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 nonrational 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 electrochemical processes: the reduction of iron and a traction battery