All Questions
Tagged with numerics or computational-physics
1,932 questions
0
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An elementary question about an integration formula (nomenclature probably archaic)
so I am working on this research paper: https://docdro.id/sZsZiYL
Basically, the authors use a so-called Yee grid in order to discretize Maxwell's equations for computational purposes. In the paper, ...
- 21
0
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0
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56
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How to numerically solve non-linear 1D diffusion equation in time-domain?
The equation to be solved is this:
$$\frac{\partial H_y(x,t)}{\partial t}=\left(\frac{1}{\sigma\:\mu(H_y)}\right)\frac{\partial^{2}{H_y(x,t)}}{\partial{x^{2}}}$$
But note that the magnetic ...
- 101
2
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1
answer
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Numerically solving the TOV equations: how to find the max radius and mass?
I'm solving the TOV (Tolman-Oppenheimer-Volkoff) equations using Mathematica 13.2, and I'm having some issues at finding the outer radius $r_{\text{max}}$ and mass $M_{\text{max}}$ of the spherical ...
- 7,677
2
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1
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233
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(Weakly compressible) Smoothed Particle Hydrodynamics (SPH) and speed of sound
In SPH (weakly compressible approach) the Cole state equation is used to compute pressure from density:
$$p(\rho)=\frac{\rho_0c^2}{\gamma}\left(\left(\frac{\rho}{\rho_0}\right)^\gamma-1\right)+p_0$$
$...
- 121
1
vote
1
answer
99
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Suscpectibility in Ising networks
I am struggling to find good references on how the susceptibility described phase transitions in Ising networks. First of all i struggle to find a good defintion for the susceptibility.
I understood ...
1
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0
answers
160
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How does convex splitting method work?
I'm an undergraduate physics student and I'm simulating some partial differential equations using finite element method. For non-linear equations I found a method called linear convex splitting ...
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1
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0
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36
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Is the Lennard-Jones system in Newtonian mechanics ergodic?
A large part of the computational physics literature relies on solving Newtons equations for deriving phase diagrams and related properties of the LJ system.
In many cases this approach does not ...
- 905
2
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0
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69
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Extreme Kerr render engine issue
So, me and a friend have been working on a Kerr render engine. It uses the Kerr metric of general relativity to draw the image of a black hole. Our current results look like this;
The accounted for ...
- 308
3
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1
answer
90
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Modelling a fully relativistic White Dwarf Star
I am trying to model a fully relativistic white dwarf using different central densities. Using the below equations:
$\frac{dP}{dm} = -\frac{Gm}{4\pi r^4}$
$\frac{dr}{dm} = -\frac{1}{4\pi\rho r^2}$
and ...
- 31
1
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1
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111
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If spacetime is discrete, would we observe continuous models to show non-rounding and non-truncation errors?
Typically, the ground truth is taken to be the continuous model. Numerical simulations are taken to be the approximation. These simulations deviate from the continuous model due to both a constant ...
- 900
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1
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166
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How does the pressure inside a pipe drop for a compressible gas (hydrogen)?
It is about turbulent compressible fluid, in this case, hydrogen gas.
I have hydrogen gas at Ti = 25 K, pi = 3 bars, and ṁi = 0.001 kg/s (so 2.214 m/s) at the inlet of the tube. The pipe is 12.7 mm in ...
0
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0
answers
48
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Asking about a clarification of a rather strange notation of a Yee Grid used for discretizing Maxwell's Equations
The thesis I am following requires me to discuss a rather strange formulation of a Yee grid used to discretize Maxwell's equations in order to solve them numerically mentioned in a research paper. The ...
- 21
1
vote
1
answer
143
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Gauge freedom issues when numerically calculating overlap of states
Calculations of quantities of the form:
$$\langle\psi(k)|\partial_k|\psi(k) \rangle \ ,$$
require a smooth choice of the wave function $|\psi(k)\rangle$ over the whole BZ. This is not a problem. ...
- 11
1
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0
answers
49
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What machine learning technique can help generate spectrum line profiles?
I'm trying to work with Calcium-K line profiles from the Sun.
Image for reference. Please ignore the labels on the image and note that my profiles are not in image format (more info below).
I have ...
1
vote
1
answer
52
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Aggregating an atmospheric gas concentration profile
I have a list of CO2 gas concentrations in the atmosphere in g/g relative to dry air according to a pressure profile. I have the top and bottom pressures for each level.
The list corresponds to a 40 ...
- 11
1
vote
1
answer
68
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How do I model particle motion using normalized position magnitude and unit vectors?
I am trying to model a particle moving in a non-linear trajectory. I am working with real-time motion equipment, so I have already accounted for simple linear translation in 3D space using S-curve ...
- 11
0
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1
answer
79
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How to handle collisions in a game? [closed]
This must seem like a very basic question, but I'm building a game engine and need some help. Let's say that two objects, o1 and o2 collide with each other (defined by the first time their bounds ...
- 3
1
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0
answers
99
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Good Mathematica package for computing Feynman graphs (resource request)?
I was wondering if anyone had any go-to Mathematica packages for computing higher-order Feynman graphs. Specifically ones that would allow me to construct higher spin fields like $h_{\mu\nu}$ and then ...
0
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1
answer
107
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Why, if the potential is different from the Coulomb one, but has spherical symmetry, the eigenvalues of the system are non-degenerate?
I have found the eigenvalues of the following systems: $H=-\frac{1}{2}\Delta+V_1$ and $H=-\frac{1}{2}\Delta+V_2$, using NDEigensystem by Wolfram Mathematica.
In the ...
- 233
0
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1
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44
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How do I calculate the Reynolds Number of fluid parcels around an aritrary object (with respect to CFD)? [closed]
Purpose: I am trying to create my own simplified rapid CFD software for custom purposes.
Given an arbitrary object surrounded by a moving fluid (from an arbitrary direction in 3D), how would I best ...
0
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1
answer
122
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How to find nonlinear conductance?
For quantum transport at the level of linear response, there is the Landauer-Buttiker formula. And for tight-binding models, there are programs targeting such calculations, such as the kwant package.
...
- 3,802
2
votes
1
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87
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Measuring vortices in numerical $XY$-like models
I am simulating an $XY$ model, meaning that I have a $L\times L$ lattice with a unit vector $\vec s_i$ associated with each site. Each $\vec s_i$ is univocally specified by its angle $\theta \in [0,2\...
- 123
3
votes
0
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133
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How to use Python to get mathematical expressions in General Relativity [duplicate]
I'd like to get the metric tensor that describes a non-rotating, uncharged, perfectly spherical black hole whose radius grows with time (it gains mass). For now, I have:
$g_{\mu\nu}=\begin{pmatrix}
-c^...
3
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0
answers
118
views
Is there a software that computes simple particle decay kinematics?
I was trying to figure out some details about a specific decay channel for a generic particle accelerator experiment. For instance if I have a proton proton collider with fixed energy, I would like to ...
0
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0
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84
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Numerical Method for solving Newtonian Equation of Motion for Particle experiencing drag in fluid flow
Currently, I have a fluid solver that can calculate the lift and drag forces acting on a body on a per timestep basis. This means that I have data regarding the hydrodynamic forces only for the ...
- 11
0
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1
answer
77
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Sampling a 2D Ising Model [closed]
I am fairly new to statistical mechanics and I am coming from a computing background. I am trying to calculate the mutual information of a lattice representing the 2D ferromagnetic Ising Model using ...
- 3
2
votes
2
answers
150
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Computational modelling of sand pile
I'm currently working on a computational model of the way sand acts when being pushed around, say, by a bulldozer. Specifically, I'm trying to determine the dynamic equations which govern the way that ...
- 123
1
vote
1
answer
68
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Relation between the 2 interpretations of the Courant–Friedrichs–Lewy (CFL) condition
In computational fluid dynamics, one tries to ensure that the Courant–Friedrichs–Lewy (CFL) number of the discretization scheme is less than 1. This is done to ensure that the errors made at a certain ...
- 105
1
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1
answer
191
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Numerical Integration for White Dwarf Model [closed]
I'm creating a numerical integration model of a white dwarf. So I've started with calculating electron pressure vs number density across a wide range of values.
Using the equations of state in ...
- 11
0
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0
answers
69
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Is it true that particle-in-cell (PIC) simulation apply both Lagranian/Eulerian method in?
I'm learning about particle-in-cell (PIC simulation) of plasma and I'm having some questions on the description of PIC method. I still have somes questions how PIC simulation works with Eulerian and ...
- 33
3
votes
1
answer
111
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What exactly is KAM stability and how can I determine if an orbit is KAM stable or not?
I have been working on the three-body problem lately and came across KAM stability. I read that KAM stability generally means that the solution is stable at different initial conditions (that of ...
- 360
0
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0
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27
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How to model ferrofluid - water interaction correctly?
The system I am trying to model is essentially moving water interacts with ferrofluid. The ferrofluid is in a box that contains air and ferrofluid, such that the setup is buoyant. The ferrofluid ...
user320191
0
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1
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348
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Calculating the average of fluctuations of a given time series
I have a given data set, 4500 time data points approx, and the instantaneous velocity at each point. To calculate the time average of the velocity, I attempted to integrate the velocity function ...
- 348
1
vote
2
answers
554
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Numeric Solution vs Analytic Solution (1D Quantum Harmonic Oscillator)
We probably all know the analytic solution of the 1D Quantum Harmonic Oscillator is given as follows:
$$\Psi_n(x) = \dfrac{1}{\sqrt{2^n\,n!}}\,\left(\dfrac{m\,\omega}{\pi\,\hbar}\right)^{(1/4)}\,e^{\...
- 471
4
votes
2
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123
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Where can I find interpolation formulas or tabulated data for phase diagram(s)?
In order to program it, where can I find accurate representations of the water (or others - e.g.: CO2) phase diagrams, in the form of mathematical functions or in the form of interpolable tabulated ...
1
vote
0
answers
46
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Simulating Dirichlet Boundary Conditions for Lattice Boltzmann Method
So, I'm going through A.A. Mohammad's book "Lattice Boltzmann Method : Fundamentals and Engineering Applications with Computer Codes." And I'm currently coding the D2Q9 lattice with respect ...
- 11
1
vote
1
answer
167
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Books and review articles for numerical relativity?
What are good books or review articles to read for numerical relativity?
I have read some textbooks on the 3+1 formalism (such as the book by Baumgarte and Shapiro), but I would like to have a ...
0
votes
0
answers
193
views
Varying an action with respect to the metric in mathematica
I want to Varying an action with respect to the metric to obtain the Einstein equation $G_{\mu\nu}=k^2 T_{\mu\nu}$. Is there any way to do that in Mathematica? Can mathematica do that?
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0
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0
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59
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How to obtain transition amplitude from non-Hermitian operator using only expectation values?
First of all, I'm aiming to use this approach on quantum computers - that means, no statevector is available in non-simulated run, as the only tool we have is measurement of expectation values. In ...
- 194
0
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0
answers
65
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FDTD solution vs fresnel equation solutiom for reflectivity
I am comparing reflectance intensity of silicon structure with a hole.
I am getting oscillating solution for 0 roughness factor in equation based model, but the spectrum shape of FDTD and equation ...
- 1
1
vote
1
answer
51
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Determining the location of light receivers using signals propagating in anisotropic media
Problem.
I have a set of $16$ light receivers with entirely unknown locations, and a pair of light transmitters with exactly known locations. One light transmitter is stationary, and located near to ...
1
vote
0
answers
36
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What percentage of Mars' surface would be under the water if we dropped all of the water from moon Enceladus on it? [closed]
Enceladus, one of the Saturn's moons that is known for water geysers, is estimated to contain a body of water as big as a ball $220 ~\mathrm{km}$ in radius. That's about $\sim 4.46 \times 10^{7} ~\...
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0
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1
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148
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Question about the 'reduced basis transformation'
I' ve been reading the review Ulrich Schollwöck: The density-matrix renormalization group in the age of
matrix product states (arXiv link)
and encountered with a question about the so called 'reduced ...
- 143
0
votes
1
answer
193
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Why we cannot solve many-body Schrodinger equation like this in finite different method? [closed]
why we cannot solve many body Schrodinger equation like this in finite different method?
Could you give me some details?
- 23
1
vote
1
answer
80
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Modelling phase noise for self-hetrodyne method
I am trying to model the phase noise $\phi(t)$ of laser used in self-hetrodyne method using python code. The noise is time-dependent. The noise follows the condition that
$$<(\phi(t)-\phi(t-\tau))^...
- 636
0
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1
answer
121
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Kinetic Monte-Carlo Simulation to solve master equation
Kinetic monte Carlo can be used to simulate Master equation for Markov processes.For simple 1D random walk the master equation is -
$$\frac{\partial P(n,t)}{\partial t}=pP(n-1,t)+qP(n+1,t)-(p+q)P(n,t)$...
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2
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1
answer
200
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1-loop Feynman diagrams of $g \to gg$ in pure QCD
I'm very new to QFT, and I'm drawing one-loop Feynman diagrams of the process $g \to gg$ in pure QCD. I use MadGraph to generate all the diagrams by
...
- 21
2
votes
0
answers
93
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CalcHEP and FeynCalc giving different amplitudes--spin averaging?
I've done a simple amplitude calculation involving neutrinos and fermions scattering or annihilating through a BSM gauge boson. I'm checking with FeynCalc and CalcHEP, but the two are giving ...
user367500
6
votes
1
answer
216
views
How to numerically simulate a rolling object? [closed]
I am a maths person and definitely not a physics person, so maybe this is taught somewhere and I haven't learned it. I am trying to understand and figure out how to simulate rolling an object on a ...
- 171
4
votes
0
answers
104
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Estimating the correlation length on a periodic lattice
I am trying to estimate the distance dependent correlation length of on a 2D lattice. Usually if $C(r)$ is the correlation function, I can estimate it as:
$$\frac{1}{\xi(r)} = - \ln\{C(r+1) / C(r)\} $$...
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