I am trying to clarify the relation between random walk and diffusion, and the source book proposes the following which I can't get. Starting from the diffusion equation $$ \\frac{\\partial C}{\\part...

"The traditional diffusion equation bore a family resemblance to the standard Schrödinger equation; the crucial difference lay in a single exponent where the quantum mechanical version was an imaginary …

Convection is the collective motion of particles in a fluid and actually encompasses both diffusion and advection. Advection is the motion of particles along the bulk flow Diffusion is the net movement of …

Jan 7, 2021 · With this definition, the diffusion equation is time-reversal symmetric if, for all solutions $\rho (x,t)$, we have that $\rho (x,-t)$ is also a solution. Since this is clearly false, the diffusion …

Dec 6, 2022 · Note that diffusion equation is a particular case of Fokker-Planck equation, which describes many stochastic processes under rather general conditions. Another way to think of it: we …

I know that the diffusion equation is a more general version of the heat equation. But what is the exact difference informally?

Dec 9, 2021 · The reason is that your dynamics with a given step $\ell$ does not fix the diffusion constant in different dimensions to be the same. So your diffusion constant in the 2d case is half the …

Jul 30, 2020 · For normal diffusion, the MSD is $$\langle x^2\rangle=2Dt$$ and therefore the RMSD equals $$\sqrt {\langle x^2\rangle}=\sqrt {2Dt}.$$ But if I say, this is more or less the expectation …

This causes the equation's solutions to osculate instead of decay with time because $$ \exp (-Dt)=\exp (-iD't) $$ Which is why the Schrödinger equation has wave solutions like the wave equation's. It seems …

The Einstein equation, often called Stokes-Einstein, assumes that the thermodynamic force that moves the particle is opposed by the drag of the fluid, which is expressed by the Stokes law, hence Stokes …