Biased, efficient sampling of polymer conformations using Brownian bridges

In this talk, we introduce a mathematical concept known as a Brownian bridge, and describe how it can be utilized in many areas of polymer physics. A Brownian bridge is a random process whose start and end regions in phase space are specified. Such processes naturally find utility in situations when one wants to sample polymer conformations with a given topology and/or energy. In the first part of the talk, we expand upon our previous work and discuss how one can systematically generate bridge processes for continuous polymer chains described by a stochastic differential equation. We will then discuss how to use such ideas to generate polymer conformations of a given topology (e.g., rings, polymers with fixed winding or twist, etc.). We will then study a polymer under an external field and show how a bridge formulation allows one to exactly sample polymer conformations in a given range of total energy. This latter idea thus allows one to sample rare events (i.e., high energy) efficiently, or conversely most probable configurations (i.e., low energy). We will conclude on how to to scale these ideas to larger dimensional systems through approximation methods, and discuss some advantages and disadvantages of using bridge processes compared to other biased sampling strategies.