darklight03/StackMIAsub huggingface dataset:
In the Vlasov variant of Boltzmann equation, the Coulomb pair forces are included via the force term that appears as the prefactor of the derivative of the density with respect to velocity. In that case, one is effectively calculating a mean force or a "force field" by averaging over all the pair forces. The average is obtained by an integral over the pair potential weighted with the density. Since this Vlasov approach allows to have good analytical insight into systems mainly governed by Coulomb forces (i.e Landau damping and other), is it possible to apply the same approach for Lennard Jones pair forces ? I could not find references and I do not understand why this is the case.
I'm junior student in physics major, and i didn't study QFT or other graduate course yet, just undergraduated QM. Recently I take brief explanation class about SUSY, and in the class I heard that simple harmonic oscillation (SHO) is important because it is unique potential which is invariant under some gauge transform therefore it doesn't change some kinds of scattering properties (reflection coefficient, etc). Is SHO only example which is invariant under the gauge transform in SUSY QM? In the description, what kind of gauge transform is meant? How does the gauge transform relate to SUSY?
I have a bit confusion of understanding. The central limit theorem in statistics states that, given a sufficiently large sample size, the sampling distribution of the mean for a variable will approximate a normal distribution. But the definition of sampling distribution is the probability distribution of a statistic that is obtained from many random samples of a specific population. I don't get it and see a contradiction of how getting a sample distribution from one large sample as CLT states while sampling distribution definition says it needs more than one sample?
I am trying to understand the hall effects and have a few problems with them. So let's consider the classical Hall effect. We know that we consider a sample, where the electrons flow, we apply the perpendicular magnetic field, and the electron's motion is curved so they reach the sample's edge. There appears a "new" electric field. On the other hand, the quantum Hall effect sometimes showed that electrons move in a closed circular orbit, but not in the edge where they can go through "skipping orbits". So my question is, why in classical hall effect the electrons teachers the sample's edge and don't just move in a circle? What is more, do they move also along the edge like in the quantum hall effect?
I want to say that a particular painting never gets old because you notice something new each time you look at it. What is a noun to describe this quality? An example sentence would be: "Due to the xxxx of the painting, you see something new each time you look at it." An example to the opposite of this word would be a pop song that you get bored of after a few listens. Compound words are fine as long as they are nouns. The answers to this question come close to what I'm looking for but don't fit exactly since in my situation it's not the object that changes but it's so complex that your perception of it is different each time.
Leaving school seems like such a huge event in our lives. There's this single summer where you have more freedom than you've ever had before with a group of people you've grown up with before you all go off in different directions in life: work, uni, travel, whatever. It might be the last chance to spend time with these people before you ever see them again, and so people want to make the most of this time, moreso than other summer breaks. It therefore seems strange to me that I've never heard that summer be given a special name, even in slang. Whether it's a formal term, colloquialism, slang, or TikTok hashtag, has anyone ever heard a name for this liminal period straight after compulsory education?
In my understanding, light works as follows: every point in space where there is light, this light works as a point source. When we progress in time, the light spreads out from there in all directions (spherically). The new locations where the light is now, act as new point sources. From this it follows that the light from a laser beam would go in all directions, not just in the direction of a laser. However, we see in practice that (most of) the light only goes in the direction of the laser. How is this possible?
I'm studying about method of undetermined coefficient. But i can't make sure when method of undetermined coefficient can be used. I know that the differential equation need to be non-homogeneous and the non-homogeneous terms need to speical form such as polynomials, trigonometric functions, or exponential functions. what I'm wandering is following: To use the method of undetermined coefficient, the coefficient need to be constant? and the differential equation need to be linear??
According to the dictionary, the "e" is optional when a word ends in "-dg(e)ment". Dictionary examples: oxfordlearnersdictionaries.com: "acknowledgement" (also "acknowledgment") oxfordlearnersdictionaries.com: "judgement" (also "judgment", especially in North American English) oxfordlearnersdictionaries.com: "abridgement" (also "abridgment") ...And some other similar examples from the internet: ledg(e)ment, lodg(e)ment, grudg(e)ment. Of these, only judgment is explicitly said to be found "especially in North American English"; regional distinctions don't seem to play a role in any of the other options. Is this statement verifiable? What is the evidence, and how widespread is the variation? Is there a historical reason for judgment being unique in this sense? (If it even is unique...)
Given two points and a line in the plane, is it possible to construct a circle tangent to the line which passes through the two points using ruler and compass? For those who don't know, these are the rules of ruler and compass constructions: you start with a set of initial objects (points, lines, etc.), at every step you can do one of the following: Construct a line or segment between two points in the set Construct a circle with a segment within the set being its radius Intersect two curves within the set Each of these moves add the outcoming curve/point to the set.
If I understand correctly, the intensity of light is proportional to the number of photons hitting a certain area. If we then look at a single photon when described as a transverse wave, is its own energy equal to the square of the amplitude of that photon's wave? If we have a high energy photon this would mean the amplitude would be large, and the converse for a low energy wave.
For example a car with a known speed and mass crashes with a completely unyielding wall. The car has a crumple zone, (and you know the modulus of the crumple zone) so it doesn't stop immediately, but how can you calculate the time it takes for it to stop? I've been reading a relevant article (Analytical approach for vehicle body structures behavior under crash at aspects of overloading and crumple zone length) but their equations are beyond me. First question, had a hard time finding any help with this. Thanks! The journal article in question: Analytical Approach for Vehicle Body Structures Behaviour Under Crash at Aspects of Overloading and Crumple Zone Length
I am a Physics Major. I have done an undergraduate level course of differential geometry. I want to get into symplectic and Riemannian geometry, but I would like to start over from differential one again. I found this book that seems to cover what I want, but I am not sure if it is a good book or not. Can someone recommend a book or other sources (or even roadmap of multiple books) that start from differential geometry and teaches till (or gives proper introduction to) Riemannian and symplectic geometry (physics perspective is preferred but not necessary).
Consider that I have a piece of paper, and I do a drawing on such paper. Now, consider the set of all possible "transformations" I can apply to this piece of paper that do not tear it. For example, I can rotate it, I can do an origami, I can make it into a cylinder... Is there a name for the set of all of such transformations? Could I say that all these transformations are within the conformal transformations, i.e. since conformal transformations also have scaling, could I say that the set of such transformations that do not tear the paper are within the set of conformal transformations?
I've known that the distance between a compact set and a closed set is zero if and only if they are not disjoint, and I can also find counterexamples in which two disjoint closed set has zero distance. But how about a closed set and a bounded closed set? Does there exist a closed set and a bounded closed set with zero distance between them, and they are disjoint? The counterexample should not be found in Euclidean spaces though.
I use xsim to create exams and it works very well. I kove the way it handles exercises and solutions. Now I'm starting to create a script and I was wondering if there is a way to hide the numbering in exercises so I can just write an unnumbered exercise and hide the solution for the students but leave a blank space for them to write in.
I have an experiment where I have to find the damping coefficient of a compound pendulum situated in a clock. It swings at a very low amplitude, so I think I can make a small angle approximation. Because if I assume it has SHM, I can simply use logarithmic decrement to find the coefficient, which would make my work a lot easier. I cannot find much literature on whether a compound pendulum can even display SHM.
This is a naive question. I am studying the surface-adsorbate systems using DFT calculations implemented in VASP. By setting LVHAR = True, I obtain LOCPOT which contains information about the ionic and electrostatic potential. I would like to clarify whether this information is actually the electrostatic potential or the electrostatic potential energy. My source of confusion is that VaspWiki states that the electrostatic potential is written in terms of eV, which indicates it should be an energetic quantity.
The first pair of these sentences with perfect participles, shows a reason while the second shows a time, and this is how the teacher taught me their meaning, so I want to know why one is reason and the other is time. How can I know that one describes reason and the other time? Please convince me. He has failed four times already, he doesn't want to appear in the examination again. (Reason) Having failed four times, he doesn't want to appear in the examination again. (Reason) He has a lot of money in business, he doesn't want to risk his money any more. (Time) Having lost a lot of money in business, he doesn't want to risk his money any more. (Time)
I am a person who gets bored all the time, so I found that counting something in my head helps occupy my time. I started counting in binary, but after a while this started getting old as I was doing it in the back of my mind, so I got bored again. So, my question is, can you count up prime numbers in your head using a "mind-friendly" formula, or is there something different you can count that keeps your mind busy?
In the adjoining table, a dot indicates the combination of chemicals that cannot be placed in the same location as the other because of safety issues. If a company is dealing with the chemicals a,b,c,d,e,f,g,h,i,j listed in the table, what is the minimum number of storage locations needed by the company? My idea of the solution is something like this: I start with 'a'. I can collocate it with c,d,f,g,h,i, but not with b,e,j. But then, I note that d and f cannot be collocated. How/where do I go from here?
I'm learning the grammar of relative pronouns; I thought all relative pronouns should be at the start of a clause, and then I learned that pronouns can be put after a preposition, as in "The bed on which I was lying...", but again, I came across some other examples that showed that we can put more words before the relative pronoun, as in "The bed, the owner of which we had seen previously, ...", or "The bed, lying on which was a small cat, ..." Does anyone know what are the rules? Can we put the relative pronoun anywhere in a clause? What about these sentences: "The bed, we had seen the owner of which previously, ..."?, are they grammatically correct?
A ball is bouncing elastically after its collision from ground so can we call it SHM as it is oscillating and also it is periodic and it seems similar to other cases of SHM? If yes then where is it's mean position? But the thing is in SHM force always opposes direction of motion but here it is always in the same direction that is downward force(due to g). Also in SHM force is zero at the mean position but here force is never zero. There can be some flaws in my understanding of SHM as I am new to this. But all the answers are welcome!!
I have generators for my group in GAP. Additionally, I possess a specific unitary element and wish to determine whether this unitary element arises from the Lie algebra of my group's generators. Initially, I considered a brute-force approach, intending to compute the matrix exponential of a particular generator of the group. However, I couldn't find any matrix exponential function in GAP (e.g., expm, ExpMat, MatExp, etc.). Now, I have two questions: How can I compute the matrix exponential in GAP? Is there a systematic method to compute the Lie algebra of the group generators, allowing me to identify my specific unitary element, and subsequently terminate the computation in GAP?
I am doing a review for an article where I need to write some equations myself and want/have to stay anonymous. So far I plan to just LaTeX my notes, compile them with latexmk -view=pdf and send them in. My fear is that latexmk/pdflatex adds metadata that will break the anonymity of the review process. I checked the result with pdfinfo, and could not find info that would identify me in this case. But in general I would like to not only rely on some defaults of pdflatex, but to know if there is a cheap way (preferably via CLI options) to guarantee, that there is no identifying metadata.
I'm making a roster in a spreadsheet of all the current employees, volunteers, sports coaches, and other workers at a school. What is the best way to label the column showing if someone is Full-time, Part-time, Volunteer, or On-call (like substitute teachers)? What word represents this? I already have a Status field denoting Current vs. Former. Should I just merge this unnamed field so that Current becomes more precise as Full-time/Part-time and then Former? It's in the same logical realm, I think.
I am looking for an algorithm that could determine adjacent extreme rays of a polyhedral cone (extreme rays that share a face), given the set of inequalities defining the cone and an extreme ray for which the adjacent rays are to be determined. I was hoping there exist a python library that might already have coded up, but I could only find pycddlib, which seems to need to determine all extreme rays first. This seems inefficient to me: I was hoping there would be a method that doesn't neccesitate computing all extreme rays first. Thank you for help!
I want a certain path that I generate to remain hidden (so I use the path command without actually drawing it), so that I can use that path to compute other points of interest such as intersections, but I don't want that hidden path to affect the overall scaling of my shown figure. Is there a way to generate such a path that does not affect the overall figure scaling?
I am writing an article about data mapping, and discussing the various types of challenges in mapping data elements from one system to another. One of these challenges is assuming that a data element called X in one system is the same as a data element named X in a different system, simply because they are named the same. I am looking for a classification for words that have multiple, disparate meanings. My mind keeps jumping to polynomial, but I need that type of word that would relate to the meaning of words. Poly-meaning-al?
I am trying to understand the following to defintions of being "intrinsic". They are from Differential Geometry of Curves and Surfaces by Tapp. Question: In what way are these defintions consistent? To call quantity intrinsic if it can be expressed completely in terms of the first fundamental form makes sense. To me it seems that requiering invariance w.r.t. isometries captures different properties that I would expect from intrinisc properties. For example that deforming a surfaces should not alter the length of a curve on that surfaces. It seems to me that there are two types of intrinisc properties and that the "intrinisic geometry" consists out of these. Many thanks in advance for any hints or explanations!
If we consider a charge in space then we can draw infinite number of spheres (taking the distance between the spheres equal) around the charge and these spheres act as equipotential surfaces. Now, As the distance of all points on the sphere are same from the charge then why does equipotential surface gets farther apart when electric field decreases??i mean my questions is what is the problem with taking the distance between equipotential surface equal??
When someone tends to hesitate to acknowledge a problem and avoid involving trouble even if needed, is it ok to say in a negative nuance that He/She always has a "don't rock the boat" attitude. I found the below definition at Collins Dictionary and considering that, it seems that not rocking the boat doesn't necessarily have a negative meaning: If you say that someone is rocking the boat, you mean that they are upsetting a calm situation and causing trouble. (www.collinsdictionary.com I'd like to describe a person who usually avoids troubles and never speaks up regarding existing issues such as social issues with a negative implication. I'd appreciate it if you tell me appropriate phrases to describe such a person.
I'm struggling to explain it, but some examples are (mention does not imply endorsement!): Sir Keir Starmer -> Sir Kid Starver (criticism of his stance on child benefits) Benedict Cumberbatch -> Butterscotch Candybatch (surreal humour) Financial Conduct Authority -> Fundamentally Complicit Authority (critical of regulatory capture) Saddam Hussein -> Sadman Insane (general derision) These are nicknames, i suppose, but they are a specific kind of nickname.
I was attending lectures om holography where the lecturer kept on mentioning that a QFT lives on a Cauchy slice. What does that mean? Is it such that each point of the slice is associated to a unique vector in the Hilbert space? Can this be generalized to QM? Does that mean that the harmonic oscillator lives on an integer lattice? Is this geometric correspondence the motivation behind the operator state correspondence?
I am just a high school student. I had already heard that we can't determine the exact location of big bang. So now i have a question can't we approximate it? Like say divide the observable universe in many grids and you take the Average age of each grid and do this for all the grids. I assume intuitively that on average the parts of the observable universe which were formed earlier would be closer to the point of origin of the big bang right? I know that there are other effects to consider such as expansion of space but still it is not possible so my question is why?
Let (B, S) a multi period binomial model that is arbitrage free. Prove that the unique time for an American call is the maturity T. I would like to prove that the unique optimal exercise time for an American call option is the maturity time T. My idea is to prove this result by contradiction. I want to find an exercise time t<T, such that there exists an arbitrage opportunity, so that the value of the portfolio at time t is greater than zero, starting with an initial value equal to zero. Is this a good idea, and how can I find such strategy explicitely?
Let's say a small magnet is attached with its South pole on to the north pole of a bigger magnet vertically.There is no friction between the magnets so this means the normal force increased due to the attraction doesn't have any effect on its tendency to fall.My question is that : Does the small magnet slide down OR Do the magnetic field lines have such a property to pull the magnet up. Also, what changes are seen if the small magnet is attached vertically to a iron bar (frictionless again).
I'm attempting to self-study real analysis and was looking at the popular textbook recommendations. So far, I've seen Abbott and Cummings for beginners. With Rudin, Stein, Bartle, and Zorich for more advanced books. My question is : What book is the sort of "Bible of Real Analysis" or reference book, where if one knows the book from cover to cover he would have a colossal grasp on the subject. To clarify my question, I mean a textbook that would cover the whole surface of analysis after learning it from a more elementary book such as Abbott or Zorich.
I understand that if there are different capacitors of different capacitance then they can store same charge at different voltage differences only. But I wanted to understand that why the above happens when the capacitors are arranged in series...I want to know the mechanism behind that if we arrange different capacitors in series then they store same charge at different potential differences.....why they store same charge only that is flowing in the whole circuit due to net potential difference of the circuit....why they don't store different charges whose sum is equal to the net charge flowing in the circuit?
I am currently studying the method of characteristics. So far I understand what I read in literature. The problem is that I didn't find a good explanation for imposing boundary conditions anywhere. Also, in the textbook problems, only the initial conditions are given. Please recommend me some literature where I can study how to impose boundary conditions on the solutions obtained using this method. A hyperlink to the literature would be of great help.
Are there any public stats that demonstrate how much literature is produced in LaTeX as opposed to Microsoft Word, Adobe InDesign, etc? When I search "latex market share" every single result talks about rubber/pillow/mattress companies and not the typesetter. From what I have heard LaTeX is heavily used in Math & Science theses, and I would like to find specific numbers to back that claim. Does LaTeX stand a chance against other software outside the Natural Sciences, its stronghold?
I have read a recently published paper on arXiv where the scientists claim to have developed a superconductor material working at room temperature and pressure. While it is clear that the results - if proven true - are preliminary, and that a lot of refinement would be necessary anyway, I am wondering what technological advances can we expect from such a discovery? Or, what technologies are currently impractical, impossible or unexplored due to the impracticality of currently industrially available superconductors?
Our teacher told us that objects store potential energy in them according the position of the object above the ground because of gravitational force. Like we are holding a box up and it stores potential energy, and if we drop it, its potential energy gets converted to kinetic energy. My doubt is, If, we send a rocket outside the Earth, then after some point, the influence of Earth's gravitational field nearly comes to an end, Then where does the potential energy of the rocket go if we stop providing it velocity (Like dropping the box)?
I'm studying a math book. There is a definition as seen below. A category is a class C of objects (denoted a,b,c ...) together with (i) a class of disjoint sets, denoted hom(a,b), one for each pair of objects in C... (ii) ... I want to ask which one of the following meanings should be deduced from this statement regarding the grammer rules; hom(a,b) is one of the sets of a class. hom(a,b) is a class of disjoint sets. The whole thing may confuse you so please just consider the part saying: " a class of disjoint sets, denoted hom(a,b), one for each pair of objects in C..."