Essential spectrum in vibrations of thin shells in membrane approximation. Propagation of singularities

The spectral problem of thin elastic shells in membrane approximation does not satisfy the classical properties of compactness and so there exists an essential spectrum. In the first part, we propose to determinate this spectrum and the weakness directions in the shell. We particularly study the case of homogeneous and isotropic shells with some examples. In the second part, we consider an elementary model problem to study the propagation of singularities and their reflections at the boundary of the domain. In the last, we study the problem of propagation for an isotropic cylindrical shell and we show that the equation of propagation does not depend on the Poisson coefficient

Simple factorization of unitary transformations

We demonstrate a method for general linear optical networks that allows one to factorize any SU($n$) matrix in terms of two SU($n-1)$ blocks coupled by an SU(2) entangling beam splitter. The process can be recursively continued in an efficient way, ending in a tidy arrangement of SU(2) transformations. The method hinges only on a linear relationship between input and output states, and can thus be applied to a variety of scenarios, such as microwaves, acoustics, and quantum fields.Comment: 5 pages, 4 figures. Comments welcome

Inequivalent classes of closed three-level systems

We show here that the $\Lambda$ and V configurations of three-level atomic systems, while they have recently been shown to be equivalent for many important physical quantities when driven with classical fields [M. B. Plenio, Phys. Rev. A \textbf{62}, 015802 (2000)], are no longer equivalent when coupled via a quantum field. We analyze the physical origin of such behavior and show how the equivalence between these two configurations emerges in the semiclassical limit.Comment: 4 pages, 1 figure. To appear as Brief Report in Physical Review

Spin Wave Eigenmodes of Dzyaloshinskii Domain Walls

A theory for the spin wave eigenmodes of a Dzyaloshinskii domain wall is presented. These walls are N\'eel-type domain walls that can appear in perpendicularly-magnetized ultrathin ferromagnets in the presence of a sizeable Dzyaloshinskii-Moriya interaction. The mode frequencies for spin waves propagating parallel and perpendicular to the domain wall are computed using a continuum approximation. In contrast to Bloch-type walls, it is found that the spin wave potential associated with Dzyaloshinskii domain walls is not reflectionless, which leads to a finite scattering cross-section for interactions between spin waves and domain walls. A gap produced by the Dzyaloshinskii interaction emerges, and consequences for spin wave driven domain wall motion and band structures arising from periodic wall arrays are discussed

Spectral approach to homogenization of an elliptic operator periodic in some directions

The operator $$A_{\varepsilon}= D_{1} g_{1}(x_{1}/\varepsilon, x_{2}) D_{1} + D_{2} g_{2}(x_{1}/\varepsilon, x_{2}) D_{2}$$ is considered in $L_{2}({\mathbb{R}}^{2})$, where $g_{j}(x_{1},x_{2})$, $j=1,2,$ are periodic in $x_{1}$ with period 1, bounded and positive definite. Let function $Q(x_{1},x_{2})$ be bounded, positive definite and periodic in $x_{1}$ with period 1. Let $Q^{\varepsilon}(x_{1},x_{2})= Q(x_{1}/\varepsilon, x_{2})$. The behavior of the operator $(A_{\varepsilon}+ Q^{\varepsilon}$ as $\varepsilon\to0$ is studied. It is proved that the operator $(A_{\varepsilon}+ Q^{\varepsilon})^{-1}$ tends to $(A^{0} + Q^{0})^{-1}$ in the operator norm in $L_{2}(\mathbb{R}^{2})$. Here $A^{0}$ is the effective operator whose coefficients depend only on $x_{2}$, $Q^{0}$ is the mean value of $Q$ in $x_{1}$. A sharp order estimate for the norm of the difference $(A_{\varepsilon}+ Q^{\varepsilon})^{-1}- (A^{0} + Q^{0})^{-1}$ is obtained. The result is applied to homogenization of the Schr\"odinger operator with a singular potential periodic in one direction.Comment: 3

Low and high frequency approximations to eigenvibrations of string with double contrasts

We study eigenvibrations for inhomogeneous string consisting of two parts with strongly contrasting stiffness and mass density. In this work we treat a critical case for the high frequency approximations, namely the case when the order of mass density inhomogeneity is the same as the order of stiffness inhomogeneity, with heavier part being softer. The limit problem for high frequency approximations depends nonlinearly on the spectral parameter. The quantization of the spectral semiaxies is applied in order to get a close approximations of eigenvalues as well as eigenfunctions for the prime problem under perturbation.Comment: 13 pages, 6 plots; submitted for publication; typos added

PathwayExplorer: web service for visualizing high-throughput expression data on biological pathways

While generation of high-throughput expression data is becoming routine, the fast, easy, and systematic presentation and analysis of these data in a biological context is still an obstacle. To address this need, we have developed PathwayExplorer, which maps expression profiles of genes or proteins simultaneously onto major, currently available regulatory, metabolic and cellular pathways from KEGG, BioCarta and GenMAPP. PathwayExplorer is a platform-independent web server application with an optional standalone Java application using a SOAP (simple object access protocol) interface. Mapped pathways are ranked for the easy selection of the pathway of interest, displaying all available genes of this pathway with their expression profiles in a selectable and intuitive color code. Pathway maps produced can be downloaded as PNG, JPG or as high-resolution vector graphics SVG. The web service is freely available at ; the standalone client can be downloaded at

Fluid Dynamics and Secondary Currents in an Asymmetrical Rectangular Canal with Sidewall Streamwise Rib

Channels with streamwise ribs have been studied for decades in chemical engineering, environmental and sanitary engineering, aeronautics, astronautics, biology and geology. Some designs have been used for close to a century in water treatment plants. Longitudinal ribs along channel walls have been successfully tested for the increased heat and mass transfer rates. In alluvial channels, long-lasting three-dimensional large-scale turbulent vortices may yield the development of longitudinal ridges on the mobile bed with preferential sediment transport in between. Herein a detailed hydrodynamic study was conducted in an asymmetrical rectangular channel equipped with a sidewall streamwise rib. Both free-surface, velocity and boundary shear stress measurements showed strong secondary currents of Prandtl's second kind. The sidewall rib and channel asymmetry contributed to very-strong secondary motion, associated with turbulent dissipation. A key feature of the channel design was the provision of a well-defined highly-turbulent low-velocity zone (LVZ) beneath the rib. The configuration might be applied to hydraulic structure design, but uttermost care must be considered. A number of practical considerations showed major technical challenges, and in many instances, alternative designs should be preferred, particularly in hydraulic structures. Altogether this detailed investigation demonstrated how the introduction of a seemingly simple streamwise shape, i.e. square rib, may induce a major change in hydrodynamic properties, in comparison to a simple rectangular channel flow