Authors:

Kashif Khan

Date Created:

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About Paper:

Simulating the equilibrium conformations of polymers in complex systems has been used to calculate the macroscopic polymer properties in such systems. However, rare conformations of polymers require many samples to be produced which becomes computationally expensive for complex systems. For example, to study polymers in an external field that form a ring, we must restrict the state space to account only for the polymers that have the same starting and ending point, which is a very small subset of all possible conformations. The Brownian Bridge is a biasing technique that leads paths to a desired outcome and has been employed for the simulation of such rare events. Although applicable in theory, the Brownian Bridge requires the solution to the Backward Fokker-Planck (BFP) equation, which becomes computationally expensive for complex or higher dimensional systems. To avoid this, one can use the Wong-Zakai Theorem to generate the exact statistics by solving a boundary value problem. This paper plans to solve such boundary problems to produce the exact statistics of semi-flexible polymer chains with a desired conformation. Since this procedure avoids the solution to the BFP equation, we will show that it will accelerate the generation of polymers conditioned to a certain conformation, whilst producing the exact conditioned statistics.

Source:

Purdue University / 2023

Topics:

No topics listed

Co-authors:

Kashif Khan