Homogenization of the planar waveguide with frequently alternating boundary conditions

We consider Laplacian in a planar strip with Dirichlet boundary condition on the upper boundary and with frequent alternation boundary condition on the lower boundary. The alternation is introduced by the periodic partition of the boundary into small segments on which Dirichlet and Neumann conditions are imposed in turns. We show that under the certain condition the homogenized operator is the Dirichlet Laplacian and prove the uniform resolvent convergence. The spectrum of the perturbed operator consists of its essential part only and has a band structure. We construct the leading terms of the asymptotic expansions for the first band functions. We also construct the complete asymptotic expansion for the bottom of the spectrum

Dynamical Toroidal Hopfions in a Ferromagnet with Easy-Axis Anisotropy

Three-dimensional toroidal precession solitons with a nonzero Hopf index, which uniformly move along the anisotropy axis in a uniaxial ferromagnet, have been found. The structure and existence region of the solitons have been numerically determined by solving the Landau-Lifshitz equation.Comment: 6 pages, 4 figure

Multi-filament structures in relativistic self-focusing

A simple model is derived to prove the multi-filament structure of relativistic self-focusing with ultra-intense lasers. Exact analytical solutions describing the transverse structure of waveguide channels with electron cavitation, for which both the relativistic and ponderomotive nonlinearities are taken into account, are presented.Comment: 21 pages, 12 figures, submitted to Physical Review

Dynamical variables in Gauge-Translational Gravity

Assuming that the natural gauge group of gravity is given by the group of isometries of a given space, for a maximally symmetric space we derive a model in which gravity is essentially a gauge theory of translations. Starting from first principles we verify that a nonlinear realization of the symmetry provides the general structure of this gauge theory, leading to a simple choice of dynamical variables of the gravity field corresponding, at first order, to a diagonal matrix, whereas the non-diagonal elements contribute only to higher orders.Comment: 15 page

A small-angle neutron scattering study of sodium dodecyl sulfate-poly(propylene oxide) methacrylate mixed micelles

cited By 3International audienceMixed micelle of protonated or deuterated sodium dodecyl sulfate (SDS and SDSd25, respectively) and poly(propylene oxide) methacrylate (PPOMA) are studied by small-angle neutron scattering (SANS). In all the cases the scattering curves exhibit a peak whose position changes with the composition of the system. The main parameters which characterize mixed micelles, i.e., aggregation numbers of SDS and PPOMA, geometrical dimensions of the micelles and degree of ionisation are evaluated from the analysis of the SANS curves. The position qmax of the correlation peak can be related to the average aggregation numbers of SDS-PPOMA and SDSd25-PPOMA mixed micelles. It is found that the aggregation number of SDS decreases upon increasing the weight ratio PPOMA/SDS (or SDSd25). The isotopic combination, which uses the "contrast effect" between the two micellar systems, has allowed us to determine the mixed micelle composition. Finally, the SANS curves were adjusted using the RMSA for the structure factor S(q) of charged spherical particles and the form factor P(q) of spherical core-shell particle. This analysis confirms the particular core-shell structure of the SDS-PPOMA mixed micelle, i.e., a SDS "core" micelle surrounded by the shell formed by PPOMA macromonomers. The structural parameters of mixed micelles obtained from the analysis of the SANS data are in good agreement with those determined previously by conductimetry and fluorescence studies. © 2005 Elsevier Inc. All rights reserved

Nonlocal symmetries of integrable two-field divergent evolutionary systems

Nonlocal symmetries for exactly integrable two-field evolutionary systems of the third order have been computed. Differentiation of the nonlocal symmetries with respect to spatial variable gives a few nonevolutionary systems for each evolutionary system. Zero curvature representations for some new nonevolution systems are presented

A Hardy inequality in twisted waveguides

We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes. Namely, it is known that any local bending, no matter how small, generates eigenvalues below the essential spectrum of the Laplacian in the tubes with arbitrary cross-sections rotated along a reference curve in an appropriate way. In the present paper we show that for any other rotation some critical strength of the bending is needed in order to induce a non-empty discrete spectrum.Comment: LaTeX, 20 page