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.

108 questions with no upvoted or accepted answers
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499 views

DIIS method to accelerate SCF convergence for stretched geometries

I am implementing from scratch an Hartree-Fock calculation in the STO-3G basis set to perform Born-Oppenheimer molecular dynamics. I have a Restricted Hartree-Fock procedure that can reproduce very ...
6
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124 views

Is a complete bacteria simulation with an exascale supercomputer possible?

Will it be possible to simulate a complete (at least simple) bacteria atom by atom on an exascale supercomputer? or is it possible already today with the largest systems? Here, I've read that ...
4
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54 views

Phase dislocations and numerical accuracy

I am solving the nonlinear Schrodinger equation (NLSE), $$A_t+iA_{xx}+i|A|^2A=0$$ where $A$ is a complex valued function, which can be written as $A=ae^{i\theta}$ for $a,\theta$ real. Now, for ...
4
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1answer
674 views

Help with Fourier beam propagation method

I am working on implementing the Fourier beam propagation method in C++. I am really more of a programmer than a physicist but I think I have a good understanding of what I am trying to do. Here is ...
3
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51 views

Choosing good modelling method for solving Boltzmann equation

I'm writing a solver for Boltzmann Equations (BE) including a force term in rarefied plasma, for my PhD. The aim is to see if an instability occurs inside an electric streamer (theoretically it should,...
3
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68 views

Computation of Troullier-Martins pseudowavefunctions

The computation of Troullier-Martins pseudowavefunctions has been described in [1]. The pseudowavefunction $R^{\textrm{PP}}_l$ is defined by $$ R^{\textrm{PP}}_l(r) = \left\{ \begin{array}{ll} R^{\...
3
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0answers
65 views

Should I expect computational gains using a second-order splitting method here?

I am trying to solve a three-dimensional baroclinic transport problem. The hydrodynamic (three-dimensional shallow water) equations are: \begin{align} \nabla \cdot \vec{v} = 0, \tag{1} \\ \frac{\...
3
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0answers
138 views

Non-reflecting boundary conditions for compressible Navier-Stokes equations

I have some questions about the implementation of non-reflecting OUTFLOW boundary condition for Navier Stokes equations. Following Poinsot, Lele "Boundary Conditions for Direct Simulations of ...
3
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0answers
142 views

Crank-Nicolson integrator: oscillations with complex matrix

I'm working on a Real-Time TDDFT implementation and I am currently comparing different propagation schemes for the propagation of the Kohn-Sham wave function, $$ \phi(t+\Delta t) = \hat{\mathcal{U}}\...
3
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0answers
103 views

How can I evaluate the accuracy of my n-body simulation?

I am making an n-body simulation in python. There are many different methods to numerically solve the system of differential equations governing the gravitational interactions between the $n$ ...
3
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72 views

Cavity Flow CFD Boundary conditions and strange waves

So I have a PDE that I use to describe how material flows through a volume(2D or 3D). $$\frac{\partial C}{\partial t} + \vec{u} \cdot \nabla C = (D' + D )\nabla^2C$$ Now using finite differences I get ...
3
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100 views

Journals that publish theoretical analyses of existing algorithms

In computational physics, the vast majority of papers has the following structure They propose some new algorithm, or improvement to an existing one They give numerical examples, ideally comparing ...
3
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69 views

Numerical Euler Rotation Equation

The problem I have may be really simple, but still getting a hard time solving it. So I have the Euler rotation equations: $$I_{1}\dot{\omega}_{1}+\left(I_{3}-I_{2}\right)\omega_{2}\omega_{3}=\...
3
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53 views

Coupled Diff Equation from Bose Einstein distribution

I am a student doing physics hons and have had very little experience in programming. This semester we are supposed to do a computational project in thermodynamics. I have to solve these two coupled ...
3
votes
1answer
382 views

General case Kutta condition

I'm working on a 2D inviscid fluid simulation using a "panel method", with Potential being used to enforce the no-through boundary condition. I'm trying to incorporate the Kutta condition, which says ...
2
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0answers
160 views

Heisenberg Model python : Specific heat capacity for spin 2

I have the correct plot for specific heat capacity when I am using the formula which is $C_V$ = differentiation of entropy with respect to temperature. However, When I try to calculate $C_V$, by using ...
2
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0answers
40 views

What is the best methodology for physics simulators of large floating base rigid body systems?

I want to implement a physics simulator for large floating base rigid body systems from scratch. The Rigid Body Dynamics Systems (RBD) should typically have the following characteristics: About ~50 ...
2
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1answer
402 views

1-D turbulent energy spectra in homogeneous direction (non-isotropic)

I am trying to compute the one-dimensional energy spectra for my channel-flow simulation. I have already written a post-processing script to achieve this; however, I need to validate my code before ...
2
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0answers
1k views

Using RK2 Method to solve the simple harmonic oscillator of a horizontal mass on a spring (1D)

Being new to numerical analysis techniques, in particular RK2, I decided the best way to jump in is by using python to solve the well known mass-spring oscillator using RK2 techniques. My problem is ...
2
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0answers
61 views

How to model pedestrian flow through subway systems?

I'm a New Yorker and take the subways every day. I have a growing interest in understanding the distribution of paths people take on the subways to work every day. I.e. if there are $n$ subway ...
2
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0answers
77 views

Numerical error in implementation of iterative algorithm

I am trying to implement (in Python for now) low thrust orbit propagation for spacecraft using universal variables. For a given central body with the gravitational parameter $\mu$ and an orbit with ...
2
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0answers
207 views

Solving a 3D (almost radial) convolution with FFT

I have a 3D integral that is almost a radial convolution of the form $$ \int d^{3}k'h(\mathbf{k'})g(|\mathbf{k-k'}|) $$ and I am looking for a fast and efficient algorithm (e.g. FFT) to solve it ...
2
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0answers
134 views

Solving Schrodinger's Equation Numerically in a Bunimovich Stadium

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 ...
2
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0answers
286 views

Implementation of no-slip boundary conditions in lattice Boltzmann method fluid simulation

My faculty advisor recommended that I take a look at the lattice Boltzmann method as an introduction to scientific computing and potentially an undergraduate honors thesis topic. I cooked up a some ...
2
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0answers
69 views

Method for calculating the stopping distance using only integers

I am trying to find how much an engine would turn until it stops accelerating with an acceleration of $a = A \sin^2(x)$. Acceleration Integrating the acceleration I get velocity $v = A(x/2 - \sin(...
2
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0answers
699 views

Precession of Mercury Python simulation

I was trying to simulate the precession of Mercury based on the perturbed solution: $$\frac{1}{r}=\frac{m}{B^{2}}(1+e\cos\phi+3\frac{m^{2}}{B^{2}}(1+e\phi \sin\phi +e^{2}(\frac{1}{2}-\frac{1}{6}\cos2\...
2
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0answers
205 views

Modeling simple laser induced population transfer via adiabatic passage in python

I'm trying to model adiabatic passage between two levels in a three-level atom interacting with two laser fields using Scipy and Numpy.. I'm not sure if my model is wrong due to my incorrectly ...
2
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0answers
130 views

Arbitrary Choosing of the Solution Domain - Navier Stokes and Manufactured Solutions

I want to verify a finite-volume solver (SIMPLE-Algorithm) for the incompressible Navier-Stokes equations by using a manufactured solution. I use Dirichlet boundary conditions for the velocity at all ...
2
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0answers
92 views

Tracking the speed of 2D oscillations on a lattice

I wrote a Monte Carlo simulation of the 2D Lotka-Volterra model on a discrete lattice (with periodic boundary conditions). A video that I produced (which images the system after some number of monte ...
2
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0answers
148 views

Why does my Finite Difference approximation not work?

I am trying to find out the magnitude of the acceleration of my object based on non-uniformly sampled 3D position data. I'm using the standard approximation of the 2nd order derivative on a non-...
1
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0answers
52 views

Problems with simulation of a spatial filter 4f setup (Python)

I have a question about my code which computes numerically the output field of a 4f setup with a pinhole in the middle which works as a spatial filter. My setup consists of two lenses with 50mm focal ...
1
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0answers
69 views

More efficient way to calculate magnetic field using Biot-Savart

I am writing a program in python that is supposed to calculate the magnetic field along a conducting coil that is made up of a bunch of points, and the magnetic field is generated by other conducting ...
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0answers
45 views

Lattice spring models vs. finite element models

I am a beginning graduate student in the field of continuum mechanics. It is my understanding that most problems in this field are numerically solved via finite element methods (FEM). However, I have ...
1
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0answers
29 views

Tackling multiscale problem in numerical simulation

In a dusty plasma system there are more than one component with different masses, i.e, electrons, ions,neutrals and dust grains. Accordingly, there are more than one temporal and spatial scales ...
1
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0answers
58 views

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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0answers
36 views

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 ...
1
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0answers
60 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 ...
1
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0answers
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\...
1
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0answers
81 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 ...
1
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0answers
51 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 ...
1
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0answers
48 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 ...
1
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0answers
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 ...
1
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0answers
126 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 ...
1
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0answers
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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0answers
757 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: ...
1
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0answers
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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0answers
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}{...
1
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0answers
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 ...
1
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0answers
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 ...
1
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0answers
108 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 ...