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Galanti M., Fanelli C. and Piazza F.

Nonlinear macroscopic transport equations in many-body systems from microscopic exclusion processes

Frontiers in Physics. Special research topic “Macromolecular crowding in the cell : current state of the art, challenges and future perspectives” (2016) 18 (30) 20758-20767 - arXiv:1309.2563

par Frapart - publié le , mis à jour le

Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in biology to diffusion in porous media. Yet, often the nature of the constraints coming from many-body interactions or reflecting a complex and confining environment are better understood and modeled at the microscopic level.
In this paper we investigate the subtle link between microscopic exclusion processes and the mean-field equations that ensue from them in the continuum limit. We derive a generalized nonlinear advection diffusion equation suitable for describing transport in a inhomogeneous medium in the presence of an external field. Furthermore, taking inspiration from a recently introduced exclusion process involving agents with non-zero size, we introduce a modified diffusion equation appropriate for describing transport in a non-ideal fluid of d-dimensional hard spheres.
We consider applications of our equations to the problem of diffusion to an absorbing sphere in a non-ideal self-crowded fluid and to the problem of gravitational sedimentation. We show that our formalism allows one to recover known results. Moreover, we introduce the notions of point-like and extended crowding, which specify distinct routes for obtaining macroscopic transport equations from microscopic exclusion processes.