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## New answers tagged computational-physics

0

I found an answer in the book Monte Carlo simulations in statistical physics - an introduction (by K.Binder, D.W.Hermann), page 35. To determine equilibration we need to run the simulation a few times, let's say $n_{run}$ times. we define the average $<>_T$ as an average after $t$ steps of the simulation: $$<A(t)>_T = \frac{1}{n_{run}} ... 2 In kinetic Monte Carlo, the idea is to describe a trajectory as a set of events, at which the system makes a transition from one state (i) to another (j). To generate such a trajectory, we need to randomly select both the states that are visited and the intervals between them. The time interval t between a pair of events is the time in which nothing ... 2 From the wikipedia article you cited "It is important to note that the timestep involved is a function of the probability that all events j, did not occur." (note they use i in wikipedia but we are using j so I changed the quote to match) This probability is u which can be constructed from the multiple poisson distributions for each individual event ... 2 Typos stops your evaluation of trilinears at[t] and ab[t] - you wrote (1/16Pi^2) as loop factor for these terms by mistake, and blow up at[0] and ab[0] seriously. There are also 2 other typos, one appears in the beta function of ab[t] \hbbis[t] should be hbbis[t]; the other one is systema should be system for the interpolation of mhu2 and mhd2. I feel, ... 0 As many comments say, there is not a single and best answer, each one uses a different method. The solution that you found is a good one, but how do you define when the equilibrium has been reached? In order to do that you need check the last values of the simulation (Energy, pressure, etc.), so you choose a set of previous configurations that you'll check: ... 1 I think you have the wrong idea when you ask how specific heat is "defined". In computational physics, the starting point is an experimental measurement that one could measure, or at least, a physical quantity that one might care about ... and then the question is, "how do I compute it?" The wrong approach is to have in mind a certain formula. You should ... 0 The "only" thing you need to do is to establish a mapping. You have a basis function at$$ \vec{R} = a\vec{X} + b\vec{Y} with index i. In other words, your basis is $\phi_{abi}$. Since Matlab only understands (well) vectors and matrices, you need to map this to a continuous index n. For example, a square with sides $N_a$, and $N_b$ and $N_i$ basis ...

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Regardless of the system, Cv will be proportional to the variance of energy. If you have peaks at higher energies, that will increase its value. But at high enough energies the occupation of those states will be so low they won't significantly affect the variance. In this case the variance of the distribution isn't just the width² of one of the peaks, you ...

2

This is more of a comment than an answer, but I can't fit this into the amount of characters; Writing a quick bit of code, it looks to me like there's not much wrong with the method: The numerical and the analytical solution go on top of one another. N = 256 T = 256*128 L = 1. dt = 0.000001 x = linspace(0., N-1, N)*L/N psix = exp(1j*2*pi*x) psik = ...

5

This actually extends beyond just computational approaches and applies to experimental approaches also. And it's not at all a trivial problem to address. Generally speaking, we construct a model of some physical system -- either computationally or experimentally -- and we make certain assumptions to simplify the problem. In your circuit example, maybe we ...

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