28,130 research outputs found
Error estimation in the histogram Monte Carlo method
We examine the sources of error in the histogram reweighting method for Monte
Carlo data analysis. We demonstrate that, in addition to the standard
statistical error which has been studied elsewhere, there are two other sources
of error, one arising through correlations in the reweighted samples, and one
arising from the finite range of energies sampled by a simulation of finite
length. We demonstrate that while the former correction is usually negligible
by comparison with statistical fluctuations, the latter may not be, and give
criteria for judging the range of validity of histogram extrapolations based on
the size of this latter correction.Comment: 7 pages including 3 postscript figures, typeset in LaTeX using the
RevTeX macro packag
Diffusion constant for the repton model of gel electrophoresis
The repton model is a simple model of the "reptation" motion by which DNA
diffuses through a gel during electrophoresis. In this paper we show that the
model can be mapped onto a system consisting of two types of particles with
hard-sphere interactions diffusing on a one-dimensional lattice. Using this
mapping we formulate an efficient Monte Carlo algorithm for the model which
allows us to simulate systems more than twice the size of those studied before.
Our results confirm scaling hypotheses which have previously been put forward
for the model. We also show how the particle version of the model can be used
to construct a transfer matrix which allows us to solve exactly for the
diffusion constant of small repton systems. We give results for systems of up
to 20 reptons.Comment: 19 pages including five PostScript figures, typeset in LaTeX using
RevTeX 3.
Large-scale structure of time evolving citation networks
In this paper we examine a number of methods for probing and understanding
the large-scale structure of networks that evolve over time. We focus in
particular on citation networks, networks of references between documents such
as papers, patents, or court cases. We describe three different methods of
analysis, one based on an expectation-maximization algorithm, one based on
modularity optimization, and one based on eigenvector centrality. Using the
network of citations between opinions of the United States Supreme Court as an
example, we demonstrate how each of these methods can reveal significant
structural divisions in the network, and how, ultimately, the combination of
all three can help us develop a coherent overall picture of the network's
shape.Comment: 10 pages, 6 figures; journal names for 4 references fixe
The Universal Cut Function and Type II Metrics
In analogy with classical electromagnetic theory, where one determines the
total charge and both electric and magnetic multipole moments of a source from
certain surface integrals of the asymptotic (or far) fields, it has been known
for many years - from the work of Hermann Bondi - that energy and momentum of
gravitational sources could be determined by similar integrals of the
asymptotic Weyl tensor. Recently we observed that there were certain overlooked
structures, {defined at future null infinity,} that allowed one to determine
(or define) further properties of both electromagnetic and gravitating sources.
These structures, families of {complex} `slices' or `cuts' of Penrose's null
infinity, are referred to as Universal Cut Functions, (UCF). In particular, one
can define from these structures a (complex) center of mass (and center of
charge) and its equations of motion - with rather surprising consequences. It
appears as if these asymptotic structures contain in their imaginary part, a
well defined total spin-angular momentum of the source. We apply these ideas to
the type II algebraically special metrics, both twisting and twist-free.Comment: 32 page
Making electromagnetic wavelets
Electromagnetic wavelets are constructed using scalar wavelets as
superpotentials, together with an appropriate polarization. It is shown that
oblate spheroidal antennas, which are ideal for their production and reception,
can be made by deforming and merging two branch cuts. This determines a unique
field on the interior of the spheroid which gives the boundary conditions for
the surface charge-current density necessary to radiate the wavelets. These
sources are computed, including the impulse response of the antenna.Comment: 29 pages, 4 figures; minor corrections and addition
Interfaces (and Regional Congruence?) in Spin Glasses
We present a general theorem restricting properties of interfaces between
thermodynamic states and apply it to the spin glass excitations observed
numerically by Krzakala-Martin and Palassini-Young in spatial dimensions d=3
and 4. We show that such excitations, with interface dimension smaller than d,
cannot yield regionally congruent thermodynamic states. More generally, zero
density interfaces of translation-covariant excitations cannot be pinned (by
the disorder) in any d but rather must deflect to infinity in the thermodynamic
limit. Additional consequences concerning regional congruence in spin glasses
and other systems are discussed.Comment: 4 pages (ReVTeX); 1 figure; submitted to Physical Review Letter
Spin and Center of Mass in Axially Symmetric Einstein-Maxwell Spacetimes
We give a definition and derive the equations of motion for the center of
mass and angular momentum of an axially symmetric, isolated system that emits
gravitational and electromagnetic radiation. A central feature of this
formulation is the use of Newman-Unti cuts at null infinity that are generated
by worldlines of the spacetime. We analyze some consequences of the results and
comment on the generalization of this work to general asymptotically flat
spacetimes.Comment: 20 page
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