32,234 research outputs found
Viscosity solutions of general viscous Hamilton-Jacobi equations
We present comparison principles, Lipschitz estimates and study state
constraints problems for degenerate, second-order Hamilton-Jacobi equations.Comment: 35 pages, minor revisio
Looking at a soliton through the prism of optical supercontinuum
A traditional view on solitons in optical fibers as robust particle-like
structures suited for informa- tion transmission has been significantly altered
and broadened over the past decade, when solitons have been found to play the
major role in generation of octave broad supercontinuum spectra in
photonic-crystal and other types of optical fibers. This remarkable spectral
broadening is achieved through complex processes of dispersive radiation being
scattered from, emitted and transformed by solitons. Thus solitons have emerged
as the major players in nonlinear frequency conversion in optical fibers.
Unexpected analogies of these processes have been found with dynamics of
ultracold atoms and ocean waves. This colloquium focuses on recent
understanding and new insights into physics of soliton-radiation interaction
and supercontinuum generation.Comment: http://rmp.aps.org/abstract/RMP/v82/i2/p1287_1 (some figures have
been deleted due to space limits imposed by archive
Prediction of the functional properties of ceramic materials from composition using artificial neural networks
We describe the development of artificial neural networks (ANN) for the
prediction of the properties of ceramic materials. The ceramics studied here
include polycrystalline, inorganic, non-metallic materials and are investigated
on the basis of their dielectric and ionic properties. Dielectric materials are
of interest in telecommunication applications where they are used in tuning and
filtering equipment. Ionic and mixed conductors are the subjects of a concerted
effort in the search for new materials that can be incorporated into efficient,
clean electrochemical devices of interest in energy production and greenhouse
gas reduction applications. Multi-layer perceptron ANNs are trained using the
back-propagation algorithm and utilise data obtained from the literature to
learn composition-property relationships between the inputs and outputs of the
system. The trained networks use compositional information to predict the
relative permittivity and oxygen diffusion properties of ceramic materials. The
results show that ANNs are able to produce accurate predictions of the
properties of these ceramic materials which can be used to develop materials
suitable for use in telecommunication and energy production applications
Droplet and cluster formation in freely falling granular streams
Particle beams are important tools for probing atomic and molecular
interactions. Here we demonstrate that particle beams also offer a unique
opportunity to investigate interactions in macroscopic systems, such as
granular media. Motivated by recent experiments on streams of grains that
exhibit liquid-like breakup into droplets, we use molecular dynamics
simulations to investigate the evolution of a dense stream of macroscopic
spheres accelerating out of an opening at the bottom of a reservoir. We show
how nanoscale details associated with energy dissipation during collisions
modify the stream's macroscopic behavior. We find that inelastic collisions
collimate the stream, while the presence of short-range attractive interactions
drives structure formation. Parameterizing the collision dynamics by the
coefficient of restitution (i.e., the ratio of relative velocities before and
after impact) and the strength of the cohesive interaction, we map out a
spectrum of behaviors that ranges from gas-like jets in which all grains drift
apart to liquid-like streams that break into large droplets containing hundreds
of grains. We also find a new, intermediate regime in which small aggregates
form by capture from the gas phase, similar to what can be observed in
molecular beams. Our results show that nearly all aspects of stream behavior
are closely related to the velocity gradient associated with vertical free
fall. Led by this observation, we propose a simple energy balance model to
explain the droplet formation process. The qualitative as well as many
quantitative features of the simulations and the model compare well with
available experimental data and provide a first quantitative measure of the
role of attractions in freely cooling granular streams
Dynamical structure factor of a nonlinear Klein-Gordon lattice
The quantum modes of a nonlinear Klein-Gordon lattice have been computed
numerically [L. Proville, Phys. Rev. B 71, 104306 (2005)]. The on-site
nonlinearity has been found to lead to phonon bound states. In the present
paper, we compute numerically the dynamical structure factor so as to simulate
the coherent scattering cross section at low temperature. The inelastic
contribution is studied as a function of the on-site anharmonicity.
Interestingly, our numerical method is not limited to the weak anharmonicity
and permits one to study thoroughly the spectra of nonlinear phonons
The tropospheric gas composition of Jupiter's north equatorial belt (NH3, PH3, CH3D, GeH4, H2O) and the Jovian D/H isotropic ratio
The gas composition of the troposphere of Jupiter in the clearest regions of the North Equatorial Belt (NEB) was derived from the Voyager 1 IRIS data. The infrared spectrum for this homogeneous cloud free region was modeled to infer altitude profiles for NH3, PH3, GeH4 and H2O. The Profiles for NH3 and PH3 were found to be depleted in the upper troposphere but otherwise in agreement with their solar values at the 1 bar level. The mole fraction for CH3D was determined to be 3.5(+1.0 or -1.3) x 10 to the minus 7th power. The GeH4 mole fraction of 7+ or -2 x 10 to the minus 10th power at the 2 to 3 bar level is a factor of 10 lower than the solar value. The H2O mole fraction is approximately 1 x 0.00001 at the 2.5 bar level and is increasing to approximately 3 x 0.00001 at 4 bars where it is a factor of 30 lower than solar. Using IRIS infrared values for the mole fractions of CH3D and CH4 a value of D/H = 3.6(+1.0 or -1.4)x 0.00001 is derived. Assuming this Jovian D/H ratio is representative of the protosolar nebula, and correcting for chemical galactic evolution, yields a value of 5.5 - 9.0 x 0.00001 for the primordial D/H ratio and an upper limit of 1.8 to 2.4 x 10 to the minus 31st power cu cm for the present day baryon density
Condensation of microturbulence-generated shear flows into global modes
In full flux-surface computer studies of tokamak edge turbulence, a spectrum
of shear flows is found to control the turbulence level and not just the
conventional (0,0)-mode flows. Flux tube domains too small for the large
poloidal scale lengths of the continuous spectrum tend to overestimate the
flows, and thus underestimate the transport. It is shown analytically and
numerically that under certain conditions dominant (0,0)-mode flows independent
of the domain size develop, essentially through Bose-Einstein condensation of
the shear flows.Comment: 5 pages, 4 figure
AC induced damping of a fluxon in long Josephson junction
We present a theoretical and experimental study of Josephson vortex (fluxon)
moving in the presence of spatially homogeneous dc and ac bias currents. By
mapping this problem to the problem of calculating the current-voltage
characteristic of a small Josephson junction, we derive the dependence of the
average fluxon velocity on the dc bias current. In particular we find that the
low frequency ac bias current results in an additional nonlinear damping of
fluxon motion. Such ac induced damping crucially depends on the intrinsic
damping parameter and increases drastically as this parameter is reduced. We
find a good agreement of the analysis with both the direct numerical
simulations and the experimentally measured current-voltage characteristics of
a long annular Josephson junction with one trapped fluxon.Comment: Physical Review B, in pres
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