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

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 $\kappa$, the Ginzburg--Landau parameter. The secondary bifurcation in which the asymmetric solution branches reconnect with the symmetric solution branch is studied for values of $(\kappa,d)$ for which it is close to the primary bifurcation from the normal state. These values of $(\kappa,d)$ form a curve in the $\kappa d$-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

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

Photoionization and Photoelectric Loading of Barium Ion Traps

Simple and effective techniques for loading barium ions into linear Paul traps are demonstrated. Two-step photoionization of neutral barium is achieved using a weak intercombination line (6s2 1S0 6s6p 3P1, 791 nm) followed by excitation above the ionization threshold using a nitrogen gas laser (337 nm). Isotopic selectivity is achieved by using a near Doppler-free geometry for excitation of the triplet 6s6p 3P1 state. Additionally, we report a particularly simple and efficient trap loading technique that employs an in-expensive UV epoxy curing lamp to generate photoelectrons.Comment: 5 pages, Accepted to PRA 3/20/2007 -fixed typo -clarified figure 3 caption -added reference [15

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

Motion and homogenization of vortices in anisotropic Type II superconductors

The motion of vortices in an anisotropic superconductor is considered. For a system of well-separated vortices, each vortex is found to obey a law of motion analogous to the local induction approximation, in which velocity of the vortex depends upon the local curvature and orientation. A system of closely packed vortices is then considered, and a mean field model is formulated in which the individual vortex lines are replaced by a vortex density

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

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 $f^{(0)}$ (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 $f^{(0)}$ 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