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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What numerical methods are used to model deformations in elastic physics?

What numerical methods are used to model deformations in elastic physics? For example, here's an example of a hyperelastic deformation in Ansys: Perhaps more simply than hyperelasticity, for linear ...
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159 views

How can I learn Scientific Python?

I am an intermediate user of Matlab and Mathematica, but I would really love to start learning Python language for scientific purposes (I am interested in Maths and Physics). Could please someone ...
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243 views

Can Runga-Kutta method be used to solve non-linear differential equations?

Consider two-body central force problem in polar co-ordinates $r,θ$. Corresponding 2nd order differential equation is obtained by using conservation of angular momentum. This equation is : $ d^2r/dt^...
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147 views

Solving a small non-symmetric, non-diagonally dominant, and non-sparse system

I want to solve a small (20 $\times$ 20 up to 30$\times$30) system which is not symmetric, not diagonally dominant, and not sparse. Each row contains a modified form of the Legendre coefficient of a ...
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1answer
100 views

Numerical bottlenecks

On a desktop scale computer, what are the most important bottlenecks (RAM vs. CPU, single vs. multithread) for numerical calculations? I'm specifically most interested in exact diagonalization and ...
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1answer
95 views

Evaluating an indefinite integral that has no closed form

I need to evaluate the following indefinite integral: $$I=\int\frac{x^5+2ax^3+a^2x-4a}{x^7+ax^5+2ax^4}dx=\int\frac{x^5+2ax^3+a^2x-4a}{x^4(x^3+ax+2a)}dx$$ The solution that I obtained while ...
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1answer
48 views

What are the things I should keep in mind before doing an analysis of my gromacs simulation?

I did a liquid argon simulation at 100k. I forgot during analysis that I need to accommodate for the Periodic Boundary Conditions before doing any analysis which included distance. What are other such ...
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1answer
329 views

Performing a random walk on a lattice that traps the particles

I am trying to solve this problem where we have a 1D-lattice of size 100 and the particle can start from any position in the lattice and moves randomly on it(with equal probability of moving to either ...
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2answers
109 views

Trotter expansions in ode solver?

Trotter expansions say: $$ e^{A+B} = \lim_{P\to\infty} \big(e^{A/2P} e^{B/P} e^{A/2P} \big)^P. $$ With $P = 2$, it becomes (with high accuracy) $$ e^{A/4} e^{B/2} e^{A/2} e^{B/2} e^{A/4}. $$ Let's ...
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945 views

How to implement Newton method in solving 1D PDE system? (ie. Poisson eq, continuity eq, drift-diffusion eq.)

I want to solve PDE system, which consists of Poisson equation, continuity equations for electron and hole with drift-diffusion equation numerically, by using method called Newton's method. This ...
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2answers
67 views

Numerical minimization of the action in python

I want to find the trajectory $x(t)$ which minimizes the action $S = \int_{t_i}^{t_f} L(x(t), \dot{x}(t)) \mathrm{d}t$ numerically. I am trying to do it by discretizing the action so it is more of a ...
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1answer
70 views

Solution of Coupled Differential equation for a 2d linear flow using RK4 method in python 3

I want to study the dynamics of a 2d linear flow, whose dynamical equation is- $\begin{pmatrix} \dot{x_1}\\ \dot{x_2}\\ \end{pmatrix}=\begin{pmatrix} 1 & 1\\ 4 & -2\\ \end{pmatrix}\begin{...
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1answer
62 views

Which are the right configurations in the Markov chain of a Hamiltonian Monte Carlo algorithm?

I have a question about the Markov Chain Hamiltonian Monte Carlo (MCHMC). Hamiltonian Monte Carlo is known as Hybrid Monte Carlo too. I'll describe the steps of the algorithm. We have at the ...
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1answer
290 views

Runge-Kutta fourth order method. Integrating backwards

I am using a Runge-Kutta fourth order method to solve numerically the usual equation of motion of a background scalar field in curved spacetime with a quartic potential: $\phi^{''}=-3\left(1+\frac{H^{...
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1answer
134 views

How to do Weierstrass-transform in MATLAB?

I have a diagonalization problem. I have the eigenstates correctly, and I want to do a Gaussian-smearing (Weierstrass-transform) on them. So I have the wave functions ($\Psi$), and the continuous ...
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1answer
3k views

Is there an advantage of using a staggered grid over a regular one when combined with high order methods?

The title says is all. This question is in the contest of an incompressible Navier-Stokes solver. Specifically, I am currently working on a new solver while referring myself to an older code for ...
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1answer
494 views

Implementing velocity verlet for harmonic oscillator in C gives error wrt conservation of energy

I'm attempting to implement velocity Verlet with a harmonic oscillator in C, but I have some errors: Energy is not being conserved Energy oscillates much more than I would expect I believe the error ...
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1answer
52 views

Modifying finite difference solution to Schrodinger eqn to account for fermion/boson effects

I have been playing with an implementation of Visscher's explicit method for solving the time dependent Schrodinger equation (Are there simple ways to numerically solve the time-dependent Schö...
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1answer
224 views

Coupled PDE: a confusion in boundary condition setup

I have a coupled PDE problem(Poisson-Schrondinger system), i.e. first I need to solve an eigenvalue problem (Schrodinger problem discretized by Galerkin method) $$Ax=\lambda x, ~~~A=A(u)$$ the ...
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2answers
119 views

Diagonalization using LAPACK

Say, we have a Hamiltonian which for simplicity does not mix particle hole sectors. It is just a simple Hamiltonian in real space as shown, $H=\sum_{ij,\sigma} A(i,j)(c_{i\sigma}^{\dagger}c_{j\sigma} +...
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1answer
88 views

Applications of Julia in Chemistry and Molecular Physics?

I was wondering if there are any Theoretical & Computational Chemistry (MM, QM) codes or publications out there that are based primarily on the Julia programming language?
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1answer
484 views

What is the relationship between shape functions, interpolation functions, and degrees of freedom?

I am a newbie in FEM. I would like to get clarity regarding a few questions on shape functions in this post (please use as simple language as possible). What is the relation between Shape function ...
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1answer
376 views

Problem concerning a part of a simulation for the Ising Model

I was wondering if anyone could help me with a simulation in Python (there is a small part of the code where I have a question) about the Ising model. First, I wanted to get the magnetization $M$ ...
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2answers
79 views

Guaranteed equality between binary results with increasing MPI processes

Testing on an MPI scientific code for compressible flow dynamics I noticed that the results may depend on the number of processors used for the calculation. In fact, comparing the binary files they ...
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2answers
3k views

Solving the 1D Particle-in-a-Box using C++

I've just finished learning the physics behind the problem and would like to write a program in C++ than can solve the problem. I'm actually stuck at the start. I've quite a bit of research, the ...
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1answer
141 views

Oil/Water interface simulation using GROMACS

I would like to perform a decane/water(tip4p) interface simulation using GROMACS to analyse the fluctuation of the interface over a long period of time (50ps - 1ns). Though I have a rough idea on ...
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1answer
343 views

Higher-order Verlet integration

I'm using a simple version of Verlet integration for a particle–particle interaction system with collisions. At the end of each iteration, I integrate like this: ...
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1answer
328 views

Numerical Free Fall Analysis with RK4

I am trying to calculate real speed and time in free fall of a body. I wrote a code in Fortran and I am trying to improve it by using RK4 method x=time y=total free fall Purple line using: ...
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2answers
100 views

Should energy be conserved in an N-body simulation where particles don't lose energy in collisions?

In an N-body simulation where forces between particles are attractive and particles do not lose energy on colliding with walls or each other, should energy be conserved? How could it be, with total ...
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1answer
66 views

nodal lines of wave-function $\psi(x,y) = \sin 12x \sin y + (1 + \epsilon) \sin x \sin 12y$

I am trying to reproduce this figure of nodal lines of a wavefunction from this work of Berry $$\psi = \sin 2r\,x \sin y + (1 + \epsilon) \sin x \sin 2r\,y$$ Here the image. The first is $\epsilon = ...
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1answer
107 views

What is a good algorithm, and framework, to calculate centres of gravity or mass (cog)?

I'd like to take an photograph, subdivide it into a tesselation, either of squares, or (ideally), hexagons, and then find the centre of gravity (or, if you prefer, centre of mass) of each cell of the ...
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1answer
159 views

Boundary treatment with higher order methods

I wrote a code which solves the 2D Poisson equation with homogeneous Dirichlet BC everywhere and a source term of -1. I am using the classical Jacobi iteration method. The grid is $N_x \, \mathrm{x} \,...
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2answers
111 views

Definition of inflow boundary in CFD

If $w$ is the vector of conservative variables, $f=f(w)$ the flux function, I think have read somewhere (I can not find it anymore) that the inflow boundary $\Sigma$_ is characterized by: $\Sigma_{-}...
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2answers
98 views

Propagation of error using Euler's first order method [duplicate]

I was estimating a falling object's position versus time by using a simple first order step function, where ...
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1answer
52 views

Anisotropic invariant expansion

I am trying to calculate the second and third invariants for a turbulent flow. I have the second order statistics (both transient and averaged). i.e $uu$, $vv$, $ww$, $uv$, $vw$ and $uw$. These are ...
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1answer
56 views

Electrostatic Force - Simulate Trajectory of Test Particle using Runge Kutta - Force always Repels

In the center of a 2D-Plane a positive static charge Q is placed with position r_prime. This charge creates a static electrical Field E. Now i want to place a test particle with charge Q and position ...
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1answer
195 views

Solving an ODE using odeint in Python and continuing the integration

The following relates to the linked question: Scattering of waves in a symmetrical potential (using python) I have attempted to solve the problem for $U(r)$ using ...
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1answer
62 views

How long should the hyperelastic equations be solved before updating the mesh?

How long should the hyperelastic equations be solved before updating the mesh? To be specific, I'm interested in the hyperelastic model with a neo-Hookean solid: $$ \nabla\cdot\sigma + f = \rho\ddot{...
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1answer
136 views

Operator splitting to solve time dependent Schrödinger equation

I encountered the split operator method to solve the time dependent Schrödinger equation during a lecture. I understand the method on a theoretical basis (I think at least), but I'm struggling to ...
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1answer
229 views

For a determined (known) Space charge density, what are the conditions to obtain the Electric potential/field distribution? (COMSOL, MATLAB)

Theoretic part From the theory, in Electrostatics inside a real dielectric material between real conductors, in a simple 1D plane geometry between points $P1$ and $P2$, according to the current ...
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1answer
87 views

Manual for library Libxc

Where can I find the manual for software library Libxc for exchange-correlation functionals? Links with domain www.tddft.org don't work.
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1answer
57 views

Should the derivative of an array be calculated array by array or element by element in CFD codes?

I am making my own finite difference computational magnetohydrodynamic code in Fortran 90. Looking at other codes they appear to calculate for example their $x$-derivatives, bb of their variables, e.g....
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1answer
87 views

Loss of energy when using Roe Solver for solving onedimensional Shallow Water Equations

I have written a Roe solver with Harten entropy fix code in Matlab to numerically solve the one-dimensional Shallow Water Equations. : \begin{eqnarray} \dfrac{\partial h(x,t)}{\partial t} + \dfrac{\...
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1answer
1k views

Boole's Rule in python

This is my first post in this forum so please forgive me if it is not the way it should be. My problem is about implementing "Boole's rule" into python. I have succesfully implementet trapezoidal and ...
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1answer
681 views

Can we simulate rigid body motion using finite element analysis?

I was wondering if we could model rigid body motion of bodies using finite element models. Particularly I'm interested to know if we can model motion of objects with no constraints or with some ...
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1answer
74 views

Defining dimensionless tempearture for Periodic flow systems

Given a flow inside a square duct with constant temperature at the walls $(T_{w1} = T_{w2} = T_w)$ the physical property in terms of temperature that repeats itself in a periodic fashion is the $\...
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1answer
766 views

Proper boundary conditions for potential flow around cylinder

I am computing the stationary, incompressible, inviscid and irrotational flow around a circular cylinder using a discretization in general coordinates. I derived a PDE and proper boundary conditions ...
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2answers
180 views

Discussing the energy spectrum of Langevin Dynamics simulation of many atoms

UPDATED I've coded a multiparticle MD simulation in 3D. It is based on Langevin Dynamics, with random impulse and dissipation. I think the program works correctly now? I have attached the plots of ...
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2answers
166 views

Computational Physics: Finding the Diffusion Coefficient from the Discretized Diffusion Equation

I'm pretty new to translating simulation to reality so please forgive the perhaps naive approach I'm taking here. If we have a (quasi-2D) experimental video of a certain concentration changing with ...
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1answer
139 views

Finding the lowest $n$ eigenvalues of a band-diagonal Matrix

I have a real sparse matrix of the form $$ \left( \begin{array}{ccc} h_{11} & h_{12} & 0 & h_{14} & & & \\ h_{21} & h_{22} & h_{23} & 0 & h_{25} & & ...

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