# Tagged Questions

DO NOT USE THIS TAG just because the question contains numerics!

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### Capturing superfluid condensation with exact diagonalization

Doing exact diagonalization on bosonic systems is tricky, because the possibility of multiple occupancy means that even the single-site Hilbert space is infinite-dimensional. It's my understanding ...
212 views

### Smoothed particle hydrodynamics in cosmological N-body simulations

What is the role of smoothed particle hydrodynamics (SPH) in cosmological N-body simulations like the Millenium Run (performed with Gadget-2)?
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### How to conserve momentum when numerically-integrating the path of a charged particle through a magnetic field

I have the python script attached below, which is intended to track the trajectory of a charged particle in a static, uniform magnetic field. It is very simple to calculate the instantaneous force ...
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### Which procedure is correct? [closed]

A problem is given in my textbook pg.no-191 as Example 5.10 A solenoid has a core of a material with relative permeability $\mu_r=400$. The windings of the solenoid are insulated from the core and ...
714 views

### Binary Black Hole Solution of General Relativity?

This is rather a technical question for experts in General Relativity. An accessible link would be an accepable answer, although any additional discussion is welcome. GR has well known solutions ...
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### Numeric fermiomic creation operators and unit cell

I have to do some numerics (e.g. FFT in Maple/Octave) on a 1D fermionic chain without forces between the particles. The description says that two sites build an unit cell. What does this mean? And ...
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### How can I get the boundary and initial conditions of the convectionâ€“diffusion equation consistant?

I want to solve the 1D convectionâ€“diffusion equation. The boundary conditions are a flux in from the bottom and a flux out on the top. Furthermore I want no concentration inside at the beginning. I ...
1k views

### Can we infer the existence of periodic solutions to the three-body problem from numerical evidence?

I recently found out about the discovery of 13 beautiful periodic solutions to the three-body problem, described in the paper Three Classes of Newtonian Three-Body Planar Periodic Orbits. Milovan ...
77 views

### Evaluate singularity in numerical iterative physical optics integral

My goal is to implement a code to numerically compute the radar cross section (RCS) of an open-ended PEC cavity by the approach of "iterative physical optics" [1]. The idea is to iteratively compute ...
220 views

### Geodesics in Kerr

I'm interested in plotting the trajectories of null geodesics near an uncharged rotating black hole (described by the Kerr solution) which involves a system of first order differential equations. Kerr ...
77 views

### Calculate Euler equations of fluid dynamics without division?

I'm working on the calculation of the Euler equations with the finite volume method. Unfortunately I'm not allowed to do a division. So I'm wondering if there's a form which does not need a division. ...
1k views

### Numerical analytic continuation for Green's function

Recently, I happened to hear about the possibility of doing analytic continuation numerically. That sounds attractive for the ubiquitous $\mathrm{i}\omega_n\rightarrow\omega+\mathrm{i}0^+$ procedure, ...
391 views

### 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 ...
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### Solving coupled nonlinear ODEs, controlling numerical instability through numerical viscosity

I'm solving a problem numerically that takes the form $Q_{ij} \ddot{y}_j +S_{ijk}\dot{y}_j\dot{y}_k +V_i=0$, where $(Q_{ij},S_{ijk},V_i)$ are all low order polynomial functions of the dependent ...
245 views

### Numerical solution of the BCS gap equation, with Coulomb potential

I'm interested in the excitons condensation, which is described by an equation which is very similar to the standard BCS gap equation. I will be referring to this article: http://arxiv.org/abs/cond-...
108 views

### Does physics have some division schema which divide physical amounts into these two classes?

Does physics have some division schema which divide amounts into these two classes? : A) amounts which can be counted by natural numbers (for example many units can be counted by number of electrons,...
189 views

### Simulating a 1-dimensional wave on (a segment of) an infinite line

I'm trying to numerically simulate a 1-dimensional with a chain of linked harmonic oscillators as described here (the result can be seen here). The simulation behaves like a wave on a finite line ...
645 views

### Numerical schemes, time integration algorithms and energy conservation

What does it mean when someone says a numerical scheme or a time integration algorithm is "energy conserving". How can a numerical scheme "gain" or "lose" or "conserve" energy apart from the numerical ...
117 views

### numerical diagonalisation comparison of complex Hermition matrix and real matrix

we are doing K space calculation(transnational invariant basis) of Hamiltonian, and trying to compare with exact method for same nos of sites and particles, we are getting big difference in ground ...
525 views

### Transparent boundary condition [closed]

I am interested in the finite-difference beam propagation method and its applications. I try to solve the Helmholtz equation. At first, i would like to solve numerically it for the easiest case, ...
4k views

### Superconducting gap, temperature dependence: how to calculate this integral?

Tinkham (page 63) states that the temperature dependence of the gap energy of a superconductor $\Delta(T)$ can be calculated using the following integral: How can this actually be carried out? I am ...
125 views

### neutron transport approximations for nuclear rocket modelling

I'm pretty ignorant regarding neutron and nuclear transport modelling, but i'm interested in trying to pursue it for a particular pet project. It regards modelling of nuclear reactions like those ...
129 views

### Monte Carlo for Random Bond Ising ferromagnet

The set-up: Consider the Ising model on an $L \times L$ square lattice, where the coupling of each bond is chosen to be $+J$ (ferromagnetic) with probability $(1-p)$ and $-J$ (antiferromagnetic) with ...
212 views

### Electric current streamlines in induction cooking vessel

I am looking for a plot of the typical streamlines of the electric induced currents ("eddy currents") in a induction cooking vessel. How can one theoretically predict the streamlines? How is it ...
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### Numerical algorithms to generate a random wavefunction from a thermal ensemble

I am seeking an algorithm to generate a random wavefunction = $\sum {c_i |\varphi _i\rangle }$ from a thermal ensemble, whose density matrix $\rho \sim e^{-\beta H}$, without the need to diagonalize ...
579 views

### Numeric method to calculate the charge distribution on a conducting surface?

If I have an arbitrary (closed?) conducting surface and a nearby charge density, is there a simple numeric way of computing the induced charge distribution on the surface?
923 views

### Numerical software to manipulate a light beam in its plane wave representation?

Any light field can be expressed as a sum of plane waves. Such an ensemble of plane waves is called the plane wave spectrum of the light field. The plane wave spectrum is the Fourier transform of the ...
371 views

### History of the use of the concept of phase space in engineering

Engineering textbooks constantly use the concept of 'phase space' (see e.g. http://www.cs.cmu.edu/~baraff/sigcourse/notesc.pdf). That is, they think of the state of a mechanical system as a high-...
883 views

### Physics needed to build a top down billiards game [duplicate]

Possible Duplicate: How are these balls reflected after they hit each other? I was wondering what sort of physics equations would I need in order to build a top down billiards game? I tried ...
2k views

### Basic mechanics problems, unsolvable by brute-force numerical integration

I'm looking for simple problems in theoretical mechanics that are impossible or unreasonably difficult to solve by means of "brute-force" numerical integration of Newton or Euler-lagrange equations. ...
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### Degenerated Anderson Model Simulation

I'm trying to simulate the degenerative Anderson model. So depending on an energy difference first orbital and afterwards spin magnetism occurs. First i try to solve an easier ansatz with a limitation ...
1k views

### Using Fourier Transforms to Solve Systems with springs of high frequency

I'm trying to numerically solve the differential equations of motion in a system with multiple springs of very high frequency. Because the solution is often a combination of rapidly-oscillating sine ...
605 views

### Mathematica to help for an Hamiltonian problem

I have an Hamiltonian problem whose 2D phase space exhibit islands of stability (elliptic fixed points). I can calculate the area of these islands in some cases, but for other cases I would like to ...