MULTISCALE SIMULATION OF REACTION DYNAMICS IN CHEMICAL, BIOLOGICAL AND MATERIALS SYSTEMS

In this dissertation, we introduce a novel accelerated-stochastic simulation method, known as the ‘partitioned-leaping algorithm ’ (PLA), for efficiently sim-ulating chemical reaction networks. The technique is multiscale in that it con-siders dynamics at scales ranging from the discrete-stochastic to the continuous-deterministic. It is particularly useful when considering nanoscale-sized systems that exhibit fluctuating dynamics and contain species with large disparities in populations. We present the theoretical foundations of the PLA, discuss various extensions and variants of the method and provide illustrative examples demon-strating its practical utility in chemistry, biology and materials science. In Chapter 1, we provide a general overview of the origins and consequences of stochastic “noise ” in nanoscale-sized systems. We elucidate the implications of this phenomenon, which arises because of the discrete and probabilistic nature of molecular interactions, in both biological and materials settings and discuss math-ematical approaches that have been applied previously to model such behaviors. The shortcomings of these methods provide the primary motivation for the wor