Slice Stretching Effects for Maximal Slicing of a Schwarzschild Black Hole

Slice stretching effects such as slice sucking and slice wrapping arise when foliating the extended Schwarzschild spacetime with maximal slices. For arbitrary spatial coordinates these effects can be quantified in the context of boundary conditions where the lapse arises as a linear combination of odd and even lapse. Favorable boundary conditions are then derived which make the overall slice stretching occur late in numerical simulations. Allowing the lapse to become negative, this requirement leads to lapse functions which approach at late times the odd lapse corresponding to the static Schwarzschild metric. Demanding in addition that a numerically favorable lapse remains non-negative, as result the average of odd and even lapse is obtained. At late times the lapse with zero gradient at the puncture arising for the puncture evolution is precisely of this form. Finally, analytic arguments are given on how slice stretching effects can be avoided. Here the excision technique and the working mechanism of the shift function are studied in detail.Comment: 16 pages, 4 figures, revised version including a study on how slice stretching can be avoided by using excision and/or shift

Interplay of frequency-synchronization with noise: current resonances, giant diffusion and diffusion-crests

We elucidate how the presence of noise may significantly interact with the synchronization mechanism of systems exhibiting frequency-locking. The response of these systems exhibits a rich variety of behaviors, such as resonances and anti-resonances which can be controlled by the intensity of noise. The transition between different locked regimes provokes the development of a multiple enhancement of the effective diffusion. This diffusion behavior is accompanied by a crest-like peak-splitting cascade when the distribution of the lockings is self-similar, as it occurs in periodic systems that are able to exhibit a Devil's staircase sequence of frequency-lockings.Comment: 7 pages, 6 figures, epl.cls. Accepted for publication in Europhysics Letter

Slice Stretching at the Event Horizon when Geodesically Slicing the Schwarzschild Spacetime with Excision

Slice-stretching effects are discussed as they arise at the event horizon when geodesically slicing the extended Schwarzschild black-hole spacetime while using singularity excision. In particular, for Novikov and isotropic spatial coordinates the outward movement of the event horizon (``slice sucking'') and the unbounded growth there of the radial metric component (``slice wrapping'') are analyzed. For the overall slice stretching, very similar late time behavior is found when comparing with maximal slicing. Thus, the intuitive argument that attributes slice stretching to singularity avoidance is incorrect.Comment: 5 pages, 2 figures, published version including minor amendments suggested by the refere

Circular 78

Historically, sales of exotic meats have been limited only by supply. As supply has increased in recent years, national and international exotic game markets have grown rapidly. In the United States, growth has occurred primarily in the restaurant section, although over-the-counter sales have also increased. The Alaskan reindeer industry is exploring the potential of expanding its meat sales as well as antler sales. Meat production increased from 320,000 pounds in 1987 to 432,000 pounds in 1988. This production increase is reflected in a 27 percent increase in dollar value (Alaska Crop and Livestock Reporting Service, 1989). Under current management procedures, potential meat production has been estimated at 500,000 pounds (Pearson and Lewis, 1988). Any future market expansion is likely to occur in urban Alaska and in areas outside the state (Jones, 1988)

Hexagons become second if symmetry is broken

Pattern formation on the free surface of a magnetic fluid subjected to a magnetic field is investigated experimentally. By tilting the magnetic field the symmetry can be broken in a controllable manner. When increasing the amplitude of the tilted field, the flat surface gives way to liquid ridges. A further increase results in a hysteretic transition to a pattern of stretched hexagons. The instabilities are detected by means of a linear array of magnetic hall sensors and compared with theoretical predictions.Comment: accepted for publication by Physical Review E/Rapid Communicatio

The flashing ratchet and unidirectional transport of matter

We study the flashing ratchet model of a Brownian motor, which consists in cyclical switching between the Fokker-Planck equation with an asymmetric ratchet-like potential and the pure diffusion equation. We show that the motor really performs unidirectional transport of mass, for proper parameters of the model, by analyzing the attractor of the problem and the stationary vector of a related Markov chain.Comment: 11 page

Transition from anomalous to normal hysteresis in a system of coupled Brownian motors: a mean field approach

We address a recently introduced model describing a system of periodically coupled nonlinear phase oscillators submitted to multiplicative white noises, wherein a ratchet-like transport mechanism arises through a symmetry-breaking noise-induced nonequilibrium phase transition. Numerical simulations of this system reveal amazing novel features such as negative zero-bias conductance and anomalous hysteresis, explained resorting to a strong-coupling analysis in the thermodynamic limit. Using an explicit mean-field approximation we explore the whole ordered phase finding a transition from anomalous to normal hysteresis inside this phase, estimating its locus and identifying (within this scheme) a mechanism whereby it takes place.Comment: RevTex, 21 pgs, 15 figures. Submited to Physical Review E (2000

Constraint and gauge shocks in one-dimensional numerical relativity

We study how different types of blowups can occur in systems of hyperbolic evolution equations of the type found in general relativity. In particular, we discuss two independent criteria that can be used to determine when such blowups can be expected. One criteria is related to the so-called geometric blowup leading to gradient catastrophes, while the other is based upon the ODE-mechanism leading to blowups within finite time. We show how both mechanisms work in the case of a simple one-dimensional wave equation with a dynamic wave speed and sources, and later explore how those blowups can appear in one-dimensional numerical relativity. In the latter case we recover the well known "gauge shocks" associated with Bona-Massó–type slicing conditions. However, a crucial result of this study has been the identification of a second family of blowups associated with the way in which the constraints have been used to construct a hyperbolic formulation. We call these blowups "constraint shocks" and show that they are formulation specific, and that choices can be made to eliminate them or at least make them less severe

Rotating Bose-Einstein condensates: Closing the gap between exact and mean-field solutions

When a Bose-Einstein condensed cloud of atoms is given some angular momentum, it forms vortices arranged in structures with a discrete rotational symmetry. For these vortex states, the Hilbert space of the exact solution separates into a "primary" space related to the mean-field Gross-Pitaevskii solution and a "complementary" space including the corrections beyond mean-field. Considering a weakly-interacting Bose-Einstein condensate of harmonically-trapped atoms, we demonstrate how this separation can be used to close the conceptual gap between exact solutions for systems with only a few atoms and the thermodynamic limit for which the mean-field is the correct leading-order approximation. Although we illustrate this approach for the case of weak interactions, it is expected to be more generally valid.Comment: 8 pages, 5 figure

Brownian motion exhibiting absolute negative mobility

We consider a single Brownian particle in a spatially symmetric, periodic system far from thermal equilibrium. This setup can be readily realized experimentally. Upon application of an external static force F, the average particle velocity is negative for F>0 and positive for F<0 (absolute negative mobility).Comment: 4 pages, 3 figures, to be published in PR