A theory of nonlinear AC response in coated composites

A method for determining effective dielectric responses of Kerr-like coated nonlinear composites under the alternating current (AC) electric field is proposed by using perturbation approach. As an example, we have investigated the composite with coated cylindrical inclusions randomly embedded in a host under an external sinusoidal field with finite frequency omega. The local field and potential of composites in general consists of components with all harmonic frequencies. The effective nonlinear AC responses at all harmonics are induced by the coated nonlinear composites because of the nonlinear constitutive relation. Moreover, we have derived the formulae of effective nonlinear AC responses at the fundamental frequency and the third harmonic in the dilute limit.

Dielectric responses of graded cylindrical composites

The effective dielectric responses of linear composites with graded cylindrical particles are investigated under an external uniform electric field. As an example, with the Kummer function, we have obtained the analytical solutions of electric potentials of graded composites with a cylindrical inclusion particle of dielectric function profile epsilon(i) = cr(k)e(betar), where r is the inside distance of a point in cylindrical particle from the original point of cylindrical coordinates. In the dilute limit, the effective dielectric response is derived by means of the mean field method. For larger volume fraction, we have estimated the dielectric response of the graded composites with an effective medium approximation. Furthermore, from our results, we have discussed the effective responses of graded composites for power-law and exponential dielectric function profiles, respectively. (C) 2004 Elsevier B.V. All rights reserved.

Effective dielectric response of composites witli graded material

The effective dielectric response of linear composites containing graded material is investigated under an applied electric field Eo. For the cylindrical inclusion with gradient dielectric function, epsilon(i)(r) = b + cr, randomly embedded in a host with dielectric constant epsilon(m), we have obtained the exact solution of local electric potential of the composite media regions, which obeys a linear constitutive relation D = epsilonE, using hypergeometric function. In dilute limit, we have derived the effective dielectric response of the linear composite media. Furthermore, for larger volume fraction, the formulas of effective dielectric response of the graded composite media, are given.

Effective dielectric response of graded spherical composites

The effective dielectric response of composites containing graded material is investigated when an external uniform electric field E-0 is applied to it. For a spherical particle with gradient dielectric constant, epsilon(i) (r) = b + cr, randomly embedded in a host with dielectric constant epsilon(m), we have obtained the exact solution of local electric potential in the composite media regions, which obey a linear constitutive relation D = epsilonE, using hypergeometric function. In dilute limit, the effective dielectric response of the linear graded composite media is derived. Furthermore, for larger volume fraction, we have given an effective medium approximation to estimate the effective dielectric response of the graded composite media. (C) 2003 Elsevier B.V All rights reserved.

Higher order response of nonlinear composite in external AC electric field

The fifth-order effective nonlinear responses at fundament frequency and higher-order harmonics are given for nonlinear composites, which obey a current-field relation of the form J = sigmaE + x\E\(2) E, if a sinusoidal alternating current (AC) external field with finite frequency omega is applied. As two examples, we have investigated the cylinder and spherical inclusion embedded in a host and, for larger volume fraction, also derived the formulae of effective nonlinear responses at higher-order harmonics by the aid of the general effective response definition. Furthermore, the relationships between effective nonlinear responses at harmonics are given. (C) 2003 Elsevier Science B.V. All rights reserved.

Thermal conductivity of graded spherical composites with contact resistance

The effective thermal conductivity of graded composites with contact resistance on the inclusion surface is investigated. As an example, we have considered the graded composite media with a spherical particle embedded in a homogeneous matrix, where the thermal conductivity of spherical inclusion is an exponential function k(i) = c exp(betar) (where r is the inside distance of a point in particle from the center of the spherical particle in a spherical coordinate). For both heat contact resistance and perfect contact cases, we have given a reasonable effective medium approximation to calculate the effective conductivity. (C) 2003 Elsevier B.V. All rights reserved.

Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents

In the present paper, the random inter facial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order a symptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen (2006) as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song (2005) for second-order solutions for random interfacial waves with steady uniform currents if N=2.

Effects of buoyancy on Langmuir circulation

Based on the Navier-Stokes equation, an equation describing the Langmuir circulation is derived by a perturbation method when the influences of Coriolis force and buoyancy force are both considered. The approach used in the analysis is similar to the works carried out by Craik and Leibovich [J. Fluid Mech. 73 (1976) 401], Leibovich [J. Fluid Mech. 79 (1977) 715] and Huang [J. Fluid Mech. 91 (1979) 191]. Potential applications of the equation proposed are discussed in the area of Antarctic circumpolar current.

Effective ac dielectric response of graded cylindrical composites

Under an external alternating current (ac) field, the effective ac dielectric response of graded composites consisting of the graded cylindrical inclusion having complex permittivity profiles has been investigated theoretically. A model that the dielectric function is assumed to be a constant while the conductivity has a power-law dependence on the radial variable r, namely epsilon(i)(r) = A + cr(k)/i omega. is studied and the local analytical potentials of the inclusion and the host regions are derived in terms of hyper-geometric function. In the dilute limit, the effective ac dielectric response is predicted. Meanwhile, we have given the exact proof of the differential effective dipole approximation (DEDA) method, which is suitable to arbitrary graded profiles. Furthermore, we have given the analytical potentials and the effective ac dielectric responses of coated graded cylindrical composites for two cases, case (a) graded core and case (b) graded coated layer, having the graded dielectric profiles, respectively. (c) 2005 Elsevier B.V. All rights reserved.

Effective thermal conductivity of graded nonlinear composites with heat contact resistance

The perturbation expansion method is used to find the effective thermal conductivity of graded nonlinear composites having thermal contact resistance on the inclusion surface. As an example, we have studied the graded composites with cylindrical inclusions immersed in a homogeneous matrix. The thermal conductivity of the cylindrical inclusion is assumed to have a power-law profile of the radial distance r measured from its origin. For weakly nonlinear constitutive relations between the heat flow density q and the temperature field T, namely, q = -mu del T - chi vertical bar del T vertical bar(2) del T, in both the inclusion and the matrix regions, we have derived the temperature distributions using the perturbation expansion method. A nonlinear effective medium approximation of graded composites is proposed to estimate the effective linear and nonlinear thermal conductivities. by considering the temperature singularity on the inclusion surface due to the heat contact resistance. (c) 2006 Elsevier B.V. All rights reserved.

Conservative force fields in non-Gaussian statistics

In this Letter, we determine the kappa-distribution function for a gas in the presence of an external field of force described by a potential U(r). In the case of a dilute gas, we show that the kappa-power law distribution including the potential energy factor term can rigorously be deduced in the framework of kinetic theory with basis on the Vlasov equation. Such a result is significant as a preliminary to the discussion on the role of long range interactions in the Kaniadakis thermostatistics and the underlying kinetic theory. (C) 2008 Elsevier B.V. All rights reserved.

Evolution of primordial black holes in a radiation and phantom energy environment

In this work we extend previous work on the evolution of a primordial black hole (PBH) to address the presence of a dark energy component with a super-negative equation of state as a background, investigating the competition between the radiation accretion, the Hawking evaporation and the phantom accretion, the latter two causing a decrease on black hole mass. It is found that there is an instant during the matter-dominated era after which the radiation accretion becomes negligible compared to the phantom accretion. The Hawking evaporation may become important again depending on a mass threshold. The evaporation of PBHs is quite modified at late times by these effects, but only if the generalized second law of thermodynamics is violated.

CMB and LSS constraints on a single-field model of inflation

A new inflationary scenario whose exponential potential V (Phi) has a quadratic dependence on the field Phi in addition to the standard linear term is confronted with the five-year observations of the Wilkinson-Microwave Anisotropy Probe and the Sloan Digital Sky Survey data. The number of e-folds (N), the ratio of tensor-to-scalar perturbations (r), the spectral scalar index of the primordial power spectrum (n(s)) and its running (dn(s)/d ln k) depend on the dimensionless parameter a multiplying the quadratic term in the potential. In the limit a. 0 all the results of the exponential potential are fully recovered. For values of alpha not equal 0, we find that the model predictions are in good agreement with the current observations of the Cosmic Microwave Background (CMB) anisotropies and Large-Scale Structure (LSS) in the Universe. Copyright (C) EPLA, 2008.

Could the cosmic acceleration be transient? A cosmographic evaluation

A possible slowing down of the cosmic expansion is investigated through a cosmographic approach. By expanding the luminosity distance to fourth order and fitting the SN Ia data from the most recent compilations (Union, Constitution and Union 2), the marginal likelihood distributions for the deceleration parameter today suggest a recent reduction of the cosmic acceleration and indicate that there is a considerable probability for q(0) > 0. Also in contrast to the prediction of the Lambda CDM model, the cosmographic q(z) reconstruction permits a cosmic expansion history where the cosmic acceleration could already have peaked and be presently slowing down, which would imply that the recent accelerated expansion of the universe is a transient phenomenon. It is also shown that to describe a transient acceleration the luminosity distance needs to be expanded at least to fourth order. The present cosmographic results depend neither on the validity of general relativity nor on the matter-energy contents of the universe.

Lines of heavy elements and Fe II in the UV of CS 31082-001

The abundance of heavy r-elements may provide a better understanding of the r-process, and the determination of several reference r-elements should allow a better determination of a star`s age. The space UV region (lambda < 3000 angstrom) presents a large number of lines of the heavy elements, and in the case of some elements, such as Bi, Pt, Au, detectable lines are not available elsewhere. The extreme ""r-process star"" CS 31082-001 ([Fe/H] = -2.9) was observed in the space UV to determine abundances of the heaviest stable elements, using STIS on board Hubble Space Telescope.