4,846 research outputs found
Population Annealing with Weighted Averages: A Monte Carlo Method for Rough Free Energy Landscapes
The population annealing algorithm introduced by Hukushima and Iba is
described. Population annealing combines simulated annealing and Boltzmann
weighted differential reproduction within a population of replicas to sample
equilibrium states. Population annealing gives direct access to the free
energy. It is shown that unbiased measurements of observables can be obtained
by weighted averages over many runs with weight factors related to the free
energy estimate from the run. Population annealing is well suited to
parallelization and may be a useful alternative to parallel tempering for
systems with rough free energy landscapes such as spin glasses. The method is
demonstrated for spin glasses.Comment: 9 pages, 5 figures; version 2 has improved figure 5 and new titl
Strengths and Weaknesses of Parallel Tempering
Parallel tempering, also known as replica exchange Monte Carlo, is studied in
the context of two simple free energy landscapes. The first is a double well
potential defined by two macrostates separated by a barrier. The second is a
`golf course' potential defined by microstates having two possible energies
with exponentially more high energy states than low energy states. The
equilibration time for replica exchange is analyzed for both systems. For the
double well system, parallel tempering with a number of replicas that scales as
the square root of the barrier height yields exponential speedup of the
equilibration time. On the other hand, replica exchange yields only marginal
speed-up for the golf course system. For the double well system, the free
energy difference between the two wells has a large effect on the equilibration
time. Nearly degenerate wells equilibrate much more slowly than strongly
asymmetric wells. It is proposed that this difference in equilibration time may
lead to a bias in measuring overlaps in spin glasses. These examples illustrate
the strengths and weaknesses of replica exchange and may serve as a guide for
understanding and improving the method in various applications.Comment: 18 pages, 4 figures. v2: typos fixed and wording changes to improve
clarit
Microcanonical versus Canonical Analysis of Protein Folding
The microcanonical analysis is shown to be a powerful tool to characterize
the protein folding transition and to neatly distinguish between good and bad
folders. An off-lattice model with parameter chosen to represent polymers of
these two types is used to illustrate this approach. Both canonical and
microcanonical ensembles are employed. The required calculations were performed
using parallel tempering Monte Carlo simulations. The most revealing features
of the folding transition are related to its first-order-like character,
namely, the S-bend pattern in the caloric curve, which gives rise to negative
microcanonical specific heats, and the bimodality of the energy distribution
function at the transition temperatures. Models for a good folder are shown to
be quite robust against perturbations in the interaction potential parameters.Comment: 4 pages, 4 figure
Activated sampling in complex materials at finite temperature: the properly-obeying-probability activation-relaxation technique
While the dynamics of many complex systems is dominated by activated events,
there are very few simulation methods that take advantage of this fact. Most of
these procedures are restricted to relatively simple systems or, as with the
activation-relaxation technique (ART), sample the conformation space
efficiently at the cost of a correct thermodynamical description. We present
here an extension of ART, the properly-obeying-probability ART (POP-ART), that
obeys detailed balance and samples correctly the thermodynamic ensemble.
Testing POP-ART on two model systems, a vacancy and an interstitial in
crystalline silicon, we show that this method recovers the proper
thermodynamical weights associated with the various accessible states and is
significantly faster than MD in the diffusion of a vacancy below 700 K.Comment: 10 pages, 3 figure
Entropic effects in large-scale Monte Carlo simulations
The efficiency of Monte Carlo samplers is dictated not only by energetic
effects, such as large barriers, but also by entropic effects that are due to
the sheer volume that is sampled. The latter effects appear in the form of an
entropic mismatch or divergence between the direct and reverse trial moves. We
provide lower and upper bounds for the average acceptance probability in terms
of the Renyi divergence of order 1/2. We show that the asymptotic finitude of
the entropic divergence is the necessary and sufficient condition for
non-vanishing acceptance probabilities in the limit of large dimensions.
Furthermore, we demonstrate that the upper bound is reasonably tight by showing
that the exponent is asymptotically exact for systems made up of a large number
of independent and identically distributed subsystems. For the last statement,
we provide an alternative proof that relies on the reformulation of the
acceptance probability as a large deviation problem. The reformulation also
leads to a class of low-variance estimators for strongly asymmetric
distributions. We show that the entropy divergence causes a decay in the
average displacements with the number of dimensions n that are simultaneously
updated. For systems that have a well-defined thermodynamic limit, the decay is
demonstrated to be n^{-1/2} for random-walk Monte Carlo and n^{-1/6} for Smart
Monte Carlo (SMC). Numerical simulations of the LJ_38 cluster show that SMC is
virtually as efficient as the Markov chain implementation of the Gibbs sampler,
which is normally utilized for Lennard-Jones clusters. An application of the
entropic inequalities to the parallel tempering method demonstrates that the
number of replicas increases as the square root of the heat capacity of the
system.Comment: minor corrections; the best compromise for the value of the epsilon
parameter in Eq. A9 is now shown to be log(2); 13 pages, 4 figures, to appear
in PR
Dynamical stabilization of classical multi electron targets against autoionization
We demonstrate that a recently published quasiclassical M\oller type approach
[Geyer and Rost 2002, J. Phys. B 35 1479] can be used to overcome the problem
of autoionization, which arises in classical trajectory calculations for many
electron targets. In this method the target is stabilized dynamically by a
backward--forward propagation scheme. We illustrate this refocusing and present
total cross sections for single and double ionization of helium by electron
impact.Comment: LaTeX, 6 pages, 2 figures; submitted to J. Phys.
Make life simple: unleash the full power of the parallel tempering algorithm
We introduce a new update scheme to systematically improve the efficiency of
parallel tempering simulations. We show that by adapting the number of sweeps
between replica exchanges to the canonical autocorrelation time, the average
round-trip time of a replica in temperature space can be significantly
decreased. The temperatures are not dynamically adjusted as in previous
attempts but chosen to yield a 50% exchange rate of adjacent replicas. We
illustrate the new algorithm with results for the Ising model in two and the
Edwards-Anderson Ising spin glass in three dimensionsComment: 4 pages, 5 figure
Design of a low-noise aeroacoustic wind tunnel facility at Brunel University
This paper represents the design principle of a quiet, low turbulence and moderately high speed aeroacoustic wind tunnel which was recently commissioned at Brunel University. A new hemi-anechoic chamber was purposely built to facilitate aeroacoustic measurements. The wind tunnel can achieve a maximum speed of about 80 ms-1. The turbulence intensity of the free jet in the potential core is between 0.1–0.2%. The noise characteristic of the aeroacoustic wind tunnel was validated by three case studies. All of which can demonstrate a very low background noise produced by the bare jet in comparison to the noise radiated from the cylinder rod/flat plate/airfoil in the air stream.The constructions of the aeroacoustic wind tunnel and the hemi-anechoic chamber are financially supported by the School of Engineering and Design at Brunel University
Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection
We propose a method for detecting significant interactions in very large
multivariate spatial point patterns. This methodology develops high dimensional
data understanding in the point process setting. The method is based on
modelling the patterns using a flexible Gibbs point process model to directly
characterise point-to-point interactions at different spatial scales. By using
the Gibbs framework significant interactions can also be captured at small
scales. Subsequently, the Gibbs point process is fitted using a
pseudo-likelihood approximation, and we select significant interactions
automatically using the group lasso penalty with this likelihood approximation.
Thus we estimate the multivariate interactions stably even in this setting. We
demonstrate the feasibility of the method with a simulation study and show its
power by applying it to a large and complex rainforest plant population data
set of 83 species
Superspace formulation of general massive gauge theories and geometric interpretation of mass-dependent BRST symmetries
A superspace formulation is proposed for the osp(1,2)-covariant Lagrangian
quantization of general massive gauge theories. The superalgebra os0(1,2) is
considered as subalgebra of sl(1,2); the latter may be considered as the
algebra of generators of the conformal group in a superspace with two
anticommuting coordinates. The mass-dependent (anti)BRST symmetries of proper
solutions of the quantum master equations in the osp(1,2)-covariant formalism
are realized in that superspace as invariance under translations combined with
mass-dependent special conformal transformations. The Sp(2) symmetry - in
particular the ghost number conservation - and the "new ghost number"
conservation are realized as invariance under symplectic rotations and
dilatations, respectively. The transformations of the gauge fields - and of the
full set of necessarily required (anti)ghost and auxiliary fields - under the
superalgebra sl(1,2) are determined both for irreducible and first-stage
reducible theories with closed gauge algebra.Comment: 35 pages, AMSTEX, precision of reference
- …