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

Limits on the validity of the thin-layer model of the ionosphere for radio interferometric calibration

For a ground-based radio interferometer observing at low frequencies, the ionosphere causes propagation delays and refraction of cosmic radio waves which result in phase errors in the received signal. These phase errors can be corrected using a calibration method that assumes a two-dimensional phase screen at a fixed altitude above the surface of the Earth, known as the thin-layer model. Here we investigate the validity of the thin-layer model and provide a simple equation with which users can check when this approximation can be applied to observations for varying time of day, zenith angle, interferometer latitude, baseline length, ionospheric electron content and observing frequency.Comment: 8 pages, 10 figures, accepted MNRA

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

Non-equilibrium Phase-Ordering with a Global Conservation Law

In all dimensions, infinite-range Kawasaki spin exchange in a quenched Ising model leads to an asymptotic length-scale $L \sim (\rho t)^{1/2} \sim t^{1/3}$ at $T=0$ because the kinetic coefficient is renormalized by the broken-bond density, $\rho \sim L^{-1}$. For $T>0$, activated kinetics recovers the standard asymptotic growth-law, $L \sim t^{1/2}$. However, at all temperatures, infinite-range energy-transport is allowed by the spin-exchange dynamics. A better implementation of global conservation, the microcanonical Creutz algorithm, is well behaved and exhibits the standard non-conserved growth law, $L \sim t^{1/2}$, at all temperatures.Comment: 2 pages and 2 figures, uses epsf.st

Drowsy Cheetah Hunting Antelopes: A Diffusing Predator Seeking Fleeing Prey

We consider a system of three random walkers (a `cheetah' surrounded by two `antelopes') diffusing in one dimension. The cheetah and the antelopes diffuse, but the antelopes experience in addition a deterministic relative drift velocity, away from the cheetah, proportional to their distance from the cheetah, such that they tend to move away from the cheetah with increasing time. Using the backward Fokker-Planck equation we calculate, as a function of their initial separations, the probability that the cheetah has caught neither antelope after infinite time.Comment: 5 page

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

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 $O(n)$ model with nonconserved order parameter, in spatial dimension $2\le d\le 3$ and spin dimension $1\le n\le d$. 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 $d=2$ $O(2)$ model. Figures (23) are available on request - email [email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2

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

Identification of the critical temperature from non-equilibrium time-dependent quantities

We present a new procedure able to identify and measure the critical temperature. This method is based on the divergence of the relaxation time approaching the critical point in quenches from infinite temperature. We introduce a dimensionless quantity that turns out to be time-independent at the critical temperature. The procedure does not need equilibration and allows for a relatively fast identification of the critical temperature. The method is first tested in the ferromagnetic Ising model and then applied to the one-dimensional Ising spin glass with power-law interactions. Here we always find a finite critical temperature also in presence of a uniform external field, in agreement with the mean-field picture for the low temperature phase of spin glasses.Comment: 6 pages, 10 figure

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