Minimalist theory for mesoscale reaction dynamics
Craven, Galen Thomas
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The prediction of an atomistic system's macroscopic observables from microscopic physical characteristics is often intractable, either by theory or computation, due to the intrinsic complexity of the underlying dynamical rules. This complexity can be simplified by identifying key mechanisms that drive behavior and considering the system in a reduced representation that captures these mechanisms. Through theory, this thesis examines complex relationships in structured assembly and reaction mechanisms that occur when effective interactions are applied to mesoscale structures. In the first part of this thesis, the structure and assembly of soft matter systems are characterized while varying the interpenetrability of the constituent particles. The nature of the underlying softness allows these systems to be packed at ever higher density, albeit with an increasing penalty in energy. Stochastic equations of motion are developed in which mesoscopic structures are mapped to single degrees of freedom through a coarse-graining procedure. The effective interactions between these coarse-grained sites are modeled using stochastic potentials that capture the spatial behavior observed in systems governed by deterministic bounded potentials. The second part of this thesis presents advancements in time-dependent transition state theory, focusing on chemical reactions that are induced by oscillatory external forces. The optimal dividing surface for a model driven reaction is constructed over a transition state trajectory. The stability of the transition state trajectory is found to directly dictate the reaction rate, and it is thus the fundamental and singular object needed to predict barrier-crossing rates in periodically driven chemical reactions. This thesis demonstrates that using minimalist models to examine these complex systems can provide valuable insight into the dynamical mechanisms that drive behavior.