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Syracuse University

1. Patch, Adam Edward. Motility-induced phases: out-of-equilibrium droplets, surfaces, and survival.

Degree: PhD, Physics, 2018, Syracuse University

Active matter represents a unique kind of out-of-equilibrium matter that is endowed with motility, the ability of each individual unit to move according to its own self-propulsion force. Objects of study in active matter include entities like birds and cells, which become particularly interesting at scales larger than the individuals, where we find emergent collective behavior like flocking and morphogenetic self-organization, respectively. One can study both microscopic and macroscopic behaviors of these particles using theory, simulation, and experiment, but largescale simulations are critically important to understanding some of the underlying statistical mechanical properties of active matter. Motility-induced phase separation (MIPS) is a unique example of out-of-equilibrium emergent behavior, in which a fluid of active particles with repulsive-only interactions use their motility to spontaneously separate into coexisting dense and dilute phases. In this emergent collective behavior, particles nucleate stable clusters that eventually coarsen and coalesce into system-spanning bulk phases that stabilize in a steady state, much like nucle- ation and spinodal decomposition in liquid-gas phase coexistence. This dissertation covers the work I have done studying the fundamental physics of MIPS. The spontaneous aggregation of MIPS results from the random and uncoordinated ef- forts of many particles that are driven by non-Markovian, randomized forces at the level of individual units. Building off of ideas of classical Brownian motion, in this thesis I first review some basics of Langevin dynamics and the Fluctuation-Dissipation Theorem (FDT) in order to describe how run-and-tumble particles (RTPs) and active Brownian particles (ABPs) break from equilibrium by utilizing their short-time ballistic motion, which becomes diffusive on long timescales. I review some continuum descriptions that provide an effective equilibrium picture of MIPS as well as experimentally engineered synthetic systems that exhibit life-like self-assembly and mesoscopic clustering. My work studying MIPS has relied on simulations of large ensembles of Active Brownian Particles (ABPs). Using these, I can directly measuring quantities like pressure, surface tension, density, currents, and cluster growth exponents of systems of ABPs. All of these quantities can be compared to continuum models and experiments. As described by the main chapters of this thesis, my work has focused on studying the pressure and kinetics of MIPS, and more recently, its uniquely out-of-equilibrium surface “tension”. Additionally, I have worked in collaboration with biologists to study the… Advisors/Committee Members: M. C. Marchetti.

Subjects/Keywords: active matter; non-equilibrium; out-of-equilibrium; phase separation; self-organization; soft matter; Physical Sciences and Mathematics

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APA (6th Edition):

Patch, A. E. (2018). Motility-induced phases: out-of-equilibrium droplets, surfaces, and survival. (Doctoral Dissertation). Syracuse University. Retrieved from

Chicago Manual of Style (16th Edition):

Patch, Adam Edward. “Motility-induced phases: out-of-equilibrium droplets, surfaces, and survival.” 2018. Doctoral Dissertation, Syracuse University. Accessed December 16, 2018.

MLA Handbook (7th Edition):

Patch, Adam Edward. “Motility-induced phases: out-of-equilibrium droplets, surfaces, and survival.” 2018. Web. 16 Dec 2018.


Patch AE. Motility-induced phases: out-of-equilibrium droplets, surfaces, and survival. [Internet] [Doctoral dissertation]. Syracuse University; 2018. [cited 2018 Dec 16]. Available from:

Council of Science Editors:

Patch AE. Motility-induced phases: out-of-equilibrium droplets, surfaces, and survival. [Doctoral Dissertation]. Syracuse University; 2018. Available from: