Subdiscipline of theoretical physics which consists in the study of physics problems using numerical algorithms. PLEASE NOTE that questions about computational methods and/or programming are OFF-TOPIC on Physics.SE.

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81 views

Question about Metropolis Monte Carlo in the case of equal energies

If configuration A is equal to configuration B in a Metropolis Monte Carlo method, do you still do the attempted update?
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38 views

Coefficients and Parameters for contracted Gaussian basis sets

This is a repost from Chemistry.stackexchange in the hopes that someone here will be able to help me. Any help at all would be greatly appreciated. As far as I understand, an STO-NG contracted ...
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2answers
228 views

How do you measure numerically the central charge of a system?

Let's say that you are doing some Monte-Carlo simulations of a statistical system on a lattice and you observe scale invariance, meaning that you are at a conformal point. Can you get a numerical ...
2
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1answer
375 views

Unexpected eccentricity in moon orbit simulation

I've used Mathematica's NDSolve function to calculate the orbit of the Moon around the Earth. I used the following initial positions (perigee): ...
3
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1answer
100 views

Complex semi-definite programming

I'm doing some calculations and I want to simulate them in python or matlab (or whatever). However I use hermitian matrices and I don't really manage to find a library which enables me to calculate ...
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2answers
139 views

Modeling a potential well

I attempted to simulate the interaction of a moving particle and a potential well in Mathematica. The particle should experience a force of -$1/r^2$, if the equation for the potential well is -$1/r$. ...
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1answer
185 views

Is there a normalized form of the Euler equation discretized with finite volumes?

I want to calculate a flux on my fpga using the Euler equations with the finite volume method. Unfortunately the values of the state variables differ a lot. For example the pressure has a value of ...
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0answers
135 views

How to numerically solve a complex equation? [closed]

I want to know that if you are given a very complex equation g(x)=A(T). How could you solve for x, which is a function of variable T. To be more specific, I encounter a polylogarithmic function I need ...
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0answers
179 views

XCrysDen Structure file [closed]

Does anyone know how to directly convert a .cif file to a Xcryden structure file(.xsf) ? I know how to extract the lattice vectors and the atom positions from a .cif file, but don't whether the .cif ...
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2answers
254 views

Boundary Element Method or Boundary Integral Method Computational Aspects

I have to solve a Helmholtz equation inside a simply connected domain. I know that in general the boundary integral can be written as, $$\phi(x)=\int_V G(x,x') \rho(x')\ d^3x'+\int_S ...
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107 views

Nature as a calculator [closed]

I wondered whether physical experiments can find the outcome of otherwise intractable mathematical problems. For example, solitons or other non-perturbative effects in QFT cannot be seen at any ...
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51 views

Poisson equation solver with specific boundary condition

I want to solve 2d Poisson equation with this Boundary conditions below $$u(-5,y) = 0 , \\ \frac{\partial u(x,y)}{ \partial x} = 0 \,\,{\rm at}\,\, x = -5\\ u(x,-5) = u(x,5)$$ Now my question is ...
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149 views

Lattice Gas Cellular Automata - HPP model square lattice

In the HPP model of LGCA, a square lattice is used and there is only one collision configuration as mentioned in figure (taken from the book Lattice Gas Cellular Automata and Lattice Boltzmann models ...
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1answer
294 views

Simulation of fluid flow using Euler equation

I have been looking on Euler's equations for a while and can't grasp one thing. Suppose we have initial system state with volumes of fluid "hanging" in air (time is frozen and equal to zero), each of ...
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0answers
113 views

Doing numerics in physics [closed]

Soon, I am going to write my master thesis in theoretical physics. I assume there, and later on in my career, I will have to do more serious numerics than I did up to this point. That's why I want to ...
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1answer
239 views

Ground state Phase Diagram of Bose-Hubbard Model

The Hamiltonian of Bose-Hubbard model reads as $$H=-J\sum\limits_{<i,j>}b_i^{\dagger}b_j+h.c.+\frac{U}{2}\sum\limits_{i}n_i(n_i-1)-\mu\sum\limits_in_i~~~~~~~~~(1)$$ For this we plot phase ...
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41 views

Verlet timestep

I am using velocity Verlet in molecular dynamics. Is just a simple question, if a simulation using time-step femtosecond, in velocity Verlet is just necessary $dt = 10^{-15}$ to use femtosecond?
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1answer
76 views

Calculate Euler equations of fluid dynamics without division?

I'm working on the calculation of the Euler equations with the finite volume method. Unfortunately I'm not allowed to do a division. So I'm wondering if there's a form which does not need a division. ...
2
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1answer
372 views

Numerical Ising Model: Swendsen–Wang algorithm, Percolation theory?

When you look at the original paper of Swendsen and Wang in 1987: "Nonuniversal critical dynamics in Monte Carlo simulations" it is somewhat mentioned that the proposed algorithm uses percolation ...
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86 views

Difference in calculated and simulated ellipsies

My task here is to determine orbit parameters, using current values: $\mu=GM$ - standard gravitational parameter $r$ - distance to the object with Mass $M$ $v$ - speed of the object in the point $r$ ...
3
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1answer
285 views

Euler Equations, Sod shock tube & conservation

Conservation of momentum? I am considering the Euler equations in conservative form and solving the Sod shock tube problem I have written a Godunov finite volume type solver. It solves for density ρ, ...
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0answers
63 views

Euler equation with single state variables [duplicate]

I want to simulate a flow using the Euler equations. For this reason I'm wondering if there's a modified version of the Euler equations. At the moment my formula looks like this: $$ ...
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0answers
139 views

Need help simulating a fan

I'm trying to write some code to approximately simulate a number fans in an arbitrarily shaped room. I'm not real strong in physics, and could use some help. If it helps I'm not interested in fine ...
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2answers
131 views

Energy of damped harmonic oscillator begins to increase with very large Q in numerical integration

I have numerically integrated the (reduced) homogeneous equation of a damped harmonic oscillator in order to see how the error propagates. $$\frac{d^2 X}{d\phi^2} + ...
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2answers
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How do I calculate the Reynolds number in multiphase flows?

I am modeling a gas flowing through a liquid. How do I calculate the Reynolds number in multiphase flows? And, at what Reynolds number should I consider the flow to be turbulent? The problem is of a ...
3
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1answer
135 views

Update velocity or position first in computation?

I am trying to make a simulation of a vibrating string. The string is divided into $n$ points, and each point along the string is acted upon by a force due to the positioning of its neighbors. I ...
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1answer
897 views

Numerical analytic continuation for Green's function

Recently, I happened to hear about the possibility of doing analytic continuation numerically. That sounds attractive for the ubiquitous $\mathrm{i}\omega_n\rightarrow\omega+\mathrm{i}0^+$ procedure, ...
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1answer
71 views

Numerical Computation of Linbald Equation [closed]

Can anybody suggest me a good algorithm for the time evolution of the reduced density matrix using Linbald equation. My Hamiltonian is time dependent. I am aware about Qotoolbox and Qutip. I have ...
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2answers
474 views

Numerical solving of 2D and 3D Schrodinger equations

I am studying 2D quantum scattering models for my Bachelor's thesis. Somewhat like these: ,with Dirichlet ($\psi \mid_\Gamma = 0$) boundary conditions on the "walls" of the waveguide and the ...
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3answers
349 views

Runge Kutta Method for a Lindblad Equation

I am solving a Lindblad equation for a dissipative Harmonic Oscillator. My Hamiltonian is time dependent, My Lindblad Equation can be written as \begin{equation} ...
5
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1answer
374 views

Discretizing the Wave Equation in polar coordinates

I want to discretize the wave equation $$\frac{1}{c^2}\frac{\partial^2\psi\left(\vec{r},t\right)}{\partial t^2}=\triangle\psi\left(\vec{r},t\right)$$ in polar coordinates. I find the following ...
14
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3answers
858 views

What limitations are there in measuring physical properties accurately?

In a StackOverflow answer, I attempted to explain why a 32-bit float was perfectly adequate for representing the questioner's weight measurement: Physical properties are inaccurately measured ...
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1answer
458 views

I'm getting weird autocorrelations when simulating an Ising model below the critical temperature

So I'm simulating an Ising model using Monte Carlo and the Metropolis algorithm. After letting it reach equilibrium, I try to calculate the autocorrelation of the magnetization. As long as the system ...
7
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1answer
229 views

Feynman's infinite amount of logic for one tiny bit of space

Watching one of Feynman's lectures, I came across something that puzzled me. What was Feynman referring to when he said the following? What goes on in no matter how tiny a region of space and no ...
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235 views

Monte-Carlo and $O(n)$ models for non-integer n

$O(n)$ lattice statistical models can be generalized to non integer values of n, starting from their (expanded and resumed in graphs) partition function: $$Z = \sum_{\text{loop configurations}} n^{\# ...
3
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2answers
210 views

Simulate the universe?

Alright, Lets assume that I have a computer with limited calculation speed (1-4GHz) but unlimited parallel processing capability and unlimited memory capacity to go with it. Under this assumption ...
3
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1answer
287 views

Exact diagonalization to resolve ground state degeneracies

I am studying a perturbed Toric Code model that is not analytically solvable. On a torus the ground state degeneracy of the unperturbed model is 4. Once we turn on the perturbation there is a change ...
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0answers
690 views

Hysteresis Curve and how to implement it using Preisach model or other models

As a homework I need to draw a hysteresis curve (preferably an interactive one) using Matlab or any other programming language. The problem is I have trouble finding a good algorithm to do so. I need ...
3
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2answers
123 views

Numerical Tools to find Braiding Statistics of Quasiparticles

While certain classes of systems that exhibit topological order can be solved exactly (such as the Toric Code, Abelian FQH Edges, etc.) there also exist systems (think of perturbed versions of the ...
3
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1answer
303 views

Epsilon Tensor in FeynCalc

A few days ago I started to use the Mathematica package FeynCalc and one thing confuses me: Assume we have a four-vector $p_\mu$ and we contract it with the epsilon tensor. FeynCalc produces ...
4
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1answer
471 views

How to solve the heat equation for compound materials with different heat conductivities numerically?

I'm solving the heat equation with time dependent boundary conditions numerically in a 2D system using the ADI scheme. For the purpose of this question, let's assume a constant heat conductivity and ...
3
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1answer
192 views

How much computer power would we need to model every physical aspect of the universe [closed]

So I know there are equations that give you the total energy in the Universe(Friedman). So about if we we to simulate every single interaction from neurons to physical forces, strong and weak, ...
3
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1answer
148 views

Why is the objective function used in Nudged Elastic Band method reasonable?

In Nudged Elastic Band (NEB) method, which is used to find reaction pathways when both initial and final states are know, an objective function is first constructed and then minimized to find reaction ...
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3answers
1k views

Correct way to write the eigenvector of a diagonalized hamiltonian in second quantization

I am studying diagonalization of a quadratic bosonic Hamiltonian of the type: $$ H = \displaystyle\sum_{<i,j>} A_{ij} a_i^\dagger a_j + \frac{1}{2}\displaystyle\sum_{<i,j>} [B_{ij} ...
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1answer
156 views

How to Extend Relaxation Methods for 2D Laplace Equation given in Jackson E&M to 3D?

In Jackson (3 ed) chapter 1.13 an outline is given for using relaxation to solve laplace equation in 2D. The general procedure in 3D involves minimizing the quantity $$I[\Psi]=\frac{1}{2}\int_V ...
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0answers
337 views

Comparison between Cadabra and other Symbolic Computer Algebra software [closed]

Does anyone has some experience about working with Cadabra and it's (dis)advantage in comparison to other Symbolic Computer Algebra software such as Maple and Mathematica (physics package) in the ...
1
vote
1answer
179 views

Rigid body collision, 3 circles in contact

I'm working on a 2d physics simulation. It's a continuous time simulation, that is, it uses swept shapes over the time-frame and geometrical/vector 'analysis' to determine most immediate time of ...
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0answers
60 views

How to get discretization coefficients of matrix $A$ in Finite Volume Method (FVM)? [closed]

First we have Discretization of the Transport Equation $$ \frac{\partial \rho \phi}{\partial t} + \nabla(\rho U \phi) - \nabla (\rho \Gamma_\phi \nabla \phi) = S_\phi (\phi) $$ In Finite Volume ...
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1answer
88 views

Failure of a simple stat mech simulation

so I did a simple simulation that I thought would yield a Boltzmann distribution, but it failed to, and I was wondering if anyone has insight into why it failed. Ok, so I had a simple discrete system ...
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1answer
82 views

Getting nonphysical results when solving for the index of refraction of a slab?

I'm trying to computationally find the refractive indices (real and imaginary) for a thin slab suspended in air (so the only indices to deal with are air and my material's). I've experimentally taken ...