900 research outputs found
Competition and bistability of ordered undulations and undulation chaos in inclined layer convection
Experimental and theoretical investigations of undulation patterns in
high-pressure, inclined layer gas convection at a Prandtl number near unity are
reported. Particular focus is given to the competition between the
spatiotemporal chaotic state of undulation chaos and stationary patterns of
ordered undulations. In experiments a competition and bistability between the
two states is observed, with ordered undulations most prevalent at higher
Rayleigh number. The spectral pattern entropy, spatial correlation lengths, and
defect statistics are used to characterize the competing states. The
experiments are complemented by a theoretical analysis of the
Oberbeck-Boussinesq equations. The stability region of the ordered undulation
as a function of their wavevectors and the Rayleigh number is obtained with
Galerkin techniques. In addition, direct numerical simulations are used to
investigate the spatiotemporal dynamics. In the simulations both ordered
undulations and undulation chaos were observed dependent on initial conditions.
Experiment and theory are found to agree well.Comment: Reduced-resolution figure
Numerical study of domain coarsening in anisotropic stripe patterns
We study the coarsening of two-dimensional smectic polycrystals characterized
by grains of oblique stripes with only two possible orientations. For this
purpose, an anisotropic Swift-Hohenberg equation is solved. For quenches close
enough to the onset of stripe formation, the average domain size increases with
time as . Further from onset, anisotropic pinning forces similar to
Peierls stresses in solid crystals slow down defects, and growth becomes
anisotropic. In a wide range of quench depths, dislocation arrays remain mobile
and dislocation density roughly decays as , while chevron boundaries
are totally pinned. We discuss some agreements and disagreements found with
recent experimental results on the coarsening of anisotropic electroconvection
patterns.Comment: 8 pages, 11 figures. Phys. Rev E, to appea
Spatio-temporal patterns in inclined layer convection
This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle γ and the Rayleigh number R. The present numerical investigation of the inclined layer convection system is based on the standard Oberbeck–Boussinesq equations. The patterns are shown to originate from a complicated competition of buoyancy driven and shear-flow driven pattern forming
mechanisms. The former are expressed as longitudinal convection rolls with their axes oriented parallel to the incline, the latter as perpendicular transverse rolls. Along with conventional methods to study roll patterns and their stability, we employ direct numerical simulations in large spatial domains, comparable with the experimental ones. As a result, we determine the phase diagram of the characteristic complex 3-D convection patterns above onset of convection in the γ–R plane, and find
that it compares very well with the experiments. In particular we demonstrate that interactions of specific Fourier modes, characterized by a resonant interaction of their wavevectors in the layer plane, are key to understanding the pattern morphologies
Specific heat and thermal conductivity in the vortex state of the two-gap superconductor MgB_2
The specific heat coefficient gamma_s(H) and the electronic thermal
conductivity kappa_{es}(H) are calculated for Abrikosov's vortex lattice by
taking into account the effects of supercurrent flow and Andreev scattering.
First we solve the gap equation for the entire range of magnetic fields. We
take into account vertex corrections due to impurity scattering calculated in
the Born approximation. The function gamma_s(H)/gamma_n increases from zero and
becomes approximately linear above H/H_{c2} \sim 0.1. The dependence on
impurity scattering is substantially reduced by the vertex corrections. The
upward curvature of kappa_{es}(H)/kappa_{en}, which is caused by decreasing
Andreev scattering for increasing field, is reduced for increasing impurity
scattering. We also calculate the temperature dependence of the scattering
rates 1/tau_{ps}(H) of a phonon and 1/tau_{es}(H) of a quasiparticle due to
quasiparticle and phonon scattering, respectively. At low temperatures the
ratio tau_{pn}/tau_{ps}(H) increases rapidly to one as H tends to H_{c2} which
yields a rapid drop in the phononic thermal conductivity kappa_{ph}. Our
results are in qualitative agreement with the experiments on the two-gap
superconductor MgB_2.Comment: 12 pages, 5 figures, additions to figures 1, 2, and 3. Accepted by
Phys. Rev.
On retracts, absolute retracts, and folds in cographs
Let G and H be two cographs. We show that the problem to determine whether H
is a retract of G is NP-complete. We show that this problem is fixed-parameter
tractable when parameterized by the size of H. When restricted to the class of
threshold graphs or to the class of trivially perfect graphs, the problem
becomes tractable in polynomial time. The problem is also soluble when one
cograph is given as an induced subgraph of the other. We characterize absolute
retracts of cographs.Comment: 15 page
Multimodal transistors as ReLU activation functions in physical neural network classifiers
Artificial neural networks (ANNs) providing sophisticated, power-efficient classification are finding their way into thin-film electronics. Thin-film technologies require robust, layout-efficient devices with facile manufacturability. Here, we show how the multimodal transistor’s (MMT’s) transfer characteristic, with linear dependence in saturation, replicates the rectified linear unit (ReLU) activation function of convolutional ANNs (CNNs). Using MATLAB, we evaluate CNN performance using systematically distorted ReLU functions, then substitute measured and simulated MMT transfer characteristics as proxies for ReLU. High classification accuracy is maintained, despite large variations in geometrical and electrical parameters, as CNNs use the same activation functions for training and classification
Whirling Hexagons and Defect Chaos in Hexagonal Non-Boussinesq Convection
We study hexagon patterns in non-Boussinesq convection of a thin rotating
layer of water. For realistic parameters and boundary conditions we identify
various linear instabilities of the pattern. We focus on the dynamics arising
from an oscillatory side-band instability that leads to a spatially disordered
chaotic state characterized by oscillating (whirling) hexagons. Using
triangulation we obtain the distribution functions for the number of pentagonal
and heptagonal convection cells. In contrast to the results found for defect
chaos in the complex Ginzburg-Landau equation and in inclined-layer convection,
the distribution functions can show deviations from a squared Poisson
distribution that suggest non-trivial correlations between the defects.Comment: 4 mpg-movies are available at
http://www.esam.northwestern.edu/~riecke/lit/lit.html submitted to New J.
Physic
Transient spatiotemporal chaos in the complex Ginzburg-Landau equation on long domains
Numerical simulations of the complex Ginzburg-Landau equation in one spatial dimension on periodic domains with sufficiently large spatial period reveal persistent chaotic dynamics in large parts of parameter space that extend into the Benjamin-Feir stable regime. This situation changes when nonperiodic boundary conditions are imposed, and in the Benjamin-Feir stable regime chaos takes the form of a long-lived transient decaying to a spatially uniform oscillatory state. The lifetime of the transient has Poisson statistics and no domain length is found sufficient for persistent chaos
- and -wave components induced around a vortex in -wave superconductors
Vortex structure of -wave superconductors is microscopically
analyzed in the framework of the quasi-classical Eilenberger equations. If the
pairing interaction contains an -wave (-wave) component in addition
to a -wave component, the -wave (-wave) component of
the order parameter is necessarily induced around a vortex in
-wave superconductors. The spatial distribution of the induced
-wave and -wave components is calculated. The -wave component has
opposite winding number around vortex near the -vortex core and
its amplitude has the shape of a four-lobe clover. The amplitude of
-component has the shape of an octofoil. These are consistent with
results based on the GL theory.Comment: RevTex,9 pages, 6 figures in a uuencoded fil
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