Biomedical subjects

Michael P Moody

Publications and source records attributed to Michael P Moody.

4 recordsLinked to original sources

PubMed2005

Numerical study of the accuracy and efficiency of various approaches for Monte Carlo surface hopping calculations.

A one-dimensional, two-state model problem with two well-separated avoided crossing points is employed to test the efficiency and accuracy of a semiclassical surface hopping technique. The use of a one-dimensional model allows for the accurate numerical evaluation of both fully quantum-mechanical and semiclassical transition probabilities. The calculations demonstrate that the surface hopping procedure employed accounts for the interference between different hopping trajectories very well and provides highly accurate transition probabilities. It is, in general, not computationally feasible to completely sum over all hopping trajectories in the semiclassical calculations for multidimensional problems. In this case, a Monte Carlo procedure for selecting important trajectories can be employed. However, the cancellation due to the different phases associated with different trajectories limits the accuracy and efficiency of the Monte Carlo procedure. Various approaches for improving the accuracy and efficiency of Monte Carlo surface hopping procedures are investigated. These methods are found to significantly reduce the statistical sampling errors in the calculations, thereby increasing the accuracy of the transition probabilities obtained with a fixed number of trajectories sampled.

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PubMed2004

Globally uniform semiclassical surface-hopping wave function for nonadiabatic scattering.

A globally uniform time-independent semiclassical wave function for nonadiabatic scattering is presented. This wave function, which takes the form of a surface-hopping expansion, is motivated by the globally uniform semiclassical wave function of Kay and co-workers for the single-surface case. The surface-hopping expansion is similar to a previously presented primitive semiclassical wave function for nonadiabatic problems. This earlier wave function has the important feature that it correctly incorporates all phase terms, allowing for an accurate treatment of quantum interference effects. The globally uniform expression has important numerical advantages over the primitive formulation. The globally uniform wave function does not have caustic singularities, and the globally uniform calculation avoids a root search for trajectories obeying double-ended boundary conditions that is required by the primitive semiclassical calculation.

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PubMed2004

Monte Carlo simulation methodology of the ghost interface theory for the planar surface tension.

A novel "ghost interface" expression for the surface tension of a planar liquid-vapor interface is derived in detail from consideration of the free energy of the system, and a methodology for utilization of this new technique is given. An augmented Monte Carlo computer simulation procedure is developed specifically for the ghost interface, including derivation of long-range corrections resulting from potential truncation and a modified Gibbs ensemble technique for the simulation of adjacent coexisting phases. Results generated from the ghost interface theory for the surface tension are presented and found to be in good quantitative agreement with those resulting from the Kirkwood-Buff equation. Applications of this new approach to curved and to supersaturated systems are also discussed.

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PubMed2003

Curvature-dependent surface tension of a growing droplet.

A ghost interface simulation technique is developed and applied to supersaturated Lennard-Jones liquid-vapor interfaces. It is shown that the surface tension decreases approximately linearly with the supersaturation ratio and that it vanishes at the spinodal. The effect leads to a curvature-dependent surface tension since, it is argued, the local supersaturation of the vapor above a droplet is greater than in the bulk due to slow diffusion in the vapor phase. An analytic approximation is given for the local supersaturation ratio, and an analytic expression for this contribution to Tolman's length is derived. The theory gives a smaller critical radius and reduces the free energy barrier to nucleation compared to classical homogeneous nucleation theory, which have important implications for the kinetics of droplet and bubble formation.

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