DN‐Scattering of a plane wave by wedges

We continue our study of a nonstationary scattering by wedges. In this paper we consider nonstationary scattering of plane waves by a ‘hard–soft’ wedge. We prove the uniqueness and existence of a solution to the corresponding DN‐Cauchy problem in appropriate functional spaces. We also give the explicit form of the solution and prove the Limiting Amplitude Principle. Copyright © 2011 John Wiley & Sons, Ltd.     

Projection Method for Cauchy Problem for an Operator-Differential Equation

In the current paper, we study a projection method for a Cauchy problem for an operator-differential equation with a leading self-adjoint operator A(t) and a subordinate linear operator K(t) in a Hilbert space. The projection subspaces are linear spans of eigenvectors of an operator similar to A(t). It is assumed that the operators A(t) and K(t) are sufficiently smooth. Error estimates for the approximate solutions and their derivatives are obtained. The application of the developed method for solving the initial boundary value problems is given.     

Polar nanoregions in Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> (PMN): insights from a supercell approach

We report construction of a model of polar nanoregions in the PMN relaxor ferroelectric based on first-principles lattice dynamics for chemically ordered supercells [S.A. Prosandeev et al., Phys. Rev. B 70, 134110 (2004)], combined with invariance under permutations and dipole-dipole interaction as a source supporting randomly oriented residual polarization. Representative analytical estimates of polar nanore-gion — supercell mapping reproduce both nonzero local and zero macroscopic polarization of the structure, as well as the temperature change of the supercell anisotropy at cooling and field cooling.     

Asymptotic Estimates for the p-Laplacian on Infinite Graphs with Decaying Initial Data

Potential Analysis - We consider the Cauchy problem for the evolutive discrete p-Laplacian in infinite graphs, with initial data decaying at infinity. We prove optimal sup and gradient bounds for...     

Spatially inhomogeneous enhancement of fluorescence by a monolayer of silver nanoparticles

Near-field scanning optical microscopy (NSOM) was applied to study the effect of a two-dimensional array of silver nanoparticles on the spatial distribution and magnitude of fluorescence signal enhancement for a monolayer of Rhodamine 6G (Rh6G). Twenty polyelectrolyte monolayers were deposited between the nanoparticles and the dye by a layer-by-layer deposition technique resulting in a 15-20 nm separation cushion, necessary to minimize the fluorescence signal quenching. The fluorescence signal in NSOM images was found to be distributed inhomogeneously as small (100-200 nm in diameter) fluorescent clusters with typically 5-30 times higher fluorescence intensities than a sample without nanoparticles. The position and relative intensity of the clusters was found to be dependent on the excitation wavelength, suggesting that the enhancement originates from the nanoparticle surface plasmon resonance.     

UV resonance Raman spectroscopy probes the localization of tryptophan‐containing antimicrobial peptides in lipid vesicles

In this work we employed UV resonance Raman spectroscopy with 229 nm excitation to study two tryptophan‐containing antimicrobial peptides with a broad‐spectrum activity against Gram‐positive and Gram‐negative bacteria: lactoferricin B (LfB, RRWQWRMKKLG) and pEM‐2 (KKWRWWLKALAKK). UV resonance Raman spectra of both peptides are dominated by tryptophan bands. Raman spectra of LfB and pEM‐2 in D₂O and 2,2,2‐trifluoro ethanol (TFE) have been measured and used to identify the hydrogen‐bond strength marker bands W6 and W17. The tryptophan doublet, W7, at 1340 and 1360 cm⁻¹ was used to detect an increase in the hydrophobicity of Trp environment in TFE. The spectra of LfB in complex with model cell membranes composed of zwitterionic dipalmitoylglycero‐phosphocholine (DPPC) or anionic dipalmitoyglycero‐phosphoglycerol (DPPG) lipid vesicles revealed a more hydrophobic Trp environment in DPPG, suggesting stronger interactions between the cationic peptide and anionic model cell membrane. Copyright © 2008 John Wiley & Sons, Ltd.     

Light backscattering by hexagonal ice crystals

Backscattering of light by hexagonal ice columns and plates has been calculated by means of a ray-tracing code. It is shown that backscattering by the hexagonal ice cylinders at their arbitrary orientations is caused by a peculiar corner-reflector effect. A gigantic peak of backscattering is found at the angle of about 32.5° between the principal axis of a particle and the incidence direction for both hexagonal ice columns and plates. This peak is explained by multiple total internal reflections inside the crystals that take place for a part of incident rays. The obtained results on backscattering efficiency allow one to calculate backscattering by an ensemble of the hexagonal ice cylinders of various sizes, shapes and orientations. Slant lidar remote sensing of cirrus clouds for discrimination between aligned columns and plates is suggested as an application of the results obtained.     

Asymptotic behavior for the filtration equation in domains with noncompact boundary

We consider the initial value boundary problem with zero Neumann data for an equation modeled after the porous media equation, with variable coefficients. The spatial domain is unbounded and shaped like a (general) paraboloid, and the solution u is integrable in space and nonnegative. We show that the asymptotic profile for large times of u is one dimensional and given by an explicit function, which can be regarded as the fundamental solution of a one-dimensional differential equation with weights. In the case when the domain is a cone or the whole space (Cauchy problem), we obtain a genuine multidimensional profile given by the well-known Barenblatt solution.     

Decomposition Techniques for Bilinear Saddle Point Problems and Variational Inequalities with Affine Monotone Operators

The majority of first-order methods for large-scale convex–concave saddle point problems and variational inequalities with monotone operators are proximal algorithms. To make such an algorithm practical, the problem’s domain should be proximal-friendly—admit a strongly convex function with easy to minimize linear perturbations. As a by-product, this domain admits a computationally cheap linear minimization oracle (LMO) capable to minimize linear forms. There are, however, important situations where a cheap LMO indeed is available, but the problem domain is not proximal-friendly, which motivates search for algorithms based solely on LMO. For smooth convex minimization, there exists a classical algorithm using LMO—conditional gradient. In contrast, known to us similar techniques for other problems with convex structure (nonsmooth convex minimization, convex–concave saddle point problems, even as simple as bilinear ones, and variational inequalities with monotone operators, even as simple as affine) are quite recent and utilize common approach based on Fenchel-type representations of the associated objectives/vector fields. The goal of this paper was to develop alternative (and seemingly much simpler) decomposition techniques based on LMO for bilinear saddle point problems and for variational inequalities with affine monotone operators.