Mie scattering calculation by FDTD employing a modified Debye model for Gold material

The parameters calculation for the modified Debye model in the electromagnetic finite difference time domain (FDTD) method is discussed. Validation for the selected parameters is done comparing the FDTD results with the Mie analytical solutions of a gold nanometer sphere under an optical plane wave incidence. Good agreement with an average relative error 6.7% has been demonstrated as to total electrical field amplitudes on the surface of the gold sphere. It indicates FDTD could be adopted in the optical region for a material even with a negative real relative permittivity particularly as metals.     

纳米晶永磁中面缺陷对畴壁钉扎机理的研究

畴壁钉扎模型的矫顽力可以表示为Hc=αpink2K1/μ0Ms-NeffMs，计算了微结构参数αpink随面缺陷内磁性参数A′和K′1的变化情况.结果表明，αpink可以在很宽的范围里取值.结合纳米单相Nd2Fe14B磁体，研究了晶粒边界的磁性参数和晶界厚度对αpink的影响，当A′/A=05，K′1/K1=01，以及晶界厚度r0＝332nm时，αpink最大.同时研究了纳米复相Nd2Fe14B/α-Fe磁体的αpink随α-Fe晶粒尺寸r0的变化情况，当r0＝7nm时，αpink最大. 关键词： 面缺陷 矫顽力 钉扎机理 纳米晶     

Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces

In the setting of metric measure spaces equipped with a doubling measure supporting a weak p-Poincaré inequality with 1?p<∞, we show that any uniform domain Ω is an extension domain for the Newtonian space N1,p(Ω) and that Ω, together with the metric and the measure inherited from X, supports a weak p-Poincaré inequality. For p>1, we obtain a near characterization of N1,p-extension domains with local estimates for the extension operator.     

The 8π‐problem for radially symmetric solutions of a chemotaxis model in the plane

The existence, uniqueness and large time behaviour of radially symmetric solutions to a chemotaxis system in the plane ?² are studied either for the critical value of the mass equal to 8π or in the subcritical case. Copyright © 2006 John Wiley & Sons, Ltd.     

Terahertz time-domain spectroscopic investigation on quinones

Well resolved far-infrared spectra of 1,4-benzoquinone, 1,4-naphthoquinone, and 9, 10-anthraquinonme in polycrystalline form have been measured with terahertz time domain spectroscopy at room tem- perature. The characterizations of power absorption and index of refraction in the frequency range 0.3 -2.0 THz are presented. Theoretical calculation is applied to assist the analysis and assignment of individual THz absorption spectra of the p-quinones with semiempirical AM1, Hartree-Fock (HF), and density functional theory (DFT) method. Observed THz responses are assigned to the translational and torsional vibrations of p-quinone dimer held together by weak hydrogen bonds.     

Conduction and convection phenomena through a slab with thermal heterogeneities

This paper addresses the computation of the three-dimensional transient heat transfer through a layered solid and/or fluid formation containing irregular inclusions. The use of appropriate Green’s functions for a flat layer formation in a boundary element method formulation avoids the discretization of the layer interface boundaries.     

Vortex sheets with reflection symmetry in exterior domains

In this paper we prove the existence of a weak solution of the incompressible 2D Euler equations in the exterior of a reflection symmetric smooth bluff body with symmetric initial flow corresponding to vortex sheet type data whose vorticity is of distinguished sign on each side of the symmetry axis. This work extends the results proved for full plane flow by the authors in [M.C. Lopes Filho, H.J. Nussenzveig Lopes, Z. Xin, Existence of vortex sheets with reflection symmetry in two space dimensions, Arch. Ration. Mech. Anal. 158 (3) (2001) 235-257].     

Sharp Estimates of the Distance from a Fixed Point to the Frontier of a Hele-Shaw Flow

We discuss the global shape of a Hele–Shaw flow which is produced by the injection of fluid into the narrow gap between two parallel planes. We translate the problem into a problem concerning the shape of a quadrature domain of a finite positive measure for subharmonic functions and give sharp estimates of the distance from a fixed point to the frontier of the flow.     

An analytical solution for electromagnetic wave scattering by multiple wedges

In this work an analytical solution to the problem of electromagnetic wave diffraction by multiple coplanar wedges is found by means of an infinite-order discrete superposition of non-integer cylindrical waves, i.e. products of a non-integer order Bessel function times an exponential factor. The evaluation of the expansion coefficients is accomplished by imposing the boundary conditions on every side of the geometry; the corresponding equations are solved in a ‘weak form’, i.e. by representing the dependence of the boundary fields with respect to the radial abscissa in terms of an expansion over a set of Laguerre orthogonal polynomials. A detailed study is carried out for estimating accuracy performances relevant to the finite-order numerical implementation of the method.     

A method of asymptotic constructions with improved accuracy for a quasilinear singularly perturbed parabolic convection-diffusion equation

The Dirichlet problem on an interval for quasilinear singularly perturbed parabolic convection-diffusion equation is considered. The higher order derivative of the equation is multiplied by a parameter ε that takes any values from the half-open interval (0, 1]. For this type of linear problems, the order of the ε-uniform convergence (with respect to x and t) for the well-known schemes is not higher than unity (in the maximum norm). For the boundary value problem under consideration, grid approximations are constructed that converge ε-uniformly at the rate of O(N ^?2ln² N + N ^?2 ₀), where N + 1 and N ₀ + 1 are the numbers of the mesh points with respect to x and t, respectively. On the x axis, piecewise uniform meshes that condense in the boundary layer are used. If the parameter value is small compared to the effective step of the spatial grid, the domain decomposition method is used, which is motivated by “asymptotic constructions.” Monotone approximations of “auxiliary” subproblems describing the main terms of the asymptotic expansion of the solution outside a neighborhood of the boundary layer neighborhood are used. In the neighborhood of the boundary layer (of the width O(ε ln N)) the first derivative with respect to x is approximated by the central difference derivative. These subproblems are successively solved in the subdomains on uniform grids. If the parameter values are not sufficiently small (compared to the effective step of the mesh with respect to x), the classical implicit difference schemes approximating the first derivative with respect to x by the central difference derivative are applied. To improve the accuracy in t, the defect correction technique is used. Notice that the calculation of the solution of the constructed difference scheme (the scheme based on the method of asymptotic constructions) can be considerably simplified for sufficiently small values of the parameter ε.