19,582 research outputs found
The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics
The Helmholtz Equation (-delta-K(2)n(2))u=0 with a variable index of refraction, n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. A numerical algorithm was developed and a computer code implemented that can effectively solve this equation in the intermediate frequency range. The equation is discretized using the finite element method, thus allowing for the modeling of complicated geometrices (including interfaces) and complicated boundary conditions. A global radiation boundary condition is imposed at the far field boundary that is exact for an arbitrary number of propagating modes. The resulting large, non-selfadjoint system of linear equations with indefinite symmetric part is solved using the preconditioned conjugate gradient method applied to the normal equations. A new preconditioner is developed based on the multigrid method. This preconditioner is vectorizable and is extremely effective over a wide range of frequencies provided the number of grid levels is reduced for large frequencies. A heuristic argument is given that indicates the superior convergence properties of this preconditioner
On accuracy conditions for the numerical computation of waves
The Helmholtz equation (Delta + K(2)n(2))u = f with a variable index of refraction n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. Such problems can be solved numerically by first truncating the given unbounded domain and imposing a suitable outgoing radiation condition on an artificial boundary and then solving the resulting problem on the bounded domain by direct discretization (for example, using a finite element method). In practical applications, the mesh size h and the wave number K, are not independent but are constrained by the accuracy of the desired computation. It will be shown that the number of points per wavelength, measured by (Kh)(-1), is not sufficient to determine the accuracy of a given discretization. For example, the quantity K(3)h(2) is shown to determine the accuracy in the L(2) norm for a second-order discretization method applied to several propagation models
Electric Deflection of Rotating Molecules
We provide a theory of the deflection of polar and non-polar rotating
molecules by inhomogeneous static electric field. Rainbow-like features in the
angular distribution of the scattered molecules are analyzed in detail.
Furthermore, we demonstrate that one may efficiently control the deflection
process with the help of short and strong femtosecond laser pulses. In
particular the deflection process may by turned-off by a proper excitation, and
the angular dispersion of the deflected molecules can be substantially reduced.
We study the problem both classically and quantum mechanically, taking into
account the effects of strong deflecting field on the molecular rotations. In
both treatments we arrive at the same conclusions. The suggested control scheme
paves the way for many applications involving molecular focusing, guiding, and
trapping by inhomogeneous fields
Significant g-factor values of a two-electron ground state in quantum dots with spin-orbit coupling
The magnetization of semiconductor quantum dots in the presence of spin-orbit
coupling and interactions is investigated numerically. When the dot is occupied
by two electrons we find that a level crossing between the two lowest many-body
eigenstates may occur as a function of the spin-orbit coupling strength. This
level crossing is accompanied by a non-vanishing magnetization of the
ground-state. Using first order perturbation theory as well as exact numerical
diagonalization of small clusters we show that the tendency of interactions to
cause Stoner-like instability is enhanced by the SO coupling. The resulting
g-factor can have a significant value, and thus may influence g-factor
measurements. Finally we propose an experimental method by which the predicted
phenomenon can be observed.Comment: 7+ pages, 7 figure
Maternal age, development time, position effect variegation in Drosophila melanogaster
In Drosophila expression of position-effect variegation is enhanced by culturing flies at low temperatures. It is demonstrated that this effect may not be solely temperature dependent. Maternal age influences offspring development times. Futhermore, at a given temperature, the longer a fly takes to develop, the more likely is it to exhibit position-effect variegation.Chez la Drosophile, l’expression de la diversité de « l’effet position est favorisée lorsque les mouches se développent sous des températures basses. Il a été démontré que cet effet n’est pas uniquement dépendant de la température. L’âge maternel influence la durée de développement des descendants. De plus, pour une température donnée, il semble que plus la durée de développement est longue, plus l’expression de « l’effet position » est diversifiée
Contraction of broken symmetries via Kac-Moody formalism
I investigate contractions via Kac-Moody formalism. In particular, I show how
the symmetry algebra of the standard 2-D Kepler system, which was identified by
Daboul and Slodowy as an infinite-dimensional Kac-Moody loop algebra, and was
denoted by , gets reduced by the symmetry breaking term,
defined by the Hamiltonian For this I
define two symmetry loop algebras , by
choosing the `basic generators' differently. These
can be mapped isomorphically onto subalgebras of , of
codimension 2 or 3, revealing the reduction of symmetry. Both factor algebras
, relative to the corresponding
energy-dependent ideals , are isomorphic to
and for , respectively, just as for the
pure Kepler case. However, they yield two different non-standard contractions
as , namely to the Heisenberg-Weyl algebra or to an abelian Lie algebra, instead of the Euclidean algebra
for the pure Kepler case. The above example suggests a
general procedure for defining generalized contractions, and also illustrates
the {\em `deformation contraction hysteresis'}, where contraction which involve
two contraction parameters can yield different contracted algebras, if the
limits are carried out in different order.Comment: 21 pages, 1 figur
Galactic Spiral Structure
We describe the structure and composition of six major stellar streams in a
population of 20 574 local stars in the New Hipparcos Reduction with known
radial velocities. We find that, once fast moving stars are excluded, almost
all stars belong to one of these streams. The results of our investigation have
lead us to re-examine the hydrogen maps of the Milky Way, from which we
identify the possibility of a symmetric two-armed spiral with half the
conventionally accepted pitch angle. We describe a model of spiral arm motions
which matches the observed velocities and composition of the six major streams,
as well as the observed velocities of the Hyades and Praesepe clusters at the
extreme of the Hyades stream. We model stellar orbits as perturbed ellipses
aligned at a focus in coordinates rotating at the rate of precession of
apocentre. Stars join a spiral arm just before apocentre, follow the arm for
more than half an orbit, and leave the arm soon after pericentre. Spiral
pattern speed equals the mean rate of precession of apocentre. Spiral arms are
shown to be stable configurations of stellar orbits, up to the formation of a
bar and/or ring. Pitch angle is directly related to the distribution of orbital
eccentricities in a given spiral galaxy. We show how spiral galaxies can evolve
to form bars and rings. We show that orbits of gas clouds are stable only in
bisymmetric spirals. We conclude that spiral galaxies evolve toward grand
design two-armed spirals. We infer from the velocity distributions that the
Milky Way evolved into this form about 9 Gyrs ago.Comment: Published in Proc Roy Soc A. A high resolution version of this file
can be downloaded from http://papers.rqgravity.net/SpiralStructure.pdf. A
simplified account with animations begins at
http://rqgravity.net/SpiralStructur
Feedback Effects, Asymmetric Trading, and the Limits to Arbitrage
We analyze strategic speculators' incentives to trade on information in a model where firm value is endogenous to trading, due to feedback from the financial market to corporate decisions. Trading reveals private information to managers and improves their real decisions, enhancing fundamental value. This feedback effect has an asymmetric effect on trading behavior: it increases (reduces) the profitability of buying (selling) on good (bad)news. This gives rise to an endogenous limit to arbitrage, whereby investors may refrain from trading on negative information. Thus, bad news is incorporated more slowly into prices than good news, potentially leading to overinvestment
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