Phase separation in active matter : from schematic to realistic models

Abstract

Large density fluctuations are commonly observed in biological systems of selfpropelling particles. Examples we are all familiar with include fish schools, bird flocks, herds of animals. These density fluctuations are frequently interpreted as the manifestation of phase separation, despite the underlying system being out of thermal equilibrium. The active elements consume energy to self-propel. Due to the absence of a thermodynamic description, a question of great interest concerns the identification of the microscopic processes that induce these density fluctuations, as well as to develop of a non-equilibrium theory to predict the phase diagram of these systems.Research in this direction follows two paths. On one side, we might assume these density fluctuations originate from underlying physical processes that are universal across different biological systems. Hence, to rationalize the microscopic origin of these fluctuations, one might devise simple models which are able to reproduce them and then investigate these models in detail. On the other side, one might acknowledge that different biological systems are different, and hence try to understand a particular system. In my research work, I have followed both approaches to some extent.The most significant part of my research work, and hence of this thesis, focused on the investigation of a prototypical schematic model of the active particle, known as Active Brownian Particles (ABPs). This model describes a collection of particles interacting via short-range repulsive forces, experiencing thermal noise and selfpropelling force.The self-propulsion results from an active force acting on each particle, which differs across particles, whose directions are persistent on nature. This active force induces a velocity, known as the active velocity of the particles. At high enough particle density and high enough active velocity, ABPs undergo a transition from a i v vi Mainly, I enjoyed the friendship of my fellow Ph.D. students Wang You and Jia Guichong as we walk through Ph.D. struggles together. My special thanks to the University Well-being Centre, the staffs, and consultants working there. During a hard time of my Ph.D., they helped me to think positively towards the difficulty in life, although sometimes you cannot change it. With their help, I gradually controlled my depression state.Last but not least, I want to thank my beloved husband Dr. Bo En, my wise father, and my caring mother. Without their unconditional love, support, and understanding, I could not managed to achieve these results.