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.

Dielectric response of composites with graded cylindrical particles

Effective dielectric responses of graded cylindrical composites are investigated when an external uniform field is applied to the composites. Considering linear random composites of cylindrical particles with a specific dielectric function, which varies along the radial direction of the particles, we have studied three cases of dielectric profiles: exponential function, linear and power-law profiles. For each case, the effective dielectric response of graded composites is given on the basis of exact solutions of the local potentials of composites in the dilute limit. For a larger volume fraction, we have proposed an effective medium approximation to estimate the effective dielectric response.

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.

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.

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.

Dielectric response of spherically anisotropic graded piezoelectric composites

A graded piezoelectric composite consisting of a spherically anisotropic graded piezoelectric inclusion imbedded in an infinite nonpiezoelectric matrix, with the physical properties of the graded spherical inclusion having a power-law profile with respect to the radial variable r, is studied theoretically. Under an external uniform electric field, the electric displacement field and the elastic stress tensor field of this spherically anisotropic graded piezoelectric composite are derived exactly by means of displacement separation technique, based on the governing equations in the dilute limit. A piezoelectric response mechanism, in which the effective piezoelectric response vanishes along the z direction (or x,y directions), is revealed in this kind of graded piezoelectric composites. Furthermore, it is found that the effective dielectric constant decreases (or increases) with the volume fraction p of the inclusions if the exponent parameter k of the grading profile is larger (or smaller) than a critical value. (C) 2007 American Institute of Physics.

Dielectric responses of anisotropic graded granular composites having arbitrary inclusion shapes

The transformation field method (TFM) originated from Eshelby's transformation field theory is developed to estimate the effective permittivity of an anisotropic graded granular composite having inclusions of arbitrary shape and arbitrary anisotropic grading profile. The complicated boundary-value problem of the anisotropic graded composite is solved by introducing an appropriate transformation field within the whole composite region. As an example, the effective dielectric response for an anisotropic graded composite with inclusions having arbitrary geometrical shape and arbitrary grading profile is formulated. The validity of TFM is tested by comparing our results with the exact solution of an isotropic graded composite having inclusions with a power-law dielectric grading profile and good agreement is achieved in the dilute limit. Furthermore, it is found that the inclusion shape and the parameters of the grading profile can have profound effect on the effective permittivity at high concentrations of the inclusions. It is pointed out that TFM used in this paper can be further extended to investigate the effective elastic, thermal, and electroelastic properties of anisotropic graded granular composite materials.

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.

Feeding habits of Calanus sinicus (Crustacea : Copepoda) during spring and autumn in the Bohai Sea studied with the herbivore index

Pigment ingestion rate (PIR) and egg production rate (EPR) of the dominant copepod Calanus sinicus, as well as chlorophyll-a concentration and phytoplankton assemblages were measured in the Bohai Sea, North China in June 1997, October 1998 and May 1999. A herbivore index (H) was also calculated as the carbon specific ratio of PIR and EPR, in order to investigate its feeding habits in the spring and autumn phytoplankton bloom respectively. On average, chlorophyll-a concentration was relatively similar (1-1.34 mg m(-3)) in the three cruises, but PIR was quite different. It was 3.24 mu g C female(-1) d(-1) in October, equivalent to one half of the PIR for June and one third of the PIR for May. Average EPR was highest in May, and quite similar during the other two months. According to H values, herbivorous feeding contributed 100% of the egg production of C. sinicus in June, 82.5% in May, but only 47.8% in October. It is possible that omnivorous feeding of C. sinicus in October was induced by a prevalence of large-sized diatoms and sufficient non-phytoplankton food resources during the autumn bloom period.

Effect of graded levels of rapeseed oil in isonitrogenous diets on the development of the gastrointestinal tract, and utilisation of protein, fat and energy in broiler chickens

The effect of feeding 0, 4, 8 and 16% rapeseed oil from 12-42 days of age was studied in broiler chickens on performance, digestibility of nutrients, and development of gastrointestinal tract, protein and energy metabolism. Thirty six female chickens (Ross 208) with initial body weight average 246 g were allocated to the four groups and kept pair-wise in metabolism cages. The chickens were fed similar amounts of metabolisable energy (ME) per day and similar amounts of essential amino acids relative to ME by adjusting with crystalline amino acids. The chickens were subjected to four balance periods each of five days with two 24 h measurements of gas exchange in two open-air-circuit respiration chambers inserted on the second and third day of each period. The addition of rapeseed oil increased the amount of gutfill indicating a reduced rate of passage and causing a hypertrophy of the gastrointestinal tract. There was a positive effect on feed utilisation as well as on digestibility especially of dietary fat together with higher utilisation of protein with addition of rapeseed oil. The partial fat digestibility of rapeseed oil estimated by regression was 91.1% and the partial metabolisability (ME/GE) of the rapeseed oil was estimated to 85% yielding an apparent metabolisable energy value of 34.30 MJ/kg.

Assessing the potential of VEGETATION sensor data for mapping snow and ice cover: a Normalized Difference Snow and Ice Index

The VEGETATION (VGT) sensor in SPOT 4 has four spectral bands that are equivalent to Landsat Thematic Mapper (TM) bands (blue, red, near-infrared and mid-infrared spectral bands) and provides daily images of the global land surface at a 1-km spatial resolution. We propose a new index for identifying and mapping of snow ice cover, namely the Normalized Difference Snow/Ice Index (NDSII), which uses reflectance values of red and mid-infrared spectral bands of Landsat TM and VGT. For Landsat TM data, NDSII is calculated as NDSIITM =(TM3 -TM5)/(TM3 +TM5); for VGT data, NDSII is calculated as NDSIIVGT =(B2- MIR)/(B2 + MIR). As a case study we used a Landsat TM image that covers the eastern part of the Qilian mountain range in the Qinghai-Xizang (Tibetan) plateau of China. NDSIITM gave similar estimates of the area and spatial distribution of snow/ice cover to the Normalized Difference Snow Index (NDSI=(TM2-TM5)/(TM2+TM5)) which has been proposed by Hall et al. The results indicated that the VGT sensor might have the potential for operational monitoring and mapping of snow/ice cover from regional to global scales, when using NDSIIVGT.