Questions tagged [computational-physics]

Questions with this tag should be about computational physics, which is the study of physical situations with the use of software (commercial or in-house). Please note that details of writing and/or debugging code is OFF-TOPIC and should be asked at either Computational Science, Code Review or Stack Overflow.

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Interpretation of Stiffness Matrix and Mass Matrix in Finite Element Method

I would like to have a general interpretation of the coefficients of the stiffness matrix that appears in FEM. For instance if we are solving a linear elasticity problem and we modelize the relation ...
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6 votes
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359 views

Upper bounds on phase space momenta

Suppose I wish to calculate the phase space volume for the process $\overline{X}X \to A_1 A_2 A_3 A_4 A_5$ in the CM frame of $\overline{X}, X$ so that $\sqrt{s} = 2m_X$. The volume is given by $$ V \...
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6 votes
2 answers
249 views

Choosing initial condition for Hamilton-Jacobi PDE from initial $x$ and $p$

For separable solutions to Hamilton-Jacobi PDE (say in 2D), we treat the Hamilton's principal function $S$ as $$S= W(x) + W(y) - E*t$$ and treat the separate parts as constants and find $W(x)$, $W(y)$...
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5 votes
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Simulation of a dispersive crystal mirror

I am trying to simulate a simple setup where I have a point source of broadband light whose light is incident upon a spherical crystal at a central angle $\theta_i$. Assuming Bragg diffraction some of ...
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Do systems of fermions take longer to equilibrate than systems of bosons for complexity-theoretic reasons?

This excellent paper by Scott Aaronson persuasively argues that computational complexity can be relevant for physical processes. In particular, what's hard for a hypothetical Turing machine to do may ...
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Do exactly solvable stat mech systems admit efficient algorithms for finite sizes?

I come from a background in statistical mechanics (not algorithm design or complexity theory), and the following question occurred to me that I could use some expert help in beginning to understand. ...
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Numerical Solution of the Propagation-Dispersion equation

I have asked this question on Computational Science and also on Mathoverflow, but no satisfactory answers so far. I thought maybe the physics community could shed some insight on the issue. I am ...
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Numerical problem in solving the Bogoliubov de Gennes equations- methods to solve?

I am trying to solve an assignment on solving the Bogoliubov de Gennes equations self-consistently in Matlab. BdG equations in 1-Dimension are as follows:- $$\left(\begin{array}{cc} -\frac{\hbar^{2}}...
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An explanation for the Landauer's principle

Has anyone understood the Landauer's principle? What is the current status? In specific, is there a theoretical derivation of the Landauer's Principle?(not the heuristic one based on Salizard's ...
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Cross product of operators in exponential: numerical solution

Short version: Numerical solution to a quantum system. I have my discretised wavefunction is real space $\psi(\mathbf{r})$ and in momentum space $\tilde\psi(\mathbf{k}) = \mathcal{F} \left [ \psi(\...
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Are atoms' most precisely known electronic transition frequencies determined theoretically or experimentally?

In principle, the electronic transition energies/frequencies for a given species of atom can be calculated by solving the time-independent many-body fermionic Schrodinger equation for $n$ electrons in ...
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4 votes
1 answer
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Estimating partition function using Montecarlo methods

While working on a completely unrelated quantum computing problem, I ran into a quantity that can be mapped to a partition function of spins on a triangular lattice. It is not quite an Ising model, ...
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4 votes
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159 views

Understanding quantum field theory via simulation

I took graduate QFT course 10 years ago as an undergrad. Did all the homework assignments but it never quite stuck. I think I'd understand the subject better if it were presented differently; ...
4 votes
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226 views

$N$-body gravity simulator: why does energy conservation break down when introducing an adaptive timestep?

I am playing with an N-body gravity simulator using the velocity-verlet algorithm. In the actual simulation I normalize everything so that it is nicely behaved numerically, but I'll express things in ...
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Textbooks on algorithms for the perturbative calculation of High energy physics

For the perturbative calculation of High energy physics, I have known some packages such as FeynArts, FeynCalc, MadGraph, CompHEP, GiNaC, and so on. But I am wondering whether there exists a textbook ...
4 votes
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Computer coding of Perdew Burke and Ernzerhof (PBE) method

I have been assigned the task to write a computer code to implement the Perdew Burke and Ernzerhof (PBE) method. Does anyone know a good reference which can make the coding of this method easier?
4 votes
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Non-linear Wave Equation - Numerical Methods

Motivation: I'm working with a highly non-linear spherical wave-like equation (second order PDE). The equation can be written on the form $$\ddot{u} = f(t, \dot{u},\dot{u}',u',u'')$$ where $'=\frac{...
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3 votes
1 answer
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Numerical package for backreaction in general relativity

I am looking for numerical packages (Python/Matlab or some common languages) that can simulate the backreaction of the matter on the Kerr black hole geometry: i.e. assume I have a given initial ...
3 votes
0 answers
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Numerically calculating the berry curvature for graphene

i'm trying to reproduce this density plot for the Berry curvature in the Brillouin zone of graphene from this website. In order to do this I am attempting to use this equation for the berry curvature ...
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3 votes
1 answer
215 views

Do these Lagrange equations of 1st kind exhibit numerical instabilities?

I followed the lead of "Theoretische Physik", 1e, 2015 by Bartelmann et al. (pp. 171 - 174) to form the set of constituting Lagrange equations of the 1st kind for the double pendulum: eight ...
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3 votes
0 answers
79 views

Quartz crystal resonance frequency simulation

Is there an open source/scientific software package that would allow to simulate Quartz crystal resonance frequency for specific cut angle, crystal geometry and temperature? How would one approach ...
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3 votes
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Large-scale rotational invariance in lattice space

It is often claimed among physicists that rotational invariance can emerge at large scales in lattice space. Let's focus on quantum mechanics for now. I interpret this claim as follows (I am a ...
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No sign problem in quantum Monte carlo simulations of 1D systems?

I've heard many times people saying that there is no sign problem in the quantum Monte Carlo simulations of 1D locally interacting quantum systems. I think this means, for any 1D locally-interacting ...
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0 answers
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Continuum solutions for the Dirac equation in Coulomb potential - numerical codes

Following the representation used in [1, pag. 11] the solution of the Dirac equation in polar coordinates for energy $E$ is of the type: $$ \psi_{E\kappa m}(\bf{r})= \dfrac{1}{r} \Bigg( \begin{matrix} ...
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Decorrelation times for a 2D Ising Model over a range of temperatures

So, I'm trying to simulate the Ising Model on a 2D square lattice of spins. When exploring the auto correlation of the magnetisation: Where the auto covariance: $$A(T) = \langle(M(t)\ - \langle M\...
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3 votes
0 answers
101 views

Light by light cross section using equivalent photon approximation (EPA)

I'm trying to understand how to do a numerical calculation of the light by light cross section utilizing the Equivalent photon approximation (EPA). I'm considering two incoming electron beams of ...
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3 votes
0 answers
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What is the maximum amount of computation that can be performed in the future lifespan of the universe?

The ultimate question I have been trying to answer is the maximum universal population allowed by physical limits. Making some transhumanist assumptions I am perfectly happy with, I am equating this ...
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3 votes
0 answers
157 views

What is the correct way to perform numerical integration over Brillouin zone?

Let us have an integral $I$ over the first Brillouin zone (BZ) of a 2D lattice. $$I = \int\int \Omega(k_x,k_y) dk_x dk_y$$ where $\Omega(k_x,k_y)$ is some function (let's say it's Berry curvature). ...
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3 votes
2 answers
84 views

Using Runge-Kutta method with measurements of acceleration (what to do with half-steps?)

I'd like to perform a short-time motion estimation based on measurements from an Inertial Measurement Unit. If I use the Runge-Kutta method, I will need to compute the k values at half-time steps (Ref)...
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3 votes
1 answer
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Refocusing light field images via Fourier Slice Photograph theorem

I am trying to refocus images from a microlens array light field using Ren Ng's Fourier Slice photograph theorem found in his thesis chapter 5, equation 5.7, which is available at https://stanford.edu/...
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3 votes
0 answers
289 views

Can quantum computing solve the curse of dimensionality?

The curse of dimensionality is ubiquitous in machine learning (ML) modeling, stochastic control and reinforcement learning, arising in a probabilistic sense, with strong connections to quantum ...
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3 votes
0 answers
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Implications of thermodynamic inconsistency in CFD calculations

During my PhD work I had to use tabulated values of thermodynamic properties of gases in some Computational Fluid Dynamics (CFD in short) simulations. CFD simulations consist in the numerical solution ...
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3 votes
0 answers
216 views

Magnetic susceptibility

Currently I'm doing the simulation of Ising Model with Monte Carlo method. I got a curve which the magnetic susceptibility diverge (precisely due to finite size effect, it is not diverge but show the ...
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3 votes
0 answers
52 views

Combined effects of strain and doping on the electronic structure of semiconductors

I've read papers in DFT studies on band gap tuning in semiconductors and the usually studied methods are either through doping or application of external strain. But its always just one or the other. ...
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3 votes
0 answers
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Calculate the matrix size for ground states BEC using difference with Gross–Pitaevskii equation

The Ground states BEC at $0$ temperature can be described by Gross–Pitaevskii equation as $(-\frac{\hbar^2}{2m}\nabla^2+V(r)+g|\psi|^2)\psi(r)=\mu\psi(r)$ We limit the BEC in 2D where $V(r)=\frac{1}{...
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3 votes
1 answer
86 views

Coupling Navier-Stokes and stochastic models for particle tracking in micro-scale free convection?

I have been using a commercially available software to simulate laminar free convection in a specific small domain (let's use channel w/ heated lower wall as an example). The scale is approx 50-100 ...
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3 votes
0 answers
73 views

What are common methods to remove discretization on experimental measures?

I have some experimental data, and since the measurements are digital, the data is discretized/quantized/rounded/truncated. I need to know if there are general methods, or common methods, to "smooth" ...
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3 votes
0 answers
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Unexpected behaviour in numerical simulation of polymer

I noticed some strange behaviour when simulating the behaviour of a polymer subjected to an external pulling force at both ends, and would like to better understand its origin. I used LAMMPS to ...
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  • 311
3 votes
0 answers
114 views

Numerical solution of Parisi equations for the SK spin-glass model

I am trying to reproduce the numerical solution of the so-called Parisi equations for the Sherrington-Kirkpatrick (SK) model. There are at least two main methods to solve these equations, and ...
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3 votes
0 answers
525 views

non-symmetric spherical capacitor

The figures below illustrate (in cross-sectional view) three separate spherical capacitors: an inner solid conducting sphere is surrounded by a hollow thin conducting shell, concentric with the sphere....
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3 votes
0 answers
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Shooting Method for coefficient matching in holography

Usually when one is attempting to solve the equations of motion of a bulk field in the AdS/CFT framework the main goal is to understand if a corresponding boundary operator aqcuires a VEV (commonly ...
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3 votes
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Calculating 2 particle Partial Trace for Density Matrix in Zeeman basis for a large number of Spins

I want to trace out all spins but 2 from a density matrix in the zeeman basis for N spins. For N=3 for example I would have the basisvectors: $ |S=1.5, m=-1.5\rangle =|000\rangle, |S=1.5, m=1.5\rangle ...
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3 votes
0 answers
334 views

Simulation of plasma in tokamak

I am reading some papers on numerical algorithms for simulation of plasma in the context of nuclear fusion in a tokamak. I am getting a little lost as there is a huge number of references, and it is ...
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  • 129
3 votes
0 answers
57 views

The definition of fidelity for fermion

The definition of fidelity for two mixed ensembles is $F=Tr\sqrt{\sqrt{\rho_1}\rho_2\sqrt{\rho_1}}$. Now I came across a problem in numerical calculation, Systems A,B are identical, but attached to ...
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  • 199
3 votes
0 answers
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How are boundary consitions implemented correctly in time dependent hydrodynamics?

I posted this question more than one year ago and got an answer recently. This answer looks good to me, but indicates that something is wrong in my original approach to the problem. Can someone tell ...
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3 votes
0 answers
84 views

Open-source code for computing response functions

Summing Feynman diagrams to compute the response functions of a microscopic model is common in many areas of physics. While conceptually straightforward, the task can be computationally intensive. ...
3 votes
0 answers
419 views

How to calculate dispersion relation from a Finite Difference (FD) wave simulation

I have a python code that calculates the solution of the inhomogeneous acoustic wave equation for a 2D medium with any velocity and source configuration. It was implemented using Finite Differences ...
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  • 131
3 votes
1 answer
82 views

Comparing two versions of the same hydrodynamic code and their error

I have two versions of a hydrodynamic code that has the same underlying physics; let's call them code A and B. However, code B is more optimized and more object oriented than A. I was trying to ...
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  • 722
3 votes
0 answers
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Determining 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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