FINSIG 05

FINSIG 2005Kuopio, Finland In case of diffuse transport the time–evolution can be written as anon–homogeneous partial differential equationdθ(r, t)dt= ∇ · (ρ(r)∇θ(r, t)) + J(r, t)In case of isotropic homogeneous diffusion ρ(r) is a scalarconstant and ∇ · (ρ(r)∇θ(r, t)) = ρ∇ 2 θ(r, t). The operator ρ∇ 2equals to linear spatial filtering of the activity distribution. By approximating the derivatives with the first difference, the stateequations for both compartmental and diffusion models will be offormθ t+1 = F θ t + GJ twhere the state transition matrix F and the known input GJ t areconstructed according to the desired model.Mikko Kervinen, Department of Applied Physics, University of Kuopio Slide 12