If one wanted to incorporate a small fix to the resting state, it would be simple to add a diffusion term in space to Eq. (2).
Crystallization utilizing the counter diffusion method in space was performed with the aim to obtain high resolution diffracting crystals with better internal order to improve the accuracy of the structure.
Local drift coefficients are denoted by A ≡ (y, v 1, 2 + A 1, 2 ), diffusion coefficients by B and ζ is a normal distributed random number with mean 0 and variance 1. Diffusion coefficients B can be constructed from the corresponding diffusion matrix (D = B B T ) in (1), which in principal is a five-dimensional matrix covering diffusion in real space as well as in velocity space.
The main drawback of the CCSL-CS to date has been its high numerical diffusion in physical space, because of the 2nd order remapping that takes place at the end of each time step.
The micromixing term in the PDF transport equations, representing diffusion in composition space, is however unclosed.
We consider a model one-dimensional partial differential equation describing energy diffusion in velocity space due to Fokker Planck collisions.
Besides pitch-angle scattering by Alfvénic and magnetic field fluctuations, PUIs can experience diffusion in velocity space, both due to counter-propagating Alfvén waves and PUI excited lower hybrid waves, for example.
Investigating a simple problem, namely the dynamics of two inert polydisperse fluidized suspensions initially segregated, we highlight an important limitation of these methods, which fail to properly model diffusion in real space.
The temporal changes of the exponent index of the 11-year variation of GCR generally is connected with the various character of the diffusion in interplanetary space for minima and maxima epochs of solar activity.
