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

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

Redundancy relations and robust failure detection

All failure detection methods are based on the use of redundancy, that is on (possible dynamic) relations among the measured variables. Consequently the robustness of the failure detection process depends to a great degree on the reliability of the redundancy relations given the inevitable presence of model uncertainties. The problem of determining redundancy relations which are optimally robust in a sense which includes the major issues of importance in practical failure detection is addressed. A significant amount of intuition concerning the geometry of robust failure detection is provided

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

Determination of a Wave Function Functional

In this paper we propose the idea of expanding the space of variations in standard variational calculations for the energy by considering the wave function $\psi$ to be a functional of a set of functions $\chi: \psi = \psi[\chi]$, rather than a function. In this manner a greater flexibility to the structure of the wave function is achieved. A constrained search in a subspace over all functions $\chi$ such that the wave function functional $\psi[\chi]$ satisfies a constraint such as normalization or the Fermi-Coulomb hole charge sum rule, or the requirement that it lead to a physical observable such as the density, diamagnetic susceptibility, etc. is then performed. A rigorous upper bound to the energy is subsequently obtained by variational minimization with respect to the parameters in the approximate wave function functional. Hence, the terminology, the constrained-search variational method. The \emph{rigorous} construction of such a constrained-search--variational wave function functional is demonstrated by example of the ground state of the Helium atom.Comment: 10 pages, 2 figures, changes made, references adde

Insights into Hydration Dynamics and Cooperative Interactions in Glycerol-Water Mixtures by Terahertz Dielectric Spectroscopy.

We report relaxation dynamics of glycerol-water mixtures as probed by megahertz-to-terahertz dielectric spectroscopy in a frequency range from 50 MHz to 0.5 THz at room temperature. The dielectric relaxation spectra reveal several polarization processes at the molecular level with different time constants and dielectric strengths, providing an understanding of the hydrogen-bonding network in glycerol-water mixtures. We have determined the structure of hydration shells around glycerol molecules and the dynamics of bound water as a function of glycerol concentration in solutions using the Debye relaxation model. The experimental results show the existence of a critical glycerol concentration of ∼7.5 mol %, which is related to the number of water molecules in the hydration layer around a glycerol molecule. At higher glycerol concentrations, water molecules dispersed in a glycerol network become abundant and eventually dominate, and four distinct relaxation processes emerge in the mixtures. The relaxation dynamics and hydration structure in glycerol-water mixtures are further probed with molecular dynamics simulations, which confirm the physical picture revealed by the dielectric spectroscopy

Antimicrobial stewardship and infection prevention-leveraging the synergy: A position paper update.

Summary The issues surrounding the prevention and control of infections are intrinsically linked with the issues associated with the use of antimicrobial agents and the proliferation and spread of MDROs. The vital work of IPC and AS programs cannot be performed independently and requires interdependent and coordinated action across multiple and overlapping disciplines and clinical settings. Deliberate strategic relationship-building actions will be required of IPC and AS program leaders to bring groups together to achieve the larger purpose of keeping patients safe from infection and ensuring that effective antibiotic therapy is available for future generations

Fast magnetoacoustic waves in a randomly structured solar corona

The propagation of fast magnetoacoustic waves in a randomly structured solar corona is considered in the linear and cold plasma limits. The random field is assumed to be static and associated with plasma density inhomogeneities only. A transcendental dispersion relation for the fast magnetoacoustic waves which propagate perpendicularly to the magnetic field is derived in the weak random field approximation. It is shown analytically that the fast magnetosonic waves experience acceleration, attenuation, and dispersion in comparison to the homogeneous case. These analytical findings are essentially confirmed by numerical simulations for a wide-spectrum pulse, except that the waves were found decelerated. It is concluded that the coronal Moreton waves can be applied to MHD seismology of the solar corona

Spin Injection and Relaxation in Ferromagnet-Semiconductor Heterostructures

We present a complete description of spin injection and detection in Fe/Al_xGa_{1-x}As/GaAs heterostructures for temperatures from 2 to 295 K. Measurements of the steady-state spin polarization in the semiconductor indicate three temperature regimes for spin transport and relaxation. At temperatures below 70 K, spin-polarized electrons injected into quantum well structures form excitons, and the spin polarization in the quantum well depends strongly on the electrical bias conditions. At intermediate temperatures, the spin polarization is determined primarily by the spin relaxation rate for free electrons in the quantum well. This process is slow relative to the excitonic spin relaxation rate at lower temperatures and is responsible for a broad maximum in the spin polarization between 100 and 200 K. The spin injection efficiency of the Fe/Al_xGa_{1-x}As Schottky barrier decreases at higher temperatures, although a steady-state spin polarization of at least 6 % is observed at 295 K.Comment: 3 Figures Submitted to Phys. Rev. Let