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.

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.

Application of dynamical Lie algebraic method to atom-diatomic molecule scattering

The dynamical Lie algebraic approach developed by Alhassid and Levine combined with intermediate picture is applied to the study of translational-vibrational energy transfer in the collinear collision between an atom and an anharmonic oscillator. We find that the presence of the anharmonic terms indeed has an effect on the vibrational probabilities of the oscillator. The computed probabilities are in good agreement with those obtained using exact quantum method. It is shown that the approach of dynamical Lie algebra combining with intermediate picture is reasonable in the treating of atom-anharmonic oscillator scattering.

Magnetic resonance imaging of graded skeletal muscle injury in live rats.

INTRODUCTION: Increasing number of stretch-shortening contractions (SSCs) results in increased muscle injury. METHODS: Fischer Hybrid rats were acutely exposed to an increasing number of SSCs in vivo using a custom-designed dynamometer. Magnetic resonance imaging (MRI) imaging was conducted 72 hours after exposure when rats were infused with Prohance and imaged using a 7T rodent MRI system (GE Epic 12.0). Images were acquired in the transverse plane with typically 60 total slices acquired covering the entire length of the hind legs. Rats were euthanized after MRI, the lower limbs removed, and tibialis anterior muscles were prepared for histology and quantified stereology. RESULTS: Stereological analyses showed myofiber degeneration, and cellular infiltrates significantly increased following 70 and 150 SSC exposure compared to controls. MRI images revealed that the percent affected area significantly increased with exposure in all SSC groups in a graded fashion. Signal intensity also significantly increased with increasing SSC repetitions. DISCUSSION: These results suggest that contrast-enhanced MRI has the sensitivity to differentiate specific degrees of skeletal muscle strain injury, and imaging data are specifically representative of cellular histopathology quantified via stereological analyses.

SK1-like functors for division algebras

We investigate the group valued functor G(D) = D*/F*D' where D is a division algebra with center F and D' the commutator subgroup of D*. We show that G has the most important functorial properties of the reduced Whitehead group SK1. We then establish a fundamental connection between this group, its residue version, and relative value group when D is a Henselian division algebra. The structure of G(D) turns out to carry significant information about the arithmetic of D. Along these lines, we employ G(D) to compute the group SK1(D). As an application, we obtain theorems of reduced K-theory which require heavy machinery, as simple examples of our method.

Reduced K-theory for Azumaya algebras

Abstract In the theory of central simple algebras, often we are dealing with abelian groups which arise from the kernel or co-kernel of functors which respect transfer maps (for example K-functors). Since a central simple algebra splits and the functors above are “trivial” in the split case, one can prove certain calculus on these functors. The common examples are kernel or co-kernel of the maps Ki(F)?Ki(D), where Ki are Quillen K-groups, D is a division algebra and F its center, or the homotopy fiber arising from the long exact sequence of above map, or the reduced Whitehead group SK1. In this note we introduce an abstract functor over the category of Azumaya algebras which covers all the functors mentioned above and prove the usual calculus for it. This, for example, immediately shows that K-theory of an Azumaya algebra over a local ring is “almost” the same as K-theory of the base ring. The main result is to prove that reduced K-theory of an Azumaya algebra over a Henselian ring coincides with reduced K-theory of its residue central simple algebra. The note ends with some calculation trying to determine the homotopy fibers mentioned above.