26,411 research outputs found
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
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 related to the operators and . We establish a limiting absorption principle
for and an estimate for
, provided , where $Q =
(D_x - By)^2 + D_y^2 + V(x,y).
Stencils and problem partitionings: Their influence on the performance of multiple processor systems
Given a discretization stencil, partitioning the problem domain is an important first step for the efficient solution of partial differential equations on multiple processor systems. Partitions are derived that minimize interprocessor communication when the number of processors is known a priori and each domain partition is assigned to a different processor. This partitioning technique uses the stencil structure to select appropriate partition shapes. For square problem domains, it is shown that non-standard partitions (e.g., hexagons) are frequently preferable to the standard square partitions for a variety of commonly used stencils. This investigation is concluded with a formalization of the relationship between partition shape, stencil structure, and architecture, allowing selection of optimal partitions for a variety of parallel systems
Independent electrons model for open quantum systems: Landauer-Buettiker formula and strict positivity of the entropy production
A general argument leading from the formula for currents through an open
noninteracting mesoscopic system given by the theory of non-equilibrium steady
states (NESS) to the Landauer-Buettiker formula is pointed out. Time reversal
symmetry is not assumed. As a consequence it follows that, as far as the system
has a nontrivial scattering theory and the reservoirs have different
temperatures and/or chemical potentials, the entropy production is strictly
positive.Comment: 12 pages. Submitted for publication in J. Math. Phys. on 2006-06-05.
Revision and extension of: G. Nenciu, A general proof of Landauer-Buettiker
formula, [math-ph/0603030
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