timo

I think if you write down your diff. eq. in the form [math] \frac{d}{dt} \left( \begin{array}{c} \vec x \\ \vec v \end{array} \right)(t) = \left( \begin{array}{c} f(\vec x, \vec v, t) \\ g(\vec x, \vec v, t) \end{array}\right) [/math], where [math]\vec x, \vec v[/math] are the positions and velocities of all the objects, then numerical algorithms for solving the diff. eq. should jump up immediately. Not exactly sure if this was your problem, though.

You write down a condition for A being an element of span{A1,A2,A3} and see if the resulting equations can be satisfied.

I don't really find myself in this statement. I did and still do care a lot about my drivers: WLAN: My Internet connection is via the university's WLAN network which is spread over the city. To access it, I need a WLAN usb stick with an external antenna (computer is based on Nvidia Ion, so probably no room for a proper WLAN-card). In early versions, the stick was not supported by linux, and an alternative driver I found didn't even compile. Then, with an update, it was supported. However, with the next update (to 9.x, I think), the stick did no longer work out of the box, so I had to reinstall my system and use the older version. I later found out that by blacklisting some other drivers, I can get my stick to work on newer versions (I have to re-blacklist after each system update, though). Graphics card: Apart from the low power consumption, one of the main reasons to buy an Ion was playing around with CUDA. Needless to say, the default driver of my Linux distro (Kubuntu) did not support that. In other words: download the proper driver from NVIDIA (careful: the newest Linux driver did not support CUDA, only an older one did!), run the installer, and have it alter my configuration in I-don't-know-which-manner. Of course, the driver is compiled only for a particular kernel, so with each kernel update, I have to reinstall it with I-don't-know-which-remnants of the old configuration. It becomes better: with the latest update to 10.x, I can no longer login on the graphical interface. ASCII login works but a subsequent "startx" also fails. Partial solution: reinstall the driver from NVIDIA (which I actually wanted to get rid of because I don't program in CUDA at the moment). Now, I can chose "login via console" on the login screen, log in there, and then run "startx" to get to the graphical mode. Bottom line: I do worry about drivers quite a lot.

That is kind of what I was saying; I was a bit in a rush when I wrote it. Let me give a more elaborated version: What you are asking is how 20 tomatoes can have the same mass as two pumpkins when at the same time tomatoes are larger than pumpkins by a factor of 10 tomatoes/pumpkin. This "larger by" is comparing apples with oranges - or tomatoes with pumpkins. There is a bit more to it in this case. In a relativistic treatment it does make a lot of sense to measure time and distance in the same units, which yields [math]c=1[/math]. With these units, a lot of seemingly-different things turn out to be effectively the same, the most prominent example being the center-of-mass energy of an object and its mass (E=m). To some extend that holds true for electromagnetic fields. If you have a vacuum with no electrical charges around, a possible electric field is [math]\vec E(\vec x) = \vec E_0 \sin(\vec k \vec x - |\vec k| t)[/math] with [math] \vec k \vec E_0 = 0[/math] (in whatever units). In this case, the Maxwell equations demand that [math]\vec B(\vec x) = \vec B_0 \cos(\vec k \vec x - |\vec k| t)[/math] with [math]\vec B_0 \vec k= \vec B_0 \vec E_0 = 0[/math] and [math]|\vec B_0| = |\vec E_0|[/math] (you might want to check for yourself that this is true, btw). So the magnetic amplitude of this electromagnetic wave in "B-direction" and the wave's amplitude in "E-direction" are indeed the same (when c=1). I'm a little short on time and I notice I've possibly run off into the wrong direction. A few comments on what I just said: - This is a very special example of a plane wave in vacuum. For the electric field of a point charge, and no magnetic field around, no such scenario occurs. - Even in this special case, [math]|\vec B (\vec x, t)| = |\vec E (\vec x, t)|[/math] usually does not hold true. The value [math] \vec B \vec B + \vec E \vec E[/math] is a constant, though, and is in fact related to the energy. - The direction I probably should have run into: Under relativistic coordinate transformations, electrical fields and magnetic fields do mix. In this sense, they are indeed very related to some extent. Bottom line: there is indeed some relation between electric fields and magnetic fields that becomes more apparent with c=1. Plainly saying E=cB without giving a context is just wrong. Keep in mind that a lot of these equations that people throw around as if they knew what they mean are only valid within the context a special scenario and/or with a special meaning of the symbols (c.f. "what is the equation for time dilatation with gravitational field and velocity?") hope above makes kind of sense; it's a bit rushed. EDIT: Actually, I think you could add a constant E- or B- field to the solutions I presented above and still fulfill the Maxwell equations. Makes my point about their relation even weaker, I guess. But perhaps to still justify why the example might be relevant: such electromagnetic waves are the standard basis for those ominous "photons" that everyone seems to talk about.

Probably an effect of using units where [math]c \neq 1[/math].

There's a related idea that I had for some time, though I don't know how feasible it is to implement: Give a large group of members (say everyone with >200 posts) a "this is spam" button. The threads marked this way do not appear until approved by a mod. The idea is that obvious spam disappears quickly, but that no actual content is destroyed (since they can be restored with a simple "approved: no spam" click). As far as I see, no extra work for the mods would be needed, since instead of working throguh the reported posts, they'd work through the spam list.

Three. And a lot of Gluon stuff that is usually not mentioned to keep the picture simple. They're considered to be elementary, i.e. not made up from more fundamental building blocks. Like I said, the quark, along with the the much-easier-to-understand electrons, are supposed to be basic building blocks of the universe which are not made up from anything more fundamental. Not being composed of anything more basic is probably not the same as "made up from nothing" (whatever that may actually mean), tough. So in your math-like formulation, the standard view would be something like "1 electron = 1 electron = just that: 1 electron". Whether it is possible that we discover something actually built from basic building blocks of "nothing"? Dunno: I cannot imagine what that means. Whether I think it's probable: No. I can't even imagine what it means.

At least in the circles that I usually deal with scientifically, non-tenured scientists, the focus is "publishability" and "grantability" .

Can't help it. My first though is: the sky would probably second-order delta under the force of quantum fluctuations.

The more tricky and interesting question I think is what a "formula for time dilatation" is supposed to be in the first place. The rule for calculating the proper time of a given path through space-time is the same in any case; irrespective of whether the space-time is flat or not.

Some atoms of course do decay; that's called radioactivity. Hydrogen atoms are supposed not to decay. Some exotic physics proposes them to decay. This decay has actually been looked for in huge experiments like the Kamiokande experiment. No decay of the Hydrogen atom has been found. Note that pretty much the same question has been asked in this forum not too long ago. You might be interested in reading the other thread about it.

It's not exactly the issue A Tripolation wants to talk about, but a question that comes up in the context: does anyone know how "being white" (or "being hispanic", or "being <current politically correct term for black>") is determined/defined? Do the grant-givers judge that from photos, do you just have to convince the grant-givers that you belong to the respective group or are there really formal/official criteria?

It's kind of clear. I didn't expect that you can define the topology (the connections between the atoms) and get a reasonable and reliable geometry (connections plus spatial arrangement) out of it, which is why I was skeptical of your question.

You're probably missing the keyword "metric" and its meaning.

Might still be cool if you posted what you actually were asking for (it didn't really become clear to me) and, in case someone with a similar question reads this thread at some point in the future, what your solution is. @Captain Panic: I think all scientific programs I've been using come as source code and seem to compile on Linux as well as on Mac (checked for gromacs, ROOT, Sherpa, Pythia, the BOOST libraries, and the killer application: gnuplot).

I think your book assumed that you realize the term is the geometric series. Note that it should be [math]Z=\frac{1-e^{-(N+1)\varepsilon/\tau}}{1-e^{ -\varepsilon / \tau}}[/math], not [math]Z=\frac{1-e^{-(N+1)\varepsilon/\tau}}{1-e^{ +\varepsilon / \tau}}[/math] (i.e. that you forgot the minus sign in the denominator).

Ten years? Time machines were invented much later. Around 2042, if I remember correctly.

You probably meant "both, det(A) and det(B), be zero"? Sure. Take A=B=0 (0 meaning a matrix with all entries being zero), for example. A mathematician visits a car dealer. He looks around a bit, and then he's approached by the salesman. "Good day, sir. Already found something you like?" The mathematician answers: "Yes indeed. I'll either take the blue one here or the red one over there - but not both". I think I got this one from this forum's jokes thread. The point is: in mathematics, an "or" usually means an inclusive or, so "det A=0 or det B=0" does include the case that "det A=0 and det B=0". The determinant of a matrix M being zero means that there are non-zero vectors v for which Mv=0, because the determinant is the product of the eigenvalues. Incidently, my statement about the zero eigenvalue (and the corresponding eigenvectors) should help a lot on this one.

I've never bothered about "house rules" of a journal so far (even for formatting of the figures - I only started to bother after the publisher screwed it up with the format I sent), and no one has complained about that. I actually doubt that journals have rules about such things. Just write clearly (I like ajb's term of "effective use of English"). Since I happen to have it open in a tab right now: the abstract of our latest paper starts with "We show that...". "We" in this case means the authors. And the statement "We show that X" is simply better to read than "In this work, X will be shown". I do not like the "we" meaning the author and the reader, as is the style in many textbooks. When reading a textbook or a paper, it simply doesn't feel like the author and me exploring this wonderful wold of *yawn* together. So this "we" is very strange for me. So I would definitely prefer "Consider a space alpha" in the first post's example. Single authors talking about themselves in plural: no offense, but that I find rather weird.

All dentist' opinions I've heard on this matter so far (i.e. TV interviews, friends, and the dentist I visit) are: don't bother, just do brush your teeth at least twice a day. That doesn't rule out that one of the options is better, but at least the difference doesn't seem enough for the experts to bother. Dunno about everyone. I brush my teeth right before leaving the house and right before going to bed. The latter obviously is after dinner. I do not have regular breakfast habits, but either have breakfast at home, outside (at work of in a cafe), or simply skip it; so the order can vary (since I do not bother bringing my toothbrush to work).

Keep in mind that when the charge distribution is induced from the outside the charges get an additional exclamation mark.

I would think that a simulation equilibrating a few hundred argon atoms can be easily done on a personal computer within a few minutes. So if you're only interested in the pressure of the system, the I don't see a huge problem. Keep in mind that the results for a few hundred atoms can differ from that of [math]10^{23}[/math] atoms, though!

- What the PC? Did you mean the CP, the critical point? - The simplest way is to take one of the mainstream programs, plug in your system (or even take a setup you found on the net), and let the simulation run. - You might want to look at this lecture notes. The first tutorial is the simulation of the condensation of an argon gas in gromacs. Playing with the parameters should be relatively easy, the steps are all given and the required setup files should all be provided. - The alternative is of course writing your own program. That's also rather easy (we're talking about "F=ma"-physics, after all), but I imagine in can become very typing-intensive and boring at some point.

You already used trigonometry when constructing [math]\Phi(t)[/math], which is fine of course. Perhaps you should try to follow the formal Ansatz with the integral that I wrote down and see what happens.

It's not clear to me what you are trying to do. Obviously, if you know v, then you know [math]\Phi (t)[/math] and [math] \frac{d\Phi}{dt}(t)[/math] - by plugging in v. Perhaps this comment helps: The question is relatively easy to answer because you know that v, which is the same as dx/dt, is constant. Phi and its time-derivative [math]\frac{d\Phi}{dt}[/math] are not constant. In principle, you could write down something like [math]10^\circ = \int_{0}^{10} \! \frac{d\Phi}{dt} \, {\rm d}t[/math], plug in the term for [math]\frac{d\Phi}{dt}[/math] on the right-hand side, integrate, and solve for v. That would be the formal "for impressing first semester physics students" way to solve the problem.