Algorithms for Brownian first-passage-time estimation.
(2009)
Journal - Physical review. E, Statistical, nonlinear, and soft matter physics (United States )
Abstract :
A class of algorithms in discrete space and continuous time for Brownian first-passage-time estimation is considered. A simple algorithm is derived that yields exact mean first-passage times (MFPTs) for linear potentials in one dimension, regardless of the lattice spacing. When applied to nonlinear potentials and/or higher spatial dimensions, numerical evidence suggests that this algorithm yields MFPT estimates that either outperform or rival Langevin-based (discrete time and continuous space) estimates.
Stochastic actions for diffusive dynamics: reweighting, sampling, and minimization.
(2008)
Journal - The journal of physical chemistry. B (United States )
Abstract :
In numerical studies of diffusive dynamics, two different action functionals are often used to specify the probability distribution of trajectories, one of which requires the evaluation of the second derivative of the potential in addition to the force. Here it is argued that both actions are equivalent prescriptions for the purposes of reweighting and sampling trajectories, whereas the most probable path is more generally given by the global minimum of the action involving the second derivative term. The answer to this apparent paradox lies in the nondifferentiable character of Brownian paths, as well as in the "entropy" associated with a given trajectory.
| ISSN : | 1520-6106 |
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| Mesh Heading : | Diffusion Probability Stochastic Processes |
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| Mesh Heading Relevant : | Models, Chemical |
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Random-walk approach to the d-dimensional disordered Lorentz gas.
(2008)
Journal - Physical review. E, Statistical, nonlinear, and soft matter physics (United States )
Abstract :
A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic expression for the diffusion constant in arbitrary number of dimensions d is obtained. The result corresponds to an Enskog-like correction to the Boltzmann prediction, being exact in the dilute limit, and better or nearly exact in comparison to renormalized kinetic theory predictions for all allowed densities in d=2,3 . Extensive numerical simulations were also performed to elucidate the role of the approximations involved.
| ISSN : | 1539-3755 |
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| Mesh Heading : | Computer Simulation Gases |
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| Mesh Heading Relevant : | Models, Chemical Models, Statistical chemistry |
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Algebraic perturbation theory for dense liquids with discrete potentials.
(2007)
Journal - Physical review. E, Statistical, nonlinear, and soft matter physics (United States )
Abstract :
A simple theory for the leading-order correction g{1}(r) to the structure of a hard-sphere liquid with discrete (e.g., square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively eliminates four-particle correlations from g{1}(r) with good accuracy at high densities. For the particular case of discrete perturbations, the remaining three-particle correlations can be modeled with a simple volume-exclusion argument, resulting in an algebraic and surprisingly accurate expression for g{1}(r). The structure of a discrete "core-softened" model for liquids with anomalous thermodynamic properties is reproduced as an application.