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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48 views

Is it possible to create computational substrates from a distance?

Processors are manufactured by photolithography, shining a light on a chemically prepared object. Layer by layer, an "active" object with computational capabilities results. Does/can a ...
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How to integrate over a timestep in a mass-spring model? [closed]

I'm writing a simulation of a block of matter using a "mass-spring" model, where the matter is modelled as a 3D lattice of point masses, where each point is connected by springs to the (up ...
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1answer
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Numerical evaluation of Green function to evolve wavefunction for harmonic oscillator [closed]

Inspired by the paper "Feynman's derivation of the Schrodinger equation", I'm trying to do a simple numerical evaluation of the following equation (4.1) from the paper: $$ \psi (x,t_2) = \...
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1answer
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Does Density Functional Theory (DFT) underestimate the conduction band level only?

Based on the detailed answers provided for the reasons for the underestimation of bandgaps in DFT calculations, can we deduce that it is based on an underestimation of the conduction band level but ...
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Modeling curved light in media with “complex” indices of refraction

I've written an algorithm to solve the Time Difference of Arrival (TDoA) localization problem, using Bancroft's method (see). Given the coordinates of $n$ nodes in ...
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85 views

Dimensionality of fluid flow

In some textbooks flow is classified as one, two, or three-dimensional depending on the number of space coordinates (i.e. x,y,z) required to specify the velocity field while according to some other ...
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1answer
142 views

Interpretation of Coulomb operator in Hartree-Fock equation

I have read in a textbook (Modern Quantum Chemistry Szabo and Ostlund) that the Coulomb operator of the form \begin{equation} \mathcal{J}_{j}\left(\mathbf{x}_{1}\right)=\int d \mathbf{x}_{2}\left|\...
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2answers
89 views

Can we always integrate numerically?

I dont know if its suitable here or on Math SE, Most of the times, when I watched online lectures most lecturers say that if we cant solve a integral exactly we can always numerically integrate it. (E....
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1answer
35 views

Stochastic matrix of three states which has Boltzmann distribution as equilibrium

In my course on computational physics we are given the following exercise: I already solved the first and second part, but I'm stuck at the third. I've tried matrix multiplication of the stochastic ...
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Force field parameters for Molecular Dynamics simulation

AMBER force field From a PDB file we know the position of atoms $$r_1, r_2, ...$$ How can one find from $r_i$ the following? $$l_i, \theta_i, \omega_i, \gamma_i$$
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1answer
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Resonant tunneling for wavepackets, simulation - what exactly is happening here?

I have been learning various ways to solve TDSE and naturally, wavepacket motion seemed like a good test case to check the algorithms. Then, of course, I wanted to see one of the most interesting ...
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1answer
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Is there any point in doing Monte Carlo on classical 2D Ising spin systems? [closed]

The partition function of a classical Ising spin system with arbitrary bonds on any planar graph can be evaluated in polynomial time, through the FKT algorithm. And if I understand correctly, this ...
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How can we calculate solar and lunar longitude in java?

I want to develop panchangam logically. So, I want to find solar longitude and lunar longitude. Could you please help me to find the solar and lunar longitudes in java or any mathematical formula for ...
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Numerical discretization and the Schrodinger equation, for a simulation

i'm solving numerically the Schrodinger time dependent equation, in this case simplified to one dimension, and i don't know at all how to discretize it, or if what i have done its okay. $$i\hbar\frac{\...
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1answer
32 views

How do I initialize a 3D Velocity field with a 1D velocity vector? [closed]

I have a 1D flame solution, with velocity magnitude. I want to transform this into a 3D velocity field that is symmetric in all directions. It is an expanding spherical flame.
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1answer
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2D rocket lander vectors (gamedev)

I'm writing a game prototype with simple 2D Physics, of a 2D rocket "lander" style. Let's assume that there is a downward gravity of (0, -1). The rocket has an up-vector (that can be also ...
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1answer
53 views

$N$-Body Solar System Simulator - Why are there inaccuracies in the $x$ plane but not the others? [closed]

I have written a basic $N$-Body simulator that simulates the motion of the planets in the solar system. The system reads the positions and velocities of the planets at a given time, measures the time ...
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1answer
48 views

How is the set of states $Q$ logically replaced by a Hilbert space?

Question is: How is the set of states $Q$ logically replaced by a Hilbert space if a classical Turing machine is described by a 7-tuple $M=\langle Q,\Gamma, b,\Sigma, \delta, q_ {0},F\rangle$? I read ...
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2answers
105 views

Is the position kinematic equation an approximation?

Is the $\Delta x=v_0t+\frac{1}{2}at^2$ kinematic equation an approximation? I'm not asking with reference to relativity, but rather is it still an approximation within Newtonian Physics? I remember ...
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Question about discretizing Laplace equation of potential flow

I've learned from fluid mechanic class that the laplace equation of stream function $\Phi$ can be discretized by $\Phi_{0}=\frac{\Phi_{A}+\phi_{B}+\Phi_{C}+\Phi_{D}}{4}$, if the flow is irrotational ...
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CHSH and absolute value, plus impossibility of complete definiteness

Along the proof of CHSH inequality, the following point is reached : $$C=\int|A(a,x)B(b,x)-A(a,x)B(b',x)|+|A(a',x)B(b,x)+A(a',x)B(b',x)|dx$$ Then factorizes the A in each absolute value and deduces $C\...
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Computer code to quickly check equation of motion to first or higher order from action (4D spacetime)

I derived equations of motion up to first order from a Lagrangian for a scalar field in a 4D spacetime. Now, I would like to cross-check my results. Is there by any chance an application / code /...
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1answer
151 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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2answers
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Can we have chaotic motion due to the finite precision of our calculations? [duplicate]

I understand chaotic motion to mean that very small perturbations in the initial starting condition can lead to very different trajectories in phase space. For this reason, we can never predict the ...
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1answer
60 views

Why is the production of turbulent kinetic energy maximum in the lowest layers of the turbulent boundary layer?

I have been studying the basics of CFD from a book titled 'An Introduction to Computational Fluid Dynamics' by H.K. Versteeg. In the turbulence modelling section, the author shows how the production ...
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0answers
69 views

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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26 views

Lane-Emden. Quasi-linearization method

ow to prove this theorem? I have a doubt. Theroem: Suppose that $w(x,\alpha)$ solved $\ddot{w}+\frac{2}{x}\dot{w}+\alpha^{2}w=0$ with $w(0)=1$, $\dot{w}(0)=0$, $w(1)=0$. Then $v(x,\alpha) := \omega w(...
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56 views

COMSOL Multiphysics

As a beginner for CFD modelling of plate subduction I heard comsol to be a good software. Can anybody suggests alternatives and the demerits of using COMSOL Multiphysics?
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53 views

Mathematical model of the compression of a syringe by means of the action of a motor

Does anyone know how I can get a hydrodynamic model of the compression of a syringe by means of the force of a motor ($ F_ {M} $). Where $ F_ {atm} $ is the force due to atmospheric pressure, $ F_ {r} ...
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2answers
208 views

How can the universe be a computation?

A few physicists (or computer scientists) take it for granted that the universe is a computation. However, I am not able to understand how the universe CAN be a computation in the first place. I come ...
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29 views

Model parameter derivation, least squares fitting vs solving systems of equations

PS: Let me preface this with I barely have an idea how to ask this question so bare with my ramblings. I'm trying to fit a 5 parameter model to gravitational lenses. For this I have 2 classes of ...
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30 views

Enquiry about Kernel Polynomial Method for Hamiltonian

I read a paper (Alexander Weiße, Gerhard Wellein, Andreas Alvermann, and Holger Fehske, The kernel polynomial method, Rev. Mod. Phys. 78, 275, 2006), which discusses how to use the Kernel Polynomial ...
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1answer
148 views

What is mach number = 0?

If you look at a paper on fluid dynamics, you will see a paper that is performing CFD simulation with a mach number of 0. This means that the flow velocity is 0, so I thought that no flow would occur, ...
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25 views

Majorana number from real space hamiltonian

Kitaev paper Can a real space 2N*2N hamiltonian of a Kitaev chain be used to get the Majorana number using Pfaffian? I am very much confused about this.
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2answers
385 views

Fastest numerical method to solve Lindblad Master Equation?

The Lindblad Master Equation is a generalization of the Schrodinger Equation for open quantum systems, given by $$ \frac{\mathrm{d} \rho}{\mathrm{d}t} = -i \left[ H, \rho\right] + \sum_k \gamma_k \...
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2answers
59 views

Planck distribution integration

Does anyone know how to compute analytically or numerically the following integral (for $T=10^4$K)?: $$n_\gamma=\frac{1}{\hbar^3\pi^2c^3}\int\limits_{2.1789\cdot 10^{-18}}^{+\infty}\dfrac{E^2\mathrm{d}...
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2answers
90 views

Interactive physics simulations and animations

What are some free and open-source interactive simulations, illustrations, animations, demonstrations, videos, calculators and other resources for experimental physics and mathematics like the Wolfram ...
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0answers
26 views

Impulses in a Collision

The question I have is that of computing the impulse in a collision between two objects in real life (or in a scenario that is very close to real life). I wish to simulate collisions of objects of ...
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1answer
92 views

Solution to heat equation with changing boundary conditions

I am attempting to solve a homogeneous heat equation \begin{equation} u_t = \alpha^2 u_{xx}, \end{equation} with an initial temperature $u_0$, and time-varying boundary conditions $u(0,t) = u(L,t) = ...
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16 views

Simple method for calculating and plotting the band structure of a known periodic potential?

A thousand pardons if this is trivial, but I've been stuck here for hours. I'm trying to compute the spectrum and eigenfunctions (i.e. band structure) of the eigenvalue equation $u'' + k^2\epsilon\...
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38 views

Floquet Quasi-Energy spectrum in periodically driven lattice (Numerics)

I am trying to understand the steps for numerically diagonalizing the Hamiltonian for an amplitude modulated lattice. I am trying to follow along with the calculations in section 4.6 of this thesis. ...
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80 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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62 views

Cluster Monte Carlo for Heisenberg spins?

I am learning Monte Carlo simulation for the classical spin systems. I am wondering if there is an efficient way to do classical Monte Carlo simulation for $O(3)$ Heisenberg spins(i.e. unlike the ...
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2answers
107 views

Eigenvalues in Floquet theory

After calculating Floquet Hamiltonian and then it's eigenvalues I stumbled upon a problem with ordering of eigenvalues. I am using eigen library for c++ and for every Floquet Hamiltonian for given ...
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1answer
53 views

Applying boundary conditions to discretized hamiltonian

I am trying to implement reflecting boundary conditions of $ \begin{align} \psi_N \equiv \psi_{N-1}, \end{align} $ $ \begin{align} \psi_{-1} \equiv \psi_0, \end{align} $ to the hamiltonian matrix and ...
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1answer
64 views

Numerics for Bose-Hubbard model

For the Bose-Hubbard model, we know that there are the Mott insulator phase with $\langle a_i \rangle = 0$ and the superfluid phase with $\langle a_i \rangle \neq 0$. However, when we are trying to ...
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44 views

Is a solution to the Hartree-Fock equations guaranteed to exist? Is it a Slater determinant in any basis?

My understanding is that the Hartree-Fock equations can be derived from the variational theorem as follows: The variational theorem states that for an arbitrary wavefunction $|\psi \rangle$, $\langle \...
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1answer
56 views

What's wrong with my DFT implementation? [closed]

I am trying to write an implementation of the discrete Fourier transform myself in Python, but for some reason, the transform that I get out is wrong. There are no fancy tricks in my implementation, I ...
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0answers
29 views

Slow converging in Monte Carlo due to Shell effect [closed]

While I was reading materials, the author mentioned that Monte Carlo converges slowly due to shell effect while filling the single particle states, but using a twisted boundary will make it go much ...
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1answer
93 views

How to calculate acceleration due to gravity in a 3D $N$-Body system?

How do you calculate acceleration due to gravity for objects in 3D space? My current understanding for the force due to gravity on object $i$ from object $j$ is $$\mathbf{F}_g=(\mathbf{r}_j-\mathbf{r}...

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