18,603 research outputs found
Asymptotics of large bound states of localized structures
We analyze stationary fronts connecting uniform and periodic states emerging from a pattern-forming instability. The size of the resulting periodic domains cannot be predicted with weakly nonlinear methods. We show that what determine this size are exponentially small (but exponentially growing in space) terms. These can only be computed by going beyond all orders of the usual multiple-scale expansion. We apply the method to the Swift-Hohenberg equation and derive analytically a snaking bifurcation curve. At each fold of this bifurcation curve, a new pair of peaks is added to the periodic domain, which can thus be seen as a bound state of localized structures. Such scenarios have been reported with optical localized structures in nonlinear cavities and localized buckling
Mobile radio propagation prediction using ray tracing methods
The basic problem is to solve the two-dimensional scalar Helmholtz equation for a point source (the antenna) situated in the vicinity of an array of scatterers (such as the houses and any other relevant objects in 1 square km of urban environment). The wavelength is a few centimeters and the houses a few metres across, so there are three disparate length scales in the problem.
The question posed by BT concerned ray counting on the assumptions that:
(i) rays were subject to a reflection coefficient of about 0.5 when bouncing off a house wall and
(ii) that diffraction at corners reduced their energy by 90%. The quantity of particular interest was the number of rays that need to be accounted for at any particular point in order for those neglected to only contribute 10% of the field at that point; a secondary question concerned the use of rays to predict regions where the field was less than 1% of that in the region directly illuminated by the antenna.
The progress made in answering these two questions is described in the next two sections and possibly useful representations of the solution of the Helmholtz equations in terms other than rays are given in the final section
Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity
The bifurcation of asymmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg--Landau equations by the methods of formal asymptotics. The behavior of the bifurcating branch depends on the parameters d, the size of the superconducting slab, and , the Ginzburg--Landau parameter. The secondary bifurcation in which the asymmetric solution branches reconnect with the symmetric solution branch is studied for values of for which it is close to the primary bifurcation from the normal state. These values of form a curve in the -plane, which is determined. At one point on this curve, called the quintuple point, the primary bifurcations switch from being subcritical to supercritical, requiring a separate analysis. The results answer some of the conjectures of [A. Aftalion and W. C. Troy, Phys. D, 132 (1999), pp. 214--232]
Improving the Functional Control of Aged Ferroelectrics using Insights from Atomistic Modelling
We provide a fundamental insight into the microscopic mechanisms of the
ageing processes. Using large scale molecular dynamics simulations of the
prototypical ferroelectric material PbTiO3, we demonstrate that the
experimentally observed ageing phenomena can be reproduced from intrinsic
interactions of defect-dipoles related to dopant-vacancy associates, even in
the absence of extrinsic effects. We show that variation of the dopant
concentration modifies the material's hysteretic response. We identify a
universal method to reduce loss and tune the electromechanical properties of
inexpensive ceramics for efficient technologies.Comment: 6 pages, 3 figure
The Maximal Denumerant of a Numerical Semigroup
Given a numerical semigroup S = and n in S, we
consider the factorization n = c_0 a_0 + c_1 a_1 + ... + c_t a_t where c_i >=
0. Such a factorization is maximal if c_0 + c_1 + ... + c_t is a maximum over
all such factorizations of n. We provide an algorithm for computing the maximum
number of maximal factorizations possible for an element in S, which is called
the maximal denumerant of S. We also consider various cases that have
connections to the Cohen-Macualay and Gorenstein properties of associated
graded rings for which this algorithm simplifies.Comment: 13 Page
Realistic Expanding Source Model for Invariant One-Particle Multiplicity Distributions and Two-Particle Correlations in Relativistic Heavy-Ion Collisions
We present a realistic expanding source model with nine parameters that are
necessary and sufficient to describe the main physics occuring during
hydrodynamical freezeout of the excited hadronic matter produced in
relativistic heavy-ion collisions. As a first test of the model, we compare it
to data from central Si + Au collisions at p_lab/A = 14.6 GeV/c measured in
experiment E-802 at the AGS. An overall chi-square per degree of freedom of
1.055 is achieved for a fit to 1416 data points involving invariant pi^+, pi^-,
K^+, and K^- one-particle multiplicity distributions and pi^+ and K^+
two-particle correlations. The 99-percent-confidence region of parameter space
is identified, leading to one-dimensional error estimates on the nine fitted
parameters and other calculated physical quantities. Three of the most
important results are the freezeout temperature, longitudinal proper time, and
baryon density along the symmetry axis. For these we find values of 92.9 +/-
4.4 MeV, 8.2 +/- 2.2 fm/c, and 0.0222 + 0.0096 / - 0.0069 fm^-3, respectively.Comment: 37 pages and 12 figures. RevTeX 3.0. Submitted to Physical Review C.
Complete preprint, including device-independent (dvi), PostScript, and LaTeX
versions of the text, plus PostScript files of all figures, are available at
http://t2.lanl.gov/publications/publications.html or at
ftp://t2.lanl.gov/publications/res
Mass transport of an impurity in a strongly sheared granular gas
Transport coefficients associated with the mass flux of an impurity immersed
in a granular gas under simple shear flow are determined from the inelastic
Boltzmann equation. A normal solution is obtained via a Chapman-Enskog-like
expansion around a local shear flow distribution that retains all the
hydrodynamic orders in the shear rate. Due to the anisotropy induced by the
shear flow, tensorial quantities are required to describe the diffusion process
instead of the conventional scalar coefficients. The mass flux is determined to
first order in the deviations of the hydrodynamic fields from their values in
the reference state. The corresponding transport coefficients are given in
terms of the solutions of a set of coupled linear integral equations, which are
approximately solved by considering the leading terms in a Sonine polynomial
expansion. The results show that the deviation of these generalized
coefficients from their elastic forms is in general quite important, even for
moderate dissipation.Comment: 6 figure
Photoluminescence signature of skyrmions at \nu = 1
The photoluminescence spectrum of quantized Hall states near filling factor
\nu = 1 is investigated theoretically. For \nu >= 1 the spectrum consists of a
right-circularly polarized (RCP) line and a left-circularly polarized (LCP)
line, whose mean energy: (1) does not depend on the electron g factor for
spin-1/2 quasielectrons, (2) does depend on g for charged spin-texture
excitations (skyrmions). For \nu < 1 the spectrum consists of a LCP line
shifted down in energy from the LCP line at \nu >= 1. The g-factor dependence
of the red shift of the LCP line determines the nature of the negatively
charged excitations.Comment: 11 pages, 2 PostScript figures. Replaced with version to appear in
Physical Review B Rapid Communications. Minor changes, reference adde
Transport coefficients for an inelastic gas around uniform shear flow: Linear stability analysis
The inelastic Boltzmann equation for a granular gas is applied to spatially
inhomogeneous states close to the uniform shear flow. A normal solution is
obtained via a Chapman-Enskog-like expansion around a local shear flow
distribution. The heat and momentum fluxes are determined to first order in the
deviations of the hydrodynamic field gradients from their values in the
reference state. The corresponding transport coefficients are determined from a
set of coupled linear integral equations which are approximately solved by
using a kinetic model of the Boltzmann equation. The main new ingredient in
this expansion is that the reference state (zeroth-order
approximation) retains all the hydrodynamic orders in the shear rate. In
addition, since the collisional cooling cannot be compensated locally for
viscous heating, the distribution depends on time through its
dependence on temperature. This means that in general, for a given degree of
inelasticity, the complete nonlinear dependence of the transport coefficients
on the shear rate requires the analysis of the {\em unsteady} hydrodynamic
behavior. To simplify the analysis, the steady state conditions have been
considered here in order to perform a linear stability analysis of the
hydrodynamic equations with respect to the uniform shear flow state. Conditions
for instabilities at long wavelengths are identified and discussed.Comment: 7 figures; previous stability analysis modifie
System of elastic hard spheres which mimics the transport properties of a granular gas
The prototype model of a fluidized granular system is a gas of inelastic hard
spheres (IHS) with a constant coefficient of normal restitution . Using
a kinetic theory description we investigate the two basic ingredients that a
model of elastic hard spheres (EHS) must have in order to mimic the most
relevant transport properties of the underlying IHS gas. First, the EHS gas is
assumed to be subject to the action of an effective drag force with a friction
constant equal to half the cooling rate of the IHS gas, the latter being
evaluated in the local equilibrium approximation for simplicity. Second, the
collision rate of the EHS gas is reduced by a factor , relative
to that of the IHS gas. Comparison between the respective Navier-Stokes
transport coefficients shows that the EHS model reproduces almost perfectly the
self-diffusion coefficient and reasonably well the two transport coefficients
defining the heat flux, the shear viscosity being reproduced within a deviation
less than 14% (for ). Moreover, the EHS model is seen to agree
with the fundamental collision integrals of inelastic mixtures and dense gases.
The approximate equivalence between IHS and EHS is used to propose kinetic
models for inelastic collisions as simple extensions of known kinetic models
for elastic collisionsComment: 20 pages; 6 figures; change of title; few minor changes; accepted for
publication in PR
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