19,143 research outputs found
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
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
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
Compression and diffusion: a joint approach to detect complexity
The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular
research tool among physicists, especially when applied to a dynamical system
fitting the conditions of validity of the Pesin theorem. The study of time
series that are a manifestation of system dynamics whose rules are either
unknown or too complex for a mathematical treatment, is still a challenge since
the KS entropy is not computable, in general, in that case. Here we present a
plan of action based on the joint action of two procedures, both related to the
KS entropy, but compatible with computer implementation through fast and
efficient programs. The former procedure, called Compression Algorithm
Sensitive To Regularity (CASToRe), establishes the amount of order by the
numerical evaluation of algorithmic compressibility. The latter, called Complex
Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA),
establishes the complexity degree through the numerical evaluation of the
strength of an anomalous effect. This is the departure, of the diffusion
process generated by the observed fluctuations, from ordinary Brownian motion.
The CASSANDRA algorithm shares with CASToRe a connection with the Kolmogorov
complexity. This makes both algorithms especially suitable to study the
transition from dynamics to thermodynamics, and the case of non-stationary time
series as well. The benefit of the joint action of these two methods is proven
by the analysis of artificial sequences with the same main properties as the
real time series to which the joint use of these two methods will be applied in
future research work.Comment: 27 pages, 9 figure
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
Photoproduction off the nucleon revisited: Evidence for a narrow N(1688) resonance?
Revised analysis of beam asymmetry for the photoproduction on
the free proton reveals a structure at GeV. Fit of the
experimental data based on the E429 solution of the SAID partial wave analysis
suggests a narrow ( MeV) resonance. Possible candidates are
, or resonances. The result is considered in
conjunction with the recent evidence for a bump-like structure at GeV in the quasi-free photoproduction on the neutron.Comment: Contribution to the Workshop on the Physics of the Excited Nucleons
NSTAR2007, Bonn, Germany, Sept. 5 - 8 2007. To be published in Eur.Phys.J.
Blowup of Jang's equation at outermost marginally trapped surfaces
The aim of this paper is to collect some facts about the blowup of Jang's
equation. First, we discuss how to construct solutions that blow up at an
outermost MOTS. Second, we exclude the possibility that there are extra blowup
surfaces in data sets with non-positive mean curvature. Then we investigate the
rate of convergence of the blowup to a cylinder near a strictly stable MOTS and
show exponential convergence near a strictly stable MOTS.Comment: 15 pages. This revision corrects some typo
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
B -> Xs l_i^+ l_j^+ Decays with R-parity Violation
We derive the upper bounds on certain products of R-parity- and
lepton-flavor-violating couplings from B \ra X_s {l_i}^+ {l_j}^- decays.
These modes of B-meson decays can constrain the product combinations of the
couplings with one or more heavy generation indices which are comparable with
or stronger than the present bounds. From the studies of the invariant dilepton
mass spectrum and the forward backward asymmetry of the emitted leptons we note
the possibility of detecting R-parity-violating signals even when the total
decay rate due to R-parity violating couplings is comparable with that in the
standard model and discriminating two types of R-parity-violating signals. The
general expectation of the enhancement of the forward backward asymmetry of the
emitted leptons in the minimal supersymmetric standard model with R-parity may
be corrupted by R-parity violation.Comment: 10 pages, Revtex, 1 table and 2 figure
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