Recent content by simoncks

A software of D2Q9 method without BGK approximation would be an ideal. Higher order of Q would also be favourable.

Specifically, I want a lattice Boltzmann method which can allow me to input arbitrary collision operator. It is ok to make some approximation.

Hi everyone, I plan to do a simulation of a Boltzmann equation with experimentally known scattering between two particles. Initially I intend to incorporate the scattering into the collision integral and use Lattice Boltzmann Equation (LBE) afterwards. But I only see LGBK (DnQb) which requires...

May I ask why the rescaled hamiltonian must preserve its form under renormalization? Also, is there any example which demonstrates the rescaling of momentum space continuously in practice, so I can understand how to use a continuous rescaling to change into ODEs of parameter flow?

Hi everyone, Currently, I am self-learning Renormalization and its application to PDEs, nonequilibrium statistical mechanics and also condensed matter. One particularly problem I face is on the conservation of symmetry of hamiltonian during renormalization. Normally renormalization of...

It is a heat equation without source term. Open boundary at infinity. Initial condition is a delta function at (x,y,z) = 0.

In short, I would like to know if there are any entropy equation integrating over space.

Homework Statement The problem requires me to find the entropy of a diffusion constant as a function of time (I guess in terms of diffusion coefficient) Homework Equations Perhaps Heat / Diffusion kernel S = k p lnp The Attempt at a Solution I assume it was a delta initial condition then...

There is a famous example that electron couldn't absorb the whole incoming photon without emitting another one. Instead of the normal way, I try to prove it simply by argument ( which might be wrong ). There are four constraints in the process, one from energy conservation, three from momentum...

Thank you everyone. Should have read recent thread before asking.

Then what is the physical meaning of R? One could feel that of the Curvature tensor from parallel transport. But the contraction leaves me no clue to understand it by imagination.

Mathematically, ##T_{\mu_\nu} = 0## ##\Rightarrow~R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} = 0## Now multiply both sides by ##g_{\mu\nu}## with definition of ##R = g^{\mu\nu} R_{\mu\nu}## ##R - \frac{1}{2} R = 0## ##R = 0## Is that my imagination wrong? I thought 'empty space' might not...

Thank you very much. The links and replies are useful!

Most existing theorems only describe EM wave propagating, but how are they generated? What most textbooks say - 'they come from radiation source', which I am not satisfied without the explicit theorem for generation of EM wave

The EM wave in free space could be directly formulated from Maxwell's equations. Simply solve - ∇2E = μ0ε0∂t2E ∇2B = μ0ε0∂t2B My question might not be precise enough, sorry for that. Please let me explain in a more detailed manner. (I am not used to the symbol typing, so the equations...