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

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

Comment on ``Fragmented Condensate Ground State of Trapped Weakly Interacting Bosons in Two Dimensions"

Recently Liu et al. [PRL 87, 030404 (2001)] examined the lowest state of a weakly-interacting Bose-Einstein condensate. In addition to other interesting results, using the method of the pair correlation function, they questioned the validity of the mean-field picture of the formation of vortices and stated that the vortices are generated at the center of the cloud. This is in apparent contradiction to the Gross-Pitaevskii approach, which predicts that the vortices successively enter the cloud from its outer parts as L/N (where N is the number of atoms in the trap and hbar(L) is the angular momentum of the system) increases. We have managed to reproduce the results of Liu et al. however a more careful analysis presented below confirms the validity of the mean-field approach.Comment: 1 page, RevTex, 2 figure

Size distribution of sputtered particles from Au nanoislands due to MeV self-ion bombardment

Nanoisland gold films, deposited by vacuum evaporation of gold onto Si(100) substrates, were irradiated with 1.5 MeV Au$^{2+}$ ions up to a fluence of $5\times 10^{14}$ ions cm$^{-2}$ and at incidence angles up to $60^{\circ}$ with respect to the surface normal. The sputtered particles were collected on carbon coated grids (catcher grid) during ion irradiation and were analyzed with transmission electron microscopy and Rutherford backscattering spectrometry. The average sputtered particle size and the areal coverage are determined from transmission electron microscopy measurements, whereas the amount of gold on the substrate is found by Rutherford backscattering spectrometry. The size distributions of larger particles (number of atoms/particle, $n$ $\ge$ 1,000) show an inverse power-law with an exponent of $\sim$ -1 in broad agreement with a molecular dynamics simulation of ion impact on cluster targets.Comment: 13 pages, 8 figures, Submitted for publication in JA

Dynamical typicality for initial states with a preset measurement statistics of several commuting observables

We consider all pure or mixed states of a quantum many-body system which exhibit the same, arbitrary but fixed measurement outcome statistics for several commuting observables. Taking those states as initial conditions, which are then propagated by the pertinent Schr\"odinger or von Neumann equation up to some later time point, and invoking a few additional, fairly weak and realistic assumptions, we show that most of them still entail very similar expectation values for any given observable. This so-called dynamical typicality property thus corroborates the widespread observation that a few macroscopic features are sufficient to ensure the reproducibility of experimental measurements despite many unknown and uncontrollable microscopic details of the system. We also discuss and exemplify the usefulness of our general analytical result as a powerful numerical tool

Vortices in Bose-Einstein condensates - finite-size effects and the thermodynamic limit

For a weakly-interacting Bose gas rotating in a harmonic trap we relate the yrast states of small systems (that can be treated exactly) to the thermodynamic limit (derived within the mean-field approximation). For a few dozens of atoms, the yrast line shows distinct quasi-periodic oscillations with increasing angular momentum that originate from the internal structure of the exact many-body states. These finite-size effects disappear in the thermodynamic limit, where the Gross-Pitaevskii approximation provides the exact energy to leading order in the number of particles N. However, the exact yrast states reveal significant structure not captured by the mean-field approximation: Even in the limit of large N, the corresponding mean-field solution accounts for only a fraction of the total weight of the exact quantum state.Comment: Phys Rev A, in pres

Facilitated movement of inertial Brownian motors driven by a load under an asymmetric potential

Based on recent work [L. Machura, M. Kostur, P. Talkner, J. Luczka, and P. Hanggi, Phys. Rev. Lett. 98, 040601 (2007)], we extend the study of inertial Brownian motors to the case of an asymmetric potential. It is found that some transport phenomena appear in the presence of an asymmetric potential. Within tailored parameter regimes, there exists two optimal values of the load at which the mean velocity takes its maximum, which means that a load can facilitate the transport in the two parameter regimes. In addition, the phenomenon of multiple current reversals can be observed when the load is increased.Comment: 7 pages, 3 figure

Phase transitions in optimal unsupervised learning

We determine the optimal performance of learning the orientation of the symmetry axis of a set of P = alpha N points that are uniformly distributed in all the directions but one on the N-dimensional sphere. The components along the symmetry breaking direction, of unitary vector B, are sampled from a mixture of two gaussians of variable separation and width. The typical optimal performance is measured through the overlap Ropt=B.J* where J* is the optimal guess of the symmetry breaking direction. Within this general scenario, the learning curves Ropt(alpha) may present first order transitions if the clusters are narrow enough. Close to these transitions, high performance states can be obtained through the minimization of the corresponding optimal potential, although these solutions are metastable, and therefore not learnable, within the usual bayesian scenario.Comment: 9 pages, 8 figures, submitted to PRE, This new version of the paper contains one new section, Bayesian versus optimal solutions, where we explain in detail the results supporting our claim that bayesian learning may not be optimal. Figures 4 of the first submission was difficult to understand. We replaced it by two new figures (Figs. 4 and 5 in this new version) containing more detail

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

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)