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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13 views

Can a numerical solution transport equation be stable AND have negative numbers?

I am trying do to a very simple fluid dynamics program using one dimensional transport equation: $$ \frac{\partial Q}{\partial t} = u \frac{\partial Q}{\partial x} - \alpha \frac{\partial^2 Q}{\...
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High pass filter string systems

The differential equation of a string for small oscillations with tension $T = T_0 e^{ax}$ and $\rho = \rho_0 e^{ax}$ is (ignoring friction) $$\frac{\partial^2 y}{\partial x^2} + a \frac{\partial y}{\...
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23 views

Virial pressure of individual particles

Can the virial theorem $$PV = NT + \frac{1}{d} \langle \sum_{i<j} \vec{ r_{ij} } \cdot \vec{ f_{ij} } \rangle$$ be used to compute the individual pressure of the particles? so instead of averaging ...
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What is non-collinear magnetism?

I've just started learning about non-collinear magnetism and heusler alloys and I am finding it hard to understand the concept of non collinear magnetism. I have found few papers on it but most of ...
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Quantum Monte Carlo: arbitrary Observables in Worm Algorithm

Consider a generic Hamiltonian of interacting particles on a lattice, where $a^{\dagger}_i$ creates a particle at site $i$, and $n_i=a^{\dagger}_i a_i$ and $\langle i, j\rangle$ are nearest neighbors. ...
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Reproducing results of 'Helical Metal Inside a Topological Band Insulator' paper

I am trying to reproduce the results in the given paper. I am confused about the process to implement the given hamiltonian Eq. (2) on a diamond lattice. Like, if I want to just code the $H$ in the ...
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Can one use the variational or basis-set expansion methods to solve the Dirac equation for electrons in condensed matter or atoms/molecules?

Numerical methods such as the variational method or plane-wave basis set expansion are routinely used to solve the Schrödinger equation for electrons in condensed matter or atoms/molecules. Are there ...
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32 views

Numerical diffrential equation in physics [closed]

Consider the mass–spring system where dry friction is present between the block and the horizontal surface. The frictional force has a constant magnitude µmg (µ is the coefficient of friction) and ...
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59 views

Rotation Reference Change Transformation CRTBP Python

I have created the following script that will propagate the dynamics of the CRTBP set for the Earth-Moon system. I have the initial conditions set for a vertical Lyaponov orbit. The goal I am trying ...
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Can a Mach number be defined for a hot gas fluid element using its own temperature and velocity?

I know that the ratio of an object's speed to the local sound speed is called the Mach number: $$M = \frac{v}{c_s}$$ where $$c_s = \sqrt{\frac{\gamma kT}{\mu m_p}}$$ I have always thought of the Mach ...
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25 views

Can a high density of particles simulate fluid dynamics?

There are different ways to simulate fluids, some involve numerical solutions to PDEs. I was wondering if these PDE formulations can be thought of as an a infinite limit of a collection of particles? ...
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How to simulate or solve $n$-legged manometer without solving Euler's equations?

Consider a typical manometer tube but with $n$-legs, different heights at the initial time. Is there any way to solve it numerically or analytically without solving NS or Euler's equations? For ...
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Numerical evaluation of Green function to evolve wavefunction for harmonic oscillator: Part II

This is part 2 of my original question. Briefly, I am numerically evaluating $$ \psi (x,t_2) = \int dy \, G(x,y) \psi(y,t_1),$$ with $t_2 > t_1$. $t_2-t_1=\Delta t = \epsilon $. My $G$ is given by $...
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How to get $E$ (Eigenvalue) or $E_n$ from this transcendental complex equation? [migrated]

I want to solve this transcendental complex equation, but I don't know the step by step to get E in form equation and value of E ...
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Numerical many body physics book recommendation?

Can you recommend me a good many-body physics book with emphasis on numerical implementations? There are quite few good theoretical books in many body nowadays - Abrikosov, Gorkov, Dzyaloshinskii; ...
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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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2answers
46 views

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
52 views

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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13 views

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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20 views

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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51 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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117 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
86 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
33 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
56 views

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
64 views

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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23 views

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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1answer
50 views

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
30 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
36 views

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
50 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
91 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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62 views

How to numerically solve this scalar field equation?

Using Mathematica, I would like to numerically solve the following partial derivatives equation : $$\tag{1} \frac{\partial^2 \Phi}{\partial T^2} - \frac{\partial^2 \Phi}{\partial X^2}- \frac{\...
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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
76 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
76 views

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
20 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
49 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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20 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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23 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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34 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
151 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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19 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
53 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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13 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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