Towards a Generalized Beer-Lambert Law

Fractal and Fractional

Casasanta, Giampietro¹ 

关键词: Beer-Lambert law;    hyperbolic extinction;    poisson process;    fractional calculus;   

DOI  :  10.3390/fractalfract2010008

学科分类：数值分析

来源: mdpi

【 摘 要 】

Anomalous deviations from the Beer-Lambert law have been observed for a long time in a wide range of application. Despite all the attempts, a reliable and accepted model has not been provided so far. In addition, in some cases the attenuation of radiation seems to follow a hyperbolic more than an exponential extinction law. Starting from a probabilistic interpretation of the Beer-Lambert law based on Poissonian distribution of extinction events, in this paper we consider deviations from the classical exponential extinction introducing a weighted version of the classical law. The generalized law is able to account for both sub or super-exponential extinction of radiation, and can be extended to the case of inhomogeneous media. Focusing on this case, we consider a generalized Beer-Lambert law based on an inhomogeneous weighted Poisson distribution involving a Mittag-Leffler function, and show how it can be directly related to hyperbolic decay laws observed in some applications particularly relevant to microbiology and pharmacology.

【 授权许可】

CC BY