Towards a Generalized Beer-Lambert Law
AbstractAnomalous 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. View Full-Text
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Casasanta, G.; Garra, R. Towards a Generalized Beer-Lambert Law. Fractal Fract 2018, 2, 8.
Casasanta G, Garra R. Towards a Generalized Beer-Lambert Law. Fractal and Fractional. 2018; 2(1):8.Chicago/Turabian Style
Casasanta, Giampietro; Garra, Roberto. 2018. "Towards a Generalized Beer-Lambert Law." Fractal Fract 2, no. 1: 8.
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