18,170 research outputs found
The Richtmyer–Meshkov instability in magnetohydrodynamics
In ideal magnetohydrodynamics (MHD), the Richtmyer–Meshkov instability can be suppressed by the presence of a magnetic field. The interface still undergoes some growth, but this is bounded for a finite magnetic field. A model for this flow has been developed by considering the stability of an impulsively accelerated, sinusoidally perturbed density interface in the presence of a magnetic field that is parallel to the acceleration. This was accomplished by analytically solving the linearized initial value problem in the framework of ideal incompressible MHD. To assess the performance of the model, its predictions are compared to results obtained from numerical simulation of impulse driven linearized, shock driven linearized, and nonlinear compressible MHD for a variety of cases. It is shown that the analytical linear model collapses the data from the simulations well. The predicted interface behavior well approximates that seen in compressible linearized simulations when the shock strength, magnetic field strength, and perturbation amplitude are small. For such cases, the agreement with interface behavior that occurs in nonlinear simulations is also reasonable. The effects of increasing shock strength, magnetic field strength, and perturbation amplitude on both the flow and the performance of the model are investigated. This results in a detailed exposition of the features and behavior of the MHD Richtmyer–Meshkov flow. For strong shocks, large initial perturbation amplitudes, and strong magnetic fields, the linear model may give a rough estimate of the interface behavior, but it is not quantitatively accurate. In all cases examined the accuracy of the model is quantified and the flow physics underlying any discrepancies is examine
Oscillatory and localized perturbations of periodic structures and the bifurcation of defect modes
Let denote a periodic function on the real line. The Schr\"odinger
operator, , has spectrum equal to
the union of closed real intervals separated by open spectral gaps. In this
article we study the bifurcation of discrete eigenvalues (point spectrum) into
the spectral gaps for the operator , where is
spatially localized and highly oscillatory in the sense that its Fourier
transform, is concentrated at high frequencies. Our
assumptions imply that may be pointwise large but is
small in an average sense. For the special case where
with smooth, real-valued, localized in
, and periodic or almost periodic in , the bifurcating eigenvalues are at
a distance of order from the lower edge of the spectral gap. We
obtain the leading order asymptotics of the bifurcating eigenvalues and
eigenfunctions. Underlying this bifurcation is an effective Hamiltonian
associated with the lower edge of the spectral band:
where is the Dirac distribution,
and effective-medium parameters are
explicit and independent of . The potentials we consider are a
natural model for wave propagation in a medium with localized, high-contrast
and rapid fluctuations in material parameters about a background periodic
medium.Comment: To appear in SIAM Journal on Mathematical Analysi
Homogenized description of defect modes in periodic structures with localized defects
A spatially localized initial condition for an energy-conserving wave
equation with periodic coefficients disperses (spatially spreads) and decays in
amplitude as time advances. This dispersion is associated with the continuous
spectrum of the underlying differential operator and the absence of discrete
eigenvalues. The introduction of spatially localized perturbations in a
periodic medium leads to defect modes, states in which energy remains trapped
and spatially localized. In this paper we study weak, localized perturbations
of one-dimensional periodic Schr\"odinger operators. Such perturbations give
rise to such defect modes, and are associated with the emergence of discrete
eigenvalues from the continuous spectrum. Since these isolated eigenvalues are
located near a spectral band edge, there is strong scale-separation between the
medium period and the localization length of the defect mode. Bound states
therefore have a multi-scale structure: a "carrier Bloch wave" times a "wave
envelope", which is governed by a homogenized Schr\"odinger operator with
associated effective mass, depending on the spectral band edge which is the
site of the bifurcation. Our analysis is based on a reformulation of the
eigenvalue problem in Bloch quasi-momentum space, using the Gelfand-Bloch
transform and a Lyapunov-Schmidt reduction to a closed equation for the
near-band-edge frequency components of the bound state. A rescaling of the
latter equation yields the homogenized effective equation for the wave
envelope, and approximations to bifurcating eigenvalues and eigenfunctions.Comment: The title differs from version 1. To appear in Communications in
Mathematical Science
Handbook for MAP, volume 32. Part 1: MAP summary. Part 2: MAPSC minutes, reading, August 1989. MAP summaries from nations. Part 3: MAP data catalogue
Extended abstracts from the fourth workshop on the technical and scientific aspects of mesosphere stratosphere troposphere (MST) radar are presented. Individual sessions addressed the following topics: meteorological applications of MST and ST radars, networks, and campaigns; the dynamics of the equatorial middle atmosphere; interpretation of radar returns from clear air; techniques for studying gravity waves and turbulence, intercomparison and calibration of wind and wave measurements at various frequencies; progress in existing and planned MST and ST radars; hardware design for MST and ST radars and boundary layer/lower troposphere profilers; signal processing; and data management
A multiplexed single electron transistor for application in scalable solid-state quantum computing
Single Electron Transistors (SETs) are nanoscale electrometers of
unprecedented sensitivity, and as such have been proposed as read-out devices
in a number of quantum computer architectures. We show that the functionality
of a standard SET can be multiplexed so as to operate as both read-out device
and control gate for a solid-state qubit. Multiplexing in this way may be
critical in lowering overall gate densities in scalable quantum computer
architectures.Comment: 3 pages 3 figure
Multiple populations in globular clusters: the distinct kinematic imprints of different formation scenarios
Several scenarios have been proposed to explain the presence of multiple
stellar populations in globular clusters. Many of them invoke multiple
generations of stars to explain the observed chemical abundance anomalies, but
it has also been suggested that self-enrichment could occur via accretion of
ejecta from massive stars onto the circumstellar disc of low-mass pre-main
sequence stars. These scenarios imply different initial conditions for the
kinematics of the various stellar populations. Given some net angular momentum
initially, models for which a second generation forms from gas that collects in
a cooling flow into the core of the cluster predict an initially larger
rotational amplitude for the polluted stars compared to the pristine stars.
This is opposite to what is expected from the accretion model, where the
polluted stars are the ones crossing the core and are on preferentially radial
(low-angular momentum) orbits, such that their rotational amplitude is lower.
Here we present the results of a suite of -body simulations with initial
conditions chosen to capture the distinct kinematic properties of these
pollution scenarios. We show that initial differences in the kinematics of
polluted and pristine stars can survive to the present epoch in the outer parts
of a large fraction of Galactic globular clusters. The differential rotation of
pristine and polluted stars is identified as a unique kinematic signature that
could allow us to distinguish between various scenarios, while other kinematic
imprints are generally very similar from one scenario to the other.Comment: 22 pages, 16 figures + appendix. Accepted for publication in MNRA
Semirelativistic potential model for low-lying three-gluon glueballs
The three-gluon glueball states are studied with the generalization of a
semirelativistic potential model giving good results for two-gluon glueballs.
The Hamiltonian depends only on 3 parameters fixed on two-gluon glueball
spectra: the strong coupling constant, the string tension, and a gluon size
which removes singularities in the potential. The Casimir scaling determines
the structure of the confinement. Low-lying states are computed and
compared with recent lattice calculations. A good agreement is found for
and states, but our model predicts a state much
higher in energy than the lattice result. The mass is also computed.Comment: 2 figure
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