title: Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method.
abstract: An exact solution of the time-dependent diffusion equation for the case of a two- and a three-layered finite diffusive medium is proposed. The method is based on the decomposition of the fluence rate in a series of eigenfunctions and upon the solution of the consequent transcendental equation for the eigenvalues obtained from the boundary conditions. Comparisons among the solution of the diffusion equation and the results of Monte Carlo simulations show the correctness of the proposed model.
authors.affiliation: Dipartimento di Fisica dell'Università degli Studi di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Florence, Italy. fabrizio.martelli@unifi.it
authors.forename: Fabrizio
authors.initials: F
authors.lastname: Martelli
authors.forename: Angelo
authors.initials: A
authors.lastname: Sassaroli
authors.forename: Samuele
authors.initials: S
authors.lastname: Del Bianco
authors.forename: Yukio
authors.initials: Y
authors.lastname: Yamada
authors.forename: Giovanni
authors.initials: G
authors.lastname: Zaccanti