Dielectric response of graded composites having general power-law-graded cylindrical inclusions

The dielectric response of graded composites having general power-law-graded cylindrical inclusions under a uniform applied electric field is investigated. The dielectric profile of the cylindrical inclusions is modeled by the equation epsilon(i)(r)=c(b+r)(k) (where r is the radius of the cylindrical inclusions and c, b and k are parameters). Analytical solutions for the local electrical potentials are derived in terms of hypergeometric functions and the effective dielectric response of the graded composites is predicted in the dilute limit. Moreover, for a simple power-law dielectric profile epsilon(i)(r) = cr(k) and a linear dielectric profile epsilon(i)(r) = c(b + r), analytical expressions of the electrical potentials and the effective dielectric response are derived exactly from our results by taking the limits b -> 0 and k -> 1, respectively. For a higher concentration of inclusions, the effective dielectric response is estimated by an effective-medium approximation. In addition, we have discussed the effective response of graded cylindrical composites with a more complex dielectric profile of inclusion, epsilon(i)(r)=c(b+r)(k)e(beta r). (c) 2005 American Institute of Physics.

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.

Viewing DVM via general behaviors of zooplankton: A way bridging the success of individual and population

In this paper, we viewed the diel vertical migration (DVM) of copepod in the context of the animal's immediate behaviors of everyday concerns and constructed an instantaneous behavioral criterion effective for DVM and non-DVM behaviors. This criterion employed the function of 'venturous revenue' (VR), which is the product of the food intake and probability of the survival, to evaluate the gains and losses of the behaviors that the copepod could trade-off. The optimal behaviors are to find the optimal habitats to maximize VR. Two types of VRs are formulated and tested by the theoretical analysis and simulations. The sensed VR, monitoring the real-time changes of trade-offs and thereby determining the optimum habitat, is validated to be the effective objective function for the optimization of the behavior; whereas, the realized VR, quantifying the actual profit obtained by an optimal copepod in the sensed-VR-determined habitat, defines the life history of a specific age cohort. The achievement of a robust copepod overwintering stock through integrating the dynamics of the constituent age cohorts subjected to the instantaneous behavioral criterion for DVM clearly exemplified a possible way bridging the immediate pursuit of an individual and the end success of the population. (c) 2005 Published by Elsevier Ltd.