Conceptually simple mathematical models of filtration (and exchange) processes

On the computation of certain integrals containing the modified Bessel function 𝐼₀(𝜉)

“…The J-and/or A"-functions are encountered in many contexts. These include: the study of exchange processes in columns (such as heat exchange [1], and ion exchange including chromatography [2]- [5]); dispersive exchange processes in hydrology and soil science [6]- [8]; a probabilistic analysis of targeted missile impacts [9], [5,Appendix]; in a solution to the telegraphy equation [5,Appendix], [10]; in a recently proposed filtration model of aerosol retention by a vegetative canopy 111], and in generalizations of such a model for other environmental-impact modelling applications [12].…”

“…The L-function was encountered, though not separately identified, by Brinkley [1, (22)]; it also arises naturally in a model of filtration [11], [12].…”

“…This should greatly benefit the modelling of exchange and filtration processes [l]- [8], [11], [12], for which searches in model-parameter space necessitate successive functional evaluations. In particular, for models of dispersive exchange processes [6]- [8], multiple evaluations of the /-and/or /v-functions are required to accomplish numerical integration at each parameter vector in the search; a fast algorithm for these evaluations then becomes imperative in an extensive parameter search.…”