Speaker
Description
The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, and biomedical engineering. The mathematical challenge in these type of model systems is to match the solutions of the time-dependent diffusion equation in each layer, such that the boundary conditions at the interfaces between them are satisfied. In the talk, I will present a new computational approach to multi-layer diffusion problems [1]. In this approach, the probability distribution function (PDF) is computed from a large ensemble of independent stochastic trajectories. These are generated using the accurate GJF (Gronbech-Jensen & Farago) Langevin integrator [2], which is supplemented with algorithms for the transitions between the layers. We consider the most general Kedem-Katchalsky interfacial condition that incorporates: (i) a discontinuity in the diffusion coefficient, (ii) a semi-permeable membrane, and (iii) a step-function chemical potential. The utility and accuracy of the algorithm is demonstrated by two examples: (1) A simple two-layer model of diffusion from a drug-eluting stent [3], and (ii) the diffusion of a particle from a non-confining square potential well [4].
[1] O. Farago, Algorithms for Brownian dynamics across discontinuities, J. Comput. Phys. 423, 109802 (2020).
[2] N. Gronbech-Jensen and O. Farago, A simple and effective Verlet-type algorithm for simulating Langevin dynamics, Mol. Phys. 111, 983 (2013).
[3] O. Farago and G. Pontrelli, A Langevin dynamics approach for multi-layer mass transfer problems, Comput. Biol. Med. 124, 103932 (2020).
[4] O. Farago, Thermodynamics of a Brownian particle in a non-confining potential, cond-mat arXiv:2101.05599, to appear in Phys. Rev. E (2021).
