Rare Event Simulation in a Dynamical Model Describing the Spread of Traffic Congestions in Urban Network Systems

In this chapter, we present a mathematical framework that provides a new insight for understanding the spread of traffic congestions in an urban network system. In particular, we consider a dynamical model, based on the well-known susceptible-infected-recovered (SIR) model from mathematical epidemiology, with small random perturbations, that describes the process of traffic congestion propagation and dissipation in an urban network system. Here, we provide the asymptotic probability estimate based on the Freidlin-Wentzell theory of large deviations for certain rare events that are difficult to observe in the simulation of urban traffic network dynamics. Moreover, the framework provides a computational algorithm for constructing efficient importance sampling estimators for rare event simulations of certain events associated with the spread of traffic congestions in the dynamics of the traffic network.

Rare event simulations reveal subtle key steps in aqueous silicate condensation

A replica exchange transition interface sampling (RETIS) study combined with Born–Oppenheimer molecular dynamics (BOMD) is used to investigate the dynamics, thermodynamics and the mechanism of the early stages of the silicate condensation process.

The intrinsic rate constants in diffusion-influenced reactions

Intrinsic rate constants play a dominant role in the theory of diffusion-influenced reactions, but usually as abstract quantities that are implicitly assumed to be known. However, recently it has become clear that modeling complex processes requires explicit knowledge of these intrinsic rates. In this paper we provide microscopic expressions for the intrinsic rate constants for association and dissociation processes of isotropically interacting particles and illustrate how these rates can be computed efficiently using rare event simulations techniques. In addition, we address the role of the orientational dynamics, for particles interacting via anisotropic potentials.