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Open boundary conditions are always used in investigating the effective properties of composites. In this paper, Eshelby's transformation field method is developed to deal with the effective response of unidirectional periodic composites having an open boundary. In the method, Hermite polynomials are used to cope with the open boundary conditions of the perturbation fields induced by the inclusions. The transformation fields are introduced in the composite system to meet the interface conditions between complex structure inclusions and matrix. As an example, Eshelby's method is used to estimate the effective responses of two-dimensional unidirectional periodic dielectric composites having an open boundary. The validity is verified by comparing the effective responses calculated by the method with the exact solutions of dilute limit. It is shown that the method is valid to solve the open boundary problem of unidirectional periodic composites having complex geometric inclusions., 14pages,2figures

Transformation field method (TFM) is developed to estimate the anisotropic dielectric properties of crystal composites having arbitrary shapes and dielectric properties of crystal inclusions, whose principal dielectric axis are different from those of anisotropic crystal matrix. The complicated boundary-value problem caused by inclusion shapes is circumvented by introducing a transformation electric field into the crystal composites regions, and the effective anisotropic dielectric responses are formulated in terms of the transformation field. Furthermore, the numerical results show that the effective anisotropic dielectric responses of crystal composites periodically vary as a function of the rotating angle between the principal dielectric axes of inclusion and matrix crystal materials. It is found that at larger inclusion volume fraction the inclusion shapes induce profound effect on the effective anisotropic dielectric responses.

A general effective response is proposed for nonlinear composite media, which obey a current field relation of the form J = sigmaE + chi\E\(2) E when an external alternating current (AC) electrical field is applied. For a sinusoidal applied field with finite frequency omega, the effective constitutive relation between the current density and electric field can be defined as, = sigma(e) + chi(e) + (. . .), where sigma(e) and chi(e) are the general effective linear and nonlinear conductive responses, respectively. The angled brackets denotes the ensemble average. As two examples, we have investigated the cylindrical and spherical inclusions embedded in a host and also derived the formulae of the general effective linear and nonlinear conductive responses in dilute limit. For higher volume fraction of inclusions, we have proposed a nonlinear effective medium approximation (EMA) method to estimate the general effective response of nonlinear composites in external AC field. Furthermore, the effective nonlinear responses at harmonics are predicted by using the general effective response. (C) 2002 Elsevier Science B.V. All rights reserved.

A perturbative approach is used to study the AC response of nonlinear composite media, which obey a current-field relation of the form with components having nonlinear response at finite frequencies. For a sinusoidal applied field, we extend the local potential in terms of sinusoidal components at fundamental frequency and high-order harmonic frequencies to treat the nonlinear composites. For nonlinear composite media with a low concentrations of spherical inclusions, we give the formulae of the nonlinear effective AC susceptibility at the third harmonic frequency.

The homotopy continuation method is used to solve the electrostatic boundary-value problems of strongly nonlinear composite media, which obey a current-field relation of J = σE + χ|E|2E. With the mode expansion, the approximate analytical solutions of electric potential in host and inclusion regions are obtained by solving a set of nonlinear ordinary different equations, which are derived from the original equations with homotopy method. As an example in dimension two, we apply the method to deal with a nonlinear cylindrical inclusion embedded in a host. Comparing the approximate analytical solution of the potential obtained by homotopy method with that of numerical method, we can obverse that the homotopy method is valid for solving boundary-value problems of weakly and strongly nonlinear media.

Colloidal dispersions are common in nature with wide industrial applications. One of the central theoretical problems in the field is to determine the rheological properties of the colloidal dispersion from the microstructures of the systems. Because of the difficulties associated with the boundary-value problems of the many-particle system, existing theories for colloidal suspensions are limited to low particle concentrations. In this work, a method of transformation field is developed by which one can calculate the effective viscosity of an incompressible viscous fluid containing colloidal particles (either solid particles or liquid drops). The predictions of the theory are in good agreement with the Einstein's formula for suspensions and the Taylor's formula for emulsions at low particle concentrations. At higher particle concentrations, the results of Nunan and Keller are produced. The method is also applicable to the viscosity of colloidal systems with non-spherical particles.

Cellular automaton traffic models can include various factors in traffic systems and the corresponding computational simulations are rather simple and effective. The Biham-Middleton-Levine model (BML model) facilitates the simulation of two-dimentional traffic flow problems via the cellular automaton models. In this paper, the BML model is improved by removing its limitation of synchronized change of traffic lights. In the new model, the traffic light at each crossing could arbitrarily change its starting time and tempo of variation, and hence the model could more realistically describe the influence of traffic lights on the performance of traffic systems. Some new effects appearing in the new model are also elucidated.

The homotopy continuation method is employed to solve electrostatic boundary-value problems of nonlinear media. The difficulty associated with matching the inherently nonlinear boundary conditions on the interface is overcome by the mode expansion method, by which the nonlinear partial differential equations of the original problem are transformed into an infinite set of nonlinear ordinary differential equations. In this regard, the homotopy method has to be modified to handle the nonlinear boundary conditions. As an illustration, we study two cases:(a) nonlinear inclusion in linear host and (b) linear inclusion-in nonlinear host, both in two dimensions. The homotopy method is validated by comparing the results with the exact solution of case (a) and the results derived by perturbation method in case (b).

In this paper, a derivation of the macroscopic mean field theory of the cellular automaton (CA) model of highway traffic flow starting from the microscopic dynamical point of view is presented. Starting from an equation describing the time evolution of the Boolean state variable at each site of the basic CA model, and using a two-site approximation for the multi-site correlation functions, a dynamical mapping between the macroscopic average speeds ν(t + 1) and ν(t) at different time can be derived. Mean field results consistent with the simulation data are obtained by considering the attractors of the mapping and their corresponding basins.

A collocation method is employed to study the effective ac conductivity of a suspension of charged particles in electrolyte solution. The method is very effective over a wide range of particle concentration and no longer restricted to the assumption made by the Rayleigh method that the two phases of a suspension have the same dielectric constants.

The universal transition of Lyapunov exponents between conservative limit and dissipative limit of nonlinear dynamical system is studied. It is discovered numerically and proved analytically that for homogeneous dissipative two-dimensional maps, along the equal dissipation line in parameter space, the Lyapunov exponents of attractor orbits possess a plateau structure and strict symmetry about its plateau value. The ratios between the plateau width and the stable window width of period 1-4 orbits for Henon map are calculated. The result shows that the plateau structure of Lyapunov exponents remains invariant for the attractor orbits belonging to a period doubling bifurcation sequence. This fact reveals a new universal transition behavior between order and chaos when the dissipation of the dynamical system is weakened to zero.

We deal with the problem of calculating the effective dielectric dispersion and electrical conductivity of colloidal dispersions. A comparison of the theoretical calculation of first principles with the experimental data of Schwan shows that our technique proposed here is no longer restricted to dilute solutions and is very effective for studying the dielectric properties of colloids with highly concentrated charged spherical particles in an electrolyte solution.

Using Rayleigh model, we study dc conductivity of the composite medium with layered inclusions. A generalized identity suitable to this kind of composite medium is proved and a definition of effective conductivity of the systems is given. For the systems with cubic symmetry, an analytic formula for effective conductivity is derived.

On the basis of Ref. [1] , we analyse the sub-steps of I-V characteristics in Josephson junction theoretically. Firstly, a mathematical method is developed, then the conditions of existence of sub-steps are obtained by that method. Our results make the discussion for I-V characteristics in Josephson junction perfect.

A generalized theory of 3He-A phase superfIuid is establisped, which can comprise the Khalatnikov-Lebedev's theory treated as a special case. The starting point of this work is the Zilsel's principle in which the density of the superfluid component is defined as an independent variable. It has the advantage of including naturally the "heating effect" of 3He-A superfluid liquid, whereby overcoming the difficulties encountered in Khalatnikov-Lebedev's theory.

Using a new approach to Rayleigh model of composite, we obtain the complete solutions for many systems of orthorhombic. The evaluation of the effective conductivity tensor of the composite with anisotropic structure is also discussed in detail for the first time.

A first-principle approach to the calculation of dc conductivities of the porous medium and composite is developed. In this paper, the case of the porous medium with periodic structure is discussed in detail. The effective conductivities for many two dimensional porous systems are calculated by polynomial approximation, Fourier expansion using elimination procedure and iterative approach of Fourier expansion Critical exponents for the dc conductivity of Sierpinski carpets are also calculated by an improved iterative approach. All the theoretical results agree fairly with recent experimental measurements.

The first-principle approach for calculating the D. C. conductivities of the composites is discussed systematically. The integral equation for determining the effective conductivities of the composites with local anisotropic componentes is derived, and a convenient method for calculating effective conductivity tensor is proposed. We have dealt with effective conductivity tensor of the composites with local anisotropic components. A theoretical method which can treat the more common composites with no periodicity is developed. A new approximate method for solving integral equation by means of expansion with two bases is also proposed, by which we can calculate composites with large porosity and complicate structure with high precision, and it could have the advantage of saving lot of computing time.