Adaptive Brownian Dynamics
Brownian/Langevin dynamics is among the most ubiquitous of models used in biology, chemistry and physics. In thermal equilibrium a fluctuation-dissipation relation regulates the temperature, but it is not always easy or even possible to parameterize the system a priori. I will describe the design of ``adaptive'' forms of Brownian and Langevin dynamics based in each case on an auxiliary control law, in the manner of a thermostat, as well as associated issues of ergodicity and numerical analysis. By extending the versatility of Brownian dynamics, the new formulations widen the range of potential applications in nonequilibrium and multiscale modelling.