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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Generalized Eigenvalue Problem from linear stability analysis

I am trying to solve a generalized eigenvalue problem raised by linear stability analysis $$AV=\lambda BV.$$ $A$ and $B$ are non-symmetric complex valued matrices. The set of equations I am trying to ...
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17 views

2-D Ising model temperature of equilibrium [duplicate]

I have simulated 2-D Ising model in C#, but my scatter plot for magnetization versus temperature is an decreasing line (you know that the correct plot decreases quickly in a temperature near 2.3). ...
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20 views

Why is more difficult for a DFT to converge with non-periodic conditions?

I am simulating a cubic amorphous silica system. When all boundaries are periodic the SCF iteration converges rapidly. However, when the boundary is not periodic in the $x$ direction, the SCF ...
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59 views

Use Runge Kutta method to solve schrodinger equation

The schrodinger equation in spherical coordinates after seperation of variables as a solution of hydrogen atom is given by $$ \frac{-\hbar^{2}}{2 \ m} \left[ \frac{1}{r^{2}} \frac{d}{dr} \left(r^{2} ...
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Derivation of generation of time between two subsequent particle enters into computational domain

I have problem with understanding derivation of one equation in following problem. You have 1D computational domain (it is not 1D but because it is symmetrical and we are watching only radial ...
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32 views

Solving Schrodinger's Equation in Bunimovich Stadium Boundary Condition [closed]

I need to solve, as mentioned, Schrodinger's equation in a Bunimovich stadium-shaped infinite potential well with Dirichlet BC Numerically (this isn't possible analytically). In order to do so, I need ...
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107 views

Molecular dynamics and detailed balance

In developing methods to perform Monte Carlo simulations one sufficient condition to preserve the stationarity of the target probability distribution is to impose detailed balance i.e. [Gardiner page ...
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1answer
278 views

Determing Velocity of Moons

I have a question that I believe is relatively easy to answer, I am working on an $N$-body simulation of a fictional star system and am having trouble finding the velocity of moons so that they will ...
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1answer
82 views

Simulation of relativistic probe passing through an external solar system

I recently read about the Breakthrough Initiative to launch "StarShot", a nano-probe that is designed to travel to Alpha Centauri at $0.2c$. One of the challenges to be solved involves the precise ...
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176 views

Tight binding Hamiltonian for 2D finite dimensional lattice and nanowire

The Hamiltonian of a 1D lattice having finite $N$ atoms, (if we consider one basis per atom) is given by the following $N\times N$ matrix- Here $E$ is the onsite energy and $t$ is the hopping ...
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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 ...
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Matrix representation of the radial Laplace operator isn't symmetric (or hermition as a result)

I'm working with the cylindrical coordinates. I'm using the central difference to convert the radial part of Laplace operator into a matrix. $\nabla^2 u = \frac{\partial ^2u}{\partial ...
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machine learning feature vector for periodic point distributions in 3D [closed]

Is there any standard procedure (building feature vectors) that could be used to build machine learning models based on discrete and infinite point distributions on a hyperplane (practically 2D 3D), ...
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1answer
134 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 ...
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1answer
71 views

FCC-to-BCC phase transition in NaCl, Buckingham or Lennard-Jones potentials?

Background The transformation from B1 (face centered cubic (FCC) type) to B2 (body centered cubic (body centered cubic (BCC) type) structures is one of the best documented high pressure phase ...
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1answer
62 views

How to conserve momentum when numerically-integrating the path of a charged particle through a magnetic field

I have the python script attached below, which is intended to track the trajectory of a charged particle in a static, uniform magnetic field. It is very simple to calculate the instantaneous force ...
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1answer
249 views

Position based dynamics constraint scaling factor

Reading through Müller et al., Position Based Dynamics, 2007 I got lost when passing from equation (5) $$\Delta p = \frac{C(p)}{|\nabla_pC(p)|^2}\nabla_pC(p)$$ to equation (6) (and applying the ...
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1answer
71 views

Can I re-wind gravity?

Suppose I perform an arbitrary simulation where I integrate the motions of a collection of particles which interact only gravitationally. Suppose I use a time reversible integrator (to be specific, ...
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195 views

In a Monte Carlo NVT simulation How do I determine equilibration

I'm running an NVT (constant number of particles, volume and temperature) Monte Carlo simulation (Metropolis algorithm) of particles in two dimensions interacting via Lennard-Jonse potential ($U = ...
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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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45 views

Monte Carlo simulation of Breit-Wigner

I am using a Monte Carlo approach to integrate a scattering amplitude which has a propagator-squared term like $f(s)=\frac{1}{(s - 4)^2 + 1}$, between $s=0$ and $s=20$. Using a uniform random ...
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1answer
58 views

Numerical construction of phase space for a dynamical system

Suppose I have a standard, deterministic dynamical system. For concreteness I'll assume it's a two variable system of the form, $$ \dot x_1 = f(x_1,x_2; \theta_1)\\ \dot x_2 = g(x_1,x_2; \theta_2) $$ ...
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How is time evolution done in numerical GR?

Suppose we're simulating what happens when a fairly massive object falls into a black hole. Say the object starts far away, so that the initial condition is that the metric is the Schwarzschild metric ...
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Fermi-level of lattice model

I have a chain of $N$ lattice points with periodic boundary conditions. Every lattice point only has one orbital for an electron to occupy and spin is not included for simplicity. The lattice points ...
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66 views

Methods for handling close approaches in $N$-body simulations

In direct gravitational $N$-body simulations, what are the preferred methods for handling close approaches between bodies in order to preserve the accuracy of the evolution of the system?
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250 views

Modelling multiple heat sources?

I am working on a project to model heat transfer in a data center. I have basic models for a one dimensional heat transfer using conduction and convection. Such as, taking a server and modelling the ...
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46 views

Symmetry in program for ewald summation

The formula for Ewald summation as given in Allen and Tildesley - $$ U = U^{(r)} + U^{(k)} + U^{(bc)} + U^{self} $$ where the k-space contribution of potential is given by $$ U^{(k)} = \frac{1}{\pi ...
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Simulating TE011 mode in cylindrical cavity, Comsol [closed]

I have been trying to simulate TE011 mode in a cylindrical cavity by modifying the example given in Comsol ...
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24 views

Choosing the boundary conditions knowing the potential

So I have to apply Numerov's algorithm to solve the Schrödinger equation in spherical coordinates using the potential $V(r)=-A e^{-r/a}$, where $A=32.7MeV$ and $a=2.18fm$. I have already ...
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1answer
64 views

Schrödinger equation in spherical coordinates using Numerov's method?

So I need to solve the Schrödinger equation using Numerov's method. However, the problem I have assigned to me is in spherical coordinates. As it seems, I only need to take into account the dependance ...
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3answers
339 views

Solving the two body problem numerically

I'm trying to solve the two body problem numerically, setting up $G$, $m1$ and $m2$ to be equal to 1. then I located each mass on positions -5 and 5 respectively along the $x$ axis and gave them both ...
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16 views

Spherical Harmonic fitting excess polar magnitudes

I am trying to fit an expansion of spherical harmonic functions to a dataset distributed over the surface of a sphere using the least squares method. Each data point is in terms of ...
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1answer
43 views

Current Status of the Monte Carlo Sign Problem

I've been reading about the Monte Carlo sign problem, and I am a little confused about its current status. Specifically, after reading this post When is the "minus sign problem" in quantum ...
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Which are the best books I can refer for turbulent heat transfer and its computation?

I am a graduate student. I wanted to do computation on heat transfer problem mainly heat convection. I am working on turbulent regime. Can you kindly suggest some good books so that I can get ...
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Calculate 2D Effective mass from bulk effective mass

I am trying to create a self consistent Shrodinger Poisson Solver for various semiconductors. There is already one done by Professor Hu from UC Berkeley - QM CV Simulator. Looking at the code, they ...
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1answer
49 views

Numerically finding the energy diagram of the hamiltonian

I'm looking at a collection of three two level systems (qubits) coupled to each other (with known bare state energies and couplings). The hamiltonian is given by ...
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1answer
58k views

How does force relate to velocity?

I had originally asked this question on math overflow and it was suggested that I ask it here. So I know that a force will change the magnitude of velocity if it is at an angle other that 90 degrees. ...
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Standing waves and acoustic levitation

i am doing a new personnal project about acoustic levitation with standing waves into ambiant air using a piezo ultrasonic tranceiver and a reflective pannel. I modelised both of the emission and the ...
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21 views

Plotting EM fields

I am currently studying transformation optics and learning about electromagnetic cloaking. To plot my results(Electric and magnetic fields) i have to solve maxwell's equations given the permeability ...
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1answer
78 views

Quadratic drag projectile motion

I have calculated formulas with 1 dimensional trajectory motion (free-fall) including quadratic drag, and have created the following equations. These equations of motion are not of much use on its ...
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1answer
28 views

Simulating the Electric Field inside a Hollow Sphere of Uniform Charge

I've recently been studying Gauss's Law and have come across some results that I want to verify. For one, I am trying to verify that the electric field inside a conductor (in this case it could be ...
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63 views

Which formula was used to get Gravitational Waves animation?

I would like to make animation like this by myself It is from wikipedia article "Gravitational wave". But if I use formula from wikipedia article "Gravitational wave" subsection "7.2.2 Wave ...
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1answer
34 views

N-Body Simulation for Photons

For my undergrad optics class I am taking we have to select final projects to work on for second half of the semester. I have spent the last few weeks working on my own project which was a GPU ...
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1answer
37 views

Review article recommendation in the field of 2d materials

I am new to 2d materials. I tried to search related review articles in review of modern physics, but did not find anyone covering the whole of the 2d material area. Anybody can recommend some latest ...
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1answer
121 views

Is Machine Learning a useful tool for analyzing experimental data? [closed]

Apart from being a student of Physics I'm also a developer and recently in the context of cloud development I've been hearing a lot about cloud based Machine Learning. After looking at some examples ...
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3answers
139 views

Langevin Equation - Stochastic Differential Equation. What are the subtleties?

I am trying to find out the motion of a particle in 3D governed by the Langevin equation, numerically. Anyway, the Langevin equation is given by $$m \ddot{x} = -(6\pi a\nu) \dot{x} + F_b $$ where ...
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1answer
76 views

Do black hole merger simulations include regions inside event horizons?

Inspired by this question, I would like to ask the following specific point. In numerical simulations of general relativity that involve black holes, like the ones used to understand the black-hole ...
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2answers
72 views

About unit definition in numerical computation [closed]

I attend an undergraduate level course of quantum mechanics. I am thinking of computer computation on a quantum mechanical problem. I do not have much experience in numerical computation, so I read ...
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1answer
47 views

Calculating orbits with varying laws of physics? [closed]

The general way planets orbit stars in our universe is determined by the inverse square law and the three laws of motion. Both the inverse square law and the three laws of motion are the reason that ...
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Numerical simulation of strong field gravitational vacuum solutions colliding

I am interested in the current state of knowledge of strong field General Relativity learned from numerical investigations of gravitational wave packets colliding with each other or black holes. If ...