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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70 views

Broken Thin Lens Algorithm [closed]

We all know the thin lens equation. For $o$ being a horizontal object distance and $f$ being the focal length, the horizontal image distance $i$ is described by: $$\frac{1}{f} = \frac{1}{o} + ...
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1answer
150 views

Monte carlo simulation for continuous spin model (e.g. XY or Heisenberg model)

Unlike the Ising model, the XY model and the Heisenberg model have a continuous spectrum. So one need discretize them for a numerical simulation. But how to make sure the discretization procedure ...
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3answers
139 views

Why does the Metropolis algorithm allow changes even for ∆E > 0?

In the Metropolis Monte Carlo algorithm, why can you accept changes even for ∆E > 0 (provided that a random number is less than a given probability ratio, e.g. exp(-β∆E))?
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1answer
80 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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34 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 ...
2
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1answer
202 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
87 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
125 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
129 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
108 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
218 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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99 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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47 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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0answers
94 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
159 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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0answers
31 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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0answers
91 views

Which are the good universities for doing PHD in computational physics? [closed]

Currently i am doing MSC(physics) from Pune university, India. And I want to do PHD in computational physics as it interests me the most. So I want to know which universities will be a good option for ...
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1answer
66 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
185 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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2answers
77 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
185 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
91 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
1k views

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
86 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
544 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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3answers
284 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} ...
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1answer
234 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 ...
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3answers
613 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
303 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 ...
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1answer
129 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 ...
7
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2answers
228 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^{\# ...
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2answers
174 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 ...
2
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1answer
206 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
368 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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1answer
217 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 ...
2
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1answer
140 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
100 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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1answer
118 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
230 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
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1answer
129 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
51 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
79 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
75 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 ...
3
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0answers
844 views

Numerical problem in solving the Bogoliubov de Gennes equations- methods to solve?

I am trying to solve an assignment on solving the Bogoliubov de Gennes equations self-consistently in Matlab. BdG equations in 1-Dimension are as follows:- $$\left(\begin{array}{cc} ...
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0answers
74 views

Application of wavelets in computational electromagnetics

I am a first-year graduate student (electrical eng.); wavelets is one of the courses that I am taking presently. As part of the course, I plan to explore application of wavelets in computational ...
3
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1answer
218 views

confusion in discrete transform to solve kronig penney matrix equation in fourier space

I have a periodic potential $$V(x) =\sum_{K}e^{iKx}V_{K} =\sum_{n}e^{\iota2\pi nx/a}V_{n} $$ where $K =\frac{2\pi n}a$ is the reciprocal lattice vector and $a$ is the lattice constant and $n =\pm ...
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0answers
488 views

Numerical solution of two coupled second order differential equations of motion [closed]

Is there a numerical algorithm for solving a pair of coupled second order differential equations? This question arises from a homework problem that I have that involves two dimensional projectile ...
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0answers
105 views

How does the Lennard Jones Potential changes for interaction between particles of different sizes?

I am interested in incorporating a Lennard-Jones potential in a simulation. When the interaction only involves the same type of particle, with same characteristics, we can use reduced units, scaling ...
6
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2answers
241 views

Eigenvalue problem for differential equations in QM

I have a very simple question with regard to numerical methods in physics. I want to solve the eigenvalue problem for a particle moving in an arbitrary potential. Let's take 1D to be concrete. I.e. I ...