Self-assembly of frustrated and disordered systems -- equilibrium microphases and out-of-equilibrium active matter

Mingyuan Zheng, Ph.D. Candidate Patrick Charbonneau, Ph.D., Advisor Abstract: The potential for matter to self-assemble in complex morphologies and follow intricate dynamics is of great fundamental interest as well as for a broad array of applications in nanotechnology, catalysis, drug delivery and beyond. The inherent complexity of these processes, however, is a challenge both to theories and to numerical simulations. This dissertation focuses on two such complex systems: (i) equilibrium microphases and (ii) out-of-equilibrium active matter. In the first part, a model of microphase formers with short-range attractive and long-range repulsive (SALR) interactions is investigated. Using various advanced Monte Carlo methods, a thorough characterization of the disordered regime of this model is obtained, and the results serve as a benchmark for evaluating algorithmic performances. Around the order-disorder transition, existing algorithms nevertheless remain inefficient at sampling configurations, due to the severe critical slowdown. To understand the limitations of these algorithms, simple spin models are studied in a 1D chain, on a 2D square lattice and on the Bethe lattice. The results reveal that the existing cluster algorithms overestimate the correlation length, and therefore its divergence no longer coincides with the critical point. In fact, frustration-induced correlation length depression necessitates a negative bonding probability for a successful cluster scheme. Two proposed cluster algorithms approximate this effect and significantly improve sampling. In the second part, the out-of-equilibrium nature of active matter is confronted to achieve first-principle descriptions. Its sluggish dynamics (and arrest) at high densities is particularly challenging. To obtain insight into the thus-far unsolved dynamic mean-field theory (DMFT), which is exact as d→∞, I have conducted simulations of active Brownian particles in the heterogeneous random Lorentz gas environment, using event-driven Brownian dynamics algorithm in d spatial dimension. The results reveal that activity shifts the glass transition to higher density and saturates around the percolation threshold. The non-Gaussian behavior also markedly differs from passive systems. These findings suggest non-trivial processes might be at play in the arrest of active matter, which helps chart the way for eventually solving and extending the DMFT.