Questions tagged [computational-physics]

Computational physics is the study and implementation of numerical algorithms to solve problems in physics for which a quantitative theory already exists.

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Radial Hartree and exchange-correlation potentials

According to [1] the one-dimensional Kohn-Sham equation is given by $$ \left( -\frac{1}{2} \frac{d^2}{dr^2} + \frac{l(l+1)}{2r^2} + V[\rho;r]\right) rR_{nl}(r) = \varepsilon_{nl} rR_{nl}(r) $$ where $$...
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How to avoid density getting “deleted” in two way rigid body coupling with LBM CFD?

I've been reading this paper recently, which talks about using Lattice Boltzmann methods and two way coupling. Specifically, it outlines fluid solid coupling, and solid fluid coupling, and how simply ...
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63 views

Using MATLAB to simulate the Ising Model

I am using MATLAB to simulate a 1D Ising Chain. I am running into an issue where when trying to find heat capacity, my system has a tremendous amount of noise. I'll post my code and an image of the ...
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38 views

Pseudospectral method for Rayleigh-Benard with constant temperature gradient

$$ \nabla\cdot \mathbf{u} = 0 \\ \frac{\partial \mathbf{u}}{\partial t}+\left(\mathbf{u}\cdot \nabla\right)\mathbf{u} = -\nabla p+\nu\nabla^2\mathbf{u}+\alpha g\theta\mathbf{e}_z\\ \frac{\partial\...
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83 views

Solved : Damped spring-mass system, wrong position, correct speed and acceleration

I am modulating a spring-mass system with gravitation and aero drag, with python programming. The spring is hanging vertically and attached a weight. The user then selects a length to drag it down ...
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55 views

Why does the correlation function of this stochastic differential equation starts at different points?

I am working with the following differential equation: The equation is $$x=\beta +\sqrt{2D} \xi(t)$$ where $\xi(t)$ is a white noise term, with a reflecting wall boundary conditions. After solving ...
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1answer
158 views

How to obtain and form a 1st order differential equation for leapfrog integration from second order one in this example of coulomb drag

I am currently doing a computational physics homework which asked us to use leapfrog to give the relations between timevelocities and time-distance of these two objects. The full question is as ...
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53 views

How to numerically calculate the transition dipole integral in periodic systems?

Now I have wave functions $\psi_a$ and $\psi_b$ of two states in Gaussian CUBE format. I'd like to evaluate the transition dipole moment integral $\pmb\mu$ between these two states. As my simulation ...
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86 views

Grid Data Interpolation

What are the most sophisticated methods for interpolating a scalar field say Electric or Magnetic Field on a 3-D grid? I have scalar data on a meshgrid with equal spacing. I would like to use an ...
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136 views

How to simulate water, falling under gravity, and impinging on a curved surface, which is kept/present in a domain, containing air?

TL;DR: How do I simulate a hole, at the bottom of a (full) water tank? I am attempting to simulate water, flowing out of a hole/slit, at the bottom of a tank (Water Domain) (under the influence of ...
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39 views

Numerically solving a system of parabolic PDEs and 1st order ODEs

I'm trying to solve the following system of differential equations numerically. What are the available finite difference approaches and matlab solvers to solve such a system? Other approaches to solve ...
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779 views

Which solvers for BVP in python are the best? Is there something better that scipy.integrate.solve_bvp?

I am trying to solve a boundary value problem with Python. I have been using scipy.integrate.solve_bvp but the result that it is giving me is completely wrong. Basically my code is as follows: ...
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35 views

How to numerically transform a 2D Fourier spectrum with arbitrary frequency shift to center frequency?

Suppose $F(u,v)$ is the center frequency Fourier representation of some $f(x,y)$ in 2D. $$ f(x,y)=\int\limits_{-\infty}^{\infty}\int\limits_{-\infty}^{\infty}F(u,v)e^{2\pi i (xu+yv)}dudv $$ In ...
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119 views

Finite difference methods for coupled 2nd order nonlinear pdes

I have a system of coupled nonlinear PDEs that I cannot figure out how to solve in a smart way using FDM, so I was hoping someone here might have a clue. The equations go as: \begin{align*} \frac{1}{...
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52 views

Jacobian Elements for Coupled Drift-Diffusion System using Vertex-Centered Finite Volume

I'm trying to solve the fully coupled drift-diffusion system using Newton's Method. Although I eventually plan to potentially use a Jacobian-Free Newton-Krylov approach, this is still something that I ...
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43 views

Huge accelerations in plasma simulation

I'm trying to make a numerical simulation of pulsar magnetosphere using FDTD on a log-spherical Yee lattice for fields and PIC for plasma particles. Field part is working like charm but issue arises ...
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111 views

Band structure of nonlinear Schrodinger equation with one dimensional potential

I have a nonlinear Schrodinger equation which reads: $$ \frac{1}{2} \frac{d^2u}{dx^2}+ |u|^2u + V(x)u = -i \frac{du}{dz},$$ where $V(x)=\cos(wx)+ i a \sin(wx)$ and $w$, $a$ are numbers. How to ...
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54 views

Does radioisotope decay affect computer systems?

It is known that there exist a number of radioisotopes of elements commonly used in computer systems. Is the decay of these materials known to affect device performance over time, or is its impact so ...
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176 views

Solving complicated coupled ODE using RK4/ODE45 in Matlab

I have the following coupled differential equations also known as Guiding Center Approximation. It is used to explain the position- and velocity change of particles (electrons and protons, N = 1000) ...
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74 views

Numerical scheme to solve Maxwell equations with fixed potential boundaries?

We have a 2D electromagnetic field (in the sense that: $E=(E_x,E_y,0)$, $B=(0,0,B_z)$, and all derivatives with respect to $z$ are $0$), and we are considering a system made up of two walls at $x=-b$ ...
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1answer
134 views

Matrix exponential by eigenvectors - implementation issues

I posted a similar question yesterday but I deleted it since I think that I had to reformulate it after some insights. I want to calculate $$ \exp(-i\Delta t\,\mathcal{H}) = V\,\mathrm{diag}(\{\exp(-...
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63 views

Dealing with simultaneous collisions in N-body sim

I have written an 2d N-body simulation in Python which allows collisions between the bodies. A body is modeled as a circle whose area is proportional to its mass. Each time the sim advances by one ...
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648 views

One Dimensional Schrodinger's Equation solution using Numerov Method

I have been trying to solve Time Independent Schrodinger's equation in one dimension using Numerov Method as discussed in this excellent lecture notes I found on net. The Numerov method can solve an ...
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177 views

Second Quantization in Matlab

This question may be more suited for physics.stackexchange, but I saw this post was recommended for StackOverflow or Computational Science, so I'm asking my question here. I am trying to write a ...
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86 views

Finite difference scheme for unconfined aquifer equation

For an unconfined aquifer we have this PDE for the water table position( of course after somehow making the original Boussinesq equation linearized ): $$ \frac{\partial^2(h^2)}{\partial x^2} + \frac{\...
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262 views

Double Integrating acceleration data to obtain position: 2 Problems

I have a data sample from an accelerometer from my phone (pretty bad accelerometer though). I'm trying to double integrate it in order to obtain the position as a function of time. I'm using a program ...
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114 views

Strange solutions using Finite Element Analysis

I've implemented the Finite Element Method to model the heat transfer between two different materials where one material is surrounded by the other. When I run the model I'm getting some strange ...
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54 views

Parallelizing molecular simulation with full configuration energy

First, let just me stress that I'm not a an expert in computation chemistry, so now the problem: We have GCMC molecular simulation, in the Grand Canonical ensemble, using the standard metropolis ...
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1answer
119 views

triple cross prouct of tensor

Im trying to compute a triple cross product of vectors a,b, and c in real space and integrate over the entire space. The result is a term in the hamiltonian for an electronic system so there are ...
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230 views

Physics of explosions: just vorticity?

eg 1 2. Is it just vorticity? What's actually happening? (Similar: steam engines, volcanoes, clouds). examples are grid-based, using "vorticity confinement" in Phoenix FD. EDIT Some techniques: "...
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43 views

Software suggestion for simulating the stacking of sedimenting rods

I'd like to simulate the following problem: Define some square, horizontal and hard area onto which cylinders (aspect ratio R) sediment. Preferably, the source of cylinders sequentially generates N ...
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182 views

Mass conservation in atmospheric continuity equation numerical solution

My phd project is heavily related to numerical modeling of planetary atmospheres. In particular now I am dealing with a particular expression of the continuity equation, involving a thermodynamic flux....
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64 views

Sensitivity Analysis — Total Variation for a function with categorical arguments?

I have an application in sensitivity analysis of complex system models with moderately nonlinear interactions between arguments Arguments potentially dozens or hundreds in number Arguments mostly ...
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118 views

The Schrodinger equation for time-dependent Hamiltonian after one timestep, taking exponential or use ode solver?

The Schrodinger equation for time-dependent Hamiltonian is $$i\hbar\frac{d}{dt}\psi(t) = H(t)\psi(t) \, .$$ Assuming I knew $\psi(t)$, I want to know $\psi(t+\Delta t)$. Should I take exponential ...
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75 views

Metropolis algorithm and thermal sine-Gordon model

I try to simulate thermal version of 1D $(x, t)$ sine-Gordon field model. I am interested in finding thermal static solution that minimizes functional of energy $E$: $$E = \int dx \left( \frac{1}{2} \...
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109 views

How to get the eigenvalues of Hamiltonian in an over complete basis

Let $|\psi_i\rangle$, $i=1...N+m$, be a set of overcomplete basis vector in a $N$-dim Hilbert space. The following are known: (Einstein's summation convention assumed) $$\hat{H}|\psi_i\rangle=H_{ji}|\...
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56 views

Book Recommondation for the time-dependent Schrödinger equation [duplicate]

Can you recommend a good book that discusses several methods for the numerical solution of time-dependent and time-independent Schrödinger equation? I have searched the internet several times but ...
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74 views

RCWA for Non-Periodic Structure?

I have a quick question regarding Rigorous Coupled Wave Analysis (RCWA) for numerically solving problems (in optics). I am trying to simulate a device which is non-periodic in x, y directions (but is ...
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87 views

Representing a 3D system in 2D (Electromagnetic modelling)

Ok so I'm a complete beginner in computational modelling (I use analytical methods of physics typically) but I would like to model an anisotropic, aperiodic (but not random) finite array of metallic ...
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1answer
497 views

Shooting method - Matlab ODE

I'm trying to solve these equations of hypersonic adiabatic flow over a flat plate. I did all the simplifications and got these equations for the stagnation point flow. $$\left(Cf''\right)' + f f'' = \...
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603 views

Is this the correct way to calculate the Madelung constant?

I'm trying to compute the Madelung constant of the ZnS lattice. The method is as follows: The lattice is a face-centered-cubic with basis $S^-: (0,0,0)$ and $Zn^+: (1/4,1/4,1/4)$. The Madelung ...
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92 views

Time dependent self-consistent equations

I am facing the following problem. I need to solve numerically a set of coupled equations $$i\frac{d}{dt}f_{n}^{(i)}(t) = \left[U\cdot n(n-1) + \mu\cdot n\right]f_{n}^{(i)}(t) - \sqrt{n+1}\Phi_i^{*}\...
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886 views

BiCopter simulation in Matlab

I derived a bicopter dynamical model with two servos and two BLDC motors. And now am trying to simulate it using Matlab. As base for simulation I used this paper and this code Unfortunately, the ...
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74 views

fixed point iteration to find out second order non-linear diff equations

I am working on some model analysis, getting two diff equations and after I convert them into matrix form, I have equations looks like $$ [A][X]=C\times\big(\exp([B][X])-1\big), $$ where $C$ is a ...
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111 views

Conservation at grid interface in adaptive mesh refinement

I am using adaptive mesh refinement to solve one dimensional inviscid Burgers equation. However I am facing some difficulty to handle grid interfaces which are not uniform (coarse-fine grid interface)....
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641 views

radially averaged power spectrum of a binary image does not look like power law

It has been known that Fourier power spectrum somehow obeys power law therefore the slope of the spectrum can be used to calculate the fractal dimension of an image. Many people have used it for ...
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302 views

Spin-spin correlation functions in the Ising Model Monte Carlo [closed]

I'm using the Metropolis algorithm for 2D up to 5D for the Ising Model and I want to compute the spin-spin correlation function. $$c(r)=<s_is_r>−〈s_i〉〈s_r 〉$$ but I'm not sure how to estimate $...
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671 views

Can you provide me with the source code of DMRG writen by C++?

I want to study the Density matrix renormalization Group(DMRG). Can some one provide me with the souce code which is writen by C++ for study purpose only? The code is not necessiary very professional, ...
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301 views

Two Dimensional Nozzle Flow

I've been looking at the book "Computational Fluid Dynamics - The Basics With Applications", by John D. Anderson, and his solution for the one-dimensional subsonic-supersonic nozzle flow using the ...
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53 views

Understanding the use of Minimum Translation Vector (MTV) for an elastic collision response

So, I'm trying to simulate polygon rigid body physics, both linear and angular. To calculate the MTV is easy in SAT (Minimum Translation Vector), and to use it to adjust position is also easy: ...

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