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Jun
11
comment How close does light have to be, to orbit a perfect sphere the size and mass of Earth?
I agree with Chris White --- it would be nice to mention why light is being out of scope Newton's gravity theory, that is to specify the limitations of classical theory and when in general we do need to resort to GRT.
Jun
9
comment Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
If you require only $U_\text{max}$ being greater or equal than the initial kinetic energy, then $0=\frac{m}{2} \nu^2(0_+) + [U_\text{max} − \frac{m}{2} \nu^2(0_+)]$ may not have solutions at all with $\nu(0_+) \in \mathbb R$. It will have a solution $\nu(0_+) = 0$ only if $U_\text{max}$ equals to a kinetic energy of an incident particle, but that makes it dependent on the particle momentum.
Jun
9
comment Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
@auxsvr the problem is I do not see how they really solve the problem --- whenever I try to rigorously conduct the derivation I got stuck. And it seems to me that others hold the same opinion. I have commented on your answer on certain things I do not understand. Once again what is being sought --- Hamiltonian equations which can be solved as is, without resorting to any supplementary physical arguments. You see, Hamiltonian equations should be self contained, fully describing the system evolution, right?
Jun
9
comment Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
Oh, I got it, but still it would be nicer to be written. Moving along the derivation, as far as I understand you show that momentum when $x > 0$ is $0$ but it does not justify that is should reverse. Andy why is the energy is $1$ as you said? It should be $p^2/(2m)$ in any case. Moreover, with the potential fixed being equal $1$ does not prohibit the particle to enter the region if its kinetic energy is greater then $1$.
Jun
9
comment Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
Could you please elaborate on how you have integrated $\int_{0_-}^{0^+} \dot \nu \, dx$ ? This is not so obvious.
Apr
2
comment Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
oops, I have awfully miscalculated the time. If somebody cares, the correct reasoning should be following: The distance traveled is $\varepsilon E_0 = v_0 (\tau / 2) - 1/2 \, \varepsilon (\tau/2)^2 $. If we divide this expression by $\varepsilon$, will get the answer in the form $\tau = \varepsilon f(E,v_0)$ which is linear in $\varepsilon$.
Apr
1
comment Hamiltonian function for classical hard-sphere elastic collision
Milton, have a look at my related question physics.stackexchange.com/questions/105318 As for you derivation, I bet your calculation of $\Delta P_1$ is wrong, you should conduct the integration more accurately with greater level of details.
Mar
31
comment Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
If noone comes with an elegant framework which would avoid potential regularisation in the remaining bounty time, I will accept Qmechanic's answer.
Mar
31
comment Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)
Yes, this regularized potential works as a charm. It reverses the initial velocity and the penetration depth in the realm $x > 0$ is $\varepsilon E$, while the time spent here is $1/2 \, \pi \sqrt{\varepsilon m}$. Both these expressions go to zero with $\varepsilon \to 0^+$. I have one question though, how did you come up with this potential? Of course it is possible and probable to deduce it, but I bet you just had the right analogy from you experience. Is it so?
Jan
6
comment some hints/introductions/textbooks for LBM(Lattice Boltzmann methods) fluid simulation?
Palabos website palabos.org/software/lattice-boltzmann-method links to a brief video overview youtube.com/watch?v=I82uCa7SHSQ
May
17
comment How do we simulate Nuclear explosion?
what aspect of Nuclear explosion do you want to simulate?
May
15
comment Physical interpretation of Poisson bracket properties
What is the physical meaning of your treatment of antisymmetry? Why should it be so?
May
14
comment Physical interpretation of Poisson bracket properties
So basically you state that Poisson structure arises from the fact that we describe system evolution as a vector field generated by a Hamiltonian and Poisson structure is just desired properties of vector fields lifted (not a term) to scalar functions, am I right?
Apr
29
comment Decrease in entropy in a fluid flow
btw, there might be a flow without pressure gradient --- you can just move to another reference frame. So just the fact that fluid is flowing does not make it more ordered, but you might have already came up with that argument.
Apr
28
comment Is symplectic form in Hamiltonian mechanics a physical quantity?
@NickKidman I would refrain from answering such question however directly related to my question it is.
Apr
20
comment How can I find the temperature of this system?
$0.223 \ldots = \ln(1.25g)-\ln g \approx \frac{d \ln g}{d g} \Delta g = 0.25$ They are practically the same and both are approximations. None is more correct.
Apr
19
comment How can I find the temperature of this system?
Why do you think this is incorrect?
Apr
19
comment How to create visible reflections in shallow water?
@AnishaKaul I guess so if it doesn't destroy the paper. Look, it's Physics, not Math. You just try it instead of musing (provided it is not expensive).
Apr
17
comment How to create visible reflections in shallow water?
@AnishaKaul I've updated the answer
Apr
17
comment How to create visible reflections in shallow water?
@AnishaKaul Just make coffee without milk, I thought it should be black. I mentioned coffee because it seems to be readily available. You can use ink instead or something like that.