On the Penrose Inequality for general horizons

For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the ADM mass and the area of an outermost apparent horizon, if the data are restricted suitably. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass under a smooth inverse mean curvature flow, for data with non-negative Ricci scalar. Unlike Geroch we need not confine ourselves to minimal surfaces as horizons. Modulo smoothness issues we also show that our restrictions on the data can locally be fulfilled by a suitable choice of the initial surface in a given spacetime.Comment: 4 pages, revtex, no figures. Some comments added. No essential changes. To be published in Phys. Rev. Let

Isometric Representations of Totally Ordered Semigroups

Let S be a subsemigroup of an abelian torsion-free group G. If S is a positive cone of G, then all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic. Proved by Murphy, this statement generalized the well-known theorems of Coburn and Douglas. In this note we prove the reverse. If all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic, then S is a positive cone of G. Also we consider G = Z\times Z and prove that if S induces total order on G, then there exist at least two unitarily not equivalent irreducible isometrical representation of S. And if the order is lexicographical-product order, then all such representations are unitarily equivalent.Comment: February 21, 2012. Kazan, Russi

First Structure Formation: A Simulation of Small Scale Structure at High Redshift

We describe the results of a simulation of collisionless cold dark matter in a LambdaCDM universe to examine the properties of objects collapsing at high redshift (z=10). We analyze the halos that form at these early times in this simulation and find that the results are similar to those of simulations of large scale structure formation at low redshift. In particular, we consider halo properties such as the mass function, density profile, halo shape, spin parameter, and angular momentum alignment with the minor axis. By understanding the properties of small scale structure formation at high redshift, we can better understand the nature of the first structures in the universe, such as Population III stars.Comment: 31 pages, 14 figures; accepted for publication in ApJ. Figure 1 can also be viewed at http://cfa-www.harvard.edu/~hjang/research

Development of code evaluation criteria for assessing predictive capability and performance

Computational Fluid Dynamics (CFD), because of its unique ability to predict complex three-dimensional flows, is being applied with increasing frequency in the aerospace industry. Currently, no consistent code validation procedure is applied within the industry. Such a procedure is needed to increase confidence in CFD and reduce risk in the use of these codes as a design and analysis tool. This final contract report defines classifications for three levels of code validation, directly relating the use of CFD codes to the engineering design cycle. Evaluation criteria by which codes are measured and classified are recommended and discussed. Criteria for selecting experimental data against which CFD results can be compared are outlined. A four phase CFD code validation procedure is described in detail. Finally, the code validation procedure is demonstrated through application of the REACT CFD code to a series of cases culminating in a code to data comparison on the Space Shuttle Main Engine High Pressure Fuel Turbopump Impeller

Adaptive Power Control Method Considering Reactive Power Reserve for Wave-Offshore Hybrid Power Generator System

AbstractThe combined generator system with the wind and wave power can share the off-shore platform and therefore have the advantage of constructing the transmission system as well as the power conversion system. The established wind power generator systems do output determination by following the transmission system operator's directions and control the turbine by focusing at PCC, but when connected with the wave-power generator; it is needed to do the complex control. Especially, since the method and impact of active power control are different, it is required to distribute demanding power and responsibility to each turbine by considering the grid condition. In this paper, the control system is formed to do output determination of the combined generator system by paying attention to reactive power reserve of utility grid with the analysis of the controllable elements of the wind and wave power generator. And the comparison with the existing system is carried out based on the real system information. Through using the PSCAD/EMTDC simulation, the suitability of the new control technique of the combined system is estimated by proposing the active power control according to the reference signal of TSO and the reactive power capability followed by it

How many photons are needed to distinguish two transparencies?

We give a bound on the minimum number of photons that must be absorbed by any quantum protocol to distinguish between two transparencies. We show how a quantum Zeno method in which the angle of rotation is varied at each iteration can attain this bound in certain situations.Comment: 5 pages, 4 figure

One-Dimensional Dispersive Magnon Excitation in the Frustrated Spin-2 Chain System Ca3Co2O6

Using inelastic neutron scattering, we have observed a quasi-one-dimensional dispersive magnetic excitation in the frustrated triangular-lattice spin-2 chain oxide Ca3Co2O6. At the lowest temperature (T = 1.5 K), this magnon is characterized by a large zone-center spin gap of ~27 meV, which we attribute to the large single-ion anisotropy, and disperses along the chain direction with a bandwidth of ~3.5 meV. In the directions orthogonal to the chains, no measurable dispersion was found. With increasing temperature, the magnon dispersion shifts towards lower energies, yet persists up to at least 150 K, indicating that the ferromagnetic intrachain correlations survive up to 6 times higher temperatures than the long-range interchain antiferromagnetic order. The magnon dispersion can be well described within the predictions of linear spin-wave theory for a system of weakly coupled ferromagnetic chains with large single-ion anisotropy, enabling the direct quantitative determination of the magnetic exchange and anisotropy parameters.Comment: 7 pages, 6 figures including one animatio