221 research outputs found
Rare-Event Sampling: Occupation-Based Performance Measures for Parallel Tempering and Infinite Swapping Monte Carlo Methods
In the present paper we identify a rigorous property of a number of
tempering-based Monte Carlo sampling methods, including parallel tempering as
well as partial and infinite swapping. Based on this property we develop a
variety of performance measures for such rare-event sampling methods that are
broadly applicable, informative, and straightforward to implement. We
illustrate the use of these performance measures with a series of applications
involving the equilibrium properties of simple Lennard-Jones clusters,
applications for which the performance levels of partial and infinite swapping
approaches are found to be higher than those of conventional parallel
tempering.Comment: 18 figure
An Infinite Swapping Approach to the Rare-Event Sampling Problem
We describe a new approach to the rare-event Monte Carlo sampling problem.
This technique utilizes a symmetrization strategy to create probability
distributions that are more highly connected and thus more easily sampled than
their original, potentially sparse counterparts. After discussing the formal
outline of the approach and devising techniques for its practical
implementation, we illustrate the utility of the technique with a series of
numerical applications to Lennard-Jones clusters of varying complexity and
rare-event character.Comment: 24 pages, 16 figure
Low-energy quantum dynamics of atoms at defects. Interstitial oxygen in silicon
The problem of the low-energy highly-anharmonic quantum dynamics of isolated
impurities in solids is addressed by using path-integral Monte Carlo
simulations. Interstitial oxygen in silicon is studied as a prototypical
example showing such a behavior. The assignment of a "geometry" to the defect
is discussed. Depending on the potential (or on the impurity mass), there is a
"classical" regime, where the maximum probability-density for the oxygen
nucleus is at the potential minimum. There is another regime, associated to
highly anharmonic potentials, where this is not the case. Both regimes are
separated by a sharp transition. Also, the decoupling of the many-nuclei
problem into a one-body Hamiltonian to describe the low-energy dynamics is
studied. The adiabatic potential obtained from the relaxation of all the other
degrees of freedom at each value of the coordinate associated to the low-energy
motion, gives the best approximation to the full many-nuclei problem.Comment: RevTeX, 6 pages plus 4 figures (all the figures were not accesible
before
Discretization Dependence of Criticality in Model Fluids: a Hard-core Electrolyte
Grand canonical simulations at various levels, -20, of fine- lattice
discretization are reported for the near-critical 1:1 hard-core electrolyte or
RPM. With the aid of finite-size scaling analyses it is shown convincingly
that, contrary to recent suggestions, the universal critical behavior is
independent of (\grtsim 4); thus the continuum RPM
exhibits Ising-type (as against classical, SAW, XY, etc.) criticality. A
general consideration of lattice discretization provides effective
extrapolation of the {\em intrinsically} erratic -dependence, yielding
(\Tc^ {\ast},\rhoc^{\ast})\simeq (0.0493_{3},0.075) for the
RPM.Comment: 4 pages including 4 figure
Nondielectric long-range solvation of polar liquids in cubic symmetry
Long-range solvation properties of strongly coupled dipolar systems simulated using the Ewald and reaction field methods are assessed by using electric fluctuation formulas for a dielectric medium. Some components of the fluctuating electric multipole moments are suppressed, whereas other components are favored as the boundary of the simulation box is approached. An analysis of electrostatic interactions in a periodic cubic system suggests that these structural effects are due to the periodicity embedded in the Ewald method. Furthermore, the results obtained using the reaction field method are very similar to those obtained using the Ewald method, an effect which we attribute to the use of toroidal boundary conditions in the former case. Thus, the long-range solvation properties of polar liquids simulated using either of the two methods are nondielectric in their character. (C) 2009 American Institute of Physics. [doi:10.1063/1.3250941
Monte Carlo simulation and global optimization without parameters
We propose a new ensemble for Monte Carlo simulations, in which each state is
assigned a statistical weight , where is the number of states with
smaller or equal energy. This ensemble has robust ergodicity properties and
gives significant weight to the ground state, making it effective for hard
optimization problems. It can be used to find free energies at all temperatures
and picks up aspects of critical behaviour (if present) without any parameter
tuning. We test it on the travelling salesperson problem, the Edwards-Anderson
spin glass and the triangular antiferromagnet.Comment: 10 pages with 3 Postscript figures, to appear in Phys. Rev. Lett
A Multiscale Approach to Determination of Thermal Properties and Changes in Free Energy: Application to Reconstruction of Dislocations in Silicon
We introduce an approach to exploit the existence of multiple levels of
description of a physical system to radically accelerate the determination of
thermodynamic quantities. We first give a proof of principle of the method
using two empirical interatomic potential functions. We then apply the
technique to feed information from an interatomic potential into otherwise
inaccessible quantum mechanical tight-binding calculations of the
reconstruction of partial dislocations in silicon at finite temperature. With
this approach, comprehensive ab initio studies at finite temperature will now
be possible.Comment: 5 pages, 3 figure
Criticality in confined ionic fluids
A theory of a confined two dimensional electrolyte is presented. The positive
and negative ions, interacting by a potential, are constrained to move on
an interface separating two solvents with dielectric constants and
. It is shown that the Debye-H\"uckel type of theory predicts that
the this 2d Coulomb fluid should undergo a phase separation into a coexisting
liquid (high density) and gas (low density) phases. We argue, however, that the
formation of polymer-like chains of alternating positive and negative ions can
prevent this phase transition from taking place.Comment: RevTex, no figures, in press Phys. Rev.
Sine-Gordon mean field theory of a Coulomb Gas
Sine-Gordon field theory is used to investigate the phase diagram of a
neutral Coulomb gas. A variational mean field free energy is constructed and
the corresponding phase diagrams in two (2d) and three dimensions (3d) are
obtained. When analyzed in terms of chemical potential, the Sine-Gordon theory
predicts the phase diagram topologically identical with the Monte Carlo
simulations and a recently developed Debye-H\"uckel-Bjerrum (DHBj) theory. In
2d we find that the infinite order Kosterlitz-Thouless line terminates in a
tricritical point, after which the metal-insulator transition becomes first
order. However, when the transformation from chemical potential to the density
is made the whole of the insulating phase is mapped onto zero density.Comment: 5 pages, Revtex with twocolumn style, 2 Postscript figures. Submitted
to PR
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