electrostatics

The attached tutorial paper is yet unpublished but I am posting a pre-print since several students I know have found it to be a useful pedagogical resource. You may also access the document on arXiv.

Here is the abstract.

In this manuscript (available at http://arxiv.org/abs/1004.1765), we present a systematically improvable, linear scaling formulation for the solution of the all-electron Coulomb problem in crystalline solids. In an infinite crystal, the electrostatic (Coulomb) potential is a sum of nuclear and electronic contributions, and each of these terms diverges and the sum is only conditionally convergent due to the long-range 1/r nature of the Coulomb interaction.

Update: The position has been filled; thanks to all who responded.

A post-doctoral position is immediately available at UC Davis. The individual will work on a joint project led by myself and John Pask at LLNL on the development and application of a new finite-element based approach for large-scale quantum mechanical materials calculations.

Electro-sensitive (ES) elastomers form a class of smart materials whose mechanical properties can be changed rapidly by the application of an electric field. These materials have attracted considerable interest recently because of their potential for providing relatively cheap and light replacements for mechanical devices, such as actuators, and also for the development of artificial muscles. In this paper we are concerned with a theoretical framework for the analysis of boundary-value problems that underpin the applications of the associated electromechanical interactions. We confine attention to the static situation and first summarize the governing equations for a solid material capable of large electroelastic deformations. The general constitutive laws for the Cauchy stress tensor and the electric field vectors for an isotropic electroelastic material are developed in a compact form following recent work by the authors. The equations are then applied, in the case of an incompressible material, to the solution of a number of representative boundary-value problems. Specifically, we consider the influence of a radial electric field on the azimuthal shear response of a thick-walled circular cylindrical tube, the extension and inflation characteristics of the same tube under either a radial or an axial electric field (or both fields combined), and the effect of a radial field on the deformation of an internally pressurized spherical shell.

T. Zhu, Z. Suo, A. Winkleman, G. M. Whitesides, Applied Physics Letters, 88, 144101, (2006)