darklight03/StackMIAsub huggingface dataset:
Consider a simple chemical reaction, such as the association of two hydrogen atoms within the gas phase to form one hydrogen molecule. It is known that this reaction is related with energy release in the form of heat because the hydrogen molecule is more stable than the two hydrogen atoms. Within a gas containing hydrogen atoms and hydrogen molecules, kinetic energy can be stored in several modes, including translation, vibration and rotation. If the energy of the reaction is to be released as heat, then directly after the reaction the temperature should slightly increase locally near the reaction. This local increase of temperature results in a transfer of energy to the "bath", and this transfer of energy is the heat. Which one of the above mentioned modes of kinetic energy do you think is first activated directly after the reaction ? If I imagine two hydrogen atoms that decide to make a covalent bond at some "t", then directly after time "t" they feel a strong bonded radial force, and directly before they feel a weak "dipole force". So they should be pulled toward one another, possibly overshooting the equilibrium distance of the molecule, then relaxing back. So I guess the energy is dissipated in the vibration mode. For my understanding, I would first like to focus on the case without radiation.
I have been reading this article about the quantum vacuum state, and in the section that I linked to, there is a video showing an experiment that shows visibly that quantum fluctuations are actually happening (see the video in the link). The quantum fluctuations are visible because they amplified them using Spontaneous parametric down-conversion Now from what I learned here, quantum fluctuations (or virtual particles) do not exist (and links therein). They are just tools of perturbation theory in QFT when taking into account interactions to make the mathematics work. Another reason I learned is that the fluctuation-dissipation theorem states that when a system is in fluctuation, the energy dissipates as heat or other forms of energy. So then, the vacuum cannot be fluctuating. I seem to be confused now. Is the video fake or is what the video/wiki claiming not true and is something else entirely? This question is sort of a follow-up to my previous question.
I'm trying to figure out if a hexagonal grid can embed rectangular coordinates in whole numbers of "Y-steps". In the image below, one "Y-step" is the spacing between red hexagon centers in the Y dimension. For some arbitrary hexagonal grid size, how many hexagons do I need to produce some whole-valued number of "Y-steps" in the X dimension? Another way to ask this might be: Select four hexagons whose centers create the corners of a square. In the hexagon grid orientation shown below, how many horizontal hexagons are needed to create such a square, and then how many vertical "steps" are needed in the Y dimension? Both X and Y values need to be whole integers. In case it helps, this site provides great info in hexagonal coordinates, but I've not figured out how to pin down a way to solve this. We are using the "pointy top" orientation.
I would like to perform something that resembles a curve fitting optimization but for which i could not find much info. Lets say i have a function that yields a time series. What i would like to do is tune the parameters of this function so that the time series it yields has a specific shape. For instance i want it to output a step, or two steps back to back. What i don't know (or care about for that matter) is the height of the steps. For a single step, a naive solution would be to simply take the average of the output and compute the RMSE of the output to it's average and minimizing it. However this gets more and more complicated for more complex shapes (the two steps example is already a pain with this method) Would there be a mathematical tool that would facilitate this?
Classical mechanical systems observable on a dynamical scale are subject to Newton's laws. In this case, knowledge of the Hamiltonian allows us to minimize energy taking into account inertia. This allows us to calculate trajectories, find equilibria and derive many properties. Classical mechanical systems consisting of large sets of particles are subject to Boltzmann's law. In this case, knowledge of the Hamiltonian allows us to minimize energy and maximize entropy. This allows us to calculate phase space weights and derive many properties. Is it possible to proof that the two approaches are equivalent in some cases ? That is, proofing all assumptions made in micro-canonical and canonical formalisms based on Newtonian mechanics ? Or that the average properties generated by Newtonian trajectories are equivalent to Boltzmann average properties ? Or is it maybe possible to observe some kind of transition between the two cases if they are not equivalent ?
I have observed that when an insect is electrocuted in a bug zapper, there are typically a few sparks or flashes of light. Sometimes the insect will catch on flame in a tiny fire, and the body will burn for a few seconds before stopping burning. The lights and flames stop after a few seconds, but the insect body often, instead of falling, remains in position still connecting two wires. Given that the body is still in position connecting two wires, why is it that after a few seconds, sparks or flashes of light stop appearing, and any fire is extinguished? Does that mean that electricity is no longer flowing through the insect's body, and if so, why does the electricity stop flowing if the body is still connecting the two wires?
Is it okay (in terms of usage) to use present participle clause for an action that follows another action as a result? For instance, the following sentence seems correct to me: The bomb will explode, sending shrapnel everywhere. Yet the following sentence does not correct at all to me: I will run one mile to reach my target, grabbing him. I don't know how I feel about this sentence, I think it feels fine: The cat leaped into the air, landing in the river. This sentence feels pretty wrong: I noticed my target, shooting until I hit him. But this sentence feels fine: The man took off from one end of the street, reaching the other side just in time. And then obviously this sentence feels not great: I will live a good life, dying. But then this sentence feels fine: I will live a good life, dying when it reaches its conclusion. What's the differentiator here? Are my feelings correct?
The following problem has bugged me for a while, ever since I noticed it. On the Visible Spectrum Wikipedia, the following is the visible spectrum: Now, in Photoshop, or really any colour picker, the hue slider looks something like this: Or sometimes this: I noticed that in both of these, the colour loops back to red. Why is this? I believe that this doesn't happen on the visible spectrum. The visible spectrum goes from a violet-ish colour to a maroon-ish colour, with a whole range in between. But where does the magenta colour from the hue slider fit in? I take it that it is possible to have a purely yellow object, or a purely teal one, as it is on the colour spectrum, yet are magenta things and pink flowers inherently reflecting multiple wavelengths of light, from opposite ends of our particular viewing spectrum? All of this seems awfully odd to me, so I was hoping someone might be able to clear it up.
I understand why the temperature of the hot reservoir has to be minimally higher than the temperature of the hot working fluid during the isothermal expansion phase of the Carnot cycle (to limit new entropy being produced in the working fluid that we have to get rid of). But during the isothermal compression phase why do we need the cold reservoir to be only minimally cooler than the cold working fluid? The working fluid looses the same entropy independent of the temperature of the cold reservoir, so why do we need to minimize the new entropy created in the cold reservoir? What is wrong with just letting the cold reservoir get more and more entropy as long as the working fluid returns to the same state as before the cycle?
So, as I was browsing a bunch of the tachyon questions throughout the years in this forum, and an oddity of these hypothetical faster-than-light particles came to mind. Ordinary particles with mass always have an inertial frame of reference where they are at rest, thus their rest mass can be measured. Lightspeed particles, while never at rest, have an invariant velocity, so different frames of reference can agree on their energy. Not so for tachyons. Tachyons not only are never at rest (like lightspeed particles), but their measured velocity is frame-dependent (like ordinary particles with mass). So, my question: Question: Is there anything analogous to a rest mass that can be used as a common point of reference when working out the mass of tachyons, or is it completely frame-dependent? And, no, we cannot say the tachyon's frame of reference, because they cannot be treated as observers (same as with lightspeed particles, we cannot treat a photon as an observer).
Electricity is used for many things. One of the biggest uses is transporting energy, almost instantly, from a power plant to the machines in my home and many others'. I was wondering if a similar energy transport grid could be created using a fluid under pressure. The power plant would use its energy to pump a fluid into the main pipe, which extends all over the country, with many sub pipes coming out to each house. The high pressure liquid would act like high voltage electricity, ready to be tapped into by a user. At home, one would open a valve in the pipe, causing high pressure fluid to come out. This jet could be used to spin a rotor mechanically, in other words, energy was transmitted almost instantly from the power plant to my home. We would probably need to have the used fluid go back into another pipe which goes back to the power plant to be pumped again. In other words, something similar to an electric circuit but using fluid instead of electrons. Knowing about the analogy between electric current and hydrodynamics, I was wondering if my strange idea could be practical or at least physically valid.
I hope this isn't the completely wrong community for my question, please let me know. I did search for 'varifocal' and got some hits, it seems (still getting used to these glasses, so it is a bit hard to use my PC) So, it seems that when you get these glasses - we call them varifocal in UK, not sure if that is the international name? - they have these three zones with different strength, but for some reason, there are two blurry areas in the lower right and left corners. The top has the distance vision all across, but the computer- and reading strengths are only in the middle. I haven't been able to find an explanation online so far; does anybody here know of a good, technical reason for not simply providing three zones in the full width?
Even though a black hole has a Scwarzschild radius that indicates a finite small distance to the center of the hole, the distance traveled by an infalling particle seems a lot bigger than the Schwarzschild radius due to the extreme curvature of spacetime. An infinite curvature even seems to imply an infinite distance. Two particles falling into the hole, one after another, end up spatially separated. This holds true for all particles that fall into it. This seems to imply that the distance traveled is actually infinite. I mean, if particles end up spatially separated because of spaghettification, and they all fall the same distance to the singularity, only an infinite distance will do, so it seems. What (if) is the flaw in my reasoning? EDIT I'm not sure if the linked question is a duplicate as it asks about the time it takes to freely fall to the singularity. I'm asking about the distance traveled, and I read in a comment by @MichaelSeifert that there is a good explanation for why the concept of distance isn't well-defined in this case. I can't see why that is so. What if you, the freely falling indestructible observer, have an infinite rope, one end of which you attach somehow just above the horizon? Can't you see how much rope has rolled off from your device when you hit the singularity?
Short introduction to my understanding: As far as i understand, virtual particles are usually defined to be the internal lines in Feynman Diagrams. But we know that those are just useful tools to calculate amplitudes in interacting quantum field theories. In a free theory I have no interactions, hence no internal lines and no virtual particles. Virtual particles show up when, in interacting QFTs, we have the so called contact interactions showing up in the perturbative Dyson-Schwinger equations as deltas. My question: Can we regard virtual particles solely as mathematical tools needed to make predictions in perturbative interacting theories because we don't fully understand how interacting theories work? (I mean how they work in a non-perturbative setting) If the latter is true, and from my actual understanding I think it is true, what is our "hole" in the understanding of full interacting QFTs?
I was reading about effective field theories and wondering how much an EFT can tell you about the ''underlying'' theory which is then reflected in the EFT. Can one extrapolate back from what one sees in the EFT to derive features of the theory for the high energy degrees of freedom? As an example, general relativity is considered to be an effective field theory for quantum gravity, but that does not tell us much about what the correct quantum gravity theory would look like, with many people arguing that this underlying theory would be a string theory and not even a field theory. However, are there cases where one can say more or come to definite conclusions about the underlying theory? What is the systematic way for doing this? For example, in lecture notes of Pich on EFTs with Nambu-Goldstone modes, he mentions that one can ''uncover fingerprints of new physics scales'' from couplings in the EFT.
So, just to expand on the question in the title, I know group representation theory, and especially character theory, are quintessential tools for anyone hoping to study finite groups. That said, from what I've seen and read, some people study characters in and of themselves (say, density of zeroes, Brauer characters, etc), while another set of people uses them as tools for studying questions concerning the groups themselves (i.e., it's not clear from the get-go that characters will even get used; they are a part of a toolkit). My question is: what's the intersection between these two sets of people? Can a person spend some time working on Brauer characters and blocks and then move on to study, say, the subgroup structure of finite simple groups? Or are the areas far enough apart that character theorists simply don't have enough baggage to work in general problems on finite groups and vice-versa? Sorry for being a bit "vague", perhaps... I'm just very curious about the distinction (if it even exists at all!), since I really love both topics! Thanks so much in advance!
(Honestly I fear this is borderline off-topic... be gentle with the downvotes ;-)) Most of the packages I've written are for personal use but a couple of them are used by some other people. These packages change relatively often as I'm constantly implementing requested features. Right now I tend to ship out the most recent stable version by e-mail but then I get either answers of people that are not interested any more, or requests from other people who aren't in the mailing list yet. I do not want to upload the packages on CTAN for two reasons: There's maybe a dozen users. It's highly unlikely the packages will be useful to someone else. I find there is enough bad code on CTAN without me contributing to it. For now I've got an institutional home page but that may change any minute, so posting the code there for download (which I've done) might not be a long-term solution. Any advice? (My personal texmf tree is on Dropbox, if that may spurt a solution.)
It seems correct to write "A host of tools exists..." or "A range of tools exists...", i.e. the verb reflects the fact that you are referring to one collective noun. But, if I want to continue to talk about that collection of things, it often seems natural to say ". They aim to solve..." or ", which attempt to model...", i.e. now I am referring to the capabilities/intentions of the things within the collection. Which is strictly correct? And putting strict grammatical rules aside, which is an English speaker most likely to say? a) "A host of tools exist, which aim to solve..." b) "A host of tools exists, which aims to solve..." c) "A host of tools exists, which aim to solve..." My instinct is to avoid the construction and write "Several tools exist, with the aim of solving..."
It is currently understood that gravity is not actually a force, and a fact that is often used to show this is that an object in free fall doesn't "feel" that it is accelerating and is thus an inertial frame. However, it seems to me that Newtonian mechanics can already predict that this will be the case. Since all the parts of the object are being accelerated by the same amount simultaneously (at least approximately, like near the surface of the Earth) there won't be a tendency for this object to contract, and thus "feel" that it is accelerating. This isn't the case, for example, when I push the same object. In my understanding, the force needs to be communicated from the point I apply it to all the rest of the object, and this delay is the cause of a contraction/increase in internal forces or tension, allowing it to effectively "feel" that is accelerating. Now, suppose that there is a uniform field that accelerates any particles with constant acceleration. Like gravity, a free object in this field will not be able to detect that it is accelerating, since all of its particles are accelerating equally at the same time. My question is: Is this object inertial, or is it only inertial if this field is a gravitational one?
What is the current consensus about the age variation of the existing galaxies in our observable universe? Not to be confused with the age of very distant galaxies as observed today by our telescopes which is actually observing these distant galaxies as they were many billions of years ago in the early formation but instead I am asking about their absolute age today assuming they still exist? I mean, a hypothetical observer located in these very distant galaxies and looking at our home galaxy would also see our galaxy not at its current state but how it looked like billions of years ago. I am not asking this but if all the galaxies were formed more or less at the same time according to the Big Bang theory? In general how you estimate the age of a galaxy?
Let's assume that a cylindrical magnet is clamped by an horizontal arm extending out of the wall. The top of the magnet is its north pole and the smooth face facing down is its south pole. If I bring another cylindrical magnet and position it perfectly in line below the fixed magnet, with its top being its north pole and the bottom being the south pole, would it be possible that the weight of the magnet going down and the magnetic force attempting to pull the magnet upwards balance out so that the magnet can levitate in mid air? Conceptually, it seems to make sense as in this case, the magnet is not prone to flipping since it poles facing each other are not repelling. However, I'm not sure if this violates Earnshaw's theorem. It it's not possible, then why isn't it possible? Did I miss something in my assumptions? And if it is possible, Is it also possible for the levitating magnet to rotate about its central vertical axis and still remain suspended in space?
I'm looking for an accurate method to measure the tension in a guitar string, without using a sonometer setup nor by measuring the frequency. the current method that I have in mind is to measure the force perpendicular to the string and the string's displacement, and then try to resolve the vectors (the method is explained in more detail here), but I don't think that is an accurate method for a couple of reasons: we have to consider the uncertainty of the newton meter and the ruler the propagation of uncertainty when resolving vectors makes the final uncertainty much larger even after resolving the vectors, we are calculating the tension in the bent string, not the equilibrium position. are there any other methods I can use to measure the tension more accurately?
Clicking through the OEIS I found this sequence that seems curious - the number of "labeled" groups. It cross references the usual sequence of the number of groups up to isomorphism (the very first sequence in the OEIS) as well as saying it is "a sequence related to groups". So I've tried to look up this concept, but Google with "labeled group", "labeled group maths", "labeled group theory", and so on, to no avail at finding anything. Groupprops (essentially a wiki for group theory) doesn't seem to have anything either. I've clicked through the links on that OEIS entry and cannot find anything of help. So as a last resort I'm asking here (I know this isn't necessarily the kind of place for definition questions though, sorry). So, what is a labeled group?
Neither my wife nor I have English as our mother tongue, but we use English to communicate to each other, which sometimes causes confusion. My wife often uses the expression "until now" to mean "so far" or "yet", meaning that the action is not yet finished. I didn't receive any answer from the landlord until now. To me "until now" means that for some time she didn't get answer but now (recently), she did. So I'll usually reply something like: Nice, so what did he say? And she looks at me weirdly, as if I would have asked something silly and we both laugh. My question is. Does "until now" always imply that the action you are talking is now finished, or can sometimes be used with the same meaning as yet?
If i place some charge on a conductor then it will distribute itself in such a way that electric field everywhere inside is zero. My text book says that only one kind of such charge distribution is possible. Or if i place charges outside the conductor then charges will be induced on the surface of a conductor to make field inside zero and again such charge distribution is unique. Intuitively it all seems correct but i am trying to figure out right arguments for this. One such argument is that suppose i place some charge on conductor then i can solve poisson's equation to find potential at the surface(at boundary). Charge distribution outside the conductor is known. Then uniqueness theorem says that only one such potential function is possible which satisfies the given/known boundary conditions and poisson's equation outside. Since a particular potential function corresponds to a particular charge distribution the charge distribution must also be unique. This argument seems correct to me but at the same time something seems missing. Am i correct?