A model of nonlinear electrodynamics

A new model of nonlinear electrodynamics with two parameters is investigated. We also consider a model with one dimensional parameter. It was shown that the electric field of a point-like charge is not singular at the origin and there is the finiteness of the static electric energy of point-like charged particle. We obtain the canonical and symmetrical Belinfante energy–momentum tensors and dilatation currents. It is demonstrated that the dilatation symmetry and dual symmetry are broken in the models suggested. We have calculated the static electric energy of point-like particles.     

Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. I. Asymptotic Expansion Formulas

We consider the spectral problem for the random Schrödinger operator on the multidimensional lattice torus increasing to the whole of lattice, with an i.i.d. potential (Anderson Hamiltonian). We obtain the explicit almost sure asymptotic expansion formulas for the extreme eigenvalues and eigenfunctions in the intermediate rank case, provided the upper distributional tails of potential decay at infinity slower than the double exponential function. For the fractional-exponential tails (including Weibull’s and Gaussian distributions), extremal type limit theorems for eigenvalues are proved, and the strong influence of parameters of the model on a specification of normalizing constants is described. In the proof we use the finite-rank perturbation arguments based on the cluster expansion for resolvents. The results of our paper illustrate a close connection between extreme value theory for spectrum and extremal properties of i.i.d. potential. On the other hand, localization properties of the corresponding eigenfunctions give an essential information on long-time intermittency for the parabolic Anderson model.     

散射体排列方式对二维磁振子晶体带隙结构的影响

本文采用平面波展开法数值计算了由铁圆柱分别按正方排列、三角排列以及六角排列在氧化铕基底材料中构成的二维磁振子晶体带结构,讨论了散射体的不同排列方式对磁振子晶体带隙结构的影响.计算结果表明,三角排列散射体的磁振子晶体能够获得最大的自旋波带隙结构. 关键词： 磁振子晶体 带隙 排列方式     

Transmission properties of random point scatterers for waves with two-band dispersion law

The scattering problem is considered for the one-dimensional Dirac equation whose potential is a system of randomly distributed point scatterers. Types of such scatterers are described. The probability densities for the transmission and transformation disbalance coefficients are determined in the high-energy region and various averaged characteristic are calculated.     

A T-matrix method and computer code for randomly oriented, axially symmetric coated scatterers

A computer code is described for the calculation of light-scattering properties of randomly oriented, axially symmetric coated particles, in the framework of the T-matrix theory. The underlying mathematical background is outlined briefly and convergence procedures are discussed. After outlining the input-output interaction between user and code, benchmark results are presented for two distinct shapes: coated, centered spheroids and offset coated spheres.     

T-matrix method for electromagnetic scattering from scatterers with complex structure

We describe a T-matrix program for light scattering calculations from particles with complex structure. The code treats the cases of homogeneous, layered and composite scatterers. These results are combined with basic results concerning the scattering by inhomogeneous scatterers and aggregates to apply to more general types of scatterers. Some numerical simulations are presented.     

Analytical solutions for crack-like scatterers and sources in isotropic elastic plates

A common theoretical framework can be employed for modelling both active and passive approaches to structural health monitoring based on guided waves. The same fundamental solutions can be used to represent the scattered field due to crack-like damage in an active approach, or the acoustic emission due to various failure mechanisms in a passive approach. It is shown that the reciprocal theorem can be used to derive compact analytical formulae for those fundamental solutions expressed as sums over the propagating modes. The only detailed calculations that are required are those involved in determining the relevant dispersion curves and through-thickness mode functions. For clarity, the approach is first described for two-dimensional configurations. The subsequent extension to three-dimensional requires the stationary phase approximation. It is shown that the modal coefficients for crack-like sources (or scatterers) are proportional to the conjugate stress component of the corresponding mode. Furthermore, the approach can also be used for an edge crack or delamination in a semi-infinite plate, and the theoretical formulae are compared with experimentally validated computational results for that case. Further extensions are briefly noted.     

A modification of the factorization method for scatterers with different physical properties

We study an inverse acoustic scattering problem by the factorization method when the unknown scatterer consists of two objects with different physical properties. Especially, we consider the following two cases: One is the case when each object has the different boundary condition, and the other one is when different penetrability. Our idea here is to modify the far‐field operator depending on the cases to avoid unnecessary a priori assumptions.     

Backing effects on the underwater acoustic absorption of a viscoelastic slab with locally resonant scatterers

Backing effects on the underwater acoustic absorption of a viscoelastic polymer slab embedded with locally resonant scatterers are reported. The polymer slab is embedded with two layers of locally resonant scatterers, i.e. Al spheres coated by soft silicon rubber. Theoretical absorption coefficients of the polymer slab under different backings using a layer multiple scattering method show good agreement with the experimental results, which supports unambiguously the experimental observation. Then relations between the resonance modes and the low-frequency absorption peaks of the composite slab are clarified to address the absorption mechanisms. It shows that the mass of the steel backing affects evidently the low-frequency absorption, the absorption peak shifts to lower frequency range while increasing the backing mass.     

Detection of point-like scatterers using one type of scattered elastic waves

In this paper, we are concerned with the detection of point-like obstacles using elastic waves. We show that one type of waves, either the P or the S scattered waves, is enough for localizing the points. We also show how the use of S incident waves gives better resolution than the P waves. These affirmations are demonstrated by several numerical examples using a MUSIC type algorithm.