Telegrapher’s equation for light derived from the transport equation

Abstract

Shortcomings of diffusion theory when applied to turbid media such as biological tissue makes the development of more accurate equations desirable. Several authors developed telegrapherÕs equations in the well known P 1 approximation. The method used in this paper is different: it is based on the asymptotic evaluation of the solutions of the equation of radiative transport with respect to place and time for all values of the albedo. Various coefficients for the telegrapherÕs equations were derived, restricted to the case of isotropic scattering, and their properties are discussed. A correct diffusion coefficient for the stationary case could be obtained. However, this solution did not lead to the correct phase velocity. Correct phase velocities in combination with a correct diffusion coefficient were found for a dispersion relation that corresponds with anisotropic Henyey-Greenstein scattering with g = 0.22. It provides a time-dependent description of the fluence rate with validity for all values of the albedo.

Dissipative effects in nonlinear Klein-Gordon dynamics

“…The applications of the telegraphists equation are diverse. We can mention correlated random walks [17], tunneling processes [21], diffusion phenomena in optics [22,23], and cosmic ray transport [24,25]. The q-plane waves arise naturally within a theoretical framework where the Boltzmann-Gibbs (BG) entropy and statistical mechanics are generalized through the introduction of a power-law entropic functional S q characterized by an index q (BG being recovered in the limit q → 1).…”

“…As already mentioned, the dissipative nonlinear Klein-Gordon dynamics that we are going to explore here is described by a family of telegraph-like equations. The standard telegraph equation constitutes a cornerstone of mathematical physics, with deep theoretical significance and many applications [19][20][21][22][23][24][25][26][27][28]. Historically the telegraph equation was first formulated to describe leaky electrical transmission lines.…”

“…The applications of the telegraph equation are diverse. We can mention correlated random walks [19], tunneling processes [23], diffusion phenomena in optics [24,25], and cosmic-ray transport [26,27].…”