum trajectories. J. Cerrillo and J. Cao, Phys. Rev. Lett. 112, 110401 (2014) | {"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": 0.8725698590278625, "perplexity": 4450.446571172499}, "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-2022-21/segments/1652662517245.1/warc/CC-MAIN-20220517095022-20220517125022-00068.warc.gz"} |
https://openreview.net/forum?id=HyNbtiR9YX | ## Unsupervised Document Representation using Partition Word-Vectors Averaging
Sep 27, 2018 Blind Submission readers: everyone Show Bibtex
• Abstract: Learning effective document-level representation is essential in many important NLP tasks such as document classification, summarization, etc. Recent research has shown that simple weighted averaging of word vectors is an effective way to represent sentences, often outperforming complicated seq2seq neural models in many tasks. While it is desirable to use the same method to represent documents as well, unfortunately, the effectiveness is lost when representing long documents involving multiple sentences. One reason for this degradation is due to the fact that a longer document is likely to contain words from many different themes (or topics), and hence creating a single vector while ignoring all the thematic structure is unlikely to yield an effective representation of the document. This problem is less acute in single sentences and other short text fragments where presence of a single theme/topic is most likely. To overcome this problem, in this paper we present PSIF, a partitioned word averaging model to represent long documents. P-SIF retains the simplicity of simple weighted word averaging while taking a document's thematic structure into account. In particular, P-SIF learns topic-specific vectors from a document and finally concatenates them all to represent the overall document. Through our experiments over multiple real-world datasets and tasks, we demonstrate PSIF's effectiveness compared to simple weighted averaging and many other state-of-the-art baselines. We also show that PSIF is particularly effective in representing long multi-sentence documents. We will release PSIF's embedding source code and data-sets for reproducing results.
• Keywords: Unsupervised Learning, Natural Language Processing, Representation Learning, Document Embedding
• TL;DR: A simple unsupervised method for multi-sentence-document embedding using partition based word vectors averaging that achieve results comparable to sophisticated models.
0 Replies | {"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": 0.8628301024436951, "perplexity": 2397.025478177937}, "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/1579250592261.1/warc/CC-MAIN-20200118052321-20200118080321-00038.warc.gz"} |
https://space.stackexchange.com/questions/39879/how-to-calculate-that-required-to-change-orbit-with-same-radius-but-differe | # How to calculate 𝛥𝑣 that required to change orbit with same radius but different inclination?
How could I calculate the total 𝛥𝑣 required to change the inclination of a Geostationary orbit to another circular orbit with an inclination of 30° and the same radius? (The sidereal day is used for Geostationary orbit calculation.)
Currently my idea is to solve it from the formula of inclination, $$\arccos\left(\frac{hk}{|h|}\right)$$ where $$h = rv$$ and the change from zero to 30 degrees means the component of $$h$$ on the $$k$$ axis is increasing.
Since $$r$$ does not change and $$hk$$ is changing, the velocity $$v$$ should change. I'm not too sure what to do next.
• My idea now is to solve it from the formula of inclination, arccos(hk/|h|). where h = r*v. And the change from 0 degrees to 30 degrees means the component of h on the k axis is increasing. Since r does not change, and hk is changing, the velocity v should change. I'm not too sure what to do next. – Yibowen Zhao Nov 13 '19 at 16:47
• en.m.wikipedia.org/wiki/Orbital_inclination_change – Russell Borogove Nov 13 '19 at 17:23
• Did you just want the equation, or were you also interested in how the equation is derived? – uhoh Nov 13 '19 at 17:56
• I just want the equation, thanks – Yibowen Zhao Nov 14 '19 at 7:14
According to Wikipedia, the general equation for inclination change is:
$$\Delta{v_i}= {2\sin(\frac{\Delta{i}}{2})\sqrt{1-e^2}\cos(\omega+f)na \over {(1+e\cos(f))}}$$
Where:
• $$e\,$$ is the orbital eccentricity
• $$\omega\,$$ is the argument of periapsis
• $$f\,$$ is the true anomaly
• $$n\,$$ is the mean motion
• $$a\,$$ is the semi-major axis
For circular orbits, this simplifies considerably to:
$$\Delta{v_i}= {2v\, \sin \left(\frac{\Delta{i}}{2} \right)}$$
Where $$v\,$$ is the orbital velocity and has the same units as $$\Delta{v_i}$$. | {"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": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9597077965736389, "perplexity": 470.23571521344587}, "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/1593657134758.80/warc/CC-MAIN-20200712082512-20200712112512-00072.warc.gz"} |
https://math.meta.stackexchange.com/questions/6392/a-small-bug-period-on-the-next-line-after-mathjax | A small bug: period on the next line after MathJaX
André Nicolas wrote an answer to this question, in which he mentions "the line through $A$ and $B$." It appears in my browser window as:
the line through $A$ and $B$
.
with the period on the next line. Maybe that changes with the window geometry, or maybe not. But that shouldn't happen.
(Usually when I see this it's because someone typed some "displayed" TeX in which they put the period OUTSIDE of TeX, and the fix is to move it inside, where it should have been. But that doesn't apply here.)
Later note: In this posting, the period sits alone on the next line after displayed TeX, simply because the line is so long that it starts wrapping right at the point where the only thing left to display is the period!
A screen shot of a similar problem provided in a duplicate report:
• If the period is part of the mathematical statement, then is should be inside the $\LaTeX$. In this case, it is not, so I think it is in the proper place here. IF the period is moved to a line by itself, that is perhaps a problem with the integration of MathJax and the markup language. – robjohn Oct 19 '12 at 18:08
• So the bug I'm reporting here is "a problem with the integration of MathJax and the markup language." – Michael Hardy Oct 19 '12 at 18:34
• The line in your later note looks fine on my computer (Mac OSX 10.5.8, Firefox 15) – robjohn Oct 20 '12 at 9:31
• Both look fine to me. – Graphth Oct 23 '12 at 0:07
• Adding a screenshot would probably be a reasonable thing to do in a bug report. (Especially since another user said in a comment that both linked questions are displayed correctly for them.) This is what I get in 49.0.2623.87 with choice of HTML-CSS as Math Renderer: i.stack.imgur.com/KI87y.png – Martin Sleziak Mar 18 '16 at 22:44 | {"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": 0.8398793339729309, "perplexity": 683.8113412645706}, "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-2020-05/segments/1579251690095.81/warc/CC-MAIN-20200126165718-20200126195718-00413.warc.gz"} |
http://mathhelpforum.com/calculus/185604-supremum-closed-section-proof.html | Thread: supremum on closed section proof
1. supremum on closed section proof
f is continues on [a,b]
A={x in [a,b]|f(x)=f(a)}
prove that f(x) has a maximum
f(supA)=f(a)
??
first of all there are two kinds of maximums here
1st a supremum which is inside [a,b] is called maximum
and maximum of the function values
correct??
2. Re: supremum on closed section proof
Originally Posted by transgalactic
f is continues on [a,b]
A={x in [a,b]|f(x)=f(a)}
prove that f(x) has a maximum
f(supA)=f(a)
??
first of all there are two kinds of maximums here
1st a supremum which is inside [a,b] is called maximum
and maximum of the function values
correct??
Extreme value theorem - Wikipedia, the free encyclopedia
3. Re: supremum on closed section proof
Originally Posted by transgalactic
f is continues on [a,b]
A={x in [a,b]|f(x)=f(a)}
prove that f(x) has a maximum
f(supA)=f(a)?
Because $\left( {\forall x \in A} \right)\left[ {x \leqslant b} \right]$, you know that $\beta=\sup\{A\}$ exists and $\beta\in[a,b]$.
If it is true $\beta\in A$ you are done.
Else If you assume $\beta\notin A$ that leads to a contradiction to the continuity of $f$.
BTW: This not the Extreme value theorem. | {"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": 6, "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": 0.9693772196769714, "perplexity": 2436.342163757261}, "config": {"markdown_headings": false, "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-2016-36/segments/1471982293195.16/warc/CC-MAIN-20160823195813-00112-ip-10-153-172-175.ec2.internal.warc.gz"} |
http://gonitsora.com/if-p-is-a-prime-then-%E2%88%9Ap-is-irrational/ | ## 06 Apr If p is a prime then √p is irrational
To prove √p is irrational, where p is a prime, we will need the following theorem:
Theorem: If $p$ is prime then $p|ab,$ then $p|a$ or $p|b.$
Proof: If $p|a,$ we are done. So let us assume that $pmid a.$ Therefore, $gcd(p,a)=1.$ Hence, by Euclid’s lemma, $p|b.$ [Euclid’s lemma: If $a|bc,$ with $gcd(a,b)=1,$ then $a|c.$]
Now to prove √p is irrational (where p is a prime):
Assume that √p is rational.
Then there exists two integers a, b such that $frac{a}{b}=sqrt{p}$ where gcd(a,b)=1 and $bne 0.$
Then $frac{a^2}{b^2}=p.$ Which implies
$a^2=pb^2.$ __________(1)
$Rightarrow p$ divides $a^2.$
$Rightarrow p$ divides $a.$ (By the above theorem.)
So there exists an integer $a_1$ such that $a=pa_1.$
So, from (1), we get $(pa_1)^2=pb^2.$
$Rightarrow p^2a_1^2=pb^2.$
$Rightarrow pa_1^2=b^2.$ (Dividing both sides by p.)
This implies p divides b. This is a contradiction since gcd(a,b)=1.
Thus, when p is a prime, p is irrational.
Particular Case:- √2 is irrational. | {"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": 24, "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": 0.9929874539375305, "perplexity": 406.23539276981063}, "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-2018-05/segments/1516084889542.47/warc/CC-MAIN-20180120083038-20180120103038-00541.warc.gz"} |
https://math.stackexchange.com/questions/3223297/behaviour-of-the-solution-of-ode-for-t-to-infty | # Behaviour of the solution of ODE for $t \to \infty$
$$y^{(4)}(t)+2y''(t)+ay(t)=0, \ \ \ a \in \mathbb R$$
Determine the general solution of the ODE and its behaviour for $$t \to \infty$$.
The roots of the characteristic polynomial $$\lambda^4+2\lambda^2+a$$ are
$$\lambda_1=-\sqrt{-1-\sqrt{1-a}}\\\lambda_2=\sqrt{-1-\sqrt{1-a}}\\\lambda_3=-\sqrt{-1+\sqrt{1-a}}\\\lambda_4=\sqrt{-1+\sqrt{1-a}}$$
so $$y(t)=c_1e^{\lambda_1t}+c_2e^{\lambda_2t}+c_3e^{\lambda_3t}+c_4e^{\lambda_4t}$$
Now for the behaviour for $$t \to \infty$$: Is there some clever way to do this?
Can I work with the complex fundamental system? Or do I have to look at the different cases for $$a$$ and build a real fundamental system? Or what would be the 'best' way to solve this? It seems like the cases would take too long
• You need to understand that those roots are complex numbers and you need to explore which quadrant they fall into. // Your equation does not contain $a$. – LutzL May 12 at 16:39
• You need to separate cases $a < 1$, $a=1$, $a>1$. For every case, these roots will be complex, and the behavior depends on their real parts. – Dylan May 13 at 7:46
$$λ^4+2λ^2+a=0$$ has for $$a<0$$ one sign change in the coefficient sequence and thus by Descartes rule of signs always a positive root. This means that in general the ODE has unbounded solutions for $$t\to\infty$$.
For $$a>1$$ one gets by completing the square in the first and last term the real factorization $$(λ^2+\sqrt{a})^2-2(\sqrt{a}-1)λ^2 =\left(λ^2+\sqrt{2(\sqrt{a}-1)}λ+\sqrt{a}\right) \left(λ^2-\sqrt{2(\sqrt{a}-1)}λ+\sqrt{a}\right)$$ The second factor will always give at least one root with positive real part, giving again unbounded solutions for the ODE.
For $$a\in[0,1]$$ use standard square completion $$(λ^2+1)^2=1-a\ge 0\implies λ^2=-1\pm\sqrt{1-a}.$$ For $$a\in(0,1)$$ this gives 4 simple imaginary roots so that all solutions of the ODE are bounded. In the case $$a=0$$ or $$a=1$$ the double roots (at $$0$$ resp. $$\pm i$$) will cause basis solutions with linearly growing amplitude to appear. | {"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": 19, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9518181681632996, "perplexity": 180.85650025162647}, "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-2019-39/segments/1568514574377.11/warc/CC-MAIN-20190921084226-20190921110226-00074.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/small-particle-charge-q-q-q-mass-m-placed-atthe-origin-displaced-slightly-released-assume--q7938 | ## please help for midterm
A small particle of charge q (q<<Q) and mass m is placed atthe origin, displaced slightly, and then released. Assume that theonly subsequence forces acting are the electric forces from the twofixed charges Q at x = +a, and x=-a, and that the particle movesonly in the xy-plane. In each of the following cases, describebriefly the motion of the charged particle after it is releaed.Write an expression for its speed when far away if the resultingforce pushes it away from the origin.
d) q is positive and is displaced in the +x direction
e) q is positive and is displaced in the +y direction
f) q is negative and is displaced in the +y direction
# Answers (0)
There are no answers to this question yet. | {"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": 0.9219542145729065, "perplexity": 1077.3842079520336}, "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-2013-20/segments/1368696382851/warc/CC-MAIN-20130516092622-00043-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://mathhelpforum.com/trigonometry/10983-trig-proofing.html | # Math Help - trig proofing
1. ## trig proofing
Hello,
I am currently trying to make a difficult trig proof for my maths lesson. If someone could help me make one, that would be very helpful. I have been given a left hand side, ((cosec(x))^2)\(2+cot(x)). I need it to be changed into something as different as possible from the original, with as many steps as possible, without a very long right hand side. Feel free to use all trig rules.
If someone could do this for me it would be great.
$\tan \frac{x}{2} = \frac{2\sin x}{1-\cos x}$ | {"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": 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": 0.9441836476325989, "perplexity": 388.0591056832949}, "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-2014-52/segments/1419447548530.114/warc/CC-MAIN-20141224185908-00057-ip-10-231-17-201.ec2.internal.warc.gz"} |
http://iit-jee-physics.blogspot.com/2009/ | ## Tuesday, August 18, 2009
### More articles on Physics on Knol
More articles are added to the subdirectory of Physics.
## Friday, July 31, 2009
### Hubble Space Telescope - A Knol Useful to Know More about Optical Instruments
Selected Passages from the Article about Hubble Telescope
The Hubble Space Telescope was launched in 1990, a joint project of NASA (the National Aeronautics and Space Administration of the United States) and ESA (the European Space Agency). It carries a 2.4-m (94-inch) telescope that feeds several different instruments. It is in low Earth orbit, allowing it to be reached and serviced by astronauts, a process that made it work properly in the first place and that continues to allow its updating.
History of Hubble
The Hubble Space Telescope is the descendant of a planned Large Space Telescope, but during the 1980's it was downsized in planning both for psychological reasons, so the word "Large" wouldn't go in the proposal to Congress, and to allow it to fit in the payload bay of a space shuttle. Lyman Spitzer of Princeton University and John Bahcall of the Institute for Advanced Study, also located in Princeton, were principal scientists who worked not only scientifically but also politically to see the project advance.
The mirror was made by the Perkin-Elmer Company in Connecticut, and was said to be the most perfectly and smoothly shaped telescope mirror ever. The telescope mirror was completed and the telescope almost ready to be launched when the space-shuttle Challenger exploded in 1984. With space-shuttle launches suspended, the telescope was put into storage.
For diagrams please visit the source knol.
The telescope was launched on April 24, 1990, from Cape Canaveral on a space shuttle. It was named after Edwin P. Hubble, the astronomer at the Palomar Observatory who had discovered the important cosmological law about the expansion of the Universe, linking its rate of expansion linearly with distance. It received the name in recognition of the prospectively important cosmological work the telescope could do, and in the hope that it could refine Hubble's Law—in particular, Hubble's constant, the constant of proportionality between redshift and distance—to a higher accuracy than had been previously possible.
Science with Hubble
The Hubble Space Telescope has been used by astronomers to study objects in the Universe near and far, excepting only the Sun (which is too bright, but which was indeed detected through the back of the mirror!). A main reason for the launch of Hubble is that from its perch outside Earth's atmosphere, it can have resolution about 7 times finer than normal ground-based resolution from good telescope sites; that is, it can see detail about 7 times finer. It had often been loosely said that it could therefore see 7 times farther into space, but large ground-based telescopes had already been observing objects so far in the outer solar system that it was impossible to see 7 times farther.
In the years since Hubble's launch, ground-based capabilities have advanced, and Active Optics has allowed Hubble's resolution to be achieved in certain limited but growing circumstances from ground-based telescopes. Still, Hubble can attain its high resolution for all objects it observes without complicated post-processing.
Note, however, that Hubble is only one 2.4-m telescope, not large by today's standards. The twin Keck telescopes in Hawaii, for example, have mirrors each 10 m in diameter, about 4 times in diameter and 16 times in area compared with Hubble's. Thus many astronomical projects, particularly those that require collecting as much light as possible, are better carried out with this new generation of large, mountain-based telescopes, still leaving many, many projects best achieved with the high-resolution of Hubble.
Source
Hubble Space Telescope By Jay M. Pasachoff, Astronomer,Williams College, Williamstown, MA, and Chair of the International Astronomical Union's Working Group on Solar Eclipses
You can also visit
http://hubblesite.org
### Want to know more about music - Piano Chords
Piano Chords -- How They Are Formed & How They WorkChords: The Harmonic Background Of Melody
A chord is any group of 3 or more notes that are played at the same time. Broken chords, also known as arpeggios, are chords which are played one note at a time, but add up to 3 or more notes.
A scale is simply a row of notes in some consistent pattern. The word “scale” comes from a Latin word meaning “ladder” – notes ascend or descend the ladder rung by rung.
The notes of all 12 major scales according to their position in the scale is given as a diagram in the knol
Visit the article to know more about Piano Chords
### Sound and its measurement
NATURE OF SOUND
Origin of sound
Sound is a variation in the pressure of the air of a type which has an effect on our ears and brain. These pressure variations transfer energy from a source of vibration that can be naturally-occurring, such as by the wind or produced by humans such as by speech. Sound in the air can be caused by a variety of vibrations, such as the following.
Moving objects: examples include loudspeakers, guitar strings, vibrating walls and human vocal chords.
Moving air: examples include horns, organ pipes, mechanical fans and jet engines.
A vibrating object compresses adjacent particles of air as it moves in one direction and leaves the particles of air ‘spread out’ as it moves in the other direction. The displaced particles pass on their extra energy and a pattern of compressions and rarefactions travels out from the source, while the individual particles return to their original positions.
In addition to its link with human hearing the term sound is also used for other movement in air governed by similar physical principles. Disturbances in the air with frequencies of vibration which are too low (infrasound) or too high (ultrasound) to be heard by human hearing are also regarded as sound. Other sound terms in common usage include: underwater sound, sound in solids, or structure-borne sound.
Infrasound: frequency too low for human hearing
Ultrasound: frequency too high for human hearing
Wave motion
The mechanical vibrations of sound move forward using wave motion. This means that, although the individual particles of material such as air molecules return to their original position, the sound energy obviously travels forward. The front of the wave spreads out equally in all directions unless it is affected by an object or by another material in its path. The sound waves can travel through solids, liquids and gases, but not through a vacuum.
It is difficult to depict a longitudinal wave in a diagram so it is often convenient to represent a sound waves as a plot against time of the vibrations. The vibrations can be throught of as the movements of the souce of sound, such as a vibrating loudspeaker, or as the movements of a particle of air. For a pure sound of one frequency, as shown, the plot takes the smooth and regular form of a sine wave.
For diagram visit the source
Sound waves are like any other wave motion and therefore can be specified in terms of wavelength, frequency and velocity.
Wavelength
Wavelength (l) is the distance between any two repeating points on a wave. The unit is the metre (m)
Frequency
Frequency (f) is the number of cycles of vibration per second. The unit is the hertz (Hz)
Velocity
Velocity (v) is the distance moved per second in a fixed direction. The unit is metres per second (m/s)
For every vibration of the sound source the wave moves forward by one wavelength. The length of one wavelength multiplied by the number of vibrations per second therefore gives the total length the wave motion moves in 1 second. This total length per second is also the velocity. This relationship between velocity, frequency and wavelength is true for all wave motions and can be written as the formula.
n =f ´ l
where v = velocity in m/s
f = frequency in Hz
l = wavelength in m
The velocity of sound, for any particular material, stays constant. Therefore any increase in freqency, for example, is matched by a decrease in wavelength.
Velocity of sound
A sound wave travels away from its source with a speed of 344 m/s (770 miles per hour) when measured in dry air at 20 °C (68 °F) . This is a respectable speed within a room but slow enough over the ground for us to notice the delay between seeing a source of sound, such as a distant firework, and later hearing the explosion.
The velocity of sound is independent of the rate at which the sound vibrations occur, which means that the frequency of a sound does not affect its speed. The velocity is also unaffected by variations in atmospheric pressure such as those caused by the weather.
But the velocity of sound is affected by the properties of the material through which it is travelling, and the table gives an indication of the velocities of sound in different materials.
The velocity of sound in gases decreases with increasing density as, when the molecules are heavier, then they move less readily. Moist air contains a greater number of light molecules and therefore sound travels slightly faster in moist humid air.
Sound travels faster in liquids and solids than it does in air because of the effect of density and elasticity of those materials. The particles of such materials respond to vibrations more quickly and so convey the pressure vibrations at a faster rate. For example, steel is very elastic and sound travels through steel about 14 times faster than it does through air.
Table of Velocity of sound
Material
Typical velocity (m/s)
Air (0°C)
331
Air (20°C)
344
Water (25°C)
1498
Pine
3300
Glass
5000
Steel
5000
Granite
6000
Frequency of sound
If an object that produces sound waves vibrates 100 times a second, for example, then the frequency of that sound wave will be 100 Hz. The human ear hears this as sound of a certain pitch.
Pitch is the frequency of a sound as perceived by human hearing.
Low-pitched notes are caused by low-frequency sound waves and high-pitched notes are caused by high-frequency waves. The pitch of a note determines its position in the musical scale. The frequency range to which the human ear responds is approximately 20 to 20 000 Hz and frequencies of some typical sounds are shown in the figure.
‘bass’ = low frequency
‘treble’ = high frequency
Most sounds contain a combination of many different frequencies and it is usually convenient to measure and analyse them in ranges of frequencies, such as the octave.
An Octave Band is the range of frequencies between any one frequency and double that frequency.
Quality of sound
A pure tone is sound of only one frequency, such as that given by a tuning fork or electronic signal generator. Most sounds heard in everyday life are a mixture of more than one frequency, although a lowest fundamental frequency predominates when a particular ‘note’ is recognisable. This fundamental frequency is accompanied by overtones or harmonics.
Overtones and Harmonics are frequencies equal to whole-number multiples of the fundamental frequency.
For example, the initial overtones of the note with a fundamental of 440 Hertz are as follows:
440 Hz = fundamental or 1st harmonic
880 Hz = 1st overtone or 2nd harmonic
1320 Hz = 2nd overtone or 3rd harmonic etc.
Different voices and instruments are recognised as having a different quality when making the same note. This individual timbre results because different instruments produce different mixtures of overtones that accompany the fundamental. The frequencies of these overtones may well rise to 10 000 Hz or more and their presence is often an important factor in the overall effect of a sound. A telephone, for example, transmits few frequencies above 3000 Hz and the exclusion of the higher overtones noticeably affects reproduction of the voice and of music.
Cancellation of sound
The nature of a sound wave, such as shown in the earlier figure, means that the vibration of the wave has alternate changes in amplitude called phases. If a wave vibration in one direction meets an equal and opposite vibration, then they will cancel. The effect of this phase inversion in sound waves is to produce little or no sound and gives the possibility of ‘cancelling’ noise. This is the principle of Active Noise Reduction (ANR) used in some headsets and aircraft for example.
Resonance
Every object has a natural frequency which is the characteristic frequency at which it tends to vibrate when disturbed. For example, the sound of a metal bar dropped on the floor can be distinguished from a block of wood dropped in the same way. The natural frequency depends upon factors such as the shape, density and stiffness of the object.
Resonance occurs when the natural frequency of an object coincides with the frequency of any vibrations applied to the object. The result of resonance is extra large vibrations at this frequency.
Resonance may occur in many mechanical systems. For instance, it can cause loose parts of a car to rattle at certain speeds when they resonate with the engine vibrations. The swaying of a suspension bridge can resonate with footsteps from walkers. The shattering of a drinking glass has been attributed to resonance of the object with a singer’s top note! Less dramatic, but of practical application in buildings, is that resonance affects the transmission and absorption of sound within partitions and cavities.
MEASUREMENT OF SOUND
Decibels
The uneven sensitivities of the human hearing system lead us to measuring sound by a logarithmic decibel scale which is progressively 'squashed' rather than being a uniform scale. It happens that this is also the way that our hearing perceives sound energy or strength. So the simple energy or pressure measurements of sound are converted to sound level values in decibels (dB) which are easier numbers for humans to understand and relate to. Extra-terrestrial beings, or even your cat, might well prefer the unconverted values!
Sound levels in decibels start with a zero at the threshold of hearing which is the weakest sound that the average human ear can detect Typical effects of sound levels and changes in sound levels are shown in the illustrations. Remember that there is distinct difference between a change in energy and a change in our idea of loudness.
A change in sound level of + or - 10 dB is a useful figure to remember as it makes difference of approximately twice as loud, or half as loud. We have to say 'approximately' as the experience also depends on individual hearing, on the background noise and on the exact frequencies involved. An increase in sound level of 20 dB (10 dB then another 10 dB) will seem four times
For example, there may be a proposal to increase the average sound level of your environment from 60 dB to 70 dB. This seems a relatively small change, after all the scale runs from 0 to 140 but it will make the environment twice as noisy.
The same idea applies to reducing noise. If the manufacturers of a certain machine can reduce the sound level from 90 dB to 80 dB then the machine will sound approximately half as loud as before.
For Table of Decibel scale visit the source
Sound Meters are also explained in the source article in knol.
Visit the source for diagrams and updated versions.
Source:
Sound and its measurement, Randall McMullan
## Saturday, July 18, 2009
### Interesting Articles on Physics for Dowload
You can search for more articles on knol.
## Tuesday, May 26, 2009
### IIT JEE 2011 Physics Study Diary - Ch.4 Forces Day 3
Day 3
4.4 Nuclear Forces
4.5 Weak forces
4.6 Scope of Classical physics
Points to be Noted
Nuclear forces
The alpha particle is a bare nucleus of Helium. It contains two protons and two neutrons. It is a stable object and once created it can remain intact until it is not made to interact with other objects.
The protons in the nucleus will repel each other due to coulomb force and try to break the nucleus. Why does the Coulomb force fail to break the nucleus?
There are forces called nuclear forces and they are exerted only if the interacting particles are protons or neutrons or both. They are largely attractive, but with a short range. They are weaker than the Coulomb force if the separation between particles is more than 10^-14 m. For separation smaller than this the nuclear force is stronger than the Coulomb force and it holds the nucleus stable.
Radioactivity, nuclear energy (fission, fusion) etc. result from nuclear force.
Weak forces
A neutron can change into proton and simultaneously emit an electron and a particle called antinutrino.
A proton can also change into neutron and simultaneously emit a positron (and a neutrino). The forces responsible for these changes are called weak forces. The effect of this force is experienced inside protons and neutrons only.
Scope of classical physics
Physics based on Newton's Laws of motion, Newton's law of gravitation, Maxwell's electromagnetism, laws of thermodynamics and the Lorentz force is called classical physics. The behaviour of all the bodies of linear sizes greater than 10^-6 m are adequately described by classical physics. Grains of sands and rain drops fall into this range as well as heavenly bodies.
But sub atomic particles like atoms, nuclei, and electrons have sizes smaller than 10^-6 m and they are explained by quantum physics.
The mechanics of particles moving at velocity equal to light are explained by relativistic mechanics formulated by Einstein in 1905.
## Monday, May 25, 2009
### IIT JEE Physics Study Diary - Ch.3 Forces - Day 2
Day 2
4.3 Electromagnetic (EM) forces
Ex. 4.1
Points to note
Electromagnetic force
Apart from gravitational force between any two bodies, the particles may exert upon each other electromagnetic forces.
If two particles having charges q1 and q2 are at rest with respect to the observer, the force between them has a magnitude
F = (1/4πε0)(q1q2/r^2)
Where ε0 = permittivity of air or vacuum = 8.8549 x 10^-12 C² /N-m²
The quantity (1/4πε0) = 9.0 x 10^9 N-m² /C²
q1, q2 = charges
r distance between q1 and q2
This is called coulomb force and it acts along the line joining the particles.
Atoms are composed of electrons, protons and neutrons.
Each electron has 1.6*10^-19 coulomb of negative charge. Each proton has an equal amount of positive charge.
In atoms, the electrons are bound by the electromagnetic force exerted on them by charge on protons. Even the combination of atoms in molecules are brought about by electromagnetic forces only. A lot of atomic and molecular phenomena result from electromagnetic forces between subatomic particles (for example, theory is put forward that charged mesons are responsible for the stability of nucleus).
Examples of electromagnetic force:
1. Bodies in contact: The contact force between bodies in contact arises out of electromagnetic forces acting between the atoms and molecules of the surfaces of the two bodies. The contact force may have a component parallel to the contact surface. This component is known as friction.
2. Tension in a string: Tension in the string is due to electromagnetic forces between atoms or electrons and protons (free electrons and nucleus in metals).
3. Force due to spring: If a spring has natural length x0 and if it is extended to x, it will exert a force
F = k|x-x0| = k|∆x|
k, the proportionality constant is called the spring constant. This force comes into picture due to the electromagnetic forces between the atoms of the material.
Formulas in the session
F = (1/4πε0)(q1q2/r^2)
Where ε0 = permittivity of air or vacuum = 8.8549 x 10^-12 C² /N-m²
The quantity (1/4πε0) = 9.0 x 10^9 N-m² /C²
q1, q2 = charges
r distance between q1 and q2
Each electron has 1.6*10^-19 coulomb of negative charge. Each proton has an equal amount of positive charge.
Force due to spring: If a spring has natural length x0 and if it is extended to x, it will exert a force
F = k|x-x0| = k|∆x|
k, the proportionality constant is called the spring constant.
## Saturday, May 23, 2009
### Physics Study Diary - Ch. 4 Forces - Day 1
Day 1 Study Plan
4.1 Introduction
4.2 Gravitational forces
Points to Note
Force
Force is an interaction between two objects.
Force is exerted by an object A on another object B.
Force is a vector quantity. Hence if two or more forces act on a particle, we can find the resultant force using laws of vector addition.
The SI unit for measuring the force is called a newton.
Newton's third law of motion
If a body A exerts a force F on another body B, then B exerts a force -F on A,the two forces acting along the same line.
Gravitational force
Any two bodies attract each other by virtue of their masses.
The force of attraction between two point masses is
F = Gm1m2/r²
where m1 and m2 are the masses of the particles and r is the distance between them.
G is a universal constant having the value 6.67 x 10^-11 N-m²/kg²
The above rule was given for point masses. But it is analytically found that the gravitational force exerted by a spherically symmetric body of mass m1 on another such body of mass m2 kept outside the first body is Gm1m2/r² where r is the distance between the centres of such bodies.
Thus, for the calculation of gravitational force between two spherically symmetric bodies, they can be treated as point masses placed at their centres.
Gravitational force on small bodies by the earth
For earth, the value of radius R and mass M are 6400 km and 6 x 10^24 kg respectively. Hence, the force exerted by earth on a particle of mass m kept at its surface is, F = GMm/R². The direction of this force is towards the centre of the earth.
The quantity GM/R² is a constant and has the dimensions of acceleration.
It is called acceleration due to gravity and is denoted by letter g.
Hence, g and G are different.
Value of g is approximately 9.8 m/s².
In calculations, we often use 10 m/s².
Force exerted on a small body of mass m, kept near the earth's surface is mg in the vertically downward direction.
Gravitational constant is so small that the gravitational force becomes appreciable only when one of the masses has a very large mass.
HC Verma gives the example of Force exerted by a body of 10 kg on another body of 10 kg when they are separted by a distance of 0.5 m. The force comes out to be 2.7*10^-8 N which can hold only 3 microgram. Such forces can be neglected in practice.
Hence we consider only gravitational force exerted by earth.
Formulas
1. F = Gm1m2/r²
where m1 and m2 are the masses of the particles and r is the distance between them.
G is a universal constant having the value 6.67 x 10^-11 N-m²/kg²
2. Force exerted by earth on a particle of mass m kept at its surface is, F = gm/R².
g = approximately 9.8 m/s².
In calculations, we often use 10 m/s²
## Friday, May 22, 2009
### IIT JEE 2011 Physics Study Diary - Ch.3 Rest and Motion - Day 5
Rest and Motion
Day 5 study plan
3.9 Change of frame
Ex. 3.10, 3.11
WOE 16,17, 18
Points to Note
The main theme of the section is expressing velocity w.r.t. one Frame into velocity w.r.t. to a different frame
If XOY is one frame called S and X'O'Y' is another frame called S' we can express velocity of a body B w.r.t. S as a combination of velocity of body w.r.t. to S' and velocity of S' w.r.t to S.
V(B,S) = V(B,S')+V(S',S)
Where
V(B,S) = velocity of body w.r.t to S
V(B,S') = velocity of body w.r.t to S'
V(S',S) = velocity of S' w.r.t to S
we can rewrite above equation as
V(B,S') = V(B,S)- V(S',S)
We can interpret the above equation in terms of two bodies. Assume S', and B are two bodies. If we know velocities of two bodies with respect to a common frame (in this case S)we can find the velocity of one body with respect to the other body (V(B,S')
The above expressions for velocity were derived from the relation between position vectors of the body w.r.t. to S and S' and position vector of origin of S' with respect to origin of S.
r(B,S) = r(B,S')+r(S',S)
Differentiating the position vectors with respect to gives respective velocity
Formulas covered in the session
26. r(B,S) = r(B,S')+r(S',S)
Where
r(B,S) = Position vector
r(B,S') = Position vector
r(S',S) = Position vector
27. V(B,S) = V(B,S')+V(S',S)
Where
V(B,S) = velocity of body wrt to S)
V(B,S') = velocity of body wrt to S')
V(S',S) = velocity of S' wrt to S)
we can rewrite above equation as
28. V(B,S') = V(B,S)- V(S',S)
## Thursday, May 21, 2009
### IIT JEE 2011 Physics Study Diary - Ch.3 Rest and Motion - Day 4
Day 4 - Study Plan
3.7 Motion in a plane
Ex. 3.8
3.8 Projectile motion
Ex. 3.9
WOE 11,12, 14
Points to Note
Motion in a plane
Motion in plane is described by x coordinate and y coordinate, if we choose X-Y plane. You can imagine time t is on the third axis.
The position of the particle or the body can be described by x and y coordinates.
r = xi = yj
Displacement during time period t to t+Δt can be represented by Δr
Δr = Δxi = Δyj
Then Δr/Δt = (Δx/Δt)i = (Δy/Δt)j
Taking the limits as Δt tends to zero
v = dr/dt = (dx/dt)i+(dy/dt)j ... (3.15)
Hence x component of velocity is dx/dt
The x-coordinate, the x component of velocity, and the x component of acceleration are related by equations of straight line motion along X axis.
Similarly y components.
Projectile
Projectile motion is an important example of motion in a plane.
What is a projectile? When a particle is thrown obliquely near the earth's surface, it is called a projectile. It moves along a curved path. If we assume the particle is close to the earth and negligible air resistance to the motion of the particle, the acceleration of the particle will be constant. We solve projectile problems with the assumption that acceleration is constant.
Vertical motion of the projectile is the motion along Y axis and horizontal motion is motion along X axis.
Terms used in describing projectile motion
Point of projection
Angle of projection
Horizontal range
Time of flight
Maximum height reached
The motion of projectile can be discussed separately for the horizontal and vertical parts.
The origin is taken as the point of projection.
The instant the particle is projected is taken as t = 0.
X-Y plane is the plane of motion.
The horizontal line OX is taken as the X axis.
Vertical line OY is the Y axis.
Vertically upward direction is taken as positive direction of Y
Initial velocity of the particle = u
Angle between the velocity and horizontal axis = θ
ux – x-component of velocity = u cos θ
ax – x component of acceleration = 0
uy – y component of velocity = u sin θ
ay = y component of acceleration = -g
Horizontal motion of the projectile – Equations of motion
ux = u cos θ
ax = 0
vx = ux +axt = ux = u cos θ (as ax = 0)
Hence x component of the velocity remains constant.
Displacement in horizontal direction = x = uxt+1/2ax t²
As ax = 0, x = ux t = ut cos θ
Vertical motion – Equations of motion
uy = u sin θ
ay = -g
vy = uy – gt
Displacement in y direction = y = uyt – ½ gt²
vy² = uy² - 2gy
22. Time of flight of the projectile = (2u sin θ)/g
23. OB = (u²sin 2θ)/g
24. t = (u sin θ)/g
At t vertical component of velocity is zero.
25. Maximum height reached by the projectile = (u² sin²θ)/2g
## Wednesday, May 20, 2009
### IIT JEE Physics Study Diary - Ch.3 Rest and Motion - Day 3
Day 3 Study Plan
3.6 Motion in a straight line
Ex. 3.5.3.6, 3.7
WOE 3,4,5,6,
Points to Note
Motion in a straight line
As the motion is constrained to move on a straight line, choose the straight line in which motion is taking place as X-axis. Hence x represent the position of the particle at any time instant t. If you want you can imagine a graph between t and x but now t in on the vertical axis and x is on the horizontal axis.
Generally origin is taken at the point where the particle is situated at time t = 0.
Position of the particle at time t is given by x and also x measures displacement (not distance).
Velocity is v = dx/dt (3.9)
acceleration is a = dv/dt (3.10)
a = d²x/dt² (3.11)
Decelaration
If acceleration is negative, then it is along the negative X-axis. It is called deceleration
Motion with constant acceleration
Using integration the formulas for v velocity at any instant, x position at any instant and relation between v,u,x and a are derived in this section.
If acceleration is constant dv/dt = a (constant)
initial velocity = u (at time t =0)
final velocity = v (at time t)
Then v = u+at (3.12)
x = distance moved in time t = ut+½at² (3.13)
Also v² = u²+2ax (3.14)
u,v, and a as well as may take negative or positive values. When u, v and a are negative it shows velocity or acceleration is in the negative X direction.
Example 3.5
a) The question asked is distance travelled. The expression for x gives only displacement. But the remark is that as the particle does not turn back it is equal to distance travelled. Be careful when initial velocity is positive and the acceleration is negative.
Example 3.6
There was a past JEE question which is based on the variable defined in the example.
Freely falling bodies
In this case take the Y axis as the straight line on which the particle or body is moving.
You can take height above the ground as +y and work out the problems.
You can take the starting position of the body as the origin and work out the problem.
The choice may be yours or some choice may be more appropriate in case of some problems, be clear of the formula that you have to use depending on the choice you made.
g is approximately equal to 9.8 m/s², but for convenience in many problems it is given as 10m/s².
### Physics Study Diary for IIT JEE - Ch.3 Rest and Motion - Day 2
Plan for Day 2
4. Average velocity and instantaneous velocity
Ex. 3.4
Worked out example 2
3.5 Average accleration and instantaneous aceleration
WOE 3 to 4
Exercises: 1 to 5
Points to Note
Average velocity
Average speed and average velocity of a body over a specified time interval may not turnout to be same.
Example See the worked out example 2 of HC Verma's book.
The teacher made 10 rounds back and forth in the room and the total distance moved is 800 feet (10 rounds back and forth of 40 ft room). As the time taken is 50 minutes, average speed is 800/50 = 16ft/min.
But because he went out of the same door that he has entered, displacement is zero and hence average velocity is zero.
Instantaneous velocity
Average acceleration
Instantaneous acceleration
Position Vector: If we join the origin to the position of a particle by a straight line and put an arrow towards the position of the particle, we get the position vector of the particle.
If the particle moves from position A to position B, we can define position vector of A and position vector of B and OB - OA will give displacement ( a vector quantity).
Another point to note: slope of velocity-time diagram gives the instant acceleration at that point.
## Monday, May 18, 2009
### Physics Study Diary for IIT JEE 2011 - Ch.3 Rest and Motion
I am planning to study the Physics chapters as per the study plan that I have given. This study would be of help to me in preparing JEE Level Revision problem set for each chapter.
Today (19.5.2009) I did the following portion
Day 1
3.1 Rest and Motion
3.2 Distance and displacement
Ex. 3.1
3.3 average speed and instantaneous speed
Ex. 3.2,3.3
Worked out examples 1,2
Points to note.
3.1 Rest and Motion
Motion is a combined property of the object under study and the observer. There is no meaning of rest or motion without the viewer.
To identify the rest or motion, we need to locate the position of a particle with respect to a frame of reference. The frame of reference will have three mutually perpendicular axes (X-Y-Z) and the particle can be represented by coordinates x,y,z.
If all coordinates remain unchanged as time passes, we say that particle is at rest. If there is change in any of the coordinates with time, we say the particle or the body represented by the particle is having motion.
I some problems or situations frame of reference is specifically mentioned. Otherwise the frame of reference is understood more easily from the context.
Figure 1: A man with a pistol threatening and asking people not to move.
3.2 Distance and Displacement
If a particle moves from position A to Position B in time t, displacement is the length of the straight line joining A to B. The direction of a vector representing this displacement is from A to B. Displacement is a vector quantity. It has both magnitude and direction.
In the movement between positions A and B the particle may take the path ACB. The length of the path ACB will be distance travelled by the particle. It is only scalar quantity. It has not direction.
3.3 Average speed and Instantaneous speed
The average speed of a particle in a specific time interval is defined as the distance travelled by the particle divided by the time interval.
We can plot the distance s as a function of time. In this graph, the instantaneous speed at time t equals the slope of the tangent at the time t. The average speed in a time interval t to t+Δt become equal to the slope of the chord Δs/Δt. As Δt becomes approaches zero, this average speed becomes instantaneous speed and ds/dt becomes the instantaneous speed.
If we plot a speed versus time graph ( v versus t), the distance travelled in time t (t1 to t2) will be equal to the area bounded by the curve v = f(t), x axis, and the two ordinates t = t1 and t = t2.
In terms of integration it can be represented as s = ∫vdt from t1 to t2
For study plan for IIT JEE 2011 for the year 2009-10
http://iit-jee-2011.blogspot.com/2009/04/it-jee-2011-annual-study-plan-for.html
### Nobel Prize Winners in Physics from 1901-1925 - IIT JEE - Extra-curricular Study
Year Physics
For discovery of X-rays
1902 Lorentz, Hendrik A.
Zeeman, Pieter
1903 Becquerel, Henri;
Curie, Pierre;
Curie, Marie
1904 Rayleigh, Lord
1905 Lenard, Philipp
1906 Thomson, J. J.
1907 Michelson, Albert A.
1908 Lippmann, Gabriel
1909 Braun, Ferdinand
Marconi, Guglielmo
1910 van der Waals, Johannes Diderik
1911 Wien, Wilhelm
1912 Dalén, Gustaf
1913 Onnes, Heike Kamerlingh
1914 von Laue, Max
1915 Bragg, William Henry:
Bragg, William Lawrence
1916 None
1917 Barkla, Charles Glover
1918 Planck, Max
1919 Stark, Johannes
1920 Guillaume, Charles Edouard
1921 Einstein, Albert
1922 Bohr, Niels
1923 Millikan, Robert A.
1924 Siegbahn, Manne
1925 Franck, James
Hertz, Gustav
Sources
## Friday, May 15, 2009
### Noble Prize Winners in Physics from 2001 - IIT JEE - Extra-curricular Study
Year - Scientist/Physicist
2001 - Eric A. Cornell, Carl E. Wieman, (US), Wolfgang Ketterle (Germany)
2002 - Riccardo Giacconi, Rayond Davis Jr. (US), Masatoshi Koshiba (Jap)
2003 - Alexei A. Abrikov,(US-Rus), Vitaly I. Ginzburg (Rus). Anthony J. Leggett, (UK-US)
2004 - David J. Gross, H. David Politzer, Frank Wilczek (US)
2005 - Roy glauber, John Hall (both US), and Theodor Haensch (Germany)
2006
2007
2008
## Sunday, April 19, 2009
### IIT JEE 2010 Syllabus for Physics
IIT JEE 2010 syllabus will be available only when the JEE advertisment is released. You have to prepared using JEE 2009 syllabus up to that time.
## Monday, April 13, 2009
### Memory Maps for IIT JEE Physics - Mental Map
Memory is map linking one concept to another concept. Mind map or mental map helps in your memorizing things.
Let me try to identify main concepts in each chapter and link them to more concepts related to each of them
Chapters from "Concepts of Physics Part I and II" by H C Verma
Chapters
1. Introduction to physics
Physics - Understanding nature - Mathematics - Units - Dimensions
Units - Fundamental quantities - Derived quanties - SI units - SI Prefixes
SI Units - Metre - Kilogram - Second - Ampere - Kelvin - Mole
Dimension - Homogenuity - Conversion of Units
Understanding Nature - Structure of world
Order of magnitude
2. Physics and mathematics
3. Rest and motion :kinematics
Rest - Motion – displacement – Speed – Velocity – Acceleration – Frame of Reference
Displacement – Distance moved
Speed - average speed - instantaneous speed
Velocity - Average velocity - instantaneous velocity – Acceleration
Acceleration - Average acceleration - instantaneous acceleration
Motion - straight line - Motion in a plane - Projectile motion
Frame of Reference – Change in Frame of Reference
4. The forces
Forces - Gravitational forces - Electromagnetic (EM) forces - Nuclear Forces - Weak forces - Scope of Classical physics
Gravitational forces - G (universal constant 6.67 *106-11 N-m^2/kg^2) – Acceleration due to gravity g = GM/R^2) - Spherical body treated as a point mass at their centres
Electromagnetic (EM) forces – Coulomb forces – Forces between two surfaces in contact – Tension in a string or rope – Force due to a spring
Nuclear Forces – Exerted when interacting particles are protons or neutrons
Weak forces – Forces responsible for beta decay – antinutrino - positron
Scope of Classical physics – Applicable to bodies of linear sizes greater than 10^-6 m – Subatomic bodies – Quantum physics applicable – If the velocity of bodies are comparable to 3*10^* m/s relativistic mechanics is applicable.
5. Newtons law of motion
Newtons laws of motion - First law - second law - third law - Pseudo forces - Inertia
Newton's First law – Inertial frame of reference – Earth - Noninertial frame of reference
Newton's second law –( f = ma) - Freebody diagram
Newton's third law of motion – action - reaction
Pseudo forces – inertial forces
Inertia – a property which determines acceleration
6. Friction
Friction – Normal contact force – Friction - Kinetic friction - Static friction - Laws of friction - Atomic level friction – Rolling Friction
Kinetic friction – Opposite to motion – Coefficient of Kinetic friction –
Static friction - Limiting friction – Max. Static friction - Coefficient of static friction
Measurement of friction Coefficients- Horizontal table method – Inclined table method
7. Circular motion
Circular motion - Angular variables - Unit vectors along the radius and the tangent – Acceleration - Banking of roads in circular turns - Centrifugal force – Effects of earth's rotation
Angular variables – Angular position – Angular velocity – Angular acceleration – tangential acceleration
Unit vectors along the radius and the tangent – Tangential Unit vectors - Radial Unit vectors
Acceleration – Uniform circular motion - Nonuniform circular motion
Effects of earth's rotation – Colatitude – apparent weight
8. Work and energy
Work and energy - Work - Kinetic energy - Work energy theorem - Potential energy - Conservative and nonconservative forces - Gravitational potential energy - Different forms of energy - Mass energy equivalence
Work - Calculation of work done -
Potential energy - Potential energy of a compressed or extended spring - Gravitational potential energy
9. Centre of mass,linear momentum,collision
Centre of mass, linear momentum, collision - Centre of mass - Motion of the Centre of mass - Linear momentum – Collision – Impulse
Centre of mass - Centre of mass of continuous bodies - Motion of the Centre of mass
Linear momentum - Its conservation principle - Rocket propulsion
Collision - Elastic collision in one dimension - Perfectly inelastic collision in one dimension - Coefficient of restitution - Elastic collision in two dimensions
Impulse - Impulsive force
10. Rotational mechanics
11. Gravitation
12. Simple harmonic motion
13. Fluid mechanics
14. Some mechanical properties of matter
15. Wave motion and waves on a string
16. Sound waves
17. Light waves
18. Geometrical optics
19. Optical instruments
20. Dispersion and spectra
21. Speed of light
22. Photometry
23. Heat and Temperature
24. Kinetic theory of Gases
25. Calorimetry
26. Laws of Thermodynamics
27. Specific Heat of Capacities of Gases
28. Heat transfer
29. Electric Field and Potential
30. Gauss's Law
31. Capacitors
32. Electric Current in Conductors
32. Thermal and Chemical effects of Electric Current
33. Thermal and Chemical Effects of Electric Current
34. Magentic Field
35. Magnetic field due to a Current
36. Permanent Magnets
37. Magnetic Properties of Matter
38. Electro Magentic Induction
39. Alternating current
40. electromagentic Waves
41. Electric Current through Gases
42. Photoelectric Effect and Waveparticle Duality
43. Bohr's Model and Physics of Atom
44. X-Rays
45. SemiConductors and Semiconductor Devices
46. Nucleus
47. The Special Theory of Relativity
## Saturday, April 11, 2009
### Study Plan - Study Guide
I am posting a study plan for each of the chapter. The plan is of 20 days in which first 10 days is for study of the lesson and next 10 days is for revision and solving problems. A candidate must be able to master the chapter in these 20 days by solving every question and problem in the HC Verma text book. By taking a target of 3 chapters in each month for the detailed study 10 days each chapter, candidates can complete each text or one year's portion during the period May to December.
Click on the label HC Verma Study Guide for the plan of various chapters. I completed posting for many chapters of Book 1 and plan to complete for the required number of chapters by May 1.
## Saturday, March 7, 2009
### Blog status
I started revising the study guides of each chapter by providing a 20 days schedule for the first time study and revision of the chapter. I posted the schedule for the first chapter today. I plan to do similar posting for all the chapters.
## Tuesday, February 10, 2009
### COMPTON EFFECT
Arthur Compton and Debye both provided in 1922 a very simple mathematical framework for the momentum of these photons with Compton having experimental evidence from firing X-Rays of known frequency into graphite and looking at recoil electrons.
Let E = mc² = hf for a photon, where f is frequency, and "m" is the mass "equivalent" of the photon given they have no "rest mass". (It is important to recognise that stopping a photon to measure its mass eliminates it -so it has no "at rest" mass - crucial in Special Relativity where, to travel at the speed of light, mass would otherwise become infinite.)
Having "rigged" this mass problem,
p = momentum = mc (mass x velocity) = hf/c = E/c = h/l
The experiment shows that X-Rays and electrons behave exactly like ball bearings colliding on a table top using the same 2D vector diagrams. They enter the graphite at one wavelength and leave at a longer wavelength as they have transfered both momentum and kinetic energy to an electron. Momentum and energy are conserved in the collision if we accept the equation above for momentum of light.
When the photon enters at l0 and leaves at l1, its energy has changed from E0 to E1 and momentum from E0/c to E1/c with a change in direction of q. The electron gains Ek = E0 - E1
See for a diagram and more details
http://www.launc.tased.edu.au/online/sciences/physics/compton.html
The Compton Effect ( a different explanation)
Convincing evidence that light is made up of particles (photons), and that photons have momentum, can be seen when a photon with energy hf collides with a stationary electron. Some of the energy and momentum is transferred to the electron (this is known as the Compton effect), but both energy and momentum are conserved in this elastic collision. After the collision the photon has energy hf' and the electron has acquired a kinetic energy K.
Conservation of energy: hf = hf' + K
Combining this with the momentum conservation equations, it can be shown that the wavelength of the outgoing photon is related to the wavelength of the incident photon by the equation:
Δλ = λ' - λ = (h/mec)(1 - cosq)
The combination of factors h/mec = 2.43 x 10-12 m, where me is the mass of the electron, is known as the Compton wavelength. The collision causes the photon wavelength to increase by somewhere between 0 (for a scattering angle of 0°) and twice the Compton wavelength (for a scattering angle of 180°).
Source:
http://physics.bu.edu/~duffy/semester2/c35_compton.html
It has problems and examples and demonstration also.
## Saturday, February 7, 2009
### Schrodinger’s Equation
Quantum mechanics describes the spectra in a much better way than Bohr’s model.
Electron has a wave character as well as a particle character. The wave function of the electron ψ(r,t ) is obtained by solving Schrodinger’s wave equation. The probability of finding an electron is high where | ψ(r,t )|² is greater. Not only the information about the electron’s position but information about all the properties including energy etc. that we calculated using the Bohr’s postulates are contained in the wave function of ψ(r,t).
Quantum Mechanics of the Hydrogen Atom
The wave function of the electron ψ(r,t) is obtained from the Schrodinger’s equation
-(h²/8π²m) [∂²ψ /∂x² + ∂²ψ /∂y² + ∂²ψ/∂z²] - Ze²ψ/4πε0r = E ψ
where
(x.y,z ) refers to a point with the nucleus as the origin and r is the distance of this point from the nucleus.
E refers to the energy.
Z is the number of protons.
There are infinite number of functions ψ(r,t) which satisfy the equations.
These functions may be characterized by three parameters n,l, and ml.
For each combination of n,l, and ml there is an associated unique value of E of the atom of the ion.
The energy of the wave function of characterized by n,l, and ml depends only on n and may be written as
En = - mZ²e4/8 ε0²h²n²
These energies are identical with Bohr’s model energies.
The paramer n is called the principal quantum number, l the orbital angular momentum quantum number and ml. The magnetic quantum number.
When n = 1, the wave function of the hydrogen atom is
ψ(r) = ψ100 = √(Z³/ π a0²) *(e-r/ a0)
ψ100 denotes that n =1, l = 0 and ml = 0
In quantum mechanics, the idea of orbit is invalid. At any instant the wve function is spread over large distances in space, and wherever ψ≠ 0, the presence of electron may be felt.
The probability of finding the electron in a small volume dV is | ψ(r)| ² dV
We can calculate the probability p(r)dr of finding the electron at a distance between r and r+dr from the nucleus.
In the ground state for hydrogen atom it comes out to be
P(r) = (4/ a0)r²e -2r/ a0
The plot of P(r) versus r shows that P(r) is maximum at r = a0 Which the Bohr’s radius.
But when we put n =2, the maximum probability comes at two radii one near r = a0 and the other at r = 5.4 a0. According to Bohr model all electrons should be at r = 4 a0. | {"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": 0.8254243731498718, "perplexity": 1281.5141921976206}, "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-2018-09/segments/1518891813602.12/warc/CC-MAIN-20180221083833-20180221103833-00132.warc.gz"} |
http://link.springer.com/article/10.1007/s10710-012-9175-4 | , Volume 14, Issue 2, pp 155-190
Date: 13 Nov 2012
# Inference of hidden variables in systems of differential equations with genetic programming
Rent the article at a discount
Rent now
* Final gross prices may vary according to local VAT.
## Abstract
The data-driven modeling of dynamical systems is an important scientific activity, and many studies have applied genetic programming (GP) to the task of automatically constructing such models in the form of systems of ordinary differential equations (ODEs). These previous studies assumed that data measurements were available for all variables in the system, whereas in real-world settings, it is typically the case that one or more variables are unmeasured or “hidden.” Here, we investigate the prospect of automatically constructing ODE models of dynamical systems from time series data with GP in the presence of hidden variables. Several examples with both synthetic and physical systems demonstrate the unique challenges of this problem and the circumstances under which it is possible to reverse-engineer both the form and parameters of ODE models with hidden variables. | {"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": 0.8327020406723022, "perplexity": 468.84885546766253}, "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-2014-42/segments/1414119646209.30/warc/CC-MAIN-20141024030046-00208-ip-10-16-133-185.ec2.internal.warc.gz"} |
http://www.answers.com/Q/FAQ/4871 | General and Special Relativity
Parent Category: Physics
Relativity is the theory stating that all measurements depend on the relative motions of the observer and the observed. The theories of general and specific relativity were both proposed by Albert Einstein.
Subcategories
No they cannot. This is because while you are applying an upward force on your boots, you apply an equal downward force on your back (and by extension also on your feet and boots). Thus everything cancels each other out. This is a direct consequence of the law of conservation of momentum; if you...
Well, since anti-gravity isn't really an option at this point in time, you're going to need energy to get you moving that is greater than the force of gravity. Since you'll be going up a ramp you will start at a horizontal position before reaching the vertical ascent point. What you will need when...
He hypothesized that the speed of light is constant, no matter what the frame of reference is.
No, Einstein WAS a great scientist in the world.
The best title for your project is one that encapsulates what yourproject is about. It should be short, but still memorable. A goodtitle sets the tone for an entire project, so be sure to spend somegood time on coming up with a title.
Einstein did not invent anything because he was not an inventor.
He helped the US of today by giving us theories that helped explorenew fields of technology.
For some one time goes slower and for the other one the same timemay go faster. If one forgets himself time flies but if one is selfcentered then time goes at very slow rate. This is how public haveunderstood Einstein's theory of relativity.
Albert Einstein's cosmological constant was proved wrong by Hubble as he proved the universe is expanding so it doesn't need a constant to stop it imploding.
Special theory of relativity: 1.The laws of physics are same for all observers in uniform motion relative to one another. 2. The speed of light is same ... Later Einstein proposed General relativity.
Yes it is constant. It never stops moving.
High frequency signals can easily pass through a capacitancecompared to the low frequency. Hence the relation between frequencyand capacitive reactance is inversely related
Entropy is the universe's desire to return to disorder, and is an illusion caused by our perception of time. To picture what's going on in entropy, let's imagine a bunch of gas molecules in a jar. To make things easy, let's picture them as billiard balls. The billiard balls will have a bit of energy...
are you asleep ?
The Higgs field has a non-trivial self-interaction, which leads to spontaneous symmetry breaking: in the lowest energy state the symmetry of the potential (which includes the gauge symmetry) is broken by the condensate. In the simplest example, the spontaneously broken field is described by a...
To figure out the force of gravity between the earth and the moon, you need to use newton's equation of gravitational force, i.e. F=(G x m1 x m2)/r^2 Where F is the force of gravity, m1 and m2 are the masses of the two objects in question, r^2 is the distance between the two objects in question,...
The moon is far enough from the Earth that its environs are essentially an absolute vacuum. No air means no drag.
Never mind young children. There's not one in five reasonably intelligent adults who is able to effectively comprehend the idea of relativity or grasp a few of its implications. That's my opinion. I could be wrong.
Albert Einstein didn't invent the computer he died in the early 1900's before even the weakest computers were created.
Well, first of all, it's going to be darn hard to push the end of that thing a foot from where it is. Let's say you just hit the bottom end with a hammer, causing a loud " CLUNGGG ", and then that sound vibration travels down the pole to the other end. In order to let it move as fast as...
Yes it is..Therotically no object can move in the speed of light.But now scientists are trying to find the conditions for which a particle can move in the speed of light. No, anything massless can (and must!) move at c. No object carrying mass can ever move at c.
In this time line, Albert Einstein is not credited with discovering electricity. Einstein did however do work with the electron's role in quantum physics. In Time Line 3, a man by the name of Albert Einstein did make great scientific progress with electricity in the early twentieth century, however...
The theory of General relativity. Albert Einstein was trying to develop a theory that would better explain why the universe behaves the way it does. At the time most scientists were still using Newton's theories which did not accurately predict the movement of planets around the sun. To explain his...
No, a helicopter hovering in mid air over America will not find itself hovering over India the next day. I think you are wondering if you can suspend yourself somehow in mid air the Earth will rotate beneath you, enabling you to come down to Earth where you like. That would be wonderful, but it does...
the world line of an object cannot leave its own forward light cone because to do so it would have to travel faster than light. once another object enters the forward light cone of an object, it cannot leave it either for the same reason. The backward light cone is a different matter, but it is in...
Lagrangian (L) summarizes the dynamics of the system. Generally, in classical physics, the Lagrangian is defined as follows: L=T-V where T is kinetic energy of the system and V is its potential energy. If the Lagrangian of a system is has been defined, then the equations of motion of the...
It depends on what you mean by leading. A few good candidates are string theory, the standard model and loop quantum gravity.
Quantum mechanics and relativity are both parts of the same puzzle: how the universe works. They are both equally important, because they both explain things that are not explained by classical physics.
A quantum of light is also called a photon. Photons have energy and so must also have mass. This is from the famous equations of Einstein. We know the energy of a photon ... (Planck's constant) times (c)/(wavelength). We know the speed of the photon ... it's the speed of light. We know the...
Answer . Distance covered in nth second means the distance covered in that particular second . It cannot be more than the distance covered in n seconds which means the distance covered in a total time of n seconds.
A refrigerator pump with no moving parts so it did not need seals which wearout and then leak.
See this link for relatavistic mass: hyperphysics Dot phy-astr Dot gsu Dot edu/hbase/Relativ/tdil.html It is not letting me put the link in as normal, so I put the "dots"in. Remember that momentum is conserved. Since initial momentum is zero(since it is at rest) the net momentum of the two...
Definitely not, but using Classical mechanics you should be able to solve this question. Also, I imagine engineers in the field of fluid dynamics might be able to answer your question.
Special relativity is always applicable, but only really useful when you are considering objects moving close to the speed of light. General relativity should be used when objects are very heavy or dense.
When you're in a car and the car suddenly stops (for any reason). You'll feel that you're moving forward, that's why seatbelts are there to prevent you from being thrown out of the car. You being resistant to changes in motion, is an inertia of motion.
We currently do not have any technology to travel outside the "normal" time stream. We are carried along into the future by the currents of cause and effect. Other than moving along with the "present" in the time stream (and, therefore, into the future), no other time travel is within our capability...
Well friction is a force that acts between two surfaces in contact. Although it has unwanted effects like loss of energy or wear and tear, yet it is a very important force and is thus sometimes called 'the necessary evil'. At homes friction needs to be increased on stairs, floors, especially...
Yes, a photon moves at the speed of light, because photons have no mass.
If you go whizzing past me at a high speed, then I'll notice that your wristwatch looks like it's running slow, and the pitch of your voice has dropped. I'll think to myself, "Hey ! I'm OK, but his time has slowed down." At the same time, you'll notice that my wristwatch looks like it's...
This formula shows that matter is just a form of energy; one can convert mass into energy and vice versa.
At present, no, there is no conceivable method of safely traveling in time. Oddly enough, time travel is not prohibited by the laws of physics but there are many obstacles to making it safe or even using it to communicate. In fact, there are hypotheses that state that these obstacles will...
that no one would believe that gandi really existed
Grass is a mixture. In these terms, all living things are mixtures.
It isn't, except for die-hard physics fans!
The photon has no mass so therefore it is dimensionless .
repel force, attraction force,
No one knows but unless you ask Einstein himself we will never know
At least special theory of relativity was published 1905
It depends on how many ppl they have on set so yall jus gonna have to be pation
Einstein was a pacifist and thus against all war. But he was also wise enough to see the horrible consequences to civilization should the Nazis build and use nuclear weapons! Thus when approached by Leo Silard with a letter to FDR recommending research on the bomb, he willingly signed it. Thus...
E=mc^2 is born because of special relativity.
Einstein's Theory of Relativity can be summarized by two points: 1. the speed of light in empty space is a constant independent of the state of motion of the emitting body and 2. equality of relative motion , thus the Theory of Relativity . The first point should explain why light does not...
Of course! Psychologists have problems too, and if their pride allows it, they can get the opinion of another psychologist.
solid reactants form liquid reactants
Never, because he was never an inventor.
E represents energy in Joules, m represents mass in kilograms and c represents the speed of light. Let's say we have a gram of mass. By Einstein's energy equation, that gram of mass has 299,792,458 x 299,792,458 x 0.01b of energy. That works out to exactly 89,875,517,873,681.764 Joules of energy...
Assuming this is a fill in the blank question, relativity undermined the view that time and space were absolute.
Watts, same as light bulbs. Most pen pointer lasers are 5 mw, or 5 milliwatts (5 thousandths of a watt). Image the light of a 120 watt incandescent bulb compared to that. 120 watts vs. 0.005 watts. The light bulb consumes 24,000 times more energy, even though the laser dot is really, really bright.
Special relativity is a fundamental pillar in our understanding of the Universe. Many things are based on it, like the GPS system and nuclear power. Indirectly much of nano technology is based on special relativity so things like iPads, computers, modern cars, all have ingredients which can be...
Yes. Albert Einstein dropped out of high school at age 15.
This phenomenon occurs due to light's wave-like properties. Via diffraction, the bending of light wave about an obstacle, the light wave will interfere and exhibit dark and bright fringes on a screen as a result of this interference.
time shifting and space shifting are the acts of shifting time and space respectively, as in the sentence: "i have just shifted time and space".
Things such as Leaves on a tree even the rain even the sun in the sky these things of nature doesn't opperate by itself. These things were Created by The Creator and he alone make everything fall when it come's to nature.
first off its not weed its incense second off, online here its 3 grams for 30\$
Normally its a lowercase c, as in E=m(c) 2 . Energy=mass times the speed of light squared.
According to Einstein's special theory of relativity, mass can be converted into energy, and is given by the relation E=mc2, where c is the velocity of light. From the question, the object thus will be converted into energy
Yes, time is affected by gravity. We know that the fabric of "reality" is spacetime, and spacetime can be warped by gravity. Gravity will thus affect time, as it cannot help but do so.
This is because no matter how large objects on earth may seem, they are nothing compared to the size things have to be to have significant pull on things. Objects would have to be many hundreds of miles across to get any sort of influence.
Answer quantum field theory, quantum electrodynamics, quantum chromodynamics, string theory . Energy is quantized
This was because he did not speak until later than most children, and learned other things much more slowly as well. And if you don't fix your spelling, people might think YOU'RE intellectually challenged...
Einstein was not an inventor, and did not invent anything.
The distinction is sometimes made to distinguish normal quantum mechanics (which does not incorporate special relativity) and quantum field theory (relativistic quantum mechanics). Since we know special relativity is correct it is the relativistic form of quantum mechanics which is true, but non...
He was born exactly 300 years after Galileo I'd kinda think that it more relates to the foundations that Galileo had been able to establish of which Albert Einstein was then able to form his theories
yes because it contains more gravitational potential as its mass has increased.
Many great articles on this subject exist.. Try: http://en.wikipedia.org/wiki/Mass-energy_equivalence
i assume you mean photon but I'm not 100% but "In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic "unit" of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force . The...
what are the two forces acting immediately after leaving the launching pad of a rocket
A few examples: -UV radiation from the Sun stimulates the production of vitamin D in your skin. -UV radiation from black lights are used in the theater to make some objects glow. -UV radiation is used to check for fake money in shops. (Paper money usually has some kind of security feature...
An object is not accelerating when it is moving in a straight lineat an unchanging speed (which may be zero).
I hope I am not missing a joke. He needed it to navigate his sailing boat. | {"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": 0.814282238483429, "perplexity": 671.4047535968805}, "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-2018-17/segments/1524125945596.11/warc/CC-MAIN-20180422115536-20180422135536-00548.warc.gz"} |
http://mathhelpforum.com/algebra/2205-factors-simplest-form-concept-check-print.html | # Factors and Simplest Form: Concept check
• March 14th 2006, 05:08 AM
Euclid Alexandria
Factors and Simplest Form: Concept check
The following is my explanation of why it is false that the prime factorization of 72 is 2 * 4 * 9.
It is false that the prime factorization of 72 is 2 * 4 * 9, because 4 and 9 are not prime numbers. 4 can be further simplified to 2 * 2, and 9 can be further simplified to 3 * 3.
Is my answer clear and correct?
• March 14th 2006, 06:16 AM
CaptainBlack
Quote:
Originally Posted by Euclid Alexandria
The following is my explanation of why it is false that the prime factorization of 72 is 2 * 4 * 9.
It is false that the prime factorization of 72 is 2 * 4 * 9, because 4 and 9 are not prime numbers. 4 can be further simplified to 2 * 2, and 9 can be further simplified to 3 * 3.
Is my answer clear and correct?
Looks OK to me.
Now that you have done all the work it would be worth a few marks
to actually give the correct prime factorisation.
RonL
• March 16th 2006, 07:37 PM
Euclid Alexandria
Thanks Captain.
Oh and $2^3 * 3^2$ (if that's the correct way of writing it)!
• March 17th 2006, 01:01 AM
CaptainBlack
Quote:
Originally Posted by Euclid Alexandria
Thanks Captain.
Oh and $2^3 * 3^2$ (if that's the correct way of writing it)!
That looks good. Though you could use the following alternate TeX formats:
$2^3\ 3^2$
$2^3 \times 3^2$
which, to me at least, cosmetically look better .
RonL
• March 17th 2006, 08:27 AM
ThePerfectHacker
I prefer to write $2^3\cdot 3^2$ using the LaTeX ommand \cdot
• March 17th 2006, 08:38 AM
CaptainBlack
Quote:
Originally Posted by ThePerfectHacker
I prefer to write $2^3\cdot 3^2$ using the LaTeX ommand \cdot
I try to avoid this, as when I was 10 we were taught to use $\cdot$ as the decimal point.
So I prefer juxtaposition or a multiplication symbol.
RonL
• March 19th 2006, 12:59 PM
Euclid Alexandria
Thanks for the TeX pointers guys.
• March 19th 2006, 01:21 PM
ThePerfectHacker
Quote:
Originally Posted by CaptainBlack
I try to avoid this, as when I was 10 we were taught to use $\cdot$ as the decimal point.
So I prefer juxtaposition or a multiplication symbol.
RonL
I was taught the juxatoposition of $\times$ may be confused for $x$.
• March 19th 2006, 02:06 PM
CaptainBlack
Quote:
Originally Posted by ThePerfectHacker
I was taught the juxatoposition of $\times$ may be confused for $x$.
But we are using TeX, so its not a problem. Also its not a problem in
manuscript if you are careful.
RonL | {"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": 0.9261632561683655, "perplexity": 749.0397239861375}, "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-2016-36/segments/1471983577646.93/warc/CC-MAIN-20160823201937-00184-ip-10-153-172-175.ec2.internal.warc.gz"} |
http://mokslasplius.lt/rizikos-fizika/en/agent-based-herding-model-financial-markets | # Agent based herding model of financial markets
Kirman’s ant colony model, previously presented on our website as agent based (based on [1]) and stochastic (based on [2, 3]) model, has become classical example of herding modeling. Application of this model towards economic, financial or other social scenarios might seem doubtful as human society is far more complex than ant colony, but methodologically it is more useful to start from very simple and stylized model and later add complexity on top of it. Furthermore we have already shown that Kirman’s herding dynamics could be applicable in agent based marketing (see comparison of Kirman’s and Bass diffusion model). In this text we will consider financial market scenario and obtain stochastic differential equations similar to the existing stochastic models considered in [4, 5].
Discussion and model presented in this text is the main topic of our paper on Microscopic reasoning for the non-linear stochastic models of long-range memory [6].
## Introduction of variable event time scale
Original Kirman’s model assumes constant agent meeting rate. In financial market scenario one could draw analogy between these events and trades, as trade is pair-wise interaction of traders, or agents in modelic case, and also a great opportunity to reconsider available options. Thus we rewrite original one-step transition probabilities as
$$p(X \rightarrow X+1)=(N-X) \left[\sigma_1 + \frac{h X}{\tau(X)} \right] \Delta t ,$$
$$p(X \rightarrow X-1)=X \frac{\sigma_2 + h (N-X)}{\tau(X)} \Delta t ,$$
where $$\tau(X)$$ is characteristic inter-event time, which now depends on system state. Note that in the above transition probabilities we have already assumed that one group of agent is rational, $$N-X$$, while another is not, $$X$$. For this reason transition rate, $$\sigma_1$$, of $$N-X$$ has remained constant.
In this, more general, case derivation of stochastic differential equation in the manner it was done in [2] (also discussed on our website) is rather troublesome. Though alternatively we can use one-step process formalism [3, 7]. In such case we compactly express Master equation using one-step operators, $$\boldsymbol{E}$$ and $$\boldsymbol{E}^{-1}$$:
$$\partial_t \omega(x,t) = N^2 \left\{ (\boldsymbol{E} -1) [ \pi^{-}(x) \omega(x,t) ] + (\boldsymbol{E}^{-1} -1) [ \pi^{+}(x) \omega(x,t) ] \right\} , \label{master}$$
where $$\pi^{\pm}(x)$$ are probability fluxes related to the transitions probabilities as $$P(X \rightarrow X \pm 1)= N^2 \pi^{\pm}(x) \Delta t$$. Evidently $$x$$ is continuous system state variable, defined as $$x= \frac{X}{N}$$ (large $$N$$ values can be assumed to secure continuity of the new system state variable).
As one-step operators act on continuous functions they can be expanded using Taylor series up to the second order terms:
$$\boldsymbol{E}[f(x)] = f(x+\Delta x) \approx f(x) + \Delta x \partial_x f(x) + \frac{\Delta x^2}{2} \partial^2_x f(x) ,$$
$$\boldsymbol{E}^{-1}[f(x)] = f(x-\Delta x) \approx f(x) – \Delta x \partial_x f(x) + \frac{\Delta x^2}{2} \partial^2_x f(x) ,$$
where $$\Delta x$$ is smallest possible increment of the continuous system state variable, $$\frac{1}{N}$$. After this expansion Master equation, Eq. \eqref{master}, becomes Fokker-Planck equation:
$$\partial_t \omega(x,t) = -\partial_x [A(x) \omega(x,t)] + \frac{1}{2} \partial^2_x [D(x) \omega(x,t)] , \label{fokpla}$$
where $$A(x)$$ and $$D(x)$$ are custom functions:
$$A(x) = N (\pi^{+}(x)-\pi^{-}(x)) = \sigma_1 (1-x) – \frac{\sigma_2 x}{\tau(x)} ,$$
$$D(x) = \pi^{+}(x)+\pi^{-}(x) \approx \frac{2 h x (1-x)}{\tau(x)} .$$
The above Fokker-Planck equation, \eqref{fokpla}, can be rewritten as Langevin equation:
$$\mathrm{d} x = A(x) \mathrm{d} t + \sqrt{D(x)} \mathrm{d} W = \left[ \sigma_1 (1-x) – \frac{\sigma_2 x}{\tau(x)} \right] \mathrm{d} t + \sqrt{\frac{2 h x (1-x)}{\tau(x)}} \mathrm{d} W .$$
To simplify model we can introduce dimensionless time, $$t_s = h t$$:
$$\mathrm{d} x = \left[ \varepsilon_1 (1-x) – \frac{\varepsilon_2 x}{\tau(x)} \right] \mathrm{d} t_s + \sqrt{\frac{2 x (1-x)}{\tau(x)}} \mathrm{d} W_s , \label{lanx}$$
where $$\varepsilon_i$$ are accordingly rescaled original model parameters, $$\varepsilon_i = \frac{\sigma_i}{h}$$.
## Introducing price and return
While introducing variable time scale we assumed that there are at least two types of traders – some are rational, while some are not so. In recent agent based modeling [8] it is also very common to assume that there are two types of traders in the market – fundamentalists and noise traders. By definition fundamentalists are assumed to be rational investors aiming for the long term profits, while noise traders rely on technical trading strategies aiming for short term profits.
Fundamentalists base their decision on information about the stock’s value in the market. This information is quantified via so-called fundamental price, $$P_f(t)$$. Fundamentalists expect that in long-run market will tend towards correct estimate of the stock’s value. If $$P_f(t) > P(t)$$ fundamentalists will expect growth of prices, thus placing buying orders. In the opposite case they’ll attempt to sell stock, as they will expect decrease of price. These ideas are mathematical put down as [2]:
$$D_f(t) = N_f(t) \ln \frac{P_f(t)}{P(t)} ,$$
where $$D_f(t)$$ is fundamentalists’, $$N_f$$ entities, excess demand at a given time.
Contrary noise traders attempt to forecast future prices based on previous price movements. As they are using price charts to make forecast, they are also called chartists. As very is a wide selection of very different chartist trading strategies, chartists are likely to make very different forecasts. Difference in forecasts would lead to difference in bids. This intrinsic disagreement might be macroscopically seen as irrational mood of noise traders. Thus theirs’ excess demand can mathematical be expressed as [2]:
$$D_c(t) = – r_0 N_c(t) \xi(t) ,$$
where $$\xi(t)$$ is an average noise traders’ mood, $$r_0$$ is scaling term, which might also be seen as relative impact of chartists’ trades on the market.
Now one can use Walras law in order to obtain definition of price and, later, return. Original Walras law [9] assumes that trading in the market occurs trough the market maker, who stabilizes the market. Market is consider to be stable if all agents’ excess demands equal zero:
$$\sum_{i=1}^{N} D_i(t) = D_f(t) + D_c(t) = N_f(t) \ln \frac{P_f(t)}{P(t)} – r_0 N_c(t) \xi(t) = 0 ,$$
$$P(t) = P_f(t) \exp \left[ r_0 \frac{N_c(t)}{N_f(t)} \xi(t) \right] ,$$
here one can assume that fundamental price remains constant (i.e. it is not a function of time). As we have definition of price, now we can obtain definition of return:
$$r_{T}(t)=\ln \frac{P(t)}{P(t-T)} = r_0 \left[ \frac{x(t)}{1-x(t)} \xi(t) – \frac{x(t-T)}{1-x(t-T)} \xi(t-T) \right] . \label{fullret}$$
Note that in the above we have expressed $$N_c(t)$$ and $$N_f(t)$$ using $$x(t)$$, which we have defined previously as a systems state variable of Kirman’s model. As fundamentalists are rational we have set that $$N_f(t)/N = 1-x(t)$$, while chartists are thus directly related to $$x(t)$$.
In [2] definition of return, \eqref{fullret}, is simplified by using adiabatic approximation. Namely it is assumed that noise traders’ change their mood very quickly, if compared with $$x(t)$$. This gives simpler definition of return:
$$r(t)=r_0 \frac{x(t)}{1-x(t)} \zeta(t) , \label{return}$$
where $$\zeta(t)$$ is a change of noise traders’ mood, $$\zeta(t) = \xi(t) – \xi(t-T)$$. This change can be modeled in different ways, in [2] it is modeled using spin noise. In such case $$y(t)=\frac{x(t)}{1-x(t)}$$ can be seen as absolute return, for which we will derive stochastic model in the next section of this text.
## Derivation of stochastic model for absolute return, y
Eqs. \eqref{lanx} and \eqref{return} were derived in [2] (stochastic model was derived in a bit different way), but Alfarano et al. stopped there and did not derive stochastic differential equation for absolute return. In order to obtain stochastic model for absolute return we use Ito variable substitution formula [10]:
$$\mathrm{d} y(x) = \left[ A_x(x) \partial_x y(x) + \frac{1}{2} B_x^2(x) \partial^2_x y(x) \right] \mathrm{d} t + B_x(x) \partial_x y(x) \mathrm{d} W ,$$
to obtain stochastic model for $$y$$:
$$\mathrm{d} y = \left(\varepsilon_1 + y \frac{2-\varepsilon_2}{\tau(y)} \right) (1 + y) \mathrm{d} t_s + \sqrt{\frac{2 y}{\tau(y)}} ( 1 + y ) \mathrm{d} W_s . \label{lany}$$
If we consider $$\tau(y) = y^{-\alpha}$$, this selection might be backed by the positive correlation between trading activity and absolute return and also by the similarity of statistical properties, and a limit of large $$y$$ values Eq. \eqref{lany} becomes:
$$\mathrm{d} y = (2-\varepsilon_2) y^{2+\alpha} \mathrm{d} t_s + \sqrt{2 y^{3+\alpha}} \mathrm{d} W_s . \label{lanyour}$$
We find that Eq. \eqref{lanyour} is very similar to stochastic differential equation consider in [5]:
$$\mathrm{d} y = \left( \eta – \frac{\lambda}{2} \right) y^{2 \eta -1} \mathrm{d} t + y^\eta \mathrm{d} W , \label{oursde}$$
which is known to give power law statistics:
$$S(f) \sim \frac{1}{f^\beta}, \quad \beta=1+\frac{\lambda-3}{2(\eta-1)} ,$$
$$p(y) \sim y^{-\lambda} .$$
As relations between different model parameters are $$\eta = \frac{3+\alpha}{2}$$, $$\lambda = \varepsilon_2 + \alpha +1$$ (obtained by directly comparing stochastic differential equations \eqref{lanyour} and \eqref{oursde}), we expect that $$y$$ defined by Eq. \eqref{lany} will also have power law statistics:
$$S(f) \sim \frac{1}{f^\beta}, \quad \beta=1+\frac{\varepsilon_2+\alpha-2}{1+\alpha} ,$$
$$p(y) \sim y^{-\varepsilon_2 – \alpha -1} .$$
Using these predictions we have reproduced $$1/f$$ noise in three distinct cases (see Fig 1., this figure is featured in [6]).
The above comparison is very important as stochastic differential equation \eqref{oursde} is a more general case of our stochastic model of return [11]. Working on this approach further we might be able to create agent based model providing more sophisticated statistical features reproduced by the model consider in [11].
There is another stochastic model whose stochastic differential equation resembles Eq. \eqref{lany}. It is so-called generalized CEV process, which was consider in [4]:
$$\mathrm{d} y = a y \mathrm{d} t + b y^\eta \mathrm{d} W . \label{cev}$$
Eq. \eqref{cev} is noted to be a special case of Eq. \eqref{oursde}, when exponential diffusion restriction is applied [4]. Though comparison with generalized CEV process is important on its own, as generalized CEV process encompass many stochastic models used in risk management. In order to obtain similar stochastic differential equation we have to linearize drift function of Eq. \eqref{lany} (i.e. set $$\varepsilon_2 = 2$$). Similarity is once again obtained in the limit of large $$y$$ values:
$$\mathrm{d} y = \varepsilon_1 y \mathrm{d} t_s + \sqrt{2 y^{3+\alpha}} \mathrm{d} W_s .$$
Due to the similarity between Eqs. \eqref{oursde} and \eqref{cev}, theoretical predictions of statistical properties remain the same. Though now they have a bit simpler mathematical expression:
$$S(f) \sim \frac{1}{f^\beta}, \quad \beta=1+\frac{\alpha}{1+\alpha} ,$$
$$p(y) \sim y^{- \alpha -3} .$$
In case of generalized CEV process we can’t reproduce $$1/f$$ noise in three distinct cases, but we can still obtain three different power law spectral densities in three distinct cases (in each cases giving precise prediction). In Fig 2., this figure is featured in [6], we have shown that theoretical predictions for CEV process are also valid for $$y$$ defined by Eq. \eqref{lany}.
## Applet
This applet numerically solves Eq. \eqref{lany} using Euler-Maruyama method [12]. In such case Eq. \eqref{lany} becomes a set of difference equations:
$$y_{i+1} = y_i + \frac{\kappa^2}{1+y_i} \left[ \frac{\varepsilon_1 y_i}{\tau(y_i)} + 2 – \varepsilon_2 \right] + \kappa \sqrt{2} \varsigma_i ,$$
$$t_{i+1} = t_i + \frac{\kappa^2 \tau(y_i)}{y_i (1+y_i)^2} ,$$
where $$\kappa$$ is numerical precision parameter (numerical solution tends to improve with smaller values of the parameter (applet uses $$\kappa =0.4$$)), while $$\varsigma_i$$ is normally distributed (zero mean, unit variance) random variable. Precision and quality of numerical results are also influenced by the enforced restrictions (in applet values of $$y$$ are restricted in $$[0.01,100]$$ value interval).
The applet plots both time series and statistical properties in real time. In the first few moments it may show incorrect and very approximate results – please wait a bit for a program to “settle down”, it will start to show correct and precise results as time passes.
If you came here to find the previously used Java applet, it is still available here. The functionality of both applets is almost identical.
## References
• . Ants, rationality and recruitment. Quarterly Journal of Economics 108, 1993, pp. 137-156.
• , , . Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model. Computational Economics 26 (1), 2005, pp. 19-49.
• , , . Time variation of higher moments in a financial market with heterogeneous agents: An analytical approach. Journal of Economic Dynamics and Control 32, 2008, pp. 101-136.
• , , . Interplay between positive feedback in the generalized CEV process. Physica A 390 (8), 2011, pp. 1393-1401. arXiv: 1008.0568 [physics.data-an]. Download.
• , . 1/f noise from nonlinear stochastic differential equations. Physical Review E 81, 2010, pp. 031105. arXiv: 1002.4316 [nlin.AO].
• , . Agent based reasoning for the non-linear stochastic models of long-range memory. Physica A 391 (4), 2012, pp. 1309-1314. doi: 10.1016/j.physa.2011.08.061. arXiv: 1106.2685 [q-fin.ST]. Download.
• . Stochastic process in Physics and Chemistry. North Holland, Amsterdam, 2007.
• , , . Critical Overview of Agent-Based Models for Economics. Proceedings of the School of Physics "E. Fermi", Course CLXXVI, ed. F. Mallnace, H. E. Stanley, pp. 235 - 282. SIF-IOS, Bologna-Amsterdam, 2012. doi: 10.3254/978-1-61499-071-0-235.
• . The evolutionist economics of Lean Walras. Routledge, London and New York, 1996.
• . Handbook of stochastic methods. Springer, Berlin, 2009.
• , , . A Non-linear Stochastic Model of Return in Financial Markets. In: Stochastic Control, ed. C. Myers. InTech, 2010. doi: 10.5772/9748. Download.
• , . Numerical Solution of Stochastic Differential Equations. Springer, Berlin, 1999. | {"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": 30, "x-ck12": 0, "texerror": 0, "math_score": 0.9003499746322632, "perplexity": 1418.1062745237598}, "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-2014-52/segments/1418802767873.65/warc/CC-MAIN-20141217075247-00095-ip-10-231-17-201.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/237661/mathematical-symbol-for-vector-appending | # mathematical symbol for vector appending
Given a vector $v=<1,2,3>$ I want to have a new vector $v'$, which is the vector $v$, appends with a number $4$. How should I represent $v'$ mathematically?
What I wish to have is something like $v'=v^4=<1,2,3,4>$, where ^ is an appending symbol for vector (therefore my main question is, does it exist such "vector appending" symbol in maths?)
-
What do you mean by appending? What is "type alphabet"? – EuYu Nov 15 '12 at 2:18
This question has also been asked at tex.SE: tex.stackexchange.com/questions/8397 – Douglas S. Stones Nov 15 '12 at 3:02
We rarely append vectors. We do append other things (like words, although we use the fancier verb «to yuxtapose») and then we use no sign, just like multiplication. – Mariano Suárez-Alvarez Feb 1 at 3:39
## 2 Answers
I usually see it being represented by writing $v=\left[1, 2, 3\right]$, $w=\left[4\right]$, and then $$\left[v,w\right]=\left[v,4\right]=\left[1,2,3,4\right]$$
This is similar to MATLAB notation, so it might be more common in computing-related contexts.
-
This is a natural application of block matrix notation. If we can write $$\begin{bmatrix}\mathbf A&\mathbf b\\\mathbf b^T&c\end{bmatrix}$$ where $\mathbf A$, $\mathbf b$, and $c$ are a matrix, a column vector, and a scalar respectively, then surely we can write $$\begin{bmatrix}\mathbf v\\w\end{bmatrix}$$ to denote $$\begin{bmatrix}v_1\\v_2\\\vdots\\v_n\\w\end{bmatrix}$$ (and we do). – Rahul May 19 at 14:40
A fairly common notation for the concatenation of two sequences is $s^\frown t$. In the special case where $t$ consists of a single element $a$ you'd have $s^\frown\langle a\rangle$. The TeX code for the symbol $\frown$ is \frown, and to raise it to the desired level you'd make it a superscript.
- | {"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": 0.9860200881958008, "perplexity": 720.0943772295875}, "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-2015-32/segments/1438042989018.40/warc/CC-MAIN-20150728002309-00009-ip-10-236-191-2.ec2.internal.warc.gz"} |
http://www.math.wpi.edu/Course_Materials/MA1024B01/Labs/curves3d/node1.html | Subsections
# MA 1024 Lab 2: Curve Computations in Three Dimensions
## Purpose
The purpose of this lab is to introduce you to curve computations using Maple for parametric curves and vector-valued functions in three dimensions.
## Getting Started
To assist you, there is a worksheet associated with this lab that contains examples. You can copy that worksheet to your home directory with the following command, which must be run in a terminal window, not in Maple.
cp ~bfarr/Curves3D_start.mws ~
You can copy the worksheet now, but you should read through the lab before you load it into Maple. Once you have read to the exercises, start up Maple, load the worksheet Curves3D_start.mws, and go through it carefully. Then you can start working on the exercises
## Background
A parametric curve in three dimensions is a triple of functions , , for in some interval . A vector-valued function in three dimensions is a function that associates a vector in the plane with each value of in its domain. Such a vector valued function can always be written in component form as follows,
where , , and are functions defined on some interval . From our definition of a parametric curve, it should be clear that you can always associate a parametric curve with a vector-valued function by just considering the curve traced out by the head of the vector. However, there are lots of situations where a vector-valued function is more appropriate. This happens most often when the quantity you want to describe with the function is natural to think of as a vector, for example, a force or a displacement. For our purposes, we will focus on the case of motion of a particle in three dimensions. That is, we have a vector-valued function that gives the position at time of a moving point . The velocity of this point is given by the derivative and the acceleration is given by the second derivative, . If the velocity, , is never zero, then we can define the unit tangent vector and the curvature the same way we did in two dimensions by
and
If the curvature is never zero for a particular curve, then we can define another intrinsic property of curve, the unit normal vector by the following equation.
It can be shown that at each point on the curve the vector defined by this equation is a unit vector that is always perpendicular to the tangent vector at that point. Furthermore, the unit normal vector always points in the direction of the centripetal acceleration required to keep a particle moving on the curve. One way to see this is to compute the acceleration by differentiating both sides of the equation
Using the chain rule and the definition of the curvature and the normal vector one obtains the following important equation.
To see why this equation is useful, recall that is the speed, so is the rate of change of the speed. That is, this term measures whether the particle is speeding up or slowing down. Because this component of the acceleration is in the direction of the tangent vector it is often called the tangential acceleration, denoted by the symbol . The component of the acceleration in the direction of the normal vector is called the normal acceleration, denoted . In the case of motion on a circular path, the curvature is the reciprocal of the radius, so this term should be easily recognizable as the centripetal acceleration.
Computing these quantities is generally not an easy task. The Getting started worksheet for this lab describes commands from the CalcP package that simplify these calculations and provides examples for you to work from.
## Exercises
1. Consider the circular helix . Plot the graphs for the following sets of values of and using the VPlot command. You should also look at animations of the plots by using the ParamPlot3D command, though they won't appear in your printout.
1. , for .
2. , for .
3. , for .
Give a brief explanation of how the values of and affect the graph.
2. Consider again the circular helix .
1. Compute the curvature.
2. Compute the normal and tangential components of the acceleration.
3. Consider the function that appeared as one of the examples.
1. Compute the curvature, and plot it for .
2. Compute the normal acceleration, and plot it for .
3. Can you explain why the normal acceleration is increasing, even though the curvature is decreasing? (Hint - look at the speed.) | {"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": 0.9519001245498657, "perplexity": 226.2323183205068}, "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-2017-51/segments/1512948567042.50/warc/CC-MAIN-20171215060102-20171215080102-00046.warc.gz"} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.