Implementing an apparent-horizon finder in three dimensions

Locating apparent horizons is not only important for a complete understanding of numerically generated spacetimes, but it may also be a crucial component of the technique for evolving black-hole spacetimes accurately. A scheme proposed by Libson et al., based on expanding the location of the apparent horizon in terms of symmetric trace-free tensors, seems very promising for use with three-dimensional numerical data sets. In this paper, we generalize this scheme and perform a number of code tests to fully calibrate its behavior in black-hole spacetimes similar to those we expect to encounter in solving the binary black-hole coalescence problem. An important aspect of the generalization is that we can compute the symmetric trace-free tensor expansion to any order. This enables us to determine how far we must carry the expansion to achieve results of a desired accuracy. To accomplish this generalization, we describe a new and very convenient set of recurrence relations which apply to symmetric trace-free tensors.Comment: 14 pages (RevTeX 3.0 with 3 figures

Collapse to Black Holes in Brans-Dicke Theory: I. Horizon Boundary Conditions for Dynamical Spacetimes

We present a new numerical code that evolves a spherically symmetric configuration of collisionless matter in the Brans-Dicke theory of gravitation. In this theory the spacetime is dynamical even in spherical symmetry, where it can contain gravitational radiation. Our code is capable of accurately tracking collapse to a black hole in a dynamical spacetime arbitrarily far into the future, without encountering either coordinate pathologies or spacetime singularities. This is accomplished by truncating the spacetime at a spherical surface inside the apparent horizon, and subsequently solving the evolution and constraint equations only in the exterior region. We use our code to address a number of long-standing theoretical questions about collapse to black holes in Brans-Dicke theory.Comment: 46 pages including figures, uuencoded gz-compressed postscript, Submitted to Phys Rev

Lattice dynamics reveals a local symmetry breaking in the emergent dipole phase of PbTe

Local symmetry breaking in complex materials is emerging as an important contributor to materials properties but is inherently difficult to study. Here we follow up an earlier structural observation of such a local symmetry broken phase in the technologically important compound PbTe with a study of the lattice dynamics using inelastic neutron scattering (INS). We show that the lattice dynamics are responsive to the local symmetry broken phase, giving key insights in the behavior of PbTe, but also revealing INS as a powerful tool for studying local structure. The new result is the observation of the unexpected appearance on warming of a new zone center phonon branch in PbTe. In a harmonic solid the number of phonon branches is strictly determined by the contents and symmetry of the unit cell. The appearance of the new mode indicates a crossover to a dynamic lower symmetry structure with increasing temperature. No structural transition is seen crystallographically but the appearance of the new mode in inelastic neutron scattering coincides with the observation of local Pb off-centering dipoles observed in the local structure. The observation resembles relaxor ferroelectricity but since there are no inhomogeneous dopants in pure PbTe this anomalous behavior is an intrinsic response of the system. We call such an appearance of dipoles out of a non-dipolar ground-state "emphanisis" meaning the appearance out of nothing. It cannot be explained within the framework of conventional phase transition theories such as soft-mode theory and challenges our basic understanding of the physics of materials

Secret key distillation across a quantum wiretap channel under restricted eavesdropping

The theory of quantum cryptography aims to guarantee unconditional information-theoretic security against an omnipotent eavesdropper. In many practical scenarios, however, the assumption of an all-powerful adversary is excessive and can be relaxed considerably. In this paper we study secret key distillation across a lossy and noisy quantum wiretap channel between Alice and Bob, with a separately parameterized realistically lossy quantum channel to the eavesdropper Eve. We show that under such restricted eavesdropping, the key rates achievable can exceed the secret key distillation capacity against an unrestricted eavesdropper in the quantum wiretap channel. Further, we show upper bounds on the key rates based on the relative entropy of entanglement. This simple restricted eavesdropping model is widely applicable, e.g., to free-space quantum optical communication, where realistic collection of light by Eve is limited by the finite size of her optical aperture. Future work will include calculating bounds on the amount of light Eve can collect under various realistic scenarios.Comment: 14 pages, 19 figures. We welcome comments and suggestion

Supplemental Control of Lepidopterous Pests on Bt Transgenic Sweet Corn with Biologically-Based Spray Treatments

Biologically-based spray treatments, including nucleopolyhedroviruses, neem, and spinosad, were evaluated as supplemental controls for the fall armyworm, Spodoptera frugiperda (J. E. Smith), and corn earworm, Helicoverpa zea (Boddie) (Lepidoptera: Noctuidae), on transgenic sweet corn, Zea mays (L.) (Poales: Poaceae), expressing a Cry1Ab toxin from Bacillus thuringiensis Berliner (Bacillales: Bacillaceae) (Bt). Overall, transgenic corn supported lower densities of both pests than did nontransgenic corn. Control of the fall armyworm was improved in both whorl-stage and tassel-stage corn by the use of either a nucleopolyhedrovirus or neem, but the greatest improvement was seen with spinosad. Only spinosad consistently reduced damage to ears, which was caused by both pest species. In general, efficacy of the spray materials did not differ greatly between transgenic and nontransgenic corn

Collapse to Black Holes in Brans-Dicke Theory: II. Comparison with General Relativity

We discuss a number of long-standing theoretical questions about collapse to black holes in the Brans-Dicke theory of gravitation. Using a new numerical code, we show that Oppenheimer-Snyder collapse in this theory produces black holes that are identical to those of general relativity in final equilibrium, but are quite different from those of general relativity during dynamical evolution. We find that there are epochs during which the apparent horizon of such a black hole passes {\it outside\/} the event horizon, and that the surface area of the event horizon {\it decreases\/} with time. This behavior is possible because theorems which prove otherwise assume $R_{ab}l^al^b \ge 0$ for all null vectors $l^a$. We show that dynamical spacetimes in Brans-Dicke theory can violate this inequality, even in vacuum, for any value of $\omega$.Comment: 24 pages including figures, uuencoded gz-compressed postscript, Submitted to Phys Rev

Numerical Evolution of Black Holes with a Hyperbolic Formulation of General Relativity

We describe a numerical code that solves Einstein's equations for a Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York. This is the first time this formulation has been used to evolve a numerical spacetime containing a black hole. We excise the hole from the computational grid in order to avoid the central singularity. We describe in detail a causal differencing method that should allow one to stably evolve a hyperbolic system of equations in three spatial dimensions with an arbitrary shift vector, to second-order accuracy in both space and time. We demonstrate the success of this method in the spherically symmetric case.Comment: 23 pages RevTeX plus 7 PostScript figures. Submitted to Phys. Rev.

Treating instabilities in a hyperbolic formulation of Einstein's equations

We have recently constructed a numerical code that evolves a spherically symmetric spacetime using a hyperbolic formulation of Einstein's equations. For the case of a Schwarzschild black hole, this code works well at early times, but quickly becomes inaccurate on a time scale of 10-100 M, where M is the mass of the hole. We present an analytic method that facilitates the detection of instabilities. Using this method, we identify a term in the evolution equations that leads to a rapidly-growing mode in the solution. After eliminating this term from the evolution equations by means of algebraic constraints, we can achieve free evolution for times exceeding 10000M. We discuss the implications for three-dimensional simulations.Comment: 13 pages, 9 figures. To appear in Phys. Rev.