Effective nonlinear AC response to composite with spherical particles

An effective nonlinear alternative-current (AC) response to granular nonlinear-composite with spherical inclusions embedded in a host medium under the action of an external AC field is investigated by using a perturbation approach. The local potentials of composite at higher harmonics are derived both in a region of local inclusion particles and in a local host region under the action of a sinusoidal field E-1 sin ω t + E-3 sin 3ω t. An effective nonlinear-response to composite and the relationship between the effective nonlinear-responses at the fundamental frequency and the third harmonics are also studied for the spherical inclusions in a dilute limit.

Effective dielectric responses of graded composites of the particles with a general power-law gradation profile

The effective dielectric response of graded spherical composites having general power-law gradient inclusions is investigated under a uniform applied electric field, where the dielectric gradation profile of the spherical inclusions is modeled by the equation epsilon(i) (r) = c(b+r)(k). Analytical solutions of the local electrical potentials are derived in terms of hyper-geometric function and the effective dielectric response of the graded composites is predicted in the dilute limit. From our result, the local potentials of graded spherical composites having both simple power-law dielectric profile epsilon(i)(r) = cr(k) and linear dielectric profile epsilon(i) (r) = c(b+r) are derived exactly by taking the limits b --> 0 and k --> 1, respectively. In the dilute limit, our exact result is used to test the validity of differential effective dipole approximation (DEDA) for estimating the effective response of graded spherical composites, and it is shown that the DEDA is in excellent agreement with exact result. (C) 2005 Elsevier B.V. All rights reserved.

Effective AC response of nonlinear spherical coated composites

Under alternating current electric field, effective response of granular nonlinear composites with spherical coated inclusions is investigated in the dilute limit by using the perturbation approach. For an external sinusoidal applied field with finite frequency omega, the local fields and potentials of composites in general consist of components at all harmonics for cubic nonlinear constitutive relationships. We derive the local potentials of spherical coated composites at harmonics. Moreover, we give the formulae of the nonlinear effective AC susceptibility at the third harmonic frequency.

Effective ac response in weakly nonlinear composites

The perturbation method is developed to deal with the problem of determining the effective nonlinear conductivity of Kerr-like nonlinear media under an external ac electric field. As an example, we have considered the cylindrical inclusion embedded in a host under the sinusoidal external field E-1 sin(omegat) + E-3 sin(3omegat) with frequencies omega and 3omega. The potentials of composites at higher harmonics are derived in both local inclusion particle and host regions. The effective responses of bulk nonlinear composites at basic frequency and harmonics are given for cylindrical composites in the dilute limit. Moreover, the relationships between the nonlinear effective responses at the basic frequency and the third harmonics are derived.

Effective dielectric response of nonlinear composites with external ac and dc electric field

The perturbation method is developed to investigate the effective nonlinear dielectric response of Kerr composites when the external ac and dc electric field is applied. Under the external ac and dc electric field E-app=E-a(1+sin omegat), the effective coupling nonlinear response can be induced by the cubic nonlinearity of Kerr nonlinear materials at the zero frequency, the finite basic frequency omega, the second and the third harmonics, 2omega and 3omega, and so on. As an example, we have investigated the cylindrical inclusions randomly embedded in a host and derived the formulas of the effective nonlinear dielectric response at harmonics in dilute limit. For a higher concentration of inclusions, we have proposed a nonlinear effective-medium approximation by introducing the general effective nonlinear response. With the relationships between the effective nonlinear response at harmonics and the general effective nonlinear response, we have derived a set of formulas of the effective nonlinear dielectric responses at harmonics for a larger volume fraction. (C) 2004 American Institute of Physics.

The nonlinear effective dielectric response of graded composites

The perturbation method is developed to deal with the effective nonlinear dielectric responses of weakly nonlinear graded composites, which consist of the graded inclusion with a linear dielectric function of spatial variables of inclusion material. For Kerr-like nonlinear graded composites, as an example in two dimensions, we have used the perturbation method to solve the boundary value problems of potentials, and studied the effective responses of nonlinear graded composites, where a cylindrical inclusion with linear dielectric function and nonlinear dielectric constant is randomly embedded in a homogeneous host with linear and nonlinear dielectric constants. For the exponential function and the power-law dielectric profiles of cylindrical inclusions, in the dilute limit, we have derived the formulae of effective nonlinear responses of both graded nonlinear composites.

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.

Effective response of a non-linear composite in external AC electric field

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) <\E(x, omega, t)\(2) E(x, omega, t)> + (. . .), 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.

Effective properties of graded elliptical cylindrical composites

The effective property has been investigated theoretically in graded elliptical cylindrical composite's consisting of inhomogeneous graded elliptical cylinders and an isotropic matrix under external uniform electric field. As a theoretical model, the dielectric gradient profile in the elliptical cylinder is modeled by a power-law function of short semi-axis variable parameter (xi(2) - 1) in the elliptical cylindrical coordinates, namely epsilon(i)(xi) = c(k) (xi(2) - 1)(k), where c(k) and k are the parameters, and xi is the long semi-axis space variable in an elliptical cylindrical inclusion region. In the dilute limit, the local analytical potentials in inclusion and matrix regions are derived exactly by means of the hyper-geometric function, and the formulas are given for estimating the effective dielectric responses under the external lfield along (x) over cap- and (y) over cap -directions, respectively. Furthermore, we have demonstrated that our effective response formulas can be reduced to the well-known results of homogeneous isotropic elliptical cylindrical composites if we take the limit k -> 0 in graded elliptical cylindrical composites. (c) 2006 Elsevier B.V. All rights reserved.

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.

Effective AC and DC responses of nonlinear composites at higher concentration

For higher concentration of inclusions, an effective medium approximation (EMA) method is used to investigate the bulk effective response of weakly nonlinear composites, which are subject to the constitutive relation of electric displacement and electric field, D-alpha = epsilon E-alpha + chi(alpha)|E|(2) E. As an example of three dimensions, under the external AC and DC electric fields E-app = E-a (1 + sin omega t), we have derived the general effective nonlinear response of composites by the EMA method for higher concentration of spherical inclusions. Furthermore, the effective nonlinear responses at harmonics are predicted.

Photoperiodic regulation in energy intake, thermogenesis and body mass in root voles (Microtus oeconomus)

The present study was designed to examine whether photoperiod alone was effective to induce seasonal regulations in physiology in root voles (Microtus oeconomus) from the Qinghai-Tibetan plateau noted for its extreme cold environment. Root voles were randomly assigned into either long photoperiod (LD; 16L: 8D) or short photoperiod (SD; 8L: 16D) for 4 weeks at constant temperature (20 degrees C). At the end of acclimation, SD voles showed lower body mass and body fat coupled with higher energy intake than LD voles. SD greatly enhanced thermogenic capacities in root voles, as indicated by elevated basal metabolic rate (BMR), nonshivering thermogenesis (NST), mitochondrial protein content and uncoupling protein-1 (UCP1) content in brown adipose tissue (BAT). Although no variations in serum leptin levels were found between SD and LD voles, serum leptin levels were positively correlated with body mass and body fat mass, and negatively correlated with energy intake and UCP1 content in BAT, respectively. To summarize, SD alone is effective in inducing higher thermogenic capacities and energy intake coupled with lower body mass and body fat mass in root voles. Leptin is potentially involved in the photoperiod induced body mass regulation and thermogenesis in root voles. (c) 2006 Elsevier Inc. All rights reserved.

降雨条件下碎石土滑坡稳定性研究

Debris Landslide is one of the types of landslides with the widest distribution, largest quantity, and the closest relationship with engineering construction. It is also one of the most important types of landslides that can cause disaster. This kind of landslide often occurs in the loose slopes which are made up of loose congeries formed by earth filling, residual soil, slope wash, dilapidation, landslide or full weathered material of hard rock. Rainfall is always the chief inducing factor of debris Landslide. Therefore, to research stability of debris Landslide during rainfall not only has important theoretical significance for understanding developing law and deformation and failure mechanism of debris landslide, but also has important practical significance for investigating, appraising, forecasting, preventing and controlling debris landslides. This thesis systematically summarized the relationships between rainfall and landslide, the method to survey water table in the landslides, the deformation and failure mechanism of debris landslide, and the progress in the stability analysis of landslides based on the analyses of data collected widely at home and abroad. The problems in the study of the stability of debris landslide during rainfall was reviewed and discussed. Due to the complicated geological conditions and the random rainfall conditions, the research on the landslides' stability must be based on engineering geological qualitative analysis. Through the collection of the data about the Panxi region and the Three Gorges Reservoir region, the author systematically summarized the engineering geological conditions, hydro-geological condition, distribution characteristics of stress field in the slope, physical and mechanical properties and hydro-mechanical properties of debris. In the viewpoint of dynamics of soil water and hydromechanics, physical process of rainfall to supply groundwater of debris landslides can be divided into two phases, i.e. non-saturated steady infiltrating phase and saturated unsteady supplying phase. The former can be described by mathematical model of surface water infiltration while the latter can be described by equivalent continuous medium model of groundwater seepage. With regard to specific hydrological geology system, we can obtain the dynamic variation law of water content, water table, landslide stability of rock and soil mass, along with quantity and duration of rainfall after the boundary condition on hydrological geology has been ascertained. This is a new way to study the response law of groundwater in the landslides during rainfall. After wet face of rock and soil mass connects with ground water table, the raising of water table will occur due to the supply of rainfall. Then interaction between ground water and rock and soil mass will occur, such as the action of physics, water, chemistry and mechanics, which caused the decrease of shearing strength of sliding zone. According to the action of groundwater on rock and soil mass, a concise mechanical model of debris landslide’s deformation was established during rainfall. The static equilibrium condition of landslide mass system was achieved according to the concise mechanical model, and then the typical deformation and failure process and failure mode of debris landslide during rainfall were discussed. In this thesis, the former limiting equilibrium slice method was modified and improved based on shearing strength theory of , a stability analysis program of debris landslide was established and developed taking account of the saturated-unsaturated seepage, by introducing the shearing strength theory of unsaturated soil mass made by (1978). The program has reasonable data storage and simple interface and is easy to operate, and can be perfectly used to carry out sensitivity analysis of influencing factors of landslides' stability, integrated with the program of Office Excel. The design of drainage engineering are always bases on empirical methods and is short of effective quantitative analysis and appraise, therefore, the conception of critical water table of debris landslide was put forward. For debris landslides with different kinds of slide face in the engineering practice, a program to search the critical water table of debris landslide was developed based on native groundwater table. And groundwater table in the slope should be declined below the critical water table in the drainage works, so the program can be directly used to guide drainage works in the debris landslide. Taking the slope deformation body in the back of former factory building of Muli Shawan hydroelectric power station as an example, a systematic and detailed research on debris landslides' stability during rainfall was researched systematically, the relationship among quantity of rainfall, water table and stability of slope was established, the debris landslides' stability in process of rainfall from dynamic viewpoint was analyzed and researched.