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