Coupled KdV equations derived from atmospherical dynamics

Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable $y$-average trick (which is usually adopted in literature) is removed. The derived models are classified via Painlev\'e test. Three types of $\tau$-function solutions and multiple soliton solutions of the models are explicitly given by means of the exact solutions of the usual KdV equation. It is also interesting that for a non-Painlev\'e integrable coupled KdV system there may be multiple soliton solutions.Comment: 19 pages, 2 figure

New variable separation approach: application to nonlinear diffusion equations

The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the derivative-dependent functional separable solutions is obtained and some exact solutions to the resulting equations are described.Comment: 19 pages, 2 fig

Global axisymmetric stability analysis for a composite system of two gravitationally coupled scale-free discs

In a composite system of gravitationally coupled stellar and gaseous discs, we perform linear stability analysis for axisymmetric coplanar perturbations using the two-fluid formalism. The background stellar and gaseous discs are taken to be scale-free with all physical variables varying as powers of cylindrical radius $r$ with compatible exponents. The unstable modes set in as neutral modes or stationary perturbation configurations with angular frequency $\omega=0$.Comment: 7 pages using AAS styl

Spin injection from perpendicular magnetized ferromagnetic δ\delta-MnGa into (Al,Ga)As heterostructures

Electrical spin injection from ferromagnetic $\delta$-MnGa into an (Al,Ga)As p-i-n light emitting diode (LED) is demonstrated. The $\delta$-MnGa layers show strong perpendicular magnetocrystalline anisotropy, enabling detection of spin injection at remanence without an applied magnetic field. The bias and temperature dependence of the spin injection are found to be qualitatively similar to Fe-based spin LED devices. A Hanle effect is observed and demonstrates complete depolarization of spins in the semiconductor in a transverse magnetic field.Comment: 4 pages, 3 figure

Statistical learning bias predicts second-language reading efficiency

Statistical learning (SL) is increasingly invoked as a set of general-purpose mechanisms upon which language learning is built during infancy and childhood. Here we investigated the extent to which SL is related to adult language processing. In particular, we asked whether SL proclivities towards relations that are more informative of English are related to efficiency in reading English sentences by native speakers of Korean. We found that individuals with a stronger statistical learning sensitivity showed a larger effect of conditional word probability on word reading times, indicating that they more efficiently incorporated statistical regularities of the language during reading. In contrast, L2 English proficiency was related to overall reading speed but not to the use of statistical regularities

Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations

An approximate perturbed direct homotopy reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth order dispersion and second order dissipation. The similarity reduction equations are derived to arbitrary orders. The method is valid not only for single soliton solution but also for the Painlev\'e II waves and periodic waves expressed by Jacobi elliptic functions for both fourth order dispersion and second order dissipation. The method is valid also for strong perturbations.Comment: 8 pages, 1 figur

Reversible methane storage in porous hydrogel supported clathrates

Methane gas hydrates are a promising alternative for storage and transport of natural gas. In this paper, porous poly(2-hydroxyethyl methacrylate) (PHEMA) and poly(2-hydroxyethyl methacrylate-co-methacrylic acid) (PHEMA-co-MAA) hydrogel microspheres were synthesised and examined for their application as a reusable scaffold for methane storage in their hydrated form. The hydration kinetics, methane storage capacity of the hydrogel microspheres, and a mixed colloidal system made of hydrogel particles and dry-water droplets were investigated in a 300cm3 steel vessel at 273.2K and varying pressures. Hydration of methane in the mixed colloidal system is high in capacity and exceedingly reversible. Higher pressure and smaller size of hydrogel microspheres result in improved capacity and kinetics, however reduce the recyclability of hydration. The porous hydrogel particles alone are too soft for reuse and need to be improved for practical application. Porous hydrogel microspheres were synthesised and mixed with dry-water, forming a colloidal system. Formation of methane gas hydrates in the colloidal system was fast, and high in hydration capacity. The system is reusable for methane storage

Variational ground states of 2D antiferromagnets in the valence bond basis

We study a variational wave function for the ground state of the two-dimensional S=1/2 Heisenberg antiferromagnet in the valence bond basis. The expansion coefficients are products of amplitudes h(x,y) for valence bonds connecting spins separated by (x,y) lattice spacings. In contrast to previous studies, in which a functional form for h(x,y) was assumed, we here optimize all the amplitudes for lattices with up to 32*32 spins. We use two different schemes for optimizing the amplitudes; a Newton/conjugate-gradient method and a stochastic method which requires only the signs of the first derivatives of the energy. The latter method performs significantly better. The energy for large systems deviates by only approx. 0.06% from its exact value (calculated using unbiased quantum Monte Carlo simulations). The spin correlations are also well reproduced, falling approx. 2% below the exact ones at long distances. The amplitudes h(r) for valence bonds of long length r decay as 1/r^3. We also discuss some results for small frustrated lattices.Comment: v2: 8 pages, 5 figures, significantly expanded, new optimization method, improved result

Optical and electrical spin injection and spin transport in hybrid Fe/GaAs devices

We discuss methods for imaging the nonequilibrium spin polarization of electrons in Fe/GaAs spin transport devices. Both optically- and electrically-injected spin distributions are studied by scanning magneto-optical Kerr rotation microscopy. Related methods are used to demonstrate electrical spin detection of optically-injected spin polarized currents. Dynamical properties of spin transport are inferred from studies based on the Hanle effect, and the influence of strain on spin transport data in these devices is discussed.Comment: 5 pages, 6 figs. ICPS-28 proceedings (July'06, Vienna) for J. Appl. Phy