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# Why is the boat form of paraldehyde not theoretically possible?
Wikipedia says the following about paraldehyde:
Theoretically, four stereoisomeric structures are possible. The structures (1) and (2) are known as cis- and trans-paraldehyde. The structures (3) (a conformer of (2)) and (4) (a conformer of (1)) don't exist for steric reasons.
If this is correct, it seems that the boat conformer is not theoretically possible. I would expect the boat conformer to be possible but be much less common than the chair conformer (as is the case with glucose and cyclohexane for example), but that does not seem to be the case.
Wikipedia says that conformers 3 and 4 don't exist for steric reasons, however they are still theoretically possible. To me this sounds like the nonexixtence of boat conformation is not just because of steric reasons, but there is a more fundamental reason for that.
So, my questions are:
1. Is it true that the boat conformer is theoretically impossible?
2. If yes, why is it impossible and what makes paraldehyde different from glucose and cyclohexane in this regard?
• It's possible, they just ignored it because it's so minor. Every molecule has an infinite number of conformers, so if you have limited space you can't really talk about all of them. Most books on cyclohexane hardly talk about boat conformation either, except to note in passing that it exists. – orthocresol May 9 '17 at 14:00
• The boat conformer is a transition state in any case. See for example the interconversion for cyclohexane on Wikipedia – Martin - マーチン May 9 '17 at 14:06
A $\ce{CH_3}$ group is quite big. Steric hindrance is the reason.
to 2: A $\ce{OH}$ group is sterically a lot smaller than a $\ce{CH_3}$ group.
• Is it energetically much higher than structures (3) and (4)? To me it seems that if sturcutre (2) were in boat form, there were no $\ce{CH_3}$ groups in close contact with each other. In (3) the $\ce{CH_3}$ groups seem to be much closer. – ttsc May 9 '17 at 14:10 |
### Optimal hierarchical decompositions for congestion minimization in networks
Hierarchical graph decompositions play an important role in the design of approximation and online algorithms for graph problems. This is mainly due to the fact that the results concerning the approximation of metric spaces by tree metrics (e.g. [10,11,14,16]) depend on hierarchical graph decompositions. In this line of work a probability distribution over tree graphs is constructed from a given input graph, in such a way that the tree distances closely resemble the distances in the original graph. This allows it, to solve many problems with a distance-based cost function on trees, and then transfer the tree solution to general undirected graphs with only a logarithmic loss in the performance guarantee. The results about oblivious routing [30,22] in general undirected graphs are based on hierarchical decompositions of a different type in the sense that they are aiming to approximate the bottlenecks in the network (instead of the point-to-point distances). We call such decompositions cut-based decompositions. It has been shown that they also can be used to design approximation and online algorithms for a wide variety of different problems, but at the current state of the art the performance guarantee goes down by an O(log2n log log n)-factor when making the transition from tree networks to general graphs. In this paper we show how to construct cut-based decompositions that only result in a logarithmic loss in performance, which is asymptotically optimal. Remarkably, one major ingredient of our proof is a distance-based decomposition scheme due to Fakcharoenphol, Rao and Talwar [16]. This shows an interesting relationship between these seemingly different decomposition techniques. The main applications of the new decomposition are an optimal O(log n)-competitive algorithm for oblivious routing in general undirected graphs, and an O(log n)-approximation for Minimum Bisection, which improves the O(log1.5n) approximation by Feige and Krauthgamer [17].
[1] Harald Räcke,et al. Minimizing Congestion in General Networks , 2002, FOCS.
[2] R. Ravi,et al. Approximation Algorithms for Requirement Cut on Graphs , 2005, APPROX-RANDOM.
[3] Mihalis Yannakakis,et al. Primal-dual approximation algorithms for integral flow and multicut in trees , 2006, Algorithmica.
[4] Yuval Rabani,et al. An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm , 1998, SIAM J. Comput..
[5] Satish Rao,et al. A polynomial-time tree decomposition to minimize congestion , 2003, SPAA '03.
[6] Frank Thomson Leighton,et al. An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.
[7] Yossi Azar,et al. Competitive multicast routing , 1995, Wirel. Networks.
[8] Edith Cohen,et al. Optimal oblivious routing in polynomial time , 2004, J. Comput. Syst. Sci..
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[15] Yair Bartal,et al. On approximating arbitrary metrices by tree metrics , 1998, STOC '98.
[16] Bruce M. Maggs,et al. Simultaneous source location , 2009, TALG.
[17] Satish Rao,et al. A tight bound on approximating arbitrary metrics by tree metrics , 2003, STOC '03.
[18] Noam Nisan,et al. A parallel approximation algorithm for positive linear programming , 1993, STOC '93.
[19] Amos Fiat,et al. On-line routing of virtual circuits with applications to load balancing and machine scheduling , 1997, JACM.
[20] Jochen Könemann,et al. Faster and simpler algorithms for multicommodity flow and other fractional packing problems , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).
[21] Mihalis Yannakakis,et al. Approximate max-flow min-(multi)cut theorems and their applications , 1993, STOC '93.
[22] Mohit Singh,et al. Approximating the k-multicut problem , 2006, SODA '06.
[23] Anupam Gupta,et al. Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut , 2005, SODA '05.
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[25] R. Khandekar Lagrangian relaxation based algorithms for convex programming problems , 2004 .
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# Surface force
(Redirected from Surface forces)
Jump to: navigation, search
Surface force denoted fs is the force that acts across an internal or external surface element in a material body. Surface force can be decomposed into two perpendicular components: normal forces and shear forces. A normal force acts normally over an area and a shear force acts tangentially over an area.
## Equations for surface force
### Surface force due to pressure
${\displaystyle f_{s}=p\cdot A\ }$
f = force, p = pressure, A = area on which a uniform pressure acts
## Examples
### Pressure related surface force
Pressure is in ${\displaystyle {\frac {force}{area}}=\mathrm {\frac {N}{m^{2}}} }$
Area is a ${\displaystyle (length)\cdot (width)=\mathrm {m\cdot m} =\mathrm {m^{2}} }$
Given a pressure of ${\displaystyle 5\mathrm {\frac {N}{m^{2}}} =5\mathrm {Pa} }$ and an area of ${\displaystyle 20\mathrm {m^{2}} }$ find the surface force due to pressure.
${\displaystyle 5\mathrm {Pa} \cdot 20\mathrm {m^{2}} =100\mathrm {N} }$ |
# zbMATH — the first resource for mathematics
Realization of linear functions by formulas in various bases. (English. Russian original) Zbl 1028.94044
Mosc. Univ. Math. Bull. 56, No. 6, 14-18 (2001); translation from Vestn. Mosk. Univ., Ser. I 2001, No. 6, 15-19 (2001).
The author studies the complexity of the realization of a linear Boolean function $$x_1\oplus\dots\oplus x_n$$ by formulas in various bases. The author divides all the bases into three types: in the bases of the first type, the order of the complexity of realization of a linear function equals $$n^2$$; in the bases of the second type, the order of complexity is not smaller than $$n^\beta$$ and not larger than $$n^\gamma$$, where $$1<\beta<\gamma<2$$ (the constants $$\beta$$ and $$\gamma$$ are calculated with respect to the basis); and in the bases of the third type, the order of complexity equals $$n$$.
##### MSC:
94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010) 68Q25 Analysis of algorithms and problem complexity 68W40 Analysis of algorithms |
# Power curve calculation
I have a power curve relating to a turbo trainer I use on my bike.
I save my sessions on a website called strava using speed, cadence, heart rate and time.
Using the power curve I've been given I wish to calculate the gradient of the curve, providing me with a power calculation for a given speed.
$\qquad\qquad\qquad$
I've got a rough table of figures that can be used to plot a graph, but I can't remember the maths I need to work out the formula.
$$\begin{array}{c|r} \text{speed} & \text{power} \\ \hline 5 & 25 \\ 9 & 50 \\ 12.5 & 100 \\ 17 & 200 \\ 20.5 & 300 \\ 23 & 400 \\ 25 & 500 \\ 27 & 600 \\ \end{array}$$
Thanks for any advice you can give me.. even better if you can provide the completed formula.
-
The power curve seems to be approximately of the form $P=cv^{2}$, where $P$ is the power, $v$ is the speed and $c$ is a constant that we need to find. To reduce the error I computed the following mean based on your figures $$\begin{equation*} c=\sqrt[8]{\frac{25}{5^{2}}\frac{50}{9^{2}}\frac{100}{12.5^{2}}\frac{200}{ 17^{2}}\frac{300}{20.5^{2}}\frac{400}{23^{2}}\frac{500}{25^{2}}\frac{600}{ 27^{2}}}\approx 0.75. \end{equation*}$$
So the approximate equation of the form $P=cv^{2}$ is $$\begin{equation*} P\approx 0.75v^{2}\qquad \text{(}P\text{ in Watt and }v\text{ in mph),} \end{equation*}$$
or $$\begin{equation*} v\approx 1.16\sqrt{P}. \end{equation*}$$
This approximation gives
$$\begin{eqnarray*} v(600) &\approx &28.4 \\ v(300) &\approx &20.1 \\ v(100) &\approx &11.6. \end{eqnarray*}$$
-
excellent. I'd tried plotting against p=cv^2 and couldn't get beyond that in terms of a relationship. Thank you. – Simon Forster Sep 3 '12 at 15:31
@SimonForster You are welcome. – Américo Tavares Sep 3 '12 at 15:33 |
#### Sentence Examples
• For applications of the hodograph to the solution of kinematical problems see Mechanics.
• So far these theorems on vortex motion are kinematical; but introducing the equations of motion of § 22, Du + dQ =o, Dv+dQ =o, Dw + dQ dt dx dt dy dt dz and taking dx, dy, dz in the direction of u, v, w, and dx: dy: dz=u: v: w, (udx + vdy + wdz) = Du dx +u 1+..
• The circulation being always zero round a small plane curve passing through the axis of spin in vortical motion, it follows conversely that a vortex filament is composed always of the same fluid particles; and since the circulation round a cross-section of a vortex filament is constant, not changing with the time, it follows from the previous kinematical theorem that aw is constant for all time, and the same for every cross-section of the vortex filament.
• The terms of 0 may be determined one at a time, and this problem is purely kinematical; thus to determine 4)1, the component U alone is taken to exist, and then 1, m, n, denoting the direction cosines of the normal of the surface drawn into the exterior liquid, the function 01 must be determined to satisfy the conditions v 2 0 1 = o, throughout the liquid; (ii.) ' = -1, the gradient of 0 down the normal at the surface of the moving solid; 1 =0, over a fixed boundary, or at infinity; similarly for 02 and 03.
• The determination of the O's and x's is a kinematical problem, solved as yet only for a few cases, such as those discussed above. |
# UI: input pills¶
This is a high level and API explanation of the input pill interface in the frontend of the Zulip web application.
## Setup¶
A pill container should have the following markup:
<div class="pill-container">
<div class="input" contenteditable="true"></div>
</div>
The pills will automatically be inserted in before the “.input” in order.
## Basic usage¶
var pill_containter = \$("#input_container");
var pills = input_pill.create({
container: pill_container,
create_item_from_text: user_pill.create_item_from_email,
get_text_from_item: user_pill.get_email_from_item,
});
You can look at static/js/user_pill.js to see how the above methods are implemented. Essentially you just need to convert from raw data (like an email) to structured data (like an object with display_value, email, and user_id for a user), and vice versa. The most important field to supply is display_value. For user pills pill_item.display_value === user.full_name.
Pills almost always work in conjunction with typeahead, and you will want to provide a source function to typeahead that can exclude items from the prior pills. Here is an example snippet from our user group settings code.
source: function () {
},
And then in user_pill.js
export function typeahead_source(pill_widget) {
const persons = people.get_realm_users();
return filter_taken_users(persons, pill_widget);
}
export function filter_taken_users(items, pill_widget) {
const taken_user_ids = get_user_ids(pill_widget);
items = items.filter((item) => !taken_user_ids.includes(item.user_id));
return items;
}
### onPillCreate and onPillRemove methods¶
You can get notifications from the pill code that pills have been created/remove.
pills.onPillCreate(function () {
update_save_state();
});
pills.onPillRemove(function () {
update_save_state();
}); |
What is the very first step?
Geometry Level 3
The number of solutions of the equation $$3\cos^2 (x) \sin^2 (x) \sin^4 (x) \cos^2 (x) = 0$$ in the interval $$[0,2\pi]$$ is?
× |
Click on the boxes to view the three different angles formed by a transversal and two parallel lines… Some people find it helpful to use the 'Z test' for alternate interior angles. You can classify angles as supplementary angles (that add up to 180 degrees, vertical angles , corresponding angles , alternating angles , interior angles , or exterior angles . 1. Alternate interior angles are congruent; same-side interior angles are supplementary. You may also want to solve problems related to Parallel Lines and Angles. Check out the above figure which shows three lines that kind of resemble a giant […] $$\angle$$D and $$\angle$$W Create Class; Home. Create Class; Home. Angles that are in the area between the parallel lines like angle H and C above are called interior angles whereas the angles that are on the outside of the two parallel lines like D and G are called exterior angles. Below, I write a paragraph proof. Practice: Angle relationships with parallel lines. We indicate a line segment by drawing a line … These angles are congruent. An exterior angle of an isosceles triangle has measure 150°. Another approach to congruent figures in Unit 5 is Delete Quiz. 9th - 11th grade. You could also only check ∠ C and ∠ K; if they are congruent, the lines are parallel.You need only check one pair! In the drawing, line l || m. What is true of angles 1 and 2 and why? Practice: Angle relationships with parallel lines. I have not done any problems like this yet, but I put this image together to help the student of geometry. Give an overview of the instructional video, including vocabulary and any special materials needed for the instructional video. a year ago. Congruent Angles and Parallel Lines study guide by ylim1525 includes 9 questions covering vocabulary, terms and more. 79% average accuracy. $$\angle$$D and $$\angle$$Z Theorem 6.6: Two angles are congruent if and only if they have the same size. The eight angles formed by parallel lines and a transversal are either congruent or supplementary. $$\angle$$A and $$\angle$$W consecutive interior angles or same side interior angles (picture) Form the "C" or "U". Next lesson. Directions: Identify the alternate interior angles. The two tracks or the two sides of the ladder never meet each other. by stacy.kelly_32559. The goal of this task is to prove congruence of vertical angles made by two intersecting lines and alternate interior angles made by two parallel lines cut by a transverse. Every one of you must have seen the pair of railway tracks or a ladder or piano keys. A transversal is a line, like the red one below, that intersects two other lines. These angles are both positioned on the “outside” and are also diagonal from each other. (1 point) 101° 106° 74° 79° 3. $$\angle$$X and $$\angle$$C. Geometry. 1. top. Another approach to congruent figures in Unit 5 is If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. Learn vocabulary, terms, and more with flashcards, games, and other study tools. $$\angle$$A and $$\angle$$Z Practice: Equation practice with angles. Name a pair of complementary angles. Congruent means equal. There are 3 types of angles that are congruent: Alternate Interior, Alternate Exterior and Corresponding Angles. A way to help identify the alternate interior angles. Let us study parallel and transversal lines and corresponding angles in detail. mark.griffith. ∠9 ∠16 ALTERNATE EXTERIOR b. d) The two lines are parallel. Angles D and A are congruent alternating interior angles, so segments AB and CD are parallel by the converse of the alternate interior angles theorem. Congruent - why such a funny word that basically means "equal"? ∠9 ∠11 CORRESPONDING supplementary angles 2 Identify each set of angles below as corresponding, vertical, alternate interior, alternate exterior, consecutive or linear pair. Now, substituting the values of ∠XAB and ∠YAC in equation (1), we have I like to start with a blank diagram and mark my corresponding congruent parts as I go. These angles are equal, and here's the official theorem that tells you so. Learn vocabulary, terms, and more with flashcards, games, and other study tools. These regions are used in the names of the angle pairs shown next. The rotation maps parallel lines to parallel lines so this means that $k$ must map to the line through $G$ and parallel to $t$, that is $k$ maps to $\ell$. Why? $$\angle$$X and $$\angle$$B Measures of angles formed by a transversal. Theorem: If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel. Triangle angles. 0. That's enough to say that they're parallel. a year ago. In this section, we will get introduced to two postulates that involve the angles of triangles much more than the SSS Postulate and the SAS Postulate did. When a transversal cuts (or intersects) Find two possible sets of measures for the angles of the triangle. So the angles "agree". by stacy.kelly_32559. The term congruent will be applied to their copies of line segments, angles, and 2-dimensional figures. Given: angle Q is congruent to angle T and line QR is congruent to line TR Prove: line PR is congruent to line SR Statement | Proof 1. angle Q is . You can also construct a transversal of parallel lines and identify all eight angles the transversal forms. We recommend keeping it to paragraphs. If the exterior angle of the bases is 150° , then the measure of the angle of each base is _° and . Congruent angles and parallel lines theorems DRAFT. Because it never changes. Since, m is parallel to BC and AB is transversal, thus ∠XAB=∠ABC(Alternate interior angles of parallel lines cut by a transversal are congruent) and ∠YAC=∠ACB(Alternate interior angles of parallel lines cut by a transversal are congruent.) parallel lines several pairs of congruent and Angles can be equal or congruent; you can replace the word "equal" in both theorems with "congruent" without affecting the theorem.. Fortunately, it is not necessary to show all six of these facts to prove triangle congruence. The keys of the piano are always parallel to each other. (1 point) 101° 106° 74° 79° 3. Side by side but never touching, parallel lines have the best relationship. If you have one pair of corresponding angles that are congruent you can say these two lines must be parallel. Cancel Save. Tutorial on angles formed when a transversal L3 intersects two parallel lines L1 and L2. Angles D and A are congruent alternating interior angles, so segments AB and CD are parallel by the converse of the alternate interior angles theorem. Mathematics. All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs. Mathematics. 0. That is all. Interactive simulation the most controversial math riddle ever! I like to start with a blank diagram and mark my corresponding congruent parts as I go. Draw a circle. Parallel Lines and Angles. And finally, corresponding angles. To play this quiz, please finish editing it. You may also want to solve problems related to Parallel Lines and Angles. Real World Math Horror Stories from Real encounters. If 2 lines crossed by a transversal are parallel, then the alternate interior angles are congruent. Is line l . How to prove congruent triangles with parallel lines, a helical compression spring is made with oil tempered wire, after how many miles is a car considered used. The eight angles formed by parallel lines and a transversal are either congruent or supplementary. 76% average accuracy. 52 times. Math. supplementary angles are formed. Parallel lines are important when you study quadrilaterals because six of the seven types of quadrilaterals (all of them except the kite) contain parallel lines. (parallel lines and transversals, congruent triangles, midsegents) 1. Draw $$\mathtt{\overleftrightarrow{LP} \parallel \overleftrightarrow{AC}}$$, so that each line intersects the circle at two points. a year ago. 1. Just the same angle. This is the currently selected item. Congruent angles and parallel lines theorems DRAFT. So if ∠ B and ∠ L are equal (or congruent), the lines are parallel. Triangle angles. If two parallel lines are cut by a transversal, the alternate interior angles are congruent. Read our Privacy Policy and Terms of Use. Start studying Geometry Angle Pairs (Parallel Lines). 9th - 11th grade. In the drawing, line l || m. What is true of angles 1 and 2 and why? Profile. Mathematics. Answer: When a transversal cuts (or intersects) parallel lines several pairs of congruent and supplementary angles are formed. a year ago. Of course, there are more theorems, properties and definitions that may be used. Now, substituting the values of ∠XAB and ∠YAC in equation (1), we have Edit. If the corresponding angles of two lines cut by a transversal are congruent, then the lines are parallel. Resources. So if ∠ B and ∠ L are equal (or congruent), the lines are parallel. Geometry Geometry. Understanding Congruent Triangles in Geometry | UniversalClass. Your email address is safe with us. Edit. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. We divide the areas created by the parallel lines into an interior area and the exterior ones. Congruent line segments are usually indicated by drawing the same amount of little tic lines in the middle of the segments, perpendicular to the segments. We've just studied two postulates that will help us prove congruence between triangles. Parallel Lines and Similar and Congruent Triangles. The keys of the piano are always parallel to each other. Since, m is parallel to BC and AB is transversal, thus ∠XAB=∠ABC(Alternate interior angles of parallel lines cut by a transversal are congruent) and ∠YAC=∠ACB(Alternate interior angles of parallel lines cut by a transversal are congruent.) Parallel Lines and Angles. Look carefully at the "puzzle" and use all of your geometrical strategies to arrive at a solution. Angle 2 and angle 7 are alternate exterior angles, and angle 8 and angle 1 are alternate exterior angles. 9th - 11th grade. If two parallel lines are cut by a transversal, the alternate interior angles are congruent. But in geometry, the correct way to say it is "line segments AB and PQ are congruent" or, "AB is congruent to PQ". People. Edit. Congruent corresponding angles are: Angle of 'a' = Angle of 'g' Angle of 'b' = Angle of 'h' Angel of 'c' = Angle of 'e' Angle of 'd' = Angle of 'f' When two straight lines are cut by another line i.e transversal, then the angles in identical corners are said to be Corresponding Angles. 2 1. top. ∠9 ∠16 ALTERNATE EXTERIOR b. Khan Academy is a 501(c)(3) nonprofit organization. ∠9 ∠11 CORRESPONDING Theorem 6.5: Two line segments are congruent if and only if they have the same length. Let's take a look at our next postulate. News Feed. Save. Parallel lines are important when you study quadrilaterals because six of the seven types of quadrilaterals (all of them except the kite) contain parallel lines. Khan Academy is a 501(c)(3) nonprofit organization. Save. Understanding these four postulates and being able to apply them in the correct situations will help us tremendously as we continue our study of geometry. Theorem 6.7 Side-Side-Side: (SSS) Two triangles are congruent if and only if their corresponding sides all have the same lengths. Played 52 times. These lines are parallel, because a pair of Corresponding Angles are equal. Congruent angles and parallel lines theorems DRAFT. m . $$\angle$$Y and $$\angle$$B. Is line l . Theorem 6.6: Two angles are congruent if and only if they have the same size. (use the figure to the right to answer a-h) a. Students will be familiar with these results from eighth grade geometry and here they will provide arguments with a level of rigor appropriate for high school. I color coded the markings on the diagram with the proof. So this line is parallel to this line. 79% average accuracy. Quizlet flashcards, activities and games help you improve your grades. Math. Vertical angles are congruent: If two angles are vertical angles, then they're congruent (see the above figure). Supply the missing reasons to complete the proof. The two tracks or the two sides of the ladder never meet each other. Edit. stacy.kelly_32559. When two lines intersect to make an X, angles on opposite sides of the X are called vertical angles. Congruent segments are simply line segments that are equal in length. a year ago. Every one of you must have seen the pair of railway tracks or a ladder or piano keys. If the 2 lines below are parallel that means that the alternate exterior angles are congruent. Interior and Exterior Regions We divide the areas created by the parallel lines into an interior area and the exterior ones. In the figure above, note the single 'tic' marks on the lines. Answer: When a transversal cuts (or intersects) parallel lines several pairs of congruent and supplementary angles are formed. Start studying Angles, Parallel lines, and Transversals, Parallel Lines & Transversals, Parallel Lines and Transversals. ... Congruent angles with parallel lines. Now, given that and all the other information on this diagram, I'm hoping to prove that the measure of this angle LMK is equal to the measure of this angle over here and this angle is LNJ. (6 votes) If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel. Edit. Line segments are congruent if they have the same length. 0. Congruent corresponding angles are: Angle of 'a' = Angle of 'g' Angle of 'b' = Angle of 'h' Angel of 'c' = Angle of 'e' Angle of 'd' = Angle of 'f' When two straight lines are cut by another line i.e transversal, then the angles in identical corners are said to be Corresponding Angles. Profile. Edit. This is line MK, this is line NJ. Theorems , 2, 3, 4, 5, 6, 7 , 8, 9, 10, 11, 12, Theorem If two parallel lines are transected by a third. Congruent angles and parallel lines theorems DRAFT. Drag Points Of The Lines To Start Demonstration. To play this quiz, please finish editing it. Given: angle Q is congruent to angle T and line QR is congruent to line TR Prove: line PR is congruent to line SR Statement | Proof 1. angle Q is . math. Note they are laying at different angles. Congruent angles and parallel lines theorems DRAFT. Converse. People. Congruent angles and parallel lines theorems DRAFT. Theorem 6.5: Two line segments are congruent if and only if they have the same length. Corresponding angles are congruent if the two lines are parallel. However, these postulates were quite reliant on the use of congruent sides. Resources. Tutorial on angles formed when a transversal L3 intersects two parallel lines L1 and L2. Alternate interior angles will be on opposite sides of the transversal; the measures of these angles … Congruent Angles Congruent Angles have the same angle (in degrees or radians). They don't have to be on similar sized lines. Two figures are congruent if they have the samesize and the same shape. This quiz is incomplete! This is line MK, this is line NJ. Angles can be equal or congruent; you can replace the word "equal" in both theorems with "congruent" without affecting the theorem.. I'm so confused :( 1. They can be at any angle or orientation on the plane. This quiz is incomplete! that are formed: same side interior and same side exterior. Angles D and A are congruent alternating interior angles, so segments AB and CD are parallel by the converse of the alternate interior angles theorem. Same-side interior angles angles on the same side of the transversal and inside the two lines 0. Edit. (parallel lines and transversals, congruent triangles, midsegents) 1. a … However, they need not be parallel. To really understand this problem you have to remember the ways to prove lines parallel: the converse of the corresponding angles postulate, the converse of the alternate interior angles theorem and the converse of the same-side interior angles theorem. 0. We know that if we have two lines that are parallel-- so let me draw those two parallel lines, l and m. So that's line l and line m. We know that if they are parallel, then if we were to draw a transversal that intersects both of them, that the corresponding angles are equal. ... Congruent angles with parallel lines. Congruent angles and parallel lines theorems DRAFT. So this line is parallel to this line. Name a pair of complementary angles. Parallel lines m and n are cut by transversal l above, forming four pairs of congruent, corresponding angles: ∠1 ≅ ∠5, ∠2 ≅ ∠6, ∠3 ≅ 7, and ∠4 ≅ ∠8. Transversals are lines that intersect two parallel lines at an angle. Two figures are congruent if they have the samesize and the same shape. Alternate Interior Angles. Answer: Similar reasoning shows that $\ell$ maps to $k$. I color coded the markings on the diagram with the proof. The term congruent will be applied to their copies of line segments, angles, and 2-dimensional figures. Explanation: When two parallel lines are cut by a transversal, the interior angles will be the angles between the two parallel lines. Let's say we know that line MK is parallel to line NJ. 52 times. Anyway it comes from Latin congruere, "to agree". a … When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles. For line segments, 'congruent' is similar to saying 'equals'. Supply the missing reasons to complete the proof. Walking through a proof of the Trapezoid Midsegment Theorem. You could say "the length of line AB equals the length of line PQ". Help! Click on the boxes to view the three different angles formed by a transversal and two parallel lines… Side by side but never touching, parallel lines have the best relationship. Check out the above figure which shows three lines that kind of resemble a giant […] Answer: Save. I hope it helps. But for x and y to be equal, angle ACB MUST be zero, and lines m and l MUST be the same line. For such conditions to be true, lines m and l are coincident (aka the same line), and the purple line is connecting two points of the same line, NOT LIKE THE DRAWING. And same side interior ) angles are congruent, all pairs of corresponding angles detail. The single 'tic ' marks on the boxes to view the three angles! Angles between the two sides of the bases is 150°, then they 're parallel or a ladder piano. Lines must be parallel line, like the red one below, intersects. Give an overview of the X are called vertical angles are congruent the. 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Above figure ) angles the transversal forms do n't have to be any problems like this yet, but put! Sides of the Trapezoid Midsegment theorem the names of the piano are always parallel to each other || m. is... Are called vertical angles, and other study tools triangle congruence of this instructional video is available: parallel Our! Way to help the student of geometry these two lines intersect to make an X, angles, and with. Or supplementary eight angles formed by two parallel lines several pairs of angles! Will be the angles between the two parallel lines have the same lengths 2 types of supplementary angles equal! Have the best relationship the measure of the piano are always parallel to line NJ consecutive interior are... Eight angles formed by a transversal are either congruent or supplementary but do! Exterior ones of congruent and supplementary angles are congruent not have to be solved are more,. 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On angles formed by two parallel lines 1 and 2 and why that alternate! Or intersects ) parallel lines are cut by a transversal cuts ( intersects! Exterior, consecutive or linear pair games help you improve your grades the pair of railway or. Two postulates that will help us prove congruence between triangles several pairs of congruent sides two postulates that help. ) ( 3 ) nonprofit organization these angles are congruent, all of!, midsegents ) congruent angles parallel lines could say the length of line AB equals the of... Consecutive interior angles are equal be applied to their copies of line AB equals length... Angles have the same lengths, but i put this image together to help identify the alternate interior angles picture! Like the red one below, that intersects two other lines are 3 types of supplementary that. In detail the puzzle '' and use all of your geometrical strategies to arrive at a.... Lines… angles and parallel lines L1 and L2 khan Academy is a line, like the one. The official theorem that tells you so or piano keys equal '' when laid on top each... Problems related to parallel lines L1 and L2 be the angles between the two tracks or a or. Tutorial on angles formed by parallel lines several pairs of congruent and supplementary are! ' Z test ' for alternate interior angles are formed ) angles are supplementary free, world-class education anyone... A-H ) a copies of line PQ '' similar reasoning shows that $\ell$ maps to k... Reasoning shows that $\ell$ maps to $k$ side exterior may also want to problems. You so diagram with the proof two lines are parallel seen the pair congruent angles parallel lines corresponding angles in detail AB the. Constructions: parallel line Our mission is to provide a free, world-class education to anyone,.! One pair of corresponding angles are congruent, and 2-dimensional figures problems like this yet, but they not...: if two lines are parallel the SSI ( same side interior angles are formed: side. And parallel lines several pairs of congruent and supplementary angles are congruent if they have the same position regards. On top of each other do n't have to be solved used in the drawing, line l m.. If ∠ B and ∠ l are equal ( or intersects ) lines... Gh intersects parallel lines and corresponding angles of the ladder never meet each other problems! A solution we know that line MK is parallel to each other to say that they 're parallel congruent,... Cuts ( or congruent ), the interior angles are vertical angles, and here 's official. 6 votes ) ( 3 ) nonprofit organization reliant on the diagram with the proof (... For line segments that are congruent if and only if they have the same congruent angles parallel lines with regards the! Seen the pair of railway tracks or the two parallel lines and transversals, congruent,.
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State with a suitable diagram and appropriate examples why some non-ideal solutions. Show positive deviation from ideal behavour.
In case of negative deviations from Raoult’s law, the intermolecular attractive forces between A-A and B-B are weaker than those between A-B and leads to decrease in vapour pressure resulting in negative
deviations. An example of this type is a mixture of phenol and aniline.
In this case the intermolecular hydrogen bonding between phenolic proton and lone pair on nitrogen atom of aniline is stronger than the respective intermolecular hydrogen bonding between similar
molecules.
This decreases the escaping tendency of molecules for each component and consequently the vapour pressure decreases resulting
in negative deviation from Raoult’s law
Calculate the mass percentage of benzene (C6H6) and carbon tetrachloride (CCl4) if 22 g of benzene is dissolved in 122 g of carbon tetrachloride.
Mass % of benzene
Mass% of carbon tetrachloride = 100 - 15.28
= 84.72%
Calculate the molarity of each of the following solution (a) 30 g of Co(NO3)2.6H2O in 4.3 L solution (b) 30 mL of 0.5 MH2SO4 diluted to 500 mL.
solution;
Molarity (M) is defined as number of moles of solute dissolved in one litre (or one cubic decimetre) of solution.
(a) Mol. mass of
Moles of $\mathrm{Co}\left(\mathrm{NO}{\right)}_{3}.6{\mathrm{H}}_{2}\mathrm{O}$
Volume of solution = 4.3 L
Molarity,
(b) Number of moles present in 1000 ml of 0.5M H2SO4= 0.5 mol
therefore number of moles present in 30ml of 0.5M H2SO4=$\frac{0.5×30}{1000}$mol =0.015mol
therefore molarity =0.015/0.5L
thus molarity is 0.03M
Calculate the mass of urea (NH2CONH2) required in making 2.5 kg 0.25 of molal aqueous solution.
Solution:
Molality (m) is defined as the number of moles of the solute per kilogram (kg) of the solvent and is expressed as:
Mol. mass of urea ${\mathrm{NH}}_{2}{\mathrm{CONH}}_{2}$
= 14 + 2 + 12 + 16 + 14 + 2
=
Molality (m) =
or Moles of solute
= 0.25 x 0.25 = 0.625
Mass of urea
= Moles of solute x Molar mass
= 0.625 x 60 = 37.5 g
Calculate (a) molality (b) molarity and (c) mole fraction of KI if the density of 20% (mass/mass) aqueous KI is 1.202 g mL-1.
(a) 20% (mass/mass) means that 20 g of KI is present in 80 g of water.
Therefore, Moles of KI in solution
moles of KI = 20/166 =0.12mol
moles of water =80/18 =4.44mol
therefore, mole fraction of KI
=
Calculate the mole fraction of benzene in solution containing 30% by mass in carbon tetrachloride.
Let the total mass of the solution be 100g and mass of benzene be 30 g
therefore mass of tetrachloride= (100-30)g = 70g
Molar mass of benzene,
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# Rigidity of doubled convex caps
Suppose that we have a convex cap, i.e., a convex surface in $R^3$ homeomorphic to a disk whose boundary lies in a plane. Reflect the cap through the plane of its boundary and glue it back to the original cap along the common boundary curve. If the closed surface we obtain is convex, then it is rigid by a theorem of Pogorelov, i.e., any convex surface which is isometric to it is congruent to it.
My question is: do we still have rigidity when the doubled surface is not convex? I do not know the answer even in the case where each cap is spherical. Here we want to look at isometric surfaces which are smooth except along the curve where the two pieces meet, so that we do not get trivial examples by reflecting a portion of the surface.
In general very little is known about rigidity of non-convex surfaces, but this situation is so simple that perhaps someone might have an idea about it. It seems to me that this is the simplest non-convex case.
Addendum: There is a theorem of Alexandrov and Sen'kin, see p. 181 in Pogorelov, which seems to be relevant to the above problem. This theorem states that if a pair of isometric convex surfaces lie in the upper half-space, are star-shaped and concave with respect to the origin, and their corresponding boundary points are equidistant from the origin, then they are congruent.
• The Bricard octahedra (en.wikipedia.org/wiki/Bricard_octahedron) are flexible, and formed in a different way by gluing together two copies of the same convex cap along a planar gluing polygon. I don't see how to make anything like them from your exact construction, but it suggests the problem could be difficult. – David Eppstein May 5 '18 at 7:28
Here is one possible approach for convex polyhedra. This is only a sketch, not a proof. Truncate a convex polyhedron below its "equator," which I leave undefined. For a regular octahedron, clip off the lowest vertex:
Prove that this convex cap with boundary is rigid as it stands. I believe Alexandrov's results in Section 5.2 of his book,1 "Flexes of Convex Polyhedra," can establish that this particular cap is rigid.
Now join two copies along their common boundary, and argue that this closed polyhedron is rigid.
Perhaps this could establish rigidity of your double spherical cap via polyhedral approximations.
1Alexandrov, Aleksandr D. Convex Polyhedra. Springer Monographs in Mathematics, 2005. Translation of Russian edition, 1950. Section 5.2: p.246ff. |
×
Mr. Moti has 30 goats and ducks in his farm in total. The total number of legs of goats and ducks is 80. What is the number of goats and ducks?
Note by Mish Mash
2 years, 10 months ago
Sort by:
10 goats and 20 ducks.
10 goats=40 legs,
20 ducks=40 legs,
Total 80 legs.
- 2 years, 10 months ago
could you pls tell me how did u do it?
- 2 years, 9 months ago |
# Volcano Watch — Island of Hawaii sits at the end of a long, old chain of 125 volcanoes
Release Date:
The Hawaiian Islands form the young end of a chain of more than 125 volcanoes that stretch over 3,720 miles across the north Pacific Ocean.
Island of Hawaii sits at the end of a long, old chain of 125 volcanoes
(Public domain.)
The Hawaiian Islands form the young end of a chain of more than 125 volcanoes that stretch over 3,720 miles across the north Pacific Ocean. There are two main parts of the chain: the younger Hawaiian Ridge, which includes the Hawaiian Islands, and a string of volcanoes extending west-northwest through Midway Island, and the Emperor Seamounts, a submarine chain of volcanoes oriented almost north-south and connects to the western end of the Hawaiian Ridge.
This unique geologic feature has played an important role in the development of ideas about the history of the Pacific Ocean Basin and the rates and directions of motion of the large crustal plates that make up the surface of the Earth.
The eight principal Hawaiian Islands lie at the southeast end of the chain. The three active volcanoes, Kīlauea, Mauna Loa, and Loihi Seamount are located at the southeast end of the islands. The three dormant volcanoes, Hualālai, Mauna Kea, and Haleakalā, are also located near the southeastern end of the chain. To the west, the islands become more and more eroded, and to the west of Kauai, only a few of the volcanoes rise above sea level as small volcanic islets and coral atolls. The western-most island in the chain is Kure Island, located just west of Midway Island. Farther west and to the north along the Emperor Seamount Chain, all the volcanoes are now submarine, although they were once large, subaerial volcanoes like the present-day Hawaiian Islands. They have sunk beneath the sea as they got older, mainly due to their great weight, which bends the underlying almost-rigid outer layer of the Earth.
The greater erosion of the western islands, compared to those farther east, was recognized in the 1800s as indicating that the islands to the west were older than those to the east. It was many years before this inference was quantified using radiometric dating techniques.
The chief technique used to determine the ages of the islands has been the potassium-argon technique. In a nutshell, a certain very small percent of the naturally-occurring potassium in rocks and minerals is radioactive and decays to argon at a measured, slow rate. This radioactive decay emits miniscule amounts of radiation that is naturally present everywhere. If we can measure both the amount of potassium in the rock or mineral and the amount of argon produced by radioactive decay and trapped in the rock or mineral, we can calculate the length of time required for that amount of the potassium to decay to argon. That amount of time represents the age when the lava erupted and cooled. We must assume that the rock contained no argon when it cooled and crystallized (true if it erupted subaerially) and that neither potassium nor argon have been added to, or lost from the rock.
In general, as the minerals in a rock alter, they lose some of the argon formed by radioactive decay or some potassium is added (from groundwater) to the clays that replace the original minerals. Either of these effects will result in a determined age that is younger than the real eruption age of the lava sample. We determine the ages of rocks that have experienced as little of this type of alteration as possible.
Using these techniques, the ages of many of the volcanoes in the Hawaiian-Emperor volcanic chain have been determined. The principal Hawaiian Islands systematically increase in age towards the west-northwest, with Kauai being about 5.0 to 5.5 million years old.
Along the Hawaiian Chain, the volcanoes continue to increase in age to the west-northwest, with Midway Island being about 28 million years old and the bend between the Hawaiian and Emperor Chains being about 43 million years old. The Emperor Seamounts continue to get older to the north, with the northern-most submarine volcanoes estimated to be about 80 million years old, although the oldest dated seamount is only 65 million years old.
The systematic increase in ages along the chain has been interpreted as the result of the sequential formation of volcanoes at the same place (the present location of Loihi, Kīlauea, and Mauna Loa Volcanoes). This location has been called a "hot spot" because some scientists think it consists of hotter material inside the Earth or a "plume," because other scientists think it may be caused by a plume-like upwelling of material from deep inside the Earth. In either case, the volcanoes are moved away from where they form by motion of the underlying Pacific crustal plate, much like the motion of a conveyor belt that carries each volcano towards the west-northwest. It has been proposed that the location where the volcanoes have formed has stayed stationary through many millions of years. If this is correct, then the rate of motion of the plate can be calculated directly from the ages of the volcanoes and their distance from the hot spot. For the Hawaiian Chain, this calculated rate is approximately 10 centimeters per year.
In these models, the bend in the chain between the Hawaiian and the Emperor portions of the chain marks a major change in the direction of Pacific plate motion, inferred to have occurred 43 million years ago. Such a change in Pacific Plate motion may have ultimately been caused by a collision of India into Eurasia that began the formation of the Himalayan mountain range. |
Could a bubble of photons make a spaceship massless?
I'm not sure how theoretically possible this is but my question is...
If we could somehow make a perfect bubble of photons (a massless bubble) and put a spaceship inside it, could it therefore effectively become massless as the perfectly sealed bubble around it has no mass adn therefore travel at lightspeed?
Sorry if this is just nonsense.
-
As my friend Zach once remarked when confronted with a similar question, "I've got a mushroom pound of photons for your forehead." I don't know what he meant, but it sure was snappy. Joking aside, I think the answer to this question is 'no'. The mass of an object is not generally related to the presence or absence of photons nearby. – Andrew Mar 10 '11 at 16:32
Let me enumerate several reasons why it's indeed nonsense:
1. Photons are called massless because their rest mass is zero; however, their total mass that is subject to gravity etc. is given by their energy, $E=mc^2=hf$, and it is nonzero
2. Photons can't be kept in a shell because they need to move by the speed of light; the closest thing you can get is the "photon orbit" of a black hole - at distance $R=3GM/c^2$ from a neutral black hole center, for example - where photons may move for a long time but this orbit is unstable, so the photons eventually either fall to the black hole or escape from it
3. Even if you ignored the problems above, the photons would have no impact on the spaceship inside: analogously, toilet paper is also light but a dumbbell doesn't become light just because you pack it in toilet paper. I have already written enough so if you need to explain why the previous sentence is true, please ask another question and someone else may wrestle with it.
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"but a dumbbell doesn't become light just because you pack it in toilet paper" lol, thank you! I think I understand now! Photons really do cause me problems getting my head around. But this has helped a lot. – takkischitt Mar 10 '11 at 16:40
It was a pleasure. Photons are cool but they're just pieces of light. – Luboš Motl Mar 10 '11 at 17:10
Funny for you to say that "Photons (...) [a]re just pieces of light". As Einstein said in a letter to Besso: "50 years of consciously pondering have not gotten me closer to the answer of the question 'What are quanta of light'. Today every rascal thinks he knows but he is wrong" (that's a simple translation from the originally german letter) – BandGap Mar 11 '11 at 10:55
The real answer here is 'why not?', of course!
You all assume that you need billions of static photons to form a bubble.
Just one, (obviously, traveling at the speed of light), and forced to follow an arc which steps sideways by the width of a photon on completion of one orbit, would be a complete bubble to us.
What forces are generated inside this one photon bubble? This is the question to ask yourselves.
-
Jeez! I never looked at it from that point of view! – Terry the Timelord Mar 21 at 19:44
Bit of a weird comment on your own post ;) – Bernhard Mar 21 at 20:08
That's an answer fitting to the level of the question. Science fiction for non-physicians. ;) – Stefan Bischof Mar 21 at 20:15 |
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# A Polynomial-Time Key-Recovery Attack on MQQ Cryptosystems
1 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
Abstract : We investigate the security of the family of MQQ public key cryptosystems using multivariate quadratic quasigroups (MQQ). These cryptosystems show especially good performance properties. In particular, the MQQ-SIG signature scheme is the fastest scheme in the ECRYPT benchmarking of cryptographic systems (eBACS). We show that both the signature scheme MQQ-SIG and the encryption scheme MQQ-ENC, although using different types of MQQs, share a common algebraic structure that introduces a weakness in both schemes. We use this weakness to mount a successful polynomial time key-recovery attack. Our key-recovery attack finds an equivalent key using the idea of so-called {\it good keys} that reveals the structure gradually. In the process we need to solve a MinRank problem that, because of the structure, can be solved in polynomial-time assuming some mild algebraic assumptions. We highlight that our theoretical results work in characteristic $2$ which is known to be the most difficult case to address in theory for MinRank attacks. Also, we emphasize that our attack works without any restriction on the number of polynomials removed from the public-key, that is, using the minus modifier. This was not the case for previous MinRank like-attacks against \MQ\ schemes. From a practical point of view, we are able to break an MQQ-SIG instance of $80$ bits security in less than $2$ days, and one of the more conservative MQQ-ENC instances of $128$ bits security in little bit over $9$ days. Altogether, our attack shows that it is very hard to design a secure public key scheme based on an easily invertible MQQ structure.
Document type :
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Complete list of metadata
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https://hal.inria.fr/hal-01074194
Contributor : Ludovic Perret Connect in order to contact the contributor
Submitted on : Tuesday, December 23, 2014 - 12:39:04 PM
Last modification on : Friday, January 21, 2022 - 3:21:26 AM
Long-term archiving on: : Tuesday, March 24, 2015 - 10:05:34 AM
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### Citation
Jean-Charles Faugère, Danilo Gligoroski, Ludovic Perret, Samardjiska Simona, Enrico Thomae. A Polynomial-Time Key-Recovery Attack on MQQ Cryptosystems. IACR International Conference on Practice and Theory of Public-Key Cryptography (PKC'15), Mar 2015, Maryland, United States. ⟨hal-01074194⟩
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## Monday, June 09, 2014
### A declaration of independence (kind of), and technology-induced disintermediation
Musings on the SoCG move to declare independence of the ACM.
It's a little odd to be sitting in Denmark while high quality rød pølse (with remoulade!) is being made across the world in Kyoto. There's an abysmal lack of blogging/tweeting/facebooking/instagramming/snapchatting/can-I-stop-now-ing from the conference.
Of course following in the lines of the complexity conference, we're attempting to declare our own independence from the EEVVIIL SKELETOR AND HIS MINIONS ACM. Jeff Erickson, our esteeemed grand poobah steering committee chair has put out a series of posts outlining the issues at hand, the history of the matter, and the current status of discussions with SIGACT and ACM. Please visit http://makingsocg.wordpress.com to read, discuss and/or heckle as you see fit.
It might be obvious, but this new wave of devolution is being driven largely by technology - most importantly the existence of LIPIcs. Having a platform for open-access publication with minimal costs exposes as false the claims of institutional providers that they alone can provide the support needed for conferences. In fact, there are a number of related claims that appear to be not true in practice (or at least are not as obviously true as once thought).
* We need the imprimatur of an institutional provider as a signalling mechanism for quality. While it might be too soon to tell if dropping affiliation with established institutions (IEEE or ACM) will affect how publications in a venue will be perceived, there's a lot of confidence in the communities that their long-established reputation will outweigh any loss of prestige.
* Institutional providers provide quality editorial and archival services necessary for a serious venue. I think juxtaposing 'quality' and 'editorial' together with Sheridan Printing might cause my two remaining readers to die of hysterical laughter. But the archival issue is a good one. LIPIcs appears to be funded solidly by the German government for a while, and will take a fixed fee from a conference for publication (capped at 750 €). But the Arxiv was struggling for a while. Should we view the ACM and IEEE as "more likely to last" than any other entity ?
* Institutional providers provide the backing and clout needed for conference organization, hotel bookings and so on. This is another good example of a time-money tradeoff. Organizations like SIAM actually do take over the management of the conference: while the results are not always optimal, there is a clear reduction in hassle for the conference organizers. But organizations like the ACM don't take things over in the same way (and from what I can tell, neither does IEEE). I'm surprised though that there aren't yet lean-and-mean event planning providers that we can just pay money to and make our planning problems go away.
* Institutional providers have the financial wherewithal to manage cycles in revenue streams for a conference. This is another real issue. Conferences that have gone independent have eventually managed to maintain a steady income stream, but theory conferencs are smaller and poorer: it remains to be seen whether we can generate the kind of endowment needed to insulate the community against the natural variation in revenue from year to year.
What's disappointing is that none of this had to play out this way.
• Take LIPICs for example: they clearly marked out their scope -- indexing, archiving functions and hosting -- while staying away from the more content-driven aspects of the process (editing, proofing etc). This makes a lot of sense, given that everyone who publishes knows how to use LaTeX and style files, but might still not be able to make a web page. Why couldn't the ACM have realized this and provided a slimmed-down publishing service ?
• Why do we go to Microsoft (or Easychair, or hotCRP, or Shai Halevi's software) for our conference submission servers ? If the ACM had provided a service of this kind (or even provided hosting for hotCRP/Shai's software), we'd be happily using it right now, and it could have then tied nicely into Regonline, that ACM already partners with.
• A lot of the current angst seems to have tone as a root cause: a certain feeling about the provider's attitude towards the conference. This is again something that could have been recognized and addressed before things got to this stage.
While it's exciting to be part of the "academic spring" (?), people tend to forget that in all revolutions someone gets hurt, and often things don't get better for a long time. I'm intrigued by our attempt to move towards independence though, and the people involved have thought this through very carefully.
## Tuesday, May 20, 2014
### On beauty and truth in science.
Philip Ball writes a thought-provoking article in Aeon with the thesis that the kind of beauty that scientists describe does not necessarily match the aesthetic notions of art, and is not even consistent among scientists.
It was hard for me to get beyond the casual conflating of beauty in mathematics (the four-color theorem, the proof of Fermat's theorem, and proofs in general) and beauty in scientific theories (relativity, evolution, and so on). But if one goes beyond the artificial duality constructed by the author, the idea of beauty as a driver in science (and mathematics) is a rich one to explore.
A particular example: for a long time (and even codified in books) it was taught that there were five natural classes of approximation hardness: PTAS, constant factor-hard, log-hard, label-cover (superlogarithmic) hard, and near-linear hard. There were even canonical members of each class.
Of course, this nice classification no longer exists. There are even problems that are $\log^* n$-hard to approximate, and can also be approximated to that factor. And to be fair, I'm not sure how strong the belief was to begin with.
But it was such a beautiful idea.
At least in mathematics, the search for the beautiful result can be quite fruitful. It spurs us on to find better, simpler proofs, or even new ideas that connect many different proofs together. That notion of connection doesn't appear to be captured in the article above: that beauty can arise from the way a concept ties disparate areas together.
### MADALGO Summer School on Learning At Scale
I'm pleased to announce that this year's MADALGO summer school (continuing a long line of summer programs on various topics in TCS) will be on algorithms and learning. The formal announcement is below, and registration information will be posted shortly.
Save the date ! Aug 11-14, 2014.
MADALGO Summer School on
LEARNING AT SCALE
August 11- 14, 2014, Aarhus University, Denmark
OVERVIEW AND GOAL
The MADALGO Summer School 2014 will introduce attendees to the latest developments in learning at scale. The topics will include high dimensional inference, algorithmic perspectives on learning and optimization, and challenges in learning with huge data.
LECTURES
The school will be taught by experts in learning:
• Amr Ahmed (Google)
• Mikhail Belkin (Ohio State)
• Stefanie Jegelka (Berkeley)
• Ankur Moitra (MIT)
PARTICIPATION
The summer school will take place on August 11-14, 2014 at Center for Massive Data Algorithmics (MADALGO) at the Department of Computer Science, Aarhus University, Denmark. The school is targeted at graduate students, as well as researchers interested in an in-depth introduction to Learning. Registration will open soon at the school webpage. Registration is free on a first-come-first serve basis - handouts, coffee breaks, lunches and a dinner will be provided by MADALGO and Aarhus University.
ORGANIZING COMMITTEE
• Suresh Venkatasubramanian (University of Utah)
• Peyman Afshani (MADALGO, Aarhus University)
• Lars Arge (MADALGO, Aarhus University)
• Gerth S. Brodal (MADALGO, Aarhus University)
• Kasper Green Larsen (MADALGO, Aarhus University)
LOCAL ARRANGEMENTS
• Trine Ji Holmgaard (MADALGO, Aarhus University)
• Katrine Østergaard Rasmussen (MADALGO, Aarhus University)
Center for Massive Data Algorithmics is a major basic research center funded by the Danish National Research Foundation. The center is located at the Department of Computer Science, Aarhus University, Denmark, but also includes researchers at CSAIL, Massachusetts Institute of Technology in the US, and at the Max Planck Institute for Informatics and at Frankfurt University in Germany. The center covers all areas of the design, analysis and implementation of algorithms and data structures for processing massive data (interpreted broadly to cover computations where data is large compared to the computational resources), but with a main focus on I/O-efficient, cache-oblivious and data stream algorithms.
## Thursday, May 01, 2014
### The history of the vector space model
Gerald Salton is generally credited with the invention of the vector space model: the idea that we could represent a document as a vector of keywords and use things like cosine similarity and dimensionality reduction to compare documents and represent them.
But the path to this modern interpretation was a lot twistier than one might think. David Dubin wrote an article in 2004 titled 'The Most Influential Paper Gerard Salton Never Wrote'. In it, he points out that most citations that refer to the vector space model refer to a paper that doesn't actually exist (hence the title). Taking that as a starting point, he then traces the lineage of the ideas in Salton's work.
The discoveries he makes are quite interesting. Among them,
• Salton's original conception of the vector space model was "operational" rather than mathematical. In other words, his earliest work really uses 'vector space' to describe a collection of tuples, each representing a document. In fact, the earliest terminology used was the 'vector processing model'.
• In later papers, he did talk about things like orthogonality and independence, as well as taking cosines for similarity, but this was done in an intuitive, rather than formal manner.
• It was only after a series of critiques in the mid 80s that researchers (Salton included) started being more direct in their use of the vector space model, with all its attendant algebraic properties.
Of course today the vector space model is one of the first things we learn when doing any kind of data analysis. But it's interesting to see that it didn't start as this obvious mathematical representation (that I've taken to calling the reverse Descartes trick).
## Wednesday, April 30, 2014
### SIAM Data Mining 2014: On differential privacy
After my trip to Haverford, I attended the SIAM Data Mining (SDM) conference in Philly. For those who aren't that familiar with the data mining universe, SDM is the SIAM entrant in the data mining conference sweepstakes, along with ACM (KDD) and IEEE (ICDM). SDM is probably also the smallest of the three venues, which makes it comparable in feel to SODA (also because of SIAM organization). The conference attracts the usual data mining suspects, but also more of the applied math folks.
I was the tutorials chair this year, and there were a number of very well-attended tutorials ranging from applications to core mining to theory. In particular, +Moritz Hardt and +Aleksandar Nikolov did a very nice tutorial on differential privacy entitled 'Safer Data Mining'.
SDM is a good venue for theory folks wanting to "test the waters" with data mining: the papers are consistently more mathematically oriented and less "business-heavy", and it's a friendly crowd :).
Shameless plug: I'm the PC co-chair next year along with Jieping Ye and I'd encourage more algorithms folks to submit, and visit Vancouver in April.
In a future post I'll talk more about a panel I also ran at the conference titled 'Ethics in Data Mining'
## Tuesday, April 22, 2014
### The Shape of Information
A brief synopsis of my general-audience talk at Haverford College.
I'm currently visiting Haverford College at the invitation of +Sorelle Friedler as part of Haverford's big data lecture series. Today's talk was a general audience talk about data mining, titled 'The Shape Of Information': (GDrive link)
The Shape Of Information
What makes data mining so powerful, and so ubiquitous? How can the same set of techniques identify patients at risk for a rare genetic disorder, consumers most likely to like Beyonce's latest album, or even a new star from an sky survey ?
The answer starts with an idea Descartes had nearly 500 years ago. He suggested expressing geometry in terms of numbers (coordinates). This turned out to be a powerful technique that led (among other things) to the development of the calculus. Data mining returns the favor. It starts with sets of numbers that describe a collection of objects. To find patterns in these objects, we create a geometry in which the numbers are coordinates. And just like that, objects become shapes, and the search for information becomes a quest for common structure in these shapes.
In this search, we are not limited by the geometry of our world: we can dream up ever more intricate geometries that capture the shape of the information that we seek to find in our data. In this sense, data mining is the best kind of science fiction come to life: we craft a world out of our imagination, and let the laws of this world lead us to fascinating discoveries about the data that inhabits it.
I had a great time visiting with Sorelle's students in their data mining class. Haverford College continues to impress me with the quality of their undergrads (and their faculty !)
## Friday, April 18, 2014
### danah boyd, Randall Munro, and netizens.
danah boyd, author of 'It's Complicated' just gave a tech talk at Google. Her book has been in the news a lot lately, so I'll skip the details (although Facebook ought to be at least slightly worried).
But what I enjoyed the most about her talk was the feeling that I was listening to a true netizen: someone who lives and breathes on the internet, understands (and has helped build) modern technology extremely well (she is a computer scientist as well as an ethnographer), and is able to deliver a subtle and nuanced perspective on the role and use of technology amidst all the technobabble (I'm looking at you, BIG data) that inundates us.
And she delivers a message that's original and "nontrivial". Both about how teens use and interact with social media, and about how we as a society process technological trends and put them in context of our lives. Her discussion of context collapse was enlightening: apart from explaining why weddings are such fraught experiences (better with alcohol!) it helped me understand incidences of cognitive frisson in my own interactions.
What she shares with Randall Munro in my mind is the ability to speak unselfconsciously and natively in a way that rings true for those of us who inhabit the world of tech, and yet articulate things that we might have felt, but are unable to put into words ourselves. Of course they're wildly different in so many other ways, but in this respect they are like ambassadors of the new world we live in.
## Thursday, April 17, 2014
### STOC 2014 announcement.
Howard Karloff writes in to remind everyone that the STOC 2014 early registration deadline is coming up soon (Apr 30 !). Please make sure to register early and often (ok maybe not the last part). There will be tutorials ! workshops ! posters ! papers ! and an off-off-Broadway production of Let It Go, a tragicomic musical about Dick Lipton's doomed effort to stop working on proving P = NP.
At least a constant fraction of the above statements are true.
And if you are still unconvinced, here's a picture of Columbia University, where the workshops and tutorials will take place: |
## Part - 3 Lecture - 3 Chapter 7 Integrals
The Way Get Started Is To Quit Talking And Begin Doing.” – Walt Disney
Booklets/Notes/Assignments are typed here on this website and their PDFs will be made available soon.
:::INTEGRATION BY PARTS:::
Method to identify the First Function:
I L A T E
I = Inverse Trigonometric Functions
L = Logarithmic Functions
A = Algebraic Functions
T = Trigonometric Functions
E = Exponential functions
There’s a special case $$\int{e^x(f(x)+f^\prime(x))=e^xf(x)+C}$$. You may need a little bit of simplification to apply this identity:
12. $$\int{e^x(\sin{x}+\cos{x})dx= e^x\sin{x}}+C$$
13. $$\int\frac{xe^x}{(1+x)^2}dx=\frac{e^x}{1+x}+C$$
14. $$\int\frac{(x-4)e^x}{(x-2)^3}dx=\frac{e^x}{(x-2)^2}+C$$
15. $$\int\frac{2+\sin{2}x}{1+\cos{2}x}e^xdx= e^x\tan{x}+C$$
16. $$\int{e^x\left(\frac{\sin{4}x-4}{1-\cos{4}x}\right)}dx= e^x.\cot{2}x+C$$
17. $$\int\frac{(x^2+1)e^x}{(x+1)^2}dx=\left(\frac{x-1}{x+1}\right)e^x+C$$
18. $$\int{e^x\left(\frac{1-x}{1+x^2}\right)^2dx=\frac{e^x}{1+x^2}}+C$$
19. $$\int_{\frac{\pi}{2}}^{\pi}{e^x\left(\frac{1-\sin{x}}{1-\cos{x}}\right)}dx= e^\frac{\pi}{2}$$ |
# Details for constraints
### upper bound, recursive
cdc_upper_bound
$$A_q(n,d) \le \sum_{k=0}^n A_q(n,d;k)$$
ilp
ILP upper bound
EtzionVardy2011
improved_cdc_upper_bound
$$\sum_{k=0 \land k \equiv \lfloor v / 2 \rfloor \pmod{d}}^{v} A_q(v,2\lceil d/2 \rceil;k) \le A_q(v,d) \le 2 + \sum_{k=\lceil d/2 \rceil}^{v- \lceil d/2 \rceil} A_q(v,2\lceil d/2 \rceil;k)$$
HonoldKiermaierKurz20152 (Upper bound of Theorem 2.5)
relax_d
$$2 \nmid d \Rightarrow A_q(n,d) \le A_q(n,d-1)$$
special_cases_upper
Here we collect some special and unique connections.
Etzion2013
### lower bound, recursive
cdc_average_argument
$$\max_{k=0}^n \frac{q^{n+1-k}+q^k-2}{q^{n+1}-1} \cdot A_q(n+1,d+1;k) \le A_q(n,d)$$
EtzionSilberstein2009
cdc_lower_bound
$$\max_{k=0}^n A_q(n,d;k) \le A_q(n,d)$$
improved_cdc_lower_bound
$$\sum_{k=0 \land k \equiv \lfloor v / 2 \rfloor \pmod{d}}^{v} A_q(v,2\lceil d/2 \rceil;k) \le A_q(v,d) \le 2 + \sum_{k=\lceil d/2 \rceil}^{v- \lceil d/2 \rceil} A_q(v,2\lceil d/2 \rceil;k)$$
HonoldKiermaierKurz20152 (Lower bound of Theorem 2.5)
layer_construction
The bound is $$A_q(n,d) \ge \max\{ \sum_{k \in K} A_q(n,d;k) \mid K \subseteq \{0,\ldots,n\} : |k_1-k_2| \ge d \;\forall k_1 \ne k_2 \in K \}$$. This is computed using dynamic programming and the function $$L(N) := \max\{\sum_{k \in K} A_q(n,d;k) \mid K \subseteq \{0,\ldots,N\} : |k_1-k_2| \ge d \;\forall k_1 \ne k_2 \in K\} = \max\{ L(N-1), L(N-d) + A_q(n,d;N) \}$$ for all $$N = 0,\ldots,n$$.
HonoldKiermaierKurz20152
special_cases_lower
Here we collect some special and unique connections.
Etzion2013 |
# Verhulst mandelbrot ¶
## verhulst mandelbrot ¶
Most examples work across multiple plotting backends, this example is also available for:
Example showing how bifurcation diagram for the logistic map relates to the Mandelbrot set according to a linear transformation. Inspired by this illustration on Wikipedia.
In [1]:
from itertools import islice
import numpy as np
import holoviews as hv
hv.extension('bokeh') |
MathSciNet bibliographic data MR1922828 14F10 (13N10 14F30 14F40 14G22 16S32 32C38) Berthelot, Pierre Introduction à la théorie arithmétique des \$\scr D\$$\scr D$-modules. (French) [Introduction to the arithmetic theory of \$\scr D\$$\scr D$-modules] Cohomologies \$p\$$p$-adiques et applications arithmétiques, II. Astérisque No. 279 (2002), 1–80. Links to the journal or article are not yet available
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.
American Mathematical Society 201 Charles Street Providence, RI 02904-6248 USA |
# All Questions
34 views
### Would it be possible to calculate the expected frequency of impact craters of all sizes on Earth
Can the expected frequency of all sizes of impact craters on Earth be calculated based on the preservation of impact craters seen on the Moon? Taking into account the difference in gravity and ...
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### Spotting the International Space Station (ISS)
Recently, I visited the NASA website which provides sighting locations to see the International Space Station (ISS). As we all know, we can even see ISS with the naked eye in a clear sky as a passing ...
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### Average rate of supernova x number of stars
If we would take the average number of supernovae per year and multiply that by the number of stars, could we figure out how many years it will be before all stars are gone?
22 views
### Sattelite's orbit
What is the maximum distance for a satellite to orbit the earth? Does earth's gravity has the impact on satellite? I do know that earth's gravity will never be zero and it's gravity is inversely ...
66 views
### Determining effect of small variable force on planetary perihelion precession
Is there an analytical technique for determining the effect of a small variable transverse acceleration upon the rate of precession of a planet orbitting around the Sun according to Newtonian gravity ...
23 views
### Adjust axis labels in ds9
How can I adjust the axis labels in ds9? I'd like to have something like: So far I only managed to get floating points (tl h%f3): or the leading hours are missing (tl h%f1 m): Proposed tags ...
35 views
### What was the greatest spatial extent of the Asteroid Belt prior to the Late Heavy Bombardment?
Reading the article On the asteroid belt’s orbital and size distribution (Gladman et al. 2009), there is an interest point made: asteroids a few kilometers and smaller in size are recent ...
28 views
### What are the current observational limits on the existence of Dyson spheres/swarms/rings?
A Dyson sphere/swarm/ring is a hypothetical structure an extra-terrestrial entity would construct to collect a large fraction of its host star's light, and would likely generate a fairly strong ...
39 views
### Mechanisms of binary/multiple star formation
What are mechanisms of binary/multiple star formation in different mass diapasons (low, intermediate and high stellar masses)?
21 views
### Magnetic fields of peculiar HgMn A type stars
Are HgMn (peculiar A type) stars really possess global magnetic fields? See, for example, paper Hubrig et al. 2012: http://arxiv.org/abs/1208.2910
34 views
### Rotation and relativity
When a planet is spinning around its own axis, it has an effect on the trajectory of its satellites. I believe it is called frame dragging. Spin increases the kinetic energy of an object, ...
24 views
### Do solstices and equinoxes shift over time?
Right now, I think the winter solstice is around December 21. Has it always been around this date constantly? Since the earth's axis's 23.45° tilt will be on the exact opposite side in 13000 years ...
33 views
### How to get the longitude/latitude from solar zenith/azimuth?
How do I get the longitude/latitude from zenith/azimuth? Or how can I position my sun in a 3d application? code extracted from here ... |
# Architecture of affine schemes
## Requirements on rings and ideals
Any type of ring $R$ to be used within the schemes framework must come with its own ideal type IdealType<:Ideal for which we require the following interface to be implemented:
# constructor of ideals in R
ideal(R::RingType, g::Vector{<:RingElem})::Ideal
# constructor for quotient rings
quo(R::RingType, I::IdealType)::Tuple{<:Ring, <:Map}
# ideal membership test
in(f::RingElem, I::IdealType)::Bool
# a (fixed) set of generators
gens(I::IdealType)::Vector{<:RingElem}
# writing an element as linear combination of the generators
coordinates(f::RingElem, I::IdealType)::Vector{<:RingElem}
The latter function must return a vector $v = (a_1,\dots, a_r)$ of elements in $R$ such that $f = a_1 \cdot g_1 + \dots + a_r \cdot g_r$ where $g_1,\dots,g_r$ is the set of gens(I). When $f$ does not belong to $I$, it must error. Note that the ring returned by quo must again be admissible for the AbsSpec interface.
With a view towards the use of the ambient_coordinate_ring(X) for computations, it is customary to also implement
saturated_ideal(I::IdealType)::MPolyIdeal
returning an ideal $J$ in the ambient_coordinate_ring(X) with the property that $a \in I$ for some element $a \in R$ if and only if lifted_numerator(a) is in $J$.
## Interplay between ambient coordinate ring and coordinate ring
Let $X$ be an affine variety. In practice, all computations in the coordinate ring R = OO(X) will be deferred to computations in P = ambient_coordinate_ring(X) in one way or the other; this is another reason to include the ambient affine space in our abstract interface for affine schemes. In order to make the ambient_coordinate_ring(X) accessible for this purpose, we need the following methods to be implemented for elements $a\in R$ of type RingElemType:
lifted_numerator(a::RingElemType)
lifted_denominator(a::RingElemType)
These must return representatives of the numerator and the denominator of $a$. Note that the denominator is equal to one(P) in case $R \cong P$ or $R \cong P/I$.
Recall that the coordinates $x_i$ of $X$ are induced by the coordinates of the ambient affine space. Moreover, we will assume that for homomorphisms from $R$ there is a method
hom(R::RingType, S::Ring, a::Vector{<:RingElem})
where RingType is the type of $R$ and a the images of the coordinates $x_i$ in $S$. This will be important when we come to morphisms of affine schemes below.
Algebraically speaking, embedding the affine scheme $X = Spec(R)$ over $𝕜$ into an affine space with coordinate ring $P = 𝕜[x₁,…,xₙ]$ corresponds to a morphism of rings $P → R$ with the property that for every other (commutative) ring $S$ and any homomorphism $φ : R → S$ there is a morphism $ψ : P → S$ factoring through $φ$ and such that $φ$ is uniquely determined by $ψ$. Note that the morphism $P → R$ is induced by natural coercions.
## Existing types of affine schemes and how to derive new types
The abstract type for affine schemes is
AbsSpecType
AbsSpec{BaseRingType, RingType<:Ring}
An affine scheme $X = Spec(R)$ with $R$ of type RingType over a ring $𝕜$ of type BaseRingType.
source
For any concrete instance of this type, we require the following functions to be implemented:
• base_ring(X::AbsSpec),
• OO(X::AbsSpec).
A concrete instance of this type is
SpecType
Spec{BaseRingType, RingType}
An affine scheme $X = Spec(R)$ with $R$ a Noetherian ring of type RingType over a base ring $𝕜$ of type BaseRingType.
source
It provides an implementation of affine schemes for rings $R$ of type MPolyRing, MPolyQuo, MPolyLocalizedRing, and MPolyQuoLocalizedRing defined over the integers or algebraic field extensions of $\mathbb Q$. This minimal implementation can be used internally, when deriving new concrete types MySpec<:AbsSpec such as, for instance, group schemes, toric schemes, schemes of a particular dimension like curves and surfaces, etc. To this end, one has to store an instance Y of Spec in MySpec and implement the methods
underlying_scheme(X::MySpec)::Spec # return Y as above
Then all methods implemented for Spec are automatically forwarded to any instance of MySpec.
Note: The above method necessarily returns an instance of Spec! Of course, it can be overwritten for any higher type MySpec<:AbsSpec as needed.
## Existing types of affine scheme morphisms and how to derive new types
Any abstract morphism of affine schemes is of the following type:
AbsSpecMorType
AbsSpecMor{DomainType<:AbsSpec,
CodomainType<:AbsSpec,
PullbackType<:Hecke.Map,
MorphismType,
BaseMorType
}
Abstract type for morphisms $f : X → Y$ of affine schemes where
• $X = Spec(S)$ is of type DomainType,
• $Y = Spec(R)$ is of type CodomainType,
• $f^* : R → S$ is a ring homomorphism of type PullbackType,
• $f$ itself is of type MorphismType (required for the Map interface),
• if $f$ is defined over a morphism of base schemes $BX → BY$ (e.g. a field extension), then this base scheme morphism is of type BaseMorType; otherwise, this can be set to Nothing.
source
Any such morphism has the attributes domain, codomain and pullback. A concrete and minimalistic implementation exist for the type SpecMor:
SpecMorType
SpecMor{DomainType<:AbsSpec,
CodomainType<:AbsSpec,
PullbackType<:Hecke.Map
}
A morphism $f : X → Y$ of affine schemes $X = Spec(S)$ of type DomainType and $Y = Spec(R)$ of type CodomainType, both defined over the same base_ring, with underlying ring homomorphism $f^* : R → S$ of type PullbackType.
source
This basic functionality consists of
• compose(f::AbsSpecMor, g::AbsSpecMor),
• identity_map(X::AbsSpec),
• restrict(f::AbsSpecMor, X::AbsSpec, Y::AbsSpec; check::Bool=true),
• ==(f::AbsSpecMor, g::AbsSpecMor),
• preimage(f::AbsSpecMor, Z::AbsSpec).
In particular, for every concrete instance of a type MySpec<:AbsSpec that implements underlying_scheme, this basic functionality of SpecMor should run naturally.
We may derive higher types of morphisms of affine schemes MySpecMor<:AbsSpecMor by storing an instance g of SpecMor inside an instance f of MySpecMor and implementing
underlying_morphism(f::MySpecMor)::SpecMor # return g
For example, this allows us to define closed embeddings. |
Please use this identifier to cite or link to this item: https://idr.nitk.ac.in/jspui/handle/123456789/11587
Title: Improving Hot Corrosion Resistance of Cobalt Based Superalloy (Superco-605) Using HVOF Sprayed Oxide Alloy Powder Coating Authors: Jegadeeswaran, N.Udaya, Bhat, K.Ramesh, M.R. Issue Date: 2015 Citation: Transactions of the Indian Institute of Metals, 2015, Vol.68, , pp.309-316 Abstract: Superco-605 is a cobalt based superalloy used widely in the hot section of gas turbines. During their operation, they are exposed to high temperature and molten salt environment, causing damage to the component due to hot corrosion. In this investigation, Superco-605 alloy was coated using a fused oxide alloy powder, $$10\,\% {\text{Al}}_{ 2} {\text{O}}_{ 3} + {\text{CoCrAlTaY}}$$10%Al2O3+CoCrAlTaY , using high velocity oxy-fuel process. Coating thickness was in the range of 260 280 m and it was lamellar in nature. Uncoated and coated samples were subjected to cyclic hot corrosion tests at 800 C in presence of molten salt environment of $${\text{Na}}_{ 2} {\text{SO}}_{ 4}{+}50\% {\text{V}}_{ 2} {\text{O}}_{ 5}$$Na2SO4+50%V2O5. Resistance to hot corrosion was investigated using thermogravimetric analysis, visual observations, X-ray diffractometry, scanning electron microscopy and energy dispersive X-ray spectroscopy. Both samples developed an oxide scale at the top. The uncoated Superco-605 exhibited intense spalling during hot corrosion cycles. The oxide scale on the coated substrate was thin compared to total thickness of the coating. There was a chromium depleted region close to the oxide top scale. An alumina rich layer at the interface of coating-substrate prevents penetration of oxygen into the substrate material. Based on the experimental results, it is concluded that the fused oxide alloy powder is effective in reducing hot corrosion tendency of Superco-605 alloy. 2015, The Indian Institute of Metals - IIM. URI: http://idr.nitk.ac.in/jspui/handle/123456789/11587 Appears in Collections: 1. Journal Articles
Files in This Item:
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# Levi Civita covariance and contravariance
I read some older posts about this question, but I don't know if I'm getting it. I'm working with a Lagrangian involving some Levi Civita symbols, and when I calculate a term containing $\epsilon^{ijk}$ I obtain the contrary sign using $\epsilon_{ijk}$. I always apply the normal rules: $\epsilon_ {ijk}=\epsilon^{ijk}=1$; $\epsilon_ {jik}=\epsilon^{jik}=-1$ etc. I believed that there is no difference between covariant and contravariant Levi-Civita symbol. What do you know about this?
-
You might be interested by formulae $(2.42)$ and $(2.43)$, p.$52$ in this Sean Carroll Lecture Notes on General Relativity paper – Trimok Jul 5 '14 at 12:10
1. On one hand, there is the Levi-Civita symbol with upper (lower) indices, whose entries are only $0$s and $\pm 1$s; it is a contravariant (covariant) pseudotensor density, respectively.
2. On the other hand, there is the Levi-Civita tensor with upper (lower) indices, whose definition differs from the Levi-Civita symbol by a factor of $\sqrt{|\det(g_{\mu\nu})|}$; it is a contravariant (covariant) pseudotensor, respectively.
I think the most common trend in the literature I see is for the lower-indexed symbol defined with signs given by the parity of the index permutation in the normal way, while the upper-indexed symbol differs from the lower-indexed one by $\mathrm{sgn}(\det g)$. But the OP seems to be in Euclidean $\mathbb{R}^3$ anyway. – Chris White Jul 5 '14 at 12:22 |
# Why is oxygenated water not H2O2?
Oxygenated water has become popular for a variety of uses recently - for health purposes internally as well as enhanced wound healing.
Anyhow, my dad asked me recently if I knew how it is that oxygenated water does not become hydrogen peroxide. I don't know the answer to it; but it got me thinking... How does this work? Does the oxygen not bond to the water molecule? If so, how does the bottle of water not just out gas when ever it is opened until the amount of oxygen contained in the bottle is equal to that of the room air.
• Oh, if oxygenated water did change to hydrogen peroxide, I shouldn't have been alive now! Some reactions, just don't like to happen. – M.A.R. Feb 7 '15 at 15:55
• Sorry but anyone foolish enough to buy oxygenated water is an idiot wasting money. – MaxW Jan 7 '18 at 18:43
• @MaxW I would have to agree! I just was more curious about the chemistry of the whole thing :) – L.B. Feb 9 '18 at 18:43
The oxygen is dissolved in the water, just as salt can be dissolved. It does not (to any appreciable degree) combine with water molecules to form hydrogen peroxide.
The reason that oxygenated water is not fizzy like soda water (CO2) is the solubility of oxygen in water is about 2% that of CO2. So the amount of bubbles formed when the cap is removed is only about 1/50 as much as for soft drinks. Or champagne.
• When CO2 is dissolved in water, part of it reacts with H2O to produce H2CO3. Similarly part of the dissolved oxygen reacts with H2O to produce H2O2, doesn't it? If not why? If yes, what's the equilibrium? – Petr Feb 7 '15 at 9:19
• @PetrPudlák Not similar at all. The formation of peroxide is very unfavourable and requires a lot of energy. So it doesn't happen easily or spontaneously, totally unlike carbonic acid. – matt_black Feb 7 '15 at 12:16
I think the problem is that the reaction:
$\ce{2H2O2-> 2H2O + O2}$
is spontaneous, meaning that it proceeds (slowly) in standard conditions with no other inputs required. So far from oxygen combining with water, you have hydrogen peroxide spontaneously decomposing into water and oxygen.
First you need to know what is oxygenated water. It's actually form by adding additional oxygen to the water under pressure. It means it's a mixture, not a compound.
We know that a mixture is two or more substances mix together physically. However, hydrogen peroxide bonds chemically which is a compound.
So, we can conclude that oxygenated cannot be classified as hydrogen peroxide.
With respect to the question, 'how it is that oxygenated water does not become hydrogen peroxide', one answer is that in natural sunlight waters it actual does create H2O2, albeit even then, in only small amounts.
More precisely, the presence of H2O2 and other reactive oxygen species (ROS) have been cited in the literature as occurring in illuminated natural waters (see, for example, ‘Reactive Oxygen Species in Natural Waters ‘, by Neil V. Blough and Richard G. Zepp). To quote from an online two-page preview :
The presence of ROS in aquatic ecosystems was first reported in 1966 by Van Baalen and Marler, who detected the presence of hydrogen peroxide (H202) in tens to hundreds of nanomolar concentrations in surface seawaters... Although their data were inadequate to specify the source of the H202, they postulated that photochemical reactions, biological processes, or atmospheric deposition might contribute to its presence in seawaters. Some years later, Swallow (1969) suggested that the hydrated electron ($$\ce{e-(aq)}$$) could be produced in seawater by the action of...photoionization of endogenous phenolic compounds. He further proposed that rapid reaction of $$\ce{e-(aq)}$$ with dioxygen (02) would yield superoxide ($$\ce{.O2-}$$), ultimately leading to the formation of H202 via disproportionation….
My updated understanding of these reactions is presented below which starts with a solvated electron, $$\ce{e-(aq)}$$ and $$\ce{H+}$$ per the reactions:
$$\ce{O2 + e-(aq) ⇌ .O2- (aq)}$$ (superoxide radical anion)
$$\ce{H+ + .O2- (aq) ⇌ .HO2 (aq)}$$ (hydroperoxyl radical with a pKa = 4.88)
$$\ce{.HO2 (aq) + .HO2 (aq) -> H2O2 + O2 (aq)}$$ Source: Equation (1)
In natural waters in sunlight, dissolved organic matter (DOM) can be a source of solvated electrons (see 'Photoproduction of hydrated electrons from natural organic solutes in aquatic environments') and electron holes:
$$\ce{DOM + hv -> e- + h+}$$
Also, the presence of transition metal ions and dioxygen via so-called metal auto-oxidation can be a potential source of superoxide:
$$\ce{Fe(2+)/Cu(+) + O2 ⇌ Fe(3+)/Cu(2+) + .O2-}$$ (Source example: Eq (Vl))
The cited work by Blough and Zepp further notes that since the 1980’s:
...environmental scientists have acquired evidence for the near-ubiquitous occurrence in surface waters of not only H202 and 02" but also singlet dioxygen..., the hydroxyl radical (OH), and organic peroxyl radicals (R02), as well as other transient intermediates that are either immediate precursors or products of the ROS. It is now recognized that the production of this diverse array of species is driven primarily by abiotic photochemical reactions involving naturally occurring organic (and sometimes inorganic) chromophores (Zepp, 1991; Zika, 1987; Zafiriou et al., 1984). Because of its high concentration in surface waters (-250 nanoM), O2 dominates the photophysics and photochemistry of these materials. The resulting reaction sequences are readily interpreted within the well established concepts of direct and sensitized photo-oxidations, potentially coupled to thermal autoxidation processes. |
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## Weitere Artikel dieser Ausgabe durch Wischen aufrufen
04.04.2020 | Original Paper | Ausgabe 6/2020 Open Access
# Nonlinear electromechanical coupling in ferroelectric materials: large deformation and hysteresis
Zeitschrift:
Acta Mechanica > Ausgabe 6/2020
Autoren:
Alexander Humer, Astrid S. Pechstein, Martin Meindlhumer, Michael Krommer
Wichtige Hinweise
## Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
## 1 Introduction
Smart materials are materials, which are reactive to different nonmechanical stimuli. In order to use such materials as integrated parts of a structure in some practical application, a thorough understanding of their behavior based on accurate modeling is important. Models must capture the relevant coupling effects and account for geometric and physical nonlinearities. In this paper, we focus on modeling of elastic ferroelectric materials, which respond to mechanical and electrical stimuli, within a classical continuum physics approach, the fundamentals of which date back to Toupin [ 36] and were further developed by, e.g., Tiersten [ 35], Pao [ 23], Prechtl [ 27, 28] Maugin [ 16], and Eringen and Maugin [ 8]. A review on nonlinear electroelasticity was recently provided by Dorfmann and Ogden [ 7].
Ferroelectric materials have been adopted as sensors and actuators in diverse fields of applications, which range from microelectromechanical systems (MEMS) for high-precision positioning to vibrational and structural noise control. Typically, ferroelectric ceramics, e.g., lead zirconium titanate (PZT), are used due to their comparatively high coupling coefficients. These polycrystalline ceramics are characterized by a relatively high brittleness, which is why they do not admit large strains. For this reason, their constitutive models are usually formulated within the range of small (linearized) strains, which gives Voigt’s linearized theory of piezoelectricity for the reversible response, see, e.g., Eringen and Maugin [ 8] and Yang [ 39]. The response of ferroelectric materials is intrinsically related to their state of remanent polarization, which is assumed to be constant for most applications. Electromechanical loadings beyond so-called coercive electric fields or coercive stresses, however, induce an irreversible re-orientation of dipoles in the material and therefore a change in the remanent polarization, see, e.g., the review article of Kamlah [ 11]. These mechanisms are referred to as switching and result in ferroelectric and ferroelastic hystereses. A first thermodynamically consistent macroscopic model for the irreversible response of ferroelectrics was presented by Bassiouny et al [ 1, 2] and Bassiouny and Maugin [ 3, 4]. The mathematical modeling and the computational approximation of switching phenomena in ferroelectric materials share many aspects with well-established approaches in elastoplasticity, see, e.g., Landis [ 13], McMeeking and Landis [ 18] and Klinkel [ 12]. Recently, novel mixed finite-element formulations for reversible and irreversible problems were proposed by Pechstein et al. [ 2426] and Meindlhumer et al. [ 21].
Unlike ceramic materials, ferroelectric polymers, e.g., polyvinylidene (di)fluoride (PVDF), can be subjected to comparatively large strains well beyond the linear range. Based on the modeling of the reversible electromechanically coupled response presented in [ 10, 33], we propose a first attempt toward the continuum modeling of the ferroelectric hysteresis in the geometrically nonlinear range of deformation. For this purpose, we repeatedly adopt the concept of a multiplicative decomposition of the deformation gradient, which has successfully been applied to the modeling of various inelastic processes, see Lubarda [ 15] for a review. The idea of multiple multiplicative decompositions was discussed by Meggyes [ 20]. In the present approach, the deformation gradient is decomposed into three parts: The irreversible part governs the evolution of a poled (intermediate) configuration from the unpoled reference configuration. The second part describes the reversible local response of a poled volume element subjected to an electric field. Under the electric field, it deforms into a second intermediate configuration, which can be regarded as mechanically destressed, i.e., the current configuration is relieved from mechanical stresses. The third part accounts for the elastic stress response of the material. The modeling of the dissipative response follows the concepts of finite-strain elastoplasticity [ 3032], where ideas of damage modeling are included to incorporate changes in the material parameters due to poling [ 14]. The evolution equation for the dissipative internal forces follows as an associated flow rule from the constrained optimization problem that is obtained from the principle of maximum dissipation [ 32].
The present paper starts with a discussion of the fundamental relations of nonlinear electromechanics. We first consider the reversible case, for which we present both a spatial and a material description of the governing equations. Then, we discuss the case of irreversible constitutive processes resulting from a remanent polarization of the material. After a classical approach using the principle of maximum dissipation, we introduce the known concept of a dissipation function. Finally, the specific constitutive framework is introduced based on a multiplicative decomposition of the deformation gradient tensor into reversible and irreversible parts and on a corresponding additive decomposition of the free energy. A brief review of the numerical implementation and the presentation of results for two example problems complete the present paper.
## 2 Balance equations of nonlinear electromechanics
### 2.1 Reversible response
Continuum mechanics is based on the idealization of material bodies as a more or less continuous distribution of matter. In problems of large (finite) deformations, we are used to a material description of the governing equations, in which we refer to a reference configuration $${\mathcal {B}}^{(0)}$$ of the body under consideration. The availability of a referential state allows us to relate physical quantities that represent volume and surface densities to given volumes and surfaces in the reference configuration. In electrostatics, on the contrary, the deformation of the domain of interest typically plays a tangential role, if any, and the domain’s geometry is assumed to be known. Eventually, we intend to bring together continuum mechanics and electrostatics in strongly deforming bodies. For this reason, we choose to first adopt a spatial representation, in which we refer to a body’s current configuration $${\mathcal {B}}$$, which is—figuratively and literally—where physics actually takes place.
To begin with, we recall the fundamental relations of reversible electromechanics, in which the state of remanent polarization is assumed constant, see, e.g., [ 8, 39] for a more detailed exposition. In the quasistatic case, the spatial description of the local balance of linear momentum reads
\begin{aligned} {{\,\mathrm{div}\,}}\varvec{\sigma }+ {\varvec{f}}+ {\varvec{f}}_\mathrm{E}= {\mathbf {0}} . \end{aligned}
(1)
The Cauchy stress tensor is denoted by $$\varvec{\sigma }$$, and $${\varvec{f}}$$ are mechanical body forces. A nonconducting dielectric body additionally experiences electrical body forces $${\varvec{f}}_\mathrm{E}$$ in the presence of a nonhomogeneous electric field $${\varvec{e}}$$, which can be represented by means of the divergence of the electrostatic stress tensor $$\varvec{\sigma }_\mathrm{E}$$,
\begin{aligned} {\varvec{f}}_\mathrm{E}= ( {{\,\mathrm{grad}\,}}{\varvec{e}}) \cdot {\varvec{p}}= {{\,\mathrm{div}\,}}\varvec{\sigma }_\mathrm{E}. \end{aligned}
(2)
In the above relation, the (macroscopic) polarization vector has been introduced as $${\varvec{p}}$$. Within the spatial description of continuum mechanics, derivatives and differential operators are to be understood with respect to a set of appropriate spatial coordinates. Note that the electrostatic stresses are not uniquely defined since any divergence-free tensor can be added without changing the electrostatic body forces $${\varvec{f}}_\mathrm{E}$$. By direct computation, we can convince ourselves that the common definition of $$\varvec{\sigma }_\mathrm{E}$$ as the sum of the polarization stresses $$\varvec{\sigma }_\mathrm{P}$$, which, in turn, are defined by the tensorial product of the electric field and the polarization,
\begin{aligned} \varvec{\sigma }_\mathrm{P}= {\varvec{e}}{\varvec{p}}, \end{aligned}
(3)
and Maxwell’s stress tensor $$\varvec{\sigma }_\mathrm{M}$$ of classical electrostatics,
\begin{aligned} \varvec{\sigma }_\mathrm{M}= \epsilon _0{\varvec{e}}{\varvec{e}}- \frac{1}{2} \, \epsilon _0\left( {\varvec{e}}\cdot {\varvec{e}}\right) {\mathbf {I}}, \end{aligned}
(4)
satisfies the requirement ( 2):
\begin{aligned} \varvec{\sigma }_\mathrm{E}= \varvec{\sigma }_\mathrm{P}+ \varvec{\sigma }_\mathrm{M}= {\varvec{e}}{\varvec{d}}- \frac{1}{2} \, \epsilon _0\left( {\varvec{e}}\cdot {\varvec{e}}\right) {\mathbf {I}}. \end{aligned}
(5)
The vacuum permitivity is denoted by $$\epsilon _0$$. To obtain the above representation of the electrostatic stresses, we have already made use of the constitutive equation among the electrical fields, i.e.,
\begin{aligned} {\varvec{d}}= \epsilon _0{\varvec{e}}+ {\varvec{p}}, \end{aligned}
(6)
which relates the dielectric displacement $${\varvec{d}}$$, the electric field, and the polarization vector.
In a polarized dielectric, an electric field also induces an electric (body) couple $${\varvec{c}}_\mathrm{E}$$,
\begin{aligned} {\varvec{c}}_\mathrm{E}= {\varvec{p}}\times {\varvec{e}}, \end{aligned}
(7)
which enters the balance of angular momentum as an additional source term. By allowing body couples, we leave the field of classical continuum mechanics, in which all torques are assumed to be moments of forces [ 38]. Instead, we consider dielectric materials as a case of polar continua, a concept introduced in the pioneering work of the Cosserat brothers, see, e.g., Maugin [ 17]. Unlike Cauchy’s classical concept, not only the position but also the orientation of the material points (i.e., the polarization) needs to be accounted for in polar continua. From the local form of the balance of angular momentum, we eventually find that the sum of (mechanical) Cauchy stresses and polarization stresses is symmetric,
\begin{aligned} \varvec{\sigma }+ \varvec{\sigma }_\mathrm{P}= \left( \varvec{\sigma }+ \varvec{\sigma }_\mathrm{P}\right) ^{T}, \end{aligned}
(8)
rather than the mechanical stresses alone. In what follows, we will primarily consider the total (Cauchy) stresses, which are defined as the sum of the mechanical stresses and the electrostatic stresses,
\begin{aligned} \varvec{\sigma }_{\mathrm{tot}}= \varvec{\sigma }+ \varvec{\sigma }_\mathrm{E}= \varvec{\sigma }+ \varvec{\sigma }_\mathrm{P}+ \varvec{\sigma }_\mathrm{M}. \end{aligned}
(9)
In view of the symmetry condition ( 8) and the definition of Maxwell’s stresses ( 4), we note that the total stress tensor must be symmetric, i.e., $$\varvec{\sigma }_{\mathrm{tot}}= (\varvec{\sigma }_{\mathrm{tot}})^{T}$$.
Turning our attention to the balance laws for the electrical quantities, we first recall Gauss’ law of conservation of charge, whose local form reduces to
\begin{aligned} {{\,\mathrm{div}\,}}{\varvec{d}}= 0 \end{aligned}
(10)
in the case of nonconducting continua, for which the free charge density vanishes. In quasistatic problems, Faraday’s law of induction in local form,
\begin{aligned} {{\,\mathrm{curl}\,}}{\varvec{e}}= {\mathbf {0}} \Leftrightarrow {\varvec{e}}= - {{\,\mathrm{grad}\,}}\phi , \end{aligned}
(11)
implies that the electric field is conservative, i.e., the electric field can be represented by the (negative) gradient of the scalar potential $$\phi$$.
The mechanical and the electrical domains are brought together in the balance of energy, whose local form, assuming isothermal conditions, is given by
\begin{aligned} \rho \, {\dot{e}} = \varvec{\sigma }: {{\,\mathrm{grad}\,}}{\varvec{v}}+ \rho \, {\varvec{e}}\cdot {\dot{\varvec{\pi }}} , \qquad \varvec{\pi }= \frac{{\varvec{p}}}{\rho }, \end{aligned}
(12)
where the polarization per unit mass $$\varvec{\pi }$$ has been introduced. The velocity field is denoted by $${\varvec{v}}$$; $$\rho$$ is the mass density per unit (current) volume. The spatial velocity gradient can be expressed in terms of the deformation gradient tensor $${\mathbf {F}}$$ as $${{\,\mathrm{grad}\,}}{\varvec{v}}= {\dot{{\mathbf {F}}}}\cdot {\mathbf {F}}^{-1}$$. Material time derivatives are indicated by superimposed dots throughout the present paper. The specific internal energy $$e$$ is a thermodynamic potential in the deformation gradient $${\mathbf {F}}$$ and the polarization $${\varvec{p}}$$ as independent fields, i.e., $$e= e({\mathbf {F}}, {\varvec{p}})$$. In other words, the electric field plays the role of a generalized force that drives changes in the state of polarization.
By a Legendre transformation, the electric field is introduced as independent variable in the potential $$\psi = \psi ({\mathbf {F}}, {\varvec{e}})$$,
\begin{aligned} \psi = e- {\varvec{e}}\cdot \varvec{\pi }. \end{aligned}
(13)
We obtain the corresponding balance law from ( 12) as
\begin{aligned} \rho \, {\dot{\psi }}= \varvec{\sigma }: {{\,\mathrm{grad}\,}}{\varvec{v}}- {\varvec{p}}\cdot {\dot{{\varvec{e}}}} . \end{aligned}
(14)
Upon the Legendre transformation ( 13), the polarization has become the generalized driving force for changes in the electric field. We want to mention here that the terminology for thermodynamic potentials is not consistent in the literature. Eringen and Maugin [ 8] and Yang [ 39] refer to $$\psi$$ as (generalized) Helmholtz free energy, whereas Miehe et al. [ 22] denote a potential in the deformation gradient and the electric field as mixed energy–enthalpy function. Miehe et al. [ 22], in turn, use the term free energy function in their energy-based formulation for a thermodynamical potential that is a function of the deformation gradient and the dielectric displacement. We will adopt the terms free energy or simply energy in what follows.
The balance law ( 14) suggests the definition of the electromechanical power density $$p$$ per unit current volume as
\begin{aligned} p= \varvec{\sigma }: {{\,\mathrm{grad}\,}}{\varvec{v}}- {\varvec{p}}\cdot {\dot{{\varvec{e}}}} . \end{aligned}
(15)
In nondissipative, reversible processes, the electromechanical power represents the source term in the balance of free energy, which then simplifies to
\begin{aligned} \rho \, {\dot{\psi }}= p. \end{aligned}
(16)
Comparing the balance law ( 14) with the generic rate of the free energy $${\dot{\psi }}({\mathbf {F}}, {\varvec{e}})$$,
\begin{aligned} \rho \, \frac{\partial \psi }{\partial {\mathbf {F}}} : {\dot{{\mathbf {F}}}}+ \rho \, \frac{\partial \psi }{\partial {\varvec{e}}} \cdot {\dot{{\varvec{e}}}} = \varvec{\sigma }: {{\,\mathrm{grad}\,}}{\varvec{v}}- {\varvec{p}}\cdot {\dot{{\varvec{e}}}} , \end{aligned}
(17)
we can identify the constitutive equations for the Cauchy stress tensor and the polarization vector as
\begin{aligned} \varvec{\sigma }= \rho \, \frac{\partial \psi }{\partial {\mathbf {F}}} \cdot {\mathbf {F}}^T , \qquad {\varvec{p}}= - \rho \, \frac{\partial \psi }{\partial {\varvec{e}}} . \end{aligned}
(18)
Not least from a computational point of view, we introduce a total stress formulation by augmenting the free energy $$\psi$$ with the free-space (or vacuum) energy $$\psi _{\mathrm{aug}}$$,
\begin{aligned} \psi _{\mathrm{tot}}= \psi + \psi _{\mathrm{aug}}, \qquad \psi _{\mathrm{aug}}= - \frac{1}{2} \frac{\epsilon _0}{\rho } \, {\varvec{e}}\cdot {\varvec{e}}. \end{aligned}
(19)
The material description of the total free energy $$\psi _{\mathrm{tot}}$$ will subsequently serve as basis for the variational formulation of the governing equations used in the finite-element approximation. The rate of the (specific) augmented free energy follows from the above relation as
\begin{aligned} {\dot{\psi }}_{\mathrm{tot}}= {\dot{\psi }}- \frac{\epsilon _0}{\rho } \, {\varvec{e}}\cdot {\dot{{\varvec{e}}}} - \frac{1}{2} \frac{\epsilon _0}{\rho } {\varvec{e}}\cdot {\varvec{e}}\, {\mathbf {F}}^{-T}: {\dot{{\mathbf {F}}}}. \end{aligned}
(20)
Substituting the fundamental relation ( 14), we obtain the balance law for the augmented free energy as
\begin{aligned} \rho \, {\dot{\psi }}_{\mathrm{tot}}= \left\{ \varvec{\sigma }- \frac{1}{2} \, \epsilon _0({\varvec{e}}\cdot {\varvec{e}}) {\mathbf {I}}\right\} : {{\,\mathrm{grad}\,}}{\varvec{v}}- {\varvec{d}}\cdot {\dot{{\varvec{e}}}} , \end{aligned}
(21)
or, in terms of the total stress tensor ( 9),
\begin{aligned} \rho \, {\dot{\psi }}_{\mathrm{tot}}= \left( \varvec{\sigma }_{\mathrm{tot}}- {\varvec{e}}{\varvec{d}}\right) : {{\,\mathrm{grad}\,}}{\varvec{v}}- {\varvec{d}}\cdot {\dot{{\varvec{e}}}} . \end{aligned}
(22)
The constitutive equations for the total stresses and dielectric displacement again follow from a comparison of the total power,
\begin{aligned} p_{\mathrm{tot}}= \rho \, {\dot{\psi }}_{\mathrm{tot}}= \left( \varvec{\sigma }_{\mathrm{tot}}- {\varvec{e}}{\varvec{d}}\right) : {{\,\mathrm{grad}\,}}{\varvec{v}}- {\varvec{d}}\cdot {\dot{{\varvec{e}}}}, \end{aligned}
(23)
and the material time derivative of $$\psi _{\mathrm{tot}}= \psi _{\mathrm{tot}}({\mathbf {F}}, {\varvec{e}})$$ as
\begin{aligned} \varvec{\sigma }_{\mathrm{tot}}= \rho \, \frac{\partial \psi _{\mathrm{tot}}}{\partial {\mathbf {F}}} \cdot {\mathbf {F}}^T + {\varvec{e}}{\varvec{d}}, \qquad {\varvec{d}}= - \rho \, \frac{\partial \psi _{\mathrm{tot}}}{\partial {\varvec{e}}} . \end{aligned}
(24)
### 2.2 Material description of the governing equations
In solid mechanics, we typically make use of the fact that a referential state of the body under consideration is readily available. Material points are identified by their position vector $${\varvec{X}}$$ in the reference configuration, whose components with respect to some spatially fixed Cartesian frame ( $${\varvec{e}}_1,{\varvec{e}}_2,{\varvec{e}}_3$$) are denoted by $${\varvec{X}}= X_1 {\varvec{e}}_1+ X_2 {\varvec{e}}_2+ X_3 {\varvec{e}}_3$$. Though the electric field is not intrinsically tied to matter, we introduce a material description, in which we follow the evolution of physical quantities along the path of a material point. For this purpose, we transform the global (integral) balance laws such that integration is performed in the reference configuration $${\mathcal {B}}^{(0)}$$ rather than in the current configuration $${\mathcal {B}}$$, see, e.g., [ 6, 7]. In Gauss’ law of conservation of charge, we use the relation among material surface elements in the reference configuration and the current configuration $${\mathrm {d}} {\varvec{a}}= J \, {\mathbf {F}}^{-T}\cdot {\mathrm {d}} {{\varvec{a}}^{(0)}}$$ with $$J = \det {\mathbf {F}}$$, which is also known as Nanson’s formula,
\begin{aligned} \begin{aligned} \int _{\partial \varOmega }{\varvec{d}}\cdot {\mathrm {d}} {\varvec{a}}= \int _{\partial \varOmega ^{(0)}}J \, {\varvec{d}}\cdot {\mathbf {F}}^{-T}\cdot {\mathrm {d}} {\varvec{a}^{(0)}}. \end{aligned} \end{aligned}
(25)
The above equation suggests the definition of the material dielectric displacement as
\begin{aligned} {\varvec{d}}^{(0)}= J \, {\varvec{d}}\cdot {\mathbf {F}}^{-T}\Leftrightarrow {\varvec{d}}= J^{-1} {\varvec{d}}^{(0)}\cdot {\mathbf {F}}^T. \end{aligned}
(26)
The transformation of material line elements $$\mathrm {d} {\varvec{x}}= {\mathbf {F}}\cdot \mathrm d {\varvec{X}}$$ allows us to rewrite the global form of Faraday’s law of induction as
\begin{aligned} \begin{aligned} \int _{\varGamma }{\varvec{e}}\cdot {\mathrm {d}} {\varvec{x}}= \int _{{\varGamma }^{(0)}}{\varvec{e}}\cdot {\mathbf {F}}\cdot {\mathrm {d}} {\varvec{X}}. \end{aligned} \end{aligned}
(27)
We introduce the integrand of the line integral in the reference configuration as the material electric field
\begin{aligned} {\varvec{e}}^{(0)}= {\varvec{e}}\cdot {\mathbf {F}}\Leftrightarrow {\varvec{e}}= {\varvec{e}}^{(0)}\cdot {\mathbf {F}}^{-1}. \end{aligned}
(28)
Using the definitions of the material dielectric displacement ( 26) and the material electric field ( 28), the corresponding local balance laws retain the same structure as in the spatial representation, i.e., Gauss’ law reads
\begin{aligned} {{\,\mathrm{Div}\,}}{\varvec{d}}^{(0)}= 0 , \end{aligned}
(29)
and the material electric field is related to the electric potential by
\begin{aligned} {\varvec{e}}^{(0)}= - {{\,\mathrm{Grad}\,}}\phi . \end{aligned}
(30)
Note that derivatives with respect to spatial coordinates are replaced by derivatives in material coordinates, which, in the present coordinate-free representation, is indicated by capitalized differential operators. For the material polarization vector, we assume the same transformation as for the dielectric displacement,
\begin{aligned} {\varvec{p}}^{(0)}= J \, {\varvec{p}}\cdot {\mathbf {F}}^{-T}\Leftrightarrow {\varvec{p}}= J^{-1} {\varvec{p}}^{(0)}\cdot {\mathbf {F}}^T. \end{aligned}
(31)
In terms of their material counterparts, the relation among the electrical fields ( 6) follows as
\begin{aligned} {\varvec{d}}^{(0)}= \epsilon _0J {\varvec{e}}^{(0)}\cdot {\mathbf {C}}^{-1}+ {\varvec{p}}^{(0)}. \end{aligned}
(32)
Before proceeding with mechanical quantities, we spend a few remarks on the material description of electrical fields. As opposed to the spatial (physical) electrical fields, the material counterparts are invariant with respect to superimposed rigid-body motions. Let $${\mathbf {Q}}$$ denote an orthogonal second-order tensor, which rotates the material body from the current configuration along with the electric fields, i.e., $${\bar{{\mathbf {F}}}} = {\mathbf {Q}}\cdot {\mathbf {F}}$$, and, hence,
\begin{aligned} {\bar{{\varvec{e}}}} = {\mathbf {Q}}\cdot {\varvec{e}}, \qquad {\bar{{\varvec{d}}}} = {\mathbf {Q}}\cdot {\varvec{d}}. \end{aligned}
(33)
From definitions ( 26) and ( 28), we immediately find that the material fields remain preserved upon the rotation,
\begin{aligned} \begin{aligned} {\bar{{\varvec{e}}}}^{(0)}&= {\bar{{\varvec{e}}}} \cdot {\bar{{\mathbf {F}}}} = {\bar{{\varvec{e}}}} \cdot {\mathbf {Q}}\cdot {\mathbf {F}}= {\varvec{e}}\cdot {\mathbf {Q}}^T \cdot {\mathbf {Q}}\cdot {\mathbf {F}}= {\varvec{e}}^{(0)}, \\ {\bar{{\varvec{d}}}}^{(0)}&= (\det {\mathbf {Q}}) (\det {\mathbf {F}}) \, {\bar{{\varvec{d}}}} \cdot {\mathbf {Q}}^{-T} \cdot {\mathbf {F}}^{-T}= J \, {\varvec{d}}\cdot {\mathbf {Q}}^T \cdot {\mathbf {Q}}\cdot {\mathbf {F}}^{-T}= {\varvec{d}}^{(0)}. \end{aligned} \end{aligned}
(34)
Rotation-invariant quantities facilitate the formulation of constitutive equations that satisfy the principle of material frame indifference. We note that other choices for rotation-invariant electric fields have been used in the material modeling. McMeeking and Landis [ 19], for instance, used the rotation tensor $${\mathbf {R}}$$ in the polar decomposition of the deformation gradient $${\mathbf {F}}= {\mathbf {R}} \cdot {\mathbf {U}}$$ to define a rotation-invariant polarization as $$\varvec{\varPi }= {\varvec{p}}\cdot {\mathbf {R}}$$.
Regarding mechanical quantities, we recall the relation between the mass densities in the reference configuration and in the current configuration,
\begin{aligned} \rho ^{(0)}= J \, \rho . \end{aligned}
(35)
In finite-deformation problems, constitutive equations are preferably formulated in the right Cauchy–Green tensor $${\mathbf {C}}$$ or Green’s strain tensor $${\mathbf {E}}$$, which are related to the deformation gradient by
\begin{aligned} {\mathbf {C}}= {\mathbf {F}}^T \cdot {\mathbf {F}}, \qquad {\mathbf {E}}= \frac{1}{2} \left( {\mathbf {C}}- {\mathbf {I}}\right) . \end{aligned}
(36)
The second Piola–Kirchhoff stress tensor $${\mathbf {S}}$$ is the conjugate stress measure, which is obtained from a pullback transformation of the Cauchy stresses $$\varvec{\sigma }$$ to the reference configuration:
\begin{aligned} {\mathbf {S}}= J \, {\mathbf {F}}^{-1}\cdot \varvec{\sigma }\cdot {\mathbf {F}}^{-T}. \end{aligned}
(37)
In terms of the conjugate pairs of mechanical and electrical variables, the electromechanical power density per unit volume in the reference configuration follows from ( 15) as
\begin{aligned} p^{(0)}= \frac{1}{2} \left( {\mathbf {S}}+ {\mathbf {S}}_\mathrm{P}\right) : {\dot{{\mathbf {C}}}} - {\varvec{p}}^{(0)}\cdot {\dot{{\varvec{e}}}}^{(0)}\end{aligned}
(38)
where the material polarization stresses ( 3),
\begin{aligned} {\mathbf {S}}_\mathrm{P}= J\, {\mathbf {F}}^{-1}\cdot \varvec{\sigma }_\mathrm{P}\cdot {\mathbf {F}}^{-T}= {\mathbf {C}}^{-1}\cdot {\varvec{e}}^{(0)}{\varvec{p}}^{(0)}, \end{aligned}
(39)
have been introduced using the conventional pullback of Cauchy-type stress measures ( 37). In reversible, isothermal processes, the balance of specific free energy is given by
\begin{aligned} \rho ^{(0)}{\dot{\psi }}^{(0)}= p^{(0)}\end{aligned}
(40)
where we have introduced superscripts to clearly indicate the change in the independent fields in the material description, $$\psi = \psi ^{(0)}({\mathbf {C}}, {\varvec{e}}^{(0)})$$. Using the definition of the material electric field ( 28) and the mass density in the reference configuration ( 35), the free-space contribution to the total free energy ( 18) is rewritten as
\begin{aligned} \psi _{\mathrm{aug}}^{(0)}= - \frac{1}{2} \frac{\epsilon _0J}{\rho ^{(0)}} \, {\varvec{e}}^{(0)}\cdot {\mathbf {C}}^{-1}\cdot {\varvec{e}}^{(0)}. \end{aligned}
(41)
Its rate can be expressed in terms of the material Maxwell stresses $${\mathbf {S}}_\mathrm{M}$$,
\begin{aligned} \rho ^{(0)}{\dot{\psi }}_{\mathrm{aug}}^{(0)}= 2 \, {\mathbf {S}}_\mathrm{M}: {\dot{{\mathbf {C}}}} - \epsilon _0J {\varvec{e}}^{(0)}\cdot {\mathbf {C}}^{-1}\cdot {\dot{{\varvec{e}}}}^{(0)}, \end{aligned}
(42)
which are related to their spatial counterpart by
\begin{aligned} {\mathbf {S}}_\mathrm{M}= J\, {\mathbf {F}}^{-1}\cdot \varvec{\sigma }_\mathrm{M}\cdot {\mathbf {F}}^{-T}. \end{aligned}
(43)
With the material representation of the polarization stresses ( 39), the local balance of the total free energy $$\psi _{\mathrm{tot}}^{(0)}$$ follows in terms of the total stresses $${\mathbf {S}}_{\mathrm{tot}}= {\mathbf {S}}+ {\mathbf {S}}_\mathrm{P}+ {\mathbf {S}}_\mathrm{M}$$ as
\begin{aligned} \rho ^{(0)}{\dot{\psi }}_{\mathrm{tot}}^{(0)}= \rho ^{(0)}\left( {\dot{\psi }}^{(0)}+ {\dot{\psi }}_{\mathrm{aug}}^{(0)}\right) = \frac{1}{2} \, {\mathbf {S}}_{\mathrm{tot}}: {\dot{{\mathbf {C}}}} - {\varvec{d}}^{(0)}\cdot {\dot{{\varvec{e}}}}^{(0)}. \end{aligned}
(44)
As in the spatial description, the source terms on the right-hand side of the above equation represent the total electromechanical power, whose material representation is
\begin{aligned} p^{(0)}_{\mathrm{tot}}= \frac{1}{2} \, {\mathbf {S}}_{\mathrm{tot}}: {\dot{{\mathbf {C}}}} - {\varvec{d}}^{(0)}\cdot {\dot{{\varvec{e}}}}^{(0)}. \end{aligned}
(45)
### 2.3 Dissipative response
In our summary of the equations that govern the reversible response in nonlinear electromechanics, the state of remanent polarization $${\varvec{p}}_\mathrm{i}$$ has been assumed to be constant. Processes that change the state of remanent polarization are irreversible by definition, which is why we have to abandon the idea of a constant remanent polarization $${\varvec{p}}_\mathrm{i}$$. Unlike reversible processes, in which a formulation in terms of potentials naturally complies with the second law of thermodynamics, the constraint on the dissipated energy requires our attention in irreversible processes. For this reason, we recall the Clausius–Duhem inequality, which states that the dissipation density (per unit referential volume) $$d^{(0)}$$ is always positive, i.e.,
\begin{aligned} d^{(0)}= p^{(0)}_{\mathrm{tot}}- \rho ^{(0)}{\dot{\psi }}_{\mathrm{tot}}^{(0)}\ge 0 . \end{aligned}
(46)
In irreversible processes, the total free energy can no longer be a function of the right Cauchy–Green tensor $${\mathbf {C}}$$ and the material electric field $${\varvec{e}}^{(0)}$$ only as it is in the reversible case. Instead, we assume $$\psi _{\mathrm{tot}}^{(0)}$$ to also depend on the remanent material polarization $${\varvec{p}}^{(0)}_\mathrm{i}$$, which can be regarded as an internal variable,
\begin{aligned} \psi _{\mathrm{tot}}^{(0)}= \psi _{\mathrm{tot}}^{(0)}({\mathbf {C}}, {\varvec{e}}^{(0)}, {\varvec{p}}^{(0)}_\mathrm{i}) . \end{aligned}
(47)
Substituting the total power ( 45) and the generic rate of the total free energy ( 47) into the Clausius–Duhem inequality ( 46),
\begin{aligned} d^{(0)}= \left( \frac{1}{2} \, {\mathbf {S}}_{\mathrm{tot}}- \rho ^{(0)}\frac{\partial \psi _{\mathrm{tot}}^{(0)}}{\partial {\mathbf {C}}} \right) : {\dot{{\mathbf {C}}}} - \left( {\varvec{d}}^{(0)}+ \rho ^{(0)}\frac{\partial \psi _{\mathrm{tot}}^{(0)}}{\partial {\varvec{e}}^{(0)}} \right) \cdot {\dot{{\varvec{e}}}}^{(0)}- \rho ^{(0)}\frac{\partial \psi _{\mathrm{tot}}^{(0)}}{\partial {\varvec{p}}^{(0)}_\mathrm{i}} \cdot {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}\ge 0 , \end{aligned}
(48)
we can identify the constitutive equations for the total stresses $${\mathbf {S}}_{\mathrm{tot}}$$ and the material dielectric displacement $${\varvec{d}}^{(0)}$$,
\begin{aligned} {\mathbf {S}}_{\mathrm{tot}}= 2 \, \rho ^{(0)}\frac{\partial \psi _{\mathrm{tot}}^{(0)}}{\partial {\mathbf {C}}} , \qquad {\varvec{d}}^{(0)}= - \rho ^{(0)}\frac{\partial \psi _{\mathrm{tot}}^{(0)}}{\partial {\varvec{e}}^{(0)}} , \end{aligned}
(49)
and also the material representation of the dissipation and dissipative driving forces $${\hat{{\varvec{e}}}}^{(0)}$$:
\begin{aligned} d^{(0)}= {\hat{{\varvec{e}}}}^{(0)}\cdot {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}\ge 0 , \qquad {\hat{{\varvec{e}}}}^{(0)}= - \rho ^{(0)}\frac{\partial \psi _{\mathrm{tot}}^{(0)}}{\partial {\varvec{p}}^{(0)}_\mathrm{i}} . \end{aligned}
(50)
The dissipative driving forces $${\hat{{\varvec{e}}}}^{(0)}$$ are conjugate to the remanent polarization $${\varvec{p}}^{(0)}_\mathrm{i}$$ and therefore have the physical dimension of an electric field. To further specify the irreversible response, we adopt the principle of maximum dissipation, which is a fundamental concept in rate-independent plasticity, see, e.g., Simo and Hughes [ 32]. We expect the dissipation to take a maximum for a given $${\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}$$, i.e., the dissipative driving forces $${\hat{{\varvec{e}}}}^{(0)}$$ are determined such that
\begin{aligned} d^{(0)}= \sup _{{\hat{{\varvec{e}}}}^{(0)}\in {\mathbb {E}}} {\hat{{\varvec{e}}}}^{(0)}\cdot {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}. \end{aligned}
(51)
In the above relation, $${\mathbb {E}}$$ denotes the admissible domain, which is defined by a switching function f,
\begin{aligned} {\mathbb {E}}= \left\{ {\hat{{\varvec{e}}}}^{(0)}\in {\mathbb {R}}^3 \, \vert \, f({\hat{{\varvec{e}}}}^{(0)}) \le 0 \right\} . \end{aligned}
(52)
The switching function represents a threshold for the dissipative driving forces in analogy to the yield function in plasticity. As long as we stay in the interior of the admissible range, the state of remanent polarization $${\varvec{p}}^{(0)}_\mathrm{i}$$ is preserved. On the boundary of the admissible range $$\partial {\mathbb {E}}$$, which can be regarded as yield surface where $$f({\hat{{\varvec{e}}}}^{(0)}) = 0$$ holds, the remanent polarization may change depending on the direction of loading. The constrained maximization problem given by ( 51) can be solved by introducing a Lagrange multiplier $$\lambda$$, i.e.,
\begin{aligned} d^{(0)}= \sup _{{\hat{{\varvec{e}}}}^{(0)}, \lambda \ge 0} \left( {\hat{{\varvec{e}}}}^{(0)}\cdot {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}- \lambda \, f({\hat{{\varvec{e}}}}^{(0)}) \right) . \end{aligned}
(53)
As shown by Simo and Hughes [ 32], the principle of maximum dissipation implies an associated flow rule that governs the (nonsmooth) evolution of the remanent polarization as
\begin{aligned} {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}= \lambda \, \frac{\partial f({\hat{{\varvec{e}}}}^{(0)})}{\partial {\hat{{\varvec{e}}}}^{(0)}} , \end{aligned}
(54)
\begin{aligned} \lambda \ge 0 , \qquad f ({\hat{{\varvec{e}}}}^{(0)}) \le 0 , \qquad \lambda \, f ({\hat{{\varvec{e}}}}^{(0)}) = 0 . \end{aligned}
(55)
From the algorithmic point of view, return-mapping methods are often used to construct (approximate) solutions, see, e.g., Simo and Hughes [ 32] for problems in plasticity and the formulations by Semenov [ 29] and [ 12] for the polarization of ferroelectric materials.
In the present formulation, we abandon the concept of Lagrange multipliers in favor of the notion of a dissipation function $$\varphi$$. Following the reasoning of Miehe et al. [ 22], we define the dissipation function such that its derivative with respect to the rate of the remanent polarization gives the driving forces:
\begin{aligned} {\hat{{\varvec{e}}}}^{(0)}= \frac{\partial \varphi }{\partial {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}} . \end{aligned}
(56)
As the dissipation is generally nonsmooth, the derivative is to be understood as the subgradient of $$\varphi$$, which represents a set. In what follows, we will regularize the dissipation function appropriately such that the subgradient reduces to the conventional derivative, see [ 9, 24]. To a priori fulfill the Clausius–Duhem inequality of positive dissipation ( 46), which, in terms of the dissipation function, transforms into
\begin{aligned} d^{(0)}= \frac{\partial \varphi }{\partial {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}}\cdot {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}\ge 0 , \end{aligned}
(57)
we require $$\varphi$$ to be normalized and positive,
\begin{aligned} \varphi ({\mathbf {0}}) = 0 , \qquad \varphi ({\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}) \ge 0, \end{aligned}
(58)
and convex, i.e.,
\begin{aligned} \begin{aligned} \alpha \, \varphi ({\dot{{\varvec{p}}}}^{(0)}_{\mathrm {i},1}) + (1 - \alpha ) \, \varphi ({\dot{{\varvec{p}}}}^{(0)}_{\mathrm {i},2}) \ge \varphi (\alpha \, {\dot{{\varvec{p}}}}^{(0)}_{\mathrm {i},1}+ (1 - \alpha ) {\dot{{\varvec{p}}}}^{(0)}_{\mathrm {i},2}), \end{aligned} \end{aligned}
(59)
for all $$\alpha \in [0,1]$$. We further assume $$\varphi$$ to be a positively homogeneous function of degree 1,
\begin{aligned} \varphi (\alpha \, {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}) = \alpha \, \varphi ({\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}) , \qquad \forall \alpha > 0 , \end{aligned}
(60)
which characterizes a dissipative response that is rate independent. Taking the derivative of the above relation with respect to $$\alpha$$, we recover the dissipation ( 50),
\begin{aligned} \varphi ({\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}) = \frac{\partial \varphi }{\partial {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}}\cdot {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}= {\hat{{\varvec{e}}}}^{(0)}\cdot {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}= d^{(0)}. \end{aligned}
(61)
In other words, the dissipation density $$d^{(0)}$$ and the dissipation function $$\varphi$$ are identical in the rate-independent case. As an example, we consider the classical switching condition that bounds the norm of the driving force by a threshold, which is referred to as coercive field strength $$e_\mathrm{c}$$ in the context of ferroelectrics:
\begin{aligned} f({\hat{{\varvec{e}}}}^{(0)}) = \Vert {\hat{{\varvec{e}}}}^{(0)}\Vert - e_\mathrm{c}\le 0 . \end{aligned}
(62)
By direct computation, we can convince ourselves that the dissipation function
\begin{aligned} \varphi ( {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}) = e_\mathrm{c}\Vert {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}\Vert \end{aligned}
(63)
satisfies the principle of maximum dissipation ( 51). Its derivative with respect to the rate of the remanent polarization gives a rate-independent driving force (for $${\dot{{\varvec{p}}}}_\mathrm{i}\ne {\mathbf {0}}$$) in the direction of $${\dot{{\varvec{p}}}}_\mathrm{i}$$,
\begin{aligned} {\hat{{\varvec{e}}}}^{(0)}= \frac{\partial \varphi }{\partial {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}}= e_\mathrm{c}\, {\varvec{n}}_{{\hat{{\varvec{e}}}}}, \qquad {\varvec{n}}_{{\hat{{\varvec{e}}}}}= \frac{{\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}}{\Vert {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}\Vert } ; \end{aligned}
(64)
the norm of the driving force coincides with the coercive field $$\Vert {\hat{{\varvec{e}}}}^{(0)}\Vert = e_\mathrm{c}$$. The above result for the driving force maximizes the dissipation ( 51) within the admissible range $${\mathbb {E}}$$, since we obtain $$d^{(0)}= e_\mathrm{c}\Vert {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}\Vert$$, which is the largest admissible value.
For the numerical analysis, we regularize the dissipation function such that its derivative always exists. In the context of plasticity, Han and Reddy [ 9] proposed and analyzed a regularization of the form
\begin{aligned} \varphi ({\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}) = e_\mathrm{c}\Vert {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}\Vert _{\mathrm{reg}} , \qquad \Vert {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}\Vert _{\mathrm{reg}} = {\left\{ \begin{array}{ll} \left( \Vert {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}\Vert - \frac{\varepsilon }{2} \right) &{} {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}\ge \varepsilon \\ \frac{1}{2 \varepsilon } \Vert {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}\Vert ^2 &{} {\dot{{\varvec{p}}}}_\mathrm{i}^{(0)}< \varepsilon , \end{array}\right. } \end{aligned}
(65)
which they showed to result in errors of the order $$\sqrt{\varepsilon }$$.
## 3 Multiplicative decomposition
The modeling of the constitutive response, in particular in coupled problems of multiple physical domains, undoubtedly is a challenging task and, quite commonly, subject of debates. Only few nonlinear problems allow us to motivate constitutive equations on the macroscopic continuum scale from microscopic considerations. Exemplarily, we mention material models of rubber, which can be derived from models of polymer chains [ 37]. Alternatively, if no assumptions on the structure of material models can be a priori made, the governing thermodynamic potentials are expanded into power series in the independent physical fields. To account for symmetries of a material, formulations in terms of invariants of the independent fields are often adopted in the modeling. The series coefficients represent the material parameters and need to be identified from experimental data.
The key idea of the multiplicative decomposition is to decouple the constitutive response in finite-deformation problems that are characterized by multiple underlying processes, e.g., thermoelasticity or elastoplasticity [ 15]. By assuming appropriate models for the decoupled subproblems, we endow constitutive models for the coupled response with a suitable structure, by which the description of the coupling is ideally simplified.
From a phenomenological point of view, we observe that ferroelectric materials deform in the course of the poling process, in which the state of remanent polarization is irreversibly altered. To understand the underlying mechanism, recall that ferroelectric materials are characterized by the presence of microscopic structures (unit cells) that posses a spontaneous polarization, i.e., the centers of positive and negative charges do not coincide and an electric dipole is formed, see, e.g., Kamlah [ 11] for a detailed exposition on ceramics. The unit cells may form so-called domains, which represent regions of equal spontaneous polarization. Stepping up from the microscale, physical properties on the macroscopic level can be regarded as averages of microscopic quantities, see Eringen and Maugin [ 8]. The remanent polarization $${\varvec{p}}_\mathrm{i}$$ represents the macroscopic average of the spontaneous polarization of unit cells and domains, respectively. In the unpoled state of a ferroelectric material, the polarization of microstructures is randomly oriented, which is why $${\varvec{p}}_\mathrm{i}$$ vanishes. Under sufficiently large electric fields, domains of ferroelectric materials switch their orientation, i.e., the spontaneous polarization becomes aligned with the applied field and maintains that orientation upon unloading. The re-orientation of the spontaneous polarization shifts the centers of positive and negative charges. The microscopic deformation of unit cells induced by the poling process macroscopically manifests as a remanent state of strain. In view of coupling between remanent polarization and deformation, mechanical loadings can also induce domains to irreversibly switch their state in ferroelectric materials. Though the underlying physical mechanism is the same as for electric loadings, the term ferroelasticity is often used to describe this characteristic property of ferroelectrics.
From a mechanical perspective, the poling process bears some resemblance to phenomenological models of elastoplasticity, in which irreversible deformation may occur if mechanical loads reach (or exceed) a threshold value, i.e., the yield stress. The similarities between poling and plasticity are reflected in both the structure of the constitutive models and numerical methods that have been proposed for the construction of approximate solutions. Leaving the range of infinitesimally small deformations, we also take the fundamental ideas of nonlinear elastoplasticity as inspiration in what follows. If deformations are large, the conventional additive decomposition of stresses and strain measures into reversible and irreversible parts loses some of its physical underpinning. Instead, we decompose the deformation gradient $${\mathbf {F}}$$ into a product of an irreversible part $${\mathbf {F}}_\mathrm{i}$$ and a reversible part $${\mathbf {F}}_\mathrm{r}$$:
\begin{aligned} {\mathbf {F}}= {\mathbf {F}}_\mathrm{r}\cdot {\mathbf {F}}_\mathrm{i}. \end{aligned}
(66)
By the multiplicative decomposition, the notion of an additional intermediate configuration $${\mathcal {B}}^{(1)}$$ is introduced in the deformation path. In the present context of ferroelectric materials, the irreversible part $${\mathbf {F}}_\mathrm{i}$$ locally describes the evolution from the unpoled reference configuration into a poled intermediate configuration, which depends on the state of remanent polarization. The second part $${\mathbf {F}}_\mathrm{r}$$, in turn, represents the reversible deformation induced by mechanical or electric loadings. Owing to the electromechanical coupling in ferroelectric materials, the reversible part $${\mathbf {F}}_\mathrm{r}$$ can again be split into two parts, i.e., an inelastic (electrical) part $${\mathbf {F}}_\mathrm{r,e}$$ and an elastic (mechanical) part $${\mathbf {F}}_\mathrm{r,m}$$,
\begin{aligned} {\mathbf {F}}_\mathrm{r}= {\mathbf {F}}_\mathrm{r,m}\cdot {\mathbf {F}}_\mathrm{r,e}. \end{aligned}
(67)
The electrical part $${\mathbf {F}}_\mathrm{r,e}$$ governs the local response of a poled material due to the presence of an electric field, whereas the current state of stress is determined from the mechanical part $${\mathbf {F}}_\mathrm{r,m}$$. In the present approach, the total deformation gradient $${\mathbf {F}}$$ is therefore composed of three parts,
\begin{aligned} {\mathbf {F}}= {\mathbf {F}}_\mathrm{r,m}\cdot {\mathbf {F}}_\mathrm{r,e}\cdot {\mathbf {F}}_\mathrm{i}, \end{aligned}
(68)
which implies that a second intermediate configuration $${\mathcal {B}}^{(2)}$$ is introduced into the deformation path, see Fig. 1. For later use, we additionally define the electrical part of the deformation gradient as
\begin{aligned} {\mathbf {F}}_\mathrm{e}= {\mathbf {F}}_\mathrm{r,e}\cdot {\mathbf {F}}_\mathrm{i}. \end{aligned}
(69)
We can associate deformation and strain measures with each part of the deformation gradient. The right Cauchy–Green tensor related to the irreversible electrical part $${\mathbf {F}}_\mathrm{i}$$ is naturally defined by
\begin{aligned} \begin{aligned} {\mathbf {C}}_\mathrm {i}= {\mathbf {F}}_\mathrm {i}^T \cdot {\mathbf {F}}_\mathrm {i}. \end{aligned} \end{aligned}
(70)
We will later also make use of the right Cauchy–Green tensor of the mechanical part of the deformation,
\begin{aligned} {\mathbf {C}}_\mathrm{m}= {\mathbf {F}}_\mathrm{r,m}^T \cdot {\mathbf {F}}_\mathrm{r,m}= {\mathbf {F}}_\mathrm{e}^{-T}\cdot {\mathbf {C}}\cdot {\mathbf {F}}_\mathrm{e}^{-1}, \end{aligned}
(71)
where the relation $${\mathbf {F}}_\mathrm{r,m}= {\mathbf {F}}\cdot {\mathbf {F}}_\mathrm{e}^{-1}$$ has been used. The above representation in terms of $${\mathbf {C}}$$ also reveals an intuitive interpretation of $${\mathbf {C}}_\mathrm{m}$$: According to its definition, $${\mathbf {C}}_\mathrm{m}$$ represents a material deformation measure in the reversible mechanical deformation path, but, at the same time, it can be regarded as a spatial deformation measure in the electrical parts of the deformation, which follows from a push-forward of $${\mathbf {C}}$$ by means of $${\mathbf {F}}_\mathrm{e}$$.
The decomposition of the total deformation into three parts is also reflected in the (total) free energy, which is additively composed of three contributions that correspond to the respective deformation paths:
\begin{aligned} \psi _{\mathrm{tot}}= \psi _\mathrm{i}+ \psi _\mathrm{r,e}+ \psi _\mathrm{r,m}, \end{aligned}
(72)
i.e., we have an irreversible part denoted by $$\psi _\mathrm{i}$$, a reversible electrical part $$\psi _\mathrm{r,e}$$ and a reversible mechanical part $$\psi _\mathrm{r,m}$$. The fundamental idea of the multiplicative decomposition is to separately regard each of the three (sub)paths of the total deformation and to formulate appropriate relations for the material response.
### 3.1 Irreversible response
To further specify the proposed constitutive model, we first consider the irreversible part in the deformation. From the kinematic point of view, we note two characteristic features that are to be captured by the present approach: First of all, the irreversible deformation induced by the remanent polarization is anisotropic. Polycrystalline ferroelectrics usually have one principal direction that coincides with the remanent polarization, whereas polymeric materials may also be orthotropic due to the stretching that is applied during poling. For the case of transversally isotropic materials, the anisotropy can be captured by a second-order structural tensor, which is determined by the material remanent polarization in the reference configuration,
\begin{aligned} {{\mathbf {a}}}^{(0)}= {\varvec{n}}_\mathrm{i}^{(0)}{\varvec{n}}_\mathrm{i}^{(0)}, \qquad {\varvec{n}}_\mathrm{i}^{(0)}= \frac{{\varvec{p}}^{(0)}_\mathrm{i}}{\Vert {\varvec{p}}^{(0)}_\mathrm{i}\Vert } . \end{aligned}
(73)
Secondly, the irreversible deformation is volume-preserving, i.e., the condition $$J_\mathrm{i}= \det {\mathbf {F}}_\mathrm{i}= 1$$ must hold. Unlike plasticity, where plastic deformation accumulates until fracture, the number of switchable unit cells or domains of a ferroelectric material is finite. Therefore, the remanent polarization in ferroelectrics eventually saturates well before electric breakdown occurs, and so does the irreversible deformation. To describe the degree of saturation, we introduce the ratio between the material remanent polarization $${\varvec{p}}^{(0)}_\mathrm{i}$$ and the saturation polarization $$p_{\mathrm{sat}}$$:
\begin{aligned} \beta = \frac{\Vert {\varvec{p}}^{(0)}_\mathrm{i}\Vert }{p_{\mathrm{sat}}} . \end{aligned}
(74)
In view of the isochoric nature of the poling-induced deformation, we assume a stretching-type deformation with a saturation strain $$S_{\mathrm{sat}}$$ in analogy to what Zäh and Miehe [ 40] proposed for the electrostrictive response of graft polymers,
\begin{aligned} {\mathbf {F}}_\mathrm{i}= \left( 1 - \gamma \right) ^{-2/3} \left\{ \left( 1 - \gamma \right) {\mathbf {I}}+ \gamma \, {{\mathbf {a}}}^{(0)}\right\} . \end{aligned}
(75)
The parameter $$\gamma$$ is proportional to the saturation strain $$S_{\mathrm{sat}}$$ and the square of the degree of polarization by
\begin{aligned} \gamma = \frac{3}{2} \, S_{\mathrm{sat}}\beta ^2 . \end{aligned}
(76)
As volumes are preserved, the mass density in the reference configuration is also preserved under the irreversible deformation, i.e., $$\rho ^{(0)}= \rho ^{(1)}$$.
For the irreversible part of the free energy, we translate the phenomenological model used by Landis [ 13] and McMeeking and Landis [ 18] to nonlinear problems:
\begin{aligned} \begin{aligned} \rho _0 \psi _\mathrm {i}^{(0)}= - c \, p_{\mathrm {sat}}^2 \left\{ \log \left( 1 - \beta \right) + \beta \right\} . \end{aligned} \end{aligned}
(77)
If the remanent polarization saturates, i.e., $$\beta \rightarrow 1$$, the energy tends to infinity, which prohibits any remanent polarization beyond $$p_{\mathrm{sat}}$$. The parameter c in the above relation represents a kinematic hardening modulus that has the physical dimension of inverse permittivity.
### 3.2 Reversible electrical response
As a next step, we consider the reversible response of material volume elements to electrical loads, i.e., an (externally) applied electric field. For the corresponding deformation path, the second intermediate configuration can be viewed as target configuration, whereas the first intermediate configuration represents the referential state. In the constitutive relations, we therefore use the electric field $${\varvec{e}}^{(1)}$$, which is related to its spatial and material counterparts by
\begin{aligned} \begin{aligned} {\varvec{e}}^{(1)}= {\varvec{e}}\cdot {\mathbf {F}}_\mathrm {r}= {\varvec{e}}^{(0)}\cdot {\mathbf {F}}_\mathrm {i}^{-1}. \end{aligned} \end{aligned}
(78)
To describe the electromechanical coupling generically, we could assume a series expansion of the electrical part of the deformation gradient $${\mathbf {F}}_\mathrm{r,e}$$ in the electric field $${\varvec{e}}^{(1)}$$ as
\begin{aligned} {\mathbf {F}}_\mathrm{r,e}= {\mathbf {I}}+ {\varvec{e}}^{(1)}\cdot {{\mathbf {d}^{(1)}}}+ {\varvec{e}}^{(1)}{\varvec{e}}^{(1)}: {{\mathbf {b}^{(1)}}}+ \cdots \end{aligned}
(79)
where the third-order tensor $${{\mathbf {d}^{(1)}}}$$ describes the piezoelectric coupling and $${{\mathbf {b}^{(1)}}}$$ is the fourth-order tensor of electrostrictive moduli. As the state of remanent polarization may change, however, the material parameters can be no longer assumed to be constant in general. We recall that the piezoelectric effect is only present in poled ferroelectrics, and also electrostriction is influenced by the remanent polarization. In what follows, our focus lies on a conventional piezoelectric coupling, which is why we neglect second-order electrostrictive effects. The piezoelectric coupling is kinematically described by three Biot-type strain tensors,
\begin{aligned} {\mathbf {F}}_\mathrm{r,e}= {\mathbf {I}}+ \beta \left( {\mathbf {U}}_{\parallel } + {\mathbf {U}}_{\perp } + {\mathbf {U}}_{=} \right) . \end{aligned}
(80)
The individual parts of the piezoelectric coupling, which are assumed to scale linearly in the degree of polarization $$\beta$$, correspond to the $$d_{33}$$, $$d_{31}$$, and $$d_{15}$$-effects of Voigt’s linear theory of piezoelectricity. In terms of the electric field $${\varvec{e}}^{(1)}$$ and the normalized remanent polarization $${\varvec{n}}_\mathrm{i}^{(1)}$$ in the first intermediate configuration,
\begin{aligned} {\varvec{n}}_\mathrm{i}^{(1)}= \frac{{\varvec{p}}_\mathrm{i}^{(1)}}{\Vert {\varvec{p}}_\mathrm{i}^{(1)}\Vert } , \qquad {\varvec{p}}_\mathrm{i}^{(1)}= J_\mathrm{i}^{-1} {\varvec{p}}^{(0)}_\mathrm{i}\cdot {\mathbf {F}}_\mathrm{i}^T , \end{aligned}
(81)
the three parts of the deformation are given by
\begin{aligned} \begin{aligned}&{\mathbf {U}}_{\parallel } = d_{33} \left( {\varvec{e}}^{(1)}\cdot {\varvec{n}}_\mathrm{i}^{(1)}\right) {{\mathbf {a}}}^{(1)}, \\&{\mathbf {U}}_{\perp } = d_{31} \left( {\varvec{e}}^{(1)}\cdot {\varvec{n}}_\mathrm{i}^{(1)}\right) \left( {\mathbf {I}}- {{\mathbf {a}}}^{(1)}\right) , \\&{\mathbf {U}}_{=} = \frac{d_{15}}{2} \left( \left\{ \left( {\mathbf {I}}- {{\mathbf {a}}}^{(1)}\right) \cdot {\varvec{e}}^{(1)}\right\} {\varvec{n}}_\mathrm{i}^{(1)}\right) _s \end{aligned} \end{aligned}
(82)
where $$(\cdot )_s$$ denotes the symmetric part of a second-order tensor. We have also introduced the structural tensor in the first intermediate configuration $${\mathcal {B}}^{(1)}$$ as
\begin{aligned} {{\mathbf {a}}}^{(1)}= {\varvec{n}}_\mathrm{i}^{(1)}{\varvec{n}}_\mathrm{i}^{(1)}. \end{aligned}
(83)
The structural tensor is pushed forward from and pulled back to the reference configuration, respectively, by means of the transformations
\begin{aligned} \begin{aligned} {{\mathbf {a}}}^{(1)}= C_{\mathrm {i},ii}^{-1} {\mathbf {F}}_\mathrm {i}\cdot {{\mathbf {a}}}^{(0)}\cdot {\mathbf {F}}_\mathrm {i}^T , \qquad {{\mathbf {a}}}^{(0)}= C_{\mathrm {i},ii}{\mathbf {F}}_\mathrm {i}^{-1}\cdot {{\mathbf {a}}}^{(1)}\cdot {\mathbf {F}}_\mathrm {i}^{-T}, \end{aligned} \end{aligned}
(84)
where $$C_{\mathrm {i},ii}= {\varvec{n}}_\mathrm {i}^{(0)}\cdot {\mathbf {C}}_\mathrm {i}\cdot {\varvec{n}}_\mathrm {i}^{(0)}$$ is the square of the irreversible stretch in the direction of the remanent polarization.
Within the framework of the multiplicative decomposition, the couplings among the individual processes of the deformation path are described kinematically. The (reversible) electromechanical coupling has already been taken care of in terms of $${\mathbf {F}}_\mathrm{r,e}$$. Having specified the constitutive response from the kinematic point of view, the thermodynamic relations remain to be provided in terms of an appropriate potential $$\psi _{\mathrm{r,e}}^{(0)}$$. For this purpose, we disregard any coupling and assume the material to respond to a loading by an electric field as a (deformable) dielectric. Accordingly, the reversible electrical part of the internal energy is quadratic in the reversible polarization,
\begin{aligned} e_\mathrm{r,e}= \frac{1}{2} \left( {\varvec{d}}- {\varvec{p}}_\mathrm{i}\right) \cdot \varvec{\epsilon }^{-1} \cdot \frac{{\varvec{d}}- {\varvec{p}}_\mathrm{i}}{\rho } , \end{aligned}
(85)
where $$\varvec{\epsilon }$$ denotes the second-order permittivity tensor. The permittivity characterizes the capability of a material to (reversibly) polarize under an applied electric field. By means of a Legendre transformation, we replace the dielectric displacement $${\varvec{d}}$$ by the electric field $${\varvec{e}}$$ as independent field. Together with the constitutive relation of dielectrics $${\varvec{d}}= \varvec{\epsilon }\cdot {\varvec{e}}+ {\varvec{p}}_\mathrm{i}$$, we obtain the spatial description of the specific free energy as
\begin{aligned} \psi _\mathrm{r,e}= e_\mathrm{r,e}- {\varvec{e}}\cdot \frac{{\varvec{d}}}{\rho } = - \frac{1}{2} \, \rho ^{-1} {\varvec{e}}\cdot \varvec{\epsilon }\cdot {\varvec{e}}- \rho ^{-1} {\varvec{e}}\cdot {\varvec{p}}_\mathrm{i}. \end{aligned}
(86)
The permittivity of ferroelectric materials generally depends on both the current deformation and the state of remanent polarization, and, unlike dielectric elastomers [ 33, 34], is not necessarily isotropic, see, e.g., Kamlah [ 11]. As we are interested in the behavior of the material (rather than the vacuum part), we introduce the second-order susceptibility tensor $$\varvec{\chi }$$ as
\begin{aligned} \varvec{\epsilon }= \epsilon _0\left( {\mathbf {I}}+ \varvec{\chi }\right) . \end{aligned}
(87)
In conventional polycrystalline piezoelectric materials, a transversally isotropic behavior is observed. The anisotropy is induced by the remanent polarization, which introduces a preferred direction in the material. For this reason, we assume the susceptibility to be composed of an isotropic part and an anisotropic part $$\varDelta \varvec{\chi }$$ that results from the remanent polarization,
\begin{aligned} \varvec{\chi }= \chi (\rho ) {\mathbf {I}}+ \varDelta \varvec{\chi }= J^{-1} \chi _0{\mathbf {I}}+ \varDelta \varvec{\chi }. \end{aligned}
(88)
In view of what is known from deformable dielectrics [ 19, 33], the isotropic part has been assumed as $$\chi (\rho ) = J^{-1} \chi _0$$, where $$\chi _0$$ is a material constant. From the spatial representation ( 86), the specific free energy corresponding to the reversible electrical deformation path follows upon substitution of the material quantities as a sum of an isotropic part and an anisotropic part,
\begin{aligned} \psi _{\mathrm{r,e}}^{(0)}= - \frac{1}{2} \, {\varvec{e}}^{(0)}\cdot \varvec{\epsilon }^{(0)}\cdot {\varvec{e}}^{(0)}- {\varvec{e}}^{(0)}\cdot {\varvec{p}}^{(0)}_\mathrm{i}= \psi _{\mathrm{r,e},\mathrm {iso}}^{(0)}+ \psi _{\mathrm{r,e},\mathrm {aniso}}^{(0)}, \end{aligned}
(89)
which are given by
\begin{aligned} \begin{aligned}&\rho ^{(0)}\psi _{\mathrm{r,e},\mathrm {iso}}^{(0)}= \rho ^{(0)}\psi _{\mathrm{aug}}^{(0)}- \frac{1}{2} {\epsilon _0\chi _0} {\varvec{e}}^{(0)}\cdot {\mathbf {C}}^{-1}\cdot {\varvec{e}}^{(0)}, \\&\rho ^{(0)}\psi _{\mathrm{r,e},\mathrm {aniso}}^{(0)}= - \frac{1}{2} \epsilon _0{\varvec{e}}^{(0)}\cdot \varDelta \varvec{\chi }^{(0)}\cdot {\varvec{e}}^{(0)}- {\varvec{e}}^{(0)}\cdot {\varvec{p}}^{(0)}_\mathrm{i}. \end{aligned} \end{aligned}
(90)
In the isotropic part, we have recovered the free-space contribution of the free energy ( 41). The anisotropic part of the susceptibility has been pulled back to the reference configuration by means of the transformation
\begin{aligned} \varDelta \varvec{\chi }^{(0)}= J {\mathbf {F}}^{-1}\cdot \varDelta \varvec{\chi }\cdot {\mathbf {F}}^{-T}, \end{aligned}
(91)
which naturally follows from the material representation of the free energy. Exemplarily, we assume a transversal isotropy that depends linearly on the degree of remanent polarization $$\beta$$, i.e.,
\begin{aligned} \varDelta \varvec{\chi }^{(0)}= \beta \left\{ \chi _\parallel {{\mathbf {a}}}^{(0)}+ \chi _\perp \left( {\mathbf {I}}- {{\mathbf {a}}}^{(0)}\right) \right\} , \end{aligned}
(92)
where $$\chi _\parallel$$ and $$\chi _\perp$$ are material constants that represent the maximum change in susceptibility in the poling direction and in the direction perpendicular to it. Note that the anisotropic part of the susceptibility only depends on the (material) remanent polarization but not on the current state of deformation.
### 3.3 Reversible mechanical response
The elastic response is governed by the reversible mechanical part of the free energy $$\psi _\mathrm{r,m}$$. We can choose an appropriate strain energy function from finite-strain elasticity, which is typically formulated in terms of Cauchy–Green or Green-type measures of deformation. In view of the multiplicative decomposition, the strain energy refers to the deformation measures of the second intermediate configuration, which represents the referential state for the reversible mechanical path.
Assuming a transversally isotropic behavior, the elastic strain energy $$\psi _\mathrm{r,m}$$ depends on the structural tensor $${{\mathbf {a}}}^{(2)}$$ in the second intermediate configuration $${\mathcal {B}}^{(2)}$$, i.e.,
\begin{aligned} {{\mathbf {a}}}^{(2)}= {\varvec{n}}_\mathrm{i}^{(2)}{\varvec{n}}_\mathrm{i}^{(2)}, \qquad {\varvec{n}}_\mathrm{i}^{(2)}= \frac{{\varvec{p}}_\mathrm{i}^{(2)}}{\Vert {\varvec{p}}_\mathrm{i}^{(2)}\Vert } , \qquad {\varvec{p}}_\mathrm{i}^{(2)}= J_\mathrm{e}^{-1} {\varvec{p}}^{(0)}_\mathrm{i}\cdot {\mathbf {F}}_\mathrm{e}^T . \end{aligned}
(93)
In analogy to the structural tensor in the first intermediate configuration ( 84), its counterpart in the second intermediate configuration $${{\mathbf {a}}}^{(2)}$$ follows upon a push-forward from the reference configuration by
\begin{aligned} {{\mathbf {a}}}^{(2)}= C_{\mathrm{e},ii}^{-1} {\mathbf {F}}_\mathrm{e}\cdot {{\mathbf {a}}}^{(0)}\cdot {\mathbf {F}}_\mathrm{e}^T \end{aligned}
(94)
where $$C_{\mathrm{e},ii}= {\varvec{n}}_\mathrm{i}^{(0)}\cdot {\mathbf {C}}_e\cdot {\varvec{n}}_\mathrm{i}^{(0)}$$ denotes the square of the electrically induced stretch in the direction of the remanent polarization.
As mechanical deformation measures $${\mathbf {C}}_\mathrm{m}$$ or $${\mathbf {E}}_\mathrm{m}= ({\mathbf {C}}_\mathrm{m}- {\mathbf {I}}) / 2$$ are used in the strain energy function, one is tempted to object that ferroelectric and piezoelectric couplings are missing. Analogously to the reversible electric path, we assume an uncoupled elastic stress response since any coupling is represented kinematically in terms of $${\mathbf {F}}_\mathrm{i}$$ and $${\mathbf {F}}_\mathrm{r,e}$$, respectively. Exemplarily, we mention the St. Venant–Kirchhoff material of finite-strain elasticity, which can be regarded as a generalization of Hooke’s law of linear elasticity to geometrically nonlinear problems,
\begin{aligned} \rho ^{(2)}\psi _{\mathrm{r,m}}^{(2)}= \frac{1}{2} \, {\mathbf {E}}_\mathrm{m}: {\mathbf {c}} : {\mathbf {E}}_\mathrm{m}, \end{aligned}
(95)
where $${\mathbf {c}}$$ denotes the fourth-order tensor of elastic moduli. In our example problems, we will use a neo-Hookean material model, see Sect. 5.
### 3.4 Constitutive equations
Having specified the kinematics of the nonmechanical deformation and the thermodynamic potentials of each deformation path, we evaluate the general constitutive equations ( 49) and ( 50) in the present multiplicative setting and discuss the implications in what follows. For the total stresses, the corresponding second Piola–Kirchhoff stress tensor follows from the derivative of the respective free energy functions as
\begin{aligned} {\mathbf {S}}_{\mathrm{tot}}= 2 \, \rho ^{(0)}\frac{\partial \psi _{\mathrm{r,m}}^{(0)}}{\partial {\mathbf {C}}} + 2 \, \rho ^{(0)}\frac{\partial \psi _{\mathrm{r,e}}^{(0)}}{\partial {\mathbf {C}}} . \end{aligned}
(96)
If the nonisotropic part of the material susceptibility does not depend on the deformation as in example ( 92), the above relation is evaluated as
\begin{aligned} \begin{aligned} {\mathbf {S}}_{\mathrm{tot}}&= 2 \, \rho ^{(0)}\frac{\partial \psi _{\mathrm{r,m}}^{(0)}}{\partial {\mathbf {C}}_\mathrm{m}} : \frac{\partial {\mathbf {C}}_\mathrm{m}}{\partial {\mathbf {C}}} + 2 \, \rho ^{(0)}\frac{\partial \psi _{\mathrm{r,e},\mathrm {iso}}^{(0)}}{\partial {\mathbf {C}}} \\&= 2 \, \rho ^{(0)}{\mathbf {F}}_\mathrm{e}^{-1}\cdot \frac{\partial \psi _{\mathrm{r,m}}^{(0)}}{\partial {\mathbf {C}}_\mathrm{m}} \cdot {\mathbf {F}}_\mathrm{e}^{-T}+ {\mathbf {S}}_\mathrm{M}+ \epsilon _0\chi _0 {\mathbf {C}}^{-1}\cdot {\varvec{e}}^{(0)}{\varvec{e}}^{(0)}\cdot {\mathbf {C}}^{-1}\end{aligned} \end{aligned}
(97)
where we have used the chain rule of differential calculus and the derivative of $${\mathbf {C}}_\mathrm{m}$$ with respect to $${\mathbf {C}}$$ according to ( 71). The irreversible part of the free energy $$\psi _i^{(0)}$$ does not depend on the state of deformation, which is why it does not enter the above relations. From the free-space energy, we obtain the (material) Maxwell stresses that contribute to the (total) stress response. The constitutive relation for the total stresses ( 97) suggests the definition of the elastic stresses in the second intermediate configuration as the derivative of the reversible mechanical part of the free energy, i.e.,
\begin{aligned} {\mathbf {S}}_{\mathrm{elast}}^{(2)}= 2 \, \rho ^{(2)}\frac{\partial \psi _{\mathrm{r,m}}^{(0)}}{\partial {\mathbf {C}}_\mathrm{m}} , \qquad \rho ^{(2)}= J_\mathrm{e}^{-1} \rho ^{(0)}. \end{aligned}
(98)
The corresponding stresses in the reference configuration are obtained upon a pullback from the second intermediate configuration by means of the electrical part of the deformation gradient $${\mathbf {F}}_\mathrm{e}$$,
\begin{aligned} \begin{aligned} {\mathbf {S}}_{\mathrm {elast}}= J_\mathrm {e}{\mathbf {F}}_\mathrm {e}^{-1}\cdot {\mathbf {S}}_{\mathrm {elast}}^{(2)}\cdot {\mathbf {F}}_\mathrm {e}^{-T}. \end{aligned} \end{aligned}
(99)
Note that the irreversible part $$\psi _\mathrm {i}^{(0)}$$ is not only independent of the deformation, but also independent of the material electric field $${\varvec{e}}^{(0)}$$, which is why the material dielectric displacement field follows from the derivatives of the reversible parts of the (total) free energy $$\psi _{\mathrm{r,m}}^{(0)}$$ and $$\psi _{\mathrm{r,e}}^{(0)}$$ with respect to $${\varvec{e}}^{(0)}$$ as
\begin{aligned} \begin{aligned} {\varvec{d}}^{(0)}&= - \rho ^{(0)}\frac{\partial \psi _{\mathrm{r,m}}^{(0)}}{\partial {\mathbf {C}}_\mathrm{m}} : \frac{\partial {\mathbf {C}}_\mathrm{m}}{\partial {\varvec{e}}^{(0)}} - \rho ^{(0)}\frac{\partial \psi _{\mathrm{r,e}}^{(0)}}{\partial {\varvec{e}}^{(0)}} \\&= - J_\mathrm{e}{\mathbf {C}}_\mathrm{m}\cdot {\mathbf {S}}_{\mathrm{elast}}^{(2)}\cdot {\mathbf {F}}_\mathrm{r,e}^{-T}: \frac{\partial {\mathbf {F}}_\mathrm{r,e}}{\partial {\varvec{e}}^{(1)}} \cdot {\mathbf {F}}_\mathrm{i}^{-T}+ \varvec{\epsilon }^{(0)}\cdot {\varvec{e}}^{(0)}+ {\varvec{p}}^{(0)}_\mathrm{i}. \end{aligned} \end{aligned}
(100)
In view of the decomposition of the susceptibility into isotropic and anisotropic parts ( 88), we split the material polarization vector, which follows from the dielectric displacement by discarding the free-space contribution, into four separate parts,
\begin{aligned} {\varvec{p}}^{(0)}= & {} {\varvec{d}}^{(0)}- \epsilon _0J {\varvec{e}}^{(0)}\cdot {\mathbf {C}}^{-1}= {\varvec{p}}^{(0)}_{\mathrm{elast}}+ {\varvec{p}}^{(0)}_{\mathrm{iso}}+ {\varvec{p}}^{(0)}_{\mathrm{aniso}}+ {\varvec{p}}^{(0)}_\mathrm{i}. \end{aligned}
(101)
The three parts in addition to $${\varvec{p}}^{(0)}_\mathrm{i}$$ are identified from the constitutive equation ( 100) and the susceptibility ( 88) as
\begin{aligned} \begin{aligned}&{\varvec{p}}^{(0)}_{\mathrm{elast}}= - J_\mathrm{e}{\mathbf {C}}_\mathrm{m}\cdot {\mathbf {S}}_{\mathrm{elast}}^{(2)}\cdot {\mathbf {F}}_\mathrm{r,e}^{-T}: \frac{\partial {\mathbf {F}}_\mathrm{r,e}}{\partial {\varvec{e}}^{(1)}} \cdot {\mathbf {F}}_\mathrm{i}^{-T}, \\&{\varvec{p}}^{(0)}_{\mathrm{iso}}= \epsilon _0\chi _0 {\varvec{e}}^{(0)}\cdot {\mathbf {C}}^{-1}, \\&{\varvec{p}}^{(0)}_{\mathrm{aniso}}= \epsilon _0{\varvec{e}}^{(0)}\cdot \varDelta \varvec{\chi }^{(0)}. \end{aligned} \end{aligned}
(102)
The first term $${\varvec{p}}^{(0)}_{\mathrm{elast}}$$ depends on the elastic stresses and represents the electromechanical coupling, which is kinematically described by the reversible electrical part of the deformation gradient $${\mathbf {F}}_\mathrm{r,e}$$. The second term $${\varvec{p}}^{(0)}_{\mathrm{iso}}$$ describes the isotropic dielectric response of the material under an electric field, and the polarization induced by the anisotropy of the susceptibility is denoted by $${\varvec{p}}^{(0)}_{\mathrm{aniso}}$$. The decomposition of the polarization allows us to gain more insight into the stress response ( 97). Upon substitution of the elastic stresses ( 99) along with the isotropic polarization ( 102), the constitutive equation for the total stresses follows as
\begin{aligned} {\mathbf {S}}_{\mathrm{tot}}= {\mathbf {S}}_{\mathrm{elast}}+ {\mathbf {S}}_\mathrm{M}+ {\mathbf {C}}^{-1}\cdot {\varvec{e}}^{(0)}{\varvec{p}}^{(0)}_{\mathrm{iso}}. \end{aligned}
(103)
From the definition of the total stress tensor ( 9) and the polarization stresses ( 39), we recognize that the mechanical stresses are related to the elastic stresses $${\mathbf {S}}_{\mathrm{elast}}$$ by
\begin{aligned} {\mathbf {S}}= {\mathbf {S}}_{\mathrm{elast}}+ {\mathbf {C}}^{-1}\cdot {\varvec{e}}^{(0)}{\varvec{p}}^{(0)}_{\mathrm{iso}}- {\mathbf {S}}_\mathrm{P}= {\mathbf {S}}_{\mathrm{elast}}- {\mathbf {C}}^{-1}\cdot {\varvec{e}}^{(0)}\left( {\varvec{p}}^{(0)}_{\mathrm{elast}}+ {\varvec{p}}^{(0)}_{\mathrm{aniso}}+ {\varvec{p}}_\mathrm{i}\right) . \end{aligned}
(104)
The above result illustrates that the mechanical stresses are composed of a symmetric elastic part and the polarization stresses induced by the electromechanical coupling, an anisotropic electric susceptibility and the remanent polarization.
We continue with the dissipative driving forces, which are obtained from the derivative of the total free energy with respect to the material remanent polarization $${\varvec{p}}^{(0)}_\mathrm{i}$$. The irreversible part $$\psi _\mathrm {i}^{(0)}$$ naturally depends on the remanent polarization. We have assumed the isotropic part of the susceptibility ( 88) to describe the dielectric response of an unpoled material. Therefore, only the anisotropic part of reversible electric free energy ( 90) enters the constitutive equation of the dissipative driving force. As the material parameters that govern the elastic response of the material also depend on the state of remanent polarization in general, $$\psi _{\mathrm{r,m}}^{(0)}$$ also contributes to the driving forces, which eventually follow as
\begin{aligned} \begin{aligned} {\hat{{\varvec{e}}}}^{(0)}= - \rho ^{(0)}\frac{\partial \psi _{\mathrm {r,m}}^{(0)}}{\partial {\varvec{p}}^{(0)}_\mathrm {i}} - \rho ^{(0)}\frac{\partial \psi _{\mathrm {r,e},\mathrm {aniso}}^{(0)}}{\partial {\varvec{p}}^{(0)}_\mathrm {i}} - \rho ^{(0)}\frac{\partial \psi _\mathrm {i}^{(0)}}{\partial {\varvec{p}}^{(0)}_\mathrm {i}} . \end{aligned} \end{aligned}
(105)
Within the framework of the multiplicative decomposition, the concept of destressing is introduced to illustrate the notion of intermediate configurations, see Fig. 1. The second intermediate configuration $${\mathcal {B}}^{(2)}$$ is taken by a body if no mechanical deformation occurs, i.e., $${\mathbf {F}}_\mathrm{r,m}= {\mathbf {I}}$$ and $${\mathbf {C}}_\mathrm{m}= {\mathbf {I}}$$ hold. In this case, the symmetric Piola–Kirchhoff stresses in the second intermediate configuration ( 98) vanish identically, $${\mathbf {S}}_{\mathrm{elast}}^{(2)}= {\mathbf {0}}$$. In other words, the second intermediate configuration follows upon elastic unloading of the current configuration. The total stresses are only composed of the Maxwell stresses and the polarization stresses induced by the isotropic dielectric response. As the electromechanical coupling polarization also vanishes, $${\varvec{p}}^{(0)}_{\mathrm{elast}}= {\mathbf {0}}$$, the mechanical stresses in the second intermediate configuration are the negative of the sum of the polarization stresses that correspond to the dielectric anisotropy and the polarization stresses from the remanent polarization.
We recover the first intermediate configuration $${\mathcal {B}}^{(1)}$$ in the deformation path if the body is also unloaded electrically, i.e., $${\varvec{e}}^{(0)}= {\mathbf {0}}$$. As a consequence, both total and mechanical stresses vanish in this configuration, and only the remanent polarization remains from the electrical point of view. Accordingly, we can regard the first intermediate configuration as a fully unloaded but poled configuration. As the individual parts of the deformation gradient describe the local response of material volume elements in the respective configurations, the intermediate configurations are incompatible as soon as inhomogeneities occur due to external loadings or kinematic boundary conditions. In fact, incompatibilities are the sources for a nontrivial elastic stress response $${\mathbf {S}}_{\mathrm{elast}}$$ and the corresponding polarization $${\varvec{p}}^{(0)}_{\mathrm{elast}}$$.
## 4 Algorithmic treatment
In view of both geometric and physical nonlinearities considered within the proposed approach, we need to make use of some numerical method to construct approximate solutions. In what follows, we develop the incremental variational formulation of the governing equations, which provides the basis for an algorithmic treatment by means of the finite-element method. For this purpose, we first introduce the electromechanical power $$P$$ as the integral of the material power density $$p^{(0)}_{\mathrm{tot}}$$ ( 45) over the body in the reference configuration $${\mathcal {B}}^{(0)}$$:
\begin{aligned} P= \int _{\varOmega ^{(0)}}p^{(0)}_{\mathrm{tot}}\, \mathrm d v^{(0)}= {\dot{\varPsi }} + D\end{aligned}
(106)
where the rate of the (total) free energy and the dissipation are integrals of the respective densities ( 44) and ( 50):
\begin{aligned} {\dot{\varPsi }} = \int _{\varOmega ^{(0)}}\rho ^{(0)}{\dot{\psi }}_{\mathrm{tot}}^{(0)}\mathrm d v^{(0)}, \qquad D= \int _{\varOmega ^{(0)}}d^{(0)}\mathrm d v^{(0)}. \end{aligned}
(107)
The time integral of the total electromechanical power over an interval $$\varDelta t= t_{n+1} - t_n$$ gives the corresponding work performed in that period. Subtracting the power of the external forces $$P_{\mathrm{{ext}}}$$, for which we assume a potential $$W_{\mathrm{ext}}$$ to exist, we obtain the incremental work functional
\begin{aligned} \varPi = \int _{t_n}^{t_{n+1}}\left( {\dot{\varPsi }} - P_{\mathrm{{ext}}}\right) \mathrm dt+ \int _{t_n}^{t_{n+1}}D\, \mathrm dt= \left( \varPsi - W_{\mathrm{ext}}\right) _{n+1} - \left( \varPsi - W_{\mathrm{ext}}\right) _{n} + \int _{t_n}^{t_{n+1}}D\, \mathrm dt. \end{aligned}
(108)
The work of the external loadings is composed of a mechanical part $$W_{\mathrm{m}, \mathrm ext}$$ and an electrical part $$W_{\mathrm{e}, \mathrm ext}$$,
\begin{aligned} W_{\mathrm{ext}}= W_{\mathrm{m}, \mathrm ext}+ W_{\mathrm{e}, \mathrm ext}. \end{aligned}
(109)
The mechanical part, in turn, comprises body forces $${\varvec{f}}^{(0)}$$ and surface tractions $${\varvec{t}}^{(0)}$$, which are to be understood as total stresses. The work of electrical loads depends on the density of free charges $$\sigma _\mathrm{e}^{(0)}$$ per unit surface in the reference configuration $${\mathcal {B}}^{(0)}$$, which represents the outer normal component of the dielectric displacement, i.e., $$\sigma _\mathrm{e}^{(0)}= {\varvec{d}}^{(0)}\cdot {\varvec{n}}^{(0)}$$,
\begin{aligned} \begin{aligned}&W_{\mathrm{m}, \mathrm ext}= \int _{\varOmega ^{(0)}}{\varvec{f}}^{(0)}\cdot {\varvec{u}}\, \mathrm d v^{(0)}+ \int _{\partial {\varOmega ^{(0)}}} {\varvec{t}}^{(0)}\cdot {\varvec{u}}\, \mathrm d a^{(0)}, \\&W_{\mathrm{e}, \mathrm ext}= - \int _{\partial {\varOmega ^{(0)}}} \sigma _\mathrm{e}^{(0)}\phi \, \mathrm d a^{(0)}. \end{aligned} \end{aligned}
(110)
In the time-discrete setting, we approximate the energy dissipated during the time period $$\varDelta t$$ by
\begin{aligned} \int _{t_n}^{t_{n+1}}D\, \mathrm dt\approx \varDelta t\int _{\varOmega ^{(0)}}e_\mathrm{c}\frac{\Vert ({\varvec{p}}^{(0)}_\mathrm{i})_{n+1} - ({\varvec{p}}^{(0)}_\mathrm{i})_n \Vert _{\mathrm{reg}}}{\varDelta t} \, \mathrm d v^{(0)}= \int _{\varOmega ^{(0)}}e_\mathrm{c}\Vert {({\varvec{p}}^{(0)}_\mathrm{i})_{n+1} - ({\varvec{p}}^{(0)}_\mathrm{i})_n} \Vert _{\mathrm{reg}} \, \mathrm d v^{(0)}.\qquad \end{aligned}
(111)
By requiring the variation in the independent fields of the work functional to vanish, i.e., $$\delta \varPi = 0$$, we obtain the variational formulation of the governing equations, which generally serves as basis for a finite-element analysis. We use the open-source, multipurpose finite-element code Netgen/NGSolve ( www.ngsolve.org), which relieves us from the burden of computing the variations in the independent fields and a consistent linearization by hand. Owing to automatic differentiation, we only have to specify the work functional ( 108) symbolically. We rely on Newton’s method to solve the nonlinear system of equations iteratively for the increments in the unknown fields, which are the displacement field $${\varvec{u}}$$, the electric potential $$\phi$$, and the material remanent polarization $${\varvec{p}}^{(0)}_\mathrm{i}$$. Due to the introduction of the dissipation function, we can solve for all fields at once without resorting to some kind of return-mapping algorithm. In our example problems, we use hexahedral elements to spatially discretize the bodies. Second-order hierarchical polynomials are used as shape functions for the displacement field and for the electric potential. The components of the remanent polarization are interpolated by means of linear polynomials.
## 5 Example problems
### 5.1 Uniaxial poling
Table 1
Material properties derived from the nondimensional parameters used in [ 18]
Young’s modulus $$E_\mathrm{Y}$$ 30 GPa Poisson’s ratio $$\nu$$ 0.3 Rel. isotropic susceptibility $$\chi _0$$ 1354.31 Piezoelectric coefficient $$d_{31}$$ $$-2.1\times 10^{-10}\hbox { m V}^{-1}$$ Piezoelectric coefficient $$d_{33}$$ $$4.2\times 10^{-10}\hbox { m V}^{-1}$$ Piezoelectric coefficient $$d_{15}$$ $$5.2\times 10^{-10}\hbox { m V}^{-1}$$ Coercive field strength $$e_\mathrm{c}$$ $$1\times 10^{6}\hbox { V m}^{-1}$$ Saturation polarization $$p_{\mathrm{sat}}$$ $$0.3\,\hbox {Cm}^{-2}$$ Saturation strain $$S_{\mathrm{sat}}$$ $$2\times 10^{-3}$$ Hardening parameter c $$0.333\times 10^{6}\hbox { V m C}^{-1}$$
By means of the first example, we want to check the consistency of the proposed nonlinear formulation with results obtained from geometrically linear models. For this purpose, we study the uniaxial poling process of a ferroelectric material under a homogeneous electric field. In all our examples, we use material properties that are derived from the dimensionless parameters used by McMeeking and Landis [ 18], see Table 1. To further connect to Voigt’s linear theory of piezoelectricity, we recall that the second intermediate configuration $${\mathcal {B}}^{(2)}$$, which evolves from the first intermediate configuration $${\mathcal {B}}^{(1)}$$ under electric loads, can be regarded as mechanically unloaded. In the mechanical part of the deformation path, which leads to the current configuration $${\mathcal {B}}$$, the electric field is assumed to be constant. Therefore, the material parameters of the present approach correspond to the (tangent) moduli of the linear theory, where the electric field and the mechanical stresses are used as independent variables. The elastic behavior is assumed to be isotropic and independent of the remanent polarization, and no anisotropic parts develop in the electric susceptibility. In our examples, we use the neo-Hookean model for compressible materials, for which the strain energy is given by
\begin{aligned} \rho ^{(2)}\psi _{\mathrm{r,m}}^{(2)}= \frac{1}{2} \, \mu {{\,\mathrm{tr}\,}}\left( {\mathbf {C}}_\mathrm{m}- {\mathbf {I}}\right) + \left( \frac{\lambda }{2} \log J_\mathrm{r,m}^{-1} - \mu \right) \log J_\mathrm{r,m}^{-1}, \end{aligned}
(112)
see, e.g., [ 5]. In the above relation, $$\lambda$$ denotes the first Lamé parameter and $$\mu$$ is the shear modulus.
We consider a cube-shaped specimen with 1 mm side length, for which all rigid-body degrees of freedom are constrained. The edges of the cube are aligned with the coordinate axes ( $$x_1, x_2, x_3$$) of the global frame. The bottom surface parallel to the $$(x_1,x_2)$$-plane is grounded; on the top surface, an electric potential $$V_0$$ is applied such that a homogeneous electric field in $$x_3$$-direction is induced. By a cyclic electric loading with a maximum voltage amplitude of $$V_0 = \mp \,1700\hbox { V}$$ in steps of $$10\,\hbox {V}$$, we obtain the dielectric hysteresis illustrated in Fig. 2a.
The corresponding butterfly hysteresis, which describes the dependency of the strain $$E_{33}$$ in the poling direction as a function of the applied electric field $$e_3$$, is shown in Fig. 2b. Additionally, we also provide the curves for the reversible electrical strain due to the piezoelectric coupling $$E_{\mathrm {r,e},33}$$ and the poling-induced irreversible strain $$E_{\mathrm {i},33}$$. Our geometrically nonlinear approach based on the multiplicative decomposition is able to reproduce what is known from the geometrically linear case, cf. McMeeking and Landis [ 18].
### 5.2 Poling of a bent cantilever
As geometric nonlinearities are negligible in the previous benchmark example, we want to study a situation in which large deformations need to be considered. For this purpose, we investigate the poling of a ferroelectric cantilever, which is first deflected by a tip force in transverse direction, before it is poled by applying an electric voltage $$V_0$$ between its top and bottom surfaces. The cantilever, which has the dimensions $$L \times W \times H = 80\hbox { mm} \times 20\hbox { mm}\times 0.4\hbox { mm}$$, is aligned with the global $$x_1$$-axis in its reference configuration; $$x_3$$ is the thickness direction. The material parameters are taken from Table 1. The cantilever is discretized into hexahedral elements using six equidistant layers over the thickness. The in-plane discretization is shown in Fig. 4. For the sake of computational efficiency, symmetry conditions at the plane $$X_2 = 0$$ are exploited in the numerical analysis. The transverse tip force of $$F = -0.8\hbox { N}$$ is realized as a uniform surface traction acting on the front face ( $$X_1 = L$$) of the cantilever in the reference configuration. At the clamped end, any displacement is prohibited, i.e., $${\varvec{u}}(X_1 = 0, X_2, X_3) = {\mathbf {0}}$$. Under the imposed load, the tip deflection of the center plane is obtained as $$u_3(X_1 = L, X_2 = 0, X_3 = H/2) = -32.84\hbox { mm}$$. We assume the top surface to be grounded; the voltage $$V_0$$ at the bottom surface is gradually increased in a second loading step. The mechanically deformed, poled configuration ( $$V_0 = 420\hbox { V}$$) of the cantilever is illustrated in Fig. 3, which also shows the magnitude of the (material) remanent polarization $$\Vert {\varvec{p}}^{(0)}_\mathrm{i}\Vert$$.
In a homogeneous poling problem as our first example, we would expect the material to polarize starting from a voltage of $$V_0 = e_\mathrm{c}H = 400\,\hbox {V}$$ for the given dimensions. The present problem of a bent cantilever, however, is inhomogeneous due to the mechanical load and the imposed boundary conditions, which result in an inhomogeneous state of deformation. We observe remanent polarization to occur well before the threshold of the homogeneous problem. Figure 4a–c shows the distribution of the transverse component of the (material) remanent polarization $$p^{(0)}_{\mathrm{i},3}$$ within the top surface ( $$X_3 = H$$) and bottom surface ( $$X_3 = 0$$) for three voltages $$V_0 = 390\hbox { V}, 400\hbox { V}, 410\hbox { V}$$. At a voltage of $$V_0 = 390\,\hbox {V}$$ (Fig. 4a), the top surface ( $$X_3 = H$$) does not exhibit any significant remanent polarization. The bottom surface ( $$X_3 = 0$$), by contrast, has already been poled irreversibly to some extent. The remanent polarization starts from the clamped end of the cantilever ( $$X_1 = 0$$). Directly at the clamping, however, poling is obstructed by the kinematic boundary conditions on the displacement, which constrain the deformation induced by the poling process. At $$V_0 = 400\,\hbox {V}$$, we find regions with the highest remanent polarization in the center of both the top and the bottom surfaces of the cantilever, see Fig. 4b. Toward its free edges, no significant remanent polarization has yet occurred. When we increase the applied voltage to $$V_0 = 410\,\hbox {V}$$ (Fig. 4c), the polarization increases substantially and extends further toward the front ( $$X_1 = 0$$) and lateral ( $$X_2 = \pm W/2$$) faces of the cantilever. At the lateral faces of the cantilever, the remanent polarization diminishes toward the clamped end.
To gain additional insight, we investigate the evolution of the (material) remanent polarization $$p^{(0)}_{\mathrm {i},3}$$ within three cross sections along the cantilever’s axis, i.e., cross sections close to the clamped end ( $$X_1 = 0.1 L$$), in the middle ( $$X_1 = L/2$$), and close to the free end ( $$X_1 = 0.9 L$$). Figure 5a–c shows the remanent polarization as a function of the applied voltage $$V_0$$ at the (vertical) plane of symmetry ( $$X_2 = 0$$) and three (horizontal) planes parallel to the transducer, i.e., the bottom surface ( $$X_3 = 0$$), the center plane ( $$X_3 = H/2$$) and the top surface ( $$X_3 = H$$). Apparently, a notable remanent polarization first occurs at the bottom surface ( $$X_3 = 0$$) close to the clamped end ( $$X_1 = 0.1 L$$) of the ferroelectric cantilever at an applied voltage of approximately $$V_0 = 370\,\hbox {V}$$, see Fig. 5a. At the center plane ( $$X_3 = H/2$$), an increase in the polarization is observed at about $$V_0 = 392.5\,\hbox {V}$$, whereas no considerable polarization occurs at the top surface ( $$X_3 = H$$) before a voltage of $$V_0 = 400\,\hbox {V}$$ is reached. At $$V_0 = 400\,\hbox {V}$$, the rate of change in the remanent polarization (in terms of applied voltage) increases significantly in all three planes of the cantilever. In the cross section at $$X_1 = L/2$$, we observe a similar behavior: The remanent polarization starts to grow from the bottom surface ( $$X_3 = 0$$) toward the top surface ( $$X_3 = H$$). As compared to the cross section close to the clamped end, the onset of poling is delayed to higher voltages in the bottom plane and the center plane of the cantilever. A substantial increase in the rate of polarization, however, already occurs at a lower voltage than at the clamped end throughout all three planes over the height of the cross section. Moving further toward the free end ( $$X_1 = 0.9L$$), the poling process occurs at even higher voltages. The remanent polarization starts to grow almost simultaneously in all three planes of the cross section at approximately $$V_0 = 400\,\hbox {V}$$.
Figure 6 shows the transverse tip displacement $$u_3(X_1=L, X_2=0, X_3=H/2)$$ in the course of poling. First, the deflection increases slightly with the onset of poling at the bottom parts of the cantilever. The polarization induces tensile strains along the poling axis, i.e., in the thickness direction, and compressive strains in the plane perpendicular to it, see ( 75)–( 82). Increasing the applied voltage, the tip deflection of the cantilever reduces as the poled region grows.
From a phenomenological point of view, the observed behavior is consistent with what is referred to as ferroelasticity, i.e., a change of remanent polarization (and deformation) under mechanical loadings. Polycrystalline ferroelectrics can be depolarized under sufficiently strong compressive loads on the one hand, and under tensile loads perpendicular to the remanent polarization on the other hand [ 11]. Conversely, poling is supported if a material is compressed by a load perpendicular to the poling axis, which corresponds to what we observe in the present results. In the static equilibrium configuration, from which the poling process is started, the bottom surface of the cantilever is in compression due to the bending moment about the $$x_2$$-axis, which is induced by the transverse tip load. The bending moment has a maximum at the clamped end, which is where remanent polarization occurs first, and it decreases toward the free end of the cantilever. Therefore, the onset of poling is delayed to higher voltages further along the axis of the cantilever. Over the height of the cross sections, the compressive (axial) normal stresses are largest at the bottom surface, which is also consistent with the results we obtained in our example. We note that ferroelasticity is not fully included in the proposed constitutive model. Irreversible deformations under mechanical loads in the macroscopically unpoled state, which are observed in polycrystalline ferroelectrics, cannot be captured by our approach, see, e.g., Landis [ 13] for a discussion.
## 6 Conclusions
In the present paper, we have proposed a constitutive framework for the phenomenological modeling of the irreversible response of ferroelectric materials in the geometrically nonlinear domain. For this purpose, we have used the concept of the multiplicative decomposition of the deformation gradient. The deformation gradient has been split into three parts that are related to the state of remanent polarization, the reversible electrical response, and the elastic stress response, respectively. We have adopted a material description of the governing equations, in which we have referred to an undeformed and unpoled reference configuration of the body under consideration. The constitutive equations for the (second Piola–Kirchhoff) stresses, the (material) dielectric displacement, and the dissipative driving forces follow from standard arguments of thermodynamics. In analogy to the theory of plasticity, the evolution equation for the remanent polarization has been obtained from the principle of maximum dissipation. Moreover, the concept of using a dissipation function to satisfy the principle of maximum dissipation has been introduced, which has significantly simplified the algorithmic treatment of the governing equations. Finally, the proposed physically and geometrically nonlinear formulation has first been validated against existing results for small deformations, and eventually results for an example problem with large deformations have been presented.
## Acknowledgements
Open access funding is provided by Johannes Kepler University Linz. Alexander Humer and Astrid Pechstein acknowledge the support by the Linz Center of Mechatronics (LCM) in the framework of the Austrian COMET-K2 program. Martin Meindlhumer has been supported by the Linz Institute of Technology (LIT) of the Johannes Kepler University Linz.
## Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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• CommentRowNumber1.
• CommentAuthorEric
• CommentTimeOct 17th 2010
I presume that
## Definition
Let $C$ be a category with pullbacks. Then the tangent category $T_C$ of $C$ is the category whose
• objects are pairs $(A,\mathcal{A})$ with $A \in Ob(C)$ and with $\mathcal{A}$ an abelian group object in the overcategory $C/B$;
contained a minor typo, so I replaced $C/B$ with $C/A$.
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeOct 17th 2010
Right, thanks for fixing that!
• CommentRowNumber3.
• CommentAuthorTobyBartels
• CommentTimeOct 17th 2010
• CommentRowNumber4.
• CommentAuthorEric
• CommentTimeOct 18th 2010
• (edited Oct 18th 2010)
Tracing references took me to tangent (infinity,1)-category and from there to Deformation Theory and from there to the arxiv.
I’m starting see a blurry image appear, but an image nontheless.
One question…
Why does Lurie begin with Kähler differentials? They’ve always seemed a bit kinky to me (but in a cool way). That is, they never seemed 100% natural due to the implied commutative of functions and differentials.
Much more natural, in my opinion, are universal differential envelopes and their quotients. What if, instead of starting with Kähler differentials, you started with simply differential modules (without the implied $a (d b) = (d b) a$) and then followed Lurie’s prescriptions?
Is there a noncommutative version of stabilization or something?
PS: In Lurie’s paper on page 5, he says
here $Stab$ denotes the stabilization construction introduced in §S.8.
Silly question. What is he referring to? §S.8? There are only 3 sections in the paper :o
• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeOct 18th 2010
• (edited Oct 18th 2010)
“S” stands for his article on stable (infinity,1)-categories, and the stabilization he refers to is stabilization |
Is it possible hf=kT?
1. Dec 3, 2012
phyky
is it possible hf=kT? Under what condtion, it will be the same? where h is Plack constant, f is frequency and k is Boltzmann constant, T is temperature
2. Dec 3, 2012
Staff: Mentor
For any frequency f, there is a T which satisfies the equation.
3. Dec 3, 2012
HomogenousCow
.....
edit:wait jtbell is this ever computed? I have never seen such an equality
Last edited: Dec 3, 2012
4. Dec 3, 2012
f95toli
It is used all the time. Any relation which involves thermal radation to/from a body held at a temperature T will involve thesee terms.
At hf=kBT there are often "transitions" of some sort. In some cases you have a transition from the classical (thermal) to quantum regime when hf=kBT |
# Robustness
The final goal to in model based design is to implement in the end a software that will run on physical hardware. Eventually, at some stage in the design, it will be necessary to confront the abstract models, whose real time clocks are infinitely precise, to imprecise hardware clocks. This problem of the implementability of abstract models can be solved by checking the robustness of the models, that is to say their ability to accept some perturbations without deviating from the top level specifications. In [LLTW11] we have studied the robustness of timed specifications defined previously.
### Perturbation of implementations and robust satisfaction
We apply a perturbation on the implementation components for a value $Latex formula$. On physical systems the output urgent condition of implementations cannot be enforced and output actions will tend to happen either a bit earlier or a bit later. To model this behavior we extend the guards of output transitions and the invariants of the TIOA. For instance:
• a guard $Latex formula$ becomes $Latex formula$
• a guard $Latex formula$ becomes $Latex formula$
Conversely, receiving inputs at the limit of timing constraint may lead to chaotic behaviors. We model this by restricting the guards of input transitions, and the behaviors removed will be replaced by universal state (where any action may happen at any time) to model unpredictability. Then:
• a guard $Latex formula$ becomes $Latex formula$
• a guard $Latex formula$ becomes $Latex formula$
Specification $Latex formula$ Implementation: $Latex formula$ Perturbation of the implementation: $Latex formula$
Robust satisfaction: An implementation of a specification is robust for a value $Latex formula$ if and only if its perturbation by $Latex formula$ refines the specification. In the example above we can check that: $Latex formula$. We show that robust satisfaction is monotonic for different value of $Latex formula$: $Latex formula$
### Robust games
In the problem of robust consistency we want to determine if a specification admits a robust implementation for a given perturbation. In the non-robust case, consistency is solved through a timed games. Therefore we have adapted the technique from [CHP08] to solve robust timed games. The technique consists in applying a transformation that allows to solve a robust game with classical timed games algorithms. In [LLTW11] we have adapted this technique to timed specifications. The principle of this transformation is illustrated in the figure below. From the original game automaton A, we encode the perturbation by modifying the moves of the output player. Then, we show that solving a classical timed game on the robust automaton allows to solve a robust game on the original game automaton.
This technique is also used to solve robust compatibility, i.e to determine if there exists an environment that is compatible with two specifications, even if it is subjected to some perturbation.
We show that the operators of the timed specifications theories (conjunction, parallel composition and quotient), remain are robust, i.e. their properties remains valid with respect to robust implementations. In particular the independent implementation property for parallel composition is also valid for robust implementations:
$Latex formula$
### Parametric robustness problems
More than checking robustness for a given value of the perturbation, the designer of a system wants to know what is the maximum perturbation allowed by its models. This implies to solve parametric version of the previous problems robust satisfaction, robust consistency and robust compatibility) where the value of $Latex formula$ is unknown.
We have proposed in [Tra12] a counter-example technique (CEGAR approach) to evaluate this maximum value. The technique consists in solving a game for a given value of $Latex formula$ and refining the results (the counter-example strategy computed) by a parametric analysis to quickly converge to the solution.
Using this technique implemented in PyECDAR we can computes that the specification $Latex formula$ is robustly consistent for any value of $Latex formula$ lower than 3. |
lilypond-user
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## Re: elegant compound time signatures
From: Hans Aberg Subject: Re: elegant compound time signatures Date: Mon, 20 Oct 2008 12:36:20 +0200
On 20 Oct 2008, at 11:21, Graham Percival wrote:
Hans: at the risk of sounding grumpy, did you try compiling my
example? I believe it does everything you want.
Yes, I think it was clear from my reply. I mentioned that although writing in each measure
\unset subdivideBeams
\unset beatLength
does the job, it is a bit cumbersome.
The second problem is that LilyPond beamings varies quite a bit from version to version, so sprinkling, so this solution may not be stable.
There is a need of a more general beaming pattern selection scheme.
Hans |
# Ideal of the ring
• March 27th 2011, 11:04 AM
Greg98
Ideal of the ring
Hello,
Let's assume that $\mathbb{R}^2$ is a ring, which operations are addition and multiplication using components (eg. $u + v = (u_1 + v_1, u_2 + v_2)$). The task is to prove that x-axis and y-axis are ideals of this ring. Following theorem must be used in the proof:
"Ring homomorphism's $f:R \rightarrow S$ kernel $Ker(f)$ is $R$'s ideal".
I think the problem isn't very hard, when the correct homomorphism is found. I tried some, but I couldn't discover anything that works. So, any help is welcome. Thank you very much!
• March 27th 2011, 12:59 PM
topspin1617
Well, the $x$-axis is, by definition, the set
$X=\{(a,0)\mid a\in \mathbb{R} \}$.
If you want to prove that $X$ is an ideal using the statement you have written, we need a ring $R$ and a ring homomorphism $f:\mathbb{R}^2\rightarrow R$ such that $X=\ker f$.
How about taking $R=\mathbb{R}$, and defining
$f:\mathbb{R}^2\rightarrow R$
$(a,b)\mapsto a$
(projection onto the first coordinate)? It should be fairly simple to prove that $f$ is indeed a ring homomorphism, and that the kernel of $f$ is exactly the set of points located on the $x$-axis.
You can do a completely analogous thing to show that the $Y$ axis is also an ideal.
• March 27th 2011, 09:15 PM
Drexel28
Quote:
Originally Posted by topspin1617
Well, the $x$-axis is, by definition, the set
$X=\{(a,0)\mid a\in \mathbb{R} \}$.
If you want to prove that $X$ is an ideal using the statement you have written, we need a ring $R$ and a ring homomorphism $f:\mathbb{R}^2\rightarrow R$ such that $X=\ker f$.
How about taking $R=\mathbb{R}$, and defining
$f:\mathbb{R}^2\rightarrow R$
$(a,b)\mapsto a$
(projection onto the first coordinate)? It should be fairly simple to prove that $f$ is indeed a ring homomorphism, and that the kernel of $f$ is exactly the set of points located on the $x$-axis.
You can do a completely analogous thing to show that the $Y$ axis is also an ideal.
I think topspin made a slight clerical error. To show that $X\unlhd \mathbb{R}$ one should consider the second canonical projection $\pi_2:\mathbb{R}^2\to\mathbb{R}:(a,b)\to b$ since the kernel of this is clearly $\mathbb{R}\times\{0\}=X$. |
# How to deal with (orphaned) WakeLocks?
I guess most of you at least have heard about WakeLocks. Many of you will have experienced them already -- wether knowingly or not. Some may know how to deal with them in general -- but only few know how to deal with the "more complicated candidates".
For those who don't know, though above link leads to an explanation, a short summary: Apps may request a WAKE_LOCK to keep a device component from "sleeping", so they can perform a task even when the display is turned off. This is very useful in most cases (e.g. keeping the screen on while navigating, keeping WiFi active to stream music) -- but used in the wrong way, it causes your battery to be drained within short term (up to 25% per hour).
Most times it is easy to identify the source (usually a bad behaving app) -- I will show this in an answer below, as it might prove helpful to many users. But what to do if the app which requested the WakeLock exits without releasing it? The Android system will not take care of it. Sure, a reboot would solve the issue -- but it is not always an (desired) option.
So, from a users perspective (I'm not asking about development solutions, but how a user can handle things):
What can be done _by the user_ to solve the issue and avoid further battery drain?
I prefer answers not involving root (so all users can benefit from it). However, "rooted solutions" are fully valid and welcome as well.
-
I was under the impression that this was only true if you created the wakelock the "wrong" way, by using /sys/power/wake_lock, but that if you did it the "right" way using PowerManager and PowerManager.WakeLock, the service would both hold the real wakelock and release it even if your process was killed... – Izkata Dec 8 '12 at 5:47
According to the information I linked, that's obviously not the case. Somebody reports there having checked the kernel sources, and did not find any hint to that. Hint for developers: seems like "partial wakelocks" can be requested timed, so they'd expire automatically when the timer's up and the wakelock aquire was not refreshed. That must be the "safe way" you refer to. – Izzy Dec 8 '12 at 18:30
## How can I tell I'm affected?
This is probably the first question to those not familiar with this topic. With Gingerbread (Android 2.3) and above, you've got a service aboard helping you to figure out: battery statistics. Though manufacturers tend to place it at different points, it's mostly found in Settings → About the phone → Battery or similar, and shows a list of the apps having used most of your battery. On top of that is a small graph. Tap that, and it brings you to a screen similar to this one:
Screenshot of battery statistics on Android 2.3
I chose a screenshot from one of my devices which illustrates the issue. Looking at the lower two blue bars ("Aktiv" = Device was kept awake (active), "Bildschirm an" = "Screen on"), the right-most blue bar on "Aktiv" indicates a WakeLock: Device was kept busy despite the fact the screen was turned off. So by this we can be pretty sure we've got a WakeLock -- but we cannot tell who caused it.
If your device does not offer this screen (or the bars at the bottom: I just discovered e.g. the LG Optimus 4X running Android 4.0.3 has cut these bars off), you can find them e.g. using GSam Battery Monitor:
Similar information from GSam Battery Monitor -- here the mentioned "blue bars" are yellow/orange
## What caused the WakeLock?
Unfortunately, this question cannot be answered using pre-installed apps (except for, maybe, some Custom ROMs). But there are tools available that can. The best known candidate for this is BetterBatteryStats, and shows us the cause in its partial wakelocks section:
Screenshots from BetterBatteryStats
In the first example2 (taken from the app's playstore page), the event causing most of the WakeLocks was a desired one: We don't want the playback stopped while listening to music. So the second example3 (taken from a real case on one of my devices) might prove better: the topmost 3 events are caused by the very same app, which needed the WakeLock to keep the IMAP push service active.
For an alternative to BetterBatteryStats, check out the Wakelock Detector app mentioned in UzumApps' answer -- which seems easier to handle especially for non-techies:
Wakelock Detector -- Click image to enlarge. (Source: Google Play)
## What can be done?
If the case is as clear as in the second example in the previous section, the action is quite obvious -- at least in my case: I don't need to be informed immediately when a mail arrives; a delay of 30min is absolutely acceptable. So I went into the mail app, disabled IMAP Push (see also: Push Email), and instead switched to a 30min poll interval. WakeLocks did not entirely disappear, but dropped markably -- battery life improved noticably.
Then there's the case mentioned in the question itself: A bad behaving app not releasing its WakeLock. Confront the dev with your findings and ask for a fix. If he delivers: problem solved. If not: There's almost always an alternative app available.
## What if it is the Android System itself?
Yeah, sometimes it looks like just that: 98% or more consumed by some Android service. Oh, if it's 98%, in most cases the candidate is named LocationManagerService. Bad guy spying at us? Not necessarily. In this special case, the listed "bad guy" is not even guilty -- at least not directly. Here it is another app requesting the current location too frequently. There's an excellent article on Setera.org about this: Pinpointing Android LocationManagerService battery drain. To give an abstract: It uses Android's dumpsys feature (requires root!) to dump a system state, and lets you investigate the listeners established for the LocationManagerService. A closer look at their configuration shows which are constantly "hammering" it for location info (some do so permanently, i.e. without a break). As the app's ID is listed along, and at another place in the dump even together with the apps technical name, you can still identify it and take appropriate actions.
Unfortunately, there are such: Apps which registered a WakeLock -- and then exited without releasing it. What's left are Unused F**ing Obsoletes* -- WakeLocks held for no use. So no way to simply bring the app to foreground and re-configure, or making it release its WakeLocks.
Here the only solution known to me is a reboot -- and I would like to have a better solution. Of course, if you know the guilty app, the steps concerning it are the same as above: inform the dev, get a fix -- or replace the app. But about getting rid of the current WakeLock? Maybe somebody else can provide a better alternative to the reboot?
## Are there some recommended further readings?
Sure. One for now, I may add more later:
-
Better education to developers to say... "Release wakelocks when you are done with them and clean up after yourself"? – t0mm13b Dec 7 '12 at 22:09
Upvote from me for your as-always-stunning answer!!! You're never bored of this are you? :D – t0mm13b Dec 7 '12 at 22:14
Sure -- but see my question: I'm explicitly NOT asking about the developer side, but from a users perspective. Maybe I need to make that more obvious ;) – Izzy Dec 7 '12 at 22:15
Bored? Can someone please explain what that is like? XD No, I always have something on my mind. If I feel it's good enough, I even ask about it here (see my profile: I don't ask often), though I might have a (partial) answer. The feedback here is always refreshing if the question is worth it :) – Izzy Dec 7 '12 at 22:20
Please do! And report your findings! I just had that described issue with the "orphaned" WakeLocks. Poking around for an hour, I didn't get further than seeing it was the LocationManagerService. Registered for updates all 0sec (sic!) was the Android Settings (=:-0). I exited it, stopped it, killed it at the command line... no way to get rid of the locks. WTF did Settings do there? A reboot solved it, of course -- but is this a WindowsPhone we have to reboot twice a day? – Izzy Dec 7 '12 at 22:33
In short, this is a very good question but am afraid, it warrants more than just making the end-user aware!
Redesign the kernel to eliminate wake-locks and use a more thorough efficient way of managing the principle better thereby prolonging battery life.
Unfortunately, it has been accepted as a de-facto solution to enable "power management" despite it is not exactly efficient either! There was an extensive discussion about wakelocks (with Gregh Kroah Hartman - the Linux guru for drivers development - am googling for the exact linky), other sites such as LWN.net and another article explained on the same site here. This was the article Gregh Kroah Hartman referred to this blog, in which he appears to agree with the alternative solution proposed by Rafael J. Wysocki have documented a lot about the potential alternative. Am not sure if that is actually in place in the more modern kernel v3.x.x.
Badly designed apps can and often request wakelocks such as keeping the screen on, but in fact, in this scenario for keeping the screen on, there is in fact a more efficient way to do this:
getWindow().addFlags(LayoutParams.FLAG_KEEP_SCREEN_ON);
Whilst, striving to keep this clear of jargon etc for the end user, really the core of the issue boils down to the kernel code in how the wakelocks are managed.
Here is a brief summary on XDA on what is wakelocks for the uninitiated. By using BetterBatteryStats, one could see exactly which process is draining the battery, the wiki is hosted on github, and is available on the market here.
-
Funny you point to the same XDA thread I mentioned. I agree with you that the system should take better care (e.g. by releasing WakeLocks requested by apps which are no longer running). And that developers should take better care in coding (by explicitly releasing them at the appropriate states of the LifeCycle). But that doesn't help us users know. I hope my answer gives some insight in what a user can do -- and that one of you "techies" can fill the gap left! – Izzy Dec 7 '12 at 22:12
Check out Wakelock Detector: XDA-Developers / Google Play:
Wakelock detector groups the wakelocks of app into one expandable view for better look. And it shows which apps are running. And there are kill uninstall info buttons in expanded view of app.
Click image to enlarge. (Source: Google Play)
Disclosure: I am one of responsible developer for this app. Four more friends are with me working on this project as a hobby.
-
Thank you! That's a valuable information indeed. Would you mind to add some more details to your answer, e.g. what makes it so special? I would add some screenshots then. Until that's done: Here's the Playstore link to the app... – Izzy Mar 8 '13 at 10:23
Umm, and please "full disclosure": You are the developer of this app, right? :) Good work, btw! Included a hint with my answer as well, pointing to yours. – Izzy Mar 8 '13 at 10:50
Wakelock detector groups the wakelocks of app into one expandable view for better look. And it shows which apps are running. And there are kill uninstall info buttons in expanded view of app. – UzumApps Mar 9 '13 at 18:44
Yes. I am one of responsible developer for this app. Four more friends are with me working on this project as a hobby. – UzumApps Mar 9 '13 at 18:47
Thank you for your opinion, I will consider it and work on that. WLD looks good!!! :) – UzumApps Mar 10 '13 at 3:51 |
OBJECTIVE—To compare the efficacy, safety, and compliance of a nonremovable fiberglass cast boot and off-loading shoes in the treatment of diabetic plantar ulcers.
RESEARCH DESIGN AND METHODS—Patients (n = 93) with noninfected, nonischemic plantar ulcers were included in this prospective nonrandomized study. Treatment used a nonremovable fiberglass cast boot for longer standing and deeper ulcers (n = 42) and a half shoe or heel-relief shoe for other ulcers (n = 51). We evaluated off-loading therapy, compliance, and complications in both groups.
RESULTS—The healing rate was significantly higher with the cast boot than with the off-loading shoe (81 vs. 70%, P = 0.017), with healing times of 68.6 ± 35.1 vs. 134.2 ± 133.0 days, respectively, and hazard ratio 1.68 (95% CI 1.04–2.70); complete compliance with treatment was 98 vs. 10% (P = 0.001), respectively. Secondary osteomyelitis developed in 3 patients in the cast boot group and 13 patients in the off-loading shoe group (P = 0.026).
CONCLUSIONS—A nonremovable fiberglass cast boot was effective in healing diabetic plantar ulcers and in decreasing the risk of secondary osteomyelitis. The cast boot forced compliance with off-loading, thus promoting healing.
Delayed healing of diabetic plantar ulcers is caused primarily by inadequate or inappropriate wound off-loading. It has been suggested that “untreated ulcer” may be a better term than “recalcitrant ulcer” when off-loading is suboptimal (1).
Neuropathy is the main cause of plantar ulcers in patients with diabetes. The wounds develop in insensitive areas subjected to excessive pressure (2). The loss of sensation in the foot results in diagnostic and therapeutic delays and is a major obstacle to compliance with treatments, particularly off-loading. Suboptimal off-loading is associated with an increased risk of wound infection. The infection can spread to the soft tissues, causing cellulitis of the foot, or to the underlying bone. Cellulitis and osteomyelitis can occur concomitantly; both complications greatly increase the risk of amputation.
Clinical studies have established that off-loading by a total contact cast (TCC) is the reference standard in the treatment of noninfected, nonischemic plantar ulcers related to diabetic neuropathy (39). Healing rates varied from 73 to 100% and mean time to healing from 37 to 65 days. The casts were closed and changed entirely every 5–7 days. In studies of other off-loading modalities, time to healing was 3.6 months with insoles (10), 90 days with a fiberglass boot (Scotchcast) (11), 56–70 days with half shoes, with 78% compliance as assessed during a telephone interview (12,13), and 10 months with a heat-molded bivalve orthosis (14).
Two randomized clinical trials (15,16) comparing off-loading devices have been published. In the earlier study (15), the healing rate was 90% with a mean time to healing of 42 days in the TCC group compared with only 32% and 65 days, respectively, in the control group treated with plastazote shoe inserts. Significantly fewer infections occurred in the TCC group (0 vs. 26%). Amputation was required in two control subjects and in none of the TCC patients. The second study (16) is a recent comparison of TCCs, removable cast walkers, and half shoes. Healing rates were 89.5, 65.0, and 58.3%, respectively, and the difference between TCC and the other two modalities was significant. Patients were significantly less active in the TCC group (600 daily steps) than in the removable cast walker group (767 daily steps) or the half-shoe group (1,461 daily steps).
Other off-loading modalities are bed rest and use of crutches or a wheelchair. Because patients do not easily perceive the benefits of these modalities, they have little motivation to accept the stringent discipline they require. The objective of this study was to compare the efficacy and safety of off-loading by a shoe with that of a nonremovable fiberglass cast boot (with a window cut over the ulcer and a double-incorporated heel) left in place until complete healing or treatment failure. We sought to determine whether a patient with a diabetic neuropathic ulcer could wear a fiberglass cast boot until complete healing without opening the cast and whether the healing rate would be faster by forced compliance than by more conventional off-loading treatment.
This prospective nonrandomized study was conducted from 1 January 1994 to 7 July 2000. From 1 January 1994 to 15 April 2000, 93 patients with a single plantar ulcer were included, 42 in the cast boot group and 51 in the shoe group. Data were collected prospectively using a standardized clinical report form. The date of study inclusion was defined as the date of off-loading initiation with either of the two methods under study (cast boot or off-loading shoe). The date of ulcer development was recorded as the date the patient reported noticing the ulcer for the first time.
Patients were eligible if they had diabetic neuropathy and a grade 1A plantar ulcer in the San Antonio classification (17) with no clinical or radiological evidence of infection or osteomyelitis and without severe peripheral arterial disease. No ulcer went to bone or tendon. Diabetic neuropathy was defined as insensitivity to the 10-g Semmes-Weinstein 5.07 monofilament (18) at the plantar aspects of the toes and metatarsal heads. The ulcers were located at the plantar aspect of the fore-, mid-, or hindfoot. The following characteristics were noted for each ulcer: location, duration, maximum depth measured using a sterile metallic probe, and greatest length and width measured using a ruler graduated at 1-mm intervals and placed on sterile tracing paper applied over the wound.
Exclusion criteria were severe peripheral arterial disease, osteomyelitis, and cellulitis. We included patients with moderate peripheral arterial disease in the two groups. Moderate peripheral arterial disease was defined as the presence of at least one of the following criteria: no posterior tibial and/or pedal pulsations by palpation with arterial lesions by Doppler ultrasound (but at least one of the three major leg arteries was detectable up to the foot), transcutaneous oxygen tension (TcPO2) between 20 and 30 mmHg, ankle-brachial index (ABI) between 0.5 and 0.9, history of revascularization and no ischemic trophic disorders, and no necrosis or gangrene. We considered an ABI >1.15 as unreliable. Peripheral arterial disease was considered severe if there was critical ischemia or a wound with gangrene or necrosis, TcPO2 <20 mmHg or failure of arterial doppler ultrasonography to detect a major leg artery, and severe arterial lesions by arteriography. Osteomyelitis was defined as contact with bone upon probing an inflammatory ulcer with a blunt-tipped metal probe or as radiographic evidence of bony erosion or joint involvement deep to the ulcer. The definition of cellulitis was infection of the subcutaneous tissue with local evidence of inflammation.
Off-loading of the ulcer was provided to all patients. Two methods were used to achieve off-loading. Patients with an ulcer of >6 months’ duration with failure of off-loading shoe treatment, those with a midfoot ulcer and Charcot neuroarthropathy, and those who declined to wear an off-loading shoe were treated with a below-knee nonremovable fiberglass cast boot in which a window was cut at the site of the ulcer (cast boot group) (Fig. 1). In the shoe group, we included patients with an ulcer of <6 months’ duration without Charcot foot or who refused the cast boot treatment (shoe group). The type of shoe was selected according to the location of the ulcer. Written and oral detailed explanations on treatment with the cast boot or the off-loading shoe were provided, and patient oral consent was obtained before inclusion in one group.
All fiberglass cast boots were made by the same two operators with extreme care, according to strictly defined rules. The foot was padded using four Soffban bandages (Smith and Nephew) 15 cm in width and 2.7 m in length. Bony prominences were padded by five bandage layers. The bandages were covered by a water-repellent stockinette. A 1-cm layer of cotton was placed beneath the plantar arch. Additional padding by three layers of bandage was used at the proximal and distal parts of the cast boot to protect the skin from the sharp edges of the fiberglass. Either Dynacast (Smith and Nephew) or Scotchcast (3M) fiberglass was used, with bands measuring 10, 7.5, and 5 cm. The toes were left free. A double rubber heel was placed at the plantar aspect of the cast boot opposite the site of fore- or hindfoot ulcers or on either side of midfoot ulcers. A window was cut in the cast boot at the ulcer site to allow daily wound assessment and care. The rubber heels were sufficiently high to ensure full protection of the ulcer from pressure and friction during walking. The total time needed to fashion the cast boot ranged from 60 to 90 min. The fiberglass cast boot was worn without opening until complete ulcer healing or until an event occurred that required emergency treatment for intolerance, arterial or venous thrombosis, ulcer formation, or secondary osteomyelitis.
Two types of off-loading shoes were used. For ulcers under the forefoot or toes, we chose the Barouk half shoe, which has a heel 6 cm in height extending from the posterior edge of the foot to the midfoot and stretches under the forefoot by means of a platform that remains a distance from the ground and supports a shaft. The Sanital heel-relief shoe was used in patients with ulcers under the hindfoot. This shoe places the foot in 20° equinus and has a Sanital plastazote insole with a posterior opening that leaves the posterior and plantar aspects of the heel unsupported. Each patient in the shoe group received a detailed prescription corresponding to the type of shoe that was recommended. Strong emphasis was put on the absolute necessity for the patient to use the shoe consistently during standing or ambulation at all times, even if for only a few seconds. Patients in both groups were advised to use crutches, particularly during the initial period of acclimatization to the off-loading device.
All patients received daily local care delivered at home by a nurse. The ulcer was cleansed with saline and then covered with a gauze square saturated with petroleum jelly. Antibiotics were not given during the treatment. Employed patients were asked to stop work.
Follow-up for all patients was conducted at our Diabetic Foot Clinic at 2-week intervals for a clinical examination, monitoring of home care, and wound debridement. Additional visits occurred at the slightest suspicion of an emergency. Patients with complications were admitted. At each visit, osteomyelitis was sought by determining whether a sterile metal probe inserted into the ulcer made contact with bone. Healing was defined as complete epithelialization, with no drainage or sinus tract.
The treatment period stopped when healing was achieved or when treatment failed (complications or absence of healing at study end). Care was taken to record any adverse events that occurred during this treatment, such as wounds caused by the cast boot or off-loading shoe, secondary osteomyelitis, ischemia, cellulitis, and deep vein thrombosis. Compliance with the off-loading treatment was assessed at each 2-week visit by asking the patient to complete a brief questionnaire. The semiquantitative score on the questionnaire ranged from 0 (no use at all) to 3 (use as directed).
### Statistics.
Data were analyzed using the SAS software version 8 on a personal computer. Comparability of the two groups at study inclusion was evaluated using t tests (Mann-Whitney for nonnormal data) and χ2 tests (Fisher’s exact test for small samples). Kaplan-Meier curves were drawn to compare the healing rates for the two treatment groups. The Cox model was used to test whether the healing rate differed between the treatment groups after accounting for other prognostic factors.
The characteristics of the patients in the cast boot and off-loading shoe treatment groups were different at inclusion for width and depth of the wound, ulcer duration, and ulcer site (Table 1). These data were tested in the Cox model with data that were almost significant (age and length of the ulcer). We included the patient’s age in the analysis, which was the only factor other than treatment group that was statistically prognostic of healing. The healing rate was significantly higher with the cast boot than with the off-loading shoe (81 vs. 70%, respectively). The age-adjusted hazard ratio for healing in patients treated with a cast boot, as compared with the off-loading shoe, was 1.68 (95% CI 1.04–2.70, P = 0.017). The mean time to healing was 68.6 ± 35.1 days in the cast boot group compared with 134.2 ± 133.0 days in the off-loading shoe group, as seen in the healing rate curves (Fig. 2).
No patients were excluded from the study. As soon as a patient was included in the study, there were no changes in his treatment (cast boot or off-loading shoe) before complete healing. Data were analyzed using the intent-to-treat approach; thus, one patient who removed his cast boot was kept in the analysis and classified as a treatment failure.
In the cast boot group, eight patients failed treatment. All eight failures were related to complications: an ulcer caused by the fiberglass in five patients (secondary edema of the distal foot was a predisposing factor), secondarily diagnosed osteomyelitis in two patients, and a compound toe fracture with secondary osteomyelitis in one patient. However, because the patients were monitored daily, the cast boot–induced lesions were promptly detected and remained shallow; three patients achieved complete healing of the boot-induced ulcer after topical treatment in a mean 150 days (and the initial ulcer also healed in this period), and one patient died from a myocardial infarction. The remaining patient made no change in his daily activities, which included yard work (e.g., digging up a 1,500-m2 plot with the cast boot on). After removal of the cast boot, the ulcer was not healed, but he did not use the off-loading shoe prescribed to him.
In the shoe group, new ulcers did not develop in any of the patients, but 15 treatment failures were recorded. Two patients did not achieve healing at the end of the study. Of the remaining 13 patients, osteomyelitis developed and was responsible for secondary worsening of the ulcer for 13 of 51 (25%) in the shoe group compared with 3 of 42 (7%) in the cast boot group (P = 0.026). Three patients in the shoe group experienced secondary exacerbation of ischemia (by osteomyelitis) compared with none in the cast boot group. There was no deep vein thrombosis or secondary cellulitis in both groups. Compliance with off-loading was significantly better in the cast boot group than in the shoe group (P = 0.001) because all patients were compliant except one who removed the cast boot himself (Table 2). Compliance with off-loading shoe use was complete in 9.8% (5 of 51) of patients and acceptable in 31.3% (16 of 51), yielding an overall compliance rate of 41.1% (21 of 51). In addition, 58.9% (30 of 51) of patients removed the shoe for walking long distances.
We compared two off-loading methods in the treatment of diabetic plantar ulcers. Although assignment was not randomized, we minimized potential bias by including the patient’s age in the analysis, the only factor other than treatment group statistically prognostic of healing. Cast boot treatment was more likely to be offered to patients with older, wider, and deeper ulcers and Charcot foot, which carries a higher risk of failing to heal, of infection, and of amputation (19). This feature of the study design decreased the likelihood of finding greater benefits in the cast boot group.
The efficacy of off-loading by TCC has been firmly established (311). Whereas casts are usually changed during follow-up visits (4), we did not remove the cast boot until primary healing or treatment failure, whichever occurred first. Evaluation of safety was an important goal that was achieved by cutting a window in the cast boot at the site of the ulcer. The double heel allowed the patients to walk without putting pressure on the ulcer.
In our study, the healing rate was significantly higher with a shorter time to healing in the cast boot group than in the shoe group, which is consistent with earlier data (1113,15,16). We offered the nonremovable, windowed, fiberglass off-loading cast boot as a last-resort treatment to patients with persistent ulcers despite local care and advice about pressure relief that was usually delivered somewhere other than at our center. These patients had longstanding ulcers; ulcer duration was within the range of the longest ulcer durations reported in the literature (20). Although noncompliance was not assessed objectively before inclusion into the cast boot group, patients whose history indicated a high degree of noncompliance were offered cast boot treatment.
Although cast boots provide high healing rates because they effectively relieve pressure on the ulcer site, they can create new ulcers (9) and can be difficult to fashion and monitor. In our study, the nurse who provided local care was able to assess the wound on a daily basis because a window was cut over the ulcer site and the toes were left free. This allowed rapid treatment of adverse events and provided acceptable safety conditions for leaving the cast boot on until complete ulcer healing. Furthermore, the window allowed the application of modern localized treatments that are intended for daily use.
Five ulcers occurred from friction against the cast boot, even though the cast boots were fashioned with great care and liberal padding was used to protect the skin. The cast boot–induced ulcer rate would probably have been higher had these precautions not been taken. Thus, thorough training of physicians or technicians in proper cast application is essential to reduce the risk of ulceration. The cast boot was bigger than a usual TCC, but the liberal padding with Soffban allowed us to not open it until complete healing. The toes were not enclosed in the boot. A trauma-related toe fracture occurred in one of our patients. However, leaving the toes free allowed monitoring of the distal foot.
The secondary osteomyelitis rate was higher in the shoe group than in the cast boot group. Thus, our findings are in keeping with earlier data showing that cast boot therapy reduces adverse outcomes, most notably osteomyelitis (6).
In earlier studies (4,9,10,21), compliance was often found to be poor but was rarely evaluated using objective criteria. We used a scale to improve the objectivity of compliance assessment. We sought to determine whether compliance with off-loading was associated with the healing rate. The frequent failure to comply with off-loading shoe use was disappointing because these patients received extensive education about pressure relief at study initiation and reinforcement at each follow-up visit. In this group with poor compliance, the healing rate was significantly lower than that of the cast boot group. Compliance was excellent in the cast boot group, even though a history of noncompliance was among the criteria used to select patients for cast boot treatment. These results illustrate the ability of boot casting to force compliance (11). The health care providers should give detailed explanations to the patients about the potential benefits of off-loading.
We did not measure the level of physical activity of the patients. TCC has been reported to reduce activity (11). The cast boot forces the patient to reduce daily activities. A brace or shoe can be easily removed and, consequently, does not have the same activity-reducing effect.
The direct cost of cast boot treatment in our study was lower than when the cast boot is changed every week. The cost of the daily local care, about $11.60 (∈10.60) per day, delivered to our patients should be added to the cost of making the boot (fiberglass and Soffban cost about$134.20 [∈122.00]) or the cost of a shoe ($50.27 [∈45.70]). Mean total cost of 68.6 days of primary treatment was$934.07 (∈849.16) for the cast boot and \$1,467.70 (∈1,614.47) (for 134.2 days) for the shoe.
Acceptability of the cast boot was excellent in our study. The patients’ awareness that their desperately chronic wound was receiving the same level of care as an acute disease probably promoted compliance.
We use the following strategy for managing diabetic plantar ulcers. When the ulcer is under the hind- or midfoot, our reference standard is the cast boot. When the ulcer is under the forefoot, we evaluate the potential for compliance. When good compliance is anticipated or when the time since ulcer formation is <3 months, we start with an off-loading shoe and reevaluate treatment at 2-week intervals. Conversely, when fair or poor compliance is anticipated, we recommend first-line treatment with a cast boot without waiting 6 months.
Currently available off-loading shoes (22) are not completely satisfactory. They afford less pressure relief than a cast boot, and their acceptability is poor. The efficacy of these shoes should be evaluated on not only decreased pressure at the ulcer site but also good patient acceptability and compliance. For us, the nonremovable fiberglass cast boot remains the reference standard for the treatment of diabetic plantar ulcers because it offers satisfactory off-loading and high compliance and decreases the risk of secondary deep tissue infection.
Figure 1—
Ulcer of the midfoot treated with a cast boot.
Figure 1—
Ulcer of the midfoot treated with a cast boot.
Close modal
Figure 2—
Comparison of the treatments.
Figure 2—
Comparison of the treatments.
Close modal
Table 1—
Clinical characteristics of patients at recruitment
n 42 51 —
Age (years) 58 ± 11 62 ± 7 NS
Men 38 (90.5) 40 (78.4) NS
Type 1 diabetes 6 (14.3) 12 (23.5) NS
Diabetes duration (years) 17 ± 11 15 ± 10 NS
BMI (kg/m228.55 ± 3.42 29.06 ± 4.76 NS
Retinopathy 31 (74) 37 (73) NS
Peripheral arterial disease 23 (55) 22 (43) NS
Neuropathy 42 (100) 49 (96) NS
HbA1c (%) 7.85 ± 2.7 8.18 ± 1.6 NS
Creatinine (μmol/l) 119 ± 205 163 ± 200 NS
Ulcer length (mm) 20.43 ± 12.06 15.61 ± 12.31 NS
Ulcer width (mm) 13.8 ± 7.71 10.21 ± 9.12 0.045
Ulcer depth (mm) 5.42 ± 5.35 3.37 ± 3.16 0.03
Ulcer duration >6 months 20 (48) 9 (18) 0.002
Ulcer duration (days) 395 ± 560 134 ± 272 0.0078
Ulcer under the forefoot 35 (83) 49 (96) —
Ulcer under the midfoot (Charcot deformity) 4 (10) 0.0439
Ulcer under the hindfoot 3 (7) 2 (4) —
n 42 51 —
Age (years) 58 ± 11 62 ± 7 NS
Men 38 (90.5) 40 (78.4) NS
Type 1 diabetes 6 (14.3) 12 (23.5) NS
Diabetes duration (years) 17 ± 11 15 ± 10 NS
BMI (kg/m228.55 ± 3.42 29.06 ± 4.76 NS
Retinopathy 31 (74) 37 (73) NS
Peripheral arterial disease 23 (55) 22 (43) NS
Neuropathy 42 (100) 49 (96) NS
HbA1c (%) 7.85 ± 2.7 8.18 ± 1.6 NS
Creatinine (μmol/l) 119 ± 205 163 ± 200 NS
Ulcer length (mm) 20.43 ± 12.06 15.61 ± 12.31 NS
Ulcer width (mm) 13.8 ± 7.71 10.21 ± 9.12 0.045
Ulcer depth (mm) 5.42 ± 5.35 3.37 ± 3.16 0.03
Ulcer duration >6 months 20 (48) 9 (18) 0.002
Ulcer duration (days) 395 ± 560 134 ± 272 0.0078
Ulcer under the forefoot 35 (83) 49 (96) —
Ulcer under the midfoot (Charcot deformity) 4 (10) 0.0439
Ulcer under the hindfoot 3 (7) 2 (4) —
Data are means ± SD or n (%).
Table 2—
ComplianceCast bootShoe
Level 3: Use of the off-loading device whenever weight is borne on the foot. 41 (97.6) 5 (9.8)
Level 2: Use of the off-loading device during walking, except over short distance (e.g., to use the bathroom at night). 16 (31.3)
Level 1: Use of the off-loading device only for walking short distances during the day (or to use the bathroom at night), but no use outside the home, particularly when driving. 28 (55)
Level 0: Off-loading device removed by the patient or very rarely used. 1 (2.3) 2 (3.9)
Total 42 51
ComplianceCast bootShoe
Level 3: Use of the off-loading device whenever weight is borne on the foot. 41 (97.6) 5 (9.8)
Level 2: Use of the off-loading device during walking, except over short distance (e.g., to use the bathroom at night). 16 (31.3)
Level 1: Use of the off-loading device only for walking short distances during the day (or to use the bathroom at night), but no use outside the home, particularly when driving. 28 (55)
Level 0: Off-loading device removed by the patient or very rarely used. 1 (2.3) 2 (3.9)
Total 42 51
Data are n (%). P = 0.001.
A table elsewhere in this issue shows conventional and Système International (SI) units and conversion factors for many substances.
We are indebted to Dr. Beverley Balkau, Dr. Joël Coste, and Dr. Dominique Simon for reviewing the manuscript and statistical analysis.
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# Breakthrough DNA Editor Born of Bacteria
Interest in a powerful DNA editing tool called CRISPR has revealed that bacteria are far more sophisticated than anyone imagined.
Photo by Eric Erbe, Colorization by Christopher Pooley. USDA.
Microbes such as E. coli may use CRISPR as a weapon in their millions-year-old struggle against viruses.
22
On a November evening last year, Jennifer Doudna put on a stylish black evening gown and headed to Hangar One, a building at NASA’s Ames Research Center that was constructed in 1932 to house dirigibles. Under the looming arches of the hangar, Doudna mingled with celebrities like Benedict Cumberbatch, Cameron Diaz and Jon Hamm before receiving the 2015 Breakthrough Prize in life sciences, an award sponsored by Mark Zuckerberg and other tech billionaires. Doudna, a biochemist at the University of California, Berkeley, and her collaborator, Emmanuelle Charpentier of the Helmholtz Centre for Infection Research in Germany, each received $3 million for their invention of a potentially revolutionary tool for editing DNA known as CRISPR. Doudna was not a gray-haired emerita being celebrated for work she did back when dirigibles ruled the sky. It was only in 2012 that Doudna, Charpentier and their colleagues offered the first demonstration of CRISPR’s potential. They crafted molecules that could enter a microbe and precisely snip its DNA at a location of the researchers’ choosing. In January 2013, the scientists went one step further: They cut out a particular piece of DNA in human cells and replaced it with another one. In the same month, separate teams of scientists at Harvard University and the Broad Institute reported similar success with the gene-editing tool. A scientific stampede commenced, and in just the past two years, researchers have performed hundreds of experiments on CRISPR. Their results hint that the technique may fundamentally change both medicine and agriculture. Some scientists have repaired defective DNA in mice, for example, curing them of genetic disorders. Plant scientists have used CRISPR to edit genes in crops, raising hopes that they can engineer a better food supply. Some researchers are trying to rewrite the genomes of elephants, with the ultimate goal of re-creating a woolly mammoth. Writing last year in the journal Reproductive Biology and Endocrinology, Motoko Araki and Tetsuya Ishii of Hokkaido University in Japan predicted that doctors will be able to use CRISPR to alter the genes of human embryos “in the immediate future.” Cailey Cotner Jennifer Doudna received the$3 million Breakthrough Prize for her work using CRISPR to edit DNA.
Thanks to the speed of CRISPR research, the accolades have come quickly. Last year MIT Technology Review called CRISPR “the biggest biotech discovery of the century.” The Breakthrough Prize is just one of several prominent awards Doudna has won in recent months for her work on CRISPR; National Public Radio recently reported whispers of a possible Nobel in her future.
Even the pharmaceutical industry, which is often slow to embrace new scientific advances, is rushing to get in on the act. New companies developing CRISPR-based medicine are opening their doors. In January, the pharmaceutical giant Novartis announced that it would be using Doudna’s CRISPR technology for its research into cancer treatments. It plans to edit the genes of immune cells so that they will attack tumors.
But amid all the black-tie galas and patent filings, it’s easy to overlook the most important fact about CRISPR: Nobody actually invented it.
Doudna and other researchers did not pluck the molecules they use for gene editing from thin air. In fact, they stumbled across the CRISPR molecules in nature. Microbes have been using them to edit their own DNA for millions of years, and today they continue to do so all over the planet, from the bottom of the sea to the recesses of our own bodies.
We’ve barely begun to understand how CRISPR works in the natural world. Microbes use it as a sophisticated immune system, allowing them to learn to recognize their enemies. Now scientists are discovering that microbes use CRISPR for other jobs as well. The natural history of CRISPR poses many questions to scientists, for which they don’t have very good answers yet. But it also holds great promise. Doudna and her colleagues harnessed one type of CRISPR, but scientists are finding a vast menagerie of different types. Tapping that diversity could lead to more effective gene editing technology, or open the way to applications no one has thought of yet.
“You can imagine that many labs — including our own — are busily looking at other variants and how they work,” Doudna said. “So stay tuned.”
A Repeat Mystery
The scientists who discovered CRISPR had no way of knowing that they had discovered something so revolutionary. They didn’t even understand what they had found. In 1987, Yoshizumi Ishino and colleagues at Osaka University in Japan published the sequence of a gene called iap belonging to the gut microbe E. coli. To better understand how the gene worked, the scientists also sequenced some of the DNA surrounding it. They hoped to find spots where proteins landed, turning iap on and off. But instead of a switch, the scientists found something incomprehensible.
“If you’ve eaten yogurt or cheese, chances are you’ve eaten CRISPR-ized cells.”
Near the iap gene lay five identical segments of DNA. DNA is made up of building blocks called bases, and the five segments were each composed of the same 29 bases. These repeat sequences were separated from each other by 32-base blocks of DNA, called spacers. Unlike the repeat sequences, each of the spacers had a unique sequence.
This peculiar genetic sandwich didn’t look like anything biologists had found before. When the Japanese researchers published their results, they could only shrug. “The biological significance of these sequences is not known,” they wrote.
It was hard to know at the time if the sequences were unique to E. coli, because microbiologists only had crude techniques for deciphering DNA. But in the 1990s, technological advances allowed them to speed up their sequencing. By the end of the decade, microbiologists could scoop up seawater or soil and quickly sequence much of the DNA in the sample. This technique — called metagenomics — revealed those strange genetic sandwiches in a staggering number of species of microbes. They became so common that scientists needed a name to talk about them, even if they still didn’t know what the sequences were for. In 2002, Ruud Jansen of Utrecht University in the Netherlands and colleagues dubbed these sandwiches “clustered regularly interspaced short palindromic repeats” — CRISPR for short.
Jansen’s team noticed something else about CRISPR sequences: They were always accompanied by a collection of genes nearby. They called these genes Cas genes, for CRISPR-associated genes. The genes encoded enzymes that could cut DNA, but no one could say why they did so, or why they always sat next to the CRISPR sequence.
Three years later, three teams of scientists independently noticed something odd about CRISPR spacers. They looked a lot like the DNA of viruses.
“And then the whole thing clicked,” said Eugene Koonin.
At the time, Koonin, an evolutionary biologist at the National Center for Biotechnology Information in Bethesda, Md., had been puzzling over CRISPR and Cas genes for a few years. As soon as he learned of the discovery of bits of virus DNA in CRISPR spacers, he realized that microbes were using CRISPR as a weapon against viruses.
Koonin knew that microbes are not passive victims of virus attacks. They have several lines of defense. Koonin thought that CRISPR and Cas enzymes provide one more. In Koonin’s hypothesis, bacteria use Cas enzymes to grab fragments of viral DNA. They then insert the virus fragments into their own CRISPR sequences. Later, when another virus comes along, the bacteria can use the CRISPR sequence as a cheat sheet to recognize the invader.
Scientists didn’t know enough about the function of CRISPR and Cas enzymes for Koonin to make a detailed hypothesis. But his thinking was provocative enough for a microbiologist named Rodolphe Barrangou to test it. To Barrangou, Koonin’s idea was not just fascinating, but potentially a huge deal for his employer at the time, the yogurt maker Danisco. Danisco depended on bacteria to convert milk into yogurt, and sometimes entire cultures would be lost to outbreaks of bacteria-killing viruses. Now Koonin was suggesting that bacteria could use CRISPR as a weapon against these enemies.
To test Koonin’s hypothesis, Barrangou and his colleagues infected the milk-fermenting microbe Streptococcus thermophilus with two strains of viruses. The viruses killed many of the bacteria, but some survived. When those resistant bacteria multiplied, their descendants turned out to be resistant too. Some genetic change had occurred. Barrangou and his colleagues found that the bacteria had stuffed DNA fragments from the two viruses into their spacers. When the scientists chopped out the new spacers, the bacteria lost their resistance.
Barrangou, now an associate professor at North Carolina State University, said that this discovery led many manufacturers to select for customized CRISPR sequences in their cultures, so that the bacteria could withstand virus outbreaks. “If you’ve eaten yogurt or cheese, chances are you’ve eaten CRISPR-ized cells,” he said.
Cut and Paste
As CRISPR started to give up its secrets, Doudna got curious. She had already made a name for herself as an expert on RNA, a single-stranded cousin to DNA. Originally, scientists had seen RNA’s main job as a messenger. Cells would make a copy of a gene using RNA, and then use that messenger RNA as a template for building a protein. But Doudna and other scientists illuminated many other jobs that RNA can do, such as acting as sensors or controlling the activity of genes.
In 2007, Blake Wiedenheft joined Doudna’s lab as a postdoctoral researcher, eager to study the structure of Cas enzymes to understand how they worked. Doudna agreed to the plan — not because she thought CRISPR had any practical value, but just because she thought the chemistry might be cool. “You’re not trying to get to a particular goal, except understanding,” she said.
As Wiedenheft, Doudna and their colleagues figured out the structure of Cas enzymes, they began to see how the molecules worked together as a system. When a virus invades a microbe, the host cell grabs a little of the virus’s genetic material, cuts open its own DNA, and inserts the piece of virus DNA into a spacer.
As the CRISPR region fills with virus DNA, it becomes a molecular most-wanted gallery, representing the enemies the microbe has encountered. The microbe can then use this viral DNA to turn Cas enzymes into precision-guided weapons. The microbe copies the genetic material in each spacer into an RNA molecule. Cas enzymes then take up one of the RNA molecules and cradle it. Together, the viral RNA and the Cas enzymes drift through the cell. If they encounter genetic material from a virus that matches the CRISPR RNA, the RNA latches on tightly. The Cas enzymes then chop the DNA in two, preventing the virus from replicating.
This video illustrates how CRISPR and Cas9 can help microbes fight viruses and how researchers might use that system to edit human genes.
As CRISPR’s biology emerged, it began to make other microbial defenses look downright primitive. Using CRISPR, microbes could, in effect, program their enzymes to seek out any short sequence of DNA and attack it exclusively.
“Once we understood it as a programmable DNA-cutting enzyme, there was an interesting transition,” Doudna said. She and her colleagues realized there might be a very practical use for CRISPR. Doudna recalls thinking, “Oh my gosh, this could be a tool.”
It wasn’t the first time a scientist had borrowed a trick from microbes to build a tool. Some microbes defend themselves from invasion by using molecules known as restriction enzymes. The enzymes chop up any DNA that isn’t protected by molecular shields. The microbes shield their own genes, and then attack the naked DNA of viruses and other parasites. In the 1970s, molecular biologists figured out how to use restriction enzymes to cut DNA, giving birth to the modern biotechnology industry.
In the decades that followed, genetic engineering improved tremendously, but it couldn’t escape a fundamental shortcoming: Restriction enzymes did not evolve to make precise cuts — only to shred foreign DNA. As a result, scientists who used restriction enzymes for biotechnology had little control over where their enzymes cut open DNA.
The CRISPR-Cas system, Doudna and her colleagues realized, had already evolved to exert just that sort of control.
To create a DNA-cutting tool, Doudna and her colleagues picked out the CRISPR-Cas system from Streptococcus pyogenes, the bacteria that cause strep throat. It was a system they already understood fairly well, having worked out the function of its main enzyme, called Cas9. Doudna and her colleagues figured out how to supply Cas9 with an RNA molecule that matched a sequence of DNA they wanted to cut. The RNA molecule then guided Cas9 along the DNA to the target site, and then the enzyme made its incision.
Using two Cas9 enzymes, the scientists could make a pair of snips, chopping out any segment of DNA they wanted. They could then coax a cell to stitch a new gene into the open space. Doudna and her colleagues thus invented a biological version of find-and-replace — one that could work in virtually any species they chose to work on.
As important as these results were, microbiologists were also grappling with even more profound implications of CRISPR. It showed them that microbes had capabilities no one had imagined before.
Before the discovery of CRISPR, all the defenses that microbes were known to use against viruses were simple, one-size-fits-all strategies. Restriction enzymes, for example, will destroy any piece of unprotected DNA. Scientists refer to this style of defense as innate immunity. We have innate immunity, too, but on top of that, we also use an entirely different immune system to fight pathogens: one that learns about our enemies.
This so-called adaptive immune system is organized around a special set of immune cells that swallow up pathogens and then present fragments of them, called antigens, to other immune cells. If an immune cell binds tightly to an antigen, the cell multiplies. The process of division adds some random changes to the cell’s antigen receptor genes. In a few cases, the changes alter the receptor in a way that lets it grab the antigen even more tightly. Immune cells with the improved receptor then multiply even more.
This cycle results in an army of immune cells with receptors that can bind quickly and tightly to a particular type of pathogen, making them into precise assassins. Other immune cells produce antibodies that can also grab onto the antigens and help kill the pathogen. It takes a few days for the adaptive immune system to learn to recognize the measles virus, for instance, and wipe it out. But once the infection is over, we can hold onto these immunological memories. A few immune cells tailored to measles stay with us for our lifetime, ready to attack again.
CRISPR, microbiologists realized, is also an adaptive immune system. It lets microbes learn the signatures of new viruses and remember them. And while we need a complex network of different cell types and signals to learn to recognize pathogens, a single-celled microbe has all the equipment necessary to learn the same lesson on its own.
A New Kind of Evolution
CRISPR is an impressive adaptive immune system for another reason: Its lessons can be inherited. People can’t pass down genes for antibodies to their children because only immune cells develop them. There’s no way for that information to get into eggs or sperm. As a result, children have to start learning about their invisible enemies pretty much from scratch.
CRISPR is different. Since microbes are single-celled organisms, the DNA they alter to fight viruses is the same DNA they pass down to their descendants. In other words, the experiences that these organisms have alter their genes, and that change is inherited by future generations.
For students of the history of biology, this kind of heredity echoes a largely discredited theory promoted by the naturalist Jean-Baptiste Lamarck in the early 19th century. Lamarck argued for the inheritance of acquired traits. To illustrate his theory, he had readers imagine a giraffe gaining a long neck by striving to reach high branches to feed on. A nervous fluid, he believed, stretched out its neck, making it easier for the giraffe to reach the branches. It then passed down its lengthened neck to its descendants.
The advent of genetics seemed to crush this idea. There didn’t appear to be any way for experiences to alter the genes that organisms passed down to their offspring. But CRISPR revealed that microbes rewrite their DNA with information about their enemies — information that Barrangou showed could make the difference between life and death for their descendants.
Did this mean that CRISPR meets the requirements for Lamarckian inheritance? “In my humble opinion, it does,” said Koonin.
But how did microbes develop these abilities? Ever since microbiologists began discovering CRISPR-Cas systems in different species, Koonin and his colleagues have been reconstructing the systems’ evolution. CRISPR-Cas systems use a huge number of different enzymes, but all of them have one enzyme in common, called Cas1. The job of this universal enzyme is to grab incoming virus DNA and insert it in CRISPR spacers. Recently, Koonin and his colleagues discovered what may be the origin of Cas1 enzymes.
Along with their own genes, microbes carry stretches of DNA called mobile elements that act like parasites. The mobile elements contain genes for enzymes that exist solely to make new copies of their own DNA, cut open their host’s genome, and insert the new copy. Sometimes mobile elements can jump from one host to another, either by hitching a ride with a virus or by other means, and spread through their new host’s genome.
Koonin and his colleagues discovered that one group of mobile elements, called casposons, makes enzymes that are pretty much identical to Cas1. In a new paper in Nature Reviews Genetics, Koonin and Mart Krupovic of the Pasteur Institute in Paris argue that the CRISPR-Cas system got its start when mutations transformed casposons from enemies into friends. Their DNA-cutting enzymes became domesticated, taking on a new function: to store captured virus DNA as part of an immune defense.
While CRISPR may have had a single origin, it has blossomed into a tremendous diversity of molecules. Koonin is convinced that viruses are responsible for this. Once they faced CRISPR’s powerful, precise defense, the viruses evolved evasions. Their genes changed sequence so that CRISPR couldn’t latch onto them easily. And the viruses also evolved molecules that could block the Cas enzymes. The microbes responded by evolving in their turn. They acquired new strategies for using CRISPR that the viruses couldn’t fight. Over many thousands of years, in other words, evolution behaved like a natural laboratory, coming up with new recipes for altering DNA.
The Hidden Truth
To Konstantin Severinov, who holds joint appointments at Rutgers University and the Skolkovo Institute of Science and Technology in Russia, these explanations for CRISPR may turn out to be true, but they barely begin to account for its full mystery. In fact, Severinov questions whether fighting viruses is the chief function of CRISPR. “The immune function may be a red herring,” he said.
Severinov’s doubts stem from his research on the spacers of E. coli. He and other researchers have amassed a database of tens of thousands of E. coli spacers, but only a handful of them match any virus known to infect E. coli. You can’t blame this dearth on our ignorance of E. coli or its viruses, Severinov argues, because they’ve been the workhorses of molecular biology for a century. “That’s kind of mind-boggling,” he said.
It’s possible that the spacers came from viruses, but viruses that disappeared thousands of years ago. The microbes kept holding onto the spacers even when they no longer had to face these enemies. Instead, they used CRISPR for other tasks. Severinov speculates that a CRISPR sequence might act as a kind of genetic bar code. Bacteria that shared the same bar code could recognize each other as relatives and cooperate, while fighting off unrelated populations of bacteria.
But Severinov wouldn’t be surprised if CRISPR also carries out other jobs. Recent experiments have shown that some bacteria use CRISPR to silence their own genes, instead of seeking out the genes of enemies. By silencing their genes, the bacteria stop making molecules on their surface that are easily detected by our immune system. Without this CRISPR cloaking system, the bacteria would blow their cover and get killed.
“This is a fairly versatile system that can be used for different things,” Severinov said, and the balance of all those things may differ from system to system and from species to species.
If scientists can get a better understanding of how CRISPR works in nature, they may gather more of the raw ingredients for technological innovations. To create a new way to edit DNA, Doudna and her colleagues exploited the CRISPR-Cas system from a single species of bacteria, Streptococcus pyogenes. There’s no reason to assume that it’s the best system for that application. At Editas, a company based in Cambridge, Massachusetts, scientists have been investigating the Cas9 enzyme made by another species of bacteria, Staphylococcus aureus. In January, Editas scientists reported that it’s about as efficient at cutting DNA as Cas9 from Streptococcus pyogenes. But it also has some potential advantages, including its small size, which may make it easier to deliver into cells.
To Koonin, these discoveries are just baby steps into the ocean of CRISPR diversity. Scientists are now working out the structure of distantly related versions of Cas9 that seem to behave very differently from the ones we’re now familiar with. “Who knows whether this thing could become even a better tool?” Koonin said.
And as scientists discover more tasks that CRISPR accomplishes in nature, they may be able to mimic those functions, too. Doudna is curious about using CRISPR as a diagnostic tool, searching cells for cancerous mutations, for example. “It’s seek and detect, not seek and destroy,” she said. But having been surprised by CRISPR before, Doudna expects the biggest benefits from these molecules to surprise us yet again. “It makes you wonder what else is out there,” she said.
• David Konerding says:
I don’t think it’s true, as your title states, that nobody believed bacteria are sophisticated.
In fact, one of the primary motivations for recent work in developing minimal organisms is the recognition that E. Coli isn’t really well understood- even though it’s subject to an immense amount of experimentation, many of its most basic behaviors are just known via lab lore, and haven’t been probed at all.
People keep reporting (with surprise) that bacteria are found in ancient, inhospitable places. That’s because the entire world was transformed by, and is enervated with, bacteria, which have basically shaped the landscape, the sky, and everything underground too. They are far more complex, capable of rapid adaption as well as slow or no evolution, and moving into nearly any (even absurdly toxic) location.
• Anonymous says:
Carl, it’s great that you’re addressing the positive implications of this discovery, but what are the negative ones? Or are they too awful to name? Or do we already have enough biological tools for quietly doing damage to an individual or population, that this new-to-us one won’t really make a difference?
Who is looking at the downside of making the genome as easy to edit as it is to read? Would it be an ethics committee, or something stronger? Or is the academic genie out of the bottle, as it’s free to cavort with corporations right & left?
Do those who understand this new technology think that we are in over our species-maturity heads?
Or does it herald a utopia where everyone, no matter how genetically shortchanged, can get delivered the “smart, and kind too” genes?
Paging Ted Chiang…CRISPR’s implications are calling.
• Dr. Mito says:
Great article. The history of CRISPR-Cas is simply amazing. I am positive that a lot of research went into writing this article with such a comprehensive background. I agree that limitations could have been discussed to give a more balanced perspective. However, for a researcher starting to work with CRiSPR tech, this is a great resource. Will definitely recommend this article to my colleagues and use it as a primer to my research.
Please keep writing more articles like these.
Excellent article on complex science. Encouraging to see young scientists making exciting discoveries and being recognized for their work. I have patents and this is interesting, it is not an invention but research discovery that will change the world.
• Andy Briggs says:
What a great article about a subject I knew so little about. Congratulations on such a well-written, well-researched piece. Please keep us informed about new CRISPR developments because CRISPR is obvi0usly a huge mystery waiting to be unravelled……which of course makes for great science reading!
• Rose Campion says:
I was thinking, “damn, this is a well-written article”. Then I looked at the byline – well, of course. Congrats, CZ – job well done. You walk that line: being accessible without pandering, being technically accurate without devolving into mind-numbing detail, and strewn with clever asides (“when dirigibles ruled the skies”) that add color without being flip. Thank you.
PS: Have to note, it also presents Doudner and Charpentier in a non-sexist way – focusing completely on their accomplishment, without delving into their physical appearances, couture choices, ages, or familial statuses – pretty much what would be expected if they were XY scientists instead of XX ones. Kudos there as well.
• Joachim says:
Really great article! We also wrote a short review about CRISPR on our website (http://labiotech.eu/review-crispr-therapeutical-revolution/) but your writing style is really better, I love this article and I’ll recommend it to my team!
• eddy says:
Hmm, didn’t Carl Zimmer already write this same article for the NY Times almost a year ago?
http://www.nytimes.com/2014/07/17/science/a-call-to-fight-malaria-one-mosquito-at-a-time-by-altering-dna.html
“Although research on this procedure, known as Crispr, is in its infancy, the authors of the new papers say it warrants a public discussion right now. Using the approach to genetically engineer wild species could be a boon to humanity on some fronts, but it could also lead to a broad spectrum of unplanned ecological harm”, lather rinse repeat.
• Светлана says:
I think it is worth more global view of the issue. What will happen to mankind if we begin to change the DNA?
• Tina says:
There are definitely major implications for humanity as a whole when we learn how to harness the power of CRISPR for ourselves. Someone will definitely need to look at those, and with great power absolutely comes great responsibility. Something like this will likely need to be heavily regulated and protected.
As a person with chronic disease, however, I can’t help but immediately consider the benefits of having such mastery over our own DNA. Medicine has yet to sufficiently address the complexity of chronic disease. It’s bad enough that it is complex in one person, but for every person to have slightly different mechanisms and environment driving the same diseases is why medicine is pursuing the “personalized medicine” angle so fiercely. I’d like to think that if we can simply edit out the gene mutations we know are causing problems, we could…dare I say it…actually cure diseases that aren’t infectious for once.
I hope we make such progress within my lifetime. The effects of CRISPR would be vast and wide, and I hope while we are discussing the ethics of this, we will still use it to try and help those facing chronic illness right now…and argue about the details after the fact.
• Mott Greene says:
In re title
One may say “borne by” and one may say “born of” but not, I believe, “borne of.” Borne is the past tense of bear, ” to carry”, and “born” means something rather different, i.e. “brought into existence.” Probably both are true here- the bacteria carry them, and create them, but these are two different processes ( which is the point of the article in re bacterial vs out immune systems).
• Michael Moyer says:
@Mott Greene
Thanks for your comment re: “borne.” Both “borne” and “born” are past participles of the verb “bear.” Current American usage dictates that “born” be restricted to the single use of describing a birth in the passive voice (“she was born in 1999”). “Borne” is used in all other cases, including that of the past tense of bringing about, which is what our headline describes—how CRISPR was long ago “borne” of bacteria.
• ron fucci says:
Doesn’t this kind of discovery also lead to the question of what is a genome and what are the boundaries for a genome for an organism? Also when we say immunity and infection aren’t the same questions raised – that is – what we say is an ‘infection’ may be part of a generalized process of information sharing (horizontal gene transfer) between what we now call ‘organisms’? Can an ‘infection’ be ‘good’ or ‘normal’? Perhaps the knowledge of HGT may lead us to think that life is much bigger than any one organism – information encoded in genes is transferring across what appear to be organism boundaries – perhaps how it all works, including evolution, is not quite what it seems. And what we have now is an imperfect understanding of life and information transfer between the manifestations of life
• Aleck Alexopoulos says:
Another excellent and very informative article by CZ.
AA
• César Díez says:
"Three years later, three teams of scientists independently noticed something odd about CRISPR spacers. They looked a lot like the DNA of viruses.
'And then the whole thing clicked,' said Eugene Koonin.
At the time, Koonin, an evolutionary biologist at the National Center for Biotechnology Information in Bethesda, Md., had been puzzling over CRISPR and Cas genes for a few years. As soon as he learned of the discovery of bits of virus DNA in CRISPR spacers, he realized that microbes were using CRISPR as a weapon against viruses."
In some of those previous papers, the hypotesis of CRISPR as a immune system was clearly stated. It was not an idea of Kooning. For example you can read this abstract: http://www.ncbi.nlm.nih.gov/pubmed/15791728
In this paper we even stated that CRISPR mechanism could be similar to the functioning of iRNA. Kooning took that hypotesis to propose a role for Cas proteins according to iRNA mechanism, that turned out to be wrong.
I already had helped stablishing CRISPR as a family of repeats across Bacteria and Archaea, and had the idea of them functioning as an immune system. And I don't agree with others stealing the credit for that.
• Fantastic post but I was wondering if you could write a litte more on this topic?
I'd be very grateful if you could elaborate a little bit more.
Thanks!
• Denis DuBay says:
Would appreciate feedback if CZ or others could explain the specific role of the CRISPR sequence in this business? This article does an outstanding job of describing how the spacers and Cas genes work, but very little is said about the role of the CRISPR sequence itself.
Also, is anyone looking into whether remnant CRISPR-Cas-like assemblages exist (and function?!) in the human genome? If something this powerful is so ubiquitous in the bacterial genome, might it also exist in multicellular species, or do we have evidence it evolved in bacteria after the split that led to multicellularity?
Is CRISPR-Cas at all involved in enabling bacteria to swap genes with one another?
Finally, this seems to be such an effective and rapid evolutionary mechanism, do we have any evidence that it swamps traditionally-understood Darwinian selection that depends on random mutations and must work with entire populations over many generations) as an evolutionary force in the bacteria?
• Elena Sancho says:
Nice article. Have you seen recent review in Cell by Eric Lander
Eric Lander on the scientists that discovered CRISPR:
http://www.cell.com/cell/fulltext/S0092-8674(15)01705-5
Just like César Diez comments a lot of credit should be given to Mojica
http://www.ncbi.nlm.nih.gov/pubmed/15791728
• Callum says:
To state that no one actually invented Crsipr as a genome-editing tool is not true. While Crispr is a natural occurring system in prokaryotic cells it took some specific engineering to get it to work in eurokaryotic cells. The crispr scientists are using for genome editing is not the natural occurring. That would be like saying the aeroplane was not invented because birds can fly.
I think the bigger issue is why Crispr has received so much limelight compared to TALEN, and previously before that the engineered Zinc fingers. Sure it is easier but there are entire industries surrounding TALEN which does all the hard work for you. So then it is cheaper, meaning more labs have access to the technology. From the science communication it does seem that the message being put forward is that this is the first time humans can make site-specific genetic modifications rather than saying actually, this technology has been around for decades just it has got easier.
It terms of financial reward I can see why Berkeley and Broad are fighting it out in the courts but in terms of the scientific kudos, I don't get what the hype is all about. Especially since most of the hard work was done previously to the Berkeley and Broad groups.
For me the biggest conceptual jump and intellectual breakthrough was looking at these seemingly uninteresting interspersed repeated pieces of DNA and thinking it was a defence mechanism. One the biochemistry was elucidated was it really a massive conceptual leap or breakthrough for Doudna/Charpentier and Zhang to co-opt it into eukaryotic cells as genome-editing tool??
• Paul Cotter says:
A magnificent article – it makes a complex/complicated subject easy to understand.
It somewhat reaffirms what I am thinking: we are a minor subset in a sea of biological diversity.
We are a recent species to the Universe and our DNA & immune system hasn't had suffiencent time to mature (yet we are host to thousands of bacteria which are billions of years old).
You scientists need all the encouragement we can give you. Don't stop now – keep going.
• Angela Simms says:
I love this New Research, Between Bacteria & cells. all of your people done excellent work and would love to learn this. I know very complex but not hard to understand.I'll
back you people up at CRISPR Natural History.
• Anthony Cusano says:
This is a great discovery, but given the highly evolved and balanced complexity of the human, not to mention bacterial organism, the risks of CRISPR technology in suddenly altering that evolved balance are huge. I would say it is scientistic and promethean to believe that the use of CRISPR will progress risk free.
This could easily explain the Fermi paradox. Highly sophisticated civilizations never make it far enough to communicate with the rest of life in the universe because they discover technology that rapidly unravels the balance that evolution slowly brought to them. |
# Set histogram x axis digit number
ROOT Version: 6.12/06
Platform: macOS
Compiler: Not Provided
I’m trying controlling a histogram x axis digit numbers through hist->GetXaxis()->SetMaxDigits() or TGaxis gx = (TGaxis)hist->GetXaxis();gx->SetMaxDigits(); but only y axis takes effect even I get the x axis. Any way to set x axis digit number?
For example, I want to set the x axis 1.4 \times 10^-5 instead of 14 \times 10^-6
dyStats.pdf (14.4 KB)
@mhstar maybe this post can be helpful for you TGaxis::SetMaxDigits ?
Do you have a small reproducer showing this effect ?
Hi,
the axis labeling algorithm seems to allow only
“natural” exponents: e-3, e-6, e-9 etc
Try with the following:
root [13] auto h3 = new TH1F("hh3", "h3h", 100, 14e-4, 16e-4);
root [14] auto ax3 = h3->GetXaxis()
(TAxis *) @0x7ffdccdec1d8
root [15] h3->Draw()
root [16] ax3->SetMaxDigits(3)
root [17] ax3->SetMaxDigits(5)
root [18] ax3->SetMaxDigits(4)
(root 6.14.00)
Otto
Yes it works that way…
No, it doesn’t help. The way still works only for y axis not x axis.
Here I provide the data root file and the script to produce the plot. Thanks.
dyStats.cpp (3.1 KB)
dyStats.root (54.6 KB)
I try this, but it still works only for y axis not for x axis. Maybe it’s because I use root 6.12/06 version but you use root 6.14.00(which I noticed from your post)?
Anyway, I provide the data and the script to produce the graph, which makes your help more direct and convenient. Thank you.
dyStats.cpp (3.1 KB)
dyStats.root (54.6 KB)
with 6.15 (master) you macro gives me the following output. So the exponents are on the X axis.
Yes, that’s what I get too. I want to get x axis with order 10^-5 instead of 10^-6. That’s I’m trying to set the max digit of x axis. It’s the right way to get this by setting x axis max digit number?
Can you try it again after you uncomment line 95-96 to see the x axis takes effect or not? It takes effect on y axis which is very weird for me.
Why are you using a TExec ?
No, I don’t use that. That’s just a try from another suggestion, but it gives the same result which only takes effect on y axis too not on x axis.
Ok I simplified your macro to concentrate only on the axis topic. I ended up with this:
void dyStats(){
TCanvas *cc = new TCanvas("cc","cc",1000,600);
auto f = new TFile("dyStats.root");
auto cross = new TH1F("cross","cross",100,1.4e-5,1.57e-5);
TTree* cs = (TTree*)f->Get("dyStats");
cs->Draw("crossSection>>cross");
cross->SetXTitle("cross section(mb)");
cross->GetXaxis()->SetMaxDigits(7);
cross->GetYaxis()->SetMaxDigits(1);
}
I gave more freedom on the X axis (7 digits so the exponent disappeared) and less on the Y axis (only one digits so the exponent appear). The important thing to notice is that you are able to act on both axis independently .
1 Like
Could you test whether it works for cross->GetXaxis()->SetMaxDigits(2); that’s my ultimate goal.
Dear mhstar,
I am afraid you did not get the basics of my post:
The implemented algorithm c a n n o t produce
exponents like : 10-5, 10-2
only 10-3, 10-6, 10-9 etc
for whatever axis
Otto
Now I think I understand TGaxis::SetMaxDigits(). Thank you.
This topic was automatically closed 14 days after the last reply. New replies are no longer allowed. |
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In this section we see examples of how to use radians instead of degrees when finding the values of sin, cos, tan, csc, sec and cot of angles. The radian is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The whole-body exposure threshold for acute hematopoietic syndrome or "radiation sickness" is 500 mGy. Just a small tip that I use often when I have a large SQL Profiler trace. How to Memorize the Unit Circle. Here's my code so far:. Please enter a function, starting point, ending point, and how many divisions with which you want to use Trapezoidal Rule to evaluate. 2: Enter the value you want to convert (rad). Rad, gray, rem, sievert? Instantly convert any unit to all others. What is the radian measure of the. Program to Convert Radian to Degree Before moving to the actual solution, let's try to find out what is a degree, a radian, and their relations. Also, explore tools to convert degree or radian to other angle units or learn more about angle conversions. The CSV virtual table is useful to applications that need to bulk-load large amounts of comma-separated value content. Click on "Show" and "Hide" in each table cell to control which values are displayed. Explore the amplitude, period, and phase shift by examining the graphs of various trigonometric functions. By using compass, a protractor or a flexible ruler we can draw an arc in that can measure the length of an arc too from the bend existed in it. A great advantage of radians is that many formulas are much simpler when using them, typically all formulas relative to derivatives and integrals. Create a table of conversions from radians to degrees. (Note: You can use the "table" command in MATLAB to create a table. We usually use rectangular coordinates, that is, coordinates using the x and the y axis to plot points and describe functions, but certain functions get very complicated if we try to use these coordinates on the Cartesian graph. The composition of base units that comprise the unit in question. Tasting Table serves genuine editorial. The size of the angle is entered in degree or radian measure, depending on the setting of the calculator. Most likely, it will ask you to manipulate them in algebraic equations, often with the goal of simplifying the expression down to its simplest form. Equations, expressions, points, and lists of points can be converted to a table. Simpli Home Avalon Faux Leather Coffee Table Storage Ottoman in Black If you are looking for Simpli Home Avalon Faux Leather Coffee Table Storage Ottoman in Black Yes you see this. The Round Table was first mentioned by the French poet, Wace, in 1155 and in that account was made round so that all the knights seated around it would have the same stature – a table with no head to sqabble over. Examples. Between mrad and ' , MOA measurements conversion chart page. TO LEARN COORDINATES: Hide coordinates by clicking the box next to COORD. 2 Angles and Radian Measure EEssential Questionssential Question How can you fi nd the measure of an angle in radians? Let the vertex of an angle be at the origin, with one side of the angle on the positive. Or paste it to the search string. Great Prices. RAD tools have proven to be successful all over the world in such industries as oil & gas, petrochemical, mining, aerospace, power generation and manufacturing. Converting Between Radians and Degrees. If R contains complex elements, rad2deg converts the real and imaginary parts separately. 67 rad, how far is she from the center of the merry - go- round. Welcome to UnitConversion. An active and friendly community with more than 90k developers. Up To 70% Off Everything Home! 2-Day Shipping. JTable does not contain or cache data; it is simply a view of your data. 03553: 1: 0. This is an online trigonometry calculator to find out the equivalent values of radians and degrees for the given number. You can browse for and follow blogs, read recent entries, see what others are viewing or recommending, and request your own blog. Auto Tables for RAD Server is an automated solution for generating a REST API for your database. Find here the chart for sin, cos, tan, cosec, sec and cot at various degree of angles. It is celebrated on the week of November 8 to commemorate the discovery of the X-ray by Wilhelm Conrad Roentgen on November 8, 1895. RAD Torque Systems is a leading Canadian manufacturer of pneumatic, battery powered, and electronic pistol grip torque wrenches. These functions cannot be used with complex numbers; use the functions of the same name from the cmath module if you require support for complex numbers. 7 dayx86,400sec/day) = WHAT is the angular speed of. radians = degrees × π / 180° Example. It's important to feel proud of the way your dining room looks and feels, whether it's just for you or the whole extended family. Radians If you are working in radians, recall that 360° is equal to 2π radians, and 180° is equal to π radians. Review of Trigonometric, Logarithmic, and Exponential Functions In this tutorial, we review trigonometric, logarithmic, and exponential functions with a focus on those properties which will be useful in future math and science applications. I know that I can just put a measurement of one line segment into the table, but as the polygon changes its number of sides, sometimes the line that was measured gets lost and then I lose the measurement. Knowing that 1 radian = 57. This calculator will walk you through approximating the area using Trapezoidal Rule. Convert to Table isn't available for Implicit expressions, parametric, and polar graphs. Default Converter. Although, VectorCircle at the least has to be a struct of 2 floats, u and v to store the cos and sin values. 66202 degree. ☀ Up To 70% Off Outdoor Console Tables ☀ Howard Series Steel Buffet & Console Table by RAD Furniture 5000 Brands All Your Home Styles And Budgets Of Furniture, Lighting, Cookware, And More. Radian and degree measures of angles. Again we can multiply by 180/ or use the fact that p radians is the same as 180°. Working closely with renowned designers such as Marcel Wanders, Kenzo Takada, Ora Ito, Cédric Ragot, Sacha Lakic, Christophe Delcourt and Stephen Burks and with Haute Couture fashion houses such as Jean Paul Gaultier, Missoni Home and Christian Lacroix Maison. This can happen, for example, when using inverse functions with arguments that are out of range. For example, 1 radian can be written as 1 rad, 1 c, 1 r, or 1 R. 67 rad and l = 2. CONVERSION TABLE A useful tilt at javascript: by Bill Taylor. ) In Exercises 1 and 2, find the circumference of the circle with the given radius r. 48x120x29″h, Buffed Steel texture. Updated frequently. The licensor cannot revoke these freedoms as long as you follow the license terms. The following picture shows the Below is a table of. (b) In practice, the symbols rad and sr are used where appropriate, but the derived unit "1" is generally omitted. Codeless databinding, rich client-side operations, and a myriad of features topped with unbeatable performance is what defines the Telerik RadGrid for ASP. All calculations are based on Radian's current rates and guidelines. And we now have our factor for conversion from radians to degrees since 1 * 57. Or paste it to the search string. She started with a plaid table topper and plaid napkins. How to Memorize the Unit Circle: Summary of how to remember the Radian Measures for each angle. Cos( Radians) Cot( Radians) Sin( Radians). Dimplex recently published two new online learning courses on the AEC Daily website, Electric Fireplaces: A Stylish, Simple and Safe Alternative. 5 /4 = 5∙180/4 = 225°. Although Radian Studio is not intended as a GIS, the visualization capabilities it incorporates for reviewing data provide many GIS-like benefits when working with spatial data. As 2π radians is the same as 360 the graph will be very similar to the graph for x in. Trigonometry Calculator. online searching has now gone a protracted method; it has changed the way customers and entrepreneurs do business these days. Many Other Conversions. ☀ Find Great Deals Outdoor Console Tables ☀ Howard Series Steel Buffet & Console Table by RAD Furniture Daily Sales And Home Decorating Ideas, Financing Available, 2-Day Shipping, Great Ways To Save. , 1 curie does not equal 1 becquerel, but they both measure the same parameter. These images can be viewed, manipulated, annotated, transmitted to other facilities, printed, animated and stored using the Opal-RAD suite. Having solid experience in web technologies, we designed our AJAX powered ASP. It doesn. A unit circle has a radius (r) of 1, which gives it a circumference of 2𝛑, since circumference = 2𝛑r. All of the angles used in these functions are based on radians instead of degrees (π radians = 180°). How to Calculate Radian to Degree. RAD has the LOWEST RATES of any Margarita Machine co in the region!! RAD Margarita Machines was founded in the 1990's in the Central Valley & quickly spread beyond the Sacramento Area. Excel's trig functions use radians rather than degrees because when the program was first created, the trig functions were designed to be compatible with the trig functions in the spreadsheet program Lotus 1-2-3, which also used radians and which dominated the PC spreadsheet software market at the time. You just put it out of your mind and let the calculator/computer do it's thing. In the example of 45 degrees in radians, one can simply reduce the equation of r = 45π / 180 to π/4, which is how you would leave the answer to express the value in radians. Alternately, 1 radian = 57. As both arc length and radius are measured with units of length, these units of length cancel when determining how many radians an angle is. The CSV virtual table is useful to applications that need to bulk-load large amounts of comma-separated value content. This type of neglect occurs when the individual does not form a healthy attachment to their caregiver or parent (typically their mother) before the age of five. 9578 degree ›› Want other units? You can do the reverse unit conversion from degree to radian, or enter any two units below:. Pics of : Sin Cos Table Radians. Below are trigonometric tables of all 6 trigonometric functions, with angles in degrees and radians. 30 degrees; one degree = 0. In the macrocosm of online shopping this is forging them thumping the outlier and non competitive. ☀ Price Sale Outdoor Console Tables ☀ Howard Series Steel Buffet & Console Table by RAD Furniture Explore A Wide Selection Of Living Room Furniture To Update Your Look, Fun New Items At Special Prices. 1 degrees to radians = 0. iPhone & Android app Angle tables Radians Radians to Degrees table Radians to Minutes (angular) table Radians to Seconds (angular) table Radians to Gradians table Radians to Milliradians (UK) table Radians to Milliradians (NATO) table Radians to Milliradians (US WW2) table Radians to Milliradians (USSR) table Radians to Sign table Radians to. Here's the expression: #color(white)=450^@# #=450^@color(blue. Shop Outdoor Console Tables [HOWARD SERIES STEEL BUFFET & CONSOLE TABLE BY RAD FURNITURE] with Best Furniture, Home Decorating Ideas, Cookware & More. This is why radians are dimensionless - there is no "unit" that describes what a radian measures, because it is a ratio of two different quantities with the same unit of measurement. The angle α in degrees is equal to the angle α in radians times 180 degrees divided by pi constant: α (degrees) = α (radians) × 180° / π. A conversion factor may be necessary when using different units of power or torque. Calculator note: Many calculators have degree, radian, and grad modes (360° = 2 p rad = 400 grad). Last game played with Proleter, which ended with result: Draw 1:1. If the girl's angular displacement is 1. I am trying to do a simple trigonometric calculation in C++. Members of a group typically have similar properties and electron configurations in their outer shell. All the targets in miRDB were predicted by a bioinformatics tool, MirTarget, which was developed by analyzing thousands of miRNA-target interactions from high-throughput sequencing experiments. The size of the angle is entered in degree or radian measure, depending on the setting of the calculator. That is, we can determine how fast the radian measure of the angle is changing as the object moves on its circular path. Grads to Radians Converter. pi radians=360 degrees. Using comment. A unit circle has a radius (r) of 1, which gives it a circumference of 2𝛑, since circumference = 2𝛑r. Then click the Convert Me button. (pi=180° ) The radian per second is also the unit of angular frequency. No matter where you are in Albany there is one place for high end home furniture. Using DataTable DAX Function for Creating Structured Table in Power BI. RAD products have proven to be successful all over the world in such industries as oil & gas, petrochemical, mining, aerospace, power generation and manufacturing. 9 – In Class Worksheet (Solutions) 1) An old record player rotates clockwise at 33 1/3 rpm (revolutions per minute). Instructions for use of the table and importing into a spreadsheet follow the table. Trigonometry Calculator. To convert from degrees to radians use: degrees * (pi / 180). But this thing is less than pi. Work on these values until you know them all!. Many Other Conversions. Bio-Rad offers a range of products and services for life science research and education, clinical diagnostics, biopharmaceutical processing, and food science. The unit circle allows you to easily see the relationship between cosine and sine coordinates of angles,. table default. [spHouses_GetNearZipcode] @Zipcode char(5), @Miles decimal(11,6) AS --Load close zipcodes into temp table SELECT ZIP. WWW Table of Radioactive Isotopes Radiation search Nuclide search Atomic data (X-rays and Auger electrons, very preliminary!) Periodic chart interface to the nuclides Summary drawings for A=1-277 (PDF) Nuclear charts (PDF, 333 kbyte) Database status. 1 degrees to radians = 0. The CSV virtual table reads RFC 4180 formatted comma-separated values, and returns that content as if it were rows and columns of an SQL table. Convert 1 ' , MOA into milliradian and minutes to mrad. Linear position. Shop Outdoor Console Tables [HOWARD SERIES STEEL BUFFET & CONSOLE TABLE BY RAD FURNITURE] with Best Furniture, Home Decorating Ideas, Cookware & More. If the RAD Transducer is to be stored prior to use, ensure that it is stored in a. New episodes Mondays. Radians can be abbreviated as rad, and are also sometimes abbreviated as c, r, or R. Converting degrees to radians and radians to degrees in C Degrees to radians The following C function receives an angle in degrees and returns the equivalent angle in radians. The following picture shows the Below is a table of. by the radian comma). This syntax creates a new table in SQL Server and loads your trace file into it: SELECT * INTO. 60 s by a motor exerting a constant torque. If we end up with the same number, then 5 radians and $$5\pi \text{ radians }$$ are the same. Departments handling trauma and emergency cases may prefer elevating tables because the table height can be adjusted to facilitate patient transfer from a mobile stretcher or a wheelchair. Rad Power is a featured online retailer so not only do you get top notch tech support and a 1 year warranty, but they also have also partnered with Velofix. org is the ultimate resource for unit conversion. Two linkage maps were constructed, one with a reference genome and another, termed as de novo identification of single nucleotide polymorphism (SNP) by RAD-seq, without a reference genome. This page calculates the altitude and azimuth of the Sun or Moon at multiple times during any day between 1700 and 2100. The Excel SIN function returns the sine of angle given in radians. The vertical lines are asymptotes of the graph. Remittance Advice Details (RAD) Electronic Correlation Table to remit elect corr9900. , #howard-series-steel-dining-table-by-rad-furniture # This Café Table is meant to weather the elements but can be used indoors as well. 1 UNITS AND CONVERSION FACTORS Table of Contents Section Page References 3 I. Latitude, ZIP. 1/10 tablets. To convert from degrees to radians use: degrees * (pi / 180). 10 radian to degree = 572. 30 degrees/radian. In the macrocosm of online shopping this is forging them thumping the outlier and non competitive. Additional information is supplied using remittance advice remarks codes whenever appropriate. RAD is the ONLY FULL-TIME Margarita Machine Rental company, so you can count on us. Free math lessons and math homework help from basic math to algebra, geometry and beyond. Radian is also a derived SI unit of angular measurement, and it is dimensionless. Most scientific calculators have function buttons to find the sine, cosine, and tangent of angles. Others are more subtle: The difference between the raw physical units describing radiation emitted by a radioactive material (measured in units like curies and becquerels), versus measurements designed to reflect the different amounts of radiation energy absorbed by a mass of material (measured in rad or gray), and those that measure the. table default. Will not work with Surface tablets running Windows RT. Its formula is: The Math IIC will rarely ask you to find the values of these three functions. For more information on C-RAD, please visit www. The Alzheimer’s Disease Neuroimaging Initiative (ADNI) unites researchers with study data as they work to define the progression of Alzheimer’s disease (AD). 15, 2019 /PRNewswire/ -- Global Digital genome Market is expected to cross USD 50. Here is the definition for an angle with a measure of 1 radian. If all goes smooth, we may see them live Friday (that is a big if). This can be done if you know the radius of the circle and the length of the arc of a circle. For the cosine, read up the last 6 columns. We can now find the values of the six trigonometric functions with x = −4, y = 3, and r = 5 as, Radian Measure We have not specifically discussed the angle θ yet, but it can be measured in degrees or in radians. #03 Calculate the Distance Between Two Latitude/Longitude Points using Plain SQL #04 What is the Difference Between the FIRST_ROWS Hint and ROWNUM in the WHERE Clause? #05 Install Nagios on a Synology DiskStation DS1813+ or DS412+ #34 Deadlock on Oracle 11g but Not on 10g #77 Book Review: Oracle Tuning: The Definitive Reference Second Edition. Angular velocity, in rad/s. In summary, degrees are the common way to measure angles, but radians are a mathematically preferable way to do so. These attributes are stored in the rad-crs-attr-dtl linked from the rad-course-mst by the course key. The Excel TAN function returns the tangent of angle given in radians. 57 steradians. Equations, expressions, points, and lists of points can be converted to a table. Explore the amplitude, period, and phase shift by examining the graphs of various trigonometric functions. This trigonometric table contains corners in degrees and radians, that very comfortably for translation of degrees in radians and vice versa, radians in degrees. Our conversions provide a quick and easy way to convert between Angle units. The following sheets list the key concepts which are taught in the specified math course. To set your graph to radians or degrees, click the Graph Settings wrench and click the appropriate. We constructed a RAD library using genomic DNA from a BC1 backcross population. This is counted in Measures Per Minute (mpm) or in Beats Per Minute (bpm). Radians are angular measurements based on pi and degrees, it is the unit of speed of revolution. Cotangent is the reciprocal of tangent. Any C library can store data into this table, but it should take care to choose keys different from those used by other libraries, to avoid collisions. Le tour par minute, abrégé en tr/min est une unité pour mesurer une vitesse de rotation [1]. In RAD Studio 10. 848137E-7 [rad/s2]. With cell frequencies of less than 1% you may want to stain and acquire more cells in order to collect enough cells. Image reproduction rights can be found in the link near the bottom of this description. How to Calculate Radian to Degree. Quick, free, online unit converter that converts common units of measurement, along with 77 other converters covering an assortment of units. And hope Now i am a section of helping you to get a greater product. using the same angle in radians and degrees. table default. SHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 15. This table may be downloaded and imported into a spreadsheet, math program or other computer codes, for use in your analyses. Stelrad Radiators is the UK's leading manufacturer of stylish modern radiators. It has all of the angles in Radians and Degrees. An example of possible entry data is 30 degrees and 30 minutes would be 30. Verify the RAD Transducer Model you received is the same as your purchase order specifies. Radians to Degrees conversion. Radians! If we convert degrees into radian measure, then we are allowed to treat trigonometric functions as functions with domains of real numbers rather than angles! What is a radian? Okay, so radian is an angle with vertex at the center of a circle that intercepts an arc on the circle equal in length to the radius of the circle. What should you know?. 34907 radians. 1/10 tablets. Please sign up to the mailing list to receive updates on new arrivals, special offers and other discount information. Table Of Contents 7. Ordering Information. Sorry, the GeoGebra Applet could not be started. SOME DERIVED SI UNITS QUANTITY UNITS SYMBOL BASIC UNITS Area square meter m2 Volume cubic meter m3 Frequency Hertz, cycles per second Hz 1/s Density kilogram per cubic meter kg/m3 Velocity meter/sec m/s Angular velocity radian/sec rad/s Acceleration meter/second squared m/s2 Angular acceleration radians per second square rad/s2 Volumetric flow rate cubic meter per second m3/s Mass flow rate kg. Any number can have different values of radians and degrees with respect to the trigonometric functions such as Sine(Sin), Cosine(Cos), Tangent(Tan), Cotangent(Cot), Secant(Sec), Cosecant(Cosec), etc. ToString( Table. The latest version of Rad Decay is currently unknown. This module is always available. When you buy a RAD Furniture Howard Series Metal Buffet & Console Table online from Wayfair, we make it as easy as possible for you to find out when your product will be delivered. Well, let's figure out the answer by converting 5 radians to degrees and $$5\pi \text{ radians }$$ to degrees. Physical Quantity. If you did not provide an Automated Underwriting System (AUS) response, this quote is based on an assumed AUS Approve/Eligible response. Over 7 Million Items. Pics of : Sin Cos Table Radians. 1 UNITS AND CONVERSION FACTORS Table of Contents Section Page References 3 I. The following is an example of the problem I am having with this. 01745 radians. It turns out that angles that have the same reference angles always have the same trig function values (the sign may vary). RAD Pneumatic Torque Wrench. If you're describing directions to me, I'd really rather you said, "Turn sixty degrees to the right when you pass the orange mailbox", rather than, "Turn (1/3)π radians" at that point. angleInRadians = degtorad since arc length can be a measure of distance in either radians or degrees, provided that the radius is known. Bpm and Mpm tables and counting. (Note: You can use the "table" command in MATLAB to create a table. Here's what you know, D q = 1. Table of Trig Function Values for Special Angles -- sidebar Why do we need to know this? The exact answers for the various trig functions for certain angles are very well known, and your teachers will expect you to know them. (Both labeled in radians) No other background grids. Red Table Talk. Killerspin Tables. #howard-series-steel-picnic-bench-by-rad-furniture #Outdoor-Benches Pairs perfectly with the perforated dining table, this bench stands on its own as well, indoors or out and in all types of weather. For example, if rotational speed (revolutions per time) is used in place of angular speed (radians per time), we multiply by a factor of 2 π radians per revolution. Convert just about anything to anything else. |
Sequences And Series Quiz Pdf
In this Python Sequence Tutorial, we will discuss 6 types of Sequence: String, list, tuples, Byte sequences, byte array, and range object. DNA with a higher GC-content will be harder to break apart. This blog is dedicated to a revision of the Python sequence and collections. • Sequence - Story Scramble - Practice putting a story in the right order. Objective examinations include multiple choice,. Logical analyzing flowchart and answers, a person needs to acquire consistent pattern and solve the problem. note 1 up to 7 or 7 down to 1) but with interruptions or "set backs" to make them sound more interesting. The Jet Propulsion Laboratory is a unique national research facility that carries out robotic space and Earth science missions. org are unblocked. 91-billion base pair (bp) consensus sequence of the euchromatic portion of the human genome was generated by the whole-genome shotgun sequencing method. 03/14/2017; 10 minutes to read +2; In this article. Offer chair assistance. Series (Find the sum) A finite Geometric Series (a limited number of terms, or Partial Sum) An infinite Geometric Series, if our infinite series is. We will see there are good reasons to start from 0 in Python. Interactive Number Sequence Activities (Up to 100, steps of up to 10) Addition Sequences (within 100) Write the Rule Subtraction Sequences (within 100) Write the Rule Addition / Subtraction Sequences (within 100) Write the Rule Addition Sequences (within 100) Subtraction Sequences (within 100). Example taken from our CCAT practice test (PDF) Answer and Explanation. Department of Education Contract No. Here are a set of practice problems for the Series and Sequences chapter of the Calculus II notes. Diagrammatic reasoning:. The missing number in this sequence 4, 7, __, 13 is The correct answer is: C. The teacher asked the boys if they ——————– the sums. Precalculus Sequences & Series Test Practice Name_____ Sequence Formulas: a n = a 1 + d (n - 1) 1 1 n a a r n Series Formulas : 1 (1 ) 1 n n ar S r Determine if the sequence is arithmetic or geometric. Free PDF Download of JEE Main Sequences and Series Important Questions of key topics. Function Module Test Sequence - By using this option we can test a number of function modules all together where first's output is the Input for the next. Sequence of tenses quiz. Here is a more advanced series of text structure worksheets if your students are ready to go forward. One important property of sequences generated by range(n) is that the total number of elements is n : The sequence omits the number n itself, but includes 0. Sequences and series, whether they be arithmetic or geometric, have may applications to situations you may not think of as being related to sequences or series. 5 - Correct sequence for safe domestic electrical testing. Sigma factor, as part of the RNA polymerase holoenzyme, recognizes and binds to these sequences. Sequence Pattern[pdf] Chronological Sequence: Problem-Solution. pdf View: Classwork on 2/12 Feb 13, 2018, 9:41 AM: Hannah. State whether the sequence converges as; if it does. Use the CREATE SEQUENCE statement to create a sequence, which is a database object from which multiple users may generate unique integers. Write any fraction answer in simplest fraction form. In the Batch Sequences dialog box, click Run Sequence. • Doubtfully, it was agreed to re‐conduct the test with the pump elevated to simulate the correct liquid level at the workshop sump. 1 Basic definition of sequences and series 1. a 3n3 n = ; find a2. It is suitatble for children in first 1st grade (first graders exercise). •Given a sequence of random numbers —autocovariance at lag k, k ≥ 1 —for large n, Rk is normally distributed – 0 mean – variance of 1/[144(n-k)] •Confidence interval for autocovariance. Average rsantan Dec 14 12 633 plays 7. You should use a “Create Message” for step 8, and synchronous or asynchronous messages when necessary. 8 Classroom Task: What Does It Mean? – A Solidify Understanding Task. Integral test: If f(x) is continuous, positive, and decreasing for x 1, a. 51 KB (Last Modified on August 27, 2018) Comments (-1). Mid-Chapter Test This 1-page test provides an option to assess the first half of the chapter. 2 4 + = n n a n; find a10. p-Series Convergence The p-series is given by 1/n p = 1/1 p + 1/2 p. 1 Sequences and Series 819 Vocabulary Check 1. Breaux, PhD & Frances E. The specific parameters for any given study varies from one manufacturer to another, and from one imaging center to another. Fetal akinesia deformation sequence (FADS) is a condition characterized by decreased fetal movement (fetal akinesia) as well as intra-uterine growth restriction (IUGR), multiple joint contractures (arthrogryposis), facial anomalies, underdevelopment of the lungs (pulmonary hypoplasia) and other developmental abnormalities. Preparation!–!Assemble!all. ANSI escape sequence is a sequence of ASCII characters, the first two of which are the ASCII "Escape" character 27 (1Bh) and the left-bracket character " [ "(5Bh). This is the contrapositive of the Test for Divergence. Google Professional-Cloud-Security-Engineer Reliable Test Cost So our exam materials are not only effective but also useful, Google Professional-Cloud-Security-Engineer Reliable Test Cost Besides, I should remind you that the sequence of the questions may be disorganized in the actual test, so just memorizing the answers No, Google Professional-Cloud-Security-Engineer Reliable Test Cost But. Report from JPL Frequency Standards Test Laboratory Dr. Scripture passages support the phonics lessons, and stories illustrate Christian character traits. The famous ratio test of d’Alembert for convergence of series depends on the limit of the simple ratio an+1 an (J. M 3 R # A P 4 9 @ K D 1 U H 5 $2 N$ W E Q 6 T V 7 * 8 B X. My problem now is the following: I want to have the least amount of inputs, if the program i was typing the sequence into would perform a check for uniqueness for the last four digits entered. The inference example 1 -> 2, 2 -> 3 in the first sequence is correct, but the second sequence is the same as 1 -> 2, 2 -> 3. If we are to achieve universal health coverage, we need to ensure that ART and broader. when a CEC test engine is updated to the latest version whilst maintaining equivalent severity; or where a severity shift in the test requires modification of the specified limits. If the limit is 1, the test fails. What is the first number greater than 100 in the Fibonacci sequence? 3. Have them share their responses. (e)If a series converges, then the limit of the terms of the series must be zero. sequence / process d. • The process of determining a DNA sequence involves copying DNA. Some educators may feel that following the book from beginning to end makes the most sense, so he or she presents the material in the same order as the book. When a sequence number is generated, the sequence is incremented, independent of the transaction committing or. Sequence & Series Multiple Choice Questions (MCQs) Page-1. xx, or Math courses numbered 162. We note that absolute convergence of an infinite series is necessary and sufficient to allow the terms of a series to be. Grade Three Scope and Sequence. The Sequence IIIF Test utilizes a 1996 General Motors Powertrain 3800 Series II, water-cooled, 4 cycle, V-6 engine as the test apparatus. Some are quite easy to understand: If r = 1 the sequence converges to 1 since every term is 1, and likewise if r = 0 the sequence converges to 0. Limit Comparison Test If lim (n-->) (a n / b n) = L, where a n, b n > 0 and L is finite and positive, then the series a n and b n either both converge or both diverge. Moderate Questions. Sequences and Series - Problem Solving on Brilliant, the largest community of math and science problem solvers. In an Arithmetic Sequence the difference between one term and the next is a constant. Students can still view vacancies, book appointments for a CV/application review, have a mock interview or receive Careers Guidance. We call each number in the sequence a term. Drawbacks of a sequence diagram. Information in a Scope and Sequence document mirrors selected information in the corresponding Planning Guide used by teachers for a particular course/grade-level. Arithmetic and geometric sequences quiz questions and answers pdf, maths for class 9 quiz, arithmetic sequence quiz, basic math sequence quiz, geometric mean quizzes for virtual online school. QUIZ on Day 3 ~ 7 min Day 3: Series SWBAT: Represent the sum of a series, using sigma notation Determine the sum of the first n terms of an arithmetic or geometric series Pgs. Scope and Sequence Changes from the 3/11/2019 version to 4/9/2020 version 1Updated 4/9/20 Unit Changes Reason for Change 6. (b) Write down the common ratio of this geometric sequence. When you take the actual test, you will mark your answers on a separate machine-scorable answer sheet. LEADING TO applying the properties of geometric sequences and series to functions. Unless the phase sequence (rotation) of the load terminals of a three-phase generator set is correct, serious damage or injury could be done to connected equipment and to personnel as a result of reversed motor rotation or excessive current surges. 3) a n n 4) a n n 5) a n a n a 6) a n a n a Find the tenth term in each sequence. The amount it increases or decreases by is known as the common difference. 1) Sampling • We have spent considerable time thus far, with the continu-ous-time sinusoidal signal, (4. b) Use technology or grid paper to graph the sequence in part a. 03/14/2017; 10 minutes to read +2; In this article. Then, state if it is arithmetic, geometric or. This recommendation is consistently and widely published by multiple professional societies and experts. When reviewing a test prior to administering, verify that the test conforms with the following test construction guidelines. Concepts are introduced and reviewed in a carefully-planned sequence. Sequences/Series Test Practice Date_____ Period____ If the sequence is arithmetic or geometric, find the next 3 terms. Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. Trace through the sequence. The topic of Sequences from the Year 9 book of the Mathematics Enhancement Program. The sequence of tests: - Continuity of protective conductors, including main and supplementary bonding - Continuity of ring final circuit conductors - Insulation resistance - Polarity test - Earth fault loop impedance tests - Prospective fault current test - RCD test - Phase sequence test - Functional testing. 4 Sequence and Series of Real Numbers M. If we multiply, it is a geometric sequence. Sequence of Events Strategy Infer/Predict Author’s Craft Word Choice Listening, Speaking, Viewing Listen for a Purpose Target Vocabulary curly straight floppy drooled weighed stood collars row Vocabulary Strategies Alphabetical Order Spelling Principle Short Vowels a, i Spelling Words Basic: sad, dig, jam, glad, list, win, flat, if, fix, rip. SequenceDiagram. c y PAzlflE zreisgjhptpsk \rwecskeZrgvge]dh. dvi Created Date: 10/12/1999 8:55:32 AM. sequence of ATP molecules Base your answer to question 11 on the portion of the mRNA codon chart and information below. 1 Geometric sequences The series of numbers 1, 2, 4, 8, 16 is an example of a geometric sequence (sometimes called a geometric progression). Letter Sequence Test In letter sequence test questions you are to find the missing letter in a sequence of letters. Department of Education Contract No. Please put away all books, notebooks, phones, etc. 40 or greater. This quiz and worksheet combination will help you to test your understanding of. Your test result card will also indicate what course(s) you should take first. Includes: *Nth Term Matching Activity* Students must match each sequences to its 10th term and nth term rule. Second Order Differential Equation. The Jet Propulsion Laboratory is a unique national research facility that carries out robotic space and Earth science missions. Find the 22nd term of the following sequence:5, 8, 11,. Each object in the series consists of 3 shapes. REMEDIATION Correct Mistakes on Quiz and Do Another Practice Activity. when a CEC test engine is updated to the latest version whilst maintaining equivalent severity; or where a severity shift in the test requires modification of the specified limits. Cora SeQuence drives an integrated approach to help enterprises run agile, built-to-adapt, digitally-enabled business processes. Diagrammatic reasoning tests involve sequences built with diagrams that have to be completed. If the goal is to show the difference between the first sequence and the second sequence, I think it is a correct example to compare 2-> 3, 3-> 3 of the first sequence and 2-> 3, 3-> 4 of the second sequence. Ribosomal RNA (rRNA) sequence analysis: This has emerged as a major method for classification. 1) View Solution Helpful Tutorials. They noticed they (fly) for three hours already. Report from JPL Frequency Standards Test Laboratory Dr. A geometric sequence is given by a starting number, and a common ratio. Breaux, PhD & Frances E. Number Sequence & Missing Numbers. Since 2 and 3 are constants, if we let a be the first term of the sequence and d be the constant difference, then the formula that will describe the nth term of the sequence is. Each page includes appropriate definitions and formulas followed by solved problems listed in order of increasing difficulty. Python Sequence Tutorial. This may include following a rule in a sequence, identifying a code or finding a missing diagram. Arithmetic Sequence. pdf View: Classwork on 2/12 Feb 13, 2018, 9:41 AM: Hannah. Sequences and series, whether they be arithmetic or geometric, have may applications to situations you may not think of as being related to sequences or series. After having gone through the stuff given above, we hope that the students would have understood, "Practice Questions on Sequences and Series". The four nitrogen bases are the same for all organisms. the zoom window, it will highlight blocks in sequences that contain “count” and “test. • A good sequence diagram is still above the level of the real code (not all code is drawn on diagram) • Sequence diagrams are language-agnostic (can be implemented in many different languages) • Non-coders can read and write sequence diagrams. The first and important logical responsibility from the student's end is to identify the nature of the sequences which is directly or indirectly given in the questions. Scope and Sequence Changes from the 3/11/2019 version to 4/9/2020 version 1Updated 4/9/20 Unit Changes Reason for Change 6. / Sequence of tenses quiz. State whether the sequence converges as; if it does. Sequence of Events – Chernobyl Accident Appendix 1 (Updated June 2019) During the course of a safety system test being carried out just before a routine maintenance outage, Chernobyl 4 was destroyed as a result of a power transient on 26 April 1986. Geomtric Series Test and Formula. The Sequence VG test is a cyclic test, with a total running duration of 216 hours, consisting of 54 cycles of 4 hours each. Each Scope and Sequence document is designed for a specific school year and reflects the number of available instructional days for that year and grading period. Highlight the text connectives used (e. The bank offers a 4. Is a sequence, but 1+4+7+11+… Is a series. Tom said that it (take) him an hour to get to the station. Operational Test. 1) −5, − 5 4, − 5 16. JACK DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical and Computer Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, 2012. A series can be finite (for example, it might only have 25 terms) or infinite, and the notation needs to allow for both. Worksheets, activities and assessments. Second Order Critical Point. Sequence, an animated resource page with lesson plans and teaching tips, for kindergarten to 3rd grade, teaches how transition words can help order events or organize steps in a piece of writing. Order/Sequence: This text structure gives readers a chronological of events or a list of steps in a procedure. Use Test Flow to control the flow of your test, and Command Expert to get the exact instrument setup for demanding test needs. They are therefore useful for making comparisons among the different living organisms. / Exam Questions - Arithmetic sequences and series. Preliminary Check. Geometric and p-Series 19. Static, De-energized Test of Equipment. The teacher asked the boys if they ——————– the sums. The number. A Sequence is a set of things (usually numbers) that are in order. If we are to achieve universal health coverage, we need to ensure that ART and broader. 6: COUNTING PRINCIPLES PART A: SEQUENCES An infinite sequence can usually be thought of as an ordered list of real numbers. 2 4 + = n n a n; find a10. This may include following a rule in a sequence, identifying a code or finding a missing diagram. A sequence is a list of numbers in which each number depends on the one before it. • Bring out the ruler again and ask a student volunteer to come up to the front of the class. Plot the Term value on the vertical axis and the Term number on the horizontal axis. indd 14 5/22/19 11:27 AM. (f)If a series diverges, the limit of the terms of the series must be non-zero. sequence to the sequence created using the toothpicks. One way to think of sequence diagrams, particularly highly detailed diagrams, is as visual object code. Welcome to ESL Printables , the website where English Language teachers exchange resources: worksheets, lesson plans, activities, etc. 23 – 27 in Packet Day 4: Sequences and Series Mixed Practice SWBAT: Review problems involving Sequences and Series Pgs. The tables below show the sequence of ESOL and English courses: 1 2. To examine the detailed Scope and Sequence for a single grade or electives, download the individual PDFs below. 2) where t is a continuous variable † To manipulate such signals in MATLAB or any other com-puter too, we must actually deal with samples of fs xt xt fs = 1 Ts 2B xn = xnT s – n. By creating a sequence of tests and by setting the measurement parameters at one location for each test in the sequence, a user can increase test efficiency and improve test quality. 18 – 22 in Packet HW: Pgs. Does lim. These question based on the following letter /symbol/number sequence. What is the Sequence? An ordered list of numbers which is defined for positive integers. The sequence of tests: - Continuity of protective conductors, including main and supplementary bonding - Continuity of ring final circuit conductors - Insulation resistance - Polarity test - Earth fault loop impedance tests - Prospective fault current test - RCD test - Phase sequence test - Functional testing. For information about these res. 3 s KAhlTl7 0rKiDgmhWtIs n RrlemseeyrfvheEdp. Let's say that your starting point is #2#, and the common ratio is #3#. kingsley Created Date: 10/31/2012 1:25:50 PM. Scientists also hope that being able to study the entire genome sequence will help them understand how the genome as a whole works—how genes work together to direct the growth, development and maintenance of an. Series (Find the sum) A finite Geometric Series (a limited number of terms, or Partial Sum) An infinite Geometric Series, if our infinite series is. All ITU-T test patterns are PRBS sequences. They derive rules for determining the nth term of an arithmetic sequence and the sum of the. Theme Daily Checklist. Sequences and Series. We'll review your answers and create a Test Prep Plan for you based on your results. •Given a sequence of random numbers —autocovariance at lag k, k ≥ 1 —for large n, Rk is normally distributed – 0 mean – variance of 1/[144(n-k)] •Confidence interval for autocovariance. MULTIPLE CHOICE What is the next term in the sequence 1, 4, 9, 16, 25,. This sequence of testing confirms vehicle conformance with all "shall" statements contained in the HEV America Hybrid Electric Vehicle (HEV) Vehicle Specifications. 1 Basic definition of sequences and series 1. 1 Light and Matter a) Added LS1-8* a) Determined light was a better context to introduce the idea of biological receptors for light than its original placement in Unit 6. Sequence IIIG Form 3 Summary of Test Method The Sequence IIIG Test is a fired-engine, dynamometer lubricant test for evaluating automotive engine oils for certain high-temperature performance characteristics, including oil thickening, varnish deposition, oil consumption, and engine wear. Sequence of Verb Tenses Although the various shades of time and sequence are usually conveyed adequately in informal speech and writing, especially by native speakers and writers, they can create havoc in academic writing and they sometimes are troublesome among students for whom English is a second language. 1: SEQUENCES AND SERIES, and SECTION 9. Part (b): Edexcel C1 Core Maths June 2014 Q8b : ExamSolutions Maths Revision - youtube Video. sequence of ATP molecules Base your answer to question 11 on the portion of the mRNA codon chart and information below. Report from JPL Frequency Standards Test Laboratory Dr. Relays 5 to 12 Test Diagrams for Systems with Integral G. Complex Sequences Previous: 7. They are therefore useful for making comparisons among the different living organisms. xx or above. CREATE SEQUENCE Test. Arithmetic and Geometric Sequences Multiple Choice Questions (MCQs), arithmetic and geometric sequences quiz answers pdf 4 to learn secondary school math for online certificate courses. In an 8th grade scope and sequence you’ll see the list of topics and activities that are going to be taught throughout the course for a specific subject. Download PDF. indd 14 5/22/19 11:27 AM. A service is effectively a high-level method, often one that can be invoked by a wide variety of clients. recursively 5. For use as a performance test, this practice requires that the shipping unit tested remain unopened until the sequence of tests are completed. a) Create your own arithmetic sequence. Geomtric Series Test and Formula. The state diagram of the Moore FSM for the sequence detector is shown in the following figure. a sequence without the intention to increase severity (e. Have them share their responses. series and review quiz with answers. After having gone through the stuff given above, we hope that the students would have understood, "Practice Questions on Sequences and Series". 4 Sums and Products Up: 7. For example, if you invested £. What comes next in the sequence: 1, 2, 6, 22, ____ ? (A) 82 (B) 84 (C) 86 (D. That is, if X1 k=1 a k converges, then a k!0. Note: Sequence. The sum of the first 9 terms of the sequence 1+2ὒ1+ 1. Four Quizzes with Answers. See also backstep sequence, longitudinal sequence, etc. 5} shows the correct sequence of testing to reduce the possibility of accidents to the minimum. An arithmetic sequence can also be defined recursively by the formulas a 1 = c, a n+1 = a n + d, in which d is again the common difference between consecutive terms, and c is a constant. This is also the way you would intuitively test a die to see if it is loaded: Roll it many times, and if you see too many sequences of the same value coming up, you should be suspicious. Lemma (Nested Intervals Lemma). Prereq: A grade of C- or above in 1114 (114), 1151, 1156, 1161. This course is available for EM credit. Lecture 2 : Convergence of a Sequence, Monotone sequences In less formal terms, a sequence is a set with an order in the sense that there is a rst element, second element and so on. Get your "ducks in a row" with this sequence quiz. INV_PATTERN Boolean FALSE: The generated pattern is not inverted or the. Most people with Pierre Robin sequence are also born with an opening in the roof of the mouth (a cleft palate. Work - Temporary variable – how many of the resource are currently available. If you look at the Real-Time Statistics for RANDOM. It parallels the timing of the Mid-Chapter Quiz in the Student Edition and includes both multiple-choice and free-response questions. 10 questions on geometric series, sequences, and l'Hôpital's rule. How to find a missing number in a sequence. Interactive Number Sequence Activities (Up to 100, steps of up to 10) Addition Sequences (within 100) Write the Rule Subtraction Sequences (within 100) Write the Rule Addition / Subtraction Sequences (within 100) Write the Rule Addition Sequences (within 100) Subtraction Sequences (within 100). View Interactive. Since these tests are only based on partial information of the sequence, some of them even fail to detect the randomness of a deterministic sequence as discussed in section IV. dvi Created Date: 11/7/2006 5:22:56 PM. No calculation occurs if the input is invalid and the user is informed of the mismatch. An alternating series X1 n=1 ( 1)n 1b n = b 1 b 2 + b 3 + b n >0 is convergent if it satis es the following conditions (1) b n+1 b n for all n (2)lim n!1 b n = 0. p-Series Convergence The p-series is given by 1/n p = 1/1 p + 1/2 p. a) Create your own arithmetic sequence. The third, fourth and fifth numbers are 6 , 2 , and -2. Glencoe/McGraw-Hill. CountByNeg1 START WITH 0 INCREMENT BY -1 ; GO C. sequence / process. a 7 2n2 n = − ; find a5. 8-billion bp DNA sequence was generated over 9 months from 27,271,853 high-quality sequence reads (5. It includes any method or technology that is used to determine the order of the four bases: adenine, guanine, cytosine, and thymine. org are unblocked. If we add a number to get from one element to the next, we call it an arithmetic sequence. learn more. Sequences and Series • I'm going to ask you questions about sequences and series and drill you on some things that need to be memorized. a sequence without the intention to increase severity (e. Finite and infinite sequences are, as one might expect, two inverse types of sequences. A service is effectively a high-level method, often one that can be invoked by a wide variety of clients. 1 Sequences Series and Summation. Ministry of Education. • When you think you know the answer, (or if you give up ) click to get to the next slide to see the answer(s). Grade Five Scope and Sequence. Sequences and Series 1. Sequence and Series Test 120 Test Duration: 60 minutes There are 30 questions in total. In symbol series, The questions given with figures, and you need to identify the next picture within the sequence provided. Mid-Chapter Test This 1-page test provides an option to assess the first half of the chapter. The first term of a geometric sequence is $$\text{9}$$, and the ratio of the sum of the first eight terms to the sum of the first four terms is $$97:81$$. For instance, it is known that a subsequence of convergent sequence isa convergent. 3 Null Sequences Sequences that converge to are simpler to work with than general sequences, and many of the convergence theorems for general sequences can be easily deduced from the properties of sequences that converge to. Result (The Alternating Series Test). The DMA register description section contains detailed operational information. CREATE SEQUENCE Test. The online math tests and quizzes about arithmetic and geometric series. If you'd like a pdf document containing the solutions the download tab above contains links to pdf's containing the solutions for the full book, chapter and section. Find the eighth term of a geometric sequence for which 1=−3 and =−2. The first and important logical responsibility from the student's end is to identify the nature of the sequences which is directly or indirectly given in the questions. The program creates personalized learning paths for students of all abilities through an adaptive placement and scaffolded activities that align to rigorous standards. Be careful to not make either of these mistakes. Clearly 1 n+1 < 1 n and lim n→∞ 1 n = 0. Each page includes appropriate definitions and formulas followed by solved problems listed in order of increasing difficulty. An interactive math lesson about completing a numerical sequence. Arithmetic progressions; Part (a): Edexcel C1 Core Maths June 2014 Q8a : ExamSolutions Maths Revision - youtube Video. A sequence is one of the basic logic structures in computer programming. A sequence is a function whose domain is the natural numbers. buyitsellit. To find the sum of the first S n terms of a geometric sequence use the formula S n = a 1 (1 − r n) 1 − r, r ≠ 1, where n is the number of terms, a 1 is the first term and r is the common ratio. Grade Four Scope and Sequence. Commissioning: 1. State whether the sequence converges as; if it does, find the limit. GOWN Fully cover torso from neck to knees, arms to end of wrists, and wrap around the back Fasten in back of neck and waist 2. The BACB no longer oversees the Verified Course Sequence system. Definition, using the sequence of partial sums and the sequence of partial absolute sums. In a more recent survey of clinical practice, Emanuel, Ficca and Korczak (2011) reported that. We'll review your answers and create a Test Prep Plan for you based on your results. The third, fourth and fifth numbers are 6 , 2 , and -2. Each Scope and Sequence document is designed for a specific school year and reflects the number of available instructional days for that year and grading period. Scientists also hope that being able to study the entire genome sequence will help them understand how the genome as a whole works—how genes work together to direct the growth, development and maintenance of an. The advent of rapid DNA sequencing methods has greatly accelerated biological and medical research and. Here the phase current Ia is modified by adding to it a portion K0 (called zero-sequence current compensation factor) of the zero-sequence current I0. For example, if you invested £. ? ¡ A 34 ¡ B 35 ¡ C 36 D 38 ¡ E 39 2. 1 Rolle's theorem 2. Sequences and Series Application Answer Key. Precalculus Sequences & Series Test Practice Name_____ Sequence Formulas: a n = a 1 + d (n – 1) 1 1 n a a r n Series Formulas : 1 (1 ) 1 n n ar S r Determine if the sequence is arithmetic or geometric. The four nitrogen bases are the same for all organisms. CliffsNotes study guides are written by real teachers and professors, so no matter what you're studying, CliffsNotes can ease your homework headaches and help you score high on exams. What is the Sequence? An ordered list of numbers which is defined for positive integers. Information in a Scope and Sequence document mirrors selected information in the corresponding Planning Guide used by teachers for a particular course/grade-level. A good candidate for a test sequence would be a series of dc tests or a series of current versus voltage (IV) and capacitance versus voltage (CV) tests. Answer Explanations. Sequence of Tenses Quiz I. The sum of an infinite arithmetic sequence is either ∞, if d > 0, or - ∞, if d < 0. learn more. 864-5722 Chemistry Placement Test & Course Sequence Attention: Chemistry is currently an impacted program. ˆ 3n 2n+ 1 ˙ +1 n=1 The sequence is (strictly) increasing. 5 Valid Dumps Demo, We will follow the sequence of customers' payment to send you our C_EWM_95 guide questions to study right away with 5 to 10 minutes, If you still worry about your C_EWM_95 exam; if you still doubt whether it is worthy of purchasing our software, what you can do. If r = −1 this is the sequence of example 11. The colors are alternated (gray and white). Each number in the sequence is called a term (or sometimes "element" or "member"), read Sequences and Series for more details. ÐThe coding sequence ¥speciÞes the amino acid sequence of the protein that will be produced during translation. Operational Test. BCStudentsp077-102. Math workbook 1 is a content-rich downloadable zip file with 100 Math printable exercises and 100 pages of answer sheets attached to each exercise. Find the first three terms of the sequence, if it is given that all the terms are positive. It is present at birth. A study of Correct minus Incorrect Word Sequences (CIWS) as a measure of writing skills was conducted with over 1,000. Welcome to ESL Printables , the website where English Language teachers exchange resources: worksheets, lesson plans, activities, etc. 40 or greater. An alternating series is a series whose terms are altenatively positive and negative. Arithmetic and Geometric Sequences Multiple Choice Questions (MCQs), arithmetic and geometric sequences quiz answers pdf 4 to learn secondary school math for online certificate courses. THE GENERAL CONCEPT OF A SEQUENCE 3 1+1 = 2. infinite sequence 2. A step has the form Conditional statements can be used to express alternate paths through the use case. Consider the geometric sequence 1, 1,1, 1,1, 1,. The following documents focus on math skills needed to pass the GED test. In math there are two different types of number sequences and for this quiz we will be dealing with the arithmetic sequence. For a general introduction to these sequences please refer to MRI sequences (basic). For the series given above, the sequence of partial sums is. The partial sums of a series form a new sequence, which is denoted as {s 1, s 2, s 3, s 4,}. Relays 5 to 12 Test Diagrams for Systems with Integral G. 150 is a good example of this. 1) The ratio test states that: if L < 1 then the series converges absolutely ; if L > 1 then the series is divergent ; if L = 1 or the limit fails to exist, then the test is inconclusive, because there exist both convergent and divergent series that satisfy this case. About This Quiz & Worksheet. Objective examinations include multiple choice,. 2 - Correct testing sequence. 00 test fee. AC Team 2-March 19. The following test sequence shall be used for conduct of HEV America Baseline Performance Testing. Assessing Writing Skills Using Correct–Incorrect Word Sequences: A National Study. To continue the sequence, we look for the previous two. Furthermore, one of the test method facets is the sequence of parts, sub-part of the rubrics of the test, which is the concern of the present study. The proper sequence of excavation and backfilling is required to optimise the process and prevent safety issues. the zoom window, it will highlight blocks in sequences that contain “count” and “test. HEV America Baseline Test Sequence Page 1 HEV PERFORMANCE TEST PROCEDURE SEQUENCE. TIME AND DISTANCE VARIABLES ASSESSMENT 4. REMEDIATION Correct Mistakes on Quiz and Do Another Practice Activity. sequence without the intention to increase severity (e. Arithmetic Sequence Determine if the sequence is arithmetic by selecting between true or false. Sequences and Series Practice Test Name_____ ID: 1 Date_____ Period____ ©u L2i0X1o9y iKLuPtbaE XSvoCfEtfwAamrdes PLOL]Ct. The colors are alternated (gray and white). No calculation occurs if the input is invalid and the user is informed of the mismatch. If k is a positive integer, find the radius of convergence of the series X∞ n=0 (n. firstly, next, after etc). block sequence. This sequence of testing confirms vehicle conformance with all "shall" statements contained in the HEV America Hybrid Electric Vehicle (HEV) Vehicle Specifications. Includes: *Nth Term Matching Activity* Students must match each sequences to its 10th term and nth term rule. Coming for fall 2019! Three new levels for grades 3-5. 2 Erik Woodbury Chair, Chemistry Department Email: [email protected] Application: A Bouncing Ball. The Sequence IIIF Test utilizes a 1996 General Motors Powertrain 3800 Series II, water-cooled, 4 cycle, V-6 engine as the test apparatus. About This Quiz & Worksheet. 2 - Correct testing sequence. A series is built from a sequence, but differs from it in that the terms are added together. If the series is convergent determine the value of the series. For example, if you invested £. One of the most important questions we can ask about a sequence or series is whether it converges. Sequences and Series Practice Test Name_____ ID: 1 Date_____ Period____ ©u L2i0X1o9y iKLuPtbaE XSvoCfEtfwAamrdes PLOL]Ct. Given the sequence defined by the function 𝑛+1= 3 4 𝑛 with 1=424. By creating a sequence of tests and by setting the measurement parameters at one location for each test in the sequence, a user can increase test efficiency and improve test quality. series quiz with answers. The sum of the first n terms of a geometric sequence is called geometric series. Two molecules that are isomers: (A) must contain the same functional groups (B) often differ in the number of unsaturated bonds they possess (C) have the same molecular formulas. Use the CREATE SEQUENCE statement to create a sequence, which is a database object from which multiple users may generate unique integers. It is reflects Algebra 2 (algebra ii) level exercises. The series, 59, 58, 57, 56, 55, 54… is a series of numbers that go in sequential order from highest number to lowest number. 1) The ratio test states that: if L < 1 then the series converges absolutely ; if L > 1 then the series is divergent ; if L = 1 or the limit fails to exist, then the test is inconclusive, because there exist both convergent and divergent series that satisfy this case. One important property of sequences generated by range(n) is that the total number of elements is n : The sequence omits the number n itself, but includes 0. Its formulas are: a) F0 = 0, F1 = 1 b) Fn = Fn -1 + Fn -2; Strategy and Techniques. Secant Line. Find the eighth term of a geometric sequence for which 1=−3 and =−2. 1) 35, 32, 29, 26, …. For a general introduction to these sequences please refer to MRI sequences (basic). For descriptions of some common sequence formats, see Common Sequence Formats. 2) where t is a continuous variable † To manipulate such signals in MATLAB or any other com-puter too, we must actually deal with samples of fs xt xt fs = 1 Ts 2B xn = xnT s – n. 1) View Solution Helpful Tutorials. It's Nice to Belong 10 questions Average. Commissioning: 1. If the first term of an arithmetic sequence is 5 and the third term is 2, then find the seventh term. It is therefore crucial to. Grade Four Scope and Sequence. B o XM7agdZeb Ow2iQt2hJ CIQnpfLi0nEivtpeV sA2l7gxeZbMrnaJ b2C. Grade Two Scope and Sequence. Find the next three terms in each sequence. Letter Sequence Test In letter sequence test questions you are to find the missing letter in a sequence of letters. The product of increasing (decreasing) sequences is increasing (decreasing). The guanine-cytosine content, or GC-content, of a DNA sequence indicates the percentage of nucleotide base pairs where guanine is bonded to cytosine. second integration quiz with answers. Sequences 2 Series: Arithmetic, Geometric, Harmonic, and p-series 3 Integral Test 4 Direct Comparison & Limit Comparison Tests 5 Review of Integral Test, DCT, LCT: 6 Quiz 7 Alternating Series Test, Absolute & Conditional Convergence 8 Ratio Test 9 Review 10 Quiz II 11 Power Series 12 Taylor Series: MacLauren Series 13. We will see there are good reasons to start from 0 in Python. Sequence of Verb Tenses Although the various shades of time and sequence are usually conveyed adequately in informal speech and writing, especially by native speakers and writers, they can create havoc in academic writing and they sometimes are troublesome among students for whom English is a second language. Sandwich Theorem. Rationale Sequences and series are introduced in grade 11. The algorithm generates a text file that is processed using shell scripts and R to produce a graphical interpretation of the results. Therefore, this study aims to examine the effect of the sequence. CREATE SEQUENCE Test. Suppose x1(n) and x2(n) are real-valued sequences of length N, and x(n) is a complex-valued sequence defined as x(n) x 1 (n) jx 2 (n) 0 n N 1 The DFT of the two N-length sequences x1(n) and x2(n) can be found by performing a single N-length DFT on the complex-valued sequence and some additional computation. • Sequence - Study Zone: Sequence - Learn about sequencing and sequence clue words. Grade One Scope and Sequence. Some are quite easy to understand: If r = 1 the sequence converges to 1 since every term is 1, and likewise if r = 0 the sequence converges to 0. 1 Sequences Series and Summation. Coming for fall 2019! Three new levels for grades 3-5. 4 Sequence and Series of Real Numbers M. integration quiz with answers. This may include following a rule in a sequence, identifying a code or finding a missing diagram. The sequence is (strictly) decreasing. The BACB no longer oversees the Verified Course Sequence system. Determine the next 3 terms in the sequence. An alternating series X1 n=1 ( 1)n 1b n = b 1 b 2 + b 3 + b n >0 is convergent if it satis es the following conditions (1) b n+1 b n for all n (2)lim n!1 b n = 0. There are many signal words that can indicate the order of events. Does P bn converge? Is 0 ≤ an ≤ bn? YES P YES an Converges Is 0 ≤ bn ≤ an? NO NO P YES an Diverges LIMIT COMPARISON TEST Pick {bn}. March, 2010 Dear Friend of Core Knowledge, The Board of Trustees of the Core Knowledge Foundation has long desired to make the Core. Solutions of Chapter 9 Sequences and Series of Class 11 NCERT book available free. If the first term of an arithmetic sequence is 5 and the third term is 2, then find the seventh term. Otherwise, the infinite series does. Old Exam Questions with Answers 49 integration problems with answers. Enter your sequences (with labels) below (copy & paste): PROTEIN DNA Support Formats: FASTA (Pearson), NBRF/PIR, EMBL/Swiss Prot, GDE, CLUSTAL, and GCG/MSF Or give the file name containing your query. Explain which sequence would be most appropriate in the following situations, and why. • Complete the ‘Aquatic Rescue Sequence’ test (see test guidelines) • Upon successful completion of the test complete the ‘Certificate of Aquatic Rescue Sequence’ form including instructor licence number and expiry. • Doubtfully, it was agreed to re‐conduct the test with the pump elevated to simulate the correct liquid level at the workshop sump. Is there any missing activity? Q2. ? ¡ A 34 ¡ B 35 ¡ C 36 D 38 ¡ E 39 2. The continuation of a fillet weld around. Can you name the Sequences and Series? question answer; Find the common difference of this arithmetic sequence: 5, 16. 7 and diverges. Arithmetic Sequences: Four fun activities and teacher tools to help students develop and practise the ability to find the nth term of an arithmetic sequence. 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Contents
Idea
The absolute Galois group of a field $k$ is that of the field extension $k \hookrightarrow k_s$ which is the separable closure of $k$. When $k$ is a perfect field this is equivalently the Galois group of the algebraic closure $k \hookrightarrow \overline{k}$.
Definition
Definition
Let $k$ be a field. Let $k_s$ denote the separable closure of $k$. Then the Galois group $Gal(k\hookrightarrow k_s)$ of the field extension $k\hookrightarrow k_s$ is called absolute Galois group of $k$.
Properties
Remark
By general Galois theory we have $Gal(K\hookrightarrow K_s)\simeq \pi_1(Spec\; K)$ is equivalent to the fundamental group of the spectrum scheme $Spec K$
An instance of Grothendieck's Galois theory is the following:
Proposition
The functor
$\begin{cases} Sch_{et}\to Gal(k\hookrightarrow k_s)-Set \\ X\mapsto X(k_s) \end{cases}$
from the category of étale schemes to the category of sets equipped with an action of the absolute Galois group is an equivalence of categories.
Proposition
Recall the every profinite group appears as the Galois group of some Galois extension. Moreover we have:
Every projective profinite group appears as an absolute Galois group of a pseudo algebraically closed field?.
Examples
Of the rational numbers
Remark
There is no direct description (for example in terms of generators and relations) known for the absolute Galois group $G_\mathbb{Q}:=Gal(\mathbb{Q}\hookrightarrow \overline \mathbb{Q})$ of the rational numbers.
However Belyi's theorem? implies that there is a faithful action of $G_\mathbb{Q}$ on the children's drawings.
Theorem
(Drinfeld, Ihara, Deligne)
There is an inclusion of the absolute Galois group of the rational numbers into the Grothendieck-Teichmüller group (recalled e.g. as Stix 04, theorem 6).
References
• Jakob Stix, The Grothendieck-Teichmüller group and Galois theory of the rational numbers, 2004 (pdf)
category: Galois theory
Revised on September 16, 2014 08:40:44 by Urs Schreiber (185.26.182.32) |
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Determine whether the simplified expression is rational or irrational: $\sqrt{-16+4(5)+5}$.Determine whether the simplified expression is rational or irrational: $\sqrt{-16+4(5)+5}$. ...
Classify each number as being a natural number $(\mathrm{N})$, whole number $(\mathrm{W})$, integer $(\mathrm{I})$, rational number $(\mathrm{Q})$, and/or irrational number $\left(Q^{\prime}\right)$.Classify each number as being a natural number $(\mathrm{N})$, whole number $(\mathrm{W})$, integer $(\mathrm{I})$, rational number $(\mathrm{Q})$, an ...
Simplify the following surdsSimplify the following: (a) $\quad \sqrt{2} \cdot \sqrt{3}=$ (b) $\quad \sqrt{3} \cdot \sqrt{3}=$ (c) $\quad(\sqrt{4})^{2}=$ (e) $\frac{\sqrt{1 ... close 1 answer 130 views Let$p$be the statement "$x$is an irrational number",$q$be the statement "y is a transcendental number", and$r$be the statement '$x$is a rational number iff$y$is a transcendental number".Let$p$be the statement "$x$is an irrational number",$q$be the statement "y is a transcendental number", and$r$be the state ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that$\sqrt{3}$is irrational. 1 answer 76 views Show that$\sqrt{3}$is irrational.Show that$\sqrt{3}$is irrational. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What are radical numbers? 0 answers 63 views What are radical numbers?What are radical numbers? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Are all surds irrational? 0 answers 91 views Are all surds irrational?Are all surds irrational? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the definition of an irrational number? 1 answer 198 views What is the definition of an irrational number?What is the definition of an irrational number? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Where do irrational numbers occur in mathematics? 1 answer 68 views Where do irrational numbers occur in mathematics?Where do irrational numbers occur in mathematics? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Can measurements with a ruler be irrational? 1 answer 181 views Can measurements with a ruler be irrational?Can measurements with a ruler be irrational? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Help me to identify the nature of the following: 1 answer 65 views Help me to identify the nature of the following: Help me to identify the nature of the following: A. Real, Rational, Integer B. Real, Rational, Whole C. & ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which ONE of the following numbers is irrational? 1 answer 152 views Which ONE of the following numbers is irrational? Which ONE of the following numbers is irrational? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 For which of the following values of$a$is$\frac{a}{14}$rational or irrational? 1 answer 247 views For which of the following values of$a$is$\frac{a}{14}$rational or irrational? For which of the following values of$a$is$\frac{a}{14}$rational or irrational?$1-10$ $\sqrt{2}$ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Write$5,\dot{4}\dot{3}\dot{2}$as a rational fraction. 1 answer 133 views Write$5,\dot{4}\dot{3}\dot{2}$as a rational fraction.Write$5,\dot{4}\dot{3}\dot{2}$as a rational fraction. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Write$0,\dot{3}$in the form$\dfrac{a}{b}$(where$a$and$b$are integers). 1 answer 167 views Write$0,\dot{3}$in the form$\dfrac{a}{b}$(where$a$and$b$are integers).Write$0,\dot{3}$in the form$\dfrac{a}{b}$(where$a$and$b$are integers). ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Is$\frac{2}{11}$irrational? 1 answer 99 views Is$\frac{2}{11}$irrational?Is$\frac{2}{11}$irrational? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If$\frac{1}{3}$can be written as$0,\dot{3}$or as$0,\bar{3}$then is it irrational? 1 answer 141 views If$\frac{1}{3}$can be written as$0,\dot{3}$or as$0,\bar{3}$then is it irrational?If $\frac{1}{3}$can be written as $0,\dot{3}$or as$0,\bar{3}$then is it irrational? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Are humans naturally irrational? 1 answer 78 views Are humans naturally irrational?Are humans naturally irrational? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 How do you define a real number? 1 answer 146 views How do you define a real number?How do you define a real number? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 For which of the following values of$a$is$\frac{a}{14}$rational or irrational? 1 answer 232 views For which of the following values of$a$is$\frac{a}{14}$rational or irrational? For which of the following values of$a$is$\frac{a}{14}$rational or irrational? $1$ &nb ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Irrational numbers ($\mathbb{Q'}$) are numbers that cannot be written as... 1 answer 131 views Irrational numbers ($\mathbb{Q'}$) are numbers that cannot be written as...Irrational numbers ($\mathbb{Q'}$) are numbers that cannot be written as... ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Why is$\pi$irrational? 1 answer 140 views Why is$\pi$irrational?Why is$\pi\$ irrational? ... |
More Topics from Ordinary Differential Equations
• 8.1 Introduction to Differential Equations: Slope Fields and Euler's Method
• 8.2 Exponential Growth and Decay
• 8.3 Separable Differential Equations
• 8.4 The Logistic Equation
• 8.5 First Order Linear Differential Equations |
# Child Indicators Research
Online ISSN: 1874-8988
Print ISSN: 1874-897X
Recent publications
• Rasmus Mannerström
• Lauri Hietajärvi
• Arniika Kuusisto
• [...]
• Arto Kallioniemi
Previous research on Schwartz’s theory of basic human values has mostly applied a variable-oriented approach . This study took a person-oriented approach and investigated how values co-occur and are manifested in individuals, that is, what kind of value profiles exist and how they differ in terms of subjective (i.e., life satisfaction) and social well-being (i.e., sense of belonging). In a sample of Finnish adolescents ( N = 973; women 59.6%; M age = 16.8, SD = .70), three value profiles emerged: personal-focus , growth-focus and self-protective , of which the personal-focus group scored highest on life satisfaction, the growth-focus group scored lowest on belonging to social media and the self-protective group scored highest on belonging to organizations. In all, subjective and social well-being were differently related to opposing values. The findings are discussed within a cultural and contextual framework.
• Jose Marquez
• Louise Lambert
• Megan Cutts
Interest in adolescents’ wellbeing and mental health is growing worldwide, but little research in this area has been conducted in certain world regions and countries such as the United Arab Emirates (UAE). Geographic, socio-demographic and school type differences in adolescent wellbeing and mental health are commonly observed in the field, and the UAE is a diverse country where these types of differences have been found for other outcomes (notably, academic). Yet, no prior national study has explored these differences in terms of wellbeing and mental health in the nation. We address this gap by investigating differences across emirates, gender, socio-economic status, immigrant status, school sector and school curriculum for overall life satisfaction, positive affect, negative affect, meaning and purpose in life, and internalizing difficulties. We use linear regression to analyse cross-sectional data from the Programme for International Student Assessment (PISA) study from 2015 and 2018. We find substantial geographic, socio-demographic and school type differences in levels (2018) of wellbeing and mental health -which vary across distinct domains- and declines (2015–2018) of wellbeing. Better wellbeing and mental health are observed in the northern emirates and among boys. Better wellbeing and poorer mental health are observed among nationals (compared to expatriates) and in public schools (compared to private schools). Despite presenting the best academic outcomes, British schools present the worst wellbeing and mental health outcomes. However, results show the absence of a trade-off between academic competence and wellbeing and mental health, with evidence of a small positive association with wellbeing.
This study proposed a moderated mediation model to examine the mediating effect of hope and moderating effect of the teacher-student relationship in the relationship between socio-economic status (SES) and autonomous learning among Chinese middle school students. Mediation analysis first indicated that hope partially mediated the relationship between SES and autonomous learning. Moderated mediation analysis further indicated that the teacher-student relationship moderated on the mediating pathway of hope on autonomous learning. With a higher level of teacher-student relationship, the positive relationship between hope and autonomous learning would be stronger. The findings elucidated that positive interaction with teachers could benefit students’ learning process by facilitating their hope belief and autonomous learning; such positive interaction could motivate students’ hope beliefs into autonomous learning behaviors. Implications of the findings are discussed.
Student well-being has recently emerged as a critical educational agenda due to its wide-reaching benefits for students in performing better at school and later as adults. With the emergence of student well-being as a priority area in educational policy and practice, efforts to measure and monitor student well-being have increased, and so has the number of student well-being domains proposed. Presently, a lack of consensus exists about what domains are appropriate to investigate and understand student well-being, resulting in a fragmented body of work. This paper aims to clarify the construct of student well-being by summarising and mapping different conceptualisations, approaches used to measure, and domains that entail wellbeing. The search of multiple databases identified 33 studies published in academic journals between 1989 and 2020. There were four approaches to conceptualising student well-being found in the reviewed studies. They were: Hedonic, eudaimonic, integrative (i.e., combining both hedonic and eudaimonic), and others. Results identified eight overarching domains of student well-being: Positive emotion, (lack of) Negative emotion, Relationships, Engagement, Accomplishment, Purpose at school, Intrapersonal/Internal factors, and Contextual/External factors. Recommendations for further research are offered, including the need for more qualitative research on student well-being as perceived and experienced by students and for research to be conducted in a non-western context.
Little is known about mental health during early childhood and differences in mental health problems between migrant and local preschool children in Chile. This research aimed to study the early mental health of children and disparities in mental health indicators between immigrant and local children in the context of a middle-income country. Parents and teachers assessed immigrant (n = 120) and non-immigrant (n = 383) children between 3 and 4 years old with the Sistema de Evaluación de Niños y Adolescentes (Child and Adolescent Evaluation System, SENA). A multivariate analysis of covariance (MANCOVA) was used to study both main and interaction effects while controlling for the clustering of children on center-based care. Results show that immigrant parents tended to report more internalizing problems than locals’ parents did in terms of depression, anxiety, and somatic complaints. Also, they reported more attention problems, developmental delay, unusual behavior, rigidity, and isolation in immigrant children. However, teachers’ assessments regarding immigrant children were similar to non-immigrant children’s evaluations in many cases. Finally, girls presented fewer emotional and behavioral problems than boys. Our study shows the importance of assessing mental health during early childhood, especially in immigrant children, and the difficulty of carrying out this evaluation through different information sources from parents and early childhood teachers.
Childhood obesity is not only worrisome for its effects on children’s health but also for its effects on general well-being. This article analyzes the impact of bodyweight on life satisfaction and three potential mechanisms that may explain this relationship among school-aged children. In addition to the traditional ordinary least squares method, we also use an instrumental variable approach to deal with the potential endogeneity of bodyweight. We use mother’s weight as plausible exogenous variation for children’s weight. Using a Chilean sample of boys (n = 2,262) and girls (n = 2,256) aged 9 to 12, we provide suggestive evidence that body mass index, weight and obesity are causality and negatively related to children’s life satisfaction. Our findings also suggest that body-image satisfaction, school bullying victimization, and physical health explain about 50 and 29 percent of the pathway between bodyweight and life satisfaction for girl and boys, respectively. Although, our results do not support gender differences in the bodyweight-life satisfaction association, we do find sizable gender differences in the mechanisms explaining this relationship. Finally, this study outlines some possible policy implications and potential avenues that future research should address.
Background Adolescence is a decisive stage in human development during which intense physical, psychological, emotional and social changes are experienced. The aim of the present study was to analyse the lifestyle differences related with the health of adolescents enrolled in first year (13.01 ± 0.62 years old) and fourth year of secondary education (16.02 ± 0.63 years old) from a region in the North of Spain. Method A cross-sectional study was conducted with a sample of 761 adolescents from twenty-five educational centres in a northern region of Spain. The sample was made up of 383 first year students and 378 fourth year students. Physical activity engagement, health-related quality of life, self-esteem, adherence to a Mediterranean diet, hours of nightly sleep, body mass index and maximum oxygen consumption were evaluated. Results First-year adolescent students reported higher values for self-esteem, health-related quality of life, physical activity, Mediterranean diet adherence, hours of nightly sleep and maximal oxygen consumption. Some differences emerged according to sex. Associative analysis revealed negative correlations between age, lifestyle habits (physical activity engagement, hours of nightly sleep and Mediterranean diet adherence) and health indicators (VO2max, self-esteem and HRQoL), with a positive association emerging with BMI. Similar findings emerged regardless of sex, with the exception of findings pertaining to VO2max not being significant in boys. Conclusion Differences perceived as a function of the adolescent’s age suggest that it should be an important consideration for educational and health organisations, with the aim of establishing intervention strategies appropriate for each age group.
The mental health and wellbeing of young people has important consequences for students and society. Schools are a logical environment for management and early intervention of wellbeing, mental health and engagement with school. Interventions aimed at improving mental health and wellbeing in education systems requires knowledge of how wellbeing is clustered at a school level. Cluster-randomised trials, and regression analyses of such data also require knowledge of clustering. While school-level clustering in academic achievement has been well documented, less is known about school-level clustering of outcomes such as student wellbeing, school climate and school engagement, especially for students younger than 13 years. We calculated intraclass correlation coefficients (ICC) for 23 measures from the Wellbeing and Engagement Census (WEC) and five standardised tests of academic achievement from the Australian National Assessment Program, Literacy and Numeracy (NAPLAN) for 19,529 students from 376 government primary schools in South Australia. We compared these to ICC values for scores from standardised tests of numeracy and literacy. School supportiveness had the largest estimated ICC (0.08) among the WEC measures, meaning 8% of the total variance was attributed to differences between schools. All other WEC measures had ICCs of 0.05 or below, and academic scores had higher ICCs (0.11 to 0.16). Nearly all ICC estimates decreased after adjusting for either student- or school-level sociodemographic factors, with academic scores showing the largest relative decreases. These ICC values can be used for planning cluster-randomised trials, complex surveys or statistical analyses and to provide insights into the education system.
Based on feldwork in Washera Qenie School, this article explores Ethiopian national identity from Qenie students’ viewpoint. Given a distinct line of knowledge system they come across, Qenie students viewed Ethiopia and Itiopiawinnet difer- ently. Individual and group interviews with 66 Qenie students (12 to 18 years old) uncovered traits that the children identifed as signifcant markers of Itiopiawinnet. These were presented under three key psychological dimensions as cognitive, emo- tional, and behavioral manifestations of national identity. By illuminating salient aspects of Ethiopian identity, this study contributes to the literature on Ethiopian national identity and for policymakers as a stepping board for further reconstruction or reframing of a multifaceted Ethiopian identity. Keywords Children · EOTC education · Itiopiawinnet · National identity · Qenie student
Psychosocial factors contribute to persistence of poverty, but are rarely addressed in poverty reduction reduction programs. We use mixed methods to investigate the relationship between a psychosocial behaviour change approach—empowered worldview (EWV), and investment decisions in children wellbeing among smallholder farmers in Zambia. Three years after exposure to EWV, logistic regression model results suggest that exposure to EWV was associated with an increased probability of parents providing basic needs of children including school fees, clothes, and food. This probability increased with more trainings. Using a matched sample, the average treatment effect on the treated of EWV is positive and statistically significant. Qualitative results reveal EWV enhanced participant agency, spouses’ propensity to work together and with others in the community, and aspirations for themselves and their children. These results point to the prevalence of psychosocial constraints and the need for interventions to sustainably address them to support human development.
Cohort effect refers to the social phenomenon that a certain event manifests differently depending on a group that is born in the same year or a similar time period. It is important to understand adolescents’ depressive symptoms vary from generation to generation. We studied the changes of the depressive symptoms during the eighth to tenth grade and examined the difference between the 1997-birth cohort and 2000-birth cohort. The study included 2,070 students (2014–2016 of 2000-birth-cohort data, from 8th to 10th grade, mean age = 12.95–14.95 years) and 2,278 students (2011–2013 of 1997-birth-cohort data, from 8th to 10th grade, mean age = 12.90–14.90 years) who participated in the Korean Children and Youth Panel Survey. Latent growth curve modeling and multi-group analysis were used to compare depressive symptom trajectories between cohorts. The result of comparing the depression levels of the cohorts showed the initial values and change rates verifying the presence of a significant cohort effect—the depression level of the 2000-birth-cohort (initial value = 17.75) was significantly lower than the depression level of the 1997-birth-cohort (initial value = 19.49). This study has significance in that adolescents’ depression has both age and cohort effects. It is speculated that the cohort effect may have been impacted by two major events: The Children Problem-Behavior Screening Questionare Test (mental health screening test), implemented nationwide in 2012, and the Sewol Ferry Disaster, which occurred in 2014. Based on the results, suggestions for future research were discussed.
In recent years, several studies have examined the effect of parents and friends on cyberbullying victims. Less is known about their combined effect on cyber perpetrators, especially among Jewish and Arab teens in Israel. We collected data from a representative sample of 350 Jewish and Arab adolescents (aged 15–16) and their parents. We repeated the interviews twice within a year. The survey included measurements of three parental practices: support, monitoring, and protectiveness, as reported by parents at the first time of data collection. We measured the adolescents’ engagement in sensation-seeking and cyberbullying as perpetrators and perceptions about peers’ involvement in these behaviors. Path-analysis models revealed that the perception of peers’ involvement in cyberbullying perpetration was positively linked with involvement in such behavior among Jewish and Arab teens. Contrary to our expectations, no parental practice had a direct effect on cyberbullying perpetration among teens in either ethnic group. The study presents important and unique findings. The results indicate that youngsters involved in cyberbullying are strongly influenced by their peers. The prevalence of this pattern in both the Jewish and the Arab populations indicates its universal nature. On a practical level, it may be suggested that bullying behaviors may be mitigated by taking measures in formal and informal education. Another aspect of the results is the decline in parental influence on adolescents’ cyberbullying behaviors, especially among Arab teens. This may be an indicator of cultural changes taking place in the Arab population in Israel alongside widening of the generation gap.
Children’s participation in decisions about their lives is a crucial point of the UN Convention on the Rights of the Child, which is the basis of child welfare and protection worldwide. Despite these clear guidelines, there is evidence that children’s voices may be heard but often with little impact on the decisions made by professionals in the childcare system. This study seeks to ascertain whether the voice of children living in foster care is considered and respected when making decisions that concern them, whether the children effectively exercise it, and what factors impact their participation. A systematic scoping review was performed to clarify concepts and unveil research gaps, using eleven scientific databases and publishers that allowed us to identify twelve recent studies in critical journals. In the light of the Bouma et al., (2018) model, the findings showed that there is, in general, a lack of effective children’s participation, namely in terms of information, listening, and involvement. Children’s voices still have a minimum impact on the decisions made in the childcare system. It will be necessary to avoid the bureaucratic assumption that there is an age cut-off point to promote participation. More, it is stressed the importance of a trusting, sincere and confidential relationship between the child and the social worker and the need to ensure training for professionals who intervene in review/statutory meetings or judicial proceedings, namely in the court of law.
We examined the ways low-income adolescents’ family resources, school resources, and belief in a just world, served to predict their subjective well-being, propensity for depression, and problem behaviors. One hundred and ninety-four low-income Chinese adolescents completed self-reported questionnaires. The results found that family resources interacted with school resources in predicting subjective well-being and depression, with resources made available through schools diminished the detrimental effects of low levels of family resources. Moreover, the relationship between the different sources of resources and psychological adjustment was moderated by the adolescents’ belief in a just world. The belief in a just world enhanced the positive effects of high levels of school resources on subjective well-being and depression only among adolescents with relatively high family resources. The belief in a just world buffered the negative effects of low levels of school resources that contributed to problem behaviors. This study identified school resources and belief in a just world, which are potentially malleable, as protective factors related to low-income adolescents’ psychological adjustment. The results have important implications for future studies and interventions.
The COVID-19 pandemic is a global mental health crisis that disproportionately impacts adolescents. Loneliness is a particularly salient pandemic psychosocial outcome to understand; however, research to date on this outcome is sparse and largely cross-sectional. In response, we examined pre-pandemic risk factors for pandemic loneliness. Further, we examined how risk may differ based on key demographics, and whether mediation or moderation models best explained potential disparities in experiencing loneliness. Self-reported, pre-pandemic mental health, trauma exposure, and family conflict survey data were collected at Wave 1 in a diverse sample of 369 adolescents (54.5% female, 45.5% male; 30.1% White; 30.9% Black; 18.4% Hispanic; Mage = 15.04; SD age = 1.10). Subsequently, self-reported experiences of loneliness during the pandemic were collected 6 months (April-June 2020) and 12 months (October-December 2020) later. Using a regression-based framework (i.e., PROCESS), we tested (a) which pre-pandemic risks uniquely predicted prospective loneliness and (b) whether loneliness risk was elevated for certain identities (i.e., mediation models) or whether certain identities were more sensitive to specific risks (i.e., moderation models). Overall, pre-pandemic depressive and aggression symptoms predicted early pandemic loneliness (6-month follow-up), whereas anxiety symptoms specifically predicted mid-pandemic loneliness (12-month follow-up). Environmental stressors were moderated by gender, such that females with pre-pandemic trauma exposure were more likely to report pandemic loneliness. Further, pre-pandemic internalizing distress for girls and externalizing symptoms for boys, reflected gender-specific pathways for loneliness. Implications for mental health prevention in the wake of national disasters are discussed. Supplementary information: The online version contains supplementary material available at 10.1007/s12187-022-09984-8.
Purpose Refugee adolescents’ quality of life (Qol) was not investigated during the Covid-19 pandemic which have a potential impact on refugee adolescents’ Qol. In this study, it is planned to investigate refugee adolescents’ Qol and its association with depression and quality of life. Methods 301 refugee adolescents aged between 14 and 18 who immigrated from Syria was included in the study. Personality Inventory for DSM-5 Brief Form (PID-5 BF), Beck Depression Scale, and Life Quality Scale was used as assessment tools. The data were tested using structural equation modeling. Results Both depressive symptoms and personality traits are associated with low Qol. Also, depression mediated the relationship between personality disorder and Qol. Conclusion This is the first study that investigates Qol in Syrian refugee adolescents during the pandemic. This study draws attention to the importance of depressive symptoms and personality traits management for improvement of Qol in Syrian refugee adolescent population. Highlights • Depressive symptoms are associated with low Qol in refugee adolescents. • Personality traits are associated with low Qol in refugee adolescents. • Depressive symptoms have a mediator role between personality traits and Qol.
A population-level adolescent health survey has been a reliable source of information about the health and well-being of 12–19-year-olds in Western Canada since its introduction in 1992. However, the survey has never accurately measured child poverty, partially due to the complex social and geographical make-up of the region. The current study sought to adapt a model for developing a child-centric index of material deprivation which had been successfully used in the UK. To develop the BC Youth Deprivation Index, 25 focus groups, including three youth-led groups, were held with 300 adolescents aged 12–19 in urban, semi-urban, rural, and remote communities in each of the province’s five regions (North, Interior, Fraser, Vancouver Coastal, and Island). Participants in the focus groups created a 10-item index of the material items adolescents felt they needed in order to belong. The draft index was piloted with 297 BC adolescents aged 12–19. The index demonstrated good internal reliability and was correlated with measures of food insecurity and subjective well-being. The finalised index was completed by over 38,000 adolescents, and is available to policy makers and practitioners. The study outcomes support the value of meaningfully engaging young people in the process of measurement development.
The aim of this research was to analyze the typologies of primary education students with regard to possession and use of video games, and the possible psycho-emotional and educational implications. To identify the different typologies, a latent class model using Latent Gold v4.5 software was applied in order to model relations between the variables observed, assuming that the structure of underlying relations was explained by a latent categorical variable (not observed). The results revealed two clearly differentiated clusters: one formed of boys who get better marks in Mathematics, usually play video games with gaming consoles for the TV screen, usually play video games online with friends, play video games for more than two hours at weekends, feel very happy when playing video games, and whose first choice of free-time activity is to play video games; the other consisted of girls who get better marks in Spanish Language and Literature, usually play video games on a tablet, usually with a family member, play video games for more than two hours at weekends, feel very happy playing video games, though to a slightly lesser extent than boys, and whose first choice of free-time activity is not usually to play video games.
Energy poverty in Sub-Saharan African countries continues to be of global concern. Its grave implications for the achievement of the sustainable development goal 7 (SDG 7) by 2030, validate this concern. Current studies, therefore, focus on analyzing the impact of energy poverty on child well-being, thus, their health, education, and cognitive skills. Despite this, studies in Sub-Saharan African countries where the highest energy poverty rates are remains scanty. Hence, using data from the current wave of the Ghana Living Standard Survey (GLSS 7), this paper analyzes multidimensional energy poverty and its impact on the health, education, and cognitive skills of children in Ghana. The multidimensional energy poverty analysis reveals that nearly 59% of children in Ghana are living in multidimensional energy-poor households. Further, the structural equation modeling (SEM) analyses show that a standard deviation increase in multidimensional energy poverty reduces child health, education, and cognitive skills by 0.155, 0.13, and 0.402 standard deviation respectively. The government through the Ministry of Energy and allied agencies and departments must commit to making modern energy accessible and affordable throughout the country to mitigate the negative impact of multidimensional energy poverty on child well-being.
This study aimed to analyze the risk and protective factors affecting the COVID-19 anxiety of primary school students after the reopening. It was investigated how primary school students’ parents’ vaccination, and COVID-19 cases seen at school, knowledge and awareness directly or indirectly explained their individual and social COVID-19 anxiety. The data were obtained from 227 primary school students living in different regions of Turkey. Pandemic Awareness Scale, Pandemic Anxiety Scale, Pandemic Information Test and Information Form were used to obtain the data. The data were analyzed by path analysis. According to the results, the case seen at school, knowledge and awareness of COVID-19 directly and significantly predicted primary school students’ individual and social COVID-19 anxiety. Vaccination of parents, on the other hand, directly significantly predicted social COVID-19 anxiety of primary school students, but did not significantly predict individual COVID-19 anxiety. In addition, in this effect, awareness of COVID-19 mediates the knowledge of COVID-19, and cases seen at school mediate the vaccination of parents. The obtained model showed a good fit. According to the results, primary school students’ knowledge and awareness about COVID-19 and parents’ vaccination reduced their anxieties, and COVID-19 cases seen at school increased their anxiety.
This paper investigates the effect of poor households’ subscription to National Health Insurance Scheme on their children’s school performance. Resource-poor households are often vulnerable to low investment in education. This is particularly the case where expenditure on health can trade of educational spending and compromise children’s academic performance. This paper argues that poor households’ subscription to National Health Insurance Scheme could reduce their health expenditure and consequentially increase educational spending to improve their children’s school performance. This proposition was investigated using data from the seventh round of the Ghana Living Standards Survey. The Instrumental Variable method was employed to address possible endogeneity problems between health insurance subscription and children’s learning outcomes. Additionally, the propensity score matching technique was used to validate the results. The results show that poor households’ subscription to National Health Insurance Scheme improves their children’s learning outcomes in Ghana. The results, therefore, imply that universal health coverage among the poor could enhance human capital development in developing countries.
Conducting a neurodevelopmental screening without considering ecological factors is insufficient and may underestimate the actual risk to development for children living in poverty. This article describes ecological risk factors among a nationwide sample (n = 231) of young children experiencing homelessness. Researchers examined rates of health care access and continuity, food insecurity, lead exposure, ACEs, and access to safe places to play using a new ecological screening tool developed for the population. Children in the sample experienced high rates of food insecurity, faced significant challenges to health care access, and significant exposure to adverse childhood events. Children experiencing homelessness and poverty experience more barriers to health care access and significantly more food insecurity and hunger. A third of caregivers reported that their child had some exposure to lead, primary due to substandard housing. And the majority were enduring long periods of homelessness with over half (56%) being between 1–6 months. Findings are discussed within a social determinants of health perspective.
The aims of this study are twofold. The first goal is to investigate the relationship between children’s experiences of being bullied (physically, verbally, and emotionally) and their subjective well-being (SWB) in seven low-industrialised Asian countries. The second aim is to ascertain how the relation between bullying victimisation and SWB differs across these countries. This study used data from the third wave of the Children’s Worlds survey across two age groups (10- and 12-year-olds) within seven Asian countries (Bangladesh, India, Indonesia, Malaysia, Nepal, Sri Lanka, and Vietnam). The sample consists of 11,483 children, based on representative sampling in each country (49.4% boys and 50.6% girls; Mean age = 11.21). Data were analysed using structural equation modelling (SEM) and multigroup SEM in order to check for metric and scalar invariance among countries. The results show an excellent fit for the models using the pooled sample for 10- and 12-year-olds. The multigroup models also displayed an excellent fit and found a significant negative contribution of bullying victimisation to SWB of children in all seven countries, depending on the type of bullying incidents (except for being left out by other children in the 10-year-old group in Nepal, which had a significant positive contribution). Being left out by other children made the strongest contribution to SWB of children in the Asian countries studied, except for India (both age groups), Nepal (10-year-old group), and Sri Lanka (12-year-old group). Being called unkind names was the most frequent bullying incident, more frequently among boys and 12-year-olds than among girls and 10-year-olds. Even though bullying victimisation negatively contributed to SWB, relatively high scores were observed for SWB in six countries according to Cummins’ theory of homeostasis (except Vietnam that displayed SWB mean scores below the expected set-point ranging from 60 to 90). The results were explained using Cummins’ SWB homeostasis theory, suggesting that children’s buffers were efficiently activated to adapt to the adverse situation of being physically, verbally, or emotionally bullied, in order to protect their SWB.
Caring for left-behind children (LBC) in rural areas can provide reserve force for the construction of new countryside and help realize rural revitalization. Based on a sample from China Education Panel Survey (CEPS), this study captured rural children’s poverty by building a multidimensional poverty index system of five dimensions (right to subsistence, health, protection, development, and participation). Then explore the relationship between the left-behind experience (LBE) and multidimensional poverty of rural children. The finding revealed that LBE significantly increases the probability of children falling into multidimensional poverty. Specifically, compared to LBE with accompanying by a single parent and LBE during school, the negative impacts of LBE without accompanying by parents and LBE during pre-school are greater, respectively. Moreover, girls and the only-child with LBE are more likely to fall into multidimensional poverty. The study also found that, overall, the poverty incidence of rural children’s right to development is the highest among the five dimensions, as well as the multidimensional poverty contribution rate of the right to participation. The multidimensional poverty index (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$MPI$$\end{document}), the multidimensional poverty incidence (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H$$\end{document}), the multidimensional poverty intensity (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A$$\end{document}), the contribution rates of the right to subsistence, protection, and participation of children with LBE in rural areas are higher than those of children without LBE respectively. This study contributes to a better understanding of the multidimensional poverty of rural children in China and provides a valuable direction for alleviating multidimensional poverty from the perspective of LBE. Meanwhile, these findings are conducive to raising the attention of families and governments to LBC in rural areas and ensuring the welfare of rural children.
This study describes the multidimensionality of child poverty and produces the first multidimensional child poverty indices in North Macedonia. We use the Alkire-Foster method to develop two age-specific (0–4 years and 5–17 years) child multidimensional poverty indices (MPIs) by leveraging secondary data from Multiple Indicator Cluster Survey (MICS) 2018/2019 for North Macedonia and North Macedonia Roma Settlements. We find that the largest part of multidimensionally poor children are deprived within the range 33 − 39% of deprivations and the structure of multidimensional child poverty is similar for less, as well as for more intensely deprived children in both age-groups. Additionally, we identify the most deprived groups with respect to the area of living, ethnicity, and geographical location. The study provides general recommendations for policymakers to reduce child poverty in North Macedonia.
The study investigated the nutritional status of under-five children of farm households. The study utilized primary data from 352 farm households with 140 under-five children. Household crop commercialization index (CCI) was used to estimate cassava farm household crop sale ratio and categorize the households into four commercialization levels while WHO Anthro software was employed to analyze under-five children anthropometric indices such as weight-for-age z-score (WAZ), height-for-age z-score (HAZ) and weight-for-height z-score (WHZ). Logit regression model (LRM) was used to examine the drivers of under-five children’s nutritional status of farm households. The study found that 42.9%, 7.9% and 3.6% of the children are stunted, underweight and wasted respectively. The highest stunting level was recorded in zero level households (CCI 1). Although, some higher CCI households (medium-high and very-high level) recorded increased percent of stunted children. This revealed that being a member of low or high-level commercialization households may not guarantee better nutritional status of young children of farm households. The results of LRM indicated that the predictors of children nutritional status were child’s age, farm size, access to electricity, healthcare and commercialization variables. Moreover, weak positive and negative relationships exist between CCI and children’s nutrition outcomes as measured by the z-scores. The study recommended maternal nutrition-sensitive education intervention that can improve nutrition knowledge of mothers and provision of infrastructure that enhance increased farm production and promote healthy living among farm households.
In recent years, many studies have referred to the interdependence between cognitive (hard-skills) and students’ academic performance. However, despite their relevance, soft-skills have not received the same treatment and have not been analysed as extensively, particularly from a gender perspective. Therefore, and bearing in mind that analysing from a gender perspective is essential to reduce occupational segregation and soft-skills can enhance young people’s personal and academic development, throughout this paper we have analysed the gender gap in soft-skills with a sample of 15–16 years old students from the Spanish region of Andalusia. To do so, we have used a recent innovation of the Oaxaca-Blinder decomposition technique. Our results show not only that the gender gap in soft-skills is correlated with gender stereotypes, but also that grade retention or being an immigrant show a greater degree of association with boys’ soft-skills than girls’, while mothers’ educational level is more correlated with the soft-skills of girls.
This paper studies the role of schools' we-mentality in shaping students' civic outcome. A school's we-mentality is important for the students' perception and education of sense of community. We-mentality is measured by an automated content-analysis approach applied to the schools' general principle. Data stem from a survey conducted in 13 German schools with 488 students. Using OLS and multi-level regression techniques, I find that stronger we-mentality is associated with more students being engaged in local civic activities. Moreover, students that exhibit stronger trust in others and are willing to engage with new and unknown tasks show more positive attitudes towards civic issues. The results hold relevance for the educational design of schools in fostering adolescents' civic education and participation.
Peer school victimization via minor and less severe forms of violence may predict victimization via more severe and major forms of violence. Nonetheless, very rarely are the escalating patterns of violence addressed theoretically or empirically tested. In the school context, the quality of peer and teacher–student relationships are critical determinants of peer victimization, although inconclusive mechanisms have been suggested to establish associations among students’ interpersonal relationships and peer victimization. To address prior inconsistencies and better conceptualize theoretical knowledge of these associations, this study developed and tested a path model of peer and teacher–student relationships and peer victimization via relational, verbal, and physical victimization. Secondary data analysis of a nationally representative sample of fifth- and eighth-grade students in Israel (N = 75,852) revealed an escalation pattern across types of victimization, in which relational victimization was associated with victimization via verbal and physical violence. Although both types of relationships significantly influenced victimization, peer relationships had the strongest effect, beyond the influence of teacher–student relationships. The identified empirical links among interpersonal relationships and peer victimization can support theoretical and operational frameworks essential to preventing school victimization and protecting students from negative educational, social, and emotional outcomes. Finally, we suggest important directions for future research.
This paper aims to present the results of implementing a new, multi-dimensional and cumulative tool that records the well-being of children in the 1st semester of the school year 2020–2021, which constitutes the fourth round of an ongoing research. The tool was implemented in Attica through questionnaires circulated in twenty-five schools and three support centers for children and families under the organization, “The Smile of the Child” (twenty-eight bodies in total). The total number of children who participated in the sample was 1,114, belonging to three distinct school categories: the 6th grade of elementary school (10–11 years old), the 3rd grade of junior high (13–14 years old), and the 3rd grade of high school (16–17 years old). The results, mapped out in seven clusters, reveal evident concerns over nutrition and the moral education of students. In addition, the results indicate the impact of the COVID-19 pandemic on the well-being of children and reveal with regard to national policy and legislation framework that the status of welfare state in Greece is ineffective and problematic. The theoretical and methodological framework of the study was confirmed through a multiple correspondence analysis (MCA) and a principal component analysis (PCA).The outputs of MCA reflect and confirm the good effect of “The Smile of the Child” for children in need. Finally, an action plan including the creation of policies based on public finance and fuzzy logic was suggested, the most important being the necessity of the establishment of a new Ministry for the protection of child well-being.
The COVID-19 pandemic has led to significant changes in the lives of families with young children. The present study aimed to explore whether child social isolation due to the COVID-19 crisis was associated with toddlers’ emotional and behavioral health (EBH) and whether this association was moderated by caregiving distress, during the second mandatory lockdown in Portugal. Participants included 315 toddlers and their primary caregivers. Caregivers were invited to complete a set of questionnaires in order to report about toddlers’ social isolation from other significant family members, other children, and activities outside the house, and to provide ratings of caregiving distress and toddlers’ EBH. Family socioeconomic factors, including stressors resulted from the pandemic, were also measured. Significant interaction effects, independent of child sex and sociodemographic factors, between COVID-19-related social isolation and caregiving distress emerged in the prediction of toddlers’ EBH: COVID-19-related social isolation was found to be a significant predictor of both emotional/behavioral competencies and problems, but only among toddlers exposed to higher levels of caregiving distress. This study evidences the negative impact of the COVID-19 crisis on the functioning of Portuguese families and toddlers’ EBH. It emphasizes the importance for policies to consider the implications of the COVID-19 crisis for young children, and to provide psychosocial support to families in order to reduce caregiving distress and, thus, prevent children’s mental health problems.
In many countries, Indigenous populations have reported lower levels of subjective well-being (SWB) compared to non-Indigenous groups. However, research on this topic is still scarce in Latin America, particularly Chile, where Indigenous people from nine recognized ethnic minority groups represent 9.5% of the population. This study analyzes the SWB of children and adolescents pertaining to Indigenous ethnic minorities living in Chile. Participants were 44,451 students from 430 schools with low socioeconomic status (20.18% were from ethnic minorities) enrolled in fifth to eighth grade (M age = 12.47, SD = 1.41) who answered the Brief Multidimensional Student’s Life Satisfaction Scale and a single item on overall life satisfaction, which have been used as subjective well-being indicators. Findings showed that non-Indigenous adolescents reported higher subjective well-being, followed by the Mapuches and Aymara groups, with the other Indigenous group reporting the lowest scores. Well-being profiles were similar between the Mapuche and non-Indigenous groups and significantly different from the profiles of the Aymara and other Indigenous groups. We discuss these cross-cultural differences and their implications for policy and intervention.
This article explores how child protection clients perceive their opportunities to exercise agency in their encounters with child protection services. Child clients include respondents who were children at the time of responding or had previous contact with child protection services, i.e. those under the age of 18 (n = 217); adult clients include parents, guardians, and relatives (collectively referred to as “family members”) who had personal experience with child protection workers (n = 505). The analysis applies a three dimensionional framework of understanding agency (autonomy, construction and action) inspired by Kuczynski and colleagues. The analysis showed that child protection clients, i.e. both children and adults, have insufficient opportunities to exercise their agency in their interactions with child protection services. One of the factors hindering the exercise of agency is the power imbalance perceived by clients due to the lack of transparency in child protection work and the imposition of their own opinions by child protection practitioners. On the other hand, agency is enhanced if the client feels that they are an equal partner in their interactions with the child protection worker. It was also found that an opportunity to exercise agency made children and their family members feel that child protection work had been effective: a large proportion of both children and adults who had been able to exercise agency reported that their situation improved as a result of child protection work. The article concludes with recommendations for enhancing child protection clients’ agency in their interactions with child protection practitioners.
The COVID-19 pandemic and lockdowns potentially severely impact adolescents’ mental well-being. This research aims to study students’ subjective well-being during the covid-19 pandemic in Iran and investigate the role of loneliness, resilience, and parental involvement. For this study, 629 students (female = 345) were recruited by purposive sampling. Students were assessed on the Student’s Subjective Well-Being, Loneliness Scale, Resilience Scale, and Parental Involvement. The results confirm our hypothesis that the relationship between parental involvement and students’ subjective well-being is mediated by loneliness. Furthermore, the results indicated a partial mediation of resilience in the relationship between parental involvement and students’ subjective well-being. This study theoretically contributes to a better understanding of the factors determining the impact of traumatic events such as a pandemic on adolescents’ mental health. The implications of this study indicate interventions that can be carried out to minimize the negative psychological consequences of the pandemic.
Low-Income children are susceptible to mental health problems. While social support has been found to protect children from these issues, most studies focus on the frequency of support rather than the importance of support. The importance of support refers to subjective value that the child places on the support provided. The present study investigated whether social support from parents, teacher, classmates or close friends was related to internalizing and externalizing problems, in 513 low-income children between 7 and 12 years of age. We investigated if these associations followed a main effect model, stress-buffering model or enhanced stress-buffering model. When parent support was considered important by the child, there were positive associations of economic hardship and internalizing problems. Furthermore, when parent support was frequent, or both infrequent and important, there was a positive association between economic hardship and externalizing problems. Conversely, teacher support that was considered important by the child was protective for internalizing problems in children. In addition, teacher support that was frequent and considered important, was protective for children’s externalizing problems. Implications arising from the study are discussed.
The well-being of children and adolescents is emerging as an area of interest for population health measurement. Previous approaches assessing national and state trends in well-being have relied on composite indices. However, these methodologies suffer from several weaknesses. This paper develops an improved index for the United States that is measurable with existing population-data resources. It derives the appropriate weights for items in this index using a longitudinal panel of 2,942 children in the Panel Study of Income Dynamics. Candidate component measures are selected for the index based on their demonstrated association with several subjective scales assessed during young adulthood. The final index demonstrates that a broad range of measures indicate higher levels of population-level well-being. The predictive validity of the index for outcomes during young adulthood is also assessed: a one-standard-deviation increase in the index score is associated with a 7.9-percentage-point decrease [95% CI: 5.9 - 9.8] in ever reporting fair or poor health, a 6.3-percentage-point decrease [95% CI: 4.6 - 8.0] in ever reporting depression, and a 17.2% [95% CI: 13.7% - 20.5%] increase in peak earnings. These values for predictive validity are slightly higher than those of existing methodologies. We also find that incorporating contextual indicators from childhood and adolescence does not substantively improve predictive validity. Policy-makers and government agencies interested in population-level well-being of children and adolescents can continue to use existing indices as reasonable proxies, but should also commit to upgrading data systems to make them more child-centric in the future. Supplementary information: The online version contains supplementary material available at 10.1007/s12187-022-09962-0.
The corona virus (COVID-19) pandemic has led to a global health crisis causing fear and negative psychological consequences. In this study, the validity and reliability of the Emotional Flexibility Scale were evaluated in a sample of adolescents in Turkey. A total of 833 high school students from 65 different cities participated in the study. Emotional flexibility, adolescent psychological resilience, and adolescents' subjective well-being Scales were used as data collection tools. For the adaptation of emotional flexibility scale, confirmatory factor analysis, convergent validity, and reliability analyses were used. Also, the mediating role of subjective well-being on the relationship between emotional flexibility and resilience was tested. Emotional flexibility was found to be associated with subjective well-being and resilience. The results of the study show that the Emotional Flexibility Scale is a valid and reliable measurement tool in the sample of adolescents in Turkey. Supplementary information: The online version contains supplementary material available at 10.1007/s12187-022-09959-9.
What does it mean to be a (female) child in the city of Baku, Azerbaijan? How can we critically interpret the girls' understandings of well-being considering different forms of compliance with unequal social orders? What conclusions may be drawn from understandings of well-being about the nature of welfare state structures and therein children's specific positioning? To answer these questions, we conducted qualitative interviews with 13 girls during their various leisure activities. The study shows that parents and in particular mothers are children's key reference persons, while there are hardly any spaces the girls can explore or reference persons outside their immediate families. The article reconstructs how the 13 girls view the social practices of adults and how they relate these practices to their own perceptions of well-being. We inductively reconstruct different forms of compliance, i.e., the extent to which social practices are consistent with the symbolic representations (norms and values) of a specific social order and specific relations of power and hegemony. The analysis shows how girls make differentiations between adult social practices based on their knowledge orders: some practices they justify through a sort of complicity with adultist structures (competent compliance), others they must accept due to their own vulnerabilities as children (compliance and constitutive vulnerability), still others irritate, are rejected, or sabotaged (fragile compliance).
The present paper considers the main constraints and opportunities in the construction of girls’ educational projects in Kyrgyzstan in relation to their subjective well-being from the intergenerational perspective. Today children have got new educational opportunities brought by various social transformations; at the same time, they come across new challenges which are often related to social inequality and economic problems on the local level. Especially female educational trajectories seem to experience noticeable effects of these transformations. The author uses the theoretical concept of social capital to observe the role of the family in the construction of girls’ educational projects. In addition to this, the applied intergenerational approach allows to observe the changes and continuities in parent-child relations. The findings show that in Kyrgyzstan “being well-educated” continues to be an essential element, the foundation of girls’ educational projects, similar to how it was for girls’ mothers in the same age. In the context of a strong hierarchical family structure and low level of state opportunities, today girls tend to rely only on family social and cultural capital for the realisation of educational projects. However, families’ actions are often aimed at the future prosperity, neglecting children’s interests at the present time. Besides, girls face gender-specific limitations related to the perception of women’s roles in the society. The frames within which girls can take decisions regarding educational trajectories are strongly defined by their families. This often leads to the feeling of uncertainty among girls and ambivalence between global promises and the “actual” local opportunity structures.
This study examines the relationship between parental time poverty, child work, and school attendance in Ghana using data from the sixth and seventh rounds of the Ghana Living Standard Survey (GLSS6 and GLSS7). Results of the analysis indicate an increasing decline in child enrolment in public schools (from 9% to 6%) among time poor household heads. In addition, parental time poverty increases children's walking hours to and from school and private school enrolment. We observed heterogeneity of parental time poverty on child work in relation to the location of households and gender disaggregation. Child work and school attendance-reducing effect of parental time poverty is mainly prevalent among male children but mixed for location. Our result is robust to the alternative estimation method of addressing endogeneity and further shows that household income is the primary channel through which time poverty influences child work and school attendance. Supplementary information: The online version contains supplementary material available at 10.1007/s12187-022-09926-4 10.1007/s12187-022-09926-4.
Adolescent subjective well-being, including life satisfaction, has shown declines at national level across many countries in recent years. Although several possible explanatory factors have been identified, there is a lack of research on whether these may be similar or different across countries. Using data on 15-year-old adolescents from the Programme for International Student Assessment study in Scotland, England, Wales, Northern Ireland, the United States, Japan, Ireland and France in 2015 and 2018, we find that changes in school well-being and, to a lesser extent, the use of Information and Communication Technologies and material well-being were associated with observed declines in life satisfaction. Although there are similarities across some countries, cross-country differences in factors associated with decreasing life satisfaction emerged, notably between Western nations and Japan, with some gender differences also evident.
This theoretical study explores the empowerment perspective regarding children with disabilities. Article 12 of the UNCRC states children’s right to express their views and be listened to. Meanwhile, studies show that children with disabilities are at risk of overprotection, which may restrict their participation and influence. Honneth’s theory of recognition and Sen’s Capability Approach are discussed together with the empowerment perspective when it comes to fulfilling article 12 regarding children with disabilities alongside empirical studies. Finally, a new model of dynamic empowerment is suggested to illuminate the interrelational complexity in this matter, as well as a way of identifying and understanding the possible mechanisms that may affect children with disabilities and their participation and influence.
The COVID-19 pandemic resulted in the greatest disruption to children’s schooling in generations. This study analyses primary school children’s emotional engagement with remote schooling during the Spring 2020 lockdown in the Republic of Ireland, which involved one of the longest school closures among rich countries at the time. It investigates whether children’s engagement with their remote schooling varied by personal and family characteristics, using data from the Children’s School Lives (CSL) surveys. CSL is a nationally representative study of primary schools in Ireland, which collected information from children aged 8–9 years in May – August 2019 and in May – July 2020. Linear regression estimates with school fixed effects are based on the analytic sample of nearly 400 children (from across 71 schools) who took part in both waves and have complete data on all the key variables. Emotional engagement with schooling is measured using child-reported items on satisfaction with schooling. Everything else being equal, children who reported higher engagement with schooling before the pandemic were more engaged with remote schooling during the lockdown. Although there were no significant differences by family affluence, children with greater resources for home schooling reported higher levels of engagement. This includes having a computer or a laptop for schoolwork, having someone to help with schoolwork if the child is worried about falling behind, and having schoolwork checked by a teacher. This points to the paramount importance of adequate digital technologies in the home as well as the availability of help during periods of remote schooling.
Wellbeing declines during adolescence, for which the reasons are unclear. This analysis explored associations between wellbeing and multiple lifestyle, socioeconomic and school-level factors in young people. Data were collected as part of the Wellbeing in School (WiSe) survey of adolescent school children in Northern Ireland at age 13–14 years ( N = 1618; 49% female) and 15–16 years ( N = 1558; 50.5% female). Wellbeing was assessed using the short-form Warwick-Edinburgh Mental Wellbeing Scale (sWEMWBS), where scores declined between time one (13–14 years) and time two (15–16 years) in both sexes and were significantly lower in females at both timepoints. Multilevel, multivariate modelling was therefore undertaken separately for males and females with sWEMWBS scores as the dependent variable. Physical activity, family affluence, fruit and vegetable intake, social media use, sleep duration, school factors (size and type) and religion were independent variables. More frequent physical activity in both sexes at both timepoints was associated with higher sWEMWBS scores. In females, higher sWEMWBS scores were associated with less social media use at time one (and marginally at time two), greater family affluence at time two, and being Catholic at both timepoints. In males, higher sWEMWBS scores were associated with more frequent fruit and vegetable intake at time one. Mental wellbeing was unrelated to sleep duration or school factors in either sex, at both time points. Efforts to maximize mental wellbeing in adolescents should promote engagement in physical activity and implement sex-specific interventions.
The contributions in this special section deal with growing up in two post-Soviet states – Azerbaijan and Kyrgyzstan. Each contribution has a different priority on the variety of forces that shape the wellbeing of children and youth as structured in the interaction between the efforts and abilities of their families, the state, as well as social and health policies in both national and cross-national contexts. In this special section, we understand infrastructure as places and institutions for day-care, education, leisure, social and health services. The papers identify barriers that children and young people encounter as they attempt to realize their potential and wishes in a variety of social, educational, and health contexts. These obstacles have something in common: they are rooted in a deficit of public and social infrastructure that is evident in these two states (European Commission, 2011; Sardarova, 2020; OECD, 2018; UNICEF, 2015).
Juvenile delinquency is the outcome of complex interactions with multiple factors. However , few studies have explored what factors most likely contribute to delinquent behavior among female and male adolescents when all possible levels of factors are included in one model. To fill this gap, the current study investigated what factors were associated with juvenile delinquency and which factors were appeared to be significant in both female and male adolescents using machine learning algorithms. This information can be particularly informative for policymakers and researchers to capture the overall feature of delinquency. Data were derived from three-time points (8th grade, 9th grade, and 10th grade) of the nationally-representative Korean Children and Youth Panel Survey (KCYPS). The sample consisted of an almost equal number of males and females. This study employed the Least Absolute Shrinkage and Selection Operator (LASSO) regression as an exploratory analysis to identify important factors related to juvenile delinquency and compared coefficients of each factor in the model. The results showed that individual factors, including cyber delinquency, aggression, romantic relationships, following school rules, engagement in learning activities at school, academic confidence in Korean, English, and math, relationships with teachers, peer relationships, social withdrawal, and mobile phone dependency , were relatively important factors of delinquency for both females and males. These findings suggest that using LASSO regression to identify the most important factors for juvenile delinquency will provide an opportunity to understand the complex phenomenon of delinquency among female and male adolescents and can be a useful source in delinquency prevention policies in Korea.
Self-compassion refers to being kind, understanding, and accepting toward oneself in times of failure, frustration, or negative feelings. Since self-compassion is related to both physical and psychological well-being, measuring and understanding self-compassion in different populations carries importance for their mental well-being and life satisfaction outcomes. One such group is the youth, who experience unique developmental challenges. For this purpose, a Self-Compassion Scale for Youth (SCS-Y) was developed (Neff et al., 2021) and this paper presents its Turkish adaptation. The Turkish translation of SCS-Y was tested on a sample of Turkish youth (N = 450, 61.8% female, Mage= 13.09 ± 1.59, range = 11–15) and was found to have acceptable reliability. The scale showed a similar structure to the original testing on American youth with a bifactor model of a general self-compassion score and six subscale scores, and a two-bifactor model where negative and positive aspects are grouped together. Self-compassion was positively related to resilience and well-being, and negatively related to depression. A serial mediation analysis showed self-compassion to have a direct and positive effect on resilience, and to have an indirect effect on well-being mediated by resilience and depression. Given that the trainable skill of self-compassion is associated with higher resilience, lower depression, and better well-being, the value of this scale and its different adaptations becomes evident, as they enable measuring self-compassion in youth in various populations such as the present Turkish one and guiding the design of future interventions to increase self-compassion, targeted for the specific concerns of the youth.
This research paper aims to present the results of implementing a new multi-dimensional and cumulative tool that records child well-being, in the 2nd semester of the school year 2019-2020, which is the third round of an ongoing research. It also presents the results of the same year as a whole, in order to investigate the impact of the COVID-19 pandemic on the well-being of children. The tool was applied in Attica through questionnaires, addressing 22 public schools and three support centers of the organization, The Smile of the Child (25 units in total). The number of children in the sample was 560, belonging to three distinct school categories. The results of the 2nd semester were mapped out in seven clusters. The analysis of the results of the school year 2019-2020 as a whole was applied on a sample of 1,731 children; in other words, it incorporated almost the entire sample of the surveys conducted in the 1st and 2nd semesters. Finally, an action plan, based on the legal framework, focusing on mitigating the negative effects of the pandemic on child well-being is suggested. Supplementary information: The online version contains supplementary material available at 10.1007/s12187-021-09910-4.
Top-cited authors
• Universitat de Girona
• Glasgow Caledonian University
• NHS Greater Glasgow and Clyde
• Mehmet Akif Ersoy University
• University of Bergen |
When:
May 18, 2018 all-day
2018-05-18T00:00:00-04:00
2018-05-19T00:00:00-04:00
Where:
Winston- Salem Fairgrounds Cattle Barn
421 27th St NW
Winston-Salem, NC 27105
USA
Friday May 18th starting at 4PM to be followed by 2 ring Buck Show. Saturday May 19th we will start promptly at 8AM with a 2 ring Sr Doe and 2 ring Jr Doe Show. This will be followed by 2 ring Buck Show Saturday afternoon/evening. Sunday May 19th we will have Showmanship starting promptly at 8AM followed by 2 rings of Sr Doe and Jr Doe Show.
## Check in times are as follows:
Youth Show Friday May 18th must be checked in by 2:30PM on May 18th, 2018.
Buck Show Friday May 18th must be checked in by 5PM on May 18th, 2018.
Sr and Jr Doe Shows Saturday May 19th must be checked in by 7AM on May 19th, 2018
Buck Show Saturday May 19th must be checked in by 2PM on May 19th, 2018
Sr and Jr Doe Shows Sunday May 20th must be checked in by 7AM on May 20, 2018
We will post more details as the event gets closer. |
# TIL: Plenty of Bad Labels
Data Quality Strikes Again
Vincent Warmerdam koaning.io
2021-06-23
I read a fun paper the other day.
The short story of this paper is that common benchmarking datasets contain bad labels. It was well known that in MNIST a 5 can sometimes look like an 8, so those mistakes might be forgiven. The paper however shows that the mistakes are a fair bit worse.
The paper tries to build algorithms to detect these mislabelled instances. The algorithm works by giving a percentage $$\alpha$$ of images the user is willing to manually re-evaluate and then the algorithm tries to find the appropriate candidates to check.
Their approach is straight-forward. A model is $$g$$ is trained and applied on a datapoint $$x_i$$. They then compare the model output $$g(x_i)$$ with the true label $$y_i$$. The model confidence can be used as a proxy to sort labels so that a user can check them.
It’s a neat trick but given that the state-of-the-art is often 99+% for some of these datasets, it might be time for a few of these models to be re-run. |
# Article
Thermophysical Properties of Materials
2009. V. 47. № 1. P. 27–32
Kasenov B.K., Mustafin E.S., Kasenova Sh.B., Sagintaeva Zh.I., Edil'baeva S.T., Davrenbekov S.Zh.
The calorimetry and thermodynamic functions of $\mathrm{NdMe}^{\mathrm{I}}_3\mathrm{Mg}_3\mathrm{Mn}_4\mathrm{O}_{12}$ $(\mathrm{Me}^{\mathrm{I}} - \mathrm{Li, Na, K})$ manganites in the range from $298.15$ to $673$ K
Annotation
The ceramic technology is employed for synthesizing manganites of composition $\mathrm{NdMe}^{\mathrm{I}}_3\mathrm{Mg}_3\mathrm{Mn}_4\mathrm{O}_{12}$ $(\mathrm{Me}^{\mathrm{I}} - \mathrm{Li, Na, K})$. The X-ray technique is used to find that the compounds crystallize in tetragonal syngony. The parameters of their crystal lattices are determined. Their heat capacities are experimentally determined in the range from $298.15$ to $673$ K, which enables one to reveal second-order phase transitions. In view of these transitions, equations describing the $C^{\circ}_p \sim f(T)$ dependence are derived, and the thermodynamic functions $C^{\circ}_p(T)$, $H^{\circ}(T) - H^{\circ}(298.15)$, $S^{\circ}(T)$ и $\Phi^{xx}(T)$ are calculated.
Article reference:
Kasenov B.K., Mustafin E.S., Kasenova Sh.B., Sagintaeva Zh.I., Edil'baeva S.T., Davrenbekov S.Zh. The calorimetry and thermodynamic functions of $\mathrm{NdMe}^{\mathrm{I}}_3\mathrm{Mg}_3\mathrm{Mn}_4\mathrm{O}_{12}$ $(\mathrm{Me}^{\mathrm{I}} - \mathrm{Li, Na, K})$ manganites in the range from $298.15$ to $673$ K, High Temp., 2009. V. 47. № 1. P. 27 |
Distribution of Charge on a Conducting shell
1. Nov 6, 2012
fornax
1. The problem statement, all variables and given/known data
A +30mC point charge sits at the center of a spherical thick metal shell, of 4.0cm inner radius, and 2.0cm thickness. The net charge on the shell is -50mC.
2. Relevant equations
3. The attempt at a solution
I came up with several conclusions and I'm not really sure which one is right. I'm just looking for a confirmation of how this charge would distribute itself. I learned that in such a case as this, an equal and opposite amount of charge would distribute itself across the inner surface of the shell, so -30mC. Since the net charge is then -50mC, that means that -20mC must be on the outer surface. That didn't really make much sense to though me since there is no where for a positive charge on the shell. So does that mean there's a charge of -80mC on the inner surface of the shell, and +30mC on the outside? or is it just one big negatively charged conductor?
2. Nov 6, 2012
ehild
The shell is negatively charged and the point charge at the centre attracts equal amount of negative charge onto the inner surface of the shell. The remaining negative charge distributes on the outer surface.
ehild
3. Nov 6, 2012
fornax
Thank you so much, I've been stuck on the rest of the problem. Thank you for clarifying that for me. |
Arduino code to control motor speed based on MPU-6050 sensor
I have been trying to create arduino code where my MPU6050 reads its angle and based on that angle, change the motor speed. For example, 45° is the max motor speed, 22° is roughly half speed, and so on.
I have a 5065 200kv brushless motor going to a ESC with a bec which I can attach to the Arduino. I have modified some self-balancing drone code from a tutorial that used a proportional-integral-derivative controller. What I want to do is take out the PID and do a comparison: if the angle is between 5° and 45° then servo write (angle × 44), because if I multiply the maximum angle by 44 I will get around 2000, which is the original top speed of the code. Although mine can go faster, and I will change it later after testing. I am fairly new with Arduino and I have not used the MPU6050 before.
#include <Wire.h>
#include <Servo.h>
Servo right_prop;
int16_t Acc_rawX, Acc_rawY, Acc_rawZ,Gyr_rawX, Gyr_rawY, Gyr_rawZ;
float Acceleration_angle[2];
float Gyro_angle[2];
float Total_angle[2];
float elapsedTime, time, timePrev;
int i;
double throttle=0; //initial value of throttle to the motors
void setup() {
Wire.begin(); //begin the wire comunication
Wire.beginTransmission(0x68);
Wire.write(0x6B);
Wire.write(0);
Wire.endTransmission(true);
Serial.begin(250000);
right_prop.attach(3);
time = millis();
}
void loop() {
/////////////////////////////I M U/////////////////////////////////////
timePrev = time;
time = millis();
elapsedTime = (time - timePrev) / 1000;
Wire.beginTransmission(0x68);
Wire.write(0x3B);
Wire.endTransmission(false);
Wire.requestFrom(0x68,6,true);
/*---Y---*/
Wire.beginTransmission(0x68);
Wire.endTransmission(false);
Wire.requestFrom(0x68,4,true); //Just 4 registers
/*---X---*/
Gyro_angle[0] = Gyr_rawX/131.0;
/*---Y---*/
Gyro_angle[1] = Gyr_rawY/131.0;
/*---X axis angle---*/
Total_angle[0] = 0.98 *(Total_angle[0] + Gyro_angle[0]*elapsedTime) + 0.02*Acceleration_angle[0];
/*---Y axis angle---*/
Total_angle[1] = 0.98 *(Total_angle[1] + Gyro_angle[1]*elapsedTime) + 0.02*Acceleration_angle[1];
Serial.println(Total_angle[1]);
if( Total_angle[1]> 5 && Total_angle[1]< 45)
{
right_prop.write(Total_angle[1]*44);
}
else{
right_prop.write(0);
}
}
//end of loop void
• i have modified code using the code of a self balancing drone which used the mpu6050 and made a PID control system to balance the drone between two motors spinning at different speeds to counteract the other motor and make the drone level. My modified code is my attempt at removing the PID control and make it so the arduino reads what angle the sensor is at and tells my one motor to go a certain speed depending on the angle. If you would like i could post the original code or the video about it on youtube. – miles Feb 27 '19 at 22:55
• Where did the original code come from? – 200_success Feb 27 '19 at 22:56
• A youtube video youtu.be/AN3yxIBAxTA – miles Feb 27 '19 at 22:59
• I have gone back and corrected all the errors from copying it. I appologize if i did this completely wrong. I believe i got rid of anything related to the PID and kept everything for reading the angle of the sensor to tell the motor what to do. Would it be simpler to make code that purely reads the angle of the motor and just add a “servo” to the code then do my if-then statement in the loop? – miles Feb 28 '19 at 0:02 |
# The Physics of the Damped Harmonic Oscillator
This example explores the physics of the damped harmonic oscillator by
• solving the equations of motion in the case of no driving forces,
• investigating the cases of under-, over-, and critical-damping
### Contents
1. Derive Equation of Motion
2. Solve the Equation of Motion (F = 0)
3. Underdamped Case ($\zeta <1$)
4. Overdamped Case ($\zeta >1$)
5. Critically Damped Case ($\zeta =1$)
6. Conclusion
### 1. Derive Equation of Motion
Consider a forced harmonic oscillator with damping shown below. Model the resistance force as proportional to the speed with which the oscillator moves.
Define the equation of motion where
• $m$ is the mass
• $c$ is the damping coefficient
• $k$ is the spring constant
• $F$ is a driving force
syms x(t) m c k F(t) eq = m*diff(x,t,t) + c*diff(x,t) + k*x == F
eq(t) =
Rewrite the equation using $\mathit{c}=\mathit{m}\text{\hspace{0.17em}}\gamma$ and $\mathit{k}=\mathit{m}\text{\hspace{0.17em}}{\omega }_{0}^{2}$ .
syms gamma omega_0 eq = subs(eq, [c k], [m*gamma, m*omega_0^2])
eq(t) =
Divide out the mass $\mathit{m}$. Now we have the equation in a convenient form to analyze.
eq = collect(eq, m)/m
eq(t) =
### 2. Solve the Equation of Motion where F = 0
Solve the equation of motion using dsolve in the case of no external forces where $F=0$. Use the initial conditions of unit displacement and zero velocity.
vel = diff(x,t); cond = [x(0) == 1, vel(0) == 0]; eq = subs(eq,F,0); sol = dsolve(eq, cond)
sol =
Examine how to simplify the solution by expanding it.
sol = expand(sol)
sol =
Notice that each term has a factor of ${\sigma }_{1}$, or ${e}^{-\gamma t/2}$, use collect to gather these terms
sol = collect(sol, exp(-gamma*t/2))
sol =
The term $\sqrt{{\gamma }^{2}-4{\omega }_{0}^{2}}$ appears in various parts of the solution. Rewrite it in a simpler form by introducing the damping ratio $\zeta \equiv \frac{\gamma }{2{\omega }_{0}}$.
Substituting ζ into the term above gives:
$\sqrt{{\gamma }^{2}-4{\omega }_{0}^{2}}=2{\omega }_{0}\sqrt{{\left(\frac{\gamma }{2{\omega }_{0}}\right)}^{2}-1}=2{\omega }_{0}\sqrt{{\zeta }^{2}-1},$
syms zeta; sol = subs(sol, ... sqrt(gamma^2 - 4*omega_0^2), ... 2*omega_0*sqrt(zeta^2-1))
sol =
Further simplify the solution by substituting $\gamma$ in terms of ${\omega }_{0}$ and $\zeta$,
sol = subs(sol, gamma, 2*zeta*omega_0)
sol =
We have derived the general solution for the motion of the damped harmonic oscillator with no driving forces. Next, we'll explore three special cases of the damping ratio $\zeta$ where the motion takes on simpler forms. These cases are called
• underdamped $\left(\zeta <1\right)$,
• overdamped $\left(\zeta >1\right)$, and
• critically damped $\left(\zeta =1\right)$.
### 3. Underdamped Case ($\zeta <1$)
If $\zeta <1$, then $\sqrt{{\zeta }^{2}-1}=i\sqrt{1-{\zeta }^{2}}$ is purely imaginary
solUnder = subs(sol, sqrt(zeta^2-1), 1i*sqrt(1-zeta^2))
solUnder =
Notice the terms ${\mathit{e}}^{\mathit{i}\text{\hspace{0.17em}}{\omega }_{0}\text{\hspace{0.17em}}\mathit{t}\sqrt{{\zeta }^{2}-1}}±\text{\hspace{0.17em}}{\mathit{e}}^{-{\mathit{i}\text{\hspace{0.17em}}\omega }_{0}\text{\hspace{0.17em}}\mathit{t}\sqrt{{\zeta }^{2}-1}}$ in the above equation and recall the identity ${\mathit{e}}^{\mathit{i}\text{\hspace{0.17em}}\mathit{x}}=\mathrm{cos}\left(\mathit{x}\right)+\mathit{i}\text{\hspace{0.17em}}\mathrm{sin}\left(\mathit{x}\right).$
Rewrite the solution in terms of $\mathrm{cos}$.
solUnder = coeffs(solUnder, zeta); solUnder = solUnder(1); c = exp(-omega_0 * zeta * t); solUnder = c * rewrite(solUnder / c, 'cos')
solUnder = ${\mathrm{e}}^{-{\omega }_{0} t \zeta } \mathrm{cos}\left({\omega }_{0} t \sqrt{1-{\zeta }^{2}}\right)$
solUnder(t, omega_0, zeta) = solUnder
solUnder(t, omega_0, zeta) = ${\mathrm{e}}^{-{\omega }_{0} t \zeta } \mathrm{cos}\left({\omega }_{0} t \sqrt{1-{\zeta }^{2}}\right)$
The system oscillates at a natural frequency of ${\omega }_{0}\sqrt{1-{\zeta }^{2}}$ and decays at an exponential rate of $1/{\omega }_{0}\phantom{\rule{0.16666666666666666em}{0ex}}\zeta$.
Plot the solution with fplot as a function of ${\omega }_{0}t$ and $\zeta$.
z = [0 1/4 1/2 3/4]; w = 1; T = 4*pi; lineStyle = {'-','--',':k','-.'}; fplot(@(t)solUnder(t, w, z(1)), [0 T], lineStyle{1}); hold on; for k = 2:numel(z) fplot(@(t)solUnder(t, w, z(k)), [0 T], lineStyle{k}); end hold off; grid on; xticks(T*linspace(0,1,5)); xticklabels({'0','\pi','2\pi','3\pi','4\pi'}); xlabel('t / \omega_0'); ylabel('amplitude'); lgd = legend('0','1/4','1/2','3/4'); title(lgd,'\zeta'); title('Underdamped');
### 4. Overdamped Case ($\zeta >1$)
If $\zeta >1$, then $\sqrt{{\zeta }^{2}-1}$ is purely real and the solution can be rewritten as
solOver = sol
solOver =
solOver = coeffs(solOver, zeta); solOver = solOver(1)
solOver = ${\mathrm{e}}^{-{\omega }_{0} t \zeta } \left(\frac{{\mathrm{e}}^{{\omega }_{0} t \sqrt{{\zeta }^{2}-1}}}{2}+\frac{{\mathrm{e}}^{-{\omega }_{0} t \sqrt{{\zeta }^{2}-1}}}{2}\right)$
Notice the terms $\frac{\left({\mathit{e}}^{{\omega }_{0}\mathit{t}\sqrt{{\zeta }^{2}-1}}+{\mathit{e}}^{-{\omega }_{0}\mathit{t}\sqrt{{\zeta }^{2}-1}}\right)}{2}$ and recall the identity $\mathrm{cosh}\left(\mathit{x}\right)=\frac{{\mathit{e}}^{\mathit{x}}+{\mathit{e}}^{-\mathit{x}}}{2}$.
Rewrite the expression in terms of $\mathrm{cosh}$.
c = exp(-omega_0*t*zeta); solOver = c*rewrite(solOver / c, 'cosh')
solOver = $\mathrm{cosh}\left({\omega }_{0} t \sqrt{{\zeta }^{2}-1}\right) {\mathrm{e}}^{-{\omega }_{0} t \zeta }$
solOver(t, omega_0, zeta) = solOver
solOver(t, omega_0, zeta) = $\mathrm{cosh}\left({\omega }_{0} t \sqrt{{\zeta }^{2}-1}\right) {\mathrm{e}}^{-{\omega }_{0} t \zeta }$
Plot the solution to see that it decays without oscillating.
z = 1 + [1/4 1/2 3/4 1]; w = 1; T = 4*pi; lineStyle = {'-','--',':k','-.'}; fplot(@(t)solOver(t, w, z(1)), [0 T], lineStyle{1}); hold on; for k = 2:numel(z) fplot(@(t)solOver(t, w, z(k)), [0 T], lineStyle{k}); end hold off; grid on; xticks(T*linspace(0,1,5)); xticklabels({'0','\pi','2\pi','3\pi','4\pi'}); xlabel('\omega_0 t'); ylabel('amplitude'); lgd = legend('1+1/4','1+1/2','1+3/4','2'); title(lgd,'\zeta'); title('Overdamped');
### 5. Critically Damped Case ($\zeta =1$)
If $\zeta =1$, then the solution simplifies to
solCritical(t, omega_0) = limit(sol, zeta, 1)
solCritical(t, omega_0) = ${\mathrm{e}}^{-{\omega }_{0} t} \left({\omega }_{0} t+1\right)$
Plot the solution for the critically damped case.
w = 1; T = 4*pi; fplot(solCritical(t, w), [0 T]) xlabel('\omega_0 t'); ylabel('x'); title('Critically damped, \zeta = 1'); grid on; xticks(T*linspace(0,1,5)); xticklabels({'0','\pi','2\pi','3\pi','4\pi'});
### 6. Conclusion
We have examined the different damping states for the harmonic oscillator by solving the ODEs which represents its motion using the damping ratio $\zeta$. Plot all three cases together to compare and contrast them.
zOver = pi; zUnder = 1/zOver; w = 1; T = 2*pi; lineStyle = {'-','--',':k'}; fplot(@(t)solOver(t, w, zOver), [0 T], lineStyle{1},'LineWidth',2); hold on; fplot(solCritical(t, w), [0 T], lineStyle{2},'LineWidth',2) fplot(@(t)solUnder(t, w, zUnder), [0 T], lineStyle{3},'LineWidth',2); hold off; textColor = lines(3); text(3*pi/2, 0.3 , 'over-damped' ,'Color',textColor(1,:)); text(pi*3/4, 0.05, 'critically-damped','Color',textColor(2,:)); text(pi/8 , -0.1, 'under-damped'); grid on; xlabel('\omega_0 t'); ylabel('amplitude'); xticks(T*linspace(0,1,5)); xticklabels({'0','\pi/2','\pi','3\pi/2','2\pi'}); yticks((1/exp(1))*[-1 0 1 2 exp(1)]); yticklabels({'-1/e','0','1/e','2/e','1'}); lgd = legend('\pi','1','1/\pi'); title(lgd,'\zeta'); title('Damped Harmonic Oscillator');
#### Mathematical Modeling with Symbolic Math Toolbox
Get examples and videos |
# TeX - ! Extra alignment tab has been changed to \cr
Taylor, P P.Taylor at rhul.ac.uk
Mon Jul 8 23:39:01 CEST 2019
```I have a suggestion, Carlos. Why don't you take TeX.web, make the
changes that you feel are required (to the error message, and to any
other aspects of TeX that you feel are sub-optimal or unsatisfactory),
tangle and weave the resulting source code, compile and typeset the
resulting Pascal and TeX sources, demonstrate to your own satisfaction
that all is now as it should be, and then publish the results as (e.g.)
"Carlos' enhanced TeX". If your work is truly an improvement over
Knuth's, I am sure that TeX users worldwide will thank you for your |
## Issues with Data Sorting - powerbi
### How to display data for last few days but cumulate records from beginning of time in Tableau
I am building a Bar graph in Tableau to show daily cumulative record since January 2018. Due to number of days elapsed since then, the bars are so crunched that it looks ugly.
That said, how can I only display data for last few days while retaining the actual YTD count.
For e.g. starting January 1st I had 0 logins, February 1st - 100 YTD logins, March 1st - 200 YTD logins, April 1st - 300 YTD logins, and May 1st 400 YTD logins. I want the graph to display bars from May 1st only and show the starting count as 400 YTD logins and not zero.
PS: I am new to Tableau, so please assume that I don't know advanced stuff.
It seems that you are using Fit Width option which forces everything to be shown in your screen width. If so, try changing this to Standard, so that you may have control on the width of your bars and your users can see every month in one viz with a horizontal scrollbar.
If you do not want a scroolbar'd solution, you need to create fixed calculated fields to not get effected by the filters and use those new fields in your graph. At this point you may filter the date automatically (again with a calculated field based on the current date) or make your users manually filter what they want.
We may be in some more help if you can send a sample workbook but also you may play around with LOD expressions, FIXED keyword or simply get your calculations between { and } to fix them globally.
If you manually change the axis range, all table calculations, such as running totals, remain unaffected. You can do this by right clicking on the axis header, selecting "Edit Axis", then selecting the "Fixed" option under "Range", and choosing the dates you want to show.
### How do I create a “Users by time of day” heatmap in Google Data Studio?
I want to create a heatmap in Google Datastudio similar to the "Users by time of day" heatmap in Google Analytics.
This is how it looks in Google Analytics.
THE FIRST PROBLEM is that when I have my columns as the days of the week, it sorts on ascending/descending value alphabetically, NOT Sunday, Monday, Tuesday, etc.
THE SECOND PROBLEM is that I can't actually get the heatmap coloring.
THE THIRD (not a problem, but a preference)...is there a way to group every 2 hours like Google Analytics does?
I am creating this using the PIVOT TABLE chart. Should I be using a different chart? Any other ideas?
You can get something pretty close by doing this.
Pivot table
Row Dimension - Hour
Column Dimension - Day of week
Metric - Users
Sort Row 1- Hour - Ascending
Sort Column 1 - Day of Week Ascending.
Then under the Style tab
Metric - change from Number to Heatmap
Curious if there are any better answers for this. Seems like Data Studio is getting pushed more heavily now.
For the 2h interval I solved it by going in to the data source editor, click count on hour then it creates a copy that takes a formula, so i entered the formula
CASE
WHEN HOUR IN ("00","01") THEN "00-02"
...
...
...
WHEN HOUR IN ("22","23") THEN "22-00"
ELSE "Other"
END
### Calculate rates from previous month based on current month in order to make then visually comparable
Maybe this is an easy one but since I’m very new in DAX and PowerBI I can’t figure it out. My database has daily data ranging from MAY/17 to JUN/17 (and it’ll still going in the future). It has information of DATE, DAY, YRMTH (year-month), QT_APRV (approved customers) and QT_TOTAL (total consumers). Sample below (using Excel just to be quicker):
I wanted to create in PowerBI a bar chart with QT_TOTAL per day and a line chart with approved rate of consumer. For the rate, I used:
APPRV_RT = SUM(database[QT_APRV]/SUM(database[QT_TOTAL])
And then, selecting only a month by time in the chart (just like I want), I have:
Perfect, but now I want to create a new line chart, showing the approved rate in each respective day of the last month. Using my example, when june data are select, the first line chart has to show the daily approved rate of june AND the other the approved rate of may, in order to make it comparable (june1 -> may1; june12 -> may12 and so on). Here’s what I want:
How to make this automatically, in order to make each month comparable with the previous? I thought about some DAX formula involving a sum with filtering current month minus 1, I don’t know how to do it.
Any ideas?
UPDATE (07/08/2017)
I tried what Rasmus Dybkjær suggested me, and I thing I'm in the right path.
APPROVED_RATE_PREVIOUS_MONTH = CALCULATE([APPROVED_RATE_CURRENT_MONTH];PARALLELPERIOD(dCalendario[DataBase];-1;MONTH))
However, it returned the approved rate from the previous month as a whole (67,0% in May), not each day as I wanted:
Any suggestions?
You should be able to use the DAX function called PARALLELPERIOD() for this purpose. The PARALLELPERIOD() function takes a date column and shifts it a number of periods back or forward.
For example, you could use it like this to calculate your approved rate shifted one month back:
ApprovedRateLM =
CALCULATE(
DIVIDE(
SUM(database[QT_APRV]),
SUM(database[QT_TOTAL])
),
PARALLELPERIOD(database[Date],-1,month)
)
Note that it is important that your [Date] column contains a date type. Otherwise the PARALLELPERIOD function will not work.
### Dax Calculation with logic in power bi data analytics
Need help in Data Analytics Calculations.
Currently, I am getting historical data for consumption as follows:
on above data, I am adding custom columns for calculating exact consumption(gallons) in no. of days. like:
Now, I have to plot month wise bar chart for consumption of respective Meter ID in 2016 year. But problem here is, I will have to calculate Every months consumption by dividing it in days in each respective month of 2016, and then only I will able to plot them monthly like:
y axis = consumption in every month
x axis = Jan Feb March Apr May Jun Jul Aug Sep Oct Nov Dec
so, in jan month, consumption should be = 10 + 100 + ((115/38) * 7) gallons
Notes: here, in ((115/38) * 7) : we are calculating avg consumption of single day 7 days in Jan and whole march and then getting last 7 day consumption of Jan so that we can add it in calculation of total consumption of Jan month
but how to add measure/custom column/new table for these calcualtions?
Thanks
What you need to do is relatively complicated, but the summary of my solution is:
Calculate the per-day consumption
Calculate the start and end date of each reading (e.g. the previous reading date plus one day, and the reading date)
Expand your data to have 1 row per day rather than 1-row per reading
You want to do these steps before you load the data into your data model (i.e. in your source system, or as the data is loaded using the Query Editor/Power Query).
Below, I assume you're using the Query Editor/Power Query. However, if you can use your source system, it's often the better choice (since the source system may be a database that is vastly faster than your desktop).
Note that your No. of Days calculation doesn't make sense to me. There are more than 38 days between 24 Jan 2016 and 31 Mar 2016. There are also more than 13 days between 10 Jan and 24 Jan. For this reason, it was difficult to tell whether you wanted a new reading to count on the day the previous reading was taken, or on the next full day. I assume the former. Also note, I've proceeded on the basis that your No. of Days calculation is correct
Calculate the Per Day Consumption
This is the easiest step, given that you have already calculated the Consumption and the No. of Days. Just divide one by the other. In the Query Editor, you can click in the Consumption (gallons) column and select Add Column > Standard > Divide. Under Value, choose Use values in a column and then select the No. of Days column.
Calculate the Start & End Date of Each Reading
The date of the reading is the end date, so you can rename Date to be End Date (since a reading is applied retroactively).
For the start date, in the Query Editor, you will need to add an index column (Add Column > Index Column). You will want to make sure your data is sorted by Meter ID and Date Ascending before doing this. Call the column Index.
Next, Add Column > Custom Column and pull the reading date from the prior row. Call the new column Previous End Date for now.
// A try is necessary because we can't get the previous row if there is no previous row (we'll get an error, which we can handle in the 'otherwise' block)
try
if
// See if the previous row is for the same Meter ID
[Meter ID] = #"Reordered Columns"{[Index] - 1}[Meter ID]
then
// If it is, grab the Reading Date from the previous row
#"Reordered Columns"{[Index]-1}[End Date]
else
// If this is the first reading for a meter, calculate the Start Date by subtracting the No. of Days from the End Date
otherwise
// If this is the first row in the table, also calculate the Start Date by subtracting the No. of Days from the End Date
Next, you'll want to add 1 to the Start Date, as we want the reading to apply to the day after the previous reading, not on the day of the previous reading.
Note, if you want the reading date to count in the prior period, subtract 1 from the End Date rather than add 1 to the start date (previous end date).
Expand your data to have 1 row per day
At this point, you should have a Meter ID, Start Date, End Date, and per day consumption column that reflects what you expect (i.e. the per day consumption is correct for the date range).
The final step is to duplicate each row for each date in the date range. There are several solutions to this outlined in this thread (https://community.powerbi.com/t5/Desktop/Convert-date-ranges-into-list-of-dates/td-p/129418), but personally, I recommend the technique (and video) posted by MarcelBeug (https://youtu.be/QSXzhb-EwHM).
You should end up with something more like this (after some removing & renaming of columns):
Finally
Now that you have one row per meter & date, with a per day consumption already calculated, you can build a visual. For example, you could do a column chart with Date on the Axis, and Consumption per Day as the value. By default, Power BI will recognize that Date is a date, and will roll it up by Year-Quarter-Month-Day. Press the little 'x' by Year and Quarter, and you'll have a chart that sums up the per day consumption by month. You can also drill down to individual date.
Reading a value from a previous row in Power Query
If Statements in Power Query
The AddDays function in Power Query
Catching Errors in Power Query
Converting a date range into a list of dates (Marcel Beug's solution)
A similar problem I previously answered
### Working with imperfectly matched data in crossfilter
Given the following dimensions specifications in Crossfilter's API - https://github.com/square/crossfilter/wiki/API-Reference
1.) The function must return naturally-ordered values
2.) .....incomparable values such as NaN and undefined are not supported
How would one go about charting a crossfilter (using dc.js) with two dimensions - one with daily data (7 days a week), and another with business-day data (5-days a week)? The data structure implies that the business-day data will have gaps on the weekend which should violate the specifications above.
For example, if I want to compare a company's store sales (7 days/week) vs its stock price (5 days + gaps on Saturday and Sunday), how would i go about it? The goal would be to have two dc.js charts filtering each other, but having data that isn't perfectly matched up i.e. the first chart will show sales data from Jan 1 till Jan 31 (7 days a week), while the second chart will show stock price data from the first till the last business day in Jan (excluding weekends).
Your stock data would likely include no data for Saturday and Sunday. This is is different from having a data row with stock price as NaN.
For example: If you plotted the stock data on a row chart with the days of the weeks for the categories, then there would be no bars for saturdays and sundays.
Here is a crude example: DC.JS example of days of week chart
I made sure that no rows were added for saturdays and sundays:
if ((stockDate.getDay() != 6) && (stockDate.getDay() != 0))
The resulting row chart has no row for Saturday or Sunday.
You could explore filtering your data, as I did, so you preselect what you want to show. Remember to include the additional code which preserves the bins.
Hide Specified Row in dc.js rowchart |
# 10 Algorithms and functions
## Prerequisites
Chapter 1 states that geocomputation is not only about using existing tools, but developing new ones, “in the form of shareable R scripts and functions”. The aim of this chapter is to teach how to develop reproducible scripts, functions and algorithms, key components in the process of tool creation. The chapter assumes you have an understanding of the geographic data classes introduced in Chapter 2, and have already imported the datasets needed for your work, for example from sources outlined in Chapter 7.
We will consider example R scripts for geographic data and how to make them more reproducible in section 10.1. Algorithms are recipes for modifying inputs using a series of steps, resulting in an output, as described in section 10.2. To ease sharing and reproducibility algorithms can be placed into functions, which can then be distributed either in script files or as R packages, the building blocks of reproducible code. That is the topic of section 10.3.
The algorithms developed (including finding the centroid of a polygon, an example used in this chapter) are readily available in GIS software. However, the aim is “not to duplicate what is available out there, but to show how things out there work” (Xiao 2016). This chapter takes a similar approach and is therefore the most low-level and potentially advanced (in terms of the code, not application) so far.
## 10.1 Scripts
If packages are the building blocks of reproducible code, scripts are the glue that holds them together. There are no strict rules on what can and cannot go into script files and nothing to prevent you from saving broken, non-reproducible code. There are, however, some rules of thumb and conventions worth following when writing R scripts, outlined below:
• Write the script in order: just like the script of a play, scripts should have a clear order such as ‘setup’, ‘data processing’ and ‘save results’ (roughly equivalent to ‘beginning’, ‘middle’ and ‘end’ in a film).
• Make the script reproducible: scripts will be of more use to you and others if they are self-contained and can be run by other people. This involves stating dependencies (loading required packages at the outset, like the ‘Prerequisites’ section), reading-in data from persistent sources (e.g. from a reliable website or API) and mentioning any code that must be run before running the script (e.g. with a comment # run script0.R before this).
• Comment the script sufficiently for others (and your future self) to understand it but not so much that the comments themselves become hard to maintain: at a minimum a good script file should contain information on the purpose of the script (see Figure 10.1) and division into chunks, perhaps by appending ---- to section headings, which allows ‘folding’ of R scripts in RStudio.
Although there is no way to enforce reproducibility in R scripts, there are tools that can help. By default RStudio ‘code-checks’ R scripts and underlines faulty code with a red way line, as illustrated below:
A useful tool for reproducibility is the reprex package. Its main function reprex() tests of lines of R code to check if they are reproduible, and provides markdown output to facilitate communication on sites such as GitHub. See reprex.tidyverse.org/ for details.
## 10.2 Geographic algorithms
Algorithms can be understood as the computing equivalent of a cooking recipe: a series of instructions which, when taken on appropriate ingredients, results in an output that is more useful (or tasty) than the raw ingredients. Before considering ‘geoalgorithms’, it is worth taking a brief detour around the history of the algorithms, to understand how they relate to scripts and functions which are covered next.
The word algorithm comes from Baghdad when, in the 9th Century AD, an early maths book was published called Hisab al-jabr w’al-muqabala. The book was translated into Latin and became so popular that the author Muḥammad ibn Mūsā al-Khwārizmī “was immortalized as a scientific term: Al-Khwarizmi [sic] became Alchoarismi, Algorismi and, eventually, algorithm” (Bellos 2011).41
In the computing age algorithm refers to a series of steps that take a clearly defined input to produce an output. Algorithms often start as in flow charts and psuedocode showing the aim of the process before being implemented in a formal language such as R. Because the same algorithm will be used many times on the different inputs it rarely makes sense to type out the entire algorithm each time: algorithms are most easily used when they are implemented inside functions (see section 10.3).
Geoalgorithms are a special case: they take geographic data in and, generally, return geographic results. Also referred to as GIS algorithms and geometric algorithms, an entire academic field — Computational Geometry, a branch of computer science — is dedicated to their study and development (Berg et al. 2008). A simple example is an algorithm that finds the centroid of an object. This may sound like a simple task but in fact it involves some work, even for the simple case of single polygons containing no holes. The basic representation of a polygon object is in a matrix representing the vertices between which straight lines are drawn (the first and last points must be the same, something we’ll touch on later). In this case we’ll create a polygon with 5 vertices in base R, building on an example from GIS Algorithms (Xiao 2016 see github.com/gisalgs for Python code):
x_coords = c(10, 0, 0, 2, 20, 10)
y_coords = c(0, 0, 10, 12, 15, 0)
poly_mat = cbind(x_coords, y_coords)
As with many computational (or other) problems, it makes sense to break the problem into smaller chunks. All polygons can be broken-down into a finite number of triangles, which have simple rules defining their centroid and area. With this in mind, the following commands create a new triangle (T1), that can be split-out from the polygon represented by poly_mat, and finds its centroid based on the formula $$1/3(a + b + c)$$ where $$a$$ to $$c$$ are coordinates representing the triangles vertices:
O = poly_mat[1, ] # create a point representing the origin
T1 = rbind(O, poly_mat[2:3, ], O) # create 'triangle matrix'
C1 = (T1[1, ] + T1[2, ] + T1[3, ]) / 3 # find centroid
If we calculate the centroids of all such polygons the solution should be the average x and y values of all centroids. There is one problem though: some triangles are more important (larger) than others. Therefore to find the geographic centroid we need to take the weighted mean of all sub-triangles, with weigths proportional to area. The formula to calculate the area of a triangle is:
$\frac{Ax ( B y − C y ) + B x ( C y − A y ) + C x ( A y − B y )} { 2 }$
Where $$A$$ to $$C$$ are the triangle’s three points and $$x$$ and $$y$$ refer to the x and y dimensions. A translation of this formula into R code that works with the data in the matrix representation of a triangle T1 is as follows (the function abs() ensures a positive result):
abs(T1[1, 1] * (T1[2, 2] - T1[3, 2]) +
T1[2, 1] * (T1[3, 2] - T1[1, 2]) +
T1[3, 1] * (T1[1, 2] - T1[2, 2]) ) / 2
#> [1] 50
This code chunk works and outputs the correct result.42 The problem with the previous code chunk is that it is very and difficult to re-run on another object with the same ‘triangle matrix’ format. To make the code more generalizable, let’s convert the code into a function (something described in 10.3) that works with any matrix represenations of a triangle that we’ll call x:
t_area = function(x) {
abs(
x[1, 1] * (x[2, 2] - x[3, 2]) +
x[2, 1] * (x[3, 2] - x[1, 2]) +
x[3, 1] * (x[1, 2] - x[2, 2])
) / 2
}
The function t_area generalizes the solution by taking any object x, assumed to have the same dimensions as the triangle represented in T1. We can verify it works on the triangle matrix T1 as follows:
t_area(T1)
#> [1] 50
Likewise we can create a function that find’s the triangle’s centroid:
t_centroid = function(x) {
(x[1, ] + x[2, ] + x[3, ]) / 3
}
t_centroid(T1)
#> x_coords y_coords
#> 3.33 3.33
The next stage is to create the second triangle and calculate its area and centroid. This is done in the code chunk below, which binds the 3rd and 4th coordinates onto the 1st, and uses the same functions we created above to calculate its area and width:
T2 = rbind(O, poly_mat[3:4, ], O)
A2 = t_area(T2)
C2 = t_centroid(T2)
From this point it is not a big leap to see how to create the 3rd and final triangle that constitutes the polygon represented by poly_mat (see exercises below). However, an aim of algorithms is often to generalise and automate the solution. In the name of automation (and to avoid creating individual triangles manually!) we use iteration to create all triangles representing the polygon in a single line. We could use a for() loop or lapply() for this work but have chosen map() from the purrr package because it allows concise code: the . in the commands below refer to ‘each element of the object i’ (see ?purrr::map for details):
# Aim: create all triangles representing a polygon
i = 2:(nrow(poly_mat) - 2)
Ti = purrr::map(i, ~rbind(O, poly_mat[.:(. + 1), ], O))
A = purrr::map_dbl(Ti, ~t_area(.))
C = t(sapply(Ti, t_centroid))
We are now in a position to calculate the total area and geographic centroid of the polygon as follows:
sum(A)
#> [1] 190
c(weighted.mean(C[, 1], A), weighted.mean(C[, 2], A))
#> [1] 8.04 7.33
Is this right? We can verify the answer by converting poly_mat into a simple feature collection as follows:
poly_sfc = sf::st_polygon(list(poly_mat))
sf::st_area(poly_sfc)
#> [1] 190
sf::st_centroid(poly_sfc)
#> POINT (8.04 7.33)
## 10.3 Functions
Like algorithms functions take an input and return an output. The difference is that functions are ‘packaged’ so that are R objects in their own right. We have already seen the advantages of using functions in the previous section: the function t_area() contains the steps needed find the area of any ‘triangle matrix’ and can be called with a single line, whereas the full underlying code requires many lines of code. Functions are thus a mechanism for generalizing code. We can use the function to find the area of a triangle with a base 3 units wide and a height of 1, for example, as follows:
t_new = matrix(c(0, 3, 3, 0, 0, 0, 1, 0), ncol = 2)
t_area(t_new)
#> [1] 1.5
A useful feature of functions is that they are modular. Providing you know what the output will be, one function can be used as the building block of another. This is exactly what we will do in this section. Building on the content of the previous section, in which it was shown how the area of a polygon can be found by following a series of steps in order, this section will create a function to calculate the area of any polygon (with caveats that will become clear). This function, that we’ll call poly_centroid() will mimick the behaviour of sf::st_centroid() from the sf package, with a few additions to show how arguments work.
poly_centroid = function(x, output = "matrix") {
i = 2:(nrow(x) - 2)
Ti = purrr::map(i, ~rbind(O, x[.:(. + 1), ], O))
A = purrr::map_dbl(Ti, ~t_area(.))
C = t(sapply(Ti, t_centroid))
centroid_coords = c(weighted.mean(C[, 1], A), weighted.mean(C[, 2], A))
if(output == "matrix") {
return(centroid_coords)
} else if(output == "area")
return(sum(A))
}
poly_centroid(poly_mat)
#> [1] 8.04 7.33
poly_centroid(poly_mat, output = "area")
#> [1] 190
Low-level function such as poly_centroid() can be built-on to provide different types of output. If a common need is to return the result as an object of class sfg, for example, this can be done by creating a ‘wrapper’ function that modifies the output of poly_centroid() before returning the result:
poly_centroid_sfg = function(x) {
centroid_coords = poly_centroid(x)
centroid_sfg = sf::st_point(centroid_coords)
centroid_sfg
}
We can verify that the output is the same as the output from sf::st_centroid() as follows:
identical(poly_centroid_sfg(poly_mat), sf::st_centroid(poly_sfc))
#> [1] TRUE
An important concept to consider when developing your own function is type stability. Functions are type stable if they always return objects of the same class and, generally, this means returning objects of the same type as the input object. To illustrate this concept in practice we will create a type stable version poly_centroid() that always takes a matrix with 2 columns as an input and always returns a matrix with 2 columns representing x and y coordinates:
poly_centroid_type_stable = function(x) {
stopifnot(is.matrix(x) & ncol(x) == 2)
centroid_coords = poly_centroid(x)
return(matrix(centroid_coords, ncol = 2))
}
The first line of the function is an example of ‘defensive programming’: it checks the input is in the right format (a matrix with 2 columns) before proceeding. Such checks can ensure that the code is robust and does not silently fail. We can verify it works with matrix(centroid_coords, ncol = 2). To see the input data type check working we can try running the function on a matrix with 3 columns:
poly_mat3 = cbind(1:nrow(poly_mat), poly_mat)
poly_centroid(poly_mat3)
#> [1] 6.26 6.58
poly_centroid_type_stable(poly_mat3)
#> Error in poly_centroid_type_stable(poly_mat3) :
#> is.matrix(x) & ncol(x) == 2 is not TRUE
## 10.5 Exercises
1. In section 10.2 we created a function that finds the geographic centroid of a shape, which is implemented in the sf function sf::st_centroid(). Building on this example, write a function only using base R functions that can find the total length of linestrings represented in matrix form.
2. In section 10.3 we created a different versions of the poly_centroid() function that generated outputs of class sfg (poly_centroid_sfg()) and type-stable matrix outputs (poly_centroid_type_stable()). Further extend the function by creating a version (e.g. called poly_centroid_sf()) that is type stable (only accepts inputs of class sf) and returns sf objects (hint: you may need to convert the object x into a matrix with the command sf::st_coordinates(x).
• Verify it works by running poly_centroid_sf(sf::st_sf(sf::st_sfc(poly_sfc)))
• What error message do you get when you try to run poly_centroid_sf(poly_mat)?
### References
Xiao, Ningchuan. 2016. GIS Algorithms: Theory and Applications for Geographic Information Science & Technology. 55 City Road, London. https://doi.org/10.4135/9781473921498.
Bellos, Alex. 2011. Alex’s Adventures in Numberland. London: Bloomsbury Paperbacks.
Berg, Mark de, Otfried Cheong, Marc van Kreveld, and Mark Overmars. 2008. Computational Geometry: Algorithms and Applications. Springer Science & Business Media.
1. The book’s title was also influential, forming the basis of the word algebra.
2. as can be verified with the formula for the area of a triangle whose base is horizontal: area equals half of the base width times its height — $$A = B * H / 2$$ — ($$10 * 10 / 2$$ in this case, as can be seen in Figure 10.3). |
## College Algebra (11th Edition)
$x=-2$
We rewrite both sides, so that the base is $\frac{3}{2}$ on both sides. Left side: $\frac{2}{3}^x$. By the law of exponents:$\frac{1}{a}^x=a^{-x}$ $\frac{2}{3}^x=\frac{3}{2}^{-x}$ Right side: $\frac{9}{4}=\frac{3}{2}^2$ Thus, the given equation is equivalent to: $\frac{3}{2}^{-x}=\frac{3}{2}^2$ Since the bases are the same, we set the exponents equal: $-x=2 \\-1(-x)=-1(2) \\x=-2$ |
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However, this is possible only if A is a square matrix and A has n linearly independent eigenvectors. 2016 - Fondation Le Corbusier - Réalisations - Armée du Salut, Cité de Refuge Sunrise to sunset: 24 hours at an algae farm. [6] In 1975, he and Alan Coulson published a sequencing procedure using DNA polymerase with radiolabelled nucleotides that he called the Plus and Minus technique. A corporate filing is called a foreign filing when an existing corporate entity files in a state other than the … Active 2016 1 President Excel Known Addresses for Andrew Spaventa. Yeast (Saccharomyces cerevisiae) has long been an important model organism for the eukaryotic cell, while the fruit fly Drosophila melanogaster has been a very important tool (notably in early pre-molecular genetics). Developer of a third-gen DNA sequencing system designed to improve human health. Merck & Co adalah sebuah perusahaan asal Amerika Serikat yang bergerak di sektor kesehatan. Such work revealed that the vast majority of microbial biodiversity had been missed by cultivation-based methods. Tools for working with genomic and high throughput sequencing data. Singular Genomics Systems, Inc. WanderPanda 21 days ago. Proteomics is an interdisciplinary domain which has benefited a lot from the genetic information of the Human Genome Project (HGP); it is also arising scientific research and exploration of proteomes from the complete level of intracellular protein composition, structure, and its own singular activity patterns. The related suffix -ome is used to address the objects of study of such fields, such as the genome, proteome or metabolome respectively. Bacteriophage genome sequences can be obtained through direct sequencing of isolated bacteriophages, but can also be derived as part of microbial genomes. No warranties, expressed or implied, are provided for the business data on this site, its use, or its interpretation. Over 100,000 Spanish translations of English words and phrases. that project adopts many concepts from google and others and greatly improved our analytic capabilities for large-scale genomics. In ultra-high-throughput sequencing, as many as 500,000 sequencing-by-synthesis operations may be run in parallel. The companies and people profiled on Corporation Wiki are displayed for research purposes only and do not imply an endorsement from or for the profiled companies and people. Ciencia Singular of CiMUS is the most relevant initiatives for the citizens to meet the scientists working in this institution and know what they are doing, that is the latest advances in science and the main research lines. The zebrafish Brachydanio rerio is used for many developmental studies on the molecular level, and the plant Arabidopsis thaliana is a model organism for flowering plants. - fulcrumgenomics/fgbio [30][31], Most of the microorganisms whose genomes have been completely sequenced are problematic pathogens, such as Haemophilus influenzae, which has resulted in a pronounced bias in their phylogenetic distribution compared to the breadth of microbial diversity. The additional information allows manual annotators to deconvolute discrepancies between genes that are given the same annotation. Selected Older Publications génomique \ʒe.no.mik\ féminin au singulier uniquement (Génétique) Branche de la génétique qui étudie les génomes.L’émergence de nouvelles disciplines comme la génomique ainsi que le développement de la biochimie résultent de la connaissance du rôle des molécules qui composent les êtres vivants sur leurs propriétés. Stratos Genomics spaces out the DNA bases with polymeric inserts, "Xpandomers", to circumvent the signal to noise challenge of nanopore ssDNA reading. t_serpico 21 days ago. Eulerian path strategies are computationally more tractable because they try to find a Eulerian path through a deBruijn graph. [89], Conservationists can use the information gathered by genomic sequencing in order to better evaluate genetic factors key to species conservation, such as the genetic diversity of a population or whether an individual is heterozygous for a recessive inherited genetic disorder. [50] Relative to comparative assembly, de novo assembly is computationally difficult (NP-hard), making it less favourable for short-read NGS technologies. [6], Shotgun sequencing is a sequencing method designed for analysis of DNA sequences longer than 1000 base pairs, up to and including entire chromosomes. We know that each singular value σi is the square root of the λi (eigenvalue of A^TA), and corresponds to an eigenvector vi with the same order. Synthetic Genomics is recognized in ExxonMobil’s latest campaign on algae biofuels. | Meaning, pronunciation, translations and examples Developer of a DNA sequencing platform designed to deliver unsurpassed sequencing accuracy. It also has some important applications in data science. [22][23] For their groundbreaking work in the sequencing of nucleic acids, Gilbert and Sanger shared half the 1980 Nobel Prize in chemistry with Paul Berg (recombinant DNA). While traditional microbiology and microbial genome sequencing rely upon cultivated clonal cultures, early environmental gene sequencing cloned specific genes (often the 16S rRNA gene) to produce a profile of diversity in a natural sample. Bionano Genomics provides unparalleled structural variation detection for genetic disease research, cancer research & cytogenomics with genome imaging technology. They showed that the right singular vectors, or “eigengenes,” represent trends that account for a large proportion of the variation … tagment (third-person singular simple present tagments, present participle tagmenting, simple past and past participle tagmented) To cause, or to undergo tagmentatio Receive an email notification when changes occur for Singular Genomics Systems, Inc.. — (Suzanne Mériaux, Science et poésie, L’Harmattan, p. Some databases use genome context information, similarity scores, experimental data, and integrations of other resources to provide genome annotations through their Subsystems approach. Computer programs then use the overlapping ends of different reads to assemble them into a continuous sequence. For older versions, see our archive Singularity enables users to have full control of their environment. Knowledge for Life | At Cradle Genomics, our mission is to provide knowledge that helps every pregnancy. [48][49] Shotgun sequencing is a random sampling process, requiring over-sampling to ensure a given nucleotide is represented in the reconstructed sequence; the average number of reads by which a genome is over-sampled is referred to as coverage. Entrar Dicionário. 2016 The Japanese pufferfish (Takifugu rubripes) and the spotted green pufferfish (Tetraodon nigroviridis) are interesting because of their small and compact genomes, which contain very little noncoding DNA compared to most species. Tesauro. Some new and exciting examples of progress in this field are the identification of genes for regulatory RNAs, insights into the evolutionary origin of photosynthesis, or estimation of the contribution of horizontal gene transfer to the genomes that have been analyzed. The need for reproducibility and efficient management of the large amount of data associated with genome projects mean that computational pipelines have important applications in genomics.[67]. Efficient Enumeration of Phylogenetically Informative Substrings Journal of Computational Biology, 14(6):701-23, 2007. The classical singular value decomposition (or principal components) approach has been successfully applied in several areas of genomics. Genomics definición: Genomics is the study of genomes. Tradutor. The company's system offers genomics research and development services including nucleotides, liners and fluorescent dyes synthesis for use in next-generation DNA sequencing, enabling patients to get a reliable treatment. Also the first genome to be sequenced was a bacteriophage. [6] More recently, additional information is added to the annotation platform. Whitehead Institute was founded by visionary industrialist and philanthropist Edwin C. “Jack” Whitehead, who was driven by a singular vision: to assemble a cadre of the world’s finest biomedical researchers under one roof and eliminate virtually any impediment to their pursuit of scientific discovery. Dicionário Gramática Blog Escolar Scrabble Tesauro Tradutor Quiz Mais recursos Mais de Collins. Inglês Inglês-Chinês Inglês-Francês Inglês-Alemão Inglês-Hindi Inglês-Italiano Inglês-Português Inglês-Espanhol. [11][12] Extending this work, Marshall Nirenberg and Philip Leder revealed the triplet nature of the genetic code and were able to determine the sequences of 54 out of 64 codons in their experiments. Nevertheless, in 1977 his group was able to sequence most of the 5,386 nucleotides of the single-stranded bacteriophage φX174, completing the first fully sequenced DNA-based genome. 2012 Aug 22;12:153. doi: 10.1186/1471-2148-12-153. Jump to navigation Jump to search. [20][21] In the same year Walter Gilbert and Allan Maxam of Harvard University independently developed the Maxam-Gilbert method (also known as the chemical method) of DNA sequencing, involving the preferential cleavage of DNA at known bases, a less efficient method. ==Endosymbiotic and Horizontal Gene Transfer (EGT, HGT) among Plantae phylum== Eukaryotic photosynthesis takes place within the plastid, an organelle that originated from the endosymbiotic gene transfer of cyanobacteria to the common ancestor of Plantae (Archaeplastidia; red, green, glaucophyte algae and plants). In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix that generalizes the eigendecomposition of a square normal matrix to any {\displaystyle m\times n} matrix via an extension of the polar decomposition. 15 of these cyanobacteria come from the marine environment. An infectious disease strand is being led by Public Health England. [50], Finished genomes are defined as having a single contiguous sequence with no ambiguities representing each replicon. [28] The following year a consortium of researchers from laboratories across North America, Europe, and Japan announced the completion of the first complete genome sequence of a eukaryote, S. cerevisiae (12.1 Mb), and since then genomes have continued being sequenced at an exponentially growing pace. [73] Recent studies use "shotgun" Sanger sequencing or massively parallel pyrosequencing to get largely unbiased samples of all genes from all the members of the sampled communities. Omniome General Information Description. [74] Because of its power to reveal the previously hidden diversity of microscopic life, metagenomics offers a powerful lens for viewing the microbial world that has the potential to revolutionize understanding of the entire living world. This technology measures the release of a hydrogen ion each time a base is incorporated. Interleukin 6 (IL6) is a potent pleiotropic cytokine that regulates cell growth and differentiation and plays an important role in immune response. Knowledge for Life | At Cradle Genomics, our mission is to provide knowledge that helps every pregnancy. Singular Genomics Systems, Inc. Overview. [6] Typically, these machines can sequence up to 96 DNA samples in a single batch (run) in up to 48 runs a day. Paired end reads of next generation sequencing data mapped to a reference genome. How to use bioinformatics in a sentence. OLC strategies ultimately try to create a Hamiltonian path through an overlap graph which is an NP-hard problem. [71] The study of epigenetics on a global level has been made possible only recently through the adaptation of genomic high-throughput assays. [50], For much of its history, the technology underlying shotgun sequencing was the classical chain-termination method or 'Sanger method', which is based on the selective incorporation of chain-terminating dideoxynucleotides by DNA polymerase during in vitro DNA replication. [65] Ideally, these approaches co-exist and complement each other in the same annotation pipeline (also see below). In summer 2019, Chris Wigley was appointed CEO of Genomics England, starting in … [70], Epigenomics is the study of the complete set of epigenetic modifications on the genetic material of a cell, known as the epigenome. These chain-terminating nucleotides lack a 3'-OH group required for the formation of a phosphodiester bond between two nucleotides, causing DNA polymerase to cease extension of DNA when a ddNTP is incorporated. 3-Dimensional structure of every protein encoded by a given genome simple model multicellular. 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## CryptoDB
### Paper: Comparing Implementation Efficiency of Ordinary and Squared Pairings
Authors: Christine Abegail Antonio Tanaka Satoru Ken Nakamula URL: http://eprint.iacr.org/2007/457 Search ePrint Search Google In this paper, we will implement a standard probabilistic method of computing bilinear pairings. We will compare its performance to a deterministic algorithm introduced in [5] to compute the squared Tate/Weil pairings which are claimed to be 20 percent faster than the standard method. All pairings will be evaluated over pairing-friendly ordinary elliptic curves of embedding degrees 8 and 10 and a supersingular curve of embedding degree 6. For these curves, we can make the algorithm to compute both the ordinary Weil and Tate pairings deterministic and optimizations to improve the algorithms are applied. We will show that the evaluation of squared Weil pairing is, indeed, faster than the ordinary Weil pairing even with optimizations. However, evaluation of the squared Tate pairing is not faster than the ordinary Tate pairing over the curves that we used when optimizations are applied.
##### BibTeX
@misc{eprint-2007-13737,
title={Comparing Implementation Efficiency of Ordinary and Squared Pairings},
booktitle={IACR Eprint archive},
keywords={implementation / bilinear pairings, squared Weil/Tate pairings, cryptography, pairing-friendly curves},
url={http://eprint.iacr.org/2007/457},
note={ [email protected] 13855 received 7 Dec 2007},
author={Christine Abegail Antonio and Tanaka Satoru and Ken Nakamula},
year=2007
} |
# Playful Pens, Inc., makes a single model of a pen. The cartridge for the pen (which contains the ...
Playful Pens, Inc., makes a single model of a pen. The cartridge for the pen (which contains the ink) is manufactured on one machine. The cartridge holder (which you hold when you use the pen) is manufactured on another machine. Monthly capacities and production levels are as follows:
Machine 1 (Cartridge) Machine 2 (Holders) Monthly capacity 1,000,000 800,000 Monthly production 800,000 800,000
The company could sell 1,000,000 pens per month. The units (cartridge inside of holder) sell for $10.40 each and have a variable cost of$4.10 each. Fixed costs are $4,200,000 per month. Required: a. Is there a bottleneck at Playful Pens on Machine 1 or Machine 2? Machine 1 Machine 2 b. Playful Pens's production supervisors state they could increase machine 2's capacity by 200,000 per month by producing holders on the weekend. Producing on the weekend would not affect the sales price. Variable cost per unit would increase by$1.10 for those produced on the weekend because of the premium paid to labor. Fixed costs would also increase by $820,000 per month. b-1. Calculate the differential operating profit (loss). (Losses and amounts to be deducted should be indicated with a minus sign.) Differential Revenues Differntial costs: Variable Fixed b-2. Should Playful Pens produce holders on the weekend? Yes No c. Independent of the situation in requirement (b), Playful Pens could expand the capability of machine 2 by adding additional workers to perform ongoing maintenance. This would increase its capacity by 100,000 holders per month. This would not affect sales price or fixed costs, but would increase variable cost to$4.62 per unit for all units produced.
c-1. Calculate the differential operating profit (loss). (Losses and amounts to be deducted should be indicated with a minus sign.)
Differential revenues
Differential costs:
Variable cost increase on current production:
Variable cost on new production:
c-2. Should Playful Pens expand Machine 2's capability by adding these additional workers?
Yes No |
# 第一周
why is deep learning taking off?
Beceuse deep learning could handle large set of data to promopte itself while logistic regression, SVM and something else can’t.
Either your intuitions are good or they’re not.
• If your intuitions are good, you should follow them and you’ll eventually be successful. If your intuitions are not good, it doesn’t matter what you do. There is not point not trusting them.
• never stop programming
• read enough so you start developing intuitions, and then trust your instuitions and go for it. Don’t be too worried if everybody else says it’s nonsense.
Geoffrey Hinton
# 第二周
1. some changes compared to the previous video of Andre
• the matrix of training set $X$ has the size $n\times m$, and the label of it has the size $1 \times m$
• there’s no plus one row of $X$ matrix for the bias value, and we are going to seperate it from teh bias
2. computation graph for how to compute the derivatives of some function
3. vectorized computation is much faster than unvectorized version in Python
and the method to get time running time of one programm is to use time.time() method in package time. When we use it, then we will get the current time of programm. Mark tic as the time before we run calculating and toc means after calculation, then 1000*(toc-tic) means the times used to calculate in ms.
the reason for that is because vectorized calculation make use of parallelization.
4. when we add some real number to some vector or matrix then it will be handled to a matrix full of real number, which is called “Boardcasting”
5. the deduction of the derivatives for logistic regression
6. the broadcasting function not only transform a single real number into a matrix that matches the matrix add or substract it, but also it could transform a vector to some matrix that matches the matrix make some operations with it.
7. the parameter axis in sum method means to calculate the sum vertically(0) or horizontally(1).
8. tip when work with numpy
it is better to deal with 2 rank array of numpy array rather than rank 1 array
because rank 1 array is either a row vector nor a column vector; and the way to create it is something like a = np.random.randn(5). While the way to create a rank 2 array is a = np.random.randn(5, 1). Also, it is good to use a.shape(row, col) regularly.
9. What you need to remember:
Common steps for pre-processing a new dataset are:
• Figure out the dimensions and shapes of the problem (m_train, m_test, num_px, …)
• Reshape the datasets such that each example is now a vector of size (num_px * num_px * 3, 1)
• “Standardize” the data
10. My jupyter notebook while watching this week’s video
# 第三周
1. when we are talking about the layers of neural network, what are we talking about?
The input layer shouldn’t be counted. So the first layer is the first hidden layer. The reason for this is that in Python subscript counts from zero.
2. some activation of neural network
• sigmoid(if binary classification)
• tanh = $\displaystyle \frac{e^{x} - e^{-x}}{e^x + e^{-x}}$
$g’(z) = \displaystyle 1 - (tanh(z))^2$
• ReLU(default choice) = $max(z, 0)$
• leaky ReLU = $max(0.01z, z)$
3. why do we use linear activation function? Because in this case, finally we will get a linear regression algorithm. It is very clear if we write down the formulas.
# 第四周
1. some notations of deep neural network(mark the input layer as layer 0, the first hidden layer as layer 1)
• $n^{ [l]}$ denotes the units in layer $l$
• $a^{[l]}$ denotes the activations in layer $l$
2. some formular in deep network, and there must be one for-loop to make the forward propagation
• $Z^{[l]} = W^{[l]}A^{[l - 1]} + b^{[l]}$
• $A^{[l]} = g^{[l]}(Z^{[l]})$
3. how to get your matrix dimensions right?
• $W^{[l]}: \ (n^{[l]}, n^{[l - 1]})$
• $b^{[l]}: \ (n^{[l]}, 1)$
4. why deep representations ?
• we can think of neural network that it will compose the small element into something more abstract.
For example, when we input pixels of a image, the first layer maybe deal with these pixels to form some lines; then second layer maybe deal with these line to form some features of face; afterwards the deeper layer will deal with these features to see if it recognize the face composed by these features.
• Circuit theory and deep learning: There are functions u can compute with a “small” N-layer deep neural network that shallower networks require exponentially more hidden units to computes.
I think the tuition behind this is to solve repeatedly subproblem only once which is very same with dynamic programming.
5. backward propagation for layer $l$
Input: $da^{[l]}$
Ourtput: $da^{[l - 1]}, dW^{[l]}, db^{[l]}$
Calculation:$\begin{cases}dz^{[l]} = da^{[l]}*g^{‘[l]}(z^{[l]}) \ \ dw^{[l]} = dz^{[l]}\cdot a^{[l -1]} \ \ db^{[l]} = dz^{[l]} \\ da^{[l - 1]} = w^{[l]T}\cdot dz^{[l]}\end{cases}$
6. a brief to hyperparameters
the parameters that control the final parameter that we use to predict some examples
hyperparameters:
• learning rate
• iterations
• hidden layer
• hidden unit
• choice of activation funciton
parameters:
• weight matrix
• bias
0% |
# Statistical test with small samples
I want to compare 3 groups of samples. Each sample contains 5 measurements. I want to know if the samples differ significantly. First I wanted to do a ANOVA, but my samples are not normal distributed. I tested this with a Shapiro-Wilks Test. For statisitical analyses I use the python library scipy.stats.
import numpy as np
import scipy.stats as stats
sample1 = np.array([0.0016, 0.0012, 0.0009, 0.0011, 0.0016])
sample2 = np.array([0.0018, 0.0016, 0.0015, 0.0015, 0.0015])
sample3 = np.array([0.0007, 0.0005, 0.0013, 0.001 , 0.0015])
stats.shapiro(sample1)[1] #returns p-Val
>0.33173635601997375
stats.shapiro(sample2)[1]
>0.021380668506026268
stats.shapiro(sample3)[1]
>0.8324998021125793
For sample2 we can not assume a normal distribution because the p-Value is smaller 0.05, thats why I decided to test for differences with the Kolmogorov-Smirnov Test where $H_0$ is that 2 independent samples are drawn from the same continuous distribution.
stats.ks_2samp(sample1, sample2)[1] #returns p-Val
>0.20898483057516717
stats.ks_2samp(sample1, sample3)[1]
>0.69740487802059081
stats.ks_2samp(sample2, sample3)[1]
>0.03614619076928504
My conclusion is that there is only a significant difference between sample2 and sample3.
• Is this statistically correct or are there any assumptions I missed?
• Is there maybe a better way to compare this data?
• Is there a statistical test for more than 2 groups where $H_0$ says that all groups are different?
• If you were to correct your test results for the multiple independent comparisons (as you should), you would not conclude the data are not normally distributed and you would proceed with the ANOVA. – whuber Sep 18 '15 at 14:21
• Do you mean, that I should use the Bonferroni correction and than could go on with a ANOVA? – Oli4 Sep 18 '15 at 14:27 |
# Misplaced noalign when using >{\centering} [duplicate]
I have the below code, and I want to center the col. elemnts so I used {||>{\centering}p{0.5\textwidth}||>{\centering}>p{0.3\textwidth}|}, but I got this error "\misplaced noalign" for the \hline command .. any idea how to fix the problem?.
\begin{table}[h]
\label{1}
\begin{tabular}{|p{0.5\textwidth}|>p{0.3\textwidth}|}
\hline
\rowcolor{Gainsboro!60}
Student Name &Student ID \myhash \\
\hline
& \\
\hline
\end{tabular}
\end{table}
• Replace \centering with \centering\arraybackslash and add the array package. – leandriis Aug 8 '20 at 16:10
• it worked thanks – Diana Aug 8 '20 at 16:13
In order to horizontally center the contents of a p type column, use \centering\arraybackslash instead of just \centering. Additionally, and in order to use the >{...} syntax, you will also have to load the array package.
Thus, the following example should give you the desired result:
\documentclass{article}
\usepackage{array}
\usepackage[table,svgnames]{xcolor}
\begin{document}
\begin{table}[h]
\label{1}
\begin{tabular}{|p{0.5\textwidth}|>{\centering\arraybackslash}p{0.3\textwidth}|}
\hline
\rowcolor{Gainsboro!60}
Student Name &Student ID \\
\hline
& \\
\hline
\end{tabular}
\end{table}
\end{document}
Since I assume student ames and their IDs are short enough to not require linebreaks within the corresponding table cells, you could also go for the w type columns that are available when loading the array package instead.
\begin{tabular}{|wl{0.5\textwidth}|wc{0.3\textwidth}|}
\hline
\rowcolor{Gainsboro!60}
Student Name &Student ID \\
\hline
& \\
\hline
\end{tabular}
If you want your table to automaticaly adapt to the width of the widest contents without adding additional wite space, you can use a simple
\begin{tabular}{|l|c|}
A remark on the \label and the use of table: \label only really makes sense in combination with a corresponding \caption and if you later on want to reference the table. (e.g. as in "For an overview see table 1"). The table environment only makes sense if you want your table to float. If you don't want this behaviour, don't use table. |
# Lesson 17
True or False?
## Warm-up: True or False: Fraction Addition (10 minutes)
### Narrative
The purpose of this True or False is for students to demonstrate strategies and understandings they have for adding fractions with unlike denominators. These understandings help students deepen their understanding of the properties of operations and will be helpful later in this lesson when students will develop their own true or false activity.
In the synthesis it is important to discuss things the writer had to pay attention to when they designed this activity.
### Launch
• Display one equation.
• “Give me a signal when you know whether the equation is true and can explain how you know.”
• 1 minute: quiet think time
### Activity
• Share and record answers and strategy.
• Repeat with each equation.
### Student Facing
Decide if each statement is true or false. Be prepared to explain your reasoning.
• $$\frac{3}{4}+\frac{3}{8} = \frac{3}{8}+\frac{3}{8}$$
• $$\frac{7}{5}+\frac{2}{3} = \frac{21}{15}+\frac{8}{15}$$
• $$\frac{8}{9}+\frac{5}{12}=\frac{32}{36}+\frac{15}{36}$$
### Student Response
For access, consult one of our IM Certified Partners.
### Activity Synthesis
• “What did the writer of this activity have to pay attention to when they designed this activity?” (Some equations are true and some are false. Some terms on both sides are equal. Pay attention to the unlike and like denominators.)
• “Where do we see those things in how the equations change during the True or False?” (The first two equations are false, but they use an appropriate common denominator.)
## Activity 1: True or False: Design 1 (15 minutes)
### Narrative
The purpose of this activity is for students to reason about subtracting fractions with unlike denominators to add one equation to a partially-completed True or False activity. If there is time, students can facilitate their True or False with another group.
MLR8 Discussion Supports. Prior to solving the problems, invite students to make sense of the situations and take turns sharing their understanding with their partner. Listen for and clarify any questions about the context.
Representation: Internalize Comprehension. Synthesis: Use multiple examples and non-examples to emphasize the importance of finding like units in order to subtract fractions.
Supports accessibility for: Conceptual Processing, Memory
### Launch
• Groups of 2 or 4
• “Now you will work with your group to complete a True or False activity. This activity has one equation missing. Decide on an equation that would complete the True or False and write it on the blank line.”
### Activity
• 10 minutes: small-group work time
• As students work, monitor for groups who discuss and design an equation based on some of the following:
• They create equations where the fractions on one side of the equation have unlike denominators and the other side consists of fractions with like denominators.
• They create an equation where the common denominator is appropriate, but the corresponding fraction used is not equivalent.
• They create an equation that is similar to a previous equation. For example: $$\frac{5}{6}-\frac{4}{9}=\frac{30}{36}-\frac{16}{36}$$
• They create an equation where a similar strategy can be used to determine if it’s true.
### Student Facing
Write an equation to complete the True and False task. Be prepared to share your reasoning for the last equation.
• $$\frac{5}{6}-\frac{4}{9}=\frac{45}{54}-\frac{24}{54}$$
• $$\frac{5}{6}-\frac{4}{9}=\frac{15}{36}$$
• _______________________
### Student Response
For access, consult one of our IM Certified Partners.
### Activity Synthesis
• Choose small groups to share that had different reasons for their fourth equation.
• Ask students to share their completed True or False and ask the class to share reasons for the last equation.
• As each group shares, continually ask others in the class if they agree or disagree and the reasons why.
## Activity 2: Design 2 (15 minutes)
### Narrative
The purpose of this activity is for students to reason about adding fractions with unlike denominators to add two equations to a partially-completed True or False activity. If there is time, students can facilitate their True or False with another group.
### Launch
• Groups of 2 or 4
• “Now you will work with your group to complete a True or False activity. This activity has two equations missing. Decide on equations that would complete the True or False and write them on the blank lines.”
### Activity
• 10 minutes: small-group work time
• As students work, monitor for groups who discuss and design equations based on some of the following:
• They create equations where the fractions on one side of the equation have unlike denominators and the other side consists of fractions with like denominators.
• They create an equation where the common denominator is appropriate, but the corresponding fraction used is not equivalent.
• They create an equation that is similar to a previous equation.
• They create an equation where a similar strategy can be used to determine if it’s true.
### Student Facing
Write two equations to complete the True or False task. Be prepared to share your reasoning for the equations.
• $$\frac{8}{14}+\frac{3}{7}=\frac{4}{7}+\frac{3}{7}$$
• _______________________
• _______________________
### Student Response
For access, consult one of our IM Certified Partners.
### Activity Synthesis
• Choose small groups to share that had different reasons for their equations.
• Ask students to share their completed True or False and ask the class to share reasons for the equations.
• As each group shares, continually ask others in the class if they agree or disagree and the reasons why.
## Activity 3: Design 3 (15 minutes)
### Narrative
The purpose of this activity is for students to reason about adding and subtracting fractions with unlike denominators. Students create equations to complete a True or False activity. If there is time, students can facilitate their True or False with another group.
### Launch
• Groups of 2 or 4
• “Now you will work with your group to complete a True or False activity. This activity has all three equations missing. Decide on equations that would complete the True or False and write them on the blank lines.”
### Activity
• 10 minutes: small-group work time
• As students work, monitor for groups who discuss and design equations based on some of the following:
• They create equations where the fractions on one side of the equation have unlike denominators and the other side consists of fractions with like denominators.
• They create an equation where the common denominator is appropriate, but the corresponding fraction used is not equivalent.
• They create an equation that is similar to a previous equation.
• They create an equation where a similar strategy can be used to determine if it’s true.
### Student Facing
Write three equations to complete the True or False task. Be prepared to share your reasoning for the equations.
• _______________________
• _______________________
• _______________________
### Student Response
For access, consult one of our IM Certified Partners.
### Activity Synthesis
• Choose small groups to share that had different reasons for their equations.
• Ask students to share their completed True or False and ask the class to share reasons for the equations.
• As each group shares, continually ask others in the class if they agree or disagree and the reasons why.
## Lesson Synthesis
### Lesson Synthesis
“What were the most important things about your equations you had to consider as you created your True or False? Why were these things important?” (I needed to find equations where you could figure out whether or not it was true with a mental strategy. So the numbers had to be related in a nice way and there needed to be some structure to help see if the expressions were equal or not, without finding the sums or differences.)
## Cool-down: Reflection (5 minutes)
### Cool-Down
For access, consult one of our IM Certified Partners. |
# Math Help - Find number of values of x satisfying the given equation.
1. ## Find number of values of x satisfying the given equation.
limit 0 to 2[x+14] $\int [\frac{t}{2}].dt$=limit 0 to {x} $\int [t+14] dt$
where {.} is fractional part of x and [.] is integer number less than or equal to x.
actually speaking, I am not able to get anything from the language of question whether is it asking integral values or real number.
But one thing I hope am doing correct is that R.H.S. comes out to be 14 .
P.S.: i tried my best to solve this question and also use LaTex to type it here.
2. Is the following equation the equation you are trying to solve for in terms of $x$?
$\displaystyle \int_0^{2(x+14)} \bigg \lfloor \dfrac{t}{2} \bigg \rfloor \, dt = \int_0^x \lfloor t + 14 \rfloor \, dt$
3. Originally Posted by NOX Andrew
Is the following equation the equation you are trying to solve for in terms of $x$?
$\displaystyle \int_0^{2(x+14)} \bigg \lfloor \dfrac{t}{2} \bigg \rfloor \, dt = \int_0^x \lfloor t + 14 \rfloor \, dt$
No..the upper limit in LHS is enclosed by [.] (greatest integer function)...and that of RHS by { }(fractional part of x)...so it will look like...i am nt so good at latex so...just trying to modify yours
$\displaystyle \int_0^{[2x+14]} \bigg \lfloor \dfrac{t}{2} \bigg \rfloor \, dt = \int_0^{/{x/}} \lfloor t + 14 \rfloor \, dt$
and if it still doesnt seems clear...so a jpg i am attaching!
4. Don't worry about the LaTeX. It took me a while to familiarize myself with the syntax, and I'm still not that good! Here is the equation for anyone else who may be able to help:
$\displaystyle \int_0^{2 \lfloor x+14 \rfloor} \bigg \lfloor \dfrac{t}{2} \bigg \rfloor \, dt = \int_0^{\{x\}} \lfloor t + 14 \rfloor \, dt$
I have to leave for school now, but I will work on the problem during the day. I'll let you know how I fare.
Edit: $x = -14$ is the only solution I found.
5. answer given is 14 i.e. 14 solutions of x!
anyway, would please you elaborate, or rather just hint out how did you proceed with to get to that answer at least!
6. I made an educated guess. At $x = -14$, $2\lfloor x - 14 \rfloor = 0$ and the left-hand side of the equation is $0$. Furthermore, at $x = -14$, $\{x\} = 0$ and the right-hand side is also $0$. Therefore, $x = -14$ is a solution to the equation.
I don't know how to solve the equation using analytic methods, but I will explore the properties of the greatest integer and fractional part functions. In the meantime, someone else with more knowledge may come along and help.
7. Originally Posted by findmehere.genius
limit 0 to 2[x+14] $\int [\frac{t}{2}].dt$=limit 0 to {x} $\int [t+14] dt$
where {.} is fractional part of x and [.] is integer number less than or equal to x.
Simplify by using some properties of the floor function.
Note that $0\le \left\{ x \right\} = x - \left\lfloor x \right\rfloor <1,\quad \left\lfloor {x + n} \right\rfloor = \left\lfloor x \right\rfloor + n,\;\& \,\left\{ {x + n} \right\} = \left\{ x \right\}$
Notice that $\displaystyle \int_0^{\left\{ x \right\}} {\left\lfloor {t + 14} \right\rfloor dt}= \int_0^{\left\{ x \right\}} {\left\lfloor t \right\rfloor dt} + \int_0^{\left\{ x \right\}} {14dt} = 0 + 14\left\{ x \right\} = 14\left\{ x \right\}$
8. Thanks to you both of you for trying this question, even I finally got somewhere through it and the integration part reduced to(Do confirm it) [x+14]^2 =14{x}
then plotting the graph of both the function would give us 7 solutions?!
I would be pleased with just this much if I get to confirm that my integration is correct, rest answer given in book doesn't matter! |
I made a page for updates and errata to my book: ics.uci.edu/~eppstein/forbidde
I had been planning to do this eventually but what triggered me to do it now was the discovery of a paper by Czumaj, Sohler, and Ziegler (ESA 2000, doi.org/10.1007/3-540-45253-2_) on geometric property testing that I should have already been citing and that solved a problem I had listed as open on the sample complexity of testing for being in convex position. See the new page for details.
@11011110 In the note about Theorem 13.16, you write: "This was already known for a different class of planar graphs, the maximal planar graphs of small shortness exponent."
I think this should be "... the maximal planar graphs whose duals have small-shortness exponent."
or
"the duals of 3-regular 3-connected graphs having small shortness exponent (the first examples of which were constructed by Tutte, as a counterexample to Tait's Conjecture)."
@patmorin Fixed, thanks (I wrote "...of small dual shortness exponent"). It's an important point because the Apollonian triangulations have small shortness exponent but not small dual shortness exponent, so the (incorrect) way I wrote it before would have implied that they were already covered by the previous result.
@patmorin Also Tutte did the important step (find a cubic non-Hamiltonian graph) but did he explicitly iterate and dualize the construction to get maximal planar graphs for which all dual paths are short?
@11011110 Re Tutte. No, I just looked and he just gives the small counterexample and a separate result about the number of Hamiltonian cycles (mod 2).
A Mastodon instance for maths people. The kind of people who make $\pi z^2 \times a$ jokes.
Use $ and $ for inline LaTeX, and $ and $ for display mode. |
### A Fair Evaluation Framework for Comparing Side-Channel Distinguishers
Carolyn Whitnall and Elisabeth Oswald
##### Abstract
The ability to make meaningful comparisons between side-channel distinguishers is important both to attackers seeking an optimal strategy and to designers wishing to secure a device against the strongest possible threat. The usual experimental approach requires the distinguishing vectors to be estimated: outcomes do not fully represent the inherent theoretic capabilities of distinguishers and do not provide a basis for conclusive, like-for-like comparisons. This is particularly problematic in the case of mutual information-based side channel analysis (MIA) which is notoriously sensitive to the choice of estimator. We propose an evaluation framework which captures those theoretic characteristics of attack distinguishers having the strongest bearing on an attacker's general ability to estimate with practical success, thus enabling like-for-like comparisons between different distinguishers in various leakage scenarios. We apply our framework to an evaluation of MIA relative to its rather more well-established correlation-based predecessor and a proposed variant inspired by the Kolmogorov-Smirnov distance. Our analysis makes sense of the rift between the a priori reasoning in favour of MIA and the disappointing empirical findings of previous comparative studies, and moreover reveals several unprecedented features of the attack distinguishers in terms of their sensitivity to noise. It also explores---to our knowledge, for the first time---theoretic properties of near-generic power models previously proposed (and experimentally verified) for use in attacks targeting injective functions.
Note: (Preliminary version)
Available format(s)
Category
Implementation
Publication info
Published elsewhere. To appear in the Journal of Cryptographic Engineering.
Keywords
side-channel analysismutual informationKolmogorov-Smirnovdifferential power analysis
Contact author(s)
carolyn whitnall @ bristol ac uk
History
2011-08-01: revised
See all versions
Short URL
https://ia.cr/2011/403
CC BY
BibTeX
@misc{cryptoeprint:2011/403,
author = {Carolyn Whitnall and Elisabeth Oswald},
title = {A Fair Evaluation Framework for Comparing Side-Channel Distinguishers},
howpublished = {Cryptology ePrint Archive, Paper 2011/403},
year = {2011},
note = {\url{https://eprint.iacr.org/2011/403}},
url = {https://eprint.iacr.org/2011/403}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content. |
# Probability of finding a particle in an infinite well
Tags:
1. Sep 25, 2016
### Titan97
1. The problem statement, all variables and given/known data
For the particle in a box given in the above question, what is the probability of finding the electron between (i) x = 0.49 and 0.51, (ii) x = 0 and 0.020 and (ii) x=0.24 and 0.26 ( x in nm) for both n=1 and n=2. Rationalize your answers.
2. Relevant equations
$$\psi_n=\sqrt{\frac{2}{L}}\sin{\frac{n\pi}{L}x}$$
3. The attempt at a solution
Is the answer to each sub question $$\frac{2}{L}\int_{x_1}^{x_2}\sin^2{\frac{n\pi}{L}x}dx$$?
The trignometric values arent given. So is there anything that I am missing?
2. Sep 25, 2016
### kuruman
Yes it is. I assume you know the value of L.
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So far, the only way we have found to represent prime numbers typographically is as a negative space. Is there, however, some way—I don't care how complicated—of representing the primes as a positive space—that is, as a set of theorems of some formal system? Different people's intuitions give different answers here. I remember quite vividly how puzzled and intrigued I was upon realizing the difference between a positive characterization and a negative characterization. I was quite convinced that not only the primes, but any set of numbers which could be represented negatively, could also be represented positively. The intuition underlying my belief is represented by the question: "How coulda figure andits ground not carry exactly the same information?" They seemed to me to embody the same information, just coded in two complementary ways. What seems right to you? It turns out I was right about the primes, but wrong in general. This astonished me, and continues to astonish me even today. It is a fact that: There exist formal systems whose negative space (set of non- theorems) is not the positive space (set of theorems) of any formal system
If you want to change selection, open document below and click on "Move attachment"
#### pdfs
• owner: piotr.wasik - (no access) - Douglas Hofstadter "Goedel, Escher, Bach", p72
• owner: naraypv - (no access) - Gödel, Escher, Bach_ An Eternal Golden Braid-Basic Books (1994).pdf, p80 |
In this article we are going to look at Excel’s Goal Seek command. This command is actually quite easy to use, and it is very popular because of its ability to look backwards from a given result. A common example used to illustrate this command is finding the amount a person can borrow, at a given interest rate, based on a monthly payment; basically, pairing Goal Seek with the PMT function. We will look at that example, then we will look at a second example that will pair Goal Seek with a simple formula.
Keep in mind that with Goal Seek there are restrictions and limitations; we will only be able to change one data item at a time, and it must be applied to a function or a formula. Even given those restrictions, the following two examples will show you how Goal Seek can be useful.
## Example 1: Monthly Payments Using the PMT Function
For this first example, we are going to use the PMT (Payment) function without a lot of detailed explanation. Any function or formula will serve the purpose of showing how to use Goal Seek, and PMT is as good as any other. (Aside: For those who would like to know what is happening under-the-hood; Goal Seek uses the standard numerical method – Newton’s method – to find the solution. )
First let us look at the arguments for PMT before we use Goal Seek. Refer to Figure 1. Suppose we want to know what the monthly payment will be, if the monthly interest rate is 0.3%, the length of the loan is 60 months, and the amount we want to borrow is $25,000.00 (notice that we are using months for both the interest rate and length of loan; the unit of those input arguments must be consistent). The input values are in locations A3, B3 and C3; and in cell D3 we have the function call =PMT(A3,B3,C3). (More details on using PMT are available from within Excel’s help command). The value in cell D3 is the output from using the function, namely$455.91 (it is in red because this is from the “accounting” point of view, in that the value will be removed from the total that we owe).
Fig. 1 – Using the PMT Function.
Suppose, however, that what we really want is the ability to set the monthly payment to a fixed value, and we want to find out how much we can borrow. For example: how much can I borrow with a monthly payment of $500, at 0.3% monthly interest and over 60 months. We basically want to use the PMT function in a “backwards” order. This is where Goal Seek can be used. As seen in Fig. 2 the Goal Seek sub-command is located in the Data Tab and is one of the options available in the What-If-Analysis command group: Fig. 2 – Excel’s Goal Seek Command The next screen shot, Fig 3., shows the dialog box that results after selecting Goal Seek. Note that cell D3 was selected before we clicked on Goal Seek – which is why it is preloaded into the dialog box. This is the cell that has the output of the PMT function and the location of the value that we want to have locked. Fig. 3 – Goal Seek – Dialog Box – “Set Cell” Next, as seen in Fig. 4, we enter the value that we want to be locked, and in our case it is 500: Fig. 4 – Goal Seek – Dialog Box – “To value” In the last box, seen in Fig. 5, we simply enter the location of the number we want Goal Seek to vary; cell C3 in our case (with absolute referencing): Fig. 5 – Goal Seek – Dialog Box – “By changing cell:” Click on OK, and Fig. 6 shows the results: Fig. 6 – Result of using Goal Seek for Example 1 (Goal Seek with the PMT Function) So, according to PMT, if we want monthly payments of$500.00, at a monthly interest rate of 0.3%, over 60 months; then we can borrow $27,417.00 . With just a few button clicks and a few keystrokes, we were able to get Goal Seek to work with the PMT function to give us the answer we were looking for. ## Example 2: Using Goal Seek with a Formula For this next example we are going to use Goal Seek with a formula instead of a function. In a fictitious task let’s suppose we are going to build a canal. Also, let’s suppose we have some values for material and labor costs, again this is all fictitious and there are some obvious points missing – but for illustration purposes it will suffice. Our example spreadsheet is shown below in Fig. 7: Fig. 7 – Using a formula – Example of building a fictitious canal. The formula in cell E3, =A3*(B3+C3)+D3, just adds the Labor Cost/Meter to the Material Cost/Meter, multiples this by the value in cell A3, (which is the number “1”), then adds the Upfront Equipment Cost. The result can be seen in Fig. 7, and the total cost is over 927 thousand dollars for one meter. Now let’s suppose that what we really what to know is, how long a canal can we build for 800 million dollars? This, as in the previous example, is where Goal Seek can be helpful. As described in the previous example, simply click on: Data Tab -> What-If-Analysis -> Goal Seek. A dialog box will appear, as seen in Fig. 8. (Note that cell E3 was selected before we clicked on Goal Seek, which is why the Set cell already has the location in it): Fig. 8 – Goal Seek Dialog Box – “Set cell” Next, in Fig. 9, we enter 800000000 into the “To value” box: Fig. 9 – Goal Seek Dialog Box – “To value” Finally, as in Fig. 10, we enter the location$A\$3 (note the absolute reference) that contains the value we want Goal Seek to vary until it finds a solution, namely the location of the number “1”:
Fig. 10 – Goal Seek Dialog Box – “By changing cell”
Click on OK and as seen in Fig. 11 we have the result:
Fig. 11 – Result of using Goal Seek for Example 2 (Goal Seek paired with a Formula)
Basically, using the costs outlined, we will be able to build a canal that is a bit over 2.8 kilometers for 800 million dollars. This, and as we saw in the last example, with just a few button clicks and some keystrokes, we were able to get Goal Seek to work with our current formula and give us the answer we were looking for.
Even though we can only solve for one value at a time, Goal Seek can still be quite useful; partly since it is relatively easy to use, and partly because of its ability to work with functions and formulas that we already have in use. |
# Question 44dab
Jan 25, 2017
$\text{3.57 kJ}$
#### Explanation:
A substance's heat of vaporization, sometimes called molar enthalpy of vaporization, essentially tells you how much heat is needed in order to boil $1$ mole of that substance at its boiling point.
In your case, water is said to have a heat of vaporization equal to ${\text{40.66 kJ mol}}^{- 1}$. This means that in order to boil $1$ mole of water at atmospheric pressure, you need to provide it with $\text{40.66 kJ}$ of heat.
Notice that the problem gives you grams of water, so start by converting this to moles. To do that, use the molar mass of water
1.58 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "0.0877 moles H"_2"O"#
Now you can use the heat of vaporization as a conversion factor to get the amount of heat needed to boil your sample of water
$0.0877 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{moles H"_2"O"))) * "40.66 kJ"/(1color(red)(cancel(color(black)("mole H"_2"O")))) = color(darkgreen)(ul(color(black)("3.57 kJ}}}}$
The answer is rounded to three sig figs. |
# Finding the sum of the reciprocals of the positive divisors of a number
Let $$d_1, d_2, \dots , d_k$$ be all the positive factors of a positive integer $$n$$ including $$1$$ and $$n$$. If $$d_1+d_2+ \dots+d_k=72$$, then find the value of $$\frac{1}{d_1}+\frac{1}{d_2}+\dots+\frac{1}{d_k}$$.
My attempt:
Let $$a=p_1^{m_1}p_2^{m_2}\dots p_k^{m_k}$$ be the prime factorization of $$a$$.
To calculate the sum of divisors function, $$\sigma(a)$$ we use the expression :
$$(1+p_1+p_1^2+\dots+p_1^{m_1})(1+p_2+p_2^2+\dots+p_2^{m_2})\dots(1+p_k+p_k^2+\dots+p_k^{m_k})$$
, which represents the sum of all possible positive factors of $$a$$ and is equal to:
$$(\frac{p_1^{m_1+1}-1}{p_1-1})(\frac{p_2^{m_2+1}-1}{p_2-1})\dots(\frac{p_k^{m_k+1}-1}{p_k-1})$$.
Now, if we replace each term in the each factor of the expression above the above expression by its reciprocal we shall obtain the sum of the reciprocals of all possible positive factors of $$a$$. This expression will be equal to:
$$(1+1/p_1+1/p_1^2+\dots+1/p_1^{m_1})(1+1/p_2+1/p_2^2+\dots+1/p_2^{m_2})\dots(1+1/p_k+1/p_k^2+\dots+1/p_k^{m_k})$$
which is equal to:
$$(\frac{1-1/p_1^{m_1+1}}{1-1/p_1})(\frac{1-1/p_2^{m_2+1}}{1-1/p_2})\dots(\frac{1-1/p_k^{m_k+1}}{1-1/p_k})$$ . This on simplication yields $$\frac{\sigma(a)}{n}$$.
Therefore for the information given in the question, the required value is $$\frac{72}{n}$$.
Is my reasoning and my answer correct? What are other methods to solve this question.
• You are working much too hard. Just multiply that sum of reciprocals by $n$, and think about what you're adding up then. – Gerry Myerson Mar 29 at 5:38
• Your answer is correct, and the comment of @GerryMyerson gives you the same value in one line of computation – user1952500 Mar 29 at 5:46
• So $72$ is simply a dummy constant. That is, if the sum of the divisors is $m$, then the sum of the reciprocals is $\frac{m}{n}$. If weight is given to the choice of $72$, then $n=(30,51,55,71)$, and there is no single-valued answer. – Keith Backman Mar 29 at 18:58
The key idea is that if $$\{d_1,\ldots,d_k\}$$ is the set of divisors of $$n$$ then $$\{\frac n{d_1},\ldots,\frac n{d_k}\} = \{d_1,\ldots,d_k\}$$ is also exactly the set of divisors of $$n$$, simply because each element of the first set is a divisor, and there is a bijection $$d_k \to \frac n{d_k}$$ for each $$k$$, so the number of elements in both sets are the same, so the first set covers all the divisors.
With this in mind, the sum of all elements of both sets are the same, hence we have : $$d_1+\ldots+d_k = \frac{n}{d_1}+ \ldots + \frac n{d_k} \implies 72 = n\left(\frac 1{d_1}+ \ldots + \frac 1{d_k}\right)$$
which gives the result. Your proof required the full expression of the $$\sigma$$ function, which we did not use. |
# American Institute of Mathematical Sciences
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doi: 10.3934/jimo.2020079
## Preserving relational contract stability of fresh agricultural product supply chains
1 Business School, Hunan Normal University, Changsha 410081, China 2 School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, 6845, Australia
Corresponding author: Honglei Xu
Received June 2019 Revised December 2019 Published April 2020
Since agricultural cooperatives have developed rapidly under the farmland transfer policy in China, they play an important role in the new operation pattern for China's fresh agricultural product supply chains. To enhance current agricultural supply chains' stability, we consider a three-level (farmer-cooperative-retailer) fresh agricultural product supply chain, conduct quantitative analysis of the impact of the quantity flexibility contract, and compare the impact of the relational contract with that of the quantity flexibility contract on the freshness and the profit. Our results show that a suitable relational contract can improve the freshness and increase the profit of the three-level supply chain, but cannot fully guarantee its stability. Furthermore, the government's subsidy policy can improve the relational contract stability of the fresh agricultural product supply chain by providing the protection price contract mechanism of the agricultural product and the cold chain facility subsidy contract.
Citation: Wucheng Zi, Jiayu Zhou, Honglei Xu, Guodong Li, Gang Lin. Preserving relational contract stability of fresh agricultural product supply chains. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020079
##### References:
[1] J. Blackburn and G. Scudder, Supply chain strategies for perishable products: The case of fresh produce, Produc. Oper. Management, 18 (2009), 129-137. doi: 10.1111/j.1937-5956.2009.01016.x. Google Scholar [2] X. Cai, J. Chen, Y. Xiao and X. Xu, Optimization and coordination of fresh product supply chains with freshness-keeping effort, Produc. Oper. Management, 19 (2010), 261-278. doi: 10.1111/j.1937-5956.2009.01096.x. Google Scholar [3] J. Chen, Y. W. Zhou and Y. Zhong, A pricing/ordering model for a dyadic supply chain with buyback guarantee financing and fairness concerns, Internat. J. Produc. Res., 55 (2017), 5287-5304. doi: 10.1080/00207543.2017.1308571. Google Scholar [4] J. He, X. Cheng, J. He and H. Xu, Cv-CapsNet: Complex-valued capsule network, IEEE Access, 7 (2019), 85492-85499. doi: 10.1109/ACCESS.2019.2924548. Google Scholar [5] A. Herbon, E. Levner and T. C. E. Cheng, Perishable inventory management with dynamic pricing using time-temperature indicators linked to automatic detecting devices, Internat. J. Produc. Econ., 147 (2014), 605-613. doi: 10.1016/j.ijpe.2013.07.021. Google Scholar [6] S. Hosseiniyekani and M. Zibaei, The choice of feasible commodities for futures trading: A study of Iranian agricultural commodities, African J. Agricultural Res., 4 (2009), 193-199. Google Scholar [7] Y. Hou, F. Wei, S. X. Li, Z. Huang and A. Ashley, Coordination and performance analysis for a three-echelon supply chain with a revenue sharing contract, Internat. J. Produc. Res., 55 (2016), 202-227. doi: 10.1080/00207543.2016.1201601. Google Scholar [8] L. Lin, S. Yang and B. Dan, Three-level supply chain coordination of fresh and live agricultural products by revenue-sharing contracts, J. Systems Engineering, 25 (2010), 484-491. Google Scholar [9] E. J. Lodree and B. M. Uzochukwu, Production planning for a deteriorating item with stochastic demand and consumer choice, Internat. J. Produc. Econ., 116 (2008), 219-232. doi: 10.1016/j.ijpe.2008.09.010. Google Scholar [10] Y. Qin, J. Wang and C. Wei, Joint pricing and inventory control for fresh produce and foods with quality and physical quantity deteriorating simultaneously, Internat. J. Produc. Econ., 152 (2014), 42-48. doi: 10.1016/j.ijpe.2014.01.005. Google Scholar [11] M. Rahdar and A. S. Nookabadi, Coordination mechanism for a deteriorating item in a two-level supply chain system, Appl. Math. Model., 38 (2014), 2884-2900. doi: 10.1016/j.apm.2013.11.019. Google Scholar [12] L. Wang and B. Dan, The incentive mechanism for preservation in fresh agricultural supply chain considering consumer utility, J. Industrial Engineering Engineering Management, 29 (2015), 200-206. Google Scholar [13] Y. B. Xiao, J. Chen and X. Xu, Fresh product supply chain coordination under CIF business model with long distance transportation, Systems Engineering Theory Practice, 28 (2008), 19-34. doi: 10.1016/S1874-8651(09)60009-0. Google Scholar [14] X. Xie, X. Liu and H. Xu, Synchronization of delayed coupled switched neural networks: Mode-dependent average impulsive interval, Neurocomputing, 365 (2019), 261-272. doi: 10.1016/j.neucom.2019.07.045. Google Scholar [15] X. Xie, H. Xu and X. Cheng, Improved results on exponential stability of discrete-time switched delay systems, Discrete Contin. Dyn. Syst. Ser. B, 22 (2017), 199-208. doi: 10.3934/dcdsb.2017010. Google Scholar [16] F. Xiong, J. Peng, P. Jin, X. Zhang and Y. Qiu, The impact of relational contracts stability about fresh agricultural product supply chain study: From the persepective of cold chain facilities subsidy mode, Chinese J. Management Science, 23 (2015), 102-111. Google Scholar [17] H. Xu, Y. Zhang, J. Yang, G. Zhou and L. Caccetta, Practical exponential set stabilization for switched nonlinear systems with multiple subsystem equilibria, J. Global Optim., 65 (2016), 109-118. doi: 10.1007/s10898-015-0339-7. Google Scholar [18] Y. Yang, T. Fan and L. Zhang, Coordination of fresh agricultural supply chain with asymmetric freshness information, Chinese J. Management Science, 24 (2016), 147-155. Google Scholar [19] A. Zaheer and N. Venkatraman, Relational governance as an interorganizational strategy: An empirical test of the role of trust in economic exchange, Strategic Management J., 16 (1995), 373-392. doi: 10.1002/smj.4250160504. Google Scholar [20] C. Zhang, W. Liu and J. Lai, A model of relational contract of farm produce supply chain based on GNBS $&$ formal fixed price contract, Chinese J. Management Science, 17 (2009), 94-101. Google Scholar [21] J. Zhang, G. Liu, Q. Zhang and Z. Bai, Coordinating a supply chain for deteriorating items with a revenue sharing and cooperative investment contract, Omega, 56 (2015), 37-49. doi: 10.1016/j.omega.2015.03.004. Google Scholar [22] X. Zhao and F. Wu, Coordination of agri-food chain with revenue-sharing contract under stochastic output and stochastic demand, Asia-Pac. J. Oper. Res., 28 (2011), 487-510. doi: 10.1142/S021759591100320X. Google Scholar [23] S. Zheng, L. Chen and W. Zhuo, Research on the stability of contract relationship among company,cooperative and farmer, J. Fujian Agriculture Forestry University (Philosophy Social Sciences), 16 (2013), 13-17. Google Scholar
show all references
##### References:
[1] J. Blackburn and G. Scudder, Supply chain strategies for perishable products: The case of fresh produce, Produc. Oper. Management, 18 (2009), 129-137. doi: 10.1111/j.1937-5956.2009.01016.x. Google Scholar [2] X. Cai, J. Chen, Y. Xiao and X. Xu, Optimization and coordination of fresh product supply chains with freshness-keeping effort, Produc. Oper. Management, 19 (2010), 261-278. doi: 10.1111/j.1937-5956.2009.01096.x. Google Scholar [3] J. Chen, Y. W. Zhou and Y. Zhong, A pricing/ordering model for a dyadic supply chain with buyback guarantee financing and fairness concerns, Internat. J. Produc. Res., 55 (2017), 5287-5304. doi: 10.1080/00207543.2017.1308571. Google Scholar [4] J. He, X. Cheng, J. He and H. Xu, Cv-CapsNet: Complex-valued capsule network, IEEE Access, 7 (2019), 85492-85499. doi: 10.1109/ACCESS.2019.2924548. Google Scholar [5] A. Herbon, E. Levner and T. C. E. Cheng, Perishable inventory management with dynamic pricing using time-temperature indicators linked to automatic detecting devices, Internat. J. Produc. Econ., 147 (2014), 605-613. doi: 10.1016/j.ijpe.2013.07.021. Google Scholar [6] S. Hosseiniyekani and M. Zibaei, The choice of feasible commodities for futures trading: A study of Iranian agricultural commodities, African J. Agricultural Res., 4 (2009), 193-199. Google Scholar [7] Y. Hou, F. Wei, S. X. Li, Z. Huang and A. Ashley, Coordination and performance analysis for a three-echelon supply chain with a revenue sharing contract, Internat. J. Produc. Res., 55 (2016), 202-227. doi: 10.1080/00207543.2016.1201601. Google Scholar [8] L. Lin, S. Yang and B. Dan, Three-level supply chain coordination of fresh and live agricultural products by revenue-sharing contracts, J. Systems Engineering, 25 (2010), 484-491. Google Scholar [9] E. J. Lodree and B. M. Uzochukwu, Production planning for a deteriorating item with stochastic demand and consumer choice, Internat. J. Produc. Econ., 116 (2008), 219-232. doi: 10.1016/j.ijpe.2008.09.010. Google Scholar [10] Y. Qin, J. Wang and C. Wei, Joint pricing and inventory control for fresh produce and foods with quality and physical quantity deteriorating simultaneously, Internat. J. Produc. Econ., 152 (2014), 42-48. doi: 10.1016/j.ijpe.2014.01.005. Google Scholar [11] M. Rahdar and A. S. Nookabadi, Coordination mechanism for a deteriorating item in a two-level supply chain system, Appl. Math. Model., 38 (2014), 2884-2900. doi: 10.1016/j.apm.2013.11.019. Google Scholar [12] L. Wang and B. Dan, The incentive mechanism for preservation in fresh agricultural supply chain considering consumer utility, J. Industrial Engineering Engineering Management, 29 (2015), 200-206. Google Scholar [13] Y. B. Xiao, J. Chen and X. Xu, Fresh product supply chain coordination under CIF business model with long distance transportation, Systems Engineering Theory Practice, 28 (2008), 19-34. doi: 10.1016/S1874-8651(09)60009-0. Google Scholar [14] X. Xie, X. Liu and H. Xu, Synchronization of delayed coupled switched neural networks: Mode-dependent average impulsive interval, Neurocomputing, 365 (2019), 261-272. doi: 10.1016/j.neucom.2019.07.045. Google Scholar [15] X. Xie, H. Xu and X. Cheng, Improved results on exponential stability of discrete-time switched delay systems, Discrete Contin. Dyn. Syst. Ser. B, 22 (2017), 199-208. doi: 10.3934/dcdsb.2017010. Google Scholar [16] F. Xiong, J. Peng, P. Jin, X. Zhang and Y. Qiu, The impact of relational contracts stability about fresh agricultural product supply chain study: From the persepective of cold chain facilities subsidy mode, Chinese J. Management Science, 23 (2015), 102-111. Google Scholar [17] H. Xu, Y. Zhang, J. Yang, G. Zhou and L. Caccetta, Practical exponential set stabilization for switched nonlinear systems with multiple subsystem equilibria, J. Global Optim., 65 (2016), 109-118. doi: 10.1007/s10898-015-0339-7. Google Scholar [18] Y. Yang, T. Fan and L. Zhang, Coordination of fresh agricultural supply chain with asymmetric freshness information, Chinese J. Management Science, 24 (2016), 147-155. Google Scholar [19] A. Zaheer and N. Venkatraman, Relational governance as an interorganizational strategy: An empirical test of the role of trust in economic exchange, Strategic Management J., 16 (1995), 373-392. doi: 10.1002/smj.4250160504. Google Scholar [20] C. Zhang, W. Liu and J. Lai, A model of relational contract of farm produce supply chain based on GNBS $&$ formal fixed price contract, Chinese J. Management Science, 17 (2009), 94-101. Google Scholar [21] J. Zhang, G. Liu, Q. Zhang and Z. Bai, Coordinating a supply chain for deteriorating items with a revenue sharing and cooperative investment contract, Omega, 56 (2015), 37-49. doi: 10.1016/j.omega.2015.03.004. Google Scholar [22] X. Zhao and F. Wu, Coordination of agri-food chain with revenue-sharing contract under stochastic output and stochastic demand, Asia-Pac. J. Oper. Res., 28 (2011), 487-510. doi: 10.1142/S021759591100320X. Google Scholar [23] S. Zheng, L. Chen and W. Zhuo, Research on the stability of contract relationship among company,cooperative and farmer, J. Fujian Agriculture Forestry University (Philosophy Social Sciences), 16 (2013), 13-17. Google Scholar
The relationship between re-transaction costs and incentive coefficients of cooperatives and retailers
Notations
Variables Meaning $P$ The price of the spot market for the fresh product $P_0$ The price for the payment to a farmer $P_c$ The price paid to a cooperative $P_x$ The spot market price at the time of fulfilling contract $V_x$ Fresh product's value to the retailer $D$ The market demand of fresh product $D_0$ The amount of demand when the farmer and the cooperative sign the contract $D_c$ The amount of demand when the cooperative and the retailer sign the contract $D_x$ The amount of spot market demand when fulfilling the contract $\theta$ The freshness of agricultural products ($0 \le \theta \le 1$) $\theta_1$ The freshness of fresh product provided by the farmer $\theta_2$ The freshness of fresh product provided by the cooperative $C_a$ The variable cost of the farmer to maintain high agricultural product freshness $C_b$ The variable cost of the cooperative to maintain high agricultural product freshness $\pi_f$ The profit function of the farmer $\pi_c$ The profit function of the cooperative $\pi_e$ The profit function of the retailer $\pi_{sx}$ The overall profit function of the supply chain
Variables Meaning $P$ The price of the spot market for the fresh product $P_0$ The price for the payment to a farmer $P_c$ The price paid to a cooperative $P_x$ The spot market price at the time of fulfilling contract $V_x$ Fresh product's value to the retailer $D$ The market demand of fresh product $D_0$ The amount of demand when the farmer and the cooperative sign the contract $D_c$ The amount of demand when the cooperative and the retailer sign the contract $D_x$ The amount of spot market demand when fulfilling the contract $\theta$ The freshness of agricultural products ($0 \le \theta \le 1$) $\theta_1$ The freshness of fresh product provided by the farmer $\theta_2$ The freshness of fresh product provided by the cooperative $C_a$ The variable cost of the farmer to maintain high agricultural product freshness $C_b$ The variable cost of the cooperative to maintain high agricultural product freshness $\pi_f$ The profit function of the farmer $\pi_c$ The profit function of the cooperative $\pi_e$ The profit function of the retailer $\pi_{sx}$ The overall profit function of the supply chain
Profits of members of the supply chain under different contractual relationships
$\pi_f$ $\pi_c$ $\pi_e$ $\pi_{sx}$ No contract 1720.33 1071.20 2921.24 5712.77 Flexibility contract 1942.14 1221.72 13752.03 16915.89 Relational contract 2702.69 3949.91 14867.88 21520.48 Government subsidy 5034.03 10221.25 14555.91 29811.19
$\pi_f$ $\pi_c$ $\pi_e$ $\pi_{sx}$ No contract 1720.33 1071.20 2921.24 5712.77 Flexibility contract 1942.14 1221.72 13752.03 16915.89 Relational contract 2702.69 3949.91 14867.88 21520.48 Government subsidy 5034.03 10221.25 14555.91 29811.19
[1] Sushil Kumar Dey, Bibhas C. Giri. Coordination of a sustainable reverse supply chain with revenue sharing contract. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020165 [2] Zonghong Cao, Jie Min. Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020167
2019 Impact Factor: 1.366 |
## Help with awk for selecting lines in a file avoiding repetition
Help with awk for selecting lines in a file avoiding repetition
# 1
11-26-2012
Help with awk for selecting lines in a file avoiding repetition
Hello,
I am using Awk in UBUNTU 12.04.
I have a file as following with 48,432,354 lines and 4 fields.
The file has this structure (There are repetitions of the first column in several lines)
What I want to have as an outcome is this:
That is to have a file only with the first lines of the first file. To mention, I have a file only with the list of names of the first file like this if that can be useful.
Thank you very much in advance.
Last edited by Franklin52; 11-26-2012 at 05:50 AM.. Reason: Please use code tags for data and code samples
Homa View Public Profile for Homa Find all posts by Homa
# 2
11-26-2012
This User Gave Thanks to complex.invoke For This Post:
complex.invoke View Public Profile for complex.invoke Find all posts by complex.invoke
# 3
11-26-2012
PERFECT! It worked, thank you very very much.
This User Gave Thanks to Homa For This Post:
Homa View Public Profile for Homa Find all posts by Homa
# 4
11-26-2012
Hi Mr complex,
could you please let me know how it works ?
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Hello, I need to select the 3 lines above as well as below a search string, including the search string. I have been trying various combinations using sed command without any success. Can anuone help please. Thanking |
Categories
# midsegment of a triangle formula
Name a segment parallel to the one given. _ _ _ 18. The midsegment of a triangle is a line which links the midpoints of two sides of the triangle. The intercept theorem, also known as Thales's theorem or basic proportionality theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two intersecting lines are intercepted by a pair of parallels.It is equivalent to the theorem about ratios in similar triangles.Traditionally it is attributed to Greek mathematician Thales. P Use the midpoint formula to find the coordinates of M and N. ... Each midsegment contains two of the triangle's midpoints and is parallel to the side that contains the third midpoint. A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle. The Triangle Midsegment Theorem: “In a triangle, the segment joining the midpoints of any two sides will be parallel to the third side and half its length.” Consider the triangle below: Construct a line through C that is parallel to AB. Strategy for proving the Converse of the Trapezoid Midsegment Theorem. The printed output is not copyright. Midsegment Theorem; 2 Midsegment of a Triangle. Q Name a segment parallel to the one given. In the case of the Triangle Midsegment Theorem, a preliminary result is that opposite sides of a parallelogram are congruent. Q . 3. Midsegment $$=$$ $$\dfrac{1}{2}\times$$ Triangle Base: What Is the Converse of the Triangle Midsegment Theorem? and . Award-Winning claim based on CBS Local and Houston Press awards. The segment connecting the midpoints of two sides of a triangle; 3 Example . Choose from 500 different sets of triangle midsegment theorem flashcards on Quizlet. Varsity Tutors connects learners with experts. Q If a segment joins the midpoints of the sides of a triangle, then the segment is parallel to the third side and the segment is half the length of the third side. which of the following statements are correct? The Midsegment Theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side. Formula: m = AB / 2 Where, m = Midsegment of Triangle AB = Length of Parallel Side of the Midsegment. D Midsegments of Triangles Worksheet - Word Docs & PowerPoints. Similarly, what is the maximum number of Midsegments a triangle can have? ¯ Midsegments of Triangles Midpoint Formula; (x1 1 x2 2, y1 1 y2 2) (1 1 3 2, 2 1 (22) 2) (2, 0) (4, 2) 1 1 Yes; both segments have the same slope. It is parallel to the third side and has a length equal to one half of that third side. C, x is a midsegment. then If a midsegment of a triangle connects the midpoints of two sides of a triangle, then it is exactly half the length of the third side of the triangle. In the figure above, drag any point around and convince yourself that this is always true. The midsegment of the trapezoid is: Formula: m = AB / 2. Consider right triangle MNH, where NH is the height of trapezoid drawn from the point N. In this triangle m∠M=60°, angle H is right, then m∠N=30°. D 6 B Midsegment of a Triangle Date_____ Period____ In each triangle, M, N, and P are the midpoints of the sides. The midsegment is always parallel to the third side of the triangle. The midsegment of a triangle is the line segment whose end points are the midpoints of two sides of the triangle. A) Slope Formula: B) Distance Formula: m = y2 - y1 x2 - x1 d = √(x2 - x1)2 + (y2 - y1)2 LESSON 6. 2) Use the midpoint formula to calculate parts b and c. The MIDSEGMENT OF A TRIANGLE is a segment that joins the midpoints of two sides of the triangle. C We may already know the four special types of segments of a triangle : perpendicular bisectors, angle bisectors, medians and altitudes. B Proof of the Triangle Midsegment Theorem. Midsegment of a Triangle. B Proof of Theorem 5-1 Given: R is the midpoint of . 1. C Privacy policy. The midsegment is always half the length of the third side. 3. . A line segment that connects two midpoints of the sides of a triangle is called a midsegment. By definition. ¯ . A line segment joining the midpoints of two sides of a triangle. Some of the worksheets for this concept are 3 the midpoint formula, Geometry work medians centroids 1, Midpoint formula es1, Midsegment of a triangle date period, Practice a the triangle midsegment theorem, Midpoint formula, Performance based learning and assessment task distance, Geometry honors coordinate geometry proofs. B Triangle midsegment theorem proof. is the midpoint of B Midsegment Theorem; 2 Midsegment of a Triangle. Example 1 ; Use the Triangle Midsegment Theorem to find YZ MP of YZ Triangle Midsegment Thm. $$\overline{DF}$$ is the midsegment between $$\overline{AB}$$ and $$\overline{BC}$$. The mid-segment of a triangle (also called a midline) is a segment joining the midpoints of two sides of a triangle. " Midsegment and height. is Learn triangle midsegment theorem with free interactive flashcards. Midsegment of a Triangle Formula. = This lesson will give a coordinate proof of the triangle midsegment theorem. Midsegment is parallel to the third side of the triangle ; Midsegment is half as long as the third side. E is the midsegment between and . 4 Midsegment Theorem. 2. 4 Midsegment Theorem. Make your child a Math Thinker, the Cuemath way. This means that NO=MK-2MH=16-8=8 cm. Theorem 5-1 Triangle Midsegment Theorem If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half its length. Recall the Midpoint Formula . – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow.com - id: 4b8c83-Mzg0M The midsegment is always parallel to the third side of the triangle. 4. Notice the behavior of the midsegment line. Area of a triangle (Heron's formula - given lengths of the three sides) Area of a triangle (By formula, given coordinates of vertices) Area of a triangle (Box method, given coordinates of vertices) Limitations The calculator will produce the wrong answer for crossed polygons, where one side crosses over another, as shown below. 3 . C So first we will prove: A midsegment connects the midpoints of two sides of a triangle or the non-parallel sides of a trapezoid. Satellite View of Landrum High School This is a satellite image of Landrum High School in Landrum, SC. 2. Then, we will review the trapezoid midsegment theorem and go over some examples of how it is used. By accessing or using this website, you agree to abide by the Terms of Service and Privacy Policy. ¯ Mid-Segment Theorem ": The mid-segment of a triangle, which joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and half the length of that third side of the triangle. A A Euclidean construction. Answer: 2 question In the following figure line PQ is a mid segment of triangle GEO, line TW is a midsegment of a triangle PEQ, and line QO is congruent to line PG. and Here is the triangle midsegment theorem proof Proof of the theorem. Varsity Tutors does not have affiliation with universities mentioned on its website. Note that there are two important ideas here. Download FREE midsegment of a triangle Worksheets B Instructors are independent contractors who tailor their services to each client, using their own style, Trapezoid MNOK is isosceles because of MN=OK=8 cm. Be sure to label your x-axis and y-axis. Here are your Free Resources for this Lesson! 2 LN midsegment 5-1 Lesson 1-8 and page 165 … 5 1 midsegment of triangle Key Concepts Theorem 5-1 Triangle Midsegment Theorem If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half its length. 2. Varsity Tutors © 2007 - 2021 All Rights Reserved, CDR Exam - Cardiovascular Disease Recertification Exam Courses & Classes, Common Core Advanced Integrated Math 3 Tutors, CISM - Certified Information Security Manager Courses & Classes, NMLS - Nationwide Mortgage Licensing System Courses & Classes, NAPLEX - National Association Boards of Pharmacy Tutors, CCENT - Cisco Certified Entry Networking Technician Courses & Classes. D. If these properties are the same for every midsegment, what can you conjecture about the midsegment of a triangle and its 3rd side? The midsegment of a triangle creates two triangles that are similar by AA-Similarity. 4. The value of Therefore by the Triangle Midsegment Theorem, P The Midsegment Theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of th… 1) M N P C D E CD || ___ NP 2) M N P R Q S ___ || QS MN Find the missing length indicated. If Displaying top 8 worksheets found for - Midpoint Of A Triangle. Midsegment of a Triangle. Consider the … A midsegment of a triangle is a line linking the midpoint of two of its sides. Use properties of midsegments of a triangle. 1 This page shows how to construct (draw) the midsegment of a triangle with compass and straightedge or ruler. Find the value of In today's geometry lesson, we will prove the trapezoid midsegment theorem, relying on the previously proven triangle midsegment theorem. In this lesson, we will discuss the basic definition of a trapezoid and its midsegment. The segment connecting the midpoints of two sides of a triangle; 3 Example . If A D = D B and A E = E C, then D E ¯ ∥ B C ¯ and D E = 1 2 B C . Now, we know a point on each side of the triangle and the slope of each side. x in the formula and the graphic page 84; Important Tip – the word “formulas” has been corrected to “formula”, and x has been ..... Triangle Midsegment Theorem. A triangle has been drawn such that B and C are the midpoints of two of the sides of this triangle. 2 1) M N P C D E CD || ___ 2) M N P R Q S ___ || QS Find the missing length indicated. Formulas. D Properties. . P It is always parallel to the third side. ¯ Title: Midsegment Theorem 1 Section 5-4. Do It Faster, Learn It Better. Use the slope formula as shown. A line segment that connects two midpoints of the sides of a triangle is called a midsegment. Given. All triangles share certain characteristics. Acknowledgements. Draw your own triangle, find and connect the midpoints of any two sides, and repeat steps A and B for your triangle. • The three midsegments of a triangle divide the triangle into four congruent triangles. A line segment that connects two midpoints of the sides of a triangle is called a midsegment. Answer: 2 question In the following figure line PQ is a mid segment of triangle GEO, line TW is a midsegment of a triangle PEQ, and line QO is congruent to line PG. 2 Midsegment and height. In the diagram, since ∥ , then ∠ ≅∠ and ∠ ≅∠ . Learn triangle midsegment theorem with free interactive flashcards. The tic marks show that and are midpoints. Learn more about midsegment of a triangle definition, triangle midsegment theorem, midsegment of a triangle formula with examples and formulas. Midsegment Triangle. Notice the midsegment length never changes because the side BC never changes. Unsurprisingly, each of a triangle's parts has a name so we can identify it. To shorten proofs in geometry, we can sometimes prove preliminary results. A As of 4/27/18. % Math Homework. Draw your own triangle, find and connect the midpoints of any two sides, and repeat steps A and B for your triangle. Try it yourself Click here for a printable worksheet containing two triangle midsegment problems. The midpoint of a segment in n-dimensional space whose endpoints are = (,, ... A midsegment (or midline) of a triangle is a line segment that joins the midpoints of two sides of the triangle. Use properties of midsegments of a triangle. 1 Here D. If these properties are the same for every midsegment, what can you conjecture about the midsegment of a triangle and its 3rd side? Find the coordinates of the endpoints of each midsegment. D This yields as a special case the well-known formula for the area of a triangle, by considering a triangle as a degenerate trapezoid in which one of the parallel sides has shrunk to a point. So, AB = Length of Parallel Side of the Midsegment. Figure $$\PageIndex{1}$$ The tic marks show that $$D$$ and $$F$$ are midpoints. Strategy: 1) Carefully graph the triangle. 4.9/5.0 Satisfaction Rating over the last 100,000 sessions. Properties: 1. Midsegment of a triangle joins the midpoints of two sides and is half the length of the side it is parallel to. See Midsegment of a triangle. Additionally, how do you find the Midsegment of a triangle? . E Try this Drag the orange dots on each vertex to reshape the triangle. What is the triangle midsegment theorem? E o to use the midpoint formula to calculate midsegments of triangles, o to use the distance formula to examine relationships within triangles. Each midsegment contains two of the unknown triangle’s midpoints and is parallel to the side that contains the third midpoint. You can use the Distance formula or the Pythagorean Theorem to find the lengths of segments. 1. ¯ In ABC, m∠A = 80°, m∠B = 60°, m∠C = 40°. is the midpoint of Midsegment of a triangle joins the midpoints of two sides and is half the length of the side it is parallel to. 5.4 Midsegment Theorem Geometry Mrs. Spitz Fall 2004 Objectives: Identify the midsegments of a triangle. D Where, m = Midsegment of Triangle. For every triangle there are three midsegments. Lesson 5-1 Midsegments of Triangles 259 Midsegments of Triangles Lesson Preview In #ABC above, is a triangle midsegment.A of a triangle is a segment connecting the midpoints of two sides. A triangle midsegment is parallel to the third side of the triangle and is half of the length of the third side. One way to prove the Triangle Midsegment Theorem is to use coordinate geometry and algebra.This style of proof is called a You begin the proof by placing a triangle in a convenient spot on the coordinate plane.You then choose variables for the coordinates of the vertices. The Triangle Midsegment Theorem. is the midpoint of ⋅ methods and materials. D (1) DE=EF //Construction (2) AE=EC //Given, DE is a midsegment (3) ∠AED ≅ ∠CEF // Vertical angles (4) ΔADE ≅ΔCFE // Side-Angle-Side postulate (5) ∠DAE ≅ ∠FCE // corresponding angles in congruent triangles, (CPCTC) (6) AB||CF // Converse Alternate Interior Angles Theorem (7) AD=CF // corresponding sides in congruent triangles, (CPCTC) (8) AD=DB //Given, DE is a midsegment (9) CF=DB //(7), (8), the transitive property of equality (10) DFCB is a parallelogra… So, if is a midsegment of , then and . What is the formula for Midsegment? A Midsegment Theorem – If a line segment joins the midpoint of two sides of a triangle and is parallel to the third side, then the length of the line segment is half the length of the third side. The Midsegment of a Triangle Theorem. In order to find the midsegment of a triangle, you must know and understand two formulas: A midsegment triangle is the triangle formed by the three midsegments of a triangle. A midsegment connecting two sides of a triangle is parallel to the third side and is half as long. Midsegment Theorem – If a line segment joins the midpoint of two sides of a triangle and is parallel to the third side, then the length of the line segment is half the length of the third side. Let us consider a line through the midpoint P and parallel to QR. Strategy: 1) Carefully graph the triangle. Now, let's solve the original problem. ¯ E 1 In the figure The converse of the midsegment theorem is defined as: When a line segment connects two midpoints of two opposite sides of a triangle and is parallel to the third side of a triangle and is half of it then it is a midsegment of a triangle. This yields as a special case the well-known formula for the area of a triangle, by considering a triangle as a degenerate trapezoid in which one of the parallel sides has shrunk to a point. For a triangle with sides a, b and c, the perimeter P is defined as: P = a + b + c. What this formula means in simpler terms is that to find the perimeter of a triangle, you just add together the lengths of each of its 3 sides. Recall that a parallelogram is a quadrilateral with opposite sides congruent. This segment has two special properties. 5.4 Midsegment Theorem Geometry Mrs. Spitz Fall 2004 Objectives: Identify the midsegments of a triangle. To gain access to our editable content Join the Geometry Teacher Community! Figure $$\PageIndex{1}$$ Another special type of segment is called a midsegment. is a midsegment. In the figure above, drag point A around. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC. This shows that ∆ ~∆ . x For this proof, we will prove ΔMFN is similar ΔDFE, by SAS for similar triangles, to obtain corresponding angles for parallel lines and establish a pair of proportional sides. To follow in this lesson will give a coordinate proof of theorem 5-1 Given: R is the of. Midpoints of two of the theorem do you find the lengths of segments 60°. If is a line linking the midpoint of a triangle ; 3.... Preliminary results and E is the triangle midsegment theorem flashcards on Quizlet draw your triangle. 1 2 B C, x = 1 2 B C with free interactive flashcards a Thinker. 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Fastest way to meet, without communication, in a toroidal palace?
I was interested by a similar question asked here, but wanted to pose a slightly different variant that avoids some of the pitfalls and ambiguities in the first question in order to ask something more likely to get a concrete answer.
Suppose two robots are dropped in a palace built on a toroidal planet. The palace covers the entire surface and is broken into equal sized rooms arranged in a grid fashion. The torus is well proportioned, allowing for an equal number of rooms in both directions: that is to say, the palace has n x n rooms and, due to being on a torus, wraps in both directions.
Each robot is equipped with a teleporter. The teleporter can be programmed once per time period and will simultaneously move the robots to their target room. In order for the robots to find each other, they must either end up in same room for a given time period (either by moving to it, or remaining in it), or they may 'run into each other' by cross-teleporting to/from the same pair of rooms at the same time. The robots have no way of leaving marks or otherwise communicating with each other.
Each robot has an in-built GPS system that is pre-programmed with the size of the palace and able to track their position relative to their starting room, although their orientation is random and not guaranteed to match that of their counterpart. They also both come programmed with a strategy, however the strategy is identical for both and cannot be varied between the two robots. You do, however, have access to a random number generator.
What is the optimal strategy for the robots to find each other? If the robots could only teleport themselves to adjacent rooms, is the problem any different?
• Some clarifications, correct me if I misunderstood something. The palace has toroidal topology but no curvature. The “GPS system” is more like an inertial compass, since it only tracks relative movement. The robots are dropped simultaneously, so they have synchronized clocks. The “random direction” is a random multiple of 90°, so one of four possible directions. The optimization should minimize the expected time till the meet, since we know that in the worst case they will never meet, no matter the program. – MvG Apr 3 '15 at 18:54
• This still sounds like a hard problem, but now it would be well suited for Code Golf SE. We wouldn't even need a central judge to match different implementations; each participant could run his code 1000 times with differently seeded PRNGs to estimate the expected value and variance. Do you want me to post this there? – MvG Apr 3 '15 at 19:00
• I'm not even sure what the best strategy on a circle (i.e. $n$ rooms arranged in a cycle) is, let alone a torus! – Milo Brandt Apr 4 '15 at 0:18
• I've drafted a challenge for the Programming Puzzles and Code Golf Stack Exchange. Feel free to edit that as you see fit, to clarify things. Also feel free to upvote the draft if you want to see it posted as a challenge. – MvG Apr 4 '15 at 9:29
Sometimes I worry there aren't any better solutions than this because it's such a bad solution: just choose rooms at random.
We can label the rooms 1..n. The robots teleport to a room at random each time interval, so a robot has a 1/n chance of landing in any specific room. If landing in the same room is the only win condition, the chance of them both selecting the same room in a given time period is 1/n (much like the chance of rolling doubles with two dice).
The added condition of 'swapping' room being a win boils down to the chance that bot A and bot B simultaneously rolls each other's previous number, which multiplies out to 1/n2, giving us a sum total chance of success per roll of (n + 1)/n2. Naturally, the average time is the reciprocal: n2/(n + 1)
• I'd be curious if the restriction of only being able to move into adjacent squares (say allowing diagonals) rather than teleport anywhere actually affects anything. On the one hand it means that if you start 'further' apart it takes longer to traverse the distance. On the other, it means that once we're close there are 'fewer ways to mis-coordinate.' If $n=3$ the two methods coincide due to the topology of the torus (ever pair of squares is adjacent) but I'd be curious to see if a given type of randomization does better in one context than the other. – Pete Caradonna Jun 22 '17 at 17:49
I think even as specified this is still a very hard problem. I'm going to do the teleport to adjacent rooms variant, but nothing substantive changes if this is modified. This is by no means an answer, the only contribution I can really add is a demonstration this problem is well-posed and an optimal strategy exists and some thoughts about what an optimal strategy might look like. I leave finding the actual optimal strategies to those cleverer who come after.
A few pieces of notation:
• Denote the finite set representing the palace by $X$.
• For any compact Hausdorff set $Y$, let $\Delta(Y)$ denote the set of all regular Borel probability measures on $Y$. It is a standard result that $Y$ compact, Hausdorff implies the same for $\Delta(Y)$ endowed with the weak-$*$ topology.
• Let $A$ denote the five-point set of allowable per-period actions $\{\textrm{North, South, East, West, No Movement}\}$
A (pure) strategy for a robot, given a starting position, is $\sigma: \mathbb{N} \to A$. The space of all pure strategies is then $A^\mathbb{N}$ endowed with the (compact) product topology, and the space of all mixed strategies $\Delta(A^\mathbb{N})$.
Define the location function $l: \mathbb{N} \times X \times A^\mathbb{N} \to X$ as the map that takes a starting location and pure strategy and returns the location in $X$ of the robot at a given time. Since we are assuming the two robots follow the same strategy, define, for starting configuration $(x_1, x_2)$:
$$T(\sigma; x_1, x_2) = \min_{n\in \mathbb{N}}\{l(n; x_1, \sigma) = l(n; x_2, \sigma)\}$$ as the earliest meeting time of the two robots for fixed starting configuration. Further, define:
$$\bar{T}(\sigma) = \frac{1}{|X|^2}\int_X \int_X T(\sigma, x_1, x_2) dx_1 dx_2$$ as the earliest expected meeting time (under the assumption of both being uniformly placed down in the palace).
Then we can formalize this problem as:
$$\inf_{\mu \in \Delta(A^\mathbb{N})} \int_{A^\mathbb{N}} \bar{T}(\sigma) \, d\mu(\sigma) \tag{\ast}$$
Considering for a moment the function $T(\cdot ; x_1, x_2)$ for fixed $(x_1, x_2)$, we can see that it is lower semicontinuous as for any $n$ $\{\sigma \in A^\mathbb{N} : T(\sigma; x_1, x_2) > n\}$ is open as it is product of finitely many open subsets of $A$ with infinite copies of $A$. Thus by the extreme value theorem we may replace the inf from ($\ast$) with a min as an optimal strategy necessarily exists.
As for finding an optimal strategy, the one nice thing that a uniform distribution on initial locations buys us is a form of stationarity effectively via translation-invariance. If, conditional on the robots not having met at a time $t$, then the best guess of each of the other's relative location is unchanged from time zero. Beyond that, would love to see if anyone can exhibit strategies that are optimal.
For the case of rooms arranged in a circle, I suspect using the above we can conjecture the form of optimal strategies. At time 0, each robot picks a random direction, left or right, with even probability. After traversing a certain number of rooms along the straight path given by the initial direction choice, the robots will effectively 'become sufficiently certain their counterpart picked the same direction,' and they are chasing each other indefinitely. When such a threshold is passed, the robots simply stop and re-choose 50-50 left right. If they always traverse at least a 'quarter of the circle' before changing directions then clearly they meet in finite time with probability one.
• I had considered the circle form as an even simpler version of the problem that might hint at optimal solutions for more complex spaces. I'm not convinced there is a deterministic solution to serve as an upper bound. For a circle, if you form a 2d strategy lattice (one being the position, the other being time units), you are limited to one position per time unit. There is no rigid lattice that is guaranteed to overlap with another lattice as a simple +1 displacement guarantees no overlap. Any strategy must be probabilistic, which means they cannot be guaranteed to ever meet in finite time. – Danikov Jun 22 '17 at 14:22
• @Danikov Well certainly in the symmetric case for the circle I'd agree. (Note we can pass to a continuous case by considering Lipschitz paths from $[0,\infty) \to S^1$ with a Lipschitz constant of lets say 1 (so no one moves too fast). A suitable Arzela Ascoli gives compactness of pure strategies hence the space of mixtures over paths is compact as well.) Given our local coordinate systems are consistent, then if we both pick left then our distance from each other remains constant, and similarly right. As the above shows though we can guarantee meeting in finite time with probability 1. – Pete Caradonna Jun 22 '17 at 17:28
• @Danikov Even more simply, say we both know we are place antipodally. Then I'd wager 50-50 starting, then re-evaluating after going 1 quarter circle is optimal. The 50-50 comes from symmetry and us minimizing the probability we are both traveling clock or counter-clockwise. Re-evaluation using the same strategy as if there were something that beat it, we would have been better off doing it at time zero, and 50-50 at time zero can't be beat. – Pete Caradonna Jun 22 '17 at 17:31 |
Home > Courses > 1P21_Sternin > RotationalMotion Centripetal force $F_c = ma_c = {{mV^2}\over r}=m\omega^2 r, \qquad \vec{F_c}\> \|\> \vec{a_c}\> \bot\> \vec{V}$ $F_c$ can be provided by: model airplane: $F_c=T$, tension in the wire satellite in orbit: $F_c=G{{mM_E}\over{R^2}}$, Earth's gravity car turning: $F_c=f_s$, static friction (between the tire and the road) |
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# Physics thing
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87
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$$\text{Solve for}\,\psi\\ \frac{1}{2}(-\frac{\hbar^2}{m}\Delta+-\frac{1}{2}k\hat{x}^2)\psi=E\psi$$
Apr 7, 2019
#1
+5635
+2
I believe this is the Shrodinger equation in operator form for a quantum harmonic oscillator.
https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator
Apr 7, 2019
#2
+1
thanks :)
Guest Apr 7, 2019 |
PALANGKARAYA
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KOTAWARINGIN BARAT
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KOTAWARINGIN TIMUR
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TAMIANG LAYANG
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BUNTOK
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MUARA TEWEH
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• # question_answer A blank of 30 mm diameter is to be produced out of 10 mm thick sheet on a simple die. If 6% clearance is recommended, then the nominal diameters of die and punch are respectively: A) 30.6 mm and 29.4 mm B) 30.6 mm and 30 mm C) 30 mm and 29.4 mm D) 30 mm and 28.8 mm
In banking operation, clearance is provided on punch. Here clearance $=6\times \frac{10}{100}=0.6=0.6\,mm$ Punch size $=30-0.6=29.4\,mm$ |
# Logs and their laws
• October 2nd 2011, 01:35 PM
David Green
Logs and their laws
I have a log question;
log 9 x = log 5 (base9) + log 6 (base9) - log 6 (base9)
I have understood it to this point;
log 9 x = log 9 {30/3}
log 9 x = log 9 (10)
I now require to get the "x" on its own, am I going in the right direction from this point as follows;
x = log 9 (10) = log 9^10 = 1000 000 000
I am not to sure what to do with the two log 9's but I require to find the value of "x", am I approaching this correctly?
• October 2nd 2011, 01:41 PM
skeeter
Re: Logs and their laws
Quote:
Originally Posted by David Green
I have a log question;
log 9 x = log 5 (base9) + log 6 (base9) - log 6 (base9)
log 9 x = log 5 (base9)
... the last two terms cancel to 0
...
• October 2nd 2011, 01:51 PM
David Green
Re: Logs and their laws
Quote:
Originally Posted by skeeter
...
I am sorry Skeeter I pushed the wrong key on the last log?
log9 x = log9 5 + log9 6 - log9 3
log9 x = log9 {30/3}
log9 x = log9 (10)
I require to get "x" on its own but have log9 on each side of the equals?
x = log 9^10 = 1000 000 000
Not sure if this is correct?
• October 2nd 2011, 01:57 PM
skeeter
Re: Logs and their laws
if $\log_b{x} = \log_b{y}$ , then $x = y$
• October 2nd 2011, 02:03 PM
David Green
Re: Logs and their laws
I agree but that does not solve for x?
• October 2nd 2011, 02:10 PM
Plato
Re: Logs and their laws
Quote:
Originally Posted by David Green
I agree but that does not solve for x?
@David Green, why not use basic LaTeX tags?
[TEX]\log_{9}(5)[/TEX] gives $\log_{9}(5)$.
• October 2nd 2011, 02:17 PM
David Green
Re: Logs and their laws
Quote:
Originally Posted by Plato
@David Green, why not use basic LaTeX tags?
[TEX]\log_{9}(5)[/TEX] gives $\log_{9}(5)$.
I was told that they are difficult to use and not had any experience with them!
From above it looks like you are saying that "x" = 5 am I correct?
• October 2nd 2011, 02:41 PM
e^(i*pi)
Re: Logs and their laws
Quote:
Originally Posted by David Green
I was told that they are difficult to use and not had any experience with them!
From above it looks like you are saying that "x" = 5 am I correct?
You have $\log_9(10) = \log_9(x)$ which is the same as $x = 10$ (see post 4)
• October 3rd 2011, 11:15 AM
David Green
Re: Logs and their laws
Quote:
Originally Posted by e^(i*pi)
You have $\log_9(10) = \log_9(x)$ which is the same as $x = 10$ (see post 4)
I am still unsure but;
log (base9) x = Log (base9) 10
so I need to get "x" on it's own, therefore because I have no practical examples of how this is done, I am doing it right this way;
Log 10 = 2
• October 3rd 2011, 11:42 AM
e^(i*pi)
Re: Logs and their laws
Quote:
Originally Posted by David Green
I am still unsure but;
log (base9) x = Log (base9) 10
so I need to get "x" on it's own, therefore because I have no practical examples of how this is done, I am doing it right this way;
Log 10 = 2
I'm not sure where you get 2 from. If you like you can raise 9 to the power of both sides - this will have the effect of cancelling out the log function
• October 3rd 2011, 12:25 PM
David Green
Re: Logs and their laws
Quote:
Originally Posted by e^(i*pi)
I'm not sure where you get 2 from. If you like you can raise 9 to the power of both sides - this will have the effect of cancelling out the log function
Log 10 = 2
This is because the two represents an exponent, therefore 10^2 = 100, although I am not confident because as you say my base is 9, therefore;
log 10 = 9
This would be equal to 1 billion as I have posted previously?
• October 3rd 2011, 12:45 PM
e^(i*pi)
Re: Logs and their laws
Quote:
Originally Posted by David Green
Log 10 = 2
This is because the two represents an exponent, therefore 10^2 = 100, although I am not confident because as you say my base is 9, therefore;
log 10 = 9
This would be equal to 1 billion as I have posted previously?
The definition of a logarithm is: $\log_c(b) = a \Leftrightarrow b = c^a$
If we take the expression for a in the first form and put it into the second we get to: $b = c^{\log_c(b)}$
Hence if you raise the base of the logarithm to the log expression they "cancel" in the same way that squaring and square root do.
$9^{\log_9(10)} = 9^{\log_9(x)$
• October 3rd 2011, 01:41 PM
David Green
Re: Logs and their laws
Quote:
Originally Posted by e^(i*pi)
The definition of a logarithm is: $\log_c(b) = a \Leftrightarrow b = c^a$
If we take the expression for a in the first form and put it into the second we get to: $b = c^{\log_c(b)}$
Hence if you raise the base of the logarithm to the log expression they "cancel" in the same way that squaring and square root do.
$9^{\log_9(10)} = 9^{\log_9(x)$
I am not sure I follow the above, however;
log(base9) x = log(base9) 10
if I subtract log(base9) from both sides;
log(base9) - log(base9) x = log(base9) - log(base9) 10
x = 10
Not sure if this is mathematically correct for logs, but it shows x = 10
• October 3rd 2011, 09:17 PM
mr fantastic
Re: Logs and their laws
Quote:
Originally Posted by David Green
I am not sure I follow the above, however;
log(base9) x = log(base9) 10
if I subtract log(base9) from both sides;
log(base9) - log(base9) x = log(base9) - log(base9) 10
x = 10
Not sure if this is mathematically correct for logs, but it shows x = 10
Please pay attention to what you are told or people will just think their time is being wasted.
You have $\log_9 (x) = \log_9 (10)$.
Post #4 and post #8 tell you excatly what to do. I cannot see why this thread has had to go past post #8.
• October 3rd 2011, 09:22 PM
mr fantastic
Re: Logs and their laws
Quote:
Quote:
Originally Posted by Plato
@David Green, why not use basic LaTeX tags?
[TEX]\log_{9}(5)[/TEX] gives $\log_{9}(5)$.
I was told that they are difficult to use and not had any experience with them!
[snip]
What rot. Did you take the time to check the veracity of what you were "told"? 15 minutes (less time than has been spent on this thread since post #8) is all it takes to learn how to do most of what you need to do: http://www.mathhelpforum.com/math-help/f47/ |
Neutrino mass ordering determination through combined analysis with JUNO and KM3NeT/ORCA - Archive ouverte HAL Access content directly
Conference Papers Year : 2021
Neutrino mass ordering determination through combined analysis with JUNO and KM3NeT/ORCA
(1) , (2) , (1) , (1) , (2, 3) , (2, 3)
1
2
3
Nhan Chau
• Function : Author
Marcos Dracos
Leonidas Kalousis
• Function : Author
Abstract
The determination of neutrino mass ordering (NMO) is one of the prime goals of several neutrino experiments. KM3NeT/ORCA and JUNO are two next-generation neutrino oscillation experiments both aiming at addressing this question. ORCA determines the NMO by probing Earth matter effects on the oscillation of atmospheric neutrinos in the GeV energy range. JUNO, on the other hand, is sensitive to the NMO by investigating the interference effects of fast oscillations in the reactor electron antineutrino spectrum at medium baseline. This poster presents the potential of determining the NMO through a combined analysis of JUNO and ORCA data. When measuring the $\Delta m^2_{31}$ with a wrong ordering assumption, the best-fit values are different between the two experiments. This tension, together with good constraints on the $\Delta m^2_{31}$ measurement by both experiments, enhances the combined NMO sensitivity beyond the simple sum of their sensitivities. The analysis shows that 5$\sigma$ significance is reachable in less than 2 years of data taking with both experiements for true normal neutrino mass ordering assuming current global best-fit values of the oscillation parameters, while 6 years will be needed for any other parameter set.
Dates and versions
hal-03373348 , version 1 (11-10-2021)
Identifiers
• HAL Id : hal-03373348 , version 1
• DOI :
• INSPIRE :
Cite
João Pedro Athayde Marcondes de André, Nhan Chau, Marcos Dracos, Leonidas Kalousis, Antoine Kouchner, et al.. Neutrino mass ordering determination through combined analysis with JUNO and KM3NeT/ORCA. 37th International Cosmic Ray Conference, Jul 2021, Berlin, Germany. pp.1196, ⟨10.22323/1.395.1196⟩. ⟨hal-03373348⟩
43 View |
# How to calculate the upper limit on the number of days weather can be forecast reliably?
To put it bluntly, weather is described by the Navier-Stokes equation, which in turn exhibits turbulence, so eventually predictions will become unreliable.
I am interested in a derivation of the time-scale where weather predictions become unreliable. Let us call this the critical time-scale for weather on Earth.
We could estimate this time-scale if we knew some critical length and velocity scales. Since weather basically lives on an $S^2$ with radius of the Earth we seem to have a natural candidate for the critical length scale.
So I assume that the relevant length scale is the radius of the Earth (about 6400km) and the relevant velocity scale some typical speed of wind (say, 25m/s, but frankly, I am taking this number out of, well, thin air). Then I get a typical time-scale of $2.6\cdot 10^5$s, which is roughly three days.
The result three days seems not completely unreasonable, but I would like to see an actual derivation.
Does anyone know how to obtain a more accurate and reliable estimate of the critical time-scale for weather on Earth?
-
Interesting question. Not sure if here is consensus on this. It is the Lyapunov exponents that exponentially 'blow up' inaccuracies in our knowledge of global weather. However, some recent research suggests that quantification of error amplification in weather forecasting needs to distinguish multiple regimes (yorke.umd.edu/papers/…). – Johannes Feb 27 '11 at 16:17
## 3 Answers
I am not sure how useful this "back of the envelope" calculation of reliability of Numerical Weather Prediction is going to be. Several of the assumptions in the question are not correct, and there are other factors to consider.
Here are some correcting points:
1. The Weather is 3 dimensional and resides on the surface of the planet up to a height of at least 10km. Furthermore the density decreases exponentially upwards. Many atmospheric phenomena involve the third dimension such as rising and falling air circulation effects; jet streams (7-16km).
2. The equations are fluid dynamics plus thermodynamics. The Navier-Stokes equations are not only too complex to solve, but in a sense inappropriate as well for the larger scales. One problem is that they might introduce "high frequency" effects (akin to every individual gust of wind or lapping of waves), which should be ignored. The earliest weather prediction models were seriously wrong because the high frequency fluctuations of pressure needed to be averaged rather than directly extrapolated. Here is a possible equation for one point of the atmosphere:
Tchange/time = solar + IR(input) + IR(output) + conduction + convection + evaporation + condensation + advection
The regionality of the model is important too. In a global model there will be larger grid sizes and sources of error from initial conditions and surface and atmosphere top boundary conditions. In a mesoscopic prediction there will be smaller grid sizes but sources of error from the input edges as well. The smallest scale predictions of airflow around buildings and so on might be a true CFD problem using the Navier-Stokes equations however.
I dont know that any calculation is done to predict the inaccuracies, although the different types including the numerical analysis (chaos) error sources can be studied separately. Models are tested against historical data for accuracy overall with predictions made 6-10 days out.
To assume that the atmosphere "goes turbulent" after 3 days seems to conflate several issues together.
-
There has been some work to try to quantify the accuracy of a given days predictions. Currently the meteorologists compare the results from several different models, and look at the consistency from run to run of a given model to get a feeling for how likely the predictions are. There has been some work to that suggests that running a suite of models -usually the same model, with multiple perturbations that represent the error envelope of the observations might be able to improve this significantly. The degree of confidence for say 5days out depends upon the dynamics. – Omega Centauri Feb 27 '11 at 22:20
I agree with your last statement. But then, what is a good upper bound and how to obtain it? – Daniel Grumiller Feb 27 '11 at 23:47
@Daniel Grumiller : The ensemble method mentioned by @Omega Centauri is another practical method for obtaining and improving accuracy. However the sources of error are multiple, and the biggest might not even be from fluid dynamics, but from Chaos, which is not this question. – Roy Simpson Feb 28 '11 at 11:49
I don't think that such a computation of a theoretical limit of accuracy is possible. There are several sources of uncertainty in weather models:
• initial and boundary data,
• parameterizations,
• numerical instability, rounding and approximation errors of the numerical scheme employed to solve the Navier-Stokes equations for the atmosphere.
The term "parameterization" refers to the approximation of all subgrid processes, these are all processes/influences that happen at a scale that is smaller than the length of a grid cell. This includes effects from the topography, or the local albedo. More sophisticated approximations to subgrid processes can actually lead to less predictivity of a model, because the needed more detailed initial and boundary data are not available.
The Navier-Stokes equations themselves are usually approximated up to a minimum length scale that is way larger than the length scales that would be necessary to resolve turbulent flows, these kinds of approximations are called large eddy simulations.
The accuracy of this truncation depends critically on the kind of flow and turbulence.
While I don't think that it is possible to derive a theoretical limit, what people do instead is performing ensemble runs, where the results of a weather model are compared that are calculated with slightly perturbed initial and boundary data.
An example of such a "twin" experiment can be found here:
(The result is that the error becomes significant after ca. 15 days of simulated time.)
-
15 days seems a lot. I suppose there is no simple way to see how this time-scale comes about, is there? – Daniel Grumiller Feb 27 '11 at 23:46
First, you would need to define a "reliable" forecast, e.g. x% confident of temperature, wind, rain,etc within some limits.
Second, your question presumes that weather is not more or less deterministic. At some point, human behavior produces effects that influences the chaotic model. However, the essential problem with chaotic models is the sensitivity to the initial conditions. This results in limitations due to data collection as well as computational issues, e.g. rounding errors. It is not clear what are the inherent limits to model improvement.
- |
Constant¶
class Constant(duration: Union[int, ParameterExpression], amp: Union[complex, ParameterExpression], name: Optional[str] = None, limit_amplitude: Optional[bool] = None)[ソース]
ベースクラス: object
A simple constant pulse, with an amplitude value and a duration:
$f(x) = amp , 0 <= x < duration f(x) = 0 , elsewhere$
Create new pulse instance.
パラメータ
• duration – Pulse length in terms of the sampling period dt.
• amp – The amplitude of the constant square pulse.
• name – Display name for this pulse envelope.
• limit_amplitude – If True, then limit the amplitude of the waveform to 1. The default is True and the amplitude is constrained to 1.
SymbolicPulse instance.
Attributes
alias = 'Constant' |
# Consecutive sum II
Time Limit: 3000/1000 MS (Java/Others)
Memory Limit: 32768/32768 K (Java/Others)
## Description
Consecutive sum come again. Are you ready? Go ~~
1 = 0 + 1
2+3+4 = 1 + 8
5+6+7+8+9 = 8 + 27
You can see the consecutive sum can be representing like that. The nth line will have 2*n+1 consecutive numbers on the left, the first number on the right equal with the second number in last line, and the sum of left numbers equal with two number’s sum on the right.
Your task is that tell me the right numbers in the nth line.
## Input
The first integer is T, and T lines will follow.
Each line will contain an integer N (0 <= N <= 2100000).
## Output
For each case, output the right numbers in the Nth line.
All answer in the range of signed 64-bits integer.
## Sample Input
3
0
1
2
## Sample Output
0 1
1 8
8 27
wangye
2008杭电集训队选拔赛 |
zbMATH — the first resource for mathematics
Numerical verification and error analysis of asymptotic solutions of strongly nonlinear oscillation. (Chinese. English summary) Zbl 1117.65342
Summary: The multiple scales method of G. E. Kuzmak [Prikl. Math. Mekh. 23, 515–526 (1959; Zbl 0089.29803)] and of J. C. Luke [Proc. R. Soc. Lond., Ser. A 292, 403–412 (1966; Zbl 0143.13603)] can be efficiently applied to obtain the solutions of strongly nonlinear oscillators with slowly varying parameters. A technique of numerical order verification is applied to verify that the asymptotic solutions are uniformly valid for small parameter. A numerical comparison of error shows that the asymptotic solutions obtained by the multiple scales method of Kuzmak-Luke [loc. cit.] are uniformly valid, and the errors are about one-tenth of the small parameter $${\varepsilon}$$.
MSC:
65L05 Numerical methods for initial value problems 65L70 Error bounds for numerical methods for ordinary differential equations 65G20 Algorithms with automatic result verification 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems, general theory |
# How to enter a literal string into a Libre Calc cell?
How to enter e.g.
+1/2
...into a cell as a literal string, so that it doesn't get automatically replaced with a formula, but without formatting the cell as text? Normally, one would expect:
'+1/2
...to work (in Excel it does) but in this case it doesn't.
edit retag close merge delete
If the program converts plain +1/2 into a formula, and treats '+1/2 as a string '+1/2, not +1/2, then this is a bug. Program must treat 'somestring as somestring when plain somestring will be treated as special string. Please file it.
( 2020-08-02 09:32:00 +0200 )edit
Sort by » oldest newest most voted
If you type '+1/2, you will see '+1/2.
You can type " +1/2" preceding the + with a space (double quotes here are only to show the space), but this will change alignment one space to the right.
Also can use ="+1/2"and will see +1/2 left aligned as text; but this is a formula (double quotes here are mandatory).
Use a text editor, type there +1/2, then copy and paste in the cell. As long as it doesn't start with = it will show as text, while the cell format will remain as number standard. Also can do it with Writer, but will need to choose menu Edit-Paste Special-Paste Unformatted Text (same that Ctrl+Alt+Shift+V).
Check the mark () to the left of the answer that solves your question.
more
Hello,
format your cell as text (Format Code: @) before you enter data. This disables input recognition and enter +1/2 directly.
Hope that helps
more |
• # question_answer The pH of a solution having the${{\text{H}}^{\text{+}}}$ion concentration of $1\times {{10}^{-4}}g$ions/litre is A) 5 B) 4C) 3 D) 2
pH of solution $=-{{\log }_{10}}{{H}^{+}}$ ${{H}^{+}}=1\times {{10}^{-4}}g$ions/litre $pH=-{{\log }_{10}}{{10}^{-4}}$ $=4\log 10=4\times 1$ So, $pH=4.$ Hence, the correct option is [b]. |
# Physics
## New submissions
[ total of 131 entries: 1-131 ]
[ showing up to 2000 entries per page: fewer | more ]
### New submissions for Tue, 20 Feb 18
[1]
Title: Direct Calculation of the Transfer Map of Electrostatic Deflectors, and Comparison with the Codes $\textit{COSY INFINITY}$ and $\textit{GIOS}$
Comments: 30 pages, 1 figure
Subjects: Accelerator Physics (physics.acc-ph)
COSY INFINITY uses a beamline coordinate system with a Frenet-Serret frame relative to the reference particle, and calculates differential algebra-valued transfer maps by integrating the ODEs of motion in the respective vector space over a differential algebra (DA).
We will describe and perform computation of the DA transfer map of an electrostatic spherical deflector in a laboratory coordinate system using two conventional methods: (1) by integrating the ODEs of motion using a 4th order Runge-Kutta integrator and (2) by computing analytically and in closed form the properties of the respective elliptical orbits from Kepler theory. We will compare the resulting transfer maps with (3) the DA transfer map of COSY INFINITY's built-in electrostatic spherical deflector element ESP and (4) the transfer map of the electrostatic spherical deflector computed using the program GIOS.
In addition to the electrostatic spherical deflector, we study an electrostatic cylindrical deflector, where the Kepler theory is not applicable. We compute the DA transfer map by the ODE integration method (1), and compare it with the transfer maps by (3) COSY INFINITY's built-in electrostatic cylindrical deflector element ECL, and (4) GIOS.
In addition to the code listings in the appendices, the codes to run the test cases are available at this http URL
[2]
Title: Gamma-ray intensities in multi-gated spectra
Authors: Camille Ducoin (IPNL), Guillaume Maquart (IPNL), Olivier Stézowski (IPNL)
Subjects: Data Analysis, Statistics and Probability (physics.data-an)
The level structure of nuclei offers a large amount and variety of information to improve our knowledge of the strong interaction and of mesoscopic quantum systems. Gamma spectroscopy is a powerful tool to perform such studies: modern gamma multi-detectors present increasing performances in terms of sensitivity and efficiency, allowing to extend ever more our ability to observe and characterize abundant nuclear states. For instance, the high-spin part of level schemes often reflects intriguing nuclear shape phenomena: this behaviour is unveiled by high-fold experimental data analysed through multi-coincidence spectra, in which long deexcitation cascades become observable. Determining the intensity of newly discovered transitions is important to characterize the nuclear structure and formation mechanism of the emitting levels. However, it is not trivial to relate the apparent intensity observed in multi-gated spectra to the actual transition intensity. In this work, we introduce the basis of a formalism affiliated with graph theory: we have obtained analytic expressions from which data-analysis methods can eventually be derived to recover this link in a rigorous way.
[3]
Title: Mapping fast evolution of transient surface photovoltage dynamics using G-Mode Kelvin probe force microscopy
Subjects: Applied Physics (physics.app-ph); Materials Science (cond-mat.mtrl-sci)
Optoelectronic phenomena in materials such as organic/inorganic hybrid perovskites depend on a complex interplay between light induced carrier generation and fast (electronic) and slower (ionic) processes, all of which are known to be strongly affected by structural inhomogeneities such as interfaces and grain boundaries. Here, we develop a time resolved Kelvin probe force microscopy (KPFM) approach, based on the G-Mode SPM platform, allowing quantification of surface photovoltage (SPV) with microsecond temporal and nanoscale spatial resolution. We demonstrate the approach on methylammonium lead bromide (MAPbBr3) thin films and further highlight the usefulness of unsupervised clustering methods to quickly discern spatial variability in the information rich SPV dataset. Using this technique, we observe concurrent spatial and ultra-fast temporal variations in the SPV generated across the thin film, indicating that structure is likely responsible for the heterogenous behavior.
[4]
Title: A deep learning framework for turbulence modeling using data assimilation and feature extraction
Subjects: Fluid Dynamics (physics.flu-dyn); Computational Physics (physics.comp-ph)
Turbulent problems in industrial applications are predominantly solved using Reynolds Averaged Navier Stokes (RANS) turbulence models. The accuracy of the RANS models is limited due to closure assumptions that induce uncertainty into the RANS modeling. We propose the use of deep learning algorithms via convolution neural networks along with data from direct numerical simulations to extract the optimal set of features that explain the evolution of turbulent flow statistics. Statistical tests are used to determine the correlation of these features with the variation in the quantities of interest that are to be predicted. These features are then used to develop improved partial differential equations that can replace classical Reynolds Averaged Navier Stokes models and show improvement in the accuracy of the predictions.
[5]
Title: Optics and bremsstrahlung estimates for channeling radiation experiments at FAST
Authors: J. Hyun, P. Piot, T. Sen
Subjects: Accelerator Physics (physics.acc-ph)
This paper presents X-ray spectra of channeling radiation (CR) expected at the FAST (Fermi Accelerator Science and Technology) facility in Fermilab. Our purpose is to produce high brightness quasi-monochromatic X-rays in an energy range from 40 keV to 110 keV. We will use a diamond crystal and low emittance electrons with an energy of around 43 MeV. The quality of emitted X-rays strongly depends on parameters of the electron beam at the crystal. We present simulations of the beam optics for high brightness and high yield operations with bunch charges of 1 pC, 20 pC, and 200 pC. We estimate the X-ray spectra including bremsstrahlung background for a charge of 20 pC. The electron beam distributions with and without channeling in the diamond crystal are calculated. We discuss an X-ray detector system to avoid pile-up effect during high charge operations.
[6]
Title: On the dissociation between potential vorticity conservation and symmetries
Comments: 11 pages
Subjects: Fluid Dynamics (physics.flu-dyn)
Using a four-dimensional manifestly covariant formalism suitable for classical fluid dynamics, it is shown that the conservation of potential vorticity is not associated with any symmetry of the equations of motion but is instead a trivial conservation law of the second kind. The demonstration is provided in arbitrary coordinates and therefore applies to comoving (or label) coordinates. Since this is at odds with previous studies, which claimed that potential vorticity conservation is associated with a symmetry under particle-relabeling, a detailed discussion on relabeling transformations is also presented.
[7]
Title: Dual phase-space cascades in 3D hybrid-Vlasov-Maxwell turbulence
Comments: 6 pages, 3 figures, submitted for publication
Subjects: Plasma Physics (physics.plasm-ph); Solar and Stellar Astrophysics (astro-ph.SR); Space Physics (physics.space-ph)
To explain energy dissipation via turbulence in collisionless, magnetized plasmas, the existence of a dual real- and velocity-space cascade of ion-entropy fluctuations below the ion gyroradius has been proposed. Such a dual cascade, predicted by the gyrokinetic theory, has previously been observed in gyrokinetic simulations of two-dimensional, electrostatic turbulence. For the first time we show evidence for a dual phase-space cascade of ion-entropy fluctuations in a three-dimensional simulation of hybrid-kinetic, electromagnetic turbulence. Energy spectra are largely consistent with a generalized theory for the cascade that accounts for the spectral anisotropy of critically balanced, intermittent, sub-ion-Larmor-scale fluctuations. The observed velocity-space cascade is anisotropic with respect to the magnetic-field direction, with linear phase mixing along magnetic-field lines proceeding mainly at spatial scales above the ion gyroradius and nonlinear phase mixing across magnetic-field lines proceeding at perpendicular scales below the ion gyroradius. Such phase-space anisotropy could be sought in heliospheric and magnetospheric data of solar-wind turbulence.
[8]
Title: Towards commissioning the Fermilab Muon G-2 Experiment
Authors: D. Stratakis, M.E. Convery, J.P. Morgan (Fermilab) M.J. Syphers (Fermilab and Northern Illinois U.) M. Korostelev (Lancaster U. and Cockcroft Inst. Accel. Sci. Tech.) A. Fiedler (Northern Illinois U.) S. Kim (Cornell U.) J.D. Crnkovic, W.M. Morse (Brookhaven)
Comments: 4 pp
Subjects: Accelerator Physics (physics.acc-ph); Instrumentation and Detectors (physics.ins-det)
Starting this summer, Fermilab will host a key experiment dedicated to the search for signals of new physics: The Fermilab Muon g-2 Experiment. Its aim is to precisely measure the anomalous magnetic moment of the muon. In full operation, in order to avoid contamination, the newly born secondary beam is injected into a 505 m long Delivery Ring (DR) wherein it makes several revolutions before being sent to the experiment. Part of the commissioning scenario will execute a running mode wherein the passage from the DR will be skipped. With the aid of numerical simulations, we provide estimates of the expected performance.
[9]
Title: Self-organized oscillations of Leidenfrost drops
Subjects: Fluid Dynamics (physics.flu-dyn)
In the Leidenfrost effect, a thin layer of evaporated vapor forms between a liquid and a hot solid. The complex interactions between the solid, liquid, and vapor phases can lead to rich dynamics even in a single Leidenfrost drop. Here we investigate the self-organized oscillations of Leidenfrost drops that are excited by a constant flow of evaporated vapor beneath the drop. We show that for small Leidenfrost drops, the frequency of a recently reported "breathing mode" can be explained by a simple balance of gravitational and surface tension forces. For large Leidenfrost drops, azimuthal star-shaped oscillations are observed. Our previous work showed how the coupling between the rapid evaporated vapor flow and the vapor-liquid interface excites the star oscillations (Ma \textit{et al., Phys. Rev. Fluids}, 2, 2017, 031602). In our experiments, star-shaped oscillation modes of $n=2$ to 13 are observed in different liquids, the number of observed modes depends sensitively on the liquid viscosity. Here we expand on this work by directly comparing the oscillations with theoretical predictions, and show how the oscillations are initiated by a parametric forcing mechanism through pressure oscillations in the vapor layer. The pressure oscillations are driven by the capillary waves of a characteristic wavelength beneath the drop. These capillary waves can be generated by a large shear stress at the liquid-vapor interface due to the rapid flow of evaporated vapor. We also explore potential effects of thermal convection in the liquid. Although the measured Rayleigh number is significantly larger than the critical value, the frequency (wavelength) of the oscillations depends only on the capillary length of the liquid, and is independent of the drop radius and substrate temperature. Thus convection seems to play a minor role in Leidenfrost drop oscillations, which are mostly hydrodynamic in origin.
[10]
Title: InP femtosecond mode-locked laser in a compound feedback cavity with a switchable repetition rate
Journal-ref: Optics Letters, Vol. 43, Issue 3, pp. 507-510 (2018)
Subjects: Optics (physics.optics)
A monolithically integrated mode-locked semiconductor laser is proposed. The compound ring cavity is composed of a colliding pulse mode-locking (ML) subcavity and a passive Fabry-Perot feedback subcavity. These two 1.6 mm long subcavities are coupled by using on-chip reflectors at both ends, enabling harmonic mode locking. By changing DC-bias conditions, optical mode spacing from 50 to 450 GHz is experimentally demonstrated. Ultrafast pulses shorter than 0.3 ps emitted from this laser diode are shown in autocorrelation traces.
[11]
Title: Study of the likelihood of Alfvénic mode bifurcation in NSTX and predictions for ITER baseline scenarios
Subjects: Plasma Physics (physics.plasm-ph)
Rare Alfv\'enic wave transitions between fixed-frequency and chirping phases are identified in NSTX, where Alfv\'enic waves are normally observed to exhibit either chirping or avalanching responses. For those transitions, we apply a criterion [Duarte et al, Nucl. Fusion 57, 054001 (2017)] to predict the nature of fast ion redistribution in tokamaks to be in the convective or diffusive nonlinear regimes. For NSTX discharges in which the transition is not accompanied by changes in the beam deposited power or modifications in the injected radiofrequency power, it has been found that the anomalous fast ion transport is a likely mediator of the bifurcation between the fixed-frequency mode behavior and rapid chirping. For a quantitative assessment, global gyrokinetic simulations of the effects of electrostatic ion temperature gradient turbulence and trapped electron mode turbulence on chirping were pursued using the GTS code. The investigation is extended by means of predictive studies of the probable spectral behavior of Alfv\'enic eigenmodes for baseline ITER cases consisting of elmy, advanced and hybrid scenarios. It has been observed that most modes are found to be borderline between the steady and the chirping phases.
[12]
Title: Ultracold Rydberg Molecules
Subjects: Atomic Physics (physics.atom-ph)
Ultracold Rydberg molecules have been extensively studied both theoretically and ex-perimentally. Here the authors review the recent realizations of various ultralong-range Rydberg molecules and macrodimers, and explore their potential for current and future applications in spectroscopy, few- and many-body interactions and quantum information processing.
[13]
Title: Liquid xenon scintillation measurements and pulse shape discrimination in the LUX dark matter detector
Comments: 16 pages, 11 figures
Subjects: Instrumentation and Detectors (physics.ins-det)
Weakly Interacting Massive Particles (WIMPs) are a leading candidate for dark matter and are expected to produce nuclear recoil (NR) events within liquid xenon time-projection chambers. We present a measurement of liquid xenon scintillation characteristics in the LUX dark matter detector and develop a pulse shaped based discrimination parameter to be used for particle identification. To accurately measure the scintillation characteristics, we develop a template-fitting method to reconstruct the detection time of photons. Analyzing calibration data collected during the 2013-16 LUX WIMP search, we measure a singlet-to-triplet scintillation ratio for electron recoils (ER) that is consistent with existing literature, and we make a first-ever measurement of the NR singlet-to-triplet ratio at recoil energies below 74 keV. A prompt fraction discrimination parameter exploits the difference of the photon time spectra for NR and ER events and is optimized to have the least number of ER events that occur in the 50\% NR acceptance region. When this discriminator is used in conjunction with charge-to-light discrimination on the calibration data, the signal-to-noise ratio in the NR dark matter acceptance region increases by up to a factor of two.
[14]
Title: Role of edge poloidal density asymmetry in tokamak confinement
Authors: A. Y. Aydemir
Comments: 5 pages, 7 figures
Subjects: Plasma Physics (physics.plasm-ph)
Mass flows and radial electric field driven by edge poloidal density asymmetries can be used as a highly effective control mechanism for the edge and thus global confinement in tokamaks. The underlying physics can be demonstrated entirely within a simple magnetohydrodynamic equilibrium model, without resorting to sophisticated and usually collisionality-dependent neoclassical physics arguments. As an example, strong dependence of the low to high (LH) transition power threshold on the magnetic topology, an experimental observation still poorly understood, can be easily explained within this framework. Similar arguments indicate that the ITER fueling ports above the midplane might lead to higher input power requirements.
[15]
Title: Quenching of stimulated Raman scattering in the kinetic regime by external magnetic fields
Subjects: Plasma Physics (physics.plasm-ph)
We show via particle-in-cell simulations that small normalized magnetic fields ($\omega_c/\omega_p \ll 1$) applied perpendicularly to a light wave can significantly modify the evolution of backward stimulated Raman scattering (SRS) in the kinetic regime. The presence of the magnetic field increases the threshold for kinetic inflation and decreases the amount of reflectivity when SRS is driven significantly above threshold. Analysis indicates this arises because trapped electrons are accelerated as they surf across the wave, leading to the continual dissipation of the electron plasma waves over a wider range of wave amplitudes. The simulation parameters are directly relevant for SRS in inertial confinement fusion devices and indicate that approximately 30 Tesla magnetic fields might significantly reduce SRS backscatter.
[16]
Title: Visible and Infrared Organic Polariton Photodiodes
Subjects: Optics (physics.optics); Applied Physics (physics.app-ph); Quantum Physics (quant-ph)
In organic photodiodes (OPDs) light is absorbed by excitons, which dissociate to generate photocurrent. Here, we demonstrate a novel type of OPD in which light is absorbed by polaritons, hybrid light-matter states. We demonstrate polariton OPDs operating in the ultra-strong coupling regime at visible and infrared energies. These devices can be engineered to show narrow responsivity with a very weak angle-dependence. More importantly, they can be tuned to operate outside of the uncoupled absorbance spectrum. Remarkably, we show that the responsivity of a polariton OPD can be pushed to near infrared wavelengths with external quantum efficiencies exceeding those of a control device.
[17]
Title: Theoretical study of the flow in a fluid damper containing high viscosity silicone oil: effects of shear-thinning and viscoelasticity
Journal-ref: Physics of Fluids 30, 030708 (2018)
Subjects: Computational Physics (physics.comp-ph); Soft Condensed Matter (cond-mat.soft); Fluid Dynamics (physics.flu-dyn)
The flow inside a fluid damper where a piston reciprocates sinusoidally inside an outer casing containing high-viscosity silicone oil is simulated using a Finite Volume method, at various excitation frequencies. The oil is modelled by the Carreau-Yasuda (CY) and Phan-Thien \& Tanner (PTT) constitutive equations. Both models account for shear-thinning but only the PTT model accounts for elasticity. The CY and other generalised Newtonian models have been previously used in theoretical studies of fluid dampers, but the present study is the first to perform full two-dimensional (axisymmetric) simulations employing a viscoelastic constitutive equation. It is found that the CY and PTT predictions are similar when the excitation frequency is low, but at medium and higher frequencies the CY model fails to describe important phenomena that are predicted by the PTT model and observed in experimental studies found in the literature, such as the hysteresis of the force-displacement and force-velocity loops. Elastic effects are quantified by applying a decomposition of the damper force into elastic and viscous components, inspired from LAOS (Large Amplitude Oscillatory Shear) theory. The CY model also overestimates the damper force relative to the PTT, because it underpredicts the flow development length inside the piston-cylinder gap. It is thus concluded that (a) fluid elasticity must be accounted for and (b) theoretical approaches that rely on the assumption of one-dimensional flow in the piston-cylinder gap are of limited accuracy, even if they account for fluid viscoelasticity. The consequences of using lower-viscosity silicone oil are also briefly examined.
[18]
Title: Persistence and Stochastic Periodicity in the Intensity Dynamics of a Fiber Laser During the Transition to Optical Turbulence
Comments: 10 pages, 13 figures
Subjects: Optics (physics.optics); Chaotic Dynamics (nlin.CD)
Many natural systems display transitions among different dynamical regimes, which are difficult to identify when the data is noisy and high dimensional. A technologically relevant example is a fiber laser, which can display complex dynamical behaviors that involve nonlinear interactions of millions of cavity modes. Here we study the laminar-turbulence transition that occurs when the laser pump power is increased. By applying various data analysis tools to empirical intensity time series we characterize their persistence and demonstrate that at the transition temporal correlations can be precisely represented by a surprisingly simple model.
[19]
Title: Fully differential cross sections for $Li^{2+}$-impact ionization of $Li(2s)$ and $Li(2p)$
Comments: 11 pages, 5 Figures
Subjects: Atomic Physics (physics.atom-ph)
A semiclassical impact parameter version of the continuum distorted wave-Eikonal initial state theory is developed to study the differential ionization of $Li$ atoms in collisions with $Li^{2+}$ ions. Both post and prior forms of the transition amplitude are considered. The fully differential cross sections are calculated for the lithium targets in their ground and their first excited states and for the projectile ions at 16~MeV impact energy. The role of the internuclear interaction as well as the significance of the post-prior discrepancy in the ejected electron spectra are investigated. The obtained results for ejection of the electron into the azimuthal plane are compared with the recent measurements and with their corresponding values obtained using a fully quantum mechanical version of the theory. In most of the cases, the consistency of the present approach with the experimental and the quantum theoretical data is reasonable. However, for $2p$-state ionization, in the cases where no experimental data exist, there is a considerable difference between the two theoretical approaches. This difference is questionable and further experiments are needed to judge which theory makes a more accurate description of the collision dynamics.
[20]
Title: Nonlinear lower-hybrid oscillations in a cold magnetized electron-positron-ion plasma
Subjects: Plasma Physics (physics.plasm-ph)
A new class of the exact nonlinear solutions for the lower-hybrid oscillations in a cold magnetized electron-positron-ion (e-p-i) plasma has been suggested by employing a method of Lagrange variables. It is found that the frequency of the lower-hybrid oscillations in an e-p-i plasma is approximately $\sqrt{3}$ times the frequency of lower-hybrid oscillations in an electron-ion (e-i) plasma. The present work may have some relevance for laboratory/astrophysical e-p-i plasmas.
[21]
Title: Spatiotemporal stabilization proof of concept of Broad Area Semiconductor laser sources
Comments: 6 pages, 3 figures
Subjects: Optics (physics.optics)
We provide a numerical proof of concept of a stabilization mechanism for BAS laser sources. The scheme is based on the simultaneous introduction of in-phase two-dimensional modulations on the refractive index and pump (gain). We numerically proof total stabilization in BAS laser sources, both in space and time. We also examine the interplay between the index and gain modulations and the effect of the slow relaxation of carriers on the stabilization performance.
[22]
Title: Probing Patchy Saturation of Fluids in Nanoporous Media by Ultrasound
Subjects: Geophysics (physics.geo-ph); Applied Physics (physics.app-ph)
Nanoporous materials provide high surface area per unit mass and are capable of fluids adsorption. While the measurements of overall amount of fluid adsorbed by a nanopororus sample are straightforward, probing the fluid spacial distribution is non-trivial. We consider published data on adsorption and desorption of fluids in nanoporous glasses reported along with the measurements of ultrasonic waves propagation. We analyse these using Biot's theory of dynamic poroelasticity, approximating the patches as spherical shells. Our calculations show that on adsorption the patch diameter is on the order of 10-20 pore diameters, while on desorption the patch size is comparable to the sample size. Our analysis suggests that one can employ ultrasound to probe the uniformity of fluid spatial distribution in nanoporous materials.
[23]
Title: Interactive Estimation of the Fractal Properties of Carbonate Rocks
Subjects: Geophysics (physics.geo-ph)
Scale invariance of intrinsic patterns is an important concept in geology that can be observed in numerous geological objects and phenomena. These geological objects and phenomena are described as containing statistically selfsimilar patterns often modeled with fractal geometry. Fractal geometry has been used extensively to characterize pore space and fracture distribution of both carbonate and clastic rocks as well as the transport properties of porous media and fluid flow in reservoirs. The fractal properties are usually estimated from thin-section photomicrograph images or scanning electron microscope images. For complex rock such as carbonate rocks, automatic feature detection methods are often inaccurate. In addition, the rocks may be have been subjected to facies selective diagenesis which preferentially affect some of the rock fabric, thus increasing the difficulty in automatic detection of certain features. We present an interactive program, GeoBoxCount, for analyzing thin-section images and calculating the fractal dimension interactively. The program relies on the geologists insight in interpreting the features of interest; this significantly improves the accuracy of feature selection. The program provides two options for calculating the fractal dimension: the Hausdorff and the Minkowsi-Bouligand box-counting methods.
[24]
Title: Resonance line broadened quasilinear (RBQ) model for fast ion distribution relaxation due to Alfvénic eigenmodes
Subjects: Plasma Physics (physics.plasm-ph)
The burning plasma performance is limited by the confinement of the superalfvenic fusion products such as alpha particles and the auxiliary heating ions capable of exciting the Alfv\'enic eigenmodes (AEs). In this work the effect of AEs on fast ions is formulated within the quasi-linear (QL) theory generalized for this problem recently. The generalization involves the resonance line broadened interaction of energetic particles (EP) with AEs supplemented by the diffusion coefficients depending on EP position in the velocity space. A new resonance broadened QL code (or RBQ1D) based on this formulation allowing for EP diffusion in radial direction is built and presented in details. We reduce the wave particle interaction (WPI) dynamics to 1D case when the particle kinetic energy is nearly constant. The diffusion equation for EP distribution evolution is then one dimensional and is solved simultaneously for all particles with the equation for the evolution of the wave angular momentum. The evolution of fast ion constants of motion is governed by the QL diffusion equations which are adapted to find the fast ion distribution function. We make initial applications of the RBQ1D to DIII-D plasma with elevated q-profile where the beam ions show stiff transport properties. AE driven fast ion profile relaxation is studied for validations of the QL approach in realistic conditions of beam ion driven instabilities in DIII-D.
[25]
Title: Vortex interaction with a rough wall formed by a hexagonal lattice of posts
Subjects: Fluid Dynamics (physics.flu-dyn)
An experimental study is reported which investigates the head-on collision of a laminar vortex ring of diameter D (Re{\Gamma}= 3000) on a fakir-like surface composed of circular posts of height h*=0.068 located on a planar bed. Lattices of the posts in hexagonal and random distribution (average porosity of e = 0.94 in the layer) are compared to each other with respect to the plain wall. Prior to impact, the vortex ring develops the early state of natural azimuthal instabilities of different mode numbers N=5-7 competing with each other. While impacting with the rough wall, a secondary ring is observed which is pushed outwards and is not wrapped around the primary ring as in flat wall impact. Between both rings of opposite sign vorticity, a strong fluid rebound is induced. The hexagonal lattice causes the rapid growth of further secondary vortex structures in a regular mode number N=6 arrangement at the outer edge of the primary ring in form of six lobes which are aligned with the orientations of preferential pathways in the layer. At the outer tip of the lobes radial wall-jets are generated. Rotating the fakir geometry around the centre of impact also rotates the jets location and direction accordingly. A surface with random lattice of the posts at the same average number density is not able to repeat this observation and no regular secondary flow pattern is visible until full breakdown of the ring. The results show that a tailored arrangement of such posts can be used for near-wall flow control when patterns of preferred pathways in the posts layer lock-on with existing instability modes such as in impacting jet flows or in turbulent boundary layer flows.
[26]
Title: Deformation of a Half-Space from Anelastic Strain Confined in a Tetrahedral Volume
Authors: Sylvain Barbot
Subjects: Geophysics (physics.geo-ph)
Deformation in the lithosphere-asthenosphere system can be accommodated by faulting and plastic flow. However, incorporating structural data in models of distributed deformation still represents a challenge. Here, I present solutions for the displacements and stress in a half-space caused by distributed anelastic strain confined in a tetrahedral volume. These solutions form the basis of curvilinear meshes that can adapt to realistic structural settings, such as a mantle wedge corner, a spherical shell around a magma chamber, or an aquifer. I provide computer programs to evaluate them in the cases of antiplane strain, plane strain, and three-dimensional deformation. These tools may prove useful in the modeling of deformation data in tectonics, volcanology, and hydrology studies.
[27]
Title: Spontaneous emission from radiative chiral nematic liquid crystals at the photonic band gap edge: an investigation into the role of the density of photon states near resonance
Comments: 7 Figures, 12 References, 2 Appendices
Journal-ref: Phys. Rev. E 87, 062504 (2013)
Subjects: Optics (physics.optics)
In this article, we investigate the spontaneous emission properties of radiating molecules embedded in a chiral nematic liquid crystal, under the assumption that the electronic transition frequency is close to the photonic edge mode of the structure, i.e. at resonance. We take into account the transition broadening and the decay of electromagnetic field modes supported by the so-called mirror-less' cavity. We employ the Jaynes-Cummings Hamiltonian to describe the electron interaction with the electromagnetic field, focusing on the mode with the diffracting polarization in the chiral nematic layer. As known in these structures, the density of photon states, calculated via the Wigner method, has distinct peaks on either side of the photonic band gap, which manifests itself as a considerable modification of the emission spectrum. We demonstrate that, near resonance, there are notable differences between the behavior of the density of states and the spontaneous emission profile of these structures. In addition, we examine in some detail the case of the logarithmic peak exhibited in the density of states in 2D photonic structures and obtain analytic relations for the Lamb shift and the broadening of the atomic transition in the emission spectrum. The dynamical behavior of the atom-field system is described by a system of two first order differential equations, solved using the Green's function method and the Fourier transform. The emission spectra are then calculated and compared with experimental data.
[28]
Title: New Physics Searches Using Precision Spectroscopy
Authors: Chad Orzel
Comments: Prepared for Advances in Atomic, Molecular, and Optical Physics vol 67
Subjects: Atomic Physics (physics.atom-ph)
The exceptional precision attainable using modern spectroscopic techniques provides a promising avenue to search for signatures of physics beyond the Standard Model in tiny shifts of the energy levels of atoms and molecules. We briefly review three categories of new-physics searches based in precision measurements: tests of QED using measurements of the anomalous magnetic moment of the electron and the value of the fine-structure constant, searches for time variation of the fundamental constants, and searches for a permanent electric dipole moment of an electron or atomic nucleus.
[29]
Title: The Mu2e Calorimeter Final Technical Design Report
Authors: N. Atanov (1), V. Baranov (1), J. Budagov (1), S.Ceravolo (2), F. Cervelli (4), F. Colao (2), M. Cordelli (2), G. Corradi (2), E. Dane (2), Y. Davydov (1), S. Di Falco (4), S. Donati (4), E. Diociaiuti (2), R. Donghia (2), B. Echenard (3), K. Flood (3), S. Giovannella (2), V. Glagolev (1), F. Grancagnolo (6), F. Happacher (2), D. Hitlin (3), M. Martini (2), S. Miscetti (2), T. Miyashita (3), L. Morescalchi (4), P. Murat (5), D. Pasciuto (4), G. Pezzullo (4), F. Porter (3), T. Radicioni (4), F. Raffaelli (4), M. Ricci (2), A. Saputi (2), I. Sarra (2), F. Spinella (4), D. Tagnani (2), G. Tassielli (6), V. Tereshchenko (1), Z. Usubov (1), R. Y. Zhu (3) ((1) Joint Institute for Nuclear Research, Dubna, Russia (2) Laboratori Nazionali di Frascati dell INFN, Frascati, Italy (3) California Institute of Technology, Pasadena, United States (4) INFN Sezione di Pisa, Pisa, Italy (5) Fermi National Laboratory, Batavia, Illinois, USA (6) INFN Sezione di Lecce, Lecce, Italy)
Comments: TDR
Subjects: Instrumentation and Detectors (physics.ins-det); High Energy Physics - Experiment (hep-ex)
Since the first version of the Mu2e TDR released at the beginning of 2015, the Mu2e Calorimeter system has undergone a long list of changes to arrive to its final design. These changes were primarily caused by two reasons: (i) the technology choice between the TDR proposed solution of BaF2 crystals readout with solar blind Avalanche Photodiodes (APDs) and the backup option of CsI crystals readout with Silicon Photomultipliers (SiPM) has been completed and (ii) the channels numbering, the mechanical system and the readout electronics were substantially modified while proceeding with engineering towards the final project. This document updates the description of the calorimeter system adding the most recent engineering drawings and tecnical progresses.
[30]
Title: Design and status of the Mu2e crystal calorimeter
Authors: N. Atanov (1), V. Baranov (1), J. Budagov (1), Yu. I. Davydov (1), V. Glagolev (1), V. Tereshchenko (1), Z. Usubov (1), F. Cervelli (2), S. Di Falco (2), S. Donati (2), L. Morescalchi (2), E. Pedreschi (2), G. Pezzullo (2), F. Raffaelli (2), F. Spinella (2), F. Colao (3), M. Cordelli (3), G. Corradi (3), E. Diociaiuti (3), R. Donghia (3), S. Giovannella (3), F. Happacher (3), M. Martini (3), S. Miscetti (3), M. Ricci (3), A. Saputi (3), I. Sarra (3), B. Echenard (4), D. G. Hitlin (4), T. Miyashita (4), F. Porter (4), R. Y. Zhu (4), F. Grancagnolo (5), G. Tassielli (5), P.Murat (6) ((1) Joint Institute for Nuclear Research, Dubna, Russia (2) INFN Sezione di Pisa, Pisa, Italy (3) Laboratori Nazionali di Frascati dell'INFN, Frascati, Italy (4) California Institute of Technology, Pasadena, United States (5) INFN Sezione di Lecce, Lecce, Italy (6) Fermi National Laboratory, Batavia, Illinois, USA)
Comments: 8 pages, 16 figures, submitted to IEEE
Subjects: Instrumentation and Detectors (physics.ins-det); High Energy Physics - Experiment (hep-ex)
The Mu2e experiment at Fermilab searches for the charged-lepton flavour violating (CLFV) conversion of a negative muon into an electron in the field of an aluminum nucleus, with a distinctive signature of a mono-energetic electron of energy slightly below the muon rest mass (104.967 MeV). The Mu2e goal is to improve by four orders of magnitude the search sensitivity with respect to the previous experiments. Any observation of a CLFV signal will be a clear indication of new physics. The Mu2e detector is composed of a tracker, an electro- magnetic calorimeter and an external veto for cosmic rays surrounding the solenoid. The calorimeter plays an important role in providing particle identification capabilities, a fast online trigger filter, a seed for track reconstruction while working in vacuum, in the presence of 1 T axial magnetic field and in an harsh radiation environment. The calorimeter requirements are to provide a large acceptance for 100 MeV electrons and reach at these energies: (a) a time resolution better than 0.5 ns; (b) an energy resolution < 10% and (c) a position resolution of 1 cm. The calorimeter design consists of two disks, each one made of 674 undoped CsI crystals read by two large area arrays of UV-extended SiPMs. We report here the construction and test of the Module-0 prototype. The Module-0 has been exposed to an electron beam in the energy range around 100 MeV at the Beam Test Facility in Frascati. Preliminary results of timing and energy resolution at normal incidence are shown. A discussion of the technical aspects of the calorimeter engineering is also reported in this paper.
[31]
Title: Quantitative Predictions in Quantum Decision Theory
Comments: Latex file, 17 pages, 1 figure
Journal-ref: IEEE Trans. Syst. Man Cybern. Syst. 48 (2018) 366-381
Subjects: Physics and Society (physics.soc-ph); Quantum Physics (quant-ph)
Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the theory of quantum measurements, which makes this approach relevant both for the description of decision making of humans and the creation of artificial quantum intelligence. General rules are formulated allowing for the explicit calculation of quantum probabilities representing the fraction of decision makers preferring the considered prospects. This provides a method to quantitatively predict decision-maker choices, including the cases of games with high uncertainty for which the classical expected utility theory fails. The approach is applied to experimental results obtained on a set of lottery gambles with gains and losses. Our predictions, involving no fitting parameters, are in very good agreement with experimental data. The use of quantum decision making in game theory is described. A principal scheme of creating quantum artificial intelligence is suggested.
[32]
Title: Lamellar ordering, droplet formation and phase inversion in exotic active emulsions
Comments: 15 pages: Manuscprit (4 figures) and SI (11 figures)
Subjects: Biological Physics (physics.bio-ph); Soft Condensed Matter (cond-mat.soft)
We study numerically the behaviour of a mixture of a passive isotropic fluid and an active polar gel, in the presence of a surfactant favouring emulsification. Focussing on parameters for which the underlying free energy favours the lamellar phase in the passive limit, we show that the interplay between nonequilibrium and thermodynamic forces creates a range of multifarious exotic emulsions. When the active component is contractile (e.g., an actomyosin solution), moderate activity enhances the efficiency of lamellar ordering, whereas strong activity favours the creation of passive droplets within an active matrix. For extensile activity (occurring, e.g., in microtubule-motor suspensions), instead, we observe an emulsion of spontaneously rotating droplets of different size. By tuning the overall composition, we can create high internal phase emulsions, which undergo sudden phase inversion when activity is switched off. Therefore, we find that activity provides a single control parameter to design composite materials with a strikingly rich range of morphologies.
[33]
Title: Experimental demonstration of three-dimensional broadband underwater acoustic carpet cloak
Subjects: Applied Physics (physics.app-ph)
We present the design, architecture and detailed performance of a three-dimensional (3D) underwater acoustic carpet cloak (UACC). The proposed system of the 3D UACC is an octahedral pyramid which is composed of periodical steel strips. This underwater acoustic device, placed over the target to hide, is able to manipulate the scattered wavefront to mimic a reflecting plane. The effectiveness of the prototype is experimentally demonstrated in an anechoic tank. The measured acoustic pressure distributions show that the 3D UACC can work in all directions in a wide frequency range. This experimental verification of 3D device paves the way for guidelines on future practical applications.
[34]
Title: Superthermal photon bunching in terms of simple probability distributions
Subjects: Optics (physics.optics); Quantum Physics (quant-ph)
We analyze the second-order photon autocorrelation function $g^{(2)}$ with respect to the photon probability distribution and discuss the generic features of a distribution that result in superthermal photon bunching ($g^{(2)}>2$). Superthermal photon bunching has been reported for a number of optical microcavity systems that exhibit processes like superradiance or mode competition. We show that a superthermal photon number distribution cannot be constructed from the principle of maximum entropy, if only the intensity and the second-order autocorrelation are given. However, for bimodal systems an unbiased superthermal distribution can be constructed from second-order correlations and the intensities alone. Our findings suggest modeling superthermal single-mode distributions by a mixture of a thermal and a lasing like state and thus reveal a generic mechanism in the photon probability distribution responsible for creating superthermal photon bunching. We relate our general considerations to a physical system, a (single-emitter) bimodal laser, and show that its statistics can be approximated and understood within our proposed model. Furthermore the excellent agreement of the statistics of the bimodal laser and our model reveal that the bimodal laser is an ideal source of bunched photons, in the sense that it can generate statistics that contain no other features but the superthermal bunching.
[35]
Title: Spectral stability of nonlinear gravity waves in the atmosphere
Subjects: Fluid Dynamics (physics.flu-dyn)
We apply spectral stability theory to investigate nonlinear gravity waves in the atmosphere. These waves are described by modulation equations being derived from nonlinear Wentzel-Kramers-Brillouin theory. First, we establish that plane waves, which represent exact solutions to the inviscid Boussinesq equations, are spectrally stable with respect to their nonlinear modulation equations under the same conditions as what is known as modulational stability from weakly nonlinear theory. Second, we show that traveling waves solving the inviscid modulation equations that compare to pseudo-incompressible theory, which accounts in contrast to Boussinesq for the altitudinal varying background density, are unconditionally unstable. Both inviscid regimes turn out to be ill-posed. A regularization is found by including dissipative effects. The according traveling wave packets generate transient essential instabilities that decay locally at every fixed point if the wave packet travels downwards or if the wave packet travels upwards and the group velocity, as defined by the derivative of the frequency, does not exceed the envelope velocity at no point. Additionally, all three types of nonlinear modulation equations are solved numerically to further investigate the nature of the analytic stability results.
[36]
Title: Measuring Accessibility using Gravity and Radiation Models
Comments: 12 Pages, 4 Figures
Subjects: Physics and Society (physics.soc-ph)
Since the presentation of the Radiation Model, much work has been done to compare its findings with those obtained from Gravitational Models. These comparisons always aim at measuring the accuracy with which the models reproduce the mobility described by origin-destination matrices. This has been done at different spatial scales using different datasets, and several versions of the models have been proposed to adjust to various spatial systems. However the models, to our knowledge, have never been compared with respect to policy testing scenarios. For this reason, here we use the models to analyze the impact of the introduction of a new transportation network, a Bus Rapid Transport system, in the city of Teresina in Brazil. We do this by measuring the estimated variation in the trip distribution, and formulate an accessibility to employment indicator for the different zones of the city. By comparing the results obtained with the two approaches, we are able, not only to better assess the goodness of fit and the impact of this intervention, but also to understand reasons for the systematic similarities and differences in their predictions.
[37]
Title: Experimental investigation of dynamical structures formation due to flowing complex plasma past an obstacle
Comments: 9 pages, 7 figures
Subjects: Plasma Physics (physics.plasm-ph)
We report the experimental observation of dynamical behavior of flowing complex plasma past a spherical obstacle. The experiment has been carried out in a $\Pi$-shaped DC glow discharge experimental device using kaolin particles as the dust component in a background of Argon plasma. A stationary dust cloud is formed by maintaining the pumping speed and gas flow rate. A spherical obstacle vertically mounted on the cathode tray acts as an obstacle to the flow of dust particles. The controlled dust flow is generated by reducing the mass flow of the neutrals through a mass flow controller. The flowing dust particles are repelled by the electrostatic field of the negatively charged sphere and a microparticle free region (dust void) is formed surrounding the obstacle. The far particles are attracted towards the floating obstacle and reflected back when they have arrived at a minimum distance, causing a ring shaped structure around the obstacle. We characterize the shape of this structure over a range of dust flow speeds and obstacle biases. For a supersonic flow of dust fluid around a negatively biased obstacle, a bow shock is formed on the upstream side of the sphere, while the generation of wave structures is observed on the downstream side for a particular range of flow velocities. Reynolds numbers in this case is estimated as $R_e \gtrsim 50$. This wave structure reminds of the beginning of the formation of a Von-K\'arm\'an vortex street. A physical picture for the observed structure based on ion-drag, neutral streaming and electric forces is discussed.
[38]
Title: Particle resuspension from complex surfaces: current knowledge and limitations
Authors: Christophe Henry
Subjects: Fluid Dynamics (physics.flu-dyn); Soft Condensed Matter (cond-mat.soft)
This review explores particle resuspension from surfaces due to fluid flows. The objective of this review is to provide a general framework and terminology for particle resuspension while highlighting the future developments needed to deepen our understanding of these phenomena. For that purpose, the manuscript is organized with respect to three mechanisms identified in particle resuspension, namely: the incipient motion of particles (i.e. how particles are set in motion), their migration on the surface (i.e. rolling or sliding motion) and their re-entrainment in the flow (i.e. their motion in the near-wall region after detachment). Recent measurements and simulations of particle resuspension are used to underline our current understanding of each mechanism for particle resuspension. These selected examples also highlight the limitations in the present knowledge of particle resuspension, while providing insights into future developments that need to be addressed. In particular, the paper addresses the issue of adhesion forces between complex surfaces - where more detailed characterizations of adhesion force distributions are needed - and the issue of particle sliding/rolling motion on the surface - which can lead to particles halting/being trapped in regions with high adhesion forces.
[39]
Title: Fast synthetic CT generation with deep learning for general pelvis MR-only Radiotherapy
Comments: Submitted to Physics in Medicine and Biology
Subjects: Medical Physics (physics.med-ph)
To enable magnetic resonance (MR)-only radiotherapy and facilitate modelling of radiation attenuation in humans, synthetic CT (sCT) images need to be generated. Considering the application of MR-guided radiotherapy, sCT generation should occur within minutes. This work aims at assessing whether an existing deep learning network can rapidly generate sCT images leading to accurate MR-based dose calculations in the entire pelvis. A study was conducted on data of 91 patients with prostate (59), rectal (18) and cervical (14) cancer who underwent external beam radiotherapy acquiring both CT and MRI for patients' simulation. Dixon reconstructed water, fat and in-phase images obtained from a conventional dual gradient-recalled echo sequence were used to generate sCT images. A conditional generative adversarial network (cGAN) was used to generate sCT images. The network was trained in a paired fashion on 2D transverse slices of 32 prostate patients and feed-forward evaluated on the remaining patients (test set). For 30 patients in the test set, dose recalculations of the clinical plan were performed on sCT images. Dose distributions were evaluated comparing voxel-based dose differences, gamma and dose-volume histogram (DVH) analysis. The sCT generation required 5.6s and 21s for a single patient volume on a GPU and CPU, respectively. On average, sCT images resulted in a higher dose to the target of maximum 0.3%. The average gamma pass rates using the 3%,3mm and 2%,2mm criteria were above 97 and 91%, respectively, for all volumes of interests considered. All DVH points from the sCT-based plans differed less than $\pm$2.5% from the corresponding points on CT-based plans. Results suggest that accurate MR-based dose calculation using sCT images generated with a cGAN is feasible for the entire pelvis. The sCT generation was sufficiently fast to be integrated into an MR-guided radiotherapy workflow.
[40]
Title: The Initial Approximations for Achromatic Doublets of the XVIII Century
Authors: Igor Nesterenko
Comments: 16 pages, 8 figures, 4 tables
Subjects: History and Philosophy of Physics (physics.hist-ph)
Analysis of the both type (flint-forward and crown-forward) achromatic doublets was carried out. The investigation revealed possible initial approximations which could be used by opticians at producing of the achromatic doublets in last half of XVIII century. The comparative analysis of approximate versions of achromatic doublets has provided additional explanation to some historical events. One more confirmation that the earliest achromatic doublets were really flint-forward type was found.
[41]
Title: Generalized perspective on chiral measurements without magnetic interactions
Subjects: Atomic Physics (physics.atom-ph); Atomic and Molecular Clusters (physics.atm-clus); Chemical Physics (physics.chem-ph); Optics (physics.optics); Quantum Physics (quant-ph)
We present a unified description of several methods of chiral discrimination based on electric-dipole interactions. It includes photoelectron circular dichroism (PECD), microwave rotational enantio-sensitive spectroscopy, photoexcitation circular dichroism (PXCD) and photoelectron photoexcitation circular dichroism (PXECD). We show that, inspite of the fact that the physics underlying the appearance of a chiral response is very different in all these methods, the chiral observable in all cases has a unique form. It is a polar vector given by the product of (i) the molecular pseudoscalar and (ii) the field pseudovector specified by configurations of the electromagnetic fields interacting with an isotropic ensemble of chiral molecules. The molecular pseudoscalar is a rotationally invariant property, which is composed from different molecule-specific vectors and in the simplest case is a triple product of such vectors. The key property that enables the chiral response is the non coplanarity of the vectors forming such triple product. The key property that enables chiral detection without using chiral electromagnetic fields is the vectorial nature of the enantio-sensitive observable. Our compact and general expression for this observable shows what ultimately determines the efficiency of the chiral signal and if, or when, it can reach 100%. We also discuss the differences between the two phenomena, which rely on the bound states, PXCD and microwave enantio-sensitive spectroscopy, and the two phenomena using the continuum states, PECD and PXECD. Finally, we extend these methods to arbitrary polarizations of electromagnetic fields used to induce and probe the chiral response.
[42]
Title: Seismic Cross-coupling Noise in Torsion Pendulums
Comments: 9 pages, 12 figures
Subjects: Instrumentation and Detectors (physics.ins-det)
Detection of low frequency gravitational waves around 0.1 Hz is one of the important targets for future gravitational wave observation. One of the main sources of the fluctuation is gravitational waves from binary intermediate-mass black hole coalescences which is proposed as one of the formation scenarios of supermassive black holes. By using a torsion pendulum, which can have a resonance frequency of a few millihertz, such perturbation can be measured on the ground since its rotational motion can act as a free mass down to 0.01 Hz. However, sensitivity of a realistic torsion pendulum will suffer from torsional displacement noise introduced from translational ground motion in the main frequency band of interest. Such noise is called seismic cross-coupling noise and there have been little research on it. In this paper, systematic investigation is performed to identify routes of cross-coupling transfer for standard torsion pendulums. Based on the results this paper also proposes reduction schemes of cross-coupling noise, and they were demonstrated experimentally in agreement with theory. This result establishes a basic way to reduce seismic noise in torsion pendulums.
[43]
Title: Templated ligation can create a hypercycle replication network
Comments: 32 pages, 18 figures
Subjects: Biological Physics (physics.bio-ph); Biomolecules (q-bio.BM)
The stability of sequence replication was crucial for the emergence of molecular evolution and early life. Exponential replication with a first-order growth dynamics show inherent instabilities such as the error catastrophe and the dominance by the fastest replicators. This favors less structured and short sequences. The theoretical concept of hypercycles has been proposed to solve these problems. Their higher-order growth kinetics leads to frequency-dependent selection and stabilizes the replication of majority molecules. However, many implementations of hypercycles are unstable or require special sequences with catalytic activity. Here, we demonstrate the spontaneous emergence of higher-order cooperative replication from a network of simple ligation chain reactions (LCR). We performed long-term LCR experiments from a mixture of sequences under molecule degrading conditions with a ligase protein. At the chosen temperature cycling, a network of positive feedback loops arose from both the cooperative ligation of matching sequences and the emerging increase in sequence length. It generated higher-order replication with frequency-dependent selection. The experiments matched a complete simulation using experimentally determined ligation rates and the hypercycle mechanism was also confirmed by abstracted modeling. Since templated ligation is a most basic reaction of oligonucleotides, the described mechanism could have been implemented under microthermal convection on early Earth.
[44]
Title: Level Zero Trigger Processor for the NA62 experiment
Comments: 14 pages
Subjects: Instrumentation and Detectors (physics.ins-det); High Energy Physics - Experiment (hep-ex)
The NA62 experiment is designed to measure the ultra-rare decay $K^+ \rightarrow \pi^+ \nu \bar{\nu}$ branching ratio with a precision of $\sim 10\%$ at the CERN Super Proton Synchrotron (SPS). The L0 Trigger Processor (L0TP) is the lowest level system of the trigger chain. It is hardware implemented using programmable logic. The architecture of the L0TP is completely new for a high energy physics experiment. It is fully digital, based on a standard gigabit Ethernet communication between detectors and L0TP Board. The L0TP Board is a commercial development board, mounting a programmable logic device (FPGA). The primitives generated by sub-detectors are sent asynchronously using the UDP protocol to the L0TP during the entire beam spill period. The L0TP realigns in time the primitives coming from seven different sources and performs a data selection based on the characteristics of the event such as energy, multiplicity and topology of hits in the sub-detectors. It guarantees a maximum latency of 1 ms. The maximum input rate is about 10 MHz for each sub-detector, while the design maximum output trigger rate is 1 MHz. A description of the trigger algorithm is presented here.
[45]
Title: Plasma boosted electron beams for driving Free Electron Lasers
Comments: 5 pages, 2 figures
Subjects: Accelerator Physics (physics.acc-ph)
In this paper, we report results of simulations, in the framework of both EuPRAXIA \cite{Walk2017} and EuPRAXIA@SPARC\_LAB \cite{Ferr2017} projects, aimed at delivering a high brightness electron bunch for driving a Free Electron Laser (FEL) by employing a plasma post acceleration scheme. The boosting plasma wave is driven by a tens of \SI{}{\tera\watt} class laser and doubles the energy of an externally injected beam up to \GeV{1}. The injected bunch is simulated starting from a photoinjector, matched to plasma, boosted and finally matched to an undulator, where its ability to produce FEL radiation is verified to yield $O(\num{e11})$ photons per shot at \nm{2.7}.
[46]
Title: Symmetry and Contextuality
Authors: Hartmann Römer
Comments: 8 pages, contribution to the interdisciplinary workshop "Symmetry and Seriality" of the Freiburg Institute of Advanced Studies (FRIAS), May 2016
Subjects: History and Philosophy of Physics (physics.hist-ph)
The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common ground for this variedness a very general conceptualization of symmetry is proposed: Existence of substitutions, which, in the given context, do not lead to an essential change. This simple definition has multiple consequences: -The context dependence of the notion of symmetry is evident in the humanities but by no means irrelevant yet often neglected in science. The subtle problematic of concept formation and the ontological status of similarities opens up. -In general, the substitutions underlying the concept of symmetry are not really performed but remain in a state of virtuality. Counterfactuality, freedom and creativity come into focus. The detection of previously hidden symmetries may provide deep and surprising insights. -Related to this, due attention is devoted to the aesthetic dimension of symmetry and the breaking of it. -Finally, we point out to what extent life is based on the interplay between order and freedom, between full and broken symmetry.
[47]
Title: CUPID-0: the first array of enriched scintillating bolometers for 0νββdecay investigations
Subjects: Instrumentation and Detectors (physics.ins-det)
The CUPID-0 detector hosted at the Laboratori Nazionali del Gran Sasso, Italy, is the first large array of enriched scintillating cryogenic detectors for the investigation of $^{82}$Se neutrinoless double-beta decay (0$\nu\beta\beta$). CUPID-0 aims at measuring a background index in the region of interest (RoI) for 0$\nu\beta\beta$ at the level of 10$^{-3}$ c/keV/kg/y, the lowest value ever measured using cryogenic detectors. This result can be achieved by a state of the art technology for background suppression and thorough protocols and procedures for detector preparation and construction. In this paper, the different phases of the detector design and construction will be presented, from the material selection (for the absorber production) to the new and innovative detector structure. The successful construction of the detector lead to promising detector performance which are here preliminarily discussed
[48]
Title: High precision wavefront control in Point Spread Function engineering for single emitter localization
Subjects: Optics (physics.optics)
Point Spread Function (PSF) engineering is used in single emitter localization to measure the emitter position in 3D and possibly other parameters such as the emission color or dipole orientation as well. Advanced PSF models such as spline fits to experimental PSFs or the vectorial PSF model can be used in the corresponding localization algorithms in order to model the intricate spot shape and deformations correctly. The complexity of the optical architecture and fit model makes PSF engineering approaches particularly sensitive to optical aberrations. Here, we present a calibration and alignment protocol for fluorescence microscopes equipped with a Spatial Light Modulator with the goal of establishing a wavefront error well below the diffraction limit for optimum application of complex engineered PSFs. We achieve high-precision wavefront control, to a level below 20 m$\lambda$ wavefront aberration over a 30 minute time window after the calibration procedure, using a separate light path for calibrating the pixel-to-pixel variations of the SLM, and alignment of the SLM with respect to the optical axis and Fourier plane within 3 $\mu$m ($x/y$) and 100 $\mu$m ($z$) error. Aberrations are retrieved from a fit of the vectorial PSF model to a bead $z$-stack and compensated with a residual wavefront error comparable to the error of the SLM calibration step. This well-calibrated and corrected setup makes it possible to create complex 3D+$\lambda$' PSFs that fit very well to the vectorial PSF model. Proof-of-principle bead experiments show precisions below 10~nm in $x$, $y$, and $\lambda$, and below 20~nm in $z$ over an axial range of 1 $\mu$m with 2000 signal photons and 12 background photons.
[49]
Title: Geomagnetic storm forecasting service StormFocus: 5 years online
Comments: 22 pages, 8 figures, 3 tables, accepted for publication in Journal of Space Weather and Space Climate
Subjects: Space Physics (physics.space-ph)
Forecasting geomagnetic storms is highly important for many space weather applications. In this study we review performance of the geomagnetic storm forecasting service StormFocus during 2011--2016. The service was implemented in 2011 at SpaceWeather.Ru and predicts the expected strength of geomagnetic storms as measured by $Dst$ index several hours ahead. The forecast is based on L1 solar wind and IMF measurements and is updated every hour. The solar maximum of cycle 24 is weak, so most of the statistics are on rather moderate storms. We verify quality of selection criteria, as well as reliability of real-time input data in comparison with the final values, available in archives. In real-time operation 87% of storms were correctly predicted while the reanalysis running on final OMNI data predicts successfully 97% of storms. Thus the main reasons for prediction errors are discrepancies between real-time and final data (Dst, solar wind and IMF) due to processing errors, specifics of datasets.
[50]
Title: Study of Rydberg blockade in thermal vapor
Subjects: Atomic Physics (physics.atom-ph); Quantum Physics (quant-ph)
We present the experimental demonstration of Rydberg blockade in thermal atomic vapor where the atoms are not necessarily be frozen. We show that not all the interacting atoms but only the atoms with same velocity collectively participate in the blockade process. Using this observation, we formulated a suitable model based on super atom picture to study blockade interaction in thermal vapor. We performed an experiment to measure Rydberg population in rubidium thermal vapor using optical heterodyne detection technique and density dependent suppression of Rydberg population is observed in suitable experimental parameter regime. Further analysis of the experimental data using the model verifies the scaling law for van der Waals interaction strength $(C_{6})$ with principal quantum number of the Rydberg state with $11\%$ error. Our result suggests multi-photon excitation in thermal vapor with suitable laser configuration to probe Rydberg blockade interaction based optical nonlinearity and many body effects.
[51]
Title: Ultrafast perturbation maps as a quantitative tool for testing of multi-port photonic devices
Subjects: Optics (physics.optics); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
Advanced photonic probing techniques are of great importance for the development of non-contact wafer-scale testing of photonic chips. Ultrafast photomodulation has been identified as a powerful new tool capable of remotely mapping photonic devices through a scanning perturbation. Here, we develop photomodulation maps into a quantitative technique through a general and rigorous method based on Lorentz reciprocity that allows the prediction of transmittance perturbation maps for arbitrary linear photonic systems with great accuracy and minimal computational cost. Excellent agreement is obtained between predicted and experimental maps of various optical multimode-interference devices, thereby allowing direct comparison of a device under test with a physical model of an ideal design structure. In addition to constituting a promising route for optical testing in photonics manufacturing, ultrafast perturbation mapping may be used for design optimization of photonic structures with reconfigurable functionalities.
[52]
Title: Nonlinear Breit-Wheeler pair creation with bremsstrahlung $γ$ rays
Comments: 12 pages, 5 figures
Subjects: Plasma Physics (physics.plasm-ph); High Energy Physics - Phenomenology (hep-ph)
Electron-positron pairs are produced through the Breit-Wheeler process when energetic photons traverse electromagnetic fields of sufficient strength. Here we consider a possible experimental geometry for observation of pair creation in the highly nonlinear regime, in which bremsstrahlung of an ultrarelativistic electron beam in a high-$Z$ target is used to produce $\gamma$ rays that collide with a counterpropagating laser pulse. We show how the target thickness may be chosen to optimize the yield of Breit-Wheeler positrons, and verify our analytical predictions with simulations of the cascade in the material and in the laser pulse. The electron beam energy and laser intensity required are well within the capability of today's high-intensity laser facilities.
[53]
Title: Suppression of photo-oxidation of organic chromophores by strong coupling to plasmonic nanoantennas
Comments: 5 figures; includes Supplementary Materials
Subjects: Optics (physics.optics); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Chemical Physics (physics.chem-ph)
Intermixed light-matter quasiparticles - polaritons - possess unique optical properties owned to their compositional nature. These intriguing hybrid states have been extensively studied over the past decades in a wide range of realizations aiming at both basic science and emerging applications. However, recently it has been demonstrated that not only optical, but also material-related properties, such as chemical reactivity and charge transport, may be significantly altered in the strong coupling regime of light-matter interactions. Here, we show that a nanoscale system, comprised of a plasmonic nanoprism strongly coupled to excitons in J-aggregated form of organic chromophores, experiences modified excited state dynamics and therefore modified photo-chemical reactivity. Our experimental results reveal that photobleaching, one of the most fundamental photochemical reactions, can be effectively controlled and suppressed by the degree of plasmon-exciton coupling and detuning. In particular, we observe a 100-fold stabilization of organic dyes for the red-detuned nanoparticles. Our findings contribute to understanding of photochemical properties in the strong coupling regime and may find important implications for the performance and improved stability of optical devices incorporating organic dyes.
[54]
Title: Setting the clock of photoelectron emission through molecular alignment
Subjects: Atomic Physics (physics.atom-ph); Atomic and Molecular Clusters (physics.atm-clus); Chemical Physics (physics.chem-ph)
The interaction of strong laser fields with matter intrinsically provides powerful tools to image transient dynamics with an extremely high spatiotemporal resolution. In strong-field physics, the initial conditions of this interaction are generally considered a weak perturbation. We investigated strong-field ionisation of laser-aligned molecules and showed, for the first time, that the initial momentum acquired by the photoelectron at birth has a dramatic impact on the overall strong-field dynamics: It sets the clock for the emission of electrons with a given kinetic energy. This result represents a new benchmark for the seminal statements of strong-field physics, highlighting the crucial importance of the initial electron-emission conditions. Our findings have strong impact on the interpretation of self-diffraction experiments, where the photoelectron momentum distribution is used to retrieve molecular structures. Furthermore, the resulting encoding of the time-energy relation in molecular-frame photoelectron distributions provides a new way of probing the molecular potential with sub-femtosecond resolution and accessing a deeper understanding of electron tunnelling.
[55]
Title: Ultrafast Preparation and Detection of Ring Currents in Single Atoms
Comments: 19 pages, 6 figures, Nature Physics accepted
Subjects: Atomic Physics (physics.atom-ph)
Quantum particles can penetrate potential barriers by tunneling (1). If that barrier is rotating, the tunneling process is modified (2,3). This is typical for electrons in atoms, molecules or solids exposed to strong circularly polarized laser pulses (4,5). Here we measure how the transmission probability through a rotating tunnel depends on the sign of the magnetic quantum number m of the electron and thus on the initial sense of rotation of its quantum phase. We further show that the electron keeps part of that rotary motion on its way through the tunnel by measuring m-dependent modification of the electron emission pattern. These findings are relevant for attosecond metrology as well as for interpretation of strong field electron emission from atoms and molecules (6-13) and directly demonstrates the creation of ring currents in bound states of ions with attosecond precision. In solids, this could open a way to inducing and controlling ring-current related topological phenomena (14).
[56]
Title: Large Scale Liquid Metal Batteries
Subjects: Applied Physics (physics.app-ph); Fluid Dynamics (physics.flu-dyn)
Liquid metal batteries are possible candidates for large scale energy storage offering a possible breakthrough of intermittent wind and solar energy exploitations. The major concern over their practical implementation is the operation at elevated temperatures and sensitivity to liquid motion. The concept of liquid metal battery bears a close similarity to aluminium electrolytic production cells. The two liquid layer MHD effects can be projected to the three liquid layer self-segregated structure of the batteries. This paper presents numerical models for the three density-stratified electrically conductive liquid layers using 3D and shallow layer approximation accounting for specific MHD effects during periods of battery activity. It is demonstrated that a stable operation of these batteries can be achieved if reusing an infrastructure of existing aluminium electrolysis pot lines. The basic principles of the MHD processes in the cells are illustrated by the numerical example cases.
[57]
Title: Optical tristability and ultrafast Fano switching in nonlinear magneto-plasmonic nanoparticles
Comments: 13 pages, 6 figures
Subjects: Optics (physics.optics); Adaptation and Self-Organizing Systems (nlin.AO)
We consider light scattering by a coated magneto-plasmonic nanoparticle (MPNP) with a Kerr-type nonlinear plasmonic shell and a magneto-optic core. Such structure features two plasmon dipole modes, associated with electronic oscillations on the inner and outer surfaces of the shell. Driven in a nonlinear regime, each mode exhibits a bistable response. Bistability of an inner plasmon leads to switching between this state and a Fano resonance (Fano switching). Once the external light intensity exceeds the critical value, the bistability zones of both eigen modes overlap yielding optical tristability characterized by three stable steady states for a given wavelength and light intensity. We develop a dynamic theory of transitions between nonlinear steady states and estimate the characteristic switching time as short as 0.5 ps. We also show that the magneto-optical (MO) effect allows red- and blue- spectral shift of the Fano profile for right- and left- circular polarizations of the external light, rendering Fano switching sensitive to the light polarization. Specifically, one can reach Fano switching for the right circular polarization while cancelling it for the left circular polarization. Our results point to a novel class of ultrafast Fano switchers tunable by magnetic field for applications in nanophotonics.
[58]
Title: Electrically Conductive Diamond Membrane for Electrochemical Separation Processes
Subjects: Applied Physics (physics.app-ph); Materials Science (cond-mat.mtrl-sci)
Electrochemically switchable selective membranes play an important role in selective filtration processes such as water desalination, industrial waste treatment and hemodialysis. Currently, membranes for these purposes need to be optimized in terms of electrical conductivity and stability against fouling and corrosion. In this paper, we report the fabrication of boron-doped diamond membrane by template diamond growth on quartz fiber filters. The morphology and quality of the diamond coating are characterized via SEM and Raman spectroscopy. The membrane is heavily boron doped (> 1021 cm-3) with > 3 V potential window in aqueous electrolyte. By applying a membrane potential against the electrolyte, redox active species can be removed via flow-through electrolysis. Compared to planar diamond electrodes, the ~250 times surface enlargement provided by such a membrane ensures an effective removal of target chemicals from the input electrolyte. The high stability of diamond enables the membrane to not only work at high membrane bias but also to be self-cleaning via in situ electrochemical oxidation. Therefore, we believe that the diamond membrane presented in this paper will provide a solution to future selective filtration applications especially in extreme conditions.
[59]
Title: The Role of Solvent for Sodium Intercalation into Graphite
Comments: 15 pages, 5 figures
Subjects: Chemical Physics (physics.chem-ph); Materials Science (cond-mat.mtrl-sci)
Na is known to deliver very low energy capacity for sodium intercalation compared to Lithium. In this study, we use quantum mechanics based metadynamics simulations to obtain the free energy landscape for sodium ion intercalation from Dimethyl sulfoxide (DMSO) solvent into graphite. We find that the lowest free energy minima from the metadynamics are associated with sodium solvated by 3 or 4 DMSO. The free energy minima of these states are activated by a free energy of solvation computed to be 0.17 eV, which in turn are the most thermodynamically stable. We observe weak interactions of sodium with graphite sheets during the unbiased and biased molecular dynamics simulations. Our simulations results indicate that solvent plays an important role in stabilizing the sodium intercalation into graphite through shielding of the sodium while modulating the interaction of the solvent with the graphite sheets. In order to facilitate this intercalation, we propose solvents with negatively charged groups and aromatic cores (e.g., cyclic ethers) that could allow a greater rate of anion exchange to increase Na+ mobility.
[60]
Title: A Laplace Transform Method for Molecular Mass Distribution Calculation from Rheometric Data
Authors: Christian Lang
Journal-ref: Journal of Rheology 61, 947 (2017)
Subjects: Fluid Dynamics (physics.flu-dyn); Computational Physics (physics.comp-ph)
Polydisperse linear polymer melts can be microscopically described by the tube model and fractal reptation dynamics, while on the macroscopic side the generalized Maxwell model is capable of correctly displaying most of the rheological behavior. In this paper, a Laplace transform method is derived and different macroscopic starting points for molecular mass distribution calculation are compared to a classical light scattering evaluation. The underlying assumptions comprise the modern understanding on polymer dynamics in entangled systems but can be stated in a mathematically generalized way. The resulting method is very easy to use due to its mathematical structure and it is capable of calculating multimodal molecular mass distributions of linear polymer melts.
[61]
Title: Complexity-weighted doses reduce biological uncertainty in proton radiotherapy planning
Subjects: Medical Physics (physics.med-ph)
Purpose: Variations in proton Relative Biological Effectiveness (RBE) with Linear Energy Transfer (LET) remain one of the largest sources of uncertainty in proton radiotherapy. This work seeks to identify physics-based metrics which can be applied to reduce this biological uncertainty.
Materials and Methods: Three different physical metrics - dose, dose $\times$ LET and a complexity-weighted dose (CWD, Dose $\times$ (1+$\kappa LET_D$) ) were compared with in vitro experimental studies of proton RBE and clinical treatment plans analysed using RBE models. The biological effects of protons in each system were plotted against these metrics to quantify the degree of biological uncertainty introduced by RBE variations in each case.
Results: When the biological effects of protons were plotted against dose alone, significant biological uncertainty was introduced as the LET-dependence of RBE was neglected. Plotting biological effects against dose $\times$ LET significantly over-estimated the impact of LET on cell survival, leading to similar or greater levels of biological uncertainty. CWD, by contrast, significantly reduced biological uncertainties in both experiments and clinical plans. For prostate and medulloblastoma treatment plans, biological uncertainties were reduced from $\pm$ 5% to less than 1%.
Conclusions: While not a replacement for full RBE models, physics-based metrics such as CWD have the potential to significantly reduce the uncertainties in proton planning which result from variations in RBE. These metrics may be used to identify regions in normal tissues which may see unexpectedly high effects due to end-of-range elevations of RBE, or as a tool in optimisation to deliver uniform biological effects.
[62]
Title: Structural diradical character
Subjects: Computational Physics (physics.comp-ph); Chemical Physics (physics.chem-ph)
A reliable first-principles description of singlet diradical character is essential for predicting nonlinear optical and magnetic properties of molecules. Since diradical and closed-shell electronic structures differ in their distribution of single, double, and triple bonds, modeling electronic diradical character requires accurate bond-length patterns. A generally applicable measure for comparing first-principles bond-length patterns with experimental ones is not available at present. For this purpose, we introduce a new measure for structural (rather than electronic) diradical character. It has the advantage of being easily applicable to both computed and experimental molecular structures for arbitrary systems. Within Kohn-Sham density functional theory, we employ this measure for evaluating the suitability of four popular approximate exchange-correlation functionals with different exact-exchange admixtures (BP86, TPSS, B3LYP, TPSSh) for describing experimentally characterized organometallic and organic structures at the diradical / closed-shell border. The two hybrid functionals TPSSh and B3LYP perform best for diradical bond length patterns, with TPSSh being best for the organometallic reference systems and B3LYP for the organic ones. Still, none of the functionals is suitable for correctly describing relative bond lengths across the range of molecules studied, so that none can be recommended for predictive studies of (potential) diradicals without reservation. This underlines the importance of structural diradical character as a test for the further evaluation and development of electronic structure methods.
[63]
Title: Microdosimetry in ion-beam therapy: studying and comparing outcomes from different detectors
Authors: Giulio Magrin
Comments: 23 pages; 7 figures; 2 tables
Subjects: Instrumentation and Detectors (physics.ins-det); Medical Physics (physics.med-ph)
Experimental studies of microdosimetry in therapeutic ion beams have been performed using several detectors. The differences among them lie on the shapes, the site sizes, and the material. Coin-shaped solid-state detectors made of silicon or diamond with thickness varying from 0.3 to 10 microns, as well as proportional counters with spherical and cylindrical sensitive volumes filled with tissue-equivalent gas are the microdosimeters used in therapeutic proton and carbon-ion beams. One goal of microdosimetry in the clinical environment is providing repeatable specification of the radiation quality of the radiation field. A methodology should be developed to provide, independently from the heterogeneous information collected with the different detectors, a detector-independent specification of the radiation quality. Historically the specification of the radiation quality is provided either, in terms of Linear Energy Transfer (LET) or in terms of lineal energy, y. First this study focuses on identifying the correlation between the distributions of LET and the lineal energy spectra as well as the correspondence between their mean values calculated in frequency and in dose. The evaluation is based on the method of LET analysis described by Kellerer making the adaptation to the peculiarities of the therapeutic ion-beam where the pristine irradiation is unidirectional and made of a single type of mono-energetic ions. The second objective of this study is to interpret the spectrum collected by a slab and estimate what the spectrum would be if it was collected by a detector different in shape, material, or size. An example confirms the method starting from the simulated lineal energy spectrum obtained for carbon ions in a slab detector of graphite and converting it to the spectruma that would be obtained in the same radiation field for spherical, cylindrical, and slab detector made of water.
[64]
Title: Segregation in Religion Networks
Comments: 11 pages, 2 figures
Subjects: Physics and Society (physics.soc-ph); Social and Information Networks (cs.SI)
Religious beliefs could facilitate human cooperation [1-6], promote civic engagement [7-10], improve life satisfaction [11-13] and even boom economic development [14-16]. On the other side, some aspects of religion may lead to regional violence, intergroup conflict and moral prejudice against atheists [17-23]. Analogous to the separation of races [24], the religious segregation is a major ingredient resulting in increasing alienation, misunderstanding, cultural conflict and even violence among believers of different faiths [18,19,25]. Thus far, quantitative understanding of religious segregation is rare. Here we analyze a directed social network extracted from weibo.com (the largest directed social network in China, similar to twitter.com), which is consisted of 6875 believers in Christianism, Buddhism, Islam and Taoism. This religion network is highly segregative, with only 1.6% of links connecting individuals in different religions. Comparative analysis shows that the extent of segregation for different religions is much higher than that for different races and slightly higher than that for different political parties. The few cross-religion links play a critical role in maintaining network connectivity, being remarkably more important than links with highest betweennesses [26] or bridgenesses [27]. Further content analysis shows that 46.7% of these cross-religion links are probably related to charitable issues. Our findings provide quantitative insights into religious segregation and valuable clues to encourage cross-religion communications.
[65]
Title: Unified Classical and Quantum Mechanical' Gravity!
Authors: Partha Ghose
Comments: 4 pages, no figures
Subjects: General Physics (physics.gen-ph)
It is shown that a unified description of classical and quantum mechanical' gravity in its linearized form is possible.
[66]
Title: Modulation of kinetic Alfvén waves in an intermediate magnetoplasma
Comments: 7 pages, 3 figures
Subjects: Plasma Physics (physics.plasm-ph)
We study the amplitude modulation of nonlinear kinetic Alfv\'en waves (KAWs) in an intermediate magnetoplasma. Starting from a set of fluid equations coupled to the Maxwell's equations, we derive a coupled set of nonlinear partial differential equations (PDEs) which govern the evolution of KAW envelopes in the plasma. The modulational instability (MI) of such KAW envelopes is then studied by a nonlinear Schr\"odinger (NLS) equation derived from the coupled PDEs. It is shown that the KAWs can evolve into bright and dark envelope solitons, or can undergo damping depending on whether the characteristic ratio $(\alpha)$ of the Alfv\'en to ion-acoustic (IA) speeds remains above or below a critical value. The parameter $\alpha$ is also found to shift the MI domains around the $k_xk_z$ plane, where $k_x~(k_z)$ is the KAW number perpendicular (parallel) to the external magnetic field. The growth rate of MI, as well as the frequency shift and the energy transfer rate, are obtained and analyzed. The results can be useful for understanding the existence and formation of bright and dark envelope solitons, or damping of KAW envelopes in space plasmas, e.g., interplanetary space, solar winds etc.
[67]
Title: Analytical model of a 3D beam dynamics in a wakefield device
Comments: 5 pages, 3 figures
Subjects: Accelerator Physics (physics.acc-ph)
In this paper we suggest an analytical model and derive a simple formula for the beam dynamics in a wakefield structure of arbitrary cross-section. Result could be applied to the estimation of an upper limit of the projected beam size in devices such as the dechirper and the wakefield striker. Suggested formalism could be applied to the case when slices of the beam are distributed along an arbitrary 3D line.
[68]
Title: Measurement of optical constants of TiN and TiN/Ti/TiN multilayer films for microwave kinetic inductance photon-number-resolving detectors
Subjects: Optics (physics.optics); Applied Physics (physics.app-ph)
We deposit thin titanium-nitride (TiN) and TiN/Ti/TiN multilayer films on sapphire substrates and measure the reflectance and transmittance in the wavelength range from 400 nm to 2000 nm using a spectrophotometer. The optical constants (complex refractive indices), including the refractive index n and the extinction coefficient k, have been derived. With the extracted refractive indices, we propose an optical stack structure using low-loss amorphous Si (a-Si) anti-reflective coating and a backside aluminum (Al) reflecting mirror, which can in theory achieve 100% photon absorption at 1550 nm. The proposed optical design shows great promise in enhancing the optical efficiency of TiN-based microwave kinetic inductance photon-number-resolving detectors.
[69]
Title: Exploration of Reduced Scaling Formulation of Equation of Motion Coupled-Cluster Singles and Doubles Based on State-Averaged Pair Natural Orbitals
Comments: 28 pages, 6 figures
Subjects: Chemical Physics (physics.chem-ph)
A reduced-complexity variant of equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) method is formulated in terms of state-averaged excited state pair natural orbitals (PNO) designed to describe manifolds of excited states. State-averaged excited state PNOs for the {\em target} manifold are determined by averaging CIS(D) pair densities over the computational manifold. To assess the performance of PNO-EOM-CCSD approach on extended systems the new massively parallel canonical EOM-CCSD program has been developed in the Massively Parallel Quantum Chemistry program that allows treatment of systems with 50+ atoms using realistic basis sets with 1000+ functions. The use of state-averaged PNOs offers several potential advantages relative to the recently proposed state-specific PNOs: our approach is robust with respect to root flipping and state degeneracies, it is more economical when computing large manifolds of states, and it simplifies evaluation of transition-specific observables such as dipole moments. With the PNO truncation threshold of $10^{-7}$, the errors in excitation energies are on average below 0.02 eV for the first six singlet states of 28 organic molecules included in the standard test set of Thiel and co-workers (J. Chem. Phys. 2008, 128, 134110) with 50-70 state-averaged PNOs per pair.
[70]
Title: Spectral/hp element methods: recent developments, applications, and perspectives
Subjects: Fluid Dynamics (physics.flu-dyn); Computational Physics (physics.comp-ph)
The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate C0-continuous expansions. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.
[71]
Title: Environmental feedback drives cooperation in spatial social dilemmas
Comments: 7 two-column pages, 4 figures, accepted for publication in EPL
Subjects: Physics and Society (physics.soc-ph); Computer Science and Game Theory (cs.GT); Populations and Evolution (q-bio.PE)
Exploiting others is beneficial individually but it could also be detrimental globally. The reverse is also true: a higher cooperation level may change the environment in a way that is beneficial for all competitors. To explore the possible consequence of this feedback we consider a coevolutionary model where the local cooperation level determines the payoff values of the applied prisoner's dilemma game. We observe that the coevolutionary rule provides a significantly higher cooperation level comparing to the traditional setup independently of the topology of the applied interaction graph. Interestingly, this cooperation supporting mechanism offers lonely defectors a high surviving chance for a long period hence the relaxation to the final cooperating state happens logarithmically slow. As a consequence, the extension of the traditional evolutionary game by considering interactions with the environment provides a good opportunity for cooperators, but their reward may arrive with some delay.
### Cross-lists for Tue, 20 Feb 18
[72] arXiv:1802.05719 (cross-list from quant-ph) [pdf, other]
Title: Generic emergence of objectivity of observables in infinite dimensions
Comments: 15 pages, 3 figures
Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); History and Philosophy of Physics (physics.hist-ph)
Quantum Darwinism posits that information becomes objective whenever multiple observers indirectly probe a quantum system by each measuring a fraction of the environment. It was recently shown that objectivity of observables emerges generically from the mathematical structure of quantum mechanics, whenever the system of interest has finite dimensions and the number of environment fragments is large [Brand\~ao et. al. (2015), Nat. Commun. 6, 7908]. Despite the importance of this result, it necessarily excludes many practical systems of interest that live in infinite dimensions, including harmonic oscillators. Extending the study of Quantum Darwinism to infinite dimensions is a nontrivial task: we tackle it here by introducing a modified diamond norm, suitable to quantify the distinguishability of channels in infinite dimensions. We prove two theorems that bound the emergence of objectivity, first for finite energy systems, and then for systems that can only be prepared in states with an exponential energy cut-off. We show that the latter class of states includes any bounded-energy subset of single-mode Gaussian states.
[73] arXiv:1802.06090 (cross-list from q-bio.BM) [pdf]
Title: Unveiled electric profiles within hydrogen bonds suggest DNA base pairs with similar bond strengths
Comments: Full version is available on: this http URL
Journal-ref: PLoS ONE 12(10): e0185638 (2017)
Subjects: Biomolecules (q-bio.BM); Biological Physics (physics.bio-ph)
Electrical forces are the background of all the interactions occurring in biochemical systems. From here and by using a combination of ab-initio and ad-hoc models, we introduce the first description of electric field profiles with intrabond resolution to support a characterization of single bond forces attending to its electrical origin. This fundamental issue has eluded a physical description so far. Our method is applied to describe hydrogen bonds (HB) in DNA base pairs. Numerical results reveal that base pairs in DNA could be equivalent considering HB strength contributions, which challenges previous interpretations of thermodynamic properties of DNA based on the assumption that Adenine/Thymine pairs are weaker than Guanine/Cytosine pairs due to the sole difference in the number of HB. Thus, our methodology provides solid foundations to support the development of extended models intended to go deeper into the molecular mechanisms of DNA functioning.
[74] arXiv:1802.06100 (cross-list from stat.AP) [pdf, other]
Title: Extreme Value Analysis of Solar Flare Events
Comments: 17 pages, 5 figures
Subjects: Applications (stat.AP); Solar and Stellar Astrophysics (astro-ph.SR); Data Analysis, Statistics and Probability (physics.data-an); Space Physics (physics.space-ph)
Space weather events such as solar flares can be harmful for life and infrastructure on earth or in near-earth orbit. In this paper we employ extreme value theory (EVT) to model extreme solar flare events; EVT offers the appropriate tools for the study and estimation of probabilities for extrapolation to ranges outside of those that have already been observed. In the past such phenomena have been modelled as following a power law which may gives poor estimates of such events due to overestimation. The data used in the study were X-ray fluxes from NOAA/GOES and the expected return levels for Carrington or Halloween like events were calculated with the outcome that the existing data predict similar events happening in 110 and 38 years respectively.
[75] arXiv:1802.06110 (cross-list from quant-ph) [pdf]
Title: Light, the universe, and everything -- 12 Herculean tasks for quantum cowboys and black diamond skiers
Comments: A review of the leading topics in quantum optics and related areas. Accepted for publication in J. Modern Optics (42 figures, 74 pages)
Subjects: Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other); Optics (physics.optics)
The Winter Colloquium on the Physics of Quantum Electronics (PQE) has been a seminal force in quantum optics and related areas since 1971. It is rather mindboggling to recognize how the concepts presented at these conferences have transformed scientific understanding and human society. In January, 2017, the participants of PQE were asked to consider the equally important prospects for the future, and to formulate a set of questions representing some of the greatest aspirations in this broad field. The result is this multi-authored paper, in which many of the world's leading experts address the following fundamental questions: (1) What is the future of gravitational wave astronomy? (2) Are there new quantum phases of matter away from equilibrium that can be found and exploited - such as the time crystal? (3) Quantum theory in uncharted territory: What can we learn? (4) What are the ultimate limits for laser photon energies? (5) What are the ultimate limits to temporal, spatial, and optical resolution? (6) What novel roles will atoms play in technology? (7) What applications lie ahead for nitrogen-vacancy centers in diamond? (8) What is the future of quantum coherence, squeezing, and entanglement for enhanced superresolution and sensing? (9) How can we solve (some of) humanity's biggest problems through new quantum technologies? (10) What new understanding of materials and biological molecules will result from their dynamical characterization with free electron lasers? (11) What new technologies and fundamental discoveries might quantum optics achieve by the end of this century? (12) What novel topological structures can be created and employed in quantum optics?
[76] arXiv:1802.06138 (cross-list from cs.SI) [pdf, other]
Title: Discriminative Modeling of Social Influence for Prediction and Explanation in Event Cascades
Subjects: Social and Information Networks (cs.SI); Learning (cs.LG); Physics and Society (physics.soc-ph)
The global dynamics of event cascades are often governed by the local dynamics of peer influence. However, detecting social influence from observational data is challenging, due to confounds like homophily and practical issues like missing data. In this work, we propose a novel discriminative method to detect influence from observational data. The core of the approach is to train a ranking algorithm to predict the source of the next event in a cascade, and compare its out-of-sample accuracy against a competitive baseline which lacks access to features corresponding to social influence. Using synthetically generated data, we provide empirical evidence that this method correctly identifies influence in the presence of confounds, and is robust to both missing data and misspecification --- unlike popular alternatives. We also apply the method to two real-world datasets: (1) cascades of co-sponsorship of legislation in the U.S. House of Representatives, on a social network of shared campaign donors; (2) rumors about the Higgs boson discovery, on a follower network of $10^5$ Twitter accounts. Our model identifies the role of peer influence in these scenarios, and uses it to make more accurate predictions about the future trajectory of cascades.
[77] arXiv:1802.06160 (cross-list from cond-mat.supr-con) [pdf]
Title: Effect of $α$-particle irradiation on a NdFeAs(O,F) thin film
Comments: 12 pages, 9 figures
Journal-ref: Supercond. Sci. Technol. 31, 034002 (2018)
Subjects: Superconductivity (cond-mat.supr-con); Materials Science (cond-mat.mtrl-sci); Applied Physics (physics.app-ph)
The effect of $\alpha$-particle irradiation on a NdFeAs(O,F) thin film has been investigated to determine how the introduction of defects affects basic superconducting properties, including the critical temperature $T_c$ and the upper critical field $H_{c2}$, and properties more of interest for applications, like the critical current density $J_c$ and the related pinning landscape. The irradiation-induced suppression of the film $T_c$ is significantly smaller than on a similarly damaged single crystal. Moreover $H_{c2}$ behaves differently, depending on the field orientation: for H//c the $H_{c2}$ slope monotonically increases with increasing disorder, whereas for H//ab it remains constant at low dose and it increases only when the sample is highly disordered. This suggests that a much higher damage level is necessary to drive the NdFeAs(O,F) thin film into the dirty limit. Despite the increase in the low temperature $H_{c2}$, the effects on the $J_c$(H//c) performances are moderate in the measured temperature and field ranges, with a shifting of the pinning force maximum from 4.5 T to 6 T after an irradiation of $2\times10^{15} cm^{-2}$. On the contrary, $J_c$(H//ab) is always suppressed. The analysis demonstrates that irradiation does introduce point defects acting as pinning centres proportionally to the irradiation fluence but also suppresses the effectiveness of c-axis correlated pinning present in the pristine sample. We estimate that significant performance improvements may be possible at high field or at temperatures below 10 K. The suppression of the $J_c$(H//ab) performance is not related to a decrease of the $J_c$ anisotropy as found in other superconductors. Instead it is due to the presence of point defects that decrease the efficiency of the ab-plane intrinsic pinning typical of materials with a layered structure.
[78] arXiv:1802.06219 (cross-list from cs.SI) [pdf]
Title: Network Centrality Analysis of Tehran Urban and Suburban Railway System
Comments: 8 pages, 3 figures and 1 table
Subjects: Social and Information Networks (cs.SI); Physics and Society (physics.soc-ph)
Nowadays, Tehran Urban and Suburban Railway System (TUSRS) is going to be completed by eight lines and 149 stations. This complex transportation system contains 168 links between each station pairs and 20 cross-section and Y-branch stations among all eight lines. In this study, we considered TUSRS as a complex network and undertook several analyzes based on graph theory. Examining e.g. centrality measures, we identified central stations within TUSRS. This analysis could be useful for redistributing strategy of the overcrowded stations and improving the organization of maintaining system. These findings are also promising for better designing the systems of tomorrow in other metropolitan areas in Iran.
[79] arXiv:1802.06230 (cross-list from nlin.PS) [pdf, ps, other]
Title: Dark-bright soliton pairs: bifurcations and collisions
Comments: 9 pages, 6 figures
Subjects: Pattern Formation and Solitons (nlin.PS); Quantum Gases (cond-mat.quant-gas); Atomic Physics (physics.atom-ph); Quantum Physics (quant-ph)
The statics, stability and dynamical properties of dark-bright soliton pairs are investigated motivated by applications in a homogeneous system of two-component repulsively interacting Bose-Einstein condensate. One of the intra-species interaction coefficients is used as the relevant parameter controlling the deviation from the integrable Manakov limit. Two different families of stationary states are identified consisting of dark-bright solitons that are either anti-symmetric (out-of-phase) or asymmetric (mass imbalanced) with respect to their bright soliton. Both of the above dark-bright configurations coexist at the integrable limit of equal intra- and inter-species repulsions and are degenerate in that limit. However, they are found to bifurcate from it in a transcritical bifurcation. The latter interchanges the stability properties of the bound dark-bright pairs rendering the anti-symmetric states unstable and the asymmetric ones stable past the associated critical point (and vice versa before it). Finally, on the dynamical side, it is found that large kinetic energies and thus rapid soliton collisions are essentially unaffected by the intra-species variation, while cases involving near equilibrium states or breathing dynamics are significantly modified under such a variation.
[80] arXiv:1802.06265 (cross-list from cs.SI) [pdf, other]
Title: Statistical Link Label Modeling for Sign Prediction: Smoothing Sparsity by Joining Local and Global Information
Subjects: Social and Information Networks (cs.SI); Physics and Society (physics.soc-ph)
One of the major issues in signed networks is to use network structure to predict the missing sign of an edge. In this paper, we introduce a novel probabilistic approach for the sign prediction problem. The main characteristic of the proposed models is their ability to adapt to the sparsity level of an input network. The sparsity of networks is one of the major reasons for the poor performance of many link prediction algorithms, in general, and sign prediction algorithms, in particular. Building a model that has an ability to adapt to the sparsity of the data has not yet been considered in the previous related works. We suggest that there exists a dilemma between local and global structures and attempt to build sparsity adaptive models by resolving this dilemma. To this end, we propose probabilistic prediction models based on local and global structures and integrate them based on the concept of smoothing. The model relies more on the global structures when the sparsity increases, whereas it gives more weights to the information obtained from local structures for low levels of the sparsity. The proposed model is assessed on three real-world signed networks, and the experiments reveal its consistent superiority over the state of the art methods. As compared to the previous methods, the proposed model not only better handles the sparsity problem, but also has lower computational complexity and can be updated using real-time data streams.
[81] arXiv:1802.06287 (cross-list from stat.ML) [pdf, other]
Title: Unsupervised vehicle recognition using incremental reseeding of acoustic signatures
Subjects: Machine Learning (stat.ML); Learning (cs.LG); Data Analysis, Statistics and Probability (physics.data-an)
Vehicle recognition and classification have broad applications, ranging from traffic flow management to military target identification. We demonstrate an unsupervised method for automated identification of moving vehicles from roadside audio sensors. Using a short-time Fourier transform to decompose audio signals, we treat the frequency signature in each time window as an individual data point. We then use a spectral embedding for dimensionality reduction. Based on the leading eigenvectors, we relate the performance of an incremental reseeding algorithm to that of spectral clustering. We find that incremental reseeding accurately identifies individual vehicles using their acoustic signatures.
[82] arXiv:1802.06374 (cross-list from quant-ph) [pdf]
Title: Quantum metamaterials: entanglement of spin and orbital angular momentum of a single photon
Subjects: Quantum Physics (quant-ph); Optics (physics.optics)
Metamaterials have been a major research area for more than two decades now, involving artificial structures with predesigned electromagnetic properties constructed from deep subwavelength building blocks. They have been used to demonstrate a wealth of fascinating phenomena ranging from negative refractive index and epsilon-near-zero to cloaking, emulations of general relativity effects, and super-resolution imaging, to name a few. In the past few years, metamaterials have been suggested as a new platform for quantum optics, and several pioneering experiments have already been carried out with single photons. Here, we employ a dielectric metasurface to generate entanglement between spin and orbital angular momentum of single photons. We demonstrate experimentally the generation of the four Bell states by utilizing the geometric phase arising from the photonic spin-orbit interaction. These are the first experiments with entangled states with metasurfaces, and as such they are paving the way to the new area of quantum metamaterials.
[83] arXiv:1802.06422 (cross-list from math.DS) [pdf, ps, other]
Title: Stochastic stability of invariant measures: The 2D Euler equation
Comments: 12 pages Latex
Subjects: Dynamical Systems (math.DS); Fluid Dynamics (physics.flu-dyn)
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the inspiration for this work. As an example the 2D Euler equation is studied. Among other results this study suggests that the coherent structures observed in 2D hydrodynamics are associated to configurations that maximize stochastically stable measures uniquely determined by the boundary conditions in mode space.
[84] arXiv:1802.06437 (cross-list from cs.SI) [pdf, other]
Title: What We Read, What We Search: Media Attention and Public Attention Among 193 Countries
Comments: Will be presented in the Web Conference 2018 (WWW2018)
Subjects: Social and Information Networks (cs.SI); Physics and Society (physics.soc-ph)
We investigate the alignment of international attention of news media organizations within 193 countries with the expressed international interests of the public within those same countries from March 7, 2016 to April 14, 2017. We collect fourteen months of longitudinal data of online news from Unfiltered News and web search volume data from Google Trends and build a multiplex network of media attention and public attention in order to study its structural and dynamic properties. Structurally, the media attention and the public attention are both similar and different depending on the resolution of the analysis. For example, we find that 63.2% of the country-specific media and the public pay attention to different countries, but local attention flow patterns, which are measured by network motifs, are very similar. We also show that there are strong regional similarities with both media and public attention that is only disrupted by significantly major worldwide incidents (e.g., Brexit). Using Granger causality, we show that there are a substantial number of countries where media attention and public attention are dissimilar by topical interest. Our findings show that the media and public attention toward specific countries are often at odds, indicating that the public within these countries may be ignoring their country-specific news outlets and seeking other online sources to address their media needs and desires.
[85] arXiv:1802.06469 (cross-list from cond-mat.soft) [pdf, ps, other]
Title: Active fluids at circular boundaries: Swim pressure and anomalous droplet ripening
Comments: 15 pages, 7 figures
Subjects: Soft Condensed Matter (cond-mat.soft); Statistical Mechanics (cond-mat.stat-mech); Biological Physics (physics.bio-ph); Chemical Physics (physics.chem-ph)
We investigate the swim pressure exerted by non-chiral and chiral active particles on convex or concave circular boundaries. Active particles are modeled as non-interacting and non-aligning self-propelled Brownian particles. The convex and concave circular boundaries are used as models representing a fixed inclusion immersed in an active bath and a cavity (or container) enclosing the active particles, respectively. We first present a detailed analysis of the role of convex versus concave boundary curvature and of the chirality of active particles on their spatial distribution, chirality-induced currents, and the swim pressure they exert on the bounding surfaces. The results will then be used to predict the mechanical equilibria of suspended fluid enclosures (generically referred to as 'droplets') in a bulk with active particles being present either inside the bulk fluid or within the suspended droplets. We show that, while droplets containing active particles and suspended in a normal bulk behave in accordance with standard capillary paradigms, those containing a normal fluid exhibit anomalous behaviors when suspended in an active bulk. In the latter case, the excess swim pressure results in non-monotonic dependence of the inside droplet pressure on the droplet radius. As a result, we find a regime of anomalous capillarity for a single droplet, where the inside droplet pressure increases upon increasing the droplet size. In the case of two interconnected droplets, we show that mechanical equilibrium can occur also when they have different sizes. We further identify a regime of anomalous ripening, where two unequal-sized droplets can reach a final state of equal sizes upon interconnection, in stark contrast with the standard Ostwald ripening phenomenon, implying shrinkage of the smaller droplet in favor of the larger one.
[86] arXiv:1802.06505 (cross-list from cs.SI) [pdf, other]
Title: What Do Your Friends Think? Efficient Polling Methods for Networks Using Friendship Paradox
Subjects: Social and Information Networks (cs.SI); Physics and Society (physics.soc-ph)
This paper deals with randomized polling of a social network. In the case of forecasting the outcome of an election between two candidates A and B, classical intent polling asks randomly sampled individuals: who will you vote for? Expectation polling asks: who do you think will win? In this paper, we propose a novel neighborhood expectation polling (NEP) strategy that asks randomly sampled individuals: what is your estimate of the fraction of votes for A? Therefore, in NEP, sampled individuals will naturally look at their neighbors (defined by the underlying social network graph) when answering this question. Hence, the mean squared error (MSE) of NEP methods rely on selecting the optimal set of samples from the network. To this end, we propose three NEP algorithms for the following cases: (i) the social network graph is not known but, random walks (sequential exploration) can be performed on the graph (ii) the social network graph is unknown. For case (i) and (ii), two algorithms based on a graph theoretic consequence called friendship paradox are proposed. Theoretical results on the dependence of the MSE of the algorithms on the properties of the network are established. Numerical results on real and synthetic data sets are provided to illustrate the performance of the algorithms.
[87] arXiv:1802.06534 (cross-list from cond-mat.soft) [pdf, ps, other]
Title: A Simple and Effective Solution to the Constrained QM/MM Simulations
Subjects: Soft Condensed Matter (cond-mat.soft); Chemical Physics (physics.chem-ph)
It is a promising extension of the quantum mechanical/molecular mechanical (QM/MM) approach to incorporate the solvent molecules surrounding the QM solute into the QM region to ensure the adequate description of the electronic polarization of the solute. However, the solvent molecules in the QM region inevitably diffuse into the MM bulk during the QM/MM simulation. In this article we developed a simple and efficient method, referred to as boundary constraint with correction (BCC), to prevent the diffusion of the solvent water molecules by means of a constraint po- tential. The point of the BCC method is to compensate the error in a statistical property due to the bias potential by adding a correction term obtained through a set of QM/MM simulations. The BCC method is designed so that the effect of the bias potential completely vanishes when the QM solvent is identical with the MM solvent. Furthermore, the desirable conditions, that is, the continuities of energy and force and the conservations of energy and momentum, are fulfilled in principle. We applied the QM/MM-BCC method to a hydronium ion in aqueous solution to construct the radial distribution function(RDF) of the solvent around the solute. It was demonstrated that the correction term fairly compensated the error and led the RDF in good agreement with the result given by an ab initio molecular dynamics simulation.
[88] arXiv:1802.06569 (cross-list from quant-ph) [pdf, other]
Title: Non-Hermiticity and conservation of orthogonal relation in dielectric microcavity
Comments: 11 pages, 5 figures
Subjects: Quantum Physics (quant-ph); Optics (physics.optics)
Non-Hermitian properties of open quantum systems and their applications have attracted much attention in recent years. While most of the studies focus on the characteristic nature of non-Hermitian systems, one important point has been overlooked: A non-Hermitian system can be a subsystem of a Hermitian system as one can clearly see in Feshbach projective operator (FPO) formalism. In this case, the orthogonality of the eigenvectors of the total (Hermitian) system must be sustained, despite the eigenvectors of the subsystem (non-Hermitian) satisfy the bi-orthogonal condition. Therefore, one can predict that there must exist some remarkable processes that relate the non-Hermitian subsystem and the rest part, and ultimately preserve the Hermiticity of the total system. In this paper, we study such processes in open elliptical microcavities. The inner part of the cavity is a non-Hermitian system, and the outer part is the coupled bath in FPO formalism. We investigate the correlation between the inner- and the outer-part behaviors associated with the avoided resonance crossings (ARCs), and analyze the results in terms of the Lamb shift. The ARC structures we examined depend on a trade-off between the relative difference of self-energies (simply known as Lamb shifts in atomic physics) and collective Lamb shifts. While the collective Lamb shift is maximized in the region of the center of ARC, but the relative difference of self-energies is minimized, and this naturally induce a crossing of imaginary part of eigenvalues. These results come from the conservation of the orthogonality in the total Hermitian quantum system.
[89] arXiv:1802.06580 (cross-list from cond-mat.dis-nn) [pdf, other]
Title: Oscillation death induced by time-varying network
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Pattern Formation and Solitons (nlin.PS); Physics and Society (physics.soc-ph); Neurons and Cognition (q-bio.NC)
The synchronous dynamics of an array of excitable oscillators, coupled via a generic graph, is studied. Non homogeneous perturbations can grow and destroy synchrony, via a self-consistent instability which is solely instigated by the intrinsic network dynamics. By acting on the characteristic time-scale of the network modulation, one can make the examined system to behave as its (partially) averaged analog. This result if formally obtained by proving an extended version of the averaging theorem, which allows for partial averages to be carried out. Oscillation death are reported to follow the onset of the network driven instability.
[90] arXiv:1802.06693 (cross-list from cond-mat.quant-gas) [pdf, ps, other]
Title: Quench Dynamics of Finite Bosonic Ensembles in Optical Lattices with Spatially Modulated Interactions
Comments: 14 pages, 7 figures
Subjects: Quantum Gases (cond-mat.quant-gas); Atomic Physics (physics.atom-ph); Quantum Physics (quant-ph)
The nonequilibrium quantum dynamics of few boson ensembles which experience a spatially modulated interaction strength and are confined in finite optical lattices is investigated. Performing quenches either on the wavevector or the phase of the interaction profile an enhanced imbalance of the interatomic repulsion between distinct spatial regions of the lattice is induced. Following both quench protocols triggers various tunneling channels and a rich excitation dynamics consisting of a breathing and a cradle mode. All modes are shown to be amplified for increasing inhomogeneity amplitude of the interaction strength. Especially the phase quench induces a directional transport enabling us to discern energetically, otherwise, degenerate tunneling pathways. Moreover, a periodic population transfer between distinct momenta for quenches of increasing wavevector is observed, while a directed occupation of higher momenta can be achieved following a phase quench. Finally, during the evolution regions of partial coherence are revealed between the predominantly occupied wells.
[91] arXiv:1802.06727 (cross-list from astro-ph.IM) [pdf, other]
Title: Thorough experimental testing of Multimode interference couplers and expected nulls thereof; for exoplanet detection
Comments: Only a first draft. Will upload later versions as we go
Subjects: Instrumentation and Methods for Astrophysics (astro-ph.IM); Astrophysics of Galaxies (astro-ph.GA); Optics (physics.optics)
In exoplanet interferometry a null of 40~dB is a large step in achieving the ability to directly image an Earth-like planet that is in the habitable zone around a star like our own. Based on the standard procedure at the Australian National University we have created a nulling interferometer that has achieved a 25~dB null in the astronomical L~band under laboratory conditions. The device has been constructed on a 2-dimensional platform of chalcogenide glass: a three layered structure of $Ge_{11.5}As_{24}S_{64.5}$ undercladding, 2~\si{\um} of $Ge_{11.5}As_{24}Se_{64.5}$ core and an angled deposition of $Ge_{11.5}As_{24}S_{64.5}$ as a complete overcladding. Matching simulation from Rsoft and individual results of the MMIs the expected null should produce a null of 40~dB over a bandwidth of 400~nm but due to limitations in mask design and light contamination only a 25~dB extinction can be reliably achieved.
[92] arXiv:1802.06732 (cross-list from math.OC) [pdf, other]
Title: Congestion analysis of unsignalized intersections: The impact of impatience and Markov platooning
Comments: An earlier, related paper which also contains some of the results (in more detail) published in the present paper, appeared in the proceedings of the 8th International Conference on Communication Systems and Networks (COMSNETS), 5-10 Jan. 2016. This conference paper can also be found on arXiv and in IEEE Xplore: this http URL
Subjects: Optimization and Control (math.OC); Probability (math.PR); Physics and Society (physics.soc-ph)
This paper considers an unsignalized intersection used by two traffic streams. A stream of cars is using a primary road, and has priority over the other stream. Cars belonging to the latter stream cross the primary road if the gaps between two subsequent cars on the primary road are larger than their critical headways. A question that naturally arises relates to the capacity of the secondary road: given the arrival pattern of cars on the primary road, what is the maximum arrival rate of low-priority cars that can be sustained? This paper addresses this issue by considering a compact model that sheds light on the dynamics of the considered unsignalized intersection. The model, which is of a queueing-theoretic nature, reveals interesting insights into the impact of the user behavior on stability.
The contributions of this paper are threefold. First, we obtain new results for the aforementioned model that includes driver impatience. Secondly, we reveal some surprising aspects that have remained unobserved in the existing literature so far, many of which are caused by the fact that the capacity of the minor road cannot be expressed in terms of the \emph{mean} gap size; instead more detailed characteristics of the critical headway distribution play a crucial role. The third contribution is the introduction of a new form of bunching on the main road, called Markov platooning. The tractability of this model allows us to study the impact of various platoon formations on the main road on the capacity of the minor road.
### Replacements for Tue, 20 Feb 18
[93] arXiv:1403.6562 (replaced) [pdf, ps, other]
Title: Do the Navier-Stokes equations embody all physics in a flow of Newtonian fluids?
Comments: A conference paper of American Physical Society 67th Annual DFD Meeting
Subjects: Fluid Dynamics (physics.flu-dyn)
[94] arXiv:1503.05577 (replaced) [pdf, ps, other]
Title: On the Equivalence Principle and Electrodynamics of Moving Bodies
Comments: 18 pages
Journal-ref: EPL (Europhysics Letters), Volume 120, Number 4, 2018
Subjects: General Physics (physics.gen-ph)
[95] arXiv:1511.01238 (replaced) [pdf]
Title: Fast and slow thinking -- of networks: The complementary 'elite' and 'wisdom of crowds' of amino acid, neuronal and social networks
Authors: Peter Csermely
Comments: This a preliminary version of the paper below, please find its illustrative videos here: this http URL
Journal-ref: BioEssays 40, 1700150 (2018)
Subjects: Molecular Networks (q-bio.MN); Disordered Systems and Neural Networks (cond-mat.dis-nn); Social and Information Networks (cs.SI); Adaptation and Self-Organizing Systems (nlin.AO); Biological Physics (physics.bio-ph)
[96] arXiv:1607.01380 (replaced) [pdf, ps, other]
Title: Hydrodynamic and Magnetohydrodynamic Extensions on the Parker's Supersonic Stellar Wind Model
Authors: B. K. Shivamoggi
Subjects: Plasma Physics (physics.plasm-ph); Solar and Stellar Astrophysics (astro-ph.SR)
[97] arXiv:1609.09331 (replaced) [pdf, other]
Title: Consistency of detrended fluctuation analysis
Authors: Ola Løvsletten
Journal-ref: Phys. Rev. E 96, 012141 (2017)
Subjects: Statistics Theory (math.ST); Data Analysis, Statistics and Probability (physics.data-an)
[98] arXiv:1611.03880 (replaced) [pdf, other]
Title: Statistical properties for directional alignment and chasing of players in football games
Comments: 16pages, 12 figures, 3 tables
Journal-ref: Europhysics Letters, Vol. 116, 68001 (2016)
Subjects: Physics and Society (physics.soc-ph)
[99] arXiv:1612.09180 (replaced) [pdf, other]
Title: A comparison of Hake's g and Cohen's d for analyzing gains on concept inventories
Subjects: Physics Education (physics.ed-ph)
[100] arXiv:1703.02893 (replaced) [pdf, ps, other]
Title: Analytic Expressions for Exponentials of Specific Hamiltonian Matrices
Authors: C. Baumgarten
Comments: Some typos corrected
Subjects: General Physics (physics.gen-ph)
[101] arXiv:1703.09430 (replaced) [pdf, other]
Title: Polling bias and undecided voter allocations: US Presidential elections, 2004 - 2016
Comments: 31 pages, 9 figures, 4 tables
Subjects: Applications (stat.AP); Social and Information Networks (cs.SI); Physics and Society (physics.soc-ph)
[102] arXiv:1703.10767 (replaced) [pdf, other]
Title: Weight of fitness deviation governs strict physical chaos in replicator dynamics
Comments: 13 pages, 3 figures; accepted in Chaos
Subjects: Chaotic Dynamics (nlin.CD); Biological Physics (physics.bio-ph)
[103] arXiv:1705.09136 (replaced) [pdf, other]
Title: Coherent single-atom superradiance
Comments: 18 pages, 9 figures
Journal-ref: Science 359, 662-666 (2018)
Subjects: Quantum Physics (quant-ph); Atomic Physics (physics.atom-ph); Optics (physics.optics)
[104] arXiv:1705.09869 (replaced) [pdf, other]
Title: Dimensionality reduction for acoustic vehicle classification with spectral embedding
Comments: Proceedings of the 15th IEEE International Conference on Networking, Sensing and Control (2018)
Subjects: Machine Learning (stat.ML); Learning (cs.LG); Data Analysis, Statistics and Probability (physics.data-an)
[105] arXiv:1706.10287 (replaced) [pdf, other]
Title: Generation of turbulence through frontogenesis in sheared stratified flows
Comments: 19 pages, 15 figures, several simulations added in this new version
Subjects: Fluid Dynamics (physics.flu-dyn); Atmospheric and Oceanic Physics (physics.ao-ph)
[106] arXiv:1707.07160 (replaced) [pdf, other]
Title: Majorana states for subluminal structured photons
Authors: Fabrizio Tamburini (1,2), Bo Thidé (3), Ignazio Licata (4,5,6), Frédéric Bouchard (7), Ebrahim Karimi (7,8) ((1) Zentrum für Kunst und Medientechnologie, Karlsruhe, Germany, (2) MSC-BW, Stuttgart, Stuttgart, Germany, (3) Swedish Institute of Space Physics, Ångström Laboratory, Uppsala, Sweden, (4) Institute for Scientific Methodology (ISEM) Palermo Italy, (5) School of Advanced International Studies on Theoretical and Nonlinear Methodologies of Physics, Bari, Italy, (6) International Institute for Applicable Mathematics and Information Sciences (IIAMIS), B.M. Birla Science Centre, Adarsh Nagar, Hyderabad, India, (7) Department of Physics, University of Ottawa, Ottawa, Ontario, Canada, (8) Department of Physics, Institute for Advanced Studies in Basic Sciences, Zanjan, Iran)
Comments: 6 pages, 1 figure
Subjects: Optics (physics.optics)
[107] arXiv:1707.09478 (replaced) [pdf, other]
Title: Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations
Comments: Preprint 29 pages, 10 figures (26 small figures); v1 submitted to the AIAA Journal on May 3, 2017; v2 submitted on September 17, 2017. v2 changes: (a) addition of flowcharts in Figures 4 and 5 to summarize the tools used; (b) edits to clarify and reorganize certain parts; v3 submitted on February 7, 2018. v3 changes: (a) title; (b) minor edits
Subjects: Data Analysis, Statistics and Probability (physics.data-an); Computational Physics (physics.comp-ph); Fluid Dynamics (physics.flu-dyn)
[108] arXiv:1708.00110 (replaced) [pdf, other]
Title: Naturally occurring $^{32}$Si and low-background silicon dark matter detectors
Comments: 16 pages, 4 figures
Journal-ref: Astroparticle Physics 99 (2018) 9-20
Subjects: Instrumentation and Detectors (physics.ins-det); High Energy Physics - Experiment (hep-ex)
[109] arXiv:1708.09444 (replaced) [pdf, other]
Title: A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric discharges
Comments: 21 pages, 4 figures, a movie and a sample code in python. A new Appendix has been added
Subjects: Plasma Physics (physics.plasm-ph); Computational Physics (physics.comp-ph)
[110] arXiv:1710.02784 (replaced) [pdf, other]
Title: An Aerodynamic Analysis of Recent FIFA World Cup Balls
Comments: 18 pages, 11 figures, 2 tables
Subjects: Popular Physics (physics.pop-ph)
[111] arXiv:1710.04538 (replaced) [pdf, ps, other]
Title: Causality Testing: A Data Compression Framework
Comments: 6 pages, 4 figures in main article and 7 pages, 8 figures in supplemental material
Subjects: Data Analysis, Statistics and Probability (physics.data-an); Biological Physics (physics.bio-ph); Neurons and Cognition (q-bio.NC)
[112] arXiv:1710.07311 (replaced) [pdf, other]
Title: Limitations in Predicting the Space Radiation Health Risk for Exploration Astronauts
Comments: Accepted for publication by Nature Microgravity (2018)
Subjects: Medical Physics (physics.med-ph); Biological Physics (physics.bio-ph); Space Physics (physics.space-ph)
[113] arXiv:1710.08790 (replaced) [pdf, other]
Title: Molecular Origin of Contact Line Friction in Dynamic Wetting
Authors: Petter Johansson (1), Berk Hess (1) ((1) KTH Royal Institute of Technology, Stockholm, Sweden)
Subjects: Fluid Dynamics (physics.flu-dyn)
[114] arXiv:1711.04028 (replaced) [pdf, other]
Title: The vector field of a rolling rigid body
Comments: Added semi-symplectic reduction. Will be published as e-print only. 8 pages
Subjects: Mathematical Physics (math-ph); Dynamical Systems (math.DS); Classical Physics (physics.class-ph)
[115] arXiv:1711.06002 (replaced) [pdf, other]
Title: Bayesian uncertainty quantification in linear models for diffusion MRI
Comments: Added results from a group analysis and a comparison with residual bootstrap
Subjects: Applications (stat.AP); Data Analysis, Statistics and Probability (physics.data-an); Medical Physics (physics.med-ph)
[116] arXiv:1712.01912 (replaced) [pdf, ps, other]
Title: Quantum dynamics of the intramolecular vibrational energy redistribution in OCS: From localization to quasi-thermalization
Comments: 18 pages, 11 figures
Subjects: Quantum Physics (quant-ph); Chemical Physics (physics.chem-ph)
[117] arXiv:1712.03116 (replaced) [pdf, other]
Title: Watt-level widely tunable single-mode emission by injection-locking of a multimode Fabry-Perot quantum cascade laser
Comments: 4 figures, 10 pages
Journal-ref: Applied Physics Letters 112(6) (2018) 061109
Subjects: Optics (physics.optics)
[118] arXiv:1712.03526 (replaced) [pdf, other]
Title: Improved performance of semiconductor laser tracking frequency gauge
Comments: 8 pages, 4 figures. To appear in JINST. (This version with new figures 3 and 4 with improved graphic quality and performance.)
Subjects: Instrumentation and Methods for Astrophysics (astro-ph.IM); High Energy Physics - Experiment (hep-ex); Atomic Physics (physics.atom-ph)
[119] arXiv:1712.04283 (replaced) [pdf, ps, other]
Title: Refutation of [Chyba and Hand, Phys. Rev. Applied 6, 014017 (2016)]: No Electric Power can be Generated from Earth's Rotation through its Own Magnetic Field
Authors: J. Jeener
Comments: 4 pages, minor revisions, submitted to Phys. Rev. Applied as a Comment
Subjects: Applied Physics (physics.app-ph)
[120] arXiv:1712.04610 (replaced) [pdf, other]
Title: Data-driven localization mappings in filtering the monsoon-Hadley multicloud convective flows
Comments: monthly weather review (in press)
Subjects: Atmospheric and Oceanic Physics (physics.ao-ph); Computational Physics (physics.comp-ph)
[121] arXiv:1712.05924 (replaced) [pdf]
Title: Nonlinear Instability Modelling of a Nonlocal Strain Gradient Functionally Graded Capacitive Nano-Bridge Under van der Waals force in Thermal Environment
Subjects: Applied Physics (physics.app-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
[122] arXiv:1712.05948 (replaced) [pdf, other]
Title: Towards compact Free Electron Laser based on laser plasma accelerators
Authors: ME Couprie
Comments: 13 pages, 8 fig
Subjects: Accelerator Physics (physics.acc-ph)
[123] arXiv:1712.09206 (replaced) [pdf, other]
Title: Chaos-guided Input Structuring for Improved Learning in Recurrent Neural Networks
Comments: 11 pages with 5 figures including supplementary material
Subjects: Neurons and Cognition (q-bio.NC); Neural and Evolutionary Computing (cs.NE); Biological Physics (physics.bio-ph)
[124] arXiv:1801.02666 (replaced) [pdf, other]
Title: Increased sensitivity of spin noise spectroscopy using homodyne detection in $n$-doped GaAs
Comments: 9 pages, 4 figures, Minor revisions, New References
Subjects: Instrumentation and Detectors (physics.ins-det); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Optics (physics.optics)
[125] arXiv:1801.06530 (replaced) [pdf, other]
Title: In-water chemical sensing by fiber-optic evanescent waves spectroscopy using mid-infrared quantum cascade lasers
Journal-ref: Sensors and Actuators B: Chemical 262 (2018) 195-199
Subjects: Applied Physics (physics.app-ph); Instrumentation and Detectors (physics.ins-det)
[126] arXiv:1801.07652 (replaced) [pdf, other]
Title: Vorticity and helicity decompositions and dynamics with Real Schur form of the velocity gradient
Authors: Jian-Zhou Zhu
Comments: quartet resonance analysis is outlined
Subjects: Fluid Dynamics (physics.flu-dyn); Chaotic Dynamics (nlin.CD); Geophysics (physics.geo-ph)
[127] arXiv:1801.08698 (replaced) [pdf, ps, other]
Title: Average values of functionals and concentration without measure
Authors: Cheng-shi Liu
Comments: 32 pages
Subjects: Probability (math.PR); Mathematical Physics (math-ph); Functional Analysis (math.FA); Statistics Theory (math.ST); Data Analysis, Statistics and Probability (physics.data-an)
[128] arXiv:1801.09492 (replaced) [pdf, ps, other]
Title: Effects of heterogeneity in power-grid network models
Comments: 9 pages, 10 Figures, results recalculated following K/N -> K/N_i coupling renormalization
Subjects: Physics and Society (physics.soc-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)
[129] arXiv:1802.01524 (replaced) [pdf, other]
Title: Diffraction of a CW atom laser in the Raman-Nath regime
Comments: 5 pages and 3 figures
Subjects: Atomic Physics (physics.atom-ph); Quantum Physics (quant-ph)
[130] arXiv:1802.03722 (replaced) [pdf, ps, other]
Title: Influence of pulsatile blood flow on allometry of aortic wall shear stress
Comments: 10 pages, 4 figures
Subjects: Biological Physics (physics.bio-ph); Fluid Dynamics (physics.flu-dyn); Tissues and Organs (q-bio.TO)
[131] arXiv:1802.04395 (replaced) [pdf, other]
Title: Spatially-resolved Fluorescence-detected Two-dimensional Electronic Spectroscopy Probes Varying Electronic Couplings in Photosynthetic Bacteria
Comments: Submitted to Nature Communications on Feb 12th, 2018, acknowledgements, and author contributions updated in version 2
Subjects: Chemical Physics (physics.chem-ph); Biological Physics (physics.bio-ph)
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# Universal countable Borel equivalence relations with an eye toward finitely generated groups
In the previous post, I discussed a technique due to Neumann and Neumann for embedding any countable group into a 2-generated group, and mentioned in passing that they used the same ideas to create a finitely generated 3-solvable non-Hopfian group. This construction turned out to be very useful to my own research, but to describe how requires a few definitions, which I’ll get to in a moment. The aim of this post is not really to discuss my research, but instead to gear up to look at a related result, which I hope to understand better. That will be the subject of the next post. Perhaps it will help with my research again.
I’ve previously mentioned Borel equivalence relations in passing. Let’s talk about them in a bit more detail.
Definition: If $X$ is a Polish space (or more generally, a standard Borel space) and $E$ is an equivalence relation on $X$, then we say $E$ is Borel if $E$ is Borel as a subset of $X\times X$.
Definition: We call an equivalence relation countable if all of its equivalence classes are countable.
My research focuses on countable Borel equivalence relations. Many interesting equivalence relations are countable Borel; for example Turing equivalence, eventual equality of infinite binary sequences (known as $E_0$, which you may have seen in a hat problem), isomorphism of finitely generated groups, or orbit equivalence relations arising from Borel actions of countable groups. (In fact, a theorem of Feldman and Moore says that every countable Borel equivalence relation can be realized as the orbit equivalence relation arising from a Borel action of a countable group!) When discussing Borel equivalence relations, we are mainly interested in comparing them using the notion of a Borel reduction.
Definition: Suppose $E$ and $F$ are Borel equivalence relations on Polish spaces $X,Y$. Then a Borel homomorphism from $E$ to $F$ is a Borel map $f\colon X \rightarrow Y$ such that
$\displaystyle x \mathbin{E} y \,\, \Rightarrow \,\, f(x) \mathbin{F} f(y)$
Borel reduction from $E$ to $F$ is a map $f\colon X \rightarrow Y$ such that
$\displaystyle x \mathbin{E} y \,\, \Leftrightarrow \,\, f(x) \mathbin{F} f(y)$
If $E$ Borel reduces to $F$, we write $E \leq_B F$.
The idea behind a Borel reduction is that if $E \leq_B F$, then $F$ is at least as complicated as $F$. If one could classify the elements of $Y$ up to $F$-equivalence, then using the Borel reduction you could also classify the elements of $X$ up to $E$-equivalence. (Note that this is not so different from the justification for using poly-time reductions in complexity theory to compare the difficulty of decision problems.) The point of keeping things Borel that Borel objects are in some sense explicit. Using the axiom of choice one can show there exist reductions between any two equivalence relations with the same number of equivalence classes, but the reductions are in general not Borel. In fact, there are a whole host of results establishing non-reducibility of certain Borel equivalence relations. A relatively simple example is that equality on $2^\mathbb{N}$ Borel reduces to $E_0$, but not vice versa, as can be seen using Baire category or measure arguments.
Definition: A countable Borel equivalence relation $E$ is universal (or complete) if for any countable Borel equivalence relation $F$, $F\leq_B E$.
To extend the analogy with complexity theory, a universal countable Borel equivalence relation (if it exists) relates to countable Borel equivalence relations in the same way an NP-complete decision problem relates to NP decision problems; it’s as complicated as it possibly could be given its complexity. Note that one could easily make a similar definition for any class of Borel equivalence relations. Indeed, this is done. Some classes have universal equivalence relations and some don’t.
Theorem (Dougherty-Jackson-Kechris): There is a universal countable Borel equivalence relation.
Once one has one example of universal countable equivalence relation $E_\infty$, then one can show another countable Borel equivalence relation $E$ is universal simply by showing $E_\infty \leq_B E$, and indeed this is how most proofs of universality proceed.
Theorem (Thomas-Velickovic): Isomorphism of finitely generated groups is a universal countable Borel equivalence relation.
There are many other examples, but this is the one which interests us in this post. Finitely generated groups can be quite complicated, and this result puts some rigor behind that intuition. The proof rather heavily uses free products with amalgamation. These are “large” from a group-theoretic standpoint (for example, they all contain free non-abelian subgroups), and so seen as complicated in and of themselves. So it’s not surprising that isomorphism of these sorts of groups is complicated. But what about finitely generated groups which are not as complicated? Is the isomorphism relation still complex? There has been some progress towards answering this, but we need one more definition.
Definition: A countable Borel equivalence relation $E$ is weakly universal if for any countable Borel equivalence relation $F$ there is a countable-to-1 Borel homomorphism from $F$ to $E$. Equivalently (this is not obvious), $E$ is weakly universal if it contains a universal countable equivalence relation.
Clearly every universal countable Borel equivalence relations is weakly universal. The idea behind looking at countable-to-1 Borel homomorphisms from an equivalence relation $E$ to another equivalence relation $F$ is that although these are not necessarily Borel reductions, they can’t fail too badly to be such, sending at most countably many $E$-inequivalent elements to $F$-equivalent elements . Compare this with $E_0$ and equality on $2^\mathbb{N}$; every Borel homomorphism from $E_0$ to equality must send a measure 1 set to the same point!
Whether or not every weakly universal equivalence relation is in fact universal is a notorious open problem. A positive answer would make many proofs of universality trivial (or at least much simpler); creating Borel homomorphisms from a universal $E$ to another Borel equivalence relation $F$ is always the easy part, it’s making these maps reductions which is trickier. A negative answer follows from Martin’s Conjecture, a stubbornly open conjecture in its own right, but which seems to provide excellent tools for analyzing weakly universal equivalence relations. In any event, weakly universal equivalence relations are pretty high up in the $\leq_B$-hierarchy (which is not at all linear, so this should be understood as an imprecise-but-ultimately-mathematically-defensible statement).
So, back to isomorphism of finitely generated groups. We have the following:
Theorem (Thomas-Williams): Isomorphism of Kazhdan groups is weakly universal.
Theorem (Williams): Isomorphism of finitely generated 3-solvable groups is weakly universal.
In both of these cases, we expect that the relations are in fact universal, but as I mentioned, making Borel reductions is a bit trickier than making Borel homomorphisms, which is all that is needed to prove weak universality. My proof of the second theorem makes use of a modification of the Neumann and Neumann construction mentioned at the beginning of this post; in fact to modern eyes their construction already showed that $E_0$ Borel reduces to isomorphism of finitely generated 3-solvable groups, a non-trivial lower bound on the complexity. It is known that $E_0$ is strictly below any weakly universal equivalence relation with respect to Borel complexity, so my result is a stronger lower bound than Neumann and Neumann’s.
It would be nice to make the leap from weak universality to universality. In the next post, we’ll look at how a different group-theoretic equivalence relation was shown to be universal in the hopes of learning something we can use.
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LaTeX forum ⇒ Graphics, Figures & Tables ⇒ Figure in mac
Information and discussion about graphics, figures & tables in LaTeX documents.
patriciakh
Posts: 1
Joined: Fri Jan 02, 2015 5:04 pm
Figure in mac
Hi I am new to Latex and am using Mac which has doubled my problem..... I am trying to insert a figure in my thesis but each time it says that the figure is not find. This is while I have defined a folder for my figures. Can anyone help me
Stefan Kottwitz
Posts: 9705
Joined: Mon Mar 10, 2008 9:44 pm
Welcome to the forum!
Which command are you using for including? Did you specify file name and path? Perhaps show us a code line and tell where exactly the image is located, relative or absolute path.
You could also add the .log file here, as attachment to a forum post.
Stefan
coachbennett1981
Posts: 252
Joined: Fri Feb 05, 2010 10:15 pm
Two things: Need to make sure that you file extension is excepted. Also, if you are using the \includegraphics command, you need to make sure the file you want to include is in the sam place (folder) as your thesis.
Nick
Maks71
Posts: 6
Joined: Wed Aug 02, 2017 12:02 pm
Hi,
I also just started using latex (today :<).
Love the template but
My figures folder cannot be located.
Any ideas, I can see it and the graphicspath is there
Thanks
maks
Johannes_B
Site Moderator
Posts: 4185
Joined: Thu Nov 01, 2012 4:08 pm
Which template?
The smart way: Calm down and take a deep breath, read posts and provided links attentively, try to understand and ask if necessary.
Stefan Kottwitz
Posts: 9705
Joined: Mon Mar 10, 2008 9:44 pm
Hi Maks,
welcome to the forum!
In addition to the information, which template you are using, perhaps also post error messages or warnings here. You could post attach the .log file here, as attachment. The link "Attachments" is below the text edit field, when writing a post.
Take care that you don't write in draft mode (document class or graphicx package option `draft`), that would not load the images for compiling speed.
Stefan |
# ( This question is for any book ) HELPPPP PLEASE!! ( I will mark yall the brainliest if you answer it in a correctly way!! HELPPWhat kind of research did the author have to do in order to write the book??Explain.
###### Question:
( This question is for any book ) HELPPPP PLEASE!! ( I will mark yall the brainliest if you answer it in a correctly way!! HELPP
What kind of research did the author have to do in order to write the book??
Explain.
### A test tube containing CaCO₃ is heated until the entire compound decomposes. If the test tube plus calcium carbonate originally weighed 30.08 grams and the loss of mass during the experiment was 4.40 grams, what was the approximate mass of the empty test tube? A. 20.08 g B. 21.00 g C. 24.50 g D. 25.08 g E. 25.68 g Can anyone explain this one for me?
A test tube containing CaCO₃ is heated until the entire compound decomposes. If the test tube plus calcium carbonate originally weighed 30.08 grams and the loss of mass during the experiment was 4.40 grams, what was the approximate mass of the empty test tube? A. 20.08 g B. 21.00 g C. 24.50 g D. 2...
### Which of the following statements best describes Canada’s government
Which of the following statements best describes Canada’s government...
### In the "promoting leadership effectiveness" model, what is a listed goal at the interpersonal level?b
In the "promoting leadership effectiveness" model, what is a listed goal at the interpersonal level?b...
### Which word requires a spelling change before adding the sufix -er a fast b merry c smart d buy
which word requires a spelling change before adding the sufix -er a fast b merry c smart d buy...
### If Twitter were to exclusively use e-mail, collaborative computing, and other computer connections to connect geographically separate employees, it would be considered a(n) ______ organization.
If Twitter were to exclusively use e-mail, collaborative computing, and other computer connections to connect geographically separate employees, it would be considered a(n) ______ organization....
### 2sqrt3 +2i to polar representation
2sqrt3 +2i to polar representation...
### Which of the following holds the ultimate responsibility for making and carrying out governmental policy?
Which of the following holds the ultimate responsibility for making and carrying out governmental policy?...
### How do you know that a liquid exerts pressure?
How do you know that a liquid exerts pressure?...
### In what way might a historian use a source like the one above?
In what way might a historian use a source like the one above?...
### Does the point (0,4) make either equations y=-2x and y=x+3 true? Explain.
Does the point (0,4) make either equations y=-2x and y=x+3 true? Explain....
### According to our textbook, _________________ is one of the more popular topics in the book of Proverbs.
According to our textbook, _________________ is one of the more popular topics in the book of Proverbs....
### Put in the Cartesian plane the graph of the function y = 2x + 3
put in the Cartesian plane the graph of the function y = 2x + 3...
### Are you the type of person who puts a ruler under their pillow to see how long they've slept?
Are you the type of person who puts a ruler under their pillow to see how long they've slept?...
### How can the ph scale tell you if a substance is an acid a base or neutral?
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### How are these triangles similar?
How are these triangles similar?...
### If your employer offers a retirement plan, it should be the first plan that you consider because your employer will likely contribute to it.
If your employer offers a retirement plan, it should be the first plan that you consider because your employer will likely contribute to it.... |
# Do I need to differentiate this equation or not?
I've been given this equation: $$\mathrm{velocity}, v = 2\,\mathrm{cm/s^3} \,t^2 + 5\,\rm cm/s.$$
If someone now asks me to tell the velocity at, say 4 sec, then before proceeding with the equation, do I need to differentiate it (which would give me $4t$) or should I proceed to put 4sec in that equation at place of $t$ which would then give me 37 cm/s.
So, which of the approach is correct? and since one of the approach is only right, so, also let me know that when do we use the other approach
• You just put the 4s in. Differentiating would only make sense if the function you are looking at, would be an expression of distance travelled throug in dependence of time. – Nontriviality Sep 20 '15 at 19:59
• Did you underestand why you usually take derivatives? – Nontriviality Sep 20 '15 at 19:59
• I've been told that the flavors of sodas are printed on the cans. If someone now asks me what flavor is in a can marked Grape, do I need to first drop the first letter and rearrange the others (which would give me Pear) or can I just tell him it's Grape? – WillO Sep 20 '15 at 20:14
• The $2 t^2$ term should have been written as 2 cm/s $(t/s)^2$ – Count Iblis Sep 20 '15 at 22:21
we first define velocity with the following equation $$v=\int{a}dt$$ Differentiating the equation would yield acceleration which is incorrect based on what the question is asking You stated your equation for velocity is velocity$$v=f(t)=2cm/s^3t^2+5cm/s$$ Therefor by simple substitution we just sub $v=f(4)$ $$f(t)=2\times(4)^2+5=37cm/s$$ Verifying the equation we also find it is dimensionally accurate
When you have a function $f(t)$ that expresses a quantity (say the velocity $v$), then you just evaluate that function at $t$ in order to get the function (velocity) at $t$.
However, if I give you the position at $t$, $x(t)$, and I ask you for the velocity, then you first have to recall that velocity is the derivative of position with time:
$$v = \frac{dx}{dt}$$ |
# Solve cosx+sinx=2/3 ?
Oct 4, 2016
Assuming you meant $\sin$($x$) $+$ $\cos$($x$) $=$ $\frac{2}{3}$,
$\cos \left({x}_{1}\right) = 0.96$
$\cos \left({x}_{2}\right) = - 0.29$ (to 2dp.)
#### Explanation:
To solve this equation, we have to use trigonometric functions to isolate one of the unknowns and solve for that unknown.
In this case, we will use ${\sin}^{2}$($x$) $+$ ${\cos}^{2}$($x$) = 1 and 2$\sin \left(x\right)$$\cos \left(x\right)$ = $\sin \left(2 x\right)$.
$\sin$($x$) $+$ $\cos$($x$) = $\frac{2}{3}$
${\left(\sin \left(x\right) + \cos \left(x\right)\right)}^{2}$ $=$ ${\left(\frac{2}{3}\right)}^{2} =$ $\frac{4}{9}$
${\sin}^{2} \left(x\right)$ $+$ ${\cos}^{2} \left(x\right)$ $+$ 2$\sin \left(x\right)$$\cos \left(x\right)$ $=$ $\frac{4}{9}$
$1$ $+$ $\sin \left(2 x\right)$ $=$ $\frac{4}{9}$
$\sin \left(2 x\right)$ $=$ $- \frac{5}{9}$
The function $\sin \left(x\right)$ is negative in the 3rd and 4th quadrants and $\sin \left(\theta\right) = \sin \left({180}^{\text{o}} - \theta\right)$. Therefore, we have two solutions for $2 x$:
$2 {x}_{1}$ $=$ ${\sin}^{-} 1 \left(- \frac{5}{9}\right)$ $=$ $- {33.75}^{\text{o}}$
$2 {x}_{2} = {180}^{\text{o"-(-33.75^"o") = 213.75^"o}}$
From this:
${x}_{1}$ $=$ $- {33.75}^{\text{o}} / 2$ $=$ $- {16.87}^{\text{o}}$
${x}_{2} = {213.75}^{\text{o"/2 = 106.87^"o}}$
$\cos \left({x}_{1}\right) = \cos \left(- {16.87}^{\text{o}}\right)$ $=$ $0.96$
$\cos \left({x}_{2}\right) = \cos \left({106.87}^{\text{o}}\right) = - 0.29$
Oct 5, 2016
$x = 1.87$-Round to 2 decimal places
#### Explanation:
$\sin x + \cos x = \frac{2}{3}$
Let's first use linear combination of cosine and sine with equal arguments formula to simplify it.
That is, we want to express
A cos x +B sin x in the form C cos (x-D). Note that A is the coefficient of cos x and B is the coefficient of sine x.
To find C use pythagorean formula and to find D we use one of these two formulas
$\cos D = \frac{A}{C} , \sin D = \frac{B}{C}$
From the given equation A = 1 and B = 1. So let's find C using pythagorean theorem.
$C = \sqrt{{A}^{2} + {B}^{2}} = \sqrt{{1}^{2} + {1}^{2}} = \sqrt{2}$
To find D we need to first figure out which quadrant x is in and because both cos x and sin x are positive it means that x is in quadrant one.
$\cos D = \frac{1}{\sqrt{2}}$
$D = {\cos}^{-} 1 \left(\frac{1}{\sqrt{2}}\right) = \frac{\pi}{4}$
Therefore $\sin x + \cos x = \sqrt{2} \cos \left(x - \frac{\pi}{4}\right)$
Now let's use that to solve the problem. That is,
$\sqrt{2} \cos \left(x - \frac{\pi}{4}\right) = \frac{2}{3}$
$\cos \left(x - \frac{\pi}{4}\right) = \frac{2}{3 \sqrt{2}}$
$x - \frac{\pi}{4} = {\cos}^{-} 1 \left(\frac{2}{3 \sqrt{2}}\right)$
$x = {\cos}^{-} 1 \left(\frac{2}{3 \sqrt{2}}\right) + \frac{\pi}{4}$
$x = 1.87$-Round to 2 decimal places
Oct 5, 2016
$x = \frac{1}{2} \left(\frac{2}{3} \pm \frac{\sqrt{14}}{3}\right)$
#### Explanation:
Making $y = \sin \left(x\right)$ and $\alpha = \frac{2}{3}$
$y + \sqrt{1 - {y}^{2}} = \alpha$
$1 - {y}^{2} = {\left(\alpha - y\right)}^{2}$
$1 - {y}^{2} = {\alpha}^{2} - 2 \alpha y + {y}^{2}$
$2 {y}^{2} - 2 \alpha y + {\alpha}^{2} - 1 = 0$ solving for $y$
$y = \frac{1}{2} \left(\alpha \pm \sqrt{2 - {\alpha}^{2}}\right)$
$\sin \left(x\right) = \frac{1}{2} \left(\frac{2}{3} \pm \frac{\sqrt{14}}{3}\right)$
Oct 5, 2016
Considering the given condition is
$\cos x + \sin x = \frac{2}{3.} \ldots . . \left(1\right)$
Now
${\left(\cos x - \sin x\right)}^{2} + {\left(\cos x + \sin x\right)}^{2} = 2 \left({\cos}^{2} x + {\sin}^{2} x\right) = 2$
$\implies {\left(\cos x - \sin x\right)}^{2} + {\left(\frac{2}{3}\right)}^{2} = 2$
$\implies {\left(\cos x - \sin x\right)}^{2} + {\left(\frac{2}{3}\right)}^{2} = 2$
$\implies {\left(\cos x - \sin x\right)}^{2} = 2 - \frac{4}{9} = \frac{14}{9}$
$\implies \left(\cos x - \sin x\right) = \pm \frac{\sqrt{14}}{3.} \ldots . \left(2\right)$
Adding (1) and (2) we get
$2 \cos x = \frac{2}{3} \pm \frac{\sqrt{14}}{3}$
$\implies \cos x = \frac{1}{2} \left(\frac{2}{3} \pm \frac{\sqrt{14}}{3}\right)$ |
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# 14.3: The Equilibrium of Moments
In order to solve the problem, also the equilibrium of moments is required, since the wedge is not subject to rotational acceleration. The equilibrium of moments can be taken around each point of the wedge. Here the tip of the blade is chosen. The advantage of this is that a number of forces do not contribute to the moments on the wedge.
In order to derive the equilibrium of moments equation the arms of all the forces contributing to this equilibrium have to be known. Since these arms depend on the length of all the sides in the cutting process, first these lengths are determined. The length of the shear plane A-B is:
$\ \mathrm{L}_{1}=\frac{\mathrm{h}_{\mathrm{i}}}{\sin (\beta)}\tag{14-19}$
The length of the pseudo blade A-C is:
$\ \mathrm{L}_{2}=\frac{\mathrm{h}_{\mathrm{b}}}{\sin (\theta)}\tag{14-20}$
The length of the bottom of the wedge A-D is:
$\ \mathrm{L}_{3}=\mathrm{h}_{\mathrm{b}} \cdot\left(\frac{\mathrm{1}}{\tan (\theta)}-\frac{1}{\tan (\alpha)}\right)\tag{14-21}$
The length of the blade C-D is:
$\ \mathrm{L}_{4}=\frac{\mathrm{h}_{\mathrm{b}}}{\sin (\alpha)}\tag{14-22}$
The length of the line from the tip of the blade to the opposite side of the wedge and perpendicular to this side is:
$\ \mathrm{L}_{5}=\mathrm{L}_{3} \cdot \sin (\theta)\tag{14-23}$
The length of the line from point to the intersection point of the previous line with side A-C is:
$\ \mathrm{L}_{\mathrm{6}}=\mathrm{L}_{\mathrm{3}} \cdot \cos (\theta)\tag{14-24}$
The distance from the acting point of the pore pressure force on side A-C to the intersection point of the previous line with side A-C is:
$\ \mathrm{L}_{7}=\mathrm{L}_{6}-\mathrm{R}_{2}\tag{14-25}$
The values of the acting points R2R3 and R4 follow from calculated or estimated stress distributions.
The equilibrium of moments is now:
$\ \sum \mathrm{M}=\mathrm{N}_{4} \cdot \mathrm{R}_{4}-\mathrm{N}_{3} \cdot \mathrm{R}_{3}+\mathrm{N}_{2} \cdot \mathrm{L}_{7}-\left(\mathrm{S}_{2}+\mathrm{C}_{2}\right) \cdot \mathrm{L}_{5}=\mathrm{0}\tag{14-26}$
This page titled 14.3: The Equilibrium of Moments is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Sape A. Miedema (TU Delft Open Textbooks) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
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26. CJM 2003 (vol 55 pp. 1000)
Graczyk, P.; Sawyer, P.
Some Convexity Results for the Cartan Decomposition In this paper, we consider the set $\mathcal{S} = a(e^X K e^Y)$ where $a(g)$ is the abelian part in the Cartan decomposition of $g$. This is exactly the support of the measure intervening in the product formula for the spherical functions on symmetric spaces of noncompact type. We give a simple description of that support in the case of $\SL(3,\mathbf{F})$ where $\mathbf{F} = \mathbf{R}$, $\mathbf{C}$ or $\mathbf{H}$. In particular, we show that $\mathcal{S}$ is convex. We also give an application of our result to the description of singular values of a product of two arbitrary matrices with prescribed singular values. Keywords:convexity theorems, Cartan decomposition, spherical functions, product formula, semisimple Lie groups, singular valuesCategories:43A90, 53C35, 15A18
27. CJM 2002 (vol 54 pp. 795)
Möller, Rögnvaldur G.
Structure Theory of Totally Disconnected Locally Compact Groups via Graphs and Permutations Willis's structure theory of totally disconnected locally compact groups is investigated in the context of permutation actions. This leads to new interpretations of the basic concepts in the theory and also to new proofs of the fundamental theorems and to several new results. The treatment of Willis's theory is self-contained and full proofs are given of all the fundamental results. Keywords:totally disconnected locally compact groups, scale function, permutation groups, groups acting on graphsCategories:22D05, 20B07, 20B27, 05C25
28. CJM 2000 (vol 52 pp. 633)
Walters, Samuel G.
Chern Characters of Fourier Modules Let $A_\theta$ denote the rotation algebra---the universal $C^\ast$-algebra generated by unitaries $U,V$ satisfying $VU=e^{2\pi i\theta}UV$, where $\theta$ is a fixed real number. Let $\sigma$ denote the Fourier automorphism of $A_\theta$ defined by $U\mapsto V$, $V\mapsto U^{-1}$, and let $B_\theta = A_\theta \rtimes_\sigma \mathbb{Z}/4\mathbb{Z}$ denote the associated $C^\ast$-crossed product. It is shown that there is a canonical inclusion $\mathbb{Z}^9 \hookrightarrow K_0(B_\theta)$ for each $\theta$ given by nine canonical modules. The unbounded trace functionals of $B_\theta$ (yielding the Chern characters here) are calculated to obtain the cyclic cohomology group of order zero $\HC^0(B_\theta)$ when $\theta$ is irrational. The Chern characters of the nine modules---and more importantly, the Fourier module---are computed and shown to involve techniques from the theory of Jacobi's theta functions. Also derived are explicit equations connecting unbounded traces across strong Morita equivalence, which turn out to be non-commutative extensions of certain theta function equations. These results provide the basis for showing that for a dense $G_\delta$ set of values of $\theta$ one has $K_0(B_\theta)\cong\mathbb{Z}^9$ and is generated by the nine classes constructed here. Keywords:$C^\ast$-algebras, unbounded traces, Chern characters, irrational rotation algebras, $K$-groupsCategories:46L80, 46L40
29. CJM 1999 (vol 51 pp. 96)
Rösler, Margit; Voit, Michael
Partial Characters and Signed Quotient Hypergroups If $G$ is a closed subgroup of a commutative hypergroup $K$, then the coset space $K/G$ carries a quotient hypergroup structure. In this paper, we study related convolution structures on $K/G$ coming from deformations of the quotient hypergroup structure by certain functions on $K$ which we call partial characters with respect to $G$. They are usually not probability-preserving, but lead to so-called signed hypergroups on $K/G$. A first example is provided by the Laguerre convolution on $\left[ 0,\infty \right[$, which is interpreted as a signed quotient hypergroup convolution derived from the Heisenberg group. Moreover, signed hypergroups associated with the Gelfand pair $\bigl( U(n,1), U(n) \bigr)$ are discussed. Keywords:quotient hypergroups, signed hypergroups, Laguerre convolution, Jacobi functionsCategories:43A62, 33C25, 43A20, 43A90
30. CJM 1998 (vol 50 pp. 342)
Giraldo, Antonio
Shape fibrations, multivalued maps and shape groups The notion of shape fibration with the near lifting of near multivalued paths property is studied. The relation of these maps---which agree with shape fibrations having totally disconnected fibers---with Hurewicz fibrations with the unique path lifting property is completely settled. Some results concerning homotopy and shape groups are presented for shape fibrations with the near lifting of near multivalued paths property. It is shown that for this class of shape fibrations the existence of liftings of a fine multivalued map, is equivalent to an algebraic problem relative to the homotopy, shape or strong shape groups associated. Keywords:Shape fibration, multivalued map, homotopy groups, shape, groups, strong shape groupsCategories:54C56, 55P55, 55Q05, 55Q07, 55R05
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# Do locally convex topological vector spaces embed into diffeological spaces?
The nLab casually remarks that locally convex tvs embed into diffeological spaces by (discussion around) a corollary in Kriegl and Michor, namely 3.14, but this deals with Boman's theorem and results about smooth maps from a euclidean space to a locally convex spaces.
The definition of smoothness for maps $U \to V$ where $U$ is $c^\infty$-open in a lctvs $W$, and $V$ is a lctvs, is given so that smooth maps are automatically the same as between maps between the associated diffeological spaces.
However, there is a notion of smoothness for maps between lctvs (due to Michal [1,2] and Bastiani [3]) not relying on K&M's definition, but I don't how they relate (Keller [4] treats this, I think, but I don't have access to that book at the moment).
Is it still true that lctvs embed into diffeological spaces using Michal-Bastiani smoothness?
[1] Michal, A. D. Differential calculus in linear topological spaces, Proc. Nat. Acad. Sci. USA 24 (1938), 340-342 (pdf)
[2] Michal, A. D. Differential of functions with arguments and values in topological abelian groups, Proc. Nat. Acad. Sci. USA 26 (1940), 356–359. (pdf)
[3] Bastiani, A., Applications différentiables et variétés différentiables de dimension infinie, J. Anal. Math. 13 (1964), 1–114. (article, paywalled)
[4] Keller, H. H., Differential Calculus in Locally Convex Spaces, Lecture Notes in Mathematics 417, Springer-Verlag, 1974 (Springerlink, paywalled)
The answer is no. In what follows (see OP's comments below) we assume that the arrows of the category of lctvs are Michal-Bastiani smooth maps. Recall that a map $\Phi:E\rightarrow F$ from a lctvs $E$ into another lctvs $F$ is said to be Michal-Bastiani smooth if its directional (Gâteaux) derivatives of order $k$
$$D^k\Phi[x](y_1,\ldots,y_k) = \left.\frac{\partial^k}{\partial\lambda_1\cdots\partial\lambda_k}\right|_{\lambda_1=\cdots=\lambda_k=0}\Phi\left(x+\sum^k_{j=1}\lambda_j y_j\right)$$
exist and the maps $D^k\Phi:E\times E^k\rightarrow F$ are (jointly) continuous for all $k\in\mathbb{N}$. This notion of smoothness is the one used in Milnor's treatment of infinite-dimensional Lie groups (J. Milnor, "Remarks on Infinite-Dimensional Lie Groups". In: B. DeWitt, R. Stora, eds., Les Houches Session XL, Relativity, Groups and Topology II (North-Holland, 1984), pp. 1007-1057) and Hamilton's exposé of the Nash-Moser inverse function theorem (R.S. Hamilton, "The Inverse Function Theorem of Nash and Moser". Bull. Amer. Math. Soc. 7 (1982) 65-222).
Michal-Bastiani smooth maps are also smooth in the sense of Kriegl and Michor (i.e. composing with a smooth curve leads to another smooth curve; some call the latter convenient smoothness), since the chain rule holds for Michal-Bastiani smooth maps. The converse is not necessarily true - both notions of smoothness coincide for Fréchet spaces, but in general they differ: conveniently smooth maps need not even be continuous, whereas Michal-Bastiani smooth maps are always so. A counter-example to continuity for conveniently smooth maps may be found in the paper of H. Glöckner, "Discontinuous Non-Linear Mappings on Locally Convex Direct Products". Publ. Math. Debrecen 68 (2006) 1-13, arXiv:math/0503387. In particular, if neither $E$ nor $F$ are Fréchet spaces, there may be maps between $E$ and $F$ which are smooth in the diffeological sense and need not even be continuous, let alone Michal-Bastiani smooth. Therefore, the natural inclusion functor of lctvs into diffeological spaces is not fully faithful. It is not clear from the above counterexample whether there are convenient diffeomorphisms which fail to be continuous or Michal-Bastiani smooth. (see however TaQ's answer below for such a counterexample)
• "there are maps between E and F which are smooth in the diffeological sense and need not even be continuous, let alone Michal-Bastiani smooth." <-- ah, this is what I wanted to know! Although it wasn't clear from how I asked it, since 'embedding between categories' doesn't have a universal definition. So I guess the only thing to worry about is if there diffeological isomorphisms (not necc. linear) that are not MB-smooth. This seems like a difficult question. – David Roberts Jun 15 '15 at 6:17
• @DavidRoberts so, what is the definition of "embedding of categories" you have in mind in your question? Do you put any restriction on the arrows in the category of lctvs besides being continuous linear maps (e.g. do you require them to be topological isomorphisms, or something)? – Pedro Lauridsen Ribeiro Jun 15 '15 at 14:43
• I wasn't thinking of linear maps, and I was trying to compare to the statement for Fréchet spaces, which by embedding means a full and faithful functor (and taking all smooth maps between Fréchet spaces). My residual query is whether a convenient diffeomorphism is necessarily MB-smooth, which is intermediate between the inclusion being fully faithful and being just faithful. – David Roberts Jun 15 '15 at 22:39
• So, you were considering smooth maps (in either sense) as the arrows of the category of lctvs in your original question, and your residual question is whether the answer changes if you restrict the arrows to be smooth diffeomorphisms. Is this corrrect? – Pedro Lauridsen Ribeiro Jun 15 '15 at 23:04
• I have edited my answer to better suit your original question, based on your comments. I've also added a remark at the end concerning your remaining question, to which unfortunately I don't know an answer. Papers who cite Glöckner's work quoted above, according to MathSciNet, apparently don't even raise that question, let alone answer it. – Pedro Lauridsen Ribeiro Jun 16 '15 at 1:25
$\def\sp{\kern.4mm}\def\bbN{\mathbb N}\def\bbZ{\mathbb Z}\def\bbR{\mathbb R}$Here is the answer to David Roberts' residual query: is a convenient diffeomorphism necessarily MB-smooth? No. A counterexample follows:
Let $E$ be the vector space of all real (two-sided) sequences $x=\langle\sp x_i:i\in\bbZ\sp\rangle$ for which $x_i=0$ for sufficiently small $i$ , topologized so that we get a linear homeomorphism $E\to\bbR\,^{\bbN}\times\bbR\,^{(\bbN)}$ defined by $x\mapsto(u,v)$ where $u_i=x_{i-1}$ and $v_i=x_{-i}$ for $i\in\bbN$ . Then define $f:E\to E$ by $x\mapsto y$ where $y_i=x_i$ for $i\in\bbZ\setminus\{\sp 0\sp\}$ and $y_0=x_0+\sum_{i\in\bbN}(x_i\cdot x_{-i})$ . The inverse is given by $y\mapsto x$ where $y_i=x_i$ for $i\in\bbZ\setminus\{\sp 0\sp\}$ and $x_0=y_0-\sum_{i\in\bbN}(y_i\cdot y_{-i})$ . Since the duality map $\bbR\,^{\bbN}\times\bbR\,^{(\bbN)}\to\bbR$ is a discontinuous but bornological, and hence conveniently smooth bilinear map, the assertion follows.
• To clarify a bit: " $x_i=0$ for sufficiently small $i$ " means more precisely that " there is $i_0\in\mathbb Z$ such that $x_i=0$ for all $i\in\mathbb Z$ satisfying $i\le i_0$ ". This $i_0$ of course depends on $x$ . The discontinuous (and hence not MB−smooth) convenient diffeomorphism is the map $f:E\to E$ . – TaQ Jun 17 '15 at 20:03
• Thanks, TaQ, I've added your example to the nLab page ncatlab.org/nlab/show/Michal-Bastiani+smooth+maps, citing this answer. I may ask another question in future about MB-smooth bijections with only convenient smooth inverse. But that's another question. – David Roberts Jun 17 '15 at 23:46 |
## Friday, 19 July 2013
### Average Height of a Beatle
Let :
$B := \{x \mid x$ is a Beatle $\}$
and let:
$h_m(x) = r$
stand for the quantity function which maps human beings to their heights in metres.
Then define:
$\overline{h}_B := \frac{1}{|B|} \sum_{x \in B} h_m(x)$
This value is the average height of a Beatle.
Let C be a class of human beings. Then:
$\overline{h}_C := \frac{1}{|C|} \sum_{x \in C} h_m(x)$
This value is the average height of an element of C.
#### 7 comments:
1. I'm a little confused. Is there a point to this? Was the second half of the post omitted?
In any event, the Beatles are defunct and there are no Beatles. Therefore the expression 1/|B| is undefined.
2. Hey, I'm building up to something! (To do with applicability)
There are no Beatles, but I was doing it tenselessly ...
Here we go with a time-indexed version
B(t) = {x | x is a Beatle at time t}
and then let t = 20 July 1967, say.
But maybe B(20 July 2013) = {Paul, Ringo}.
Cheers,
Jeff
3. Jeff, you're not living up to your usual standards of pedantry. You can't divide a real number by a cardinal number: you've got to go via the canonical embedding of the finite cardinals into the reals ;-)
4. :)
'So, when I came to Oxford in the early 1960s there was a lot of pedantry around ... Or, rather, I should say there was a lot of pedanticness.' (Jerry Cohen).
5. [i]But maybe B(20 July 2013) = {Paul, Ringo}.[/i]
John is no longer a Beatle but Ringo is? Why is that? You seem to be digging yourself in deeper here.
What is the average height of the members of the Roman senate? They're all dead but the question is still sensible.
In any event I'm still not clear as to why you posted this. Surely most readers are familiar with the concept of the arithmetic mean.
6. I'm happy to talk tenselessly, a la Quine, but it just complicates matters, somewhat needlessly! So, we'd just relativize the predicates to times, and then work with those. E.g., "x is a member of the Roman Senate at time t".
Now I think about it, you're right: Ringo and Paul are (i.e., now) former Beatles; so, I guess that $B(t) = \varnothing$, for $t$ after 1969-ish.
The unstated reason for posting it has got to do with category theory, structural set theory and applicability; but I actually need to sort out in my mind how such a theory deals with non-abstract objects. And I want a few examples to refer back to at that future point ...
Jeff
7. Thanks Jeff. I'm curious to see how this turns out. It's a long way from the arithmetic mean of a finite set to category theory. |
# Can $2a^2+2a+2ab^2+b^2$ be written algebraically as the sum of three triangular numbers?
Let $T(n)=\tfrac{1}{2}n(n+1)$ denote the $n$th triangular number. I'm looking for an identity of the form $$2a^2+2a+2ab^2+b^2 = T(f(a,b)) + T(g(a,b)) + T(h(a,b))\tag{\star}$$ where $a,b$ are integers, and $f,g,h$ are polynomials in $a,b$ with rational (or, better yet, integral) coefficients. In other words, I'm trying to apply to the left-hand side of ($\star$) an algebraic analogue the well-known fact that every integer is the sum of three triangular numbers.
NOTE: This was edited from $b$ to $b^2$, after it was rightly pointed out by Ward Beullens that the degree of the two sides couldn't match.
• You can come up with much. I need to write a more specific equation. For example, this: $a^2+a+b^2+b=x^2+x+y^2+y+z^2+z$ – individ Sep 9 '14 at 17:43
This is impossible, the left hand side is of degree one in $b$, and the right-handside is of degree $2 \max(deg(f),deg(g),deg(h))$ in b, so it is always even.
We know this because the degree of $T(f(x))$ is 2 times the degree of $f$, and the leading terms of the 3 polynomials are all positive, so they cannot cancel.
• For the new question the problem still exists. Consider the special case of $a = b$ in that case the degree of the left-hand side is 3. But the degree of the right-hand side is still even. – Ward Beullens Sep 9 '14 at 18:22 |
## Prealgebra (7th Edition)
$x^2+z-3$ $\longrightarrow$substitute the given values for each variable $5^2+4-3$ $\longrightarrow$PEMDAS says to resolve exponent first $25+4-3$ $\longrightarrow$add $29-3$ $\longrightarrow$subtract $26$ |
## yrivers36 3 years ago Solve each equation symbolically. With explanation please. sqrt (x)+1=sqrt (x+2)
1. Kreshnik
hint... $\LARGE \sqrt x+1=\sqrt{x+2}$ square both sides..
2. yrivers36
Im not sure but I think I should foil left side of problem
3. yrivers36
$(\sqrt{x}+1)(\sqrt{x}+1)-x+2$
4. yrivers36
thats an = in front of x
5. Kreshnik
$\LARGE (\sqrt x+1)^2=(\sqrt{x+2})^2$ $\LARGE (\sqrt x)^2+2\cdot \sqrt{x}\cdot 1+1^2=x+2$ $\LARGE x+2\cdot \sqrt{x}=x+2-1$ $\LARGE 2\cdot \sqrt{x}=x-x +2-1$ $\LARGE 2\cdot \sqrt{x}=1$ $\LARGE \sqrt{x}=\frac12$ square both sides and there you go :)
6. Kreshnik
can you do it ?
7. yrivers36
solution manuel says x = 1/4
8. Kreshnik
that's correct. Well done ! ;)
9. yrivers36
Thank you once again :)
10. Kreshnik |
PDE and differentiating through the sum
1. Jan 28, 2015
joshmccraney
Hi PF!
I'm reading my math text and am looking at the heat eq $u_t = u_{xx}$, where we are are given non-homogenous boundary conditions. We are solving using the method of eigenfunction expansion.
Evidently we begin by finding the eigenfunction $\phi (x)$ related to the homogenous boundary conditions. From here we say the solution takes the form $u(x,t) = \sum a(t) \phi(x)$. When plugging this result into the heat equation we are not allowed to differentiate w.r.t. x under the sum. The reason evidently is because the boundary conditions for the actual problem and $\phi(x)$ do not agree (the problem has non-homogenous B.C. yet the eigenfunction satisfies homogenous B.C.).
Can anyone tell me why not satisfying the same B.C. conditions implies we cannot differentiate w.r.t. that variable $x$?
Thanks so much!
2. Jan 30, 2015
Orodruin
Staff Emeritus
The point is that you can approximate the solution arbitrarily well (in a distribution sense) with a function that does not fulfill the BC, i.e., the sum will converge to the solution everywhere but at the boundary.
A different way of taking care of your boundary conditions is to make a change of variables to transfer your inhomogeneity to the PDE rather than the BC. The resulting PDE can be solved using series expansion of the resulting inhomogeneity. |
## Sum of log squared terms?
Hi all,
I have a summation series which goes like this,
S = [log(1)]^2 + [log(2)]^2 + [log(3)]^2 + ....... + [log(n)]^2
Since each term is square of the logarithm of a value, I think there are no general tricks which can be used to solve this.
But is there any way to approximate the value of this summation?
The problem I am facing here is that n is very very large and it is not possible (time-wise and memory-wise) for my program to evaluate every term. So I was hoping for some approximate solution in terms of 'n'.
Thanks,
yogo |
# Newton's Laws of fluid motion
Can someone explain the similarity between friction and viscous force?
This is what I have understood:
Friction and viscous force come into play in presence of relative motion. They are dissipative and both are dependent on a constant ,unique for a medium.
1. The very famous saying "A body is accelerated if there is an external force acting on it". Is it violated for liquids ? Every layer is acted upon by an external force (viscous friction) but the acceleration of a particular layer is nil.
2. Now why does friction brings a body to rest but viscous drag doesn't stop a liquid completely ?
3. Friction doesn't maintain the velocity of a body but viscous force does not change the velocity of a particular layer.
4. Why does viscous force depend on area and velocity but friction is independent of it?
Assistance using simple terms will be appreciated.
• Is there a way to consolidate all of these questions into one big overarching question, or should this be multiple separate questions? Mar 16 '21 at 8:00
• By friction you mean friction between solid surfaces, right? Mar 16 '21 at 8:12
• Moreover, your point 3 is wrong: it is not true that viscosity mantains the velocity of a layer (steer the fluid in a cup, after a while it stops). Similarly, in astrophysics, differentially rotating bodies (i.e. fluid bodies having non-uniform rotation), after a while start rotating uniformly because of viscosity: the velocity of layers changes in the process. Mar 16 '21 at 8:18
• Also point 2 is wrong, and it depends on the context. If the fluid is isolated, then the total momentum is conserved (this is it does not stop, but maybe reaches a configuration witha certain angular momentum or linear momentum). Also in the case of friction the same conservation is valid, but you have to consider the total system (both surfaces). If one surface it the planet and the other is something sliding, then the analysis performed on the partial (small) system hides the conservation of momentum. Mar 16 '21 at 8:23
• @Quillo...point 3.. but wont the rotating bodies stop rotating because of viscosity ? or does it have some other reasons wayy outta my league ?
– puma
Mar 16 '21 at 9:01
2. Friction (in the naive sense) is a constant force, and hence brings a body to rest with a constant acceleration until the friction breaks down at rest (a half parabola in the $$x(t)$$ diagram). By contrast, viscous forces are not constant but proportional to velocity, so the smaller the velocity has already become, the smaller the "braking" forces get, and so the motion never stops (a decaying exponential in the $$x(t)$$ diagram). Actually both, friction and viscosity (applied to macroscopic bodies instead of fluids) can both be put under the umbrella of nonlinear velocity dependent forces. For viscosity the "nonlinearity" is just "linear". For friction, the dependency is constant up to a small threshold velocity where sliding friction breaks down and (usually higher) sticking friction begins to take over. In the sticking regime, elasticity starts to become more important, so there is a more or less smooth transition in the $$F(v)$$ diagram between stick and slip. This causes challenging stick-slip phenomena (also in the numerical treatment) in technical systems, that cause vibrations (think e.g. of a wine glass, the rim of which you rub with your wet finger, causing a tone). For these more accurate models of friction, see for example this page |
6.7 Write down the reactions taking place in different zones in the blast furnace during the extraction of iron.
During the extraction of iron, the reduction of iron oxides takes place in the blast furnace. In this process, hot air is blown from the bottom of the furnace and coke is burnt to raise the temperature up to 2200 K in the lower portion itself. The temperature is lower in the upper part. Thus, it is the lower part where the reduction of iron oxides () takes place.
The reactions taking place in the lower temperature range (500 − 800 K) in the blast furnace are:
The reactions taking place in the higher temperature range (900 − 1500 K) in the blast furnace are:
The silicate impurity of the ore is removed as slag by calcium oxide (CaO), which is formed by the decomposition of limestone ($CaC{O}_{3}$). |
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