8,224 research outputs found
Zero area singularities in general relativity and inverse mean curvature flow
First we restate the definition of a Zero Area Singularity, recently
introduced by H. Bray. We then consider several definitions of mass for these
singularities. We use the Inverse Mean Curvature Flow to prove some new results
about the mass of a singularity, the ADM mass of the manifold, and the capacity
of the singularity.Comment: 13 page
Phase Ordering Dynamics of the O(n) Model - Exact Predictions and Numerical Results
We consider the pair correlation functions of both the order parameter field
and its square for phase ordering in the model with nonconserved order
parameter, in spatial dimension and spin dimension .
We calculate, in the scaling limit, the exact short-distance singularities of
these correlation functions and compare these predictions to numerical
simulations. Our results suggest that the scaling hypothesis does not hold for
the model. Figures (23) are available on request - email
[email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2
A counter-example to a recent version of the Penrose conjecture
By considering suitable axially symmetric slices on the Kruskal spacetime, we
construct counterexamples to a recent version of the Penrose inequality in
terms of so-called generalized apparent horizons.Comment: 12 pages. Appendix added with technical details. To appear in
Classical and Quantum Gravit
Vortex annihilation in the ordering kinetics of the O(2) model
The vortex-vortex and vortex-antivortex correlation functions are determined
for the two-dimensional O(2) model undergoing phase ordering. We find
reasonably good agreement with simulation results for the vortex-vortex
correlation function where there is a short-scaled distance depletion zone due
to the repulsion of like-signed vortices. The vortex-antivortex correlation
function agrees well with simulation results for intermediate and long-scaled
distances. At short-scaled distances the simulations show a depletion zone not
seen in the theory.Comment: 28 pages, REVTeX, submitted to Phys. Rev.
Perturbative Corrections to the Ohta-Jasnow-Kawasaki Theory of Phase-Ordering Dynamics
A perturbation expansion is considered about the Ohta-Jasnow-Kawasaki theory
of phase-ordering dynamics; the non-linear terms neglected in the OJK
calculation are reinstated and treated as a perturbation to the linearised
equation. The first order correction term to the pair correlation function is
calculated in the large-d limit and found to be of order 1/(d^2).Comment: Revtex, 27 pages including 2 figures, submitted to Phys. Rev. E,
references adde
The effect of shear on persistence in coarsening systems
We analytically study the effect of a uniform shear flow on the persistence
properties of coarsening systems. The study is carried out within the
anisotropic Ohta-Jasnow-Kawasaki (OJK) approximation for a system with
nonconserved scalar order parameter. We find that the persistence exponent
theta has a non-trivial value: theta = 0.5034... in space dimension d=3, and
theta = 0.2406... for d=2, the latter being exactly twice the value found for
the unsheared system in d=1. We also find that the autocorrelation exponent
lambda is affected by shear in d=3 but not in d=2.Comment: 6 page
Persistence of Manifolds in Nonequilibrium Critical Dynamics
We study the persistence P(t) of the magnetization of a d' dimensional
manifold (i.e., the probability that the manifold magnetization does not flip
up to time t, starting from a random initial condition) in a d-dimensional spin
system at its critical point. We show analytically that there are three
distinct late time decay forms for P(t) : exponential, stretched exponential
and power law, depending on a single parameter \zeta=(D-2+\eta)/z where D=d-d'
and \eta, z are standard critical exponents. In particular, our theory predicts
that the persistence of a line magnetization decays as a power law in the d=2
Ising model at its critical point. For the d=3 critical Ising model, the
persistence of the plane magnetization decays as a power law, while that of a
line magnetization decays as a stretched exponential. Numerical results are
consistent with these analytical predictions.Comment: 4 pages revtex, 1 eps figure include
Dynamics of Ordering of Heisenberg Spins with Torque --- Nonconserved Case. I
We study the dynamics of ordering of a nonconserved Heisenberg magnet. The
dynamics consists of two parts --- an irreversible dissipation into a heat bath
and a reversible precession induced by a torque due to the local molecular
field. For quenches to zero temperature, we provide convincing arguments, both
numerically (Langevin simulation) and analytically (approximate closure scheme
due to Mazenko), that the torque is irrelevant at late times. We subject the
Mazenko closure scheme to systematic numerical tests. Such an analysis, carried
out for the first time on a vector order parameter, shows that the closure
scheme performs respectably well. For quenches to , we show, to , that the torque is irrelevant at the Wilson-Fisher fixed
point.Comment: 13 pages, REVTEX, and 19 .eps figures, compressed, Submitted to Phys.
Rev.
Evidence for existence of many pure ground states in 3d Spin Glasses
Ground states of 3d EA Ising spin glasses are calculated for sizes up to
using a combination of genetic algorithms and cluster-exact
approximation . The distribution of overlaps is calculated. For
increasing size the width of converges to a nonzero value, indicating
that many pure ground states exist for short range Ising spin glasses.Comment: 4 pages, 3 figures, 2 tables, 16 reference
Mean-field theory for a spin-glass model of neural networks: TAP free energy and paramagnetic to spin-glass transition
An approach is proposed to the Hopfield model where the mean-field treatment
is made for a given set of stored patterns (sample) and then the statistical
average over samples is taken. This corresponds to the approach made by
Thouless, Anderson and Palmer (TAP) to the infinite-range model of spin
glasses. Taking into account the fact that in the Hopfield model there exist
correlations between different elements of the interaction matrix, we obtain
its TAP free energy explicitly, which consists of a series of terms exhibiting
the cluster effect. Nature of the spin-glass transition in the model is also
examined and compared with those given by the replica method as well as the
cavity method.Comment: 12 pages, LaTex, 1 PostScript figur
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