1,175 research outputs found
Nonequilibrium effects of anisotropic compression applied to vortex lattices in Bose-Einstein condensates
We have studied the dynamics of large vortex lattices in a dilute-gas
Bose-Einstein condensate. While undisturbed lattices have a regular hexagonal
structure, large-amplitude quadrupolar shape oscillations of the condensate are
shown to induce a wealth of nonequilibrium lattice dynamics. When exciting an m
= -2 mode, we observe shifting of lattice planes, changes of lattice structure,
and sheet-like structures in which individual vortices appear to have merged.
Excitation of an m = +2 mode dissolves the regular lattice, leading to randomly
arranged but still strictly parallel vortex lines.Comment: 5 pages, 6 figure
Project for the analysis of technology transfer Quarterly report, 1 Jul. - 30 Sep. 1969
Research activities in technology transfer progra
Linear relaxation to planar Travelling Waves in Inertial Confinement Fusion
We study linear stability of planar travelling waves for a scalar
reaction-diffusion equation with non-linear anisotropic diffusion. The
mathematical model is derived from the full thermo-hydrodynamical model
describing the process of Inertial Confinement Fusion. We show that solutions
of the Cauchy problem with physically relevant initial data become planar
exponentially fast with rate s(\eps',k)>0, where
\eps'=\frac{T_{min}}{T_{max}}\ll 1 is a small temperature ratio and
the transversal wrinkling wavenumber of perturbations. We rigorously recover in
some particular limit (\eps',k)\rightarrow (0,+\infty) a dispersion relation
s(\eps',k)\sim \gamma_0 k^{\alpha} previously computed heuristically and
numerically in some physical models of Inertial Confinement Fusion
Rotation Numbers, Boundary Forces and Gap labelling
We review the Johnson-Moser rotation number and the -theoretical gap
labelling of Bellissard for one-dimensional Schr\"odinger operators. We compare
them with two further gap-labels, one being related to the motion of Dirichlet
eigenvalues, the other being a -theoretical gap label. We argue that the
latter provides a natural generalisation of the Johnson-Moser rotation number
to higher dimensions.Comment: 10 pages, version accepted for publicatio
On the stability of soliton and hairy black hole solutions of SU(N) Einstein-Yang-Mills theory with a negative cosmological constant
We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional su(N) Einstein-Yang-Mills theory with a
negative cosmological constant Λ. These solutions are described by N − 1 magnetic gauge field functions ωj. We consider linear, spherically symmetric, perturbations of these solutions. The perturbations decouple into two sectors, known as the sphaleronic and gravitational sectors. For any N, there are no instabilities in the sphaleronic sector if all the magnetic gauge field functions ωj have no zeros and satisfy a set of N − 1 inequalities. In the gravitational sector, we prove that there are solutions which have no instabilities in a neighbourhood of stable embedded su(2) solutions, provided the magnitude of the cosmological constant |Λ| is sufficiently large.
Kewywords : Stability, hairy black hole, soliton, Einstein-Yang-Mills, anti de-Sitte
Gigantic transmission band edge resonance in periodic stacks of anisotropic layers
We consider Fabry-Perot cavity resonance in periodic stacks of anisotropic
layers with misaligned in-plane anisotropy at the frequency close to a photonic
band edge. We show that in-plane dielectric anisotropy can result in a dramatic
increase in field intensity and group delay associated with the transmission
resonance. The field enhancement appears to be proportional to forth degree of
the number N of layers in the stack. By contrast, in common periodic stacks of
isotropic layers, those effects are much weaker and proportional to N^2. Thus,
the anisotropy allows to drastically reduce the size of the resonance cavity
with similar performance. The key characteristic of the periodic arrays with
the gigantic transmission resonance is that the dispersion curve omega(k)at the
photonic band edge has the degenerate form Delta(omega) ~ Delta(k)^4, rather
than the regular form Delta(omega) ~ Delta(k)^2. This can be realized in
specially arranged stacks of misaligned anisotropic layers. The degenerate band
edge cavity resonance with similar outstanding properties can also be realized
in a waveguide environment, as well as in a linear array of coupled multimode
resonators, provided that certain symmetry conditions are in place.Comment: To be submitted to Phys. Re
Project for the analysis of technology transfer Quarterly report, 1 Apr. 1969 - 30 Jun. 1969
Patterns, statistical analyses, and case studies of transfer and utilization of NASA generated technolog
On the density-potential mapping in time-dependent density functional theory
The key questions of uniqueness and existence in time-dependent density
functional theory are usually formulated only for potentials and densities that
are analytic in time. Simple examples, standard in quantum mechanics, lead
however to non-analyticities. We reformulate these questions in terms of a
non-linear Schr\"odinger equation with a potential that depends non-locally on
the wavefunction.Comment: 8 pages, 2 figure
On the harmonic Boltzmannian waves in laser-plasma interaction
We study the permanent regimes of the reduced Vlasov-Maxwell system for
laser-plasma interaction. A non-relativistic and two different relativistic
models are investigated. We prove the existence of solutions where the
distribution function is Boltzmannian and the electromagnetic variables are
time-harmonic and circularly polarized
On the notion of conditional symmetry of differential equations
Symmetry properties of PDE's are considered within a systematic and unifying
scheme: particular attention is devoted to the notion of conditional symmetry,
leading to the distinction and a precise characterization of the notions of
``true'' and ``weak'' conditional symmetry. Their relationship with exact and
partial symmetries is also discussed. An extensive use of ``symmetry-adapted''
variables is made; several clarifying examples, including the case of
Boussinesq equation, are also provided.Comment: 18 page
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