2,958 research outputs found
Perfect simulation of the hard disks model by partial rejection sampling
We present a perfect simulation of the hard disks model via the partial
rejection sampling method. Provided the density of disks is not too high, the
method produces exact samples in rounds, and total time ,
where is the expected number of disks. The method extends easily to the
hard spheres model in dimensions.Comment: v2: linear time implementation and various presentation improvement
Perfect Simulation of the Hard Disks Model by Partial Rejection Sampling
We present a perfect simulation of the hard disks model via the partial rejection sampling method. Provided the density of disks is not too high, the method produces exact samples in O(log n) rounds, and total time O(n), where n is the expected number of disks. The method extends easily to the hard spheres model in d>2 dimensions. In order to apply the partial rejection method to this continuous setting, we provide an alternative perspective of its correctness and run-time analysis that is valid for general state spaces
Disordered hyperuniformity in two-component non-additive hard disk plasmas
We study the behavior of a two-component plasma made up of non-additive hard
disks with a logarithmic Coulomb interaction. Due to the Coulomb repulsion,
long-wavelength total density fluctuations are suppressed and the system is
globally hyperuniform. Short-range volume effects lead to phase separation or
to hetero-coordination for positive or negative non-additivities, respectively.
These effects compete with the hidden long-range order imposed by
hyperuniformity. As a result, the critical behavior of the mixture is modified,
with long-wavelength concentration fluctuations partially damped when the
system is charged. It is also shown that the decrease of configurational
entropy due to hyperuniformity originates from contributions beyond the
two-particle level. Finally, despite global hyperuniformity, we show that in
our system, the spatial configuration associated with each component separately
is not hyperuniform, i.e., the system is not "multihyperuniform.
A rejection-free Monte Carlo method for the hard-disk system
We construct a rejection-free Monte Carlo method for the hard-disk system.
Rejection-free Monte Carlo methods preserve the time-evolution behavior of the
standard Monte Carlo method, and this relationship is confirmed for our method
by observing nonequilibrium relaxation of a bond-orientational order parameter.
The rejection-free method gives a greater computational efficiency than the
standard method at high densities. The rejection free method is implemented in
a shrewd manner using optimization methods to calculate a rejection probability
and to update the system. This method should allow an efficient study of the
dynamics of two-dimensional solids at high density.Comment: 8 pages, 9 figures. This paper has been combined into the
cond-mat/0508652, and published in Phys. Rev.
Fundamentals of Partial Rejection Sampling
Partial Rejection Sampling is an algorithmic approach to obtaining a perfect
sample from a specified distribution. The objects to be sampled are assumed to
be represented by a number of random variables. In contrast to classical
rejection sampling, in which all variables are resampled until a feasible
solution is found, partial rejection sampling aims at greater efficiency by
resampling only a subset of variables that `go wrong'. Partial rejection
sampling is closely related to Moser and Tardos' algorithmic version of the
Lov\'asz Local Lemma, but with the additional requirement that a specified
output distribution should be met. This article provides a largely
self-contained account of the basic form of the algorithm and its analysis
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