darklight03/StackMIAsub huggingface dataset:
This question is about how the ground state is chosen in a spontaneous symmetry breaking process. Say we have a Mexican Hat potential (e.g. the one for the Higgs field) and are sitting at the unstable equilibrium in the middle. My lecturer said that then the "state would decay into" a random one of the stable equilibria that are located on a circle around the origin. My question is now how exactly this "random" direction the symmetry is broken into is determined. To illustrate my problem: For the equivalent process in a superconductor I understand at least conceptually how that could happen. We have some thermal motion that is a statistical process, so the random choice of the direction of symmetry breaking really just comes from the chaotic dependence on the thermal initial conditions. What I don't understand is where such a random process could come from in the case of particle physics since I thought of the fields as fundamental. But maybe I am completely misunderstanding and such a decay from an unstable equilibrium to a Ground State never actually happens. EDIT From the comments knzhou seems to think that the breaking is an actual process while seeking_infinity says that it is just that you have to "expand your Taylor series" about a minimum. The latter would resolve the problem completely, but is it true that this only matters when we do perturbation theory?
I am performing a simulation involving growth of bacteria. This is an agent-based simulation where the solutes (glucose, oxygen etc.) are represented as a concentration field discretised over space, and the bacteria are discrete objects in a continuous space (spherical blobs with a size, mass and position). The concentration fields diffuse throughout space, and the bacteria provide the reaction by taking up (or releasing) these solutes. The rate of uptake at any position in space is proportional to the amount of biomass at that position. Hence this becomes a reaction-diffusion problem. The simulation is time discretised such that in one time step: concentration fields are solved to steady state by numerical integration of a reaction-diffusion equation for the current amount of biomass bacteria grow (biomass in the system changes) with respect to the updated concentration fields I want to know, how valid is this approximation? I have always justified it that diffusion happens on a much smaller timescale than growth of the bacteria. Is it worth creating a transient solver where the reaction-diffusion equation is solved over a finite length of time and the bugs are grown for the same amount of time in a leapfrog-like scheme?
I am trying to calculate an instantaneous merger of two rotating spheres into one. Two spheres each rotating around their own axis of rotation (which are generally not aligned) and moving relative to each other. Imagine two entirely inelastically colliding planets. While I can calculate their individual spin angular momentum and the orbital angular momentum, it is unclear to me how to combine this into one (spin) angular momentum for the resulting sphere. It seems to me I cannot simply add the four vectors together... or can I? After merging the two into a single body maintaining the initial momentum, can I calculate the released energy (in the inelastic collision) simply as the difference in kinetic energy, using the same reference frame? I realize this should be pretty trivial, but I have thus far not been able to neither derive nor locate and answer.
My professor of algebraic function fields class gave me a paper to make a project (give the proof details, fill some gaps, etc). As my previous question here suggests, the paper he gave me is hard for me. He says if I know another paper to work, it's ok. He is very busy and he doesn't care about me and leaves me to find another one. My background: I finished Fulton's algebraic curves book. I finished the third chapter of Stichtenoth's Algebraic function fields and codes. I've heard that if we finish the third chapter of Stichtenoth's book we're prepared to make some research in the area. However, as I said my ambition is much lower, is there some paper which I can read by myself with ONLY this background? I need some suggestions. I don't know if I have many choices, so ANY paper following these criteria not so old, it would be great, really. I hope not asking so much, I really need help, you're my last chance. Thanks very much in advance
I came across this question on Yahoo! Answers: Should M-theory read, M-hypothesis? It being limited evidence for further investigation, perhaps not yet a theory. I responded thus: (I realise the words "use" and "usage" are.. ahem.. overused. Please disregard this stylistic concern.) I believe this use of the word "theory" reflects an overlap in mathematics and theoretical physics. In mathematics, the word "theory" is used informally to refer to "a self-consistent body of definitions, axioms, theorems, examples, and so on" (reference). Examples of this usage include "field theory" and "group theory". This differs from the scientific use of the word "theory" to mean "an extensively tested hypothesis". I believe the use of the word "theory" here is a purposeful reference to the fact that the inventors were interested in laying a mathematical foundation for their model. Note that "string theory" has the exact same usage. In fact, the usage seems to be quite rampant throughout theoretical physics. However, that's quite possibly just a way to rationalise what is actually carelessness on the part of scientists using the terms. It may not even fit with the facts; my knowledge of theoretical physics is admittedly slim. Can anyone give any support for or against my explanation? I found this blog entry wherein commenter James Reed chalks it up to a combination of carelessness and an alternate definition of "theory" as "a model being developed by a theorist" (which is similar to the informal mathematical definition, I think).
If you're at the wrong place at the wrong time, is this actually a bad thing? Don't the two negatives words result in a positive meaning? For instance, being at the wrong place at the right time wouldn't be good, and being at the right place at the wrong time, that too would have a negative result. As I see it, being at the wrong place, at the wrong time, could result in the second negative cancelling out the first negative and therefore the phrase doesn't necessarily have a negative meaning, am I correct? As an example, take a sales appointment. You go to the right place at the right time, that's good, you've got there OK. However you go the right place at the wrong time, and that's not good as you aren't expected, and if you go the wrong place at the right time, well, you've missed your appointment. Go the wrong place at the right time, doesn't mean you've missed the appointment though does it? It doesn't mean that you didn't get to the appointment. Is this correct? Although it's generally seen as a negative phrase, it could be used positively? What would be the full implication of this, as all definitions I've seen give this phrase a completely negative meaning and don't take this into account.
What does it mean when a denomination or theological tradition is described to be "pietistic"? The definitions of Merriam-Webster for "pietistic" mean: of or relating to Pietism a : of or relating to religious devotion or devout persons b : marked by overly sentimental or emotional devotion to religion : RELIGIOSE I do not think the second definition is the one that is used when someone describes a theological tradition as pietistic, because that one seems to connote general piety or being a very pious person. I think the first definition is close, because it merely uses the adjectival form of Pietism. I have also done some reading in The A to Z of Lutheranism, looking for the entry on Pietism, and it characterizes Pietism as: ecumenical, emotional, lay-focused, and interested in institutions only if they are voluntary associations focus on the regeneration or conversion of the believer, and on living, active, heartfelt faith opposition toward [Lutheran] Orthodoxy for its overattention to the will and the intellect, seeing it as encouraging a barren and arid assent rather than living faith Later, Pietism opposed its own child, Enlightenment rationalism, for its overattention to reason, seeing it as setting skepticism above faith. I am aware that Pietism has greatly influenced other Christian denominations, but I am still not sure what it means essentially for a Christian denomination to be described as pietistic. Do all the definitions sum up to some sort of anti-intellectualism or something more?
This is what I'm trying to express [Foo] can be simplifiedly characterised as [bar]. However I am unable to find references for such as word as simplifiedly. What I want to say is that the following characterisation as [bar] is to be understood as being simplified for the sake of explaining [Foo] in the first place. How would you phrase it? I would prefer if the structure of the sentence would remain unchanged. But if there is no such word maybe this can be restructured without being too verbose. Edit: It's not a question of rhythm or aesthetics, it's a question of meaning. I'm not trying to say that the characterisation I'm making is simple to derive, I'm trying to say that I'm making a characterisation that is simplifying the matter of [Foo], which is in fact a bit more general/complicated than its representation as [bar] might suggest. For me "simply" has the taste of what I'm not trying to say (according to the above paragraph). Regarding the suggested "more simply", I have no gut feeling and will have to trust you as experts.
I am looking for a word or term that means something like: you are using previous results outside boundaries of the original experiment/observation earlier experience/results does not apply in all other cases you are extrapolating findings beyond original context those specific test results don't apply to every case there is no evidence that previous observations apply in all other cases those findings cannot be applied here it does not follow that... For example - someone has measured some attribute and concluded it increases efficiency (ignoring correlation and causality) - then extrapolate to claim that all other cases would benefit from increasing this attribute. I want to say that is not true, because the original observation applied to specific situation and it's faulty logic or extrapolating too much to assume the same thing works everywhere. I Found a list of fallacies on Wikipedia- the ones that I think are most appropriate are: Faulty Generalization, Hasty Generalization, Fallacy of Composition and Inductive Fallacy
There are a couple of idioms whose meaning is from time to time or occasionally. Every so often (Every) once in a while (Every) now and then/again Every actually is a determiner (or, broadly speaking, an adjective) specifying a noun or noun phrase and means that everybody or everything of the referred group is addressed, as in every day, every man, or every student. Obviously, every is also used when referring to a period or range of time, e.g., every thirty minutes or every week but, again, the time frame is given as a noun. I was looking at the entry in Etymology Online, as well at Merriam-Webster and Oxford dictionaries to get further information. Etymology Online doesn't address the matter at all. While the dictionaries at least define these phrases and list a couple of examples, they do not give any clue to answer my questions: what part of role is every playing in these expressions (from both a grammatical and logical point of view) and where did this usage come from.
I have a list of events. A few of them may be cancelled or they may be "moved" to another date. The latter are usually postponed but not necessarily. For cancelled events I add the state "Cancelled". What is the best word (or short phrase) to describe a date change of an event? Is it "Rescheduled"? I saw some answers here, but they referred to full sentences. Edit: As it has been asked for clarification. In the German sources usually only "verschoben" is used. In this case this can mean "date of event will be changed" but also "previous date of event has already been set to a new date". Im looking for such a word. But now I'm also thinking about introducing a new state in my data model to express the distinction between the state "to be rescheduled" and "rescheduled to/postponed to".
I am writing a dissertation and I have a two collections of data from my research which I would like to compare using graphs. I have the values for abscissa and ordinate and I am looking for some sort of tool into which I can input the values I have and which will plot and trace the graph so I can show the variations in both samples. Just something simple nothing very complicated. I have been searching the Internet for something like this for hours and I can't seem to find one. What I have found so far are tools which take a function before drawing the graph, but what I need is something which can take the values directly in order to draw the graph connecting them. I don't know whether my search terms are not accurate enough to describe what I need so I hope someone here may be able to help me out. Please, does anyone know a simple tool which I can use to achieve this? (Windows or - eventually - Linux would be highly appreciated)
I have always thought that colons were used to clarify, expand, provide evidence for the preceding sentence, or show an example. I have heard that this is not true. (Truly, it is a shame if it is so: colons are my favorite punctuation.) Which of the following sentences uses the colon correctly: There are three children in my class: two boys and one girl. There are three children in my class: Jack, Larry, and Susan. He is undoubtedly a true man: his beard is long and his hands are strong. It was a big fireplace: not one of those ornamental dainties you find in the houses of snobs, but a real fireplace that had a utility surpassed only by the greatest furnaces. She was a promiscuous fiend: she had seduced every guest who had dared to pass her threshold with her fiery eyes and her wealth. This is the problem with your stubbornness: if you happen to be wrong, it will be all the more embarassing. Never in my life have I been homesick: perhaps I am emotionally stronger than others, or perhaps they have a better home than I.
I am a user of LaTeX for about two years and I can see that almost every package which exists for TeX is free and these packages are maintained perfectly; packages are updated regularly and new packages or classes are developed when needed. Why people do such volunteer work? How do they benefit from the time they spend on creating and maintaining things related to TeX, LaTeX and friends? Do they do these just to have fun, fill their leisure time and learn something during the time they do not work or does working on these help people to develop their own business and work? I know that every person may have his own reason to work on open source/free softwares, but how should I answer this question and convince somebody asking such question and thinks that it is just waste of time spending time on something which has not any financial benefit? I personally really love TeX and LaTeX and spend some of my time learning about it but once somebody asked similar question and I had no answer to him.
As space-time is distorted in a gravitational field, relativistic effects such as time dilation and length contraction take effect. Time dilation is explained simply enough: closer to the source of gravity, slower the time passage. However, space contraction gives no such clear answer. for example, a single thread on the matter contains the following: gravitational field would produce a transverse expansion of distances gravitational fields produce increased distances in the direction perpendicular to the field [gravitational fields] produce decreased distances in the radial direction So, to pose the question as bluntly and directly as I can: Ignoring all other effects (relativistic or otherwise), which is shorter: a measuring stick closer to the source of gravity or a farther one? If the orientation of the stick plays a part, try to answer for both the case where it's pointing towards the source of gravity, as well as perpendicular. Similarly, if the position of the observer relative to source of gravity plays a part try to take that into account (but it doesn't seem to in the case of time dilation so I don't expect it here either)
Will a machine or a technique ever be possible that allows artificial gravity in interplanetary space? And I ask out of pure curiosity. I know there is the "Vomit Comet" that allows for a non-gravity 'simulation' (for lack of a better word) on Earth, and I was thinking about if there would be a way to reverse that and rather have gravity in space. edit: Say I was building a space shuttle because I'm dying to go to the moon (true story). Unlimited budget, the smartest people you can fathom helping me build my space shuttle. I get motion sickness and the whole "anti-gravity" thing wouldn't really work for me. Would there be a way to have gravity on my space shuttle? Perhaps by using a type of machine or magnets or something of the like?
I found some theoretical questions in an old test of my school, and would like some help with the ones I cant answer: It is said that the electric field is an intermediary of the electric interaction. What does this mean? Why the participation of this intermediate is necessary and can not establish direct interaction between charges ( as supposed by Coulomb ) ? Electrostatic field lines are open. How can you establish a relation between this and the fact that electric force is conservative? If a charge is placed inside a non-uniform electrostatic field, will it move alongside the field lines? (I think this is true, because the electric field is parallel to the electric force which is what causes the movement state variation, but I'm not sure...)
I realised, reading another Phys.SE question about balloons moving forwards in an accelerating car that I don't really understand how buoyancy works. Particularly concerning, for a SCUBA diver. The top answers to that question seem to claim that balloons get their "sense of down" from a pressure differential. They continue: when a car accelerates, the air at the back of the car becomes more dense, and at the front less dense, changing the plane of the pressure differential and so also, the balloon's sense of up. I find that extremely hard to credit. However, I realised that I don't really know why less dense things float in more dense things. I'm fairly sure it's something to do with displacement of heavier things by lighter things, and I think pressure acting on the lighter thing's surface has something to do with it, but that's about it.
I have a LaTeX document that works fine, but it does give a warning message every time I compile it. Here is the text of the warning message: LaTeX Warning: Label `' multiply defined. The name of the label that is multiply defined appears to be an empty string. I am confused about this, but I have had trouble searching for it online because the key element is the empty string, which does not make for a good search term. Does anyone know what this warning message could mean? I can post details of the document in question as needed, but at this point I have no idea what parts could be important. Got it. I guess I didn't realize that bibliography items counted as labels - since I never had any intention of referring to them anywhere, I left all of their labels blank initially.
I was reading Surtees' Young Tom Hall the other day, and came across this... Sir Thomas, whose father had been a great army tailor, was a Dublin Castle knight, but, like all truly great men, condescending withal - and no feast or fete, or wedding, or christening, in Fleecyborough, or within a radius of three miles, was considered perfect without Sir Thomas Thimbleton of Thimbleton Park (so he called his villa and twenty acres of land). Does anyone know what a Dublin Castle knight is? It doesn't sound terribly complimentary. Farmer & Henley, Partridge and Green have Dublin dissector, Dublin packet, Dublin trick and Dublin rules, but no knight. A search of the internet produces thousands of references to a song, whose lyrics I have perused but which doesn't appear to be relevant.
In the U.S. when someone orders a 'well drink' they are typically intending to order a drink (i.e. "vodka tonic, well") with the cheapest of the liquor the bar has available Where did the "well" come from? It is distinct from what is called a "call drink", which is when the customer specifies the brand (i.e. Stoli tonic). Since well liquor is also distinguished in contrast to middle- and top-shelf liquors, is "well" perhaps being used as a reference of altitude (e.g., a well is a subterranean water hole)? Is it coincidence or is it etymologically pertinent that the Hebrew word "be'er" means "well" in the sense of shaft/recepticle? To emphasize, this question is asking for information on the origin of the word "well" in its sense and usage behind a bar. Where does this usage of "well" derive from and how was it adopted for bar usage?
There are a few other topics I found that explore this idea from a different perspective: Is randomness deterministic? Can randomness exist? Is the universe fundamentally deterministic? My question is on similar lines but from the perspective of complexity and within the framework of classical mechanics. It would seem to me that what we typically describe as "random", for example in probability theory, refers to the unpredictability within a complex system. A coin flip has many different initial conditions: the size and shape of the coin, the way the hand moves when it flips it, the material of the surface the coin lands on, the movement of molecules in the air etc. It also has many many interacting parts, many of which exist on the atomic scale, and whose relationship with other parts change dynamically. Probability is a mathematical model that allows us to tell what possible average outputs the system can produce given all the internal variables that are unknown to us. Is this a fair characterization? However, if we were, in theory, to know all the initial conditions and had a way of describing all of the interactions of all variables in this dynamic system once it has begun, could we not predict the outcome (assuming theoretical computational power)? My main question: Is there any kind of dynamic system in classical mechanics in which the outcome would not be predictable and, if so, why not?
Consider these sentences: If you haven't got a fresh chicken, I'll take a frozen. If you haven't got a fresh chicken, I'll take the frozen. If you haven't got fresh cream, I'll take canned. If you haven't got (any) fresh cream, I'll take some canned. If you haven't got fresh cream, I'll take the canned. As you see, frozen and canned are adjectives that are used attributively but their accompanying nouns are left out. Is it grammatical to do so? Under what conditions? Does the phrase remain a noun phrase? Of course, the problem can be detoured by adding back the omitted nouns (frozen chicken/one, canned cream), but the question is, cannot the adjectives do alone? You can also share your native impression and tell us (preferably in the comment section) which of the sentences above you find acceptable and which unnatural.