Non-Equilibrium Pattern Formation in Multi-Species Interacting Particle Systems

Non-equilibrium systems can form complex patterns in their steady states. Examples are systems consisting of self-propelled particles or systems consisting of particles driven away from equilibrium by external energy sources. In steady states, the interacting particles spontaneously organise into complex spatial patterns. The patterns formed in steady states are sustained by the continuous energy input into the system, which is then dissipated as heat in the bulk. The formation and evolution of large coherent structures necessitate a stochastic description, using methods of non-equilibrium statistical physics. In this thesis, we study these fluctuating patterns in complex systems of multiple species of particles. We focus our study on three different types of non-equilibrium systems with complex pattern formation. In Chapter 3, we study several different lattice-based models where two species of diffusing particles are driven in opposite directions by an external force. We identify and characterise the dynamical phase transitions that involve phase separation into domains that may be parallel or perpendicular to a driving force. We also analyse how phase separations emerge from different microscopic interactions: The perpendicular state appears for weak driving, consistent with previous work. For strong driving, we introduce two models that support the parallel state. In one model, this state occurs because of the inclusion of dynamical rules that enhance lateral diffusion during collisions; in the other, it is a result of a nearest-neighbor attractive or repulsive interaction between particles of the same or opposite species. We discuss the connections between these results and the behavior found in off-lattice systems, including laning and freezing by heating. In Chapter 4, we study mixtures of oppositely driven particles, showing that their non-equilibrium steady states form lanes parallel to the drive, which coexist with transient jammed clusters where particles are temporarily immobilized. We analyze the interplay between these two types of non-equilibrium pattern formation, including their implications for macroscopic demixing perpendicular to the drive. Finite-size scaling analysis indicates that there is no critical driving force associated with demixing, which appears as a crossover in finite systems. We attribute this effect to the disruption of long-ranged order by the transient jammed clusters. In Chapter 5, we study a lattice model of three species with cyclic dominance that resembles a rock-paper-scissors game. We extend the existing rock-paper-scissors model to include natural death and hunger mechanisms. We identify a new extinction phase which happens at high natural death. The condition under which one “smart” species can increase its population and the well-known but counter-intuitive phenomenon the survival of the weakest is recovered. To understand how local environment affect the survivability of the “smart” species, we investigated four local adaptive strategies with which the “smart” species increases its population by choosing its dynamics based on its local environment. Among different local adaptive strategies, we identify the evading strategy where “smart” particles evade predators to be the best local adaptive strategy. We characterise these non-equilibrium pattern formations due to the fluctuation of different species of interacting particles. We focus on topics such as the microscopic origins of macroscopic pattern formation, the breaking of symmetry and phase transitions, long-ranged order, density fluctuations, etc. We show various theoretical and numerical tools that can be applied to characterise these systems and show these complex non-equilibrium systems share many similar features.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2024

Author dc:creator

• Yu, Honghao

Advisor dc:contributor.advisor

• Jack, Robert

• Phase Transition
• Non-equilibrium
• Pattern Formation
• Numerical Simulation
• Monte-Carlo
• Molecular Dynamics
• Soft Matter
• Complex System

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/dcbb8893-6095-4b0b-b943-2c9c3618669f/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

Author Identifier

0000-0002-9317-0433

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/377300