New localized excitations in a (2+1)-dimensional Broer—Kaup system

Starting with the extended homogeneous balance method and a variable separation approach, a general variable separation solution of the Broer—Kaup system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakon and fractal localized solutions, some new types of localized excitations, such as compacton and folded excitations, are obtained by introducing appropriate lower-dimensional piecewise smooth functions and multiple-valued functions, and some interesting novel features of these structures are revealed.     

Fabrication of a Near-Field Optical Fiber Probe with a Nanometric Metallized Protrusion

We have developed a novel probe with a nanometric metallized protrusion extending through a subwavelength aperture to increase optical near-field excitation and collection efficiencies. The apex diameter of the fabricated metallized protrusion was 35 nm. The Intensity distribution of the optical near-field at the apex of the probe was measured by scanning another probe across the apex, and it was observed that strong optical near-field was generated at the apex of the metallized protrusion. The width of the intensity distribution was 150 nm including instrumental resolution. Probes with spherical and ellipsoidal metallized protrusion were also fabricated, by which enhancement of the optical near-field is expected due to localized plasmon excitation.     

Algebraically Decaying Modes in Many Dimensions: Application of Fubini’s Identity to Guided-Wave Optics

We show analytically that application of an identity in conformal invariant field theories to multidimensional guided-wave optics predicts a generic family of modes with algebraic (power-law) tails in the evanescent field.     

多孔介质中两相不可压缩可混溶驱动问题的动态混合元方法及其特征修正格式

许多依赖时间的问题涉及到局部化现象,如突出的前沿位置、激波、边界层等, 其位置随时间而变动.多孔介质中两相不可压缩可混溶驱动问题是一典型的、有代表性 的"局部化现象"问题,其数学模型为耦合非线性偏微分方程组的初边值问题.为减轻数 值解在局部前沿位置的数值振荡,提高解的精确性,本文给出了该问题的动态混合元格 式和沿特征线修正的动态混合元格式,证明了其收敛性,并给出了误差估计.     

Uniform blow-up profiles and boundary layer for a parabolic system with localized nonlinear reaction terms

This paper deals with the blow-up properties of the solution to a semilin-ear parabolic system with localized nonlinear reaction terms, subject to the null Dirichlet boundary condition. We first give sufficient conditions for that the classical solution blows up in the finite time, secondly give necessary conditions and a sufficient condition for that two components blow up simultaneously, and then obtain the uniform blow-up profiles in the interior. Finally we describe the asymptotic behavior of the blow-up solution in the boundary layer.     

Use of pseudopotential towards time-evolution of a nonstationary state: Spatially localized excitation in a crystal

Pseudopotential is used as a formal operator to write the exact time-dependence of a pseudoexciton and hence that of an initial excitation spatially localized in a crystal. The exponential operator where pseudopotential occurs at the argument is readily evaluated using the property of projection operators. Migration of an initially localized excitation is of considerable experimental importance and can be of conceptual use since it should eventually generate the characteristics of a migrating exciton. From the formal time-dependence of a localized excitation, its spread with time can be calculated with relative ease. In a concurrent discussion, the previous work of Merrifield (1958) on the propagation of excitation is criticized and an error is pointed out. The spread, however, remains wavelike and is not dissipative in the absence of a collisional mechanism.     

A porous medium equation with nonlocal boundary condition and a localized source

This article studies the blow-up properties of solutions to a porous medium equation with nonlocal boundary condition and a general localized source. Conditions for the existence of global or blow-up solutions are obtained. Moreover, it is proved that the unique solution has global blow-up property whenever blow-up occurs. Blow-up rate estimates are also obtained for some special cases.     

Basal slip localization in zinc single crystals. The Considère analyses

The tensile and compression tests were performed on zinc single crystals oriented for slip in the basal slip system. During the first stage of the stress–strain curve, the localized necking was typical of strain localization in the tensile specimens. Single or multiple necks were formed along the specimen length. The range of temperatures and the strain rates for single necking of the sample was determined. The formation of such necking depends on strain hardening characteristics and can be predicted by the Considère criterion. On the other hand, propagation of the necked area along the sample length was not predictable by this criterion. Localized sliding and specimen kinking was indicative of the strain localization observed for different specimens compressed under the same conditions, i.e. temperature and strain rate. A decrease in the compression force and in the cross-sectional area with anvil displacements produced localized sliding. On the other hand, a continuous increase in the compression force was representative of tests leading to specimen kinking.     

Localized orbitals for optimal decomposition of molecular properties

We present the procedure for transforming delocalized molecular orbitals into the localized property-optimized orbitals (LPOs) designed for building the most accurate, in the Frobenius norm sense, approximation to the first-order reduced density matrix in form of the sum of localized monoatomic and diatomic terms. In this way, a decomposition of molecular properties into contributions associated with individual atoms and the pairs of atoms is obtained with the a priori known upper bound for the decomposition accuracy. Additional algorithm is proposed for obtaining the set of “the Chemist's LPOs” (CLPOs) containing a single localized orbital, with nearly double occupancy, per a pair of electrons. CLPOs form an idealized Lewis structure optimized for the closest possible reproduction of one-electron properties derived from the original many-electron wavefunction. The computational algorithms for constructing LPOs and CLPOs from a general wavefunction are presented and their implementation within the open-source freeware program JANPA ( http://janpa.sourceforge.net /) is discussed. The performance of the proposed procedures is assessed using the test set of density matrices of 33 432 small molecules obtained at both Hartree-Fock and second-order Moller-Plesset theory levels and excellent agreement with the chemist's Lewis-structure picture is found.     

Ammonia Oxidation Enhanced by Photopotential Generated by Plasmonic Excitation of a Bimetallic Electrocatalyst

We study how visible light influences the activity of an electrocatalyst composed of Au and Pt nanoparticles. The bimetallic composition imparts a dual functionality: the Pt component catalyzes the electrochemical oxidation of ammonia to liberate hydrogen and the Au component absorbs visible light by the excitation of localized surface plasmon resonances. Under visible-light excitation, this catalyst exhibits enhanced electrochemical ammonia oxidation kinetics, outperforming previously reported electrochemical schemes. We trace the enhancement to a photochemical potential resulting from electron–hole carriers generated in the electrocatalyst by plasmonic excitation. The photopotential responsible for enhanced kinetics scales linearly with the light intensity—a general design principle for eliciting superlative photoelectrochemical performance from catalysts comprised of plasmonic metals or hybrids. We also determine a photochemical conversion coefficient.