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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29 views

Integrating a wavelike equation with absorbing boundary conditions

I am trying to numerically solve the following equation: $\frac{\partial^{2} \phi}{\partial t^{2}}-\frac{\partial^{2} \phi}{\partial x^{2}}+V(x) \phi(x, t)=0$ On some domain, with: $\phi(x, 0) = I(x)$ ...
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1answer
42 views

Error too large in leapfrog method for solving the wave equation of a vibrating string

I have been trying to figure out what I did wrong for the last two days. I do not know if I actually did something wrong or if the error is supposed to be this large in usual leapfrog problems. I ...
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1answer
66 views

Acoustic Simulation, how are boundaries handled?

I don't have a background in numerical modeling so this question is rather broad. What I am interested in is modeling the propagation of an ultrasonic acoustic wave in 3d space. The basic 3d wave ...
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44 views

Unsteady Stokes equations in ALE framework

I'm trying to solve Unsteady Stokes equations on a moving domain, using an ALE formulation, that is $$\frac{\partial \mathbf{u}}{\partial t} - \mathbf{w}\cdot \nabla\mathbf{u} = \nu\Delta\mathbf{u} - \...
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1answer
36 views

Trouble Estimating Motor Parameters with Least Squares in MATLAB

Basically, I'm trying to use Least-Squares to estimate the parameters of a DC motor. My system can be modeled by the following matrix equation: $$\begin{bmatrix}V_{input}(t)\\0\end{bmatrix}=\begin{...
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2answers
131 views

Why are fluid simulations so hard?

Fluid simulations solving the hydrodynamic (HD) or the magneto-hydrodynamic (MHD) equations are very useful in physics, the latter being particularly useful for modeling plasmas. Of course these ...
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50 views

Why is perfect sampling not used in large-scale lattice model simulations?

The statistical physics literature is replete with papers describing simulations of lattice models, such as the Ising model. Typically, these are done through Monte Carlo methods, such as the ...
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1answer
132 views

Conserve energy by message passing?

There are $N$ particles with positions $x_i(t)$ and velocities $v_i(t)$ and mass 1. There is a potential function $U_{i,j}(x_i, x_j)$ between each pair of particles, which is $0$ unless the particles ...
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1answer
148 views

Time Reversibility of Velocity Verlet Algorithm

I'm very new to computational Physics and am finding conflicting statements on whether the velocity Verlet algorithm, defined as: $\begin{align} x_{n+1} &= x_n + v_n \Delta t + \frac{1}{2} a_n \...
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1answer
47 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
81 views

Best practice for ADTs in computational science with Fortran

I have been writing a software package in Fortran for solution of the Vlasov-Poisson system in 2D2V. I want this software to be useful beyond its current application (e.g. systems with different ...
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58 views

Solving 1D wave equation with finite difference method

I've written a code in Python to solve the 1D wave equation with the finite difference method (the explicit and the implicit methods). I'm trying to perform a mesh convergence study to estimate the ...
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1answer
68 views

Cauchy Lorentzian simulation on FFT with oscillation

Recently I do simulation on Lorentzian Function with FFT Lorentzian Function is 2a/(x**2+a**2) ...
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1answer
59 views

Sum of random variables - Check your derived distribution against a numerical calculation/histogram

Consider independent random variates $X_0, X_1, . . .$ each uniformly distributed on the support $[0, 1)$ Let's say $Y = X_0 + X_1$, where $X_0$ and $X_1$ are independent uniform random variables with ...
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1answer
96 views

Trouble Making 3rd-Order Sympletic Integrator for Planitary N-Body Problem (A Hamiltonian System)

I am doing a solar-system simulation. I am using Ruth's 3rd order sympletic integrator to avoid the problem of Energy Drift (which I had with RK4), but the the planets quickly leave orbit, and energy ...
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25 views

Negative binomial expansion of general symbolic polynomial

Using Sympy, I would like to compute the negative binomial expansion of a general symbolic polynomial, e.g., $(x_1 + x_2 + x_3 + 4 x_4)^{-1}$. I understand that I can go by recursively partitioning ...
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56 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 ...
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95 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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3answers
333 views

Finite-difference software for solving custom equations

Are there any good, easy to use, software for simulating the evolution of systems of generic differential equations? I know there are custom programs for various specific circumstances (such as ...
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28 views

Set of integrators do not consistently solve an equation in Python

I must solve the following second order differential equation: $\delta \phi^{''}_{\mathbf{k}}+(3-\epsilon)\delta \phi^{'}_{\mathbf{k}}+\left(\frac{k^2}{a^2 H^2}+\frac{V_{,\phi\phi}}{H^2}-6\epsilon +4\...
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27 views

Calypso with quantum espresso for nanoparticles

Any one uses Calypso structure prediction? http://www.calypso.cn/documentation/ I want to run a two type molecules nanoparticle structure Any suggestions will be helpfull. Or if any other tools for ...
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1answer
122 views

Why is $1/r^2$ force law giving spiral trajectory?

I have written a program to solve for Newton's 2nd Law of motion for a given force law, in 2D polar coordinates. It is known that if the force law is of the form $k/r^2$,we get conic sections as ...
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2answers
118 views

Optimization of expensive model with many parameters

I have a physical model which takes $\sim50$ parameters and gives $\sim2000$ outputs taking tens of minutes to run. I need to optimize these parameters to give outputs as close as possible to data. ...
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1answer
75 views

Why is Time evolving block decimation so efficient?

I have a short question about Time evolving block decimation (TEBD). During a lecture I was told that this method is very efficient in evolving 1D quantum spin systems with only nearest neighbor ...
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1answer
131 views

Calculating the Strange Attractor of the Duffing Oscillator in C++

I am simultaneously trying to learn computational physics methods, chaos, and C++. I think this is the right site for the question, and I apologise if not. I started working through Thijssen's ...
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1answer
58 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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0answers
55 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,...
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20 views

Hawkes Process : recursive formula for : $R'_{m,n} (k) = \sum_{ \{i : t_i^n < t_k^m \} } (t_k^m - t_i^n) \exp ( - \beta_{m,n} ( t_k^m - t_i^n ) ) $

Following the advice of a fellow mathematician, I am asking my question here from (https://mathoverflow.net/questions/365554/hawkes-process-recursive-formula-for-r-m-n-k-sum-i-t-in-t) I need to use a ...
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1answer
64 views

Getting streamline for a lid driven cavity flow in openFoam/ParaView

I have installed openFoam on Debian GNU/Linux and learning from official user guide. I have a problem with generating streamlines. I am trying to generate streamlines as explained in the post ...
2
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1answer
95 views

Calculate stable time step DG method for advection-diffusion

For stable time steps for the RKDG method for transport equations we require that $$ \Delta t \le \frac{\Delta x CFL}{(2k + 1)|\lambda|}, $$ where $\lambda$ is the eigenvalue of our conservation law ...
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1answer
67 views

Effect on methods like Crank-Nicolson of adding a potential term, changing heat equation to Schrodinger equation

I'm studying up on methods for numerically solving the Schrodinger equation. The Schrodinger equation with a zero potential is formally identical to the heat equation in the sense that we just make ...
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1answer
82 views

Plotting the difference between an exponential and its Taylor expansion as a function of number of terms?

I'm terribly green, please forgive me. I need to plot the difference between a chosen calculated Taylor expansion $e^x=1+x+\frac {x^2}{2!}+\frac {x^3}{3!}+\frac {x^4}{4!}+\frac {x^5}{5!}$... and the ...
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32 views

COMSOL Circularl polarization

I'm having some problems trying to implement circularly polarized light in COMSOL Muliphysics. For a isotropic homogenous media, I've obtained without problems the TE and TM reflectance curves. ...
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1answer
39 views

MATLAB ode45 doesn't start at initial conditions

I wrote a code in MATLAB to solve a system of differential equations, but my solution doesn't seem to take into consideration the initial conditions I specified. I am not sure how to interpret this ...
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0answers
40 views

How to plot a function for multiple values of a parameter in the same set of axes in Python?

I'm currently trying to plot a graph wich describes a photoionization cross section as a function of incident photon energy for optical transition in a semiconductor for different values of the $\...
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1answer
77 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
117 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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71 views

Applying boundary Conditions on FEM

I have a partial differential equatons as shown below. $$\dfrac{d}{dx}((1+x)\dfrac{du(x)}{dx})=0$$ With the following boundary conditions. $$u(0)=0, u(3)=10$$ To solve it using FEM, I multiplied the ...
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0answers
68 views

Solving nonlinear pendulum using Runge-Kutta 4 for smaller steps

I am trying to solve nonlinear pendulum using 4th order Runge-Kutta method for limits between a=0.0 to b=110 seconds and simulated the results to observe the pendulum movement. But when I increase the ...
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1answer
93 views

Applying weak form

I have two dimensional equation and I want to solve it using Finite Element Methods. $$ \nabla . (\alpha(x,y)\nabla u(x,y)) + \dfrac{\partial u(x,y)}{\partial x}+\dfrac{\partial u(x,y)}{\partial y}+u(...
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1answer
177 views

Difference between MoM and FEM

Method of Moments and Finite Element Methods are two of the most used methods in computational electromagnetics to solve electromagnetic equations. As it is known, in FEM sparse matrixes are used ...
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1answer
161 views

Numerical calculation of Wannier function in optical lattice

I am working out some optical lattice band structures (example here). I have no issue with setting up the eigenvalue equation: $$ H_{jj'}c_{j'}=Ec_{j'} $$ Where $H$ is the tri-diagonal matrix that ...
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1answer
137 views

Scattering of waves in a symmetrical potential (using python)

I'm looking at scattering of waves in a symmetrical potential as part of a research project. If a plane wave $e^{(ikr)}$ is incident on a spherically symmetric potential $V(r)$ the scattered wave is ...
3
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2answers
149 views

Solving a Boundary Value Question $\frac{d^2y}{dx^2}=y\cos(x)+\frac{\sin(x)}{x^2+2}$ using Python

I'm looking to solve this boundary value question using the shooting method! $$\frac{d^2y}{dx^2}=y\cos(x)+\frac{\sin(x)}{x^2+2}$$ given the initial values: $$y'(x=-1)=-1\\y'(x=5)=0$$ I'm aware of ...
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0answers
63 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 ...
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0answers
31 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 ...
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58 views

Why this LJ molecular dynamics result doesn't converge?

I am doing a molecular dynamics simulation of Leonard Jones 6-12 potential. But instead of converging to a particular value. It always stays between -5.58 to -5.62. The standard value is -5.517. The ...
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1answer
58 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
55 views

Numpys `tensordot` and what is happening mathematically

I've encountered a program where np.tensordot was used, so I tried looking it up but I can't really understand what this function is doing... I feel rather ...
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1answer
65 views

Is this behaviour normal for a Lennard-Jones monte carlo simulation?

I am simulating a Lennard-Jones fluid using MC simulation. The code always uses a reduced unit. I want to find the potential energy of the system. Periodic boundary condition implemented. I have ...

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