Single Species¶
File Structure¶
Main file
- /diffusion2d/single/single2d.m
- main function for numeric simulation of the dynamics of one single species in 2D
ALso include
- /diffusion2d/single/minmod.m
- a generalized minmod limiter function
- /diffusion2d/single/drho.m
- gives the time derivative of the density function at given configuration
- /diffusion2d/single/draw.m
- a help function for 3D visualization
- /diffusion2d/single/SSPRK3.m
- SSP-RK3 method
- /diffusion2d/single/Euler.m
- Euler method
Examples
Functions¶
single2d
rho = single2d(rho0, L, W, dt, T)
- SINGLE2D:
- numeric simulation of the dynamics of one single species in 2D
Input:
- rho0: initial density, N by N matrix
- L: domain [-L,L] x [-L,L]
- W: W(x) interacting potentials
- dt: time step
- T: simulation time. Total #iterations = T/dt
Output:
- rho: density at t = T, N by N matrix
Optional parm:
rho = single2d(.. ,H);
% H is a symbolic function for internal energy as a
% function of the density. Default H(r) = 0
--------------------------------------------------------------------------
rho = single2d(.. ,V);
% optionally sets the environmental confinement potential V,
% which is a NxNmatrix. Default: 0
--------------------------------------------------------------------------
rho = single2d(.. ,e)
% sets the diffusion coefficient for some e > 0. Default e = 0
--------------------------------------------------------------------------
rho = single2d(.. ,'v') or rho = single2d(.. ,'V')
% enables visual display during the simulation. Default disabled.
--------------------------------------------------------------------------
rho = single2d(.. ,'solver')
% where 'solver' sets the numeric method used for ODE.
% Possible options: 'Euler', 'SSPRK3'. Default 'SSPRK3'.
--------------------------------------------------------------------------
drho
dr = drho(r, K, dH, V, dx, e)
- DRHO:
- gives time derivative of the density function evaluated at r
Input:
- r: density distribution
- K: convolution matrix
- dH: a symbolic function of the derivative of H
- V: matrix of confinement potential
- dx: time step
- e: diffusion coefficient
Output:
- dr: time derivative of the density function