A deterministic model for one-dimensional excluded flow with local interactions
Kolomeisky, Anatoly B.
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental model for the unidirectional flow of particles along a one-dimensional lattice of sites with nearest-neighbor interactions between the particles. The flow between consecutive sites is governed by a “soft” simple exclusion principle and by attracting or repelling forces between neighboring particles. Using tools from contraction theory, we prove that the model admits a unique steady-state and that every trajectory converges to this steady-state. Analysis and simulations of the effect of the attracting and repelling forces on this steady-state highlight the crucial role that these forces may play in increasing the steady-state flow, and reveal that this increase stems from the alleviation of traffic jams along the lattice. Our theoretical analysis clarifies microscopic aspects of complex multi-particle dynamic processes.
Citable link to this pagehttps://hdl.handle.net/1911/97394
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Except where otherwise noted, this item's license is described as This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.