Nonlocal Monte Carlo approaches: Helium clusters and nucleic acids

One of the main challenges in the simulations of many body systems in statistical physics is the problem of generating sufficient coverage of phase space in a reasonable amount of computer time to produce accurate estimates of equilibrium properties. This work is focused on constructing and applying two different non-local Monte Carlo techniques which incorporate large-scale changes in a number of degrees of freedom. These methods were then used to study the rotational dynamics of spherical top molecules in 4He clusters and the problem of conformational sampling of RNA molecules.;Path integral simulations have been carried out to study the rotations of a methane inside a single shell of 4He atoms at 0.3 K to address the question of whether dopant molecule rotations can be used to probe the quantum statistics and super fluidity of the shell. We examined the effects of the probe molecule on the 4He exchanges and their counter effects on the renormalized rotation constant of the probe systematically by varying the intrinsic moment of inertia of the methane. The observed effects show strong dependence on the instrinsic moment of inertia of the rotating probe, with a heavy probe favoring stronger templating of the 4He density and a corresponding suppression of exchanges in the shell, as well as a large renormalization in the probe's effective rotation constant, while a light probe shows almost no effect on the shell density or the effective rotation constant. These results can be rationalized in terms of a rotational smearing effect and suggest that there is no clearly quantifiable relationship between the super fluid fraction of the shell and the renormalized rotation constant of the probe for cases where the probe molecule has weak anisotropic interactions with the 4He atoms.;The problem of loop closure is important for the conformational sampling of chain molecules like nucleic acids and proteins. Solutions to the loop closure problem can be used to generate alternative structures for an internal segment of a chain when the atomic coordinates of the rest of the chain are constrained at fixed positions. This work describes a new loop closure formulation for linear polymers based on the kinematic geometry of rigid bodies. This formulation makes use of a novel representation of the boundary constraints, allowing the loop closure problem to be reduced from the conventional 6-variable/6-constraint problem to a 4-variable/4-constraint problem. With this new formulation, loop closure can then be recast into a one-variable root search, permitting a simple analytical or numerical solution. The new formulation provides a natural framework for closing loop structures of arbitrary sizes, from as small as a five-member ring to those containing multiple segments of arbitrary lengths.