Density Fluctuations and Machine Learning in Active Matter

Citation

Dulaney, Austin Ryan (2021) Density Fluctuations and Machine Learning in Active Matter. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ne1a-je31. https://resolver.caltech.edu/CaltechTHESIS:12282020-233314685

Abstract

Active matter is a class of materials that has constituents capable of self-propulsion through the conversion of energy into mechanical motion. The origin or specific details of their method of locomotion is a rich area of research, but is not important for understanding some aspects of their dynamics. Our interest is in the single-particle dynamics and the large-scale collective motion observed in these systems. Thus, we use the minimal active Brownian particle (ABP) model to model self-propulsion. The ABP model consists of particles of radius a that swim with an intrinsic speed U₀ in some direction q and reorients on a timescale τ_R. Active motion is persistent in that a particle will continue to swim in a direction until it reorients itself, giving rise to a swim or persistence length ℓ = U₀τ_R. This persistence leads to directed motion at short times but has been shown to become diffusive at long times with a diffusivity that originates from the random swim steps. I show that while these particles do become diffusive at steady state, they display wavelike dynamics while relaxing from an initial point source, which is shown by fluctuations in the number density. The strength of these fluctuations is determined by the ratio of the swim diffusivity to thermal diffusivity. Our resulting theory predicts these dynamics in other instances where spatial gradients in number density are present. This motivated me to look into fluctuations in interacting suspensions of ABPs by studying the "isothermal" compressibility. Our theoretical perspective and simulation results show that the compressibility behaves just like a thermodynamic response function, even though these suspensions are driven far from equilibrium. As such, the compressibility is capable of predicting the critical point for the motility induced phase separation (MIPS). We then developed a machine learning (ML) model to predict particle phase identity near the MIPS critical point in the coexistence region -- where fluctuations are large -- to recreate the binodal. Our successful recreation of the binodal and understanding of compressibility resulted in our attempt to define a Widom line (an extension of the coexistence line) for ABPs. The Widom line is the collection of points where density fluctuations are maximized and marks where supercritical behavior goes from being more gas-like to more liquid-like. I conclude by discussing current works in progress to further our understanding of the MIPS transition by using ML to identify particles in the interface of the coexisting phases. From the work on compressibility, we believe the interface plays a crucial role in describing active phase behavior.

Thesis Files