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.

Application of effective medium approximation theory to ocean remote sensing under wave breaking

Based on the effective medium approximation theory of composites, the empirical model proposed by Pandey and Kakar is remedied to investigate the microwave emissivity of sea surface under wave breaking driven by strong wind. In the improved model, the effects of seawater bubbles, droplets and difference in temperature of air and sea interface (DTAS) on the emissivity of sea surface covered by whitecaps are discussed. The model results indicate that the effective emissivity of sea surface increases with DTAS increasing, and the impacts of bubble structures and thickness of whitecaps layer on the emissivity are included in the model by introducing the effective dielectric constant of whitecaps layer. Moreover, a good agreement is obtained by comparing the model results with the Rose's experimental data.

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 properties of spherically anisotropic piezoelectric composites

Piezoelectric composites consisting of spherically anisotropic piezoelectric inclusions (i.e., piezoceramic material) in an infinite nonpiezoelectric matrix under a uniform electric field are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials are derived exactly. Taking account of the coupling effects of elasticity, permittivity, and piezoelectricity, formulas are derived for the effective dielectric and piezoelectric responses in the dilute limit. A piezoelectric response mechanism is revealed, in which the effective piezoelectric response vanishes irrespective of how much spherically anisotropic piezoelectric inclusions are inside. Moreover, the effective coupled responses of the piezoelectric composites show that the effective dielectric responses decrease (increase) as the inclusion elastic (piezoelectric) constants increase.

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.

Transformation field method for calculating the effective properties of isotropic graded composites having arbitrary shapes

A method of transformation field is developed to estimate the effective properties of graded composites whose inclusions have arbitrary shapes and gradient profiles by means of a periodic cell model. The boundary-value problem of graded composites having arbitrary inclusion shapes is solved by introducing the transformation field into the inclusion region. As an example, the effective dielectric response of isotropic graded composites having arbitrary shapes and gradient profiles is handled by the transformation field method (TFM). Moreover, TFM results are validated by the exact solutions of isotropic graded spherical inclusions having a power-law profile and good agreement is obtained in the dilute limit. Furthermore, it is found that the inclusion shapes and the parameters of the gradient profiles can have profound effect on the effective properties of composite systems at high concentration of inclusions.

Effects of effective population size on the F-2 growth and survival of bay scallop Argopecten irradians irradians (Lamarck)

In 2002, six cohorts of broodstock bay scallop Argopecten irradians irradians (Ne=1, 2, 10, 30, 50 and control) were randomly chosen from a population of bay scallop to produce offspring. After one year rearing, with the progeny matured, the similar experiment was done to produce the F-2 generation. To determine the magnitude of Ne effects, the growth and survival rates in larvae and adult of six F2 groups were compared. Results showed that inbreeding depression existed not only in the Ne=1 group but also in the Ne=2 group. The growth and survival rates of the two groups were significantly lower than those of the other groups (Ne=10, 30, 50, control), and there were no significant differences among the latter (P>0.05). At the same time, the amount of depression in the Ne=1 group was significantly higher than that of the Ne=2 group (P<0.05). These results indicated that the low effective population size (Ne), which increases the possibility of inbreeding, could lead to some harmful effects on the offspring. So it is essential to maintain a high level of Ne in commercial seed production. Furthermore, as the high fecundity of bay scallop might lead to increased inbreeding, selecting broodstock from different growout sites is recommended.

Interannual fluctuations in floral longevity, pollinator visitation and pollination limitation of an alpine plant (Gentiana straminea Maxim., Gentianaceae) at two altitudes in the Qinghai-Tibetan Plateau

Prolonged floral longevity and bumblebees as dominate pollinators in alpine ecosystem have been suggested to overcome pollination limitation of alpine plants arising from the decrease of pollinator activity with increasing altitude. However, this conclusion has never been examined in the Qinghai-Tibetan Plateau (QTP), the highest and largest plateau in the world. In this study, we intended to test year-to-year correlations between floral longevity, visiting frequency and pollen limitation of this species between two populations (at 3200 m and 4000 m) of Gentiana straminea in this plateau. Pollinator exclusion elongated both male and female phases greatly at both sites, and durations of both male and female phases in natural condition varied greatly over three years. The visiting frequency of bumblebees varied greatly at the higher altitude, but seemed to be stable at the lower altitude. Seed production was pollination limited in both populations in most studied years. The floral durations, pollinator frequency and pollination limitation showed no significant and consistent variations with the increase of altitude. The previous hypothesis that the prolonged floral longevity of alpine plants can compensate for low levels of pollinator visitation therefore could not be confirmed, and our results further suggested that in the QTP platform, the altitude shows no consistent effect on the reproductive performance of this species, despite that the fluctuation of visit frequency intensified at the higher altitude.

Pollinator shift and reproductive performance of the qinghai-tibetan plateau endemic and endangered Swertia przewalskii (Gentianaceae)

Reproductive failure results in many plant species becoming endangered. However, little is known of how and to what extent pollinator shifts affect reproductive performance of endangered species as a result of the artificial introduction of alien insects. In this study we examined breeding systems, visitor species, visiting frequency and seed set coefficients of Swertia przewalskii in two years that had different dominant pollinator species (native vs. alien). Flowers of this species were protandrous and herkogamous and insects were needed for the production of seeds. The stigmatic receptivity of this species was shorter than for other gentians. No significant difference in seed set coefficient was found for hand-pollinated plants between the two years, indicating that pollinator shift only had a minor effect on this plant's breeding system. The commonest pollinators in 2002 were native bumblebees, alien honeybees and occasional solitary bees, however, only alien honeybees were observed in 2004. The flower visitation rate in both years was relatively high, although the total visit frequency decreased significantly in 2004. The control flowers without any treatment produced significantly fewer seed sets in 2004 than in 2002. In the past decade the seed production of this species may have partly decreased due to pollination by alien honeybees, however, we suggest that they might have acted as alternative pollinators ensuring seed production of S. przewalskii when native pollinators were unavailable. The main reason that this plant is endangered is probably the result of habitat destruction, but changes in land use, namely intensified agricultural practice and unfavorable animal husbandry have also contributed to its decline. We recommend that in-situ conservation, including the establishment of a protected area, is the best way to preserve this species effectively.