Computation of Effective Local Diffusion Tensor

Sammanfattning

Numerical simulations of large complex systems such as biomolecules often suffer from the full description of the system having too many dimensions for direct numerical calculations and Monte Carlo methods having trouble overcoming energy barriers. It is therefore desirable to formulate a description in lower dimension which captures the system’s macroscopic behaviour. Recently, Lindahl et al [1] proposed a metric, g(λ), on the extended space Λ based on the dynamics of the system to optimize Monte Carlo sampling within extended ensemble formalism. In this thesis, we formulate a low-dimensional effective coarse-grained dynamic on Λ as a diffusion process and ask if it is possible to use this metric to calculate thelocal effective diffusion matrix as D(λ) = g−1(λ). By testing various scenarios we conclude that computing D(λ) in this manner indeed gives a correct effective dynamic in most cases, where the scale of coarse-graining can be tuned. However, an incorrect dynamic is received for example when the scale of coarse-graining is comparable to the size of oscillations in the energy landscape.