Point interactions in acoustics: one dimensional models

A one dimensional system made up of a compressible fluid and several mechanical oscillators, coupled to the acoustic field in the fluid, is analyzed for different settings of the oscillators array. The dynamical models are formulated in terms of singular perturbations of the decoupled dynamics of the acoustic field and the mechanical oscillators. Detailed spectral properties of the generators of the dynamics are given for each model we consider. In the case of a periodic array of mechanical oscillators it is shown that the energy spectrum presents a band structure.Comment: revised version, 30 pages, 2 figure

Quantum singularities in (2+1) dimensional matter coupled black hole spacetimes

Quantum singularities considered in the 3D BTZ spacetime by Pitelli and Letelier (Phys. Rev. D77: 124030, 2008) is extended to charged BTZ and 3D Einstein-Maxwell-dilaton gravity spacetimes. The occurence of naked singularities in the Einstein-Maxwell extension of the BTZ spacetime both in linear and non-linear electrodynamics as well as in the Einstein-Maxwell-dilaton gravity spacetimes are analysed with the quantum test fields obeying the Klein-Gordon and Dirac equations. We show that with the inclusion of the matter fields; the conical geometry near r=0 is removed and restricted classes of solutions are admitted for the Klein-Gordon and Dirac equations. Hence, the classical central singularity at r=0 turns out to be quantum mechanically singular for quantum particles obeying Klein-Gordon equation but nonsingular for fermions obeying Dirac equation. Explicit calculations reveal that the occurrence of the timelike naked singularities in the considered spacetimes do not violate the cosmic censorship hypothesis as far as the Dirac fields are concerned. The role of horizons that clothes the singularity in the black hole cases is replaced by repulsive potential barrier against the propagation of Dirac fields.Comment: 13 pages, 1 figure. Final version, to appear in PR

UV Finite Field Theories on Noncommutative Spacetimes: the Quantum Wick Product and Time Independent Perturbation Theory

In this article an energy correction is calculated in the time independent perturbation setup using a regularised ultraviolet finite Hamiltonian on the noncommutative Minkowski space. The correction to the energy is invariant under rotation and translation but is not Lorentz covariant and this leads to a distortion of the dispersion relation. In the limit where the noncommutativity vanishes the common quantum field theory on the commutative Minkowski space is reobtained.Comment: 8 pages, 2 figure

Study of boundary-layer transition using transonic-cone preston tube data

The laminar boundary layer on a 10 degree cone in a transonic wind tunnel was studied. The inviscid flow and boundary layer development were simulated by computer programs. The effects of pitch and yaw angles on the boundary layer were examined. Preston-tube data, taken on the boundary-layer-transition cone in the NASA Ames 11 ft transonic wind tunnel, were used to develope a correlation which relates the measurements to theoretical values of laminar skin friction. The recommended correlation is based on a compressible form of the classical law-of-the-wall. The computer codes successfully simulates the laminar boundary layer for near-zero pitch and yaw angles. However, in cases of significant pitch and/or yaw angles, the flow is three dimensional and the boundary layer computer code used here cannot provide a satisfactory model. The skin-friction correlation is thought to be valid for body geometries other than cones

Parallel, iterative solution of sparse linear systems: Models and architectures

A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. A data transfer model predicting both the probability that data must be transferred between two tasks and the amount of data to be transferred is presented. This model is used to derive an execution time model for predicting parallel execution time and an optimal number of tasks given the dimension and sparsity of the coefficient matrix and the costs of computation, synchronization, and communication. The suitability of different parallel architectures for solving randomly sparse linear systems is discussed. Based on the complexity of task scheduling, one parallel architecture, based on a broadcast bus, is presented and analyzed

A model of asynchronous iterative algorithms for solving large, sparse, linear systems

Solving large, sparse, linear systems of equations is one of the fundamental problems in large scale scientific and engineering computation. A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. This model is then analyzed to determine the expected intertask data transfer and task computational complexity as functions of the number of tasks. Based on the analysis, recommendations for task partitioning are made. These recommendations are a function of the sparseness of the linear system, its structure (i.e., randomly sparse or banded), and dimension

On the Flux-Across-Surfaces Theorem

The quantum probability flux of a particle integrated over time and a distant surface gives the probability for the particle crossing that surface at some time. We prove the free Flux-Across-Surfaces Theorem, which was conjectured by Combes, Newton and Shtokhamer, and which relates the integrated quantum flux to the usual quantum mechanical formula for the cross section. The integrated quantum flux is equal to the probability of outward crossings of surfaces by Bohmian trajectories in the scattering regime.Comment: 13 pages, latex, 1 figure, very minor revisions, to appear in Letters in Mathematical Physics, Vol. 38, Nr.

Distribution of the very first PopIII stars and their relation to bright z~6 quasars

We discuss the link between dark matter halos hosting the first PopIII stars and the rare, massive, halos that are generally considered to host bright quasars at high redshift z~6. The main question that we intend to answer is whether the super-massive black holes powering these QSOs grew out from the seeds planted by the first intermediate massive black holes created in the universe. This question involves a dynamical range of 10^13 in mass and we address it by combining N-body simulations of structure formation to identify the most massive halos at z~6 with a Monte Carlo method based on linear theory to obtain the location and formation times of the first light halos within the whole simulation box. We show that the descendants of the first ~10^6 Msun virialized halos do not, on average, end up in the most massive halos at z~6, but rather live in a large variety of environments. The oldest PopIII progenitors of the most massive halos at z~6, form instead from density peaks that are on average one and a half standard deviations more common than the first PopIII star formed in the volume occupied by one bright high-z QSO. The intermediate mass black hole seeds planted by the very first PopIII stars at z>40 can easily grow to masses m_BH>10^9.5 Msun by z=6 assuming Eddington accretion with radiative efficiency \epsilon~0.1. Quenching of the black hole accretion is therefore crucial to avoid an overabundance of supermassive black holes at lower redshift. This can be obtained if the mass accretion is limited to a fraction \eta~6*10^{-3} of the total baryon mass of the halo hosting the black hole. The resulting high end slope of the black hole mass function at z=6 is \alpha ~ -3.7, a value within the 1\sigma error bar for the bright end slope of the observed quasar luminosity function at z=6.Comment: 30 pages, 9 figures, ApJ accepte

Spectral shift function for operators with crossed magnetic and electric fields

We obtain a representation formula for the derivative of the spectral shift function $\xi(\lambda; B, \epsilon)$ related to the operators $H_0(B,\epsilon) = (D_x - By)^2 + D_y^2 + \epsilon x$ and $H(B, \epsilon) = H_0(B, \epsilon) + V(x,y), \: B > 0, \epsilon > 0$. We establish a limiting absorption principle for $H(B, \epsilon)$ and an estimate ${\mathcal O}(\epsilon^{n-2})$ for $\xi'(\lambda; B, \epsilon)$, provided $\lambda \notin \sigma(Q)$, where $Q = (D_x - By)^2 + D_y^2 + V(x,y).