darklight03/StackMIAsub huggingface dataset:
I read this fascinating paper (RG). The total collision is a well-known singularity in Newton mechanics: the distances become zero and, therefore, the potential becomes infinite. In a paper before that one above, Paula Reichert describes a try to calculate through the singularity using shape dynamics. In shape dynamics, the absolute background space is abandoned and only relative positions and especially angles are considered. Unfortunately, shape dynamics alone turns out not to be sufficient to calculate through the singularity. Then, in the paper above, they make a reference to this paper where they calculate through the big bang singularity by adding a scalar "stiff matter" field in the Bianchi IX universe. How can one understand this scalar field? Since shape dynamics doesn't rely on an absolute space as a background, it comes to my mind that this scalar field may be interpreted as space itself, space that surrounds every single mass point as a field. Is that interpretation right or wrong? If wrong, how can one get an understanding for this scalar field?
I'm attempting to develop an understanding of how equations are developed and wondered whether or not all equations started their development in the quest to document observable phenomenon or are there any 'purely synthetic' equations, which are developed from the basis of a thought in order to produce numeric results which are useful in some way. Put another way: Do observations of phenomenon drive the development of equations or does a conceptual need for a tool drive their development instead? The reason I ask, is because as someone who is a novice in mathematics (arithmetic skill, elementary algebra and descriptive stats), the choice of the construction of equations / their form always leads me to wonder why this form was chosen. In particular as I delve further into stats I have seen descriptions where certain equations may be adjusted based 'on ones need' which further deepens the difficulty of just using a tool blindly and wondering at what point or in what way I can develop the skill to discern how to choose how to alter an equation to better fit a desired outcome... I attempted to articulate this originally HERE, then asked about whether it made sense to start a new question HERE, but for lack of feedback in either, I decided to open this query and post any positive results as link backs to those two questions for the community's later use. If there is a better way to approach asking this please let me know and I'll be happy to adjust accordingly.
In a laboratory a vessel was built which can sustain high pressure, thermostats and pressure gauge were connected, assuming closed system, dry ice was introduced in closed vessel, the temperature of vessel was increased the sublimation of dry ice resulted in formation of gaseous carbon dioxide increasing pressure in vessel, the increased pressure and temperature resulted in liquid carbon dioxide formation, after more heating critical temperature was reached and superfluid carbon dioxide was obtained, at these state gas and liquid phases became indistinguishable, ice was put upon vessel surface which resulted in decrease of temperature and the liquid carbon dioxide appeared again. My question is if we see typical pressure vs volume diagram it is observed that above critical conditions it is not possible to condense fluid by reducing temperature since the point will lie above the dome, then how come we see condensation of superfluid carbon dioxide in our experiment ? Note: the boundary liquid gas interface was seen disappearing in as it's typically seen in superfluids hence it's confirm that we had superfluid carbon dioxide.
I encountered a proof that the empty set is a subset of every set via this comment(Is "The empty set is a subset of any set" a convention?) which shows that it cannot be false that the empty set is a subset of every set. Without necessarily going into a proof of how the empty set is a subset of every set, I was wondering why the fact that it cannot be false that the empty set is a subset of every set shows that this is true- could it not be the case that the concept of subsets is meaningless with regards to the empty set, and it is not enough to show that it could not be false; that this statement could neither true or false as it has no meaning in this context? Also, I would appreciate some explanation as to how this condition holds "vacuously" as far as terminology, as I have learned that for an implication to be vacuously true, it is true when it's hypothesis is false. Thanks
I have a very abstract at the same time awkward question. In many formulas across physics we need to take several approximations and often we derive formula from previous formula which had certain approximations in them. By error analysis we know that errors keep getting carried forward. Hypothetically can there be situation in future when almost every advanced formula we use, which is a result of derivation of several heavily derived formulas(I am referring several heavily derived formulas as those which are derived from highly approximated formula), be filled error quite significantly high and our calculations are thrown off by huge percentage of error and inaccuracy. Can the error propagation in formula and theorems be a major problem we face in the future of physics? (Please note that I am not talking approximations involved in process of integration.) I am just curious to know to what level the approximations we take, effect the calculations we perform.I know this is a very awkwardly framed question. If you have any suggestions on improving the language of the question or any other changes, please let me know.
Per wikipedia: natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving force. Let's take a wine glass as an example. The wine glass sits on a table, it is not visibly moving. But since natural frequency exists, therefore it is oscillate on some minute scale. Where does the oscillation come from? Is it from the electrons and protons that are whizzing inside of the glass and getting excited due to stochastic heat? Is it because protons are hitting the surface of the glass? Or is it oscillating due to the minor tremor in the earth? Or perhaps the minute attractive force exerted upon it by all other objects? In each case, it is clear that there is a driving force: heat, proton's impact force, tremor. So clearly natural frequency must be associated with a type of oscillation that's not any one of the above. So where does the oscillation come from instead? It seems that given any source of this oscillation, you can identify a driving force. Hence such driving force is never absent, hence there is no natural frequency. Are all objects naturally oscillatory and that natural frequency is like a fundamental aspect of an object, such as its 'mass'? If so, can we identify this natural frequency in some way? E.g., I want to know my body's natural frequency at this moment.
My admittedly limited understanding of QM is that it is a matter of probabilities whether or not a photon is (re)transmitted through a polarising filter and that these are a function of the relative orientation of the polarization of the photon and that of the filter. Unfortunately, a single detection event cannot distinguish a very likely from a very unlikely one. Since the same applies to a case in which the photon is absorbed, it seems that not much information, if any, can be gained, when what would be nice is that we could learn something about the polarisation of the photon for example. Even if statistics are collected on streams of successive photons, they're likely each to be oriented differently in relation to the filter, so not much information can be gained by examining the statistics either.
Currently i include png/jpg files with graphicx package compiling with lualatex, no problem, in particular no error message because of bounding box not found. This question is about historic ways to compile because I don't want to break old code. First question: Is it true that when compiling into pdf with any of the modern compilers like lualatex with graphicx package command includegraphics, there is no special treatment necessary to get a bounding box? Second, I seem to have no problem with bounding box either when compiling into dvi. What makes me a bit nervous is, that I remember that message. I am sure i used package bmpsize and also command ebb to get the bounding box and this was necessary to avoid the error message cannot determine the size of the graphic But I cannot remember the details. My question is whether the issue with the bounding box is resolved by new compilers, even if compiling into dvi or xdv. I made a remark by hand, that bmpsize does not work with xelatex. Is it obsolete? May it be the case that behavior depends on the source of the jpg/png? Are there aspects related with the dvi to pdf converters? Are there other formats needing bmpsize or ebb? Please feel free to mention other aspects also. I am afraid about dropping ebb or bmpsize when there is still a use case. In the meantime I found out that my problem is specific for texlive distribution. Seemingly miktex neither provides bmpsize nor ebb.
The following pop science video discusses the experimental difficulty of measuring "quanta" of gravity. It seems to me that a significant argument involves how it would be difficult to investigate fluctuations of gravity on the plank scale, requiring detection methods that have densities that would collapse as a black hole. In optics, one way of "seeing" a photon is by interfering it with using homodyne detection to interfere it with a strong signal. The strong signal essentially magnifies the signal, allowing it to be seen by detectors that are much less sensitive than single photon level. Could such a scheme be used to measure gravitons? For example, if strong gravitational waves can be detected by LIGO, shouldn't a sufficiently strong wave already be measuring the "amplitude" statistics of the graviton? Similar to how a local oscillator (in a balanced homodyne detector) measures the shot noise (amplitude statistics) of the vacuum. I suppose the issue is that this needs to be a particuarly strong wave signal so be above experimental noise?
In the diagram, OA is perpendicular to PQ. O is the centre of the circle. AC and EP meet at B on the circle and QC and AE meet at D on the circle. The goal is to prove that AP=AQ. I had tried to prove this by drawing a line through E parallel to PQ and I had proved some of the triangles were similar. However, this is the part where I got stuck. I drew a line parallel to PQ through E. I named the meeting point between PE and QC "G", between the line produced at E and CQ "F" and between CA and the line produced at E "H". I then proved that triangle CBG is similar to DEG, CAD is similar to BAE, HBE is similar to ABP, FDE is similar to ADQ and FGE is similar to PGQ. It is at this point when I got stuck.
Recently, I tried to understand the effect of Quantum levitation. I read that there is some well-known fact: Relative distance between superconductor and magnet must be preserved, because of flux pinning mostly occurred in type II superconductor. My rough understanding about this is, quantisation of (penetrated) magnetic flux inside the superconductor, and continuity of magnetic flux depending on the distance from the magnet, induces the fixation of relative distance (It couldn't move continuously after fixation because there is no no-jump-but-continuous motion). I could understand the second part of the video. I guess it's because of the circular symmetry of magnetic field. There is nothing hard to understand the story. However, what about the first part? If we rotate the magnet, then what makes the superconductor follow it? Obviously, it's due to the preservation of relative distance in layman's terms. However, could we more elaborate on it? For instance, in the context of classical electrodynamics, someone could try to explain this by the induced electric fields and currents from time-varying magnetic fields. However, it may not be an answer because of the quantum nature of a superconductor. The quantised flux varies by the time dependent magnetic field, but could we describe such a variation in terms of the motion of the magnet?, and so, could we derive and describe the equation of motion of a superconductor?
I've noticed this quite often from Disney sound tracks. Lyrics are in a certain rhyming scheme - one line happens and the next line approaches the end of the line, but the last word subverts the rhyme. I have looked at this question and feel it's related, but not the same effect. Example: "In Summer" from Olaf in Frozen Da da, da doo, a bubba bubba boo The hot and the cold are both so intense Put them together ? it just makes sense! Rata ta ta dada dada da doo Winter's a good time to stay in and cuddle But put me in summer and I'll be a happy snowman! Obviously, the expectation is that the word is "puddle" It feels like a lyrical version of deceptive cadence, but I cannot find a succinct term for such an effect. The linked question accepts the answer "Broken Lyric" or "Enjambment", which may still be the answer here, but I am certain that these are two different effects.
I am a first year student of applied mathematics. I currently find myself always trying to explain any phenomenon with mathematical models- the few ones (models) that I encountered till now. I always try to fit phenomenas to models like a data scientist does when he fits data to models. Recently I found this book: Robert B. Banks Growth and Diffusion Phenomena: Mathematical Frameworks and Applications This book is different from other applied mathematics books in the sense that it focuses on a particular model unlike others that try to model the whole world in a single book. It particularly focuses on growth and diffusion phenomena. Which is , to me , great because this book studies these two models in great detail rather than just stating many models on the surface level. I also found some book that is specific to some single phenomenon like this book on Hysteresis Mathematical Models of Hysteresis and their Applications Can someone please recommend to me some books like these that describes a certain phenomena or discusses a certain mathematical framework to study in detail and apply some phenomena? Any book that discusses and models in detail some phenomena: could be growth,could be decline, could be (what happens in the limiting case)- type of thing, could be something else, could be anything...
The boundary of a simple closed curve has each point on it, touching two adjacent points one on each side. Can the entire boundary be represented as a series of circles of the same diameter "d" where each circle is touching the adjacent circle at exactly one point only without overlap in areas between the two circles. This will allow us to approximate the simple closed curve with a polygon where each side of the polygon is represented by a line joining the centers of adjacent circles and at a distance equal to the diameter "d" of the circle. Such approximation would imply that a inscribed square exists on the polygon (Toeplitz conjecture special cases) and therefore an "almost square" whose vertices are within the error range of the diameter of the circle must exist. Shrinking the size of the circles used will reduce the error of the "almost squares" to smaller and smaller values.
I'm working on an algorithm to allow a vehicle to reverse and then line up and stop on a given spot facing a specific direction. The best approach I've been able to come up with involves two internally tangent circles with the larger extending from the point of tangency of the vehicle. Vehicle starts at point A and is parallel with tangent line T. Vehicle reverses to B, then moves forward to C, then to A so that it is parallel with the vector displayed instead. r represents the minimum turning radius of the vehicle Given that line AC is always arranged vertically and knowing point A, but that the tangent line T can vary, is it possible to be able to determine points B and C? If not what other info is needed? Medium tangent Steep tangent Shallow tangent For simplicity I've made it so that the radius of the larger circle is twice the radius of the smaller. If this restriction is not required to solve the problem how could this larger radius be determined as well?
A few days ago, I came to an amazing intuition while using GeoGebra, and I could not prove whether it was previously discovered or is it new, please mention a source if it already exists... The sum of the lengths of the tangents of two circles touching a conic section, each of which touches it at two points, and starting from a point on the circumference of the conic section is equal to the distance between the centers of the two circles multiplied by the reciprocal of the coefficient of central difference, where the lengths of the two tangents are two vectors and the shortest of them will take a negative value if the point taken from the segment is not located between the two circles. These are illustrations that include different relative states: direct result: The length of a tangent to a circle tangent to a conic at two points that radiates from the point of tangency to another circle tangent to it at two points is equal to the distance between the centers of the two circles.
I've read some description of certain house design as below: Living and dining rooms are towards the front with kitchens to the rear, with bedrooms either off the hallway or upstairs if it's a two-storey terrace. and here's the corresponding house plan: the definition of "off" in google: as I understand, and which can be seen from the floor design, "bedrooms are off the hallway" sort of indicates that bedrooms are separated by and adjacent to the hallway, and here "off" is preposition, but I'm not sure which one of the two preposition definitions fits it. The definition "situated or leading in a direction away from (a main route or intersection)." seems close but I think it's used to describe something not adjacent to the main route such as in "my house is off the main road", which is obviously not the case in above house plan example. Thanks in advance for your help!
Suppose we have a closed circuit composed of a time constant voltage battery, a resistor and superconducting wires connecting them in series. In the equilibrium state, both the free charge the electric field in the interior of the superconducting wire should vanish, lest the free charge accelerates and there be no equilibrium/steady current. The electric field generated by the charges in the battery should be counteracted by nonzero surface charges on the superconducting wire in order to generate the zero electric field inside the wire. At the locations of the wire that are far from the battery and with small curvature which should approximate a straight wire, the surface charge density should be close to uniform. However, I have often read people claiming a superconducting wire with a constant equilibrium (direct) current should be free of surface charge. I would like to know what the bases is for their argument. Are there some references on this topic?
why potential at any point in a uniform electric field is not same i.e. why potential difference between any two points in the uniform electric field is not zero? According to me if i bring a test charge from infinity to a point A in uniform electric field [assume the field is due to a positive charge] then i will have to apply external force on the test charge against the electrostatic force by the uniform field such that external force is equal to electrostatic force so that kinetic energy of test charge would remain constant thus some potential energy will be stored in the test charge at point A.....NOW if i will bring the test charge from infinity to some another point in the uniform electric field...let the point be B then according to me i will do the same amount of work done on the test charge to bring it to point B because i will apply the external force that will also be equal to electrostatic force by the uniform electric field.....and because the electric field is uniform the test charge will experience the same amount of electrostatic force at each point on the uniform electric field i.e. electrostatic force at both the points A and B due the field will be same. Hence according to me the potential energy at each point on the uniform electric field will be the same thus the potential also. Kindly explain.... why not? thanks!
In the Hertz experiment, when light falls on the anode, electrons are emitted and they move towards the cathode and thus flow through the circuit. However, when reverse voltage is applied and the polarity of the electrodes is reversed, electrons being emitted from the anode (formerly, a cathode) only come out in the air/vacuum of the glass tube and do not flow in the circuit even though voltage is applied. How is it so? The emitted electrons should be repelled by the cathode and should enter the circuit through the wire attached to the anode as the increase in free electrons results in increase of current. The applied voltage should also direct the electrons to pass through the anode. In this way, a sort of capacitor might be created. Instead, the current is said to reach zero as stopping potential is reached. How can this be justified?
In fluids, in the state of equilibrium, there can only appear internal normal forces and these forces always have a tendency to compress the bounded volume in the fluid. Cited - Physics Galaxy ( Ashish Arora ) Would it be apt to say that in context with fluids, if I drop a block, the pressure exerted by the fluid on the block will be the effect of a compressive internal normal force over an area ? In addition, why is pressure independent of the amount of fluid above it, since it is the weight of the fluid that is causing the compressive force to act? What i think: Maybe somehow Pascal's principal acts on this, equalizing the forces and leading to pressure equalizing at all heights irrespective of the shape of the tube, if I'm right, could you elaborate on how it actually happens?
I want to recreate a plot where the area that is not visible from a certain point on earth (latitude and longitude) trough a full year. An example of this plots for example can be: Where in white is marked the zone a telescope is not seeing over all year. I searched in internet but i can not find anything related on how to do it, also Astropy don't seem to have any tool to do this calculus. My first idea for the approach can be first of all maybe represent in equatorial coordinates where this areas should be straight lines (but i don't know how to calculate the coordinates that this straight lines will have). And maybe after we can transform to galactic coordinates somehow. If someone have an idea on how to do this will be helpful.
Some examples needing an explanation, thank you for the help. "I came up with (an) idea, we can do..." We should use "an", shouldn't we? But why, if we have a specific idea explained further? What about "He gave me a/the idea to admit to the university" then? "The conclusion is ..." Why should we use "the", when it's the first mention of the conclusion. Maybe because that conclusion is specific, only for that situation. Then should i use "the" in the next sentence "I came up with the conclusion. The conclusion is..."? "I have a/the feeling i don't love him". "The" because i tell what specific feeling i have further? "I am gonna watch a/the video". What if only i know that video, and i want to watch a specific video, but another person in a dialogue doesn't know that video.