Asymptopic solution for a class of semilinear singularly perturbed fractional differential equation

This paper considers a class of boundary value problems for the semilinear singularly perturbed fractional differential equation.Under the suitable conditions,first,the outer solution of the original problem is obtained;secondly,using the stretched variable and the composing expansion method the boundary layer is constructed;finally,using the theory of differential inequalities the asymptotic behaviour of solution for the problem is studied and the uniformly valid asymptotic estimation is discussed.     

Controllability results for impulsive functional differential inclusions

Control problems appear in many branches of physics and technical sciences. In this paper weinvestigate the controllability of first order semilinear impulsive functional differential inclusions in the case where the right hand side is convex or nonconvex valued. All results are obtained by using fixed point results for multivalued mappings.     

Computer programs for light scattering by particles with inclusions

We present a comparison of computational results from light scattering by spherical particles with inclusions. The different simulation methods like the T-matrix method, multiple multipole method and the method of separation of variables are presented shortly. Exemplary numerical simulations involve scattering by particles with one or two spherical inclusions and scattering by particles with non-spherical inclusions.     

A global existence theorem for the nonlinear BGK equation

A global existence theorem with large initial data inL ¹ is given for the nonlinear BGK equation. The method, which is based on the recent averaging lemma of Golseet al., utilizes a weak compactness argument inL ¹.     

Jacobi Operators with Singular Continuous Spectrum

We consider a semilinear elliptic system which includes the model system of the W-strings in the cosmology as a special case. We prove existence of multi-string solutions and obtain precise asymptotic decay estimates near infinity for the solutions. As a special case of this result we solve an open problem posed by Yang [14]. AMS Subject Classifications (2000): 35J45, 35J60, 37K40, 70S15     

Scattering properties of rutile pigments located eccentrically within microvoids

We study the optical properties of opaque polymer pigmented coatings. The system consists of spherical rutile particles encapsulated in spherical microvoids embedded in a transparent polymer resin. The single-scattering properties of this system have been analyzed already, in case the rutile particle is located at the center of the microvoid . Here, we use a T-matrix approach to generalize and extend this analysis to the more realistic case when the rutile particles is located off-center within the microvoid. We also consider the multiple-scattering effects of a cluster composed by a collection of air bubbles with off-center rutile inclusions. Our calculations take into account the multiple scattering and the dependent-scattering processes of each pigment particle of the aggregate, using a new recursive T-matrix algorithm.     

Die Isolierung radioaktiv markierter nichtmetallischer Einschlüsse aus Hochlegierten Stählen

Zur Isolierung von Einshlüssen aus hochlegierten Stählen werden die Hauptkomponenten Fe, Ni, Cr und weitere Metalle durch mehrstufig ausgeführte Flüssig-Flüssig-Extraktionen mit verschiedenen Extraktionsmitteln abgetrennt. Die im Eindampfrückstand der wäβrigen Phase nach der Extraktion verbleibenden Einschlüsse können für die meisten Radionuklide ohne nennenswerte Selbstabsorption mit einem Groβflächenzählrohr oder anderen geeignetenZählvorrichtungen ausgemessen werden.     

Wave-obstacle interaction in a lossy medium: energy perturbations and negative extinction

The concept of a generalized extinction cross-section introduced in a previous paper is given in detail and exemplified by the problem of scattering by an elastic cylinder embedded in a viscoelastic matrix. It is shown that under certain conditions the presence of inclusion may have a supporting effect on wave propagation (negative extinction). The derived low-frequency expansions indicate that the Rayleigh law may not hold in the case of a lossy medium. Numerical results as well as discussions concerning separation between scattering and intrinsic viscoelastic losses are also given.     

Cloaking of 2D particle geometries in a surface medium

We theoretically examine the cloaking condition for two-dimensional particles with varying geometry embedded inside a surface medium. General solutions are obtained for multi-layer particle configurations with either all positive or partially negative constitutive parameters respectively. Cloaking of particle geometries that are large relative to the incident wavelength is demonstrated. Theoretical predictions are compared to full-wave numerical simulations for arrays of particles consisting of different geometries.     

Characterisation of FXTAS related isolated intranuclear protein inclusions using laser tweezers Raman spectroscopy

We report the analysis of the vibrational modes of intranuclear protein inclusions isolated from the brain of human subjects with the Fragile X‐associated tremor/ataxia syndrome (FXTAS). In this preliminary study, Raman spectra of optically trapped inclusions were measured and analysed to determine protein composition and structure. Our main findings are as follows: (1) The spectra of protein inclusions are characteristic of H2A and H2B histones, which correlate with previous mass spectrometry (MS) studies; (2) Tyrosine is present in its OH form and exposed at the protein surface; (3) Zn and to a lesser extent Cu bound to histidine side chains are detected in the inclusions; (4) The tryptophan side‐chain torsion angle is calculated to be 102°; (5) Several potential spectroscopic markers for the inclusions of FXTAS are identified. These results show the capability of using laser tweezers Raman spectroscopy to identify protein inclusions in a non‐perturbative way and to gain further insight into the pathogenesis and progression of FXTAS in human subjects and in experimental models of this disorder. Copyright © 2009 John Wiley & Sons, Ltd.     

太赫兹时域光谱技术在流体包裹体研究中的应用

流体包裹体是研究矿物晶体演化的重要手段之一,它能反映矿物演化最原始的信息(温度、压力、pH值等)。在演化过程中,温度压力等外界因素直接影响包裹体的数量和大小,从而影响晶体的各种性质。本文利用太赫兹时域光谱系统(THz-TDS),对不同生长温度下KCl晶体内部的包裹体进行了检测,得到了样品的时域、频域和吸收系数曲线,并通过显微镜观察、计算得到了样品内部包裹体的面积,建立了包裹体面积和吸收系数的对应关系模型。通过对样品的吸收系数和样品内部包裹体面积的对比,可以看出二者具有相同的变化趋势,即晶体内部包裹体面积越大,THz吸收系数越大,说明THz吸收系数可以反映不同生长温度的晶体内部包裹体面积的变化情况,解析包裹体面积对太赫兹光学参数的影响,为流体包裹体的研究提供了一种新的有效途径。该研究创新点在于利用THz-TDS快速检测晶体内部包裹体面积的变化情况,说明了太赫兹技术完全可以用于包裹体的研究中,为包裹体的研究提供了一种全新的快速、无损的检测方法。     

Quantitative Determination of Gaseous Phase Compositions in Fluid Inclusions by Raman Microspectrometry

ABSTRACT

Raman microspectrometry has been revealed as a powerful technique for performing qualitative analysis and estimation of relative molar fractions of the gaseous species present in minerals fluid inclusions. In this work, the methodology and calibration procedures used for the quantification of the different species in fluid inclusions are described, paying special attention to the estimation of the CO₂ molar fraction. A discussion about the Fermi resonance of CO₂ vibrations (ν₁-2ν₂; 1285–1388 cm^?1) is also included.     

Large complete band gap in two-dimensional phononic crystal slabs with elliptic inclusions

Phononic band structure with periodic elliptic inclusions for the square lattice is investigated based on the plane wave expansion method. The numerical results show the systems composed of tungsten (W) elliptic rods embedded in a silicon (Si) matrix can exhibit a larger complete band gap than the conventional circular phononic crystal (PC) slabs. The phononic band structure of the plate-mode waves and the width of the first complete band gap can be tuned by varying the ratio of the minor axis and the major axis, the orientation angle of the elliptic rods and the thickness of the PC slabs. We also study the band structure of plate-mode waves propagating in two-dimensional (2D) slabs with periodic elliptic inclusions coated on uniform substrate.     

Existence of Global-In-Time Solutions to a Generalized Dirac-Fock Type Evolution Equation

We consider a generalized DiracFock type evolution equation deduced from nophoton Quantum Electrodynamics, which describes the selfconsistent timeevolution of relativistic electrons, the observable ones as well as those filling up the Dirac sea. This equation has been originally introduced by Dirac in 1934 in a simplified form. Since we work in a Hartree-Fock type approximation, the elements describing the physical state of the electrons are infinite rank projectors. Using the Bogoliubov-Dirac-Fock formalism, introduced by ChaixIracane (J. Phys. B., 22, 37913814, 1989), and recently established by Hainzl-Lewin-Séré, we prove the existence of globalintime solutions of the considered evolution equation.     

Interaction of an inclusion and (±1)-wedge disclination in smectic C free standing films

The interaction between an inclusion and (±1)-disclination situated near it in smectic C free standing films is investigated. The inclusion is modelled by the simplified model of an inclusion represented by (+1)-wedge disclination in the inclusion centre and two (−1/2)-wedge disclinations at opposite positions on the inclusion surface. New positions of (−1/2)-wedge disclinations due to the elastic interaction with (±1)-disclination were determined.     

Melting of embedded anisotropic particles: PbIn inclusions in Al

Small particles embedded in the solid state can assume facetted shapes that indicate the anisotropy in interfacial free energy between the particle and the embedding phase. Previous in situ transmission electron microscopy (TEM) of Al–In has shown that such facetted nanoparticles with cubic symmetry embedded in a solid can produce a series of complex melt configurations. To determine the dependence of melt configuration on solid–solid facet energies, this work numerically calculates the equilibrium melt trajectory for a family of cuboctahedral particles parameterized by the ratio of matrix–particle interfacial free energies for orientations taken with respect to the crystal axes of the matrix, ??=?γ₁₀₀/γ₁₁₁. The calculations assume that equilibrium occurs with the minimization of the total interfacial free energy to determine the stable internal melt configuration for a fixed volume of melt confined within a member of the cuboctahedral family. At particular melt volume fractions, abrupt transitions in shape occur when a stable configuration reaches a touching or necking instability. In situ TEM of a dilute Al alloy containing embedded nanosized PbIn inclusions that gradually melt as the temperature is increased from 230 to 260°C is consistent with the results calculated for ??=?1.245.     

Martensitic transformation in heterogeneous austenite

The dependence of the martensite structure on the volume fraction of coherent inclusions inherited from aged austenite has been studied. An explanation for the considerable martensite lattice tetragonality in the case of thin martensite twins in comparison with their inclusion diameter is suggested. A reason for surface relief height decreasing for alloys with narrow temperature hysteresis of transformation has been discovered.     

Microprobe accessory for laser raman spectrometers

A Raman micro-focusing accessory has been designed for use with conventional laser Raman spectrometers and offers the advantage of allowing standard macro-Raman experiments to be done without removing the micro-focusing optics. Samples may be analysed with a spatial resolution adjustable to a limit of 1 μm. The viewing magnification can be varied without affecting the size of the laser focal spot. A thermocouple can be attached to the sample holder which may be flushed with cooled N₂ gas for increased sample stability. The usefulness of the Raman microprobe for the analysis of solid and fluid inclusions in geological samples is also demonstrated.     

双光折变晶体半线性相位共轭器的自脉动

在由两块光折变BaTiO3晶体(其中一块晶体为全内反射式自抽运相位共轭镜工作方式,起外反射镜作用)构成的半线性自抽运相位共轭器中观察到了相位共轭光的自脉动现象。自脉动的平均频率f与入射光功率I0的关系为f∝I01.43;相位共轭光的平均维持时间ΔT与入射光功率I0近似成反比。观察到光折变BaTiO3晶体中扇形散射光具有动态的空间结构,扇形散射光的这种特性是引起上述半线性自抽运相位共轭器中相位共轭光脉动的原因     

Stress analysis of multiple anisotropic elliptical inclusions in composites

A volume integral equation method is introduced for the solution of elastostatic problems in an unbounded isotropic elastic solid containing interacting multiple anisotropic elliptical inclusions subject to uniform remote tension or remote in-plane shear. This method is applied to two-dimensional problems involving long parallel elliptical cylindrical inclusions. A detailed analysis of the stress field at the interface between the matrix and the central elliptical inclusion is carried out for square and hexagonal packing of anisotropic inclusions. The effects of the number of anisotropic inclusions and various inclusion volume fractions on the stress field at the interface between the isotropic matrix and the central elliptical cylindrical inclusion are investigated in detail. The stress field at the interface between the isotropic matrix and the central elliptical inclusion is also compared with that between the isotropic matrix and the central circular inclusion.