8,361 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
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
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
Lifshitz-Slyozov Scaling For Late-Stage Coarsening With An Order-Parameter-Dependent Mobility
The coarsening dynamics of the Cahn-Hilliard equation with order-parameter
dependent mobility, , is addressed at
zero temperature in the Lifshitz-Slyozov limit where the minority phase
occupies a vanishingly small volume fraction. Despite the absence of bulk
diffusion for , the mean domain size is found to grow as , due to subdiffusive transport of the order parameter
through the majority phase. The domain-size distribution is determined
explicitly for the physically relevant case .Comment: 4 pages, Revtex, no figure
Dynamics and delocalisation transition for an interface driven by a uniform shear flow
We study the effect of a uniform shear flow on an interface separating the
two broken-symmetry ordered phases of a two-dimensional system with
nonconserved scalar order parameter. The interface, initially flat and
perpendicular to the flow, is distorted by the shear flow. We show that there
is a critical shear rate, \gamma_c, proportional to 1/L^2, (where L is the
system width perpendicular to the flow) below which the interface can sustain
the shear. In this regime the countermotion of the interface under its
curvature balances the shear flow, and the stretched interface stabilizes into
a time-independent shape whose form we determine analytically. For \gamma >
\gamma_c, the interface acquires a non-zero velocity, whose profile is shown to
reach a time-independent limit which we determine exactly. The analytical
results are checked by numerical integration of the equations of motion.Comment: 5 page
Dynamical properties of the hypercell spin glass model
The spreading of damage technique is used to study the sensibility to initial
conditions in a heath bath Monte Carlo simulation of the spin glass hypercubic
cell model. Since the hypercubic cell in dimension 2D and the hypercubic
lattice in dimension D resemble each other closely at finite dimensions and
both converge to mean field when dimension goes to infinity, it allows us to
study the effect of dimensionality on the dynamical behavior of spin glasses.Comment: 13 pages, RevTex, 8 ps figure
Survival probabilities in the double trapping reaction A +B -> B, B + C -> C
We consider the double trapping reaction A + B -> B, B + C -> C in one
dimension. The survival probability of a given A particle is calculated under
various conditions on the diffusion constants of the reactants, and on the
ratio of initial B and C particle densities. The results are of more general
form than those obtained in previous work on the problem.Comment: 5 page
The Stability of the Replica Symmetric State in Finite Dimensional Spin Glasses
According to the droplet picture of spin glasses, the low-temperature phase
of spin glasses should be replica symmetric. However, analysis of the stability
of this state suggested that it was unstable and this instability lends support
to the Parisi replica symmetry breaking picture of spin glasses. The
finite-size scaling functions in the critical region of spin glasses below T_c
in dimensions greater than 6 can be determined and for them the replica
symmetric solution is unstable order by order in perturbation theory.
Nevertheless the exact solution can be shown to be replica-symmetric. It is
suggested that a similar mechanism might apply in the low-temperature phase of
spin glasses in less than six dimensions, but that a replica symmetry broken
state might exist in more than six dimensions.Comment: 5 pages. Modified to include a paragraph on the relation of this work
to that of Newman and Stei
Static black hole uniqueness and Penrose inequality
Under certain conditions, we give a new way to prove the uniqueness of static
black hole in higher dimensional asymptotically flat spacetimes. In the proof,
the Penrose inequality plays a key role in higher dimensions as well as four
dimensions.Comment: 6 page
Self Consistent Screening Approximation For Critical Dynamics
We generalise Bray's self-consistent screening approximation to describe the
critical dynamics of the theory. In order to obtain the dynamical
exponent , we have to make an ansatz for the form of the scaling functions,
which fortunately can be much constrained by general arguments. Numerical
values of for , and are obtained using two different
ans\"atze, and differ by a very small amount. In particular, the value of obtained for the 3-d Ising model agrees well with recent
Monte-Carlo simulations.Comment: 21 pages, LaTeX file + 4 (EPS) figure
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