3,700 research outputs found
BDDC and FETI-DP under Minimalist Assumptions
The FETI-DP, BDDC and P-FETI-DP preconditioners are derived in a particulary
simple abstract form. It is shown that their properties can be obtained from
only on a very small set of algebraic assumptions. The presentation is purely
algebraic and it does not use any particular definition of method components,
such as substructures and coarse degrees of freedom. It is then shown that
P-FETI-DP and BDDC are in fact the same. The FETI-DP and the BDDC
preconditioned operators are of the same algebraic form, and the standard
condition number bound carries over to arbitrary abstract operators of this
form. The equality of eigenvalues of BDDC and FETI-DP also holds in the
minimalist abstract setting. The abstract framework is explained on a standard
substructuring example.Comment: 11 pages, 1 figure, also available at
http://www-math.cudenver.edu/ccm/reports
Assimilation of Perimeter Data and Coupling with Fuel Moisture in a Wildland Fire - Atmosphere DDDAS
We present a methodology to change the state of the Weather Research
Forecasting (WRF) model coupled with the fire spread code SFIRE, based on
Rothermel's formula and the level set method, and with a fuel moisture model.
The fire perimeter in the model changes in response to data while the model is
running. However, the atmosphere state takes time to develop in response to the
forcing by the heat flux from the fire. Therefore, an artificial fire history
is created from an earlier fire perimeter to the new perimeter, and replayed
with the proper heat fluxes to allow the atmosphere state to adjust. The method
is an extension of an earlier method to start the coupled fire model from a
developed fire perimeter rather than an ignition point. The level set method is
also used to identify parameters of the simulation, such as the spread rate and
the fuel moisture. The coupled model is available from openwfm.org, and it
extends the WRF-Fire code in WRF release.Comment: ICCS 2012, 10 pages; corrected some DOI typesetting in the reference
Security improvement of using modified coherent state for quantum cryptography
Weak coherent states as a photon source for quantum cryptography have limit
in secure data rate and transmission distance because of the presence of
multi-photon events and loss in transmission line. Two-photon events in a
coherent state can be taken out by a two-photon interference scheme. We
investigate the security issue of utilizing this modified coherent state in
quantum cryptography. A 4 dB improvement in secure data rate or a nearly
two-fold increase in transmission distance over the coherent state are found.
With a recently proposed and improved encoding strategy, further improvement is
possible.Comment: 5 pages, 2 figures, to appear in Physical Review
Steady-state Ab Initio Laser Theory: Generalizations and Analytic Results
We improve the steady-state ab initio laser theory (SALT) of Tureci et al. by
expressing its fundamental self-consistent equation in a basis set of threshold
constant flux states that contains the exact threshold lasing mode. For
cavities with non-uniform index and/or non-uniform gain, the new basis set
allows the steady-state lasing properties to be computed with much greater
efficiency. This formulation of the SALT can be solved in the single-pole
approximation, which gives the intensities and thresholds, including the
effects of nonlinear hole-burning interactions to all orders, with negligible
computational effort. The approximation yields a number of analytic
predictions, including a "gain-clamping" transition at which strong modal
interactions suppress all higher modes. We show that the single-pole
approximation agrees well with exact SALT calculations, particularly for high-Q
cavities. Within this range of validity, it provides an extraordinarily
efficient technique for modeling realistic and complex lasers.Comment: 17 pages, 11 figure
Radiative coupling and weak lasing of exciton-polariton condensates
In spite of having finite life-time exciton-polaritons in microcavities are
known to condense at strong enough pumping of the reservoir. We present an
analytical theory of such Bose-condensates on a set of localized one-particle
states: condensation centers. To understand physics of these arrays one has to
supplement the Josephson coupling by the radiative coupling caused by the
interference of the light emitted by different centers. Combination of these
couplings with the one-site interaction between the bosons leads to a rich
nonlinear dynamics. In particular, a new regime of radiation appears. We call
it weak lasing: the centers have macroscopic occupations and radiate
coherently, but the coupling alone is sufficient for stabilization. The system
can have several stable states and switch between them. Moreover, the time
reversal symmetry in this regime is, as a rule, broken. A number of existing
experimental puzzles find natural interpretation in the framework of this
theory.Comment: 5 pages, 2 figure
Natural orbits of atomic Cooper pairs in a nonuniform Fermi gas
We examine the basic mode structure of atomic Cooper pairs in an
inhomogeneous Fermi gas. Based on the properties of Bogoliubov quasi-particle
vacuum, the single particle density matrix and the anomalous density matrix
share the same set of eigenfunctions. These eigenfunctions correspond to
natural pairing orbits associated with the BCS ground state. We investigate
these orbits for a Fermi gas in a spherical harmonic trap, and construct the
wave function of a Cooper pair in the form of Schmidt decomposition. The issue
of spatial quantum entanglement between constituent atoms in a pair is
addressed.Comment: 14 pages, 4 figures, submitted to Phys. Rev.
Discerning Aggregation in Homogeneous Ensembles: A General Description of Photon Counting Spectroscopy in Diffusing Systems
In order to discern aggregation in solutions, we present a quantum mechanical
analog of the photon statistics from fluorescent molecules diffusing through a
focused beam. A generating functional is developed to fully describe the
experimental physical system as well as the statistics. Histograms of the
measured time delay between photon counts are fit by an analytical solution
describing the static as well as diffusing regimes. To determine empirical
fitting parameters, fluorescence correlation spectroscopy is used in parallel
to the photon counting. For expedient analysis, we find that the distribution's
deviation from a single Poisson shows a difference between two single fluor
moments or a double fluor aggregate of the same total intensities. Initial
studies were performed on fixed-state aggregates limited to dimerization.
However preliminary results on reactive species suggest that the method can be
used to characterize any aggregating system.Comment: 30 pages, 5 figure
Quantum mechanical photon-count formula derived by entangled state representation
By introducing the thermo entangled state representation, we derived four new
photocount distribution formulas for a given density operator of light field.
It is shown that these new formulas, which is convenient to calculate the
photocount, can be expressed as such integrations over Laguree-Gaussian
function with characteristic function, Wigner function, Q-function, and
P-function, respectively.Comment: 5 pages, no figur
Biased tomography schemes: an objective approach
We report on an intrinsic relationship between the maximum-likelihood
quantum-state estimation and the representation of the signal. A quantum
analogy of the transfer function determines the space where the reconstruction
should be done without the need for any ad hoc truncations of the Hilbert
space. An illustration of this method is provided by a simple yet practically
important tomography of an optical signal registered by realistic binary
detectors.Comment: 4 pages, 3 figures, accepted in PR
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