Active Particles on a 1-D Lattice

Raghu, Adarsh (2022) Active Particles on a 1-D Lattice. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Adarsh Raghu (17MS036)) 17MS036_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (717kB)

Abstract

Much recent research in Active Particles has been focused around the phenomenon of Motility Induced Phase Separation (MIPS). This is the occurrence of a condensation-like transition where clusters of active particles can form, separating into a high density phase a from the rest of the system in a condensation-like transition. This is of fundamental importance given the implication that nonequilibrium systems can show such phenomena despite the lack of any explicit attractive interaction between the particles. Motivated by this, we investigate 1D lattice models of such active particles to understand the feasibility of such phenomena representing a true condensation with the clusters being stable in the steady state. Since this phenomenon is not guided by an attractive potential but rather by mutual exclusion and restriction, the lower dimensionality should be favourable to their occurrence. We provide background and motivation, followed by an introduction of our model in full generality in the first chapter, and mention previous studies into similar models. In the second chapter we provide exact solutions for a number of scenarios in the two-particle case in such systems and examine their implications on the conclusions of previous studies. We identify a parameter γ on which the entire dependence of the steady state is reduced to. In Chapter 3, we discuss the many particle scenario, providing an exact solution which extends to the 2D case in the specific situation when γ = 1. We then discuss the feasibility of MIPS like transitions given our results and make a limiting case argument against Jamming Induced phase separations in active particles.

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