925,480 research outputs found
On the reduction of a random basis
For , let be independent vectors in
with a common distribution invariant by rotation. Considering
these vectors as a basis for the Euclidean lattice they generate, the aim of
this paper is to provide asymptotic results when concerning the
property that such a random basis is reduced in the sense of {\sc Lenstra,
Lenstra & Lov\'asz}. The proof passes by the study of the process
where is the
ratio of lengths of two consecutive vectors and
built from by the Gram--Schmidt orthogonalization
procedure, which we believe to be interesting in its own. We show that, as
, the process tends in distribution in some
sense to an explicit process ; some properties of this
latter are provided
Efficient Simulation of Quantum State Reduction
The energy-based stochastic extension of the Schrodinger equation is a rather
special nonlinear stochastic differential equation on Hilbert space, involving
a single free parameter, that has been shown to be very useful for modelling
the phenomenon of quantum state reduction. Here we construct a general closed
form solution to this equation, for any given initial condition, in terms of a
random variable representing the terminal value of the energy and an
independent Brownian motion. The solution is essentially algebraic in
character, involving no integration, and is thus suitable as a basis for
efficient simulation studies of state reduction in complex systems.Comment: 4 pages, No Figur
Electronic structure of intentionally disordered AlAs/GaAs superlattices
We use realistic pseudopotentials and a plane-wave basis to study the
electronic structure of non-periodic, three-dimensional, 2000-atom
(AlAs)_n/(GaAs)_m (001) superlattices, where the individual layer thicknesses
n,m = {1,2,3} are randomly selected. We find that while the band gap of the
equivalent (n = m = 2) ordered superlattice is indirect, random fluctuations in
layer thicknesses lead to a direct gap in the planar Brillouin zone, strong
wavefunction localization along the growth direction, short radiative
lifetimes, and a significant band-gap reduction, in agreement with experiments
on such intentionally grown disordered superlattices.Comment: 10 pages, REVTeX and EPSF macros, 4 figures in postscript. e-mail to
[email protected]
Flight flutter testing technology at Grumman
Analysis techniques used in the automated telemetry station (ATS) for on line data reduction are encompassed in a broad range of software programs. Concepts that form the basis for the algorithms used are mathematically described. The control the user has in interfacing with various on line programs is discussed. The various programs are applied to an analysis of flight data which includes unimodal and bimodal response signals excited via a swept frequency shaker and/or random aerodynamic forces. A nonlinear response error modeling analysis approach is described. Preliminary results in the analysis of a hard spring nonlinear resonant system are also included
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