Identification of linear time invariant diffusion phenomena

Linear time invariant diffusion phenomena are described by linear parabolic partial differential equations with constant coefficients. The corresponding non-rational transfer functions in the Laplace variable s have an infinite number of poles. In this paper it is shown that these infinite dimensional systems can be very well approximated in a given frequency band by a rational form in √s. Potential applications are the modeling of mass or heat transfer phenomena. The theory is illustrated on the modeling of the AC impedance of two electro-chemical processes: the reduction of iron and a traction battery