Asymptotic behaviour of the energy for electromagnetic systems in the presence of small inhomogeneities

In this article we consider solutions to the time-harmonic and time-dependent Maxwell's systems with piecewise constant coefficients with a finite number of small inhomogeneities in ?³. In time-harmonic case and for such solutions, we derive the asymptotic expansions due to the presence of small inhomogeneities embedded in the entire space. Further, we analyse the behaviour of the electromagnetic energy caused by the presence of these inhomogeneities. For a general time-dependent case, we show that the local electromagnetic energy, trapped in the total collection of these well-separated inhomogeneities, decays towards zero as the shape parameter decreases to zero or as time increases.     

Efficient smoothing of Crank-Nicolson method for pricing barrier options under stochastic volatility

Most of the option pricing problems have nonsmooth payoff. In barrier options certain aspects of the option are triggered if the asset price becomes too high or too low. Standard smoothing schemes used to solve problems with nonsmooth payoff do not work well for the barrier option because a discontinuity is introduced in the time domain each time a barrier is applied. An improved smoothing strategy is introduced for smoothing the A -stable Cranck-Nicolson scheme at each time when a barrier is applied. A partial differential equation (PDE) approach is utilized for the evaluation of complex option pricing models under stochastic volatility which brings major mathematical and computational challenges for estimation and stability of the estimates. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Numerical Way of Determining the Boundaries of a System of Bodies in a Three-Dimensional Medium by Means of Integral Equations

The propagation of acoustic waves in a three-dimensional medium with several local inhomogeneities of different shapes is analyzed. Solving the inverse problem of determining boundaries of local inhomogeneities from measurements of a field in a bounded receivers location domain is reduced to a system of integral equations. An iteration approach to solving the inverse problem is proposed, and the results from numerical experiments are presented.     

Modelling of material and structural inhomogeneities in timber structures

The numerical simulation of timber structures by means of FEM has been an object of recent research. Most of the material models developed so far are based on idealized assumptions by disregarding inhomogeneities. Here, models to capture structural inhomogeneities in terms of branches and knots and the resulting deviation in grain course in a three-dimensional FE analysis are presented. Besides, naturally varying material properties referred to as material inhomogeneities have to be considered in the structural analysis. Due to the insufficient experimental data, the uncertainty model fuzziness is applied. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Relaxation patterns and semi-Markov dynamics

Exponential relaxation to equilibrium is a typical property of physical systems, but inhomogeneities are known to distort the exponential relaxation curve, leading to a wide variety of relaxation patterns. Power law relaxation is related to fractional derivatives in the time variable. More general relaxation patterns are considered here, and the corresponding semi-Markov processes are studied. Our method, based on Bernstein functions, unifies three different approaches in the literature.     

Reconstruction of closely spaced small inhomogeneities via boundary measurements for the full time-dependent Maxwell’s equations

We consider for the full time-dependent Maxwell’s equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic boundary measurements on the boundary for a finite time interval.     

城市中心区内停车价格对出行行为的影响分析

本文通过对北京市中心区早高峰时段小汽车出行者和公共交通出行者出行方式选择意向调查,采用多项Logit模型,分析中心区停车价格变化对小汽车出行向公共交通出行方式的转移行为的影响.预测结果表明不同出行目的对停车价格的敏感程度也不同,在提高公共交通服务水平的前提下,加大中心区停车收费标准,会使小汽车出行有较大比例的转移.     

弹性动力学的等效内含物法和两椭球异质体的散射场

用Gurtin变分原理推导了一般线弹性动力学的多异质体问题的等效性方程.用“等效内含物法”求得两椭球异质体对入射弹性波的散射场和散射横截面的近似表达式,并给出了计算实例.     

Polarization tensors of planar domains as functions of the admittivity contrast

(Electric) polarization tensors describe part of the leading order term of asymptotic voltage perturbations caused by low volume fraction inhomogeneities of the electrical properties of a medium. They depend on the geometry of the support of the inhomogeneities and on their admittivity contrast. Corresponding asymptotic formulas are of particular interest in the design of reconstruction algorithms for determining the locations and the material properties of inhomogeneities inside a body from measurements of current flows and associated voltage potentials on the body’s surface. In this work, we consider the two-dimensional case only and provide an analytic representation of the polarization tensor in terms of spectral properties of the double layer integral operator associated with the support of simply connected conductivity inhomogeneities. Furthermore, we establish that an (infinitesimal) simply connected inhomogeneity has the shape of an ellipse, if and only if the polarization tensor is a rational function of the admittivity contrast with at most two poles whose residues satisfy a certain algebraic constraint. We also use the analytic representation to provide a proof of the so-called Hashin–Shtrikman bounds for polarization tensors; a similar approach has been taken previously by Golden and Papanicolaou and Kohn and Milton in the context of anisotropic composite materials.     

Limit distribution function of inhomogeneities in regions with random boundary. II

A system of charged particles and inhomogeneities randomly distributed in accordance with the same law in the neighborhoods of corresponding sites of a planar crystal lattice is investigated. The limit distribution function of the inhomogeneities is determined.Institute of Nuclear Physics, Uzbek Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 1, pp. 84–97, January, 1993.     

Stress distribution in dissimilar materials containing inhomogeneities near the interface using a novel finite element

This study is concerned with the determination of the elastic behaviour of two dissimilar materials containing a single and two interacting inhomogeneities near the interface using a novel finite element. The general form of the element, which is constructed from a cell containing a single circular inhomogeneity in a surrounding matrix, is derived explicitly in a series form using the complex potentials of Muskhelishvili. The strength of the adopted eight-noded plane element lies in its ability to treat periodically and/or arbitrarily located multiple inhomogeneities in dissimilar materials accurately and efficiently.

Pertinent stress distributions are examined to illustrate the importance of the elastic properties of the dissimilar materials, the distance between their interface and the inhomogeneities and the direction of the externally applied load with respect to that interface upon the resulting stress field. The results of our work assist in defining the design parameters which govern the elastic behaviour of the examined problem. This problem relates to fibre reinforcement in advanced composite materials, second phase particles in traditional materials and plates stiffened with stringers commonly used in the aerospace and automotive fields.     

Autoresonance excitation of a breather in weak ferromagnetics

A mathematical model of the magnetodynamics of a weak ferromagnetic in an external magnetic field with variable frequency is studied. Conditions for the appearance of autoresonance are found under which the amplitude of the local magnetic inhomogeneities is considerably increased. Mathematically, the problem is to analyze the solutions to the sine-Gordon equation subject to a specific nonautonomous perturbation. For the perturbed equation, asymptotic solutions in the form of a breather with a slowly varying amplitude and a phase shift are constructed. The solutions whose amplitude increases with time from small values to quantities of order one are associated with the autoresonance phenomenon.     

The effect of different arrival rates on the N-policy of M/G/1 with server setup

It is very important in many real-life systems to decide when the server should start his service because frequent setups inevitably make the operating cost too high. Furthermore, today's systems are too intelligent for the input to be assumed as a simple homogenous Poisson process. In this paper, an M/G/1 queue with general server setup time under a control policy is studied. We consider the case when the arrival rate varies according to the server's status: idle, setup and busy states. We derive the distribution function of the steady-state queue length, as well as the Laplace–Stieltjes transform of waiting time. For this model, the optimal N-value from which the server starts his setup is found by minimizing the total operation cost of the system. We finally investigate the behavior of system operation cost and the optimal N for various arrival rates by a numerical study.     

Actual time integration methods for elastic wave propagation analysis

For the simulation of the interaction of elastic waves in CFRP plates with inhomogeneities and defects the spectral finite element method (SEM) is under investigation. The SEM uses high-order shape functions which are composed of Lagrange polynomials with nodes at the Gauss-Lobatto quadrature (GLq) points. In this way we obtain a diagonal mass matrix which makes an explicit time scheme more efficient. In this paper we analyse how actual time integration methods perform in combination with the SEM. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Uniform Asymptotic Expansion of the Voltage Potential in the Presence of Thin Inhomogeneities with Arbitrary Conductivity

Asymptotic expansions of the voltage potential in terms of the "radius" of a diametrically small(or several diametrically small) material inhomogeneity(ies) are by now quite well-known. Such asymptotic expansions for diametrically small inhomogeneities are uniform with respect to the conductivity of the inhomogeneities.In contrast, thin inhomogeneities, whose limit set is a smooth, codimension 1 manifold,σ, are examples of inhomogeneities for which the convergence to the background potential,or the standard expansion cannot be valid uniformly with respect to the conductivity, a, of the inhomogeneity. Indeed, by taking a close to 0 or to infinity, one obtains either a nearly homogeneous Neumann condition or nearly constant Dirichlet condition at the boundary of the inhomogeneity, and this difference in boundary condition is retained in the limit.The purpose of this paper is to find a "simple" replacement for the background potential, with the following properties:(1) This replacement may be(simply) calculated from the limiting domain Ω\σ, the boundary data on the boundary of Ω, and the right-hand side.(2) This replacement depends on the thickness of the inhomogeneity and the conductivity,a, through its boundary conditions on σ.(3) The difference between this replacement and the true voltage potential converges to 0 uniformly in a, as the inhomogeneity thickness tends to 0.     

Wave Propagation m Continuous Random Media

A study is made of the way in which small random inhomogeneities in a transmission medium affect the statistical properties of a system of waves. It is shown that provided the spectral cumulants are sufficiently smooth at some initial time, a sequence of closures for the zeroth order spectral functions can be deduced which describe asymptotically the transfer of energy between wave numbers. Of particular importance is the fact that the closure equations are derived without the need to resort to ad hoc statistical assumptions. The general theory is applied to the problem of the propagation of water waves over an irregular bottom topography.     

Analysis of the influence of Spectral Elements for elastic wave propagation on the CFL-Condition

For the simulation of the interaction of elastic waves in CFRP plates with inhomogeneities and defects the spectral finite element method (SEM) is under investigation. The SEM uses high-order shape functions which are composed of Lagrange polynomials with nodes at the Gauss-Lobatto quadrature (GLq) points. In this way we obtain a diagonal mass matrix which makes an explicit time scheme more efficient. The goal of this work is to investigate the effect of SEM on the CFL-Condition. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

One class of nonscattering acoustic shells for a model of anisotropic acoustics

We consider a model of linear acoustics describing diffraction of an acoustic wave on a local anisotropic inhomogeneity. Under study is the existence of inhomogeneities which do not scatter the incident acoustic fields that are generated by any exterior compactly supported sources. We prove the existence of the above-mentioned inhomogeneities. Some constructive way is given of constructing a class of anisotropic media depending on an arbitrary function of one variable. We obtain some explicit formulas that define the main parameters of the shell.     

Improvement of direct sampling method in transverse electric polarization

Recently, the mathematical structure of the direct sampling method (DSM) was investigated in transverse-electric (TE) polarization, and the reason why the exact locations of small inhomogeneities cannot be retrieved through traditional DSM has been revealed. In this paper, we present an improved DSM for identifying the exact locations of small inhomogeneities in TE polarization. Furthermore, we investigate a multi-frequency indicator function to obtain a better result. Corresponding mathematical analysis and simulations are performed to show the feasibilities of the proposed improvement techniques.     

Localization of gas-dynamic processes and structure when the material is compressed adiabatically, in the peaking mode

Adiabatic compression of gas by a piston, the pressure on which increases in the peaking mode, is studied. The entropy is distributed over the mass. A class of selfsimilar solutions (the LS mode) is constructed and its properties are studied. It is shown that the effective dimensions of the compression wave decrease with time and all gas-dynamic perturbations are localized within a finite mass of the gas. The solutions obtained are characterized by the presence of a structure (inhomogeneities) in the density and temperature. The compression occurs without the formation of shock waves.