Questions tagged [numerical-method]
61 questions
18
votes
3 answers
Numerical solution to Schrödinger equation - eigenvalues
This is my first question on here. I'm trying to numerically solve the Schrödinger equation for the Woods-Saxon Potential and find the energy eigenvalues and eigenfunctions but I am confused about how exactly this should be done.
I've solved some…
CINA
- 189
17
votes
3 answers
Correct way to write the eigenvector of a diagonalized hamiltonian in second quantization
I am studying diagonalization of a quadratic bosonic Hamiltonian of the type:
$$ H = \displaystyle\sum_{} A_{ij} a_i^\dagger a_j + \frac{1}{2}\displaystyle\sum_{} [B_{ij} a_i^\dagger a_j^\dagger + B_{ij}^* a_j a_i ]
$$
in second…
user1906035
- 504
11
votes
1 answer
Is there an algorithm for N body simulations in General Relativity
I am new to general relativity but have a background in computer science. Why is it so hard to do n-body simulations in GR? For example, there could be a program which takes the properties (mass, position, velocity, etc.) of each particle as input…
nahano
- 569
10
votes
2 answers
Exact diagonalization to resolve ground state degeneracies
I am studying a perturbed Toric Code model that is not analytically solvable.
On a torus the ground state degeneracy of the unperturbed model is 4.
Once we turn on the perturbation there is a change in the ground state degeneracy.
I would like to…
MrLee
- 860
7
votes
1 answer
Discretizing the Wave Equation in polar coordinates
I want to discretize the wave equation
$$\frac{1}{c^2}\frac{\partial^2\psi\left(\vec{r},t\right)}{\partial t^2}=\triangle\psi\left(\vec{r},t\right)$$
in polar coordinates. I find the following…
Andy
- 393
7
votes
2 answers
Monte-Carlo and $O(n)$ models for non-integer n
$O(n)$ lattice statistical models can be generalized to non integer values of n, starting from their (expanded and resumed in graphs) partition function:
$$Z = \sum_{\text{loop configurations}} n^{\# \text{loops}} x^{\text{total length}}$$
The sum…
5
votes
0 answers
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 facing a simple (at first glance) problem. I need to…
kenny
- 51
5
votes
2 answers
Calculating a two-dimensional orbital path with infinite granularity (non-Euler integration)
For a game I am making, I am trying to calculate the position of an orbiting object around one or more bodies. I have successfully implemented this gravity simulation by calculating the force, then the acceleration, and then the velocity of the…
ben
- 153
5
votes
2 answers
Is it possible to propagate a relativistic system of particles in time using Verlet?
The Verlet algorithm and its derivations are very popular methods to integrate Newton's equations of motion in time and obtain a trajectory for a system with $N$ particles.
I work with classical molecular mechanics in several of my research…
urquiza
- 352
5
votes
2 answers
Numerical Tools to find Braiding Statistics of Quasiparticles
While certain classes of systems that exhibit topological order can be solved exactly (such as the Toric Code, Abelian FQH Edges, etc.) there also exist systems
(think of perturbed versions of the Toric Code or Abelian FQH Edges) that cannot be…
Costa
- 119
4
votes
2 answers
Rotation matrix of Euler's equations of rotation relative to inertial reference frame
I was playing with simulation of Euler's equations of rotation in MATLAB,
$$
I_1\dot{\omega}_1 + (I_3 - I_2)\omega_2\omega_3 = M_1,
$$
$$
I_2\dot{\omega}_2 + (I_1 - I_3)\omega_3\omega_1 = M_2,
$$
$$
I_3\dot{\omega}_3 + (I_2 - I_1)\omega_1\omega_2 =…
fibonatic
- 5,916
4
votes
1 answer
Incompressible Navier-Stokes pressure solve in simulations
I am a complete newcomer when it comes to fluid simulations. I'm currently working through some tutorials to understand the idea of of the discretized Navier-Stokes equations for numerical simulations.
My question is related to the pressure solve…
tdenniston
- 143
4
votes
1 answer
Integral of Sedov's self-similar solution to the spherical blast wave problem
I'm studying the Taylor-Sedov self-similar solution to the problem of a strong explosion in a homogenoeus atmosphere. The problem is discussed in Landau & Lifschitz VI (in the 2nd edition it's §106).
In these notes there's a reproduction of…
pppqqq
- 4,824
4
votes
1 answer
Philae lander simulation off by factor of ~3
I'm trying to simulate the Philae landing by writing a program to compute the position of the lander vs time. According to various mission websites, the orbiter will match its orbit to the rotation of the comet, then move toward the comet to impart…
Barry Brown
- 143
4
votes
0 answers
Non-linear Wave Equation - Numerical Methods
Motivation:
I'm working with a highly non-linear spherical wave-like equation (second order PDE). The equation can be written on the form
$$\ddot{u} = f(t, \dot{u},\dot{u}',u',u'')$$
where $'=\frac{d}{dr}$ and $\dot{} =\frac{d}{dt}$. (The expression…
Winther
- 688