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Fractal Fract 2018, 2(1), 8; https://doi.org/10.3390/fractalfract2010008

Towards a Generalized Beer-Lambert Law

1
Institute of Atmospheric Science and Climate, Italian National Research Council (CNR), 00133 Rome, Italy
2
Dipartimento di Scienze Statistiche, “Sapienza” Università di Roma, 00185 Rome, Italy
*
Author to whom correspondence should be addressed.
Received: 31 December 2017 / Revised: 26 January 2018 / Accepted: 27 January 2018 / Published: 31 January 2018
(This article belongs to the Special Issue Fractional Dynamics)
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Abstract

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. View Full-Text
Keywords: Beer-Lambert law; hyperbolic extinction; poisson process; fractional calculus Beer-Lambert law; hyperbolic extinction; poisson process; fractional calculus
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Casasanta, G.; Garra, R. Towards a Generalized Beer-Lambert Law. Fractal Fract 2018, 2, 8.

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