The electrostatics of conductors

This chapter begins by proving some important properties of (i) conductors in electrostatic equilibrium, and (ii) harmonic functions. These results underpin most of the remaining questions of Chapter 3. The coefficients of capacitance for an arbitrary arrangement of conductors are introduced at an early stage, and numerical calculations then follow in a number of subsequent questions. Some important techniques (both analytical and numerical) for finding solutions to Laplace’s equation are considered. These include: the Fourier method, the relaxation method, themethod of images and the method of conformal transformation. All of these are discussed in some detail, and with appropriate examples.

The Role of Inertia and Dissipation in the Dynamics of the Director for a Nematic Liquid Crystal Coupled with an Electric Field

We consider the dynamics of the director in a nematic liquid crystal when under the influence of an applied electric field. Using an energy variational approach we derive a dynamic model for the director including both dissipative and inertial forces.A numerical scheme for the model is proposed by extending a scheme for a related variational wave equation. Numerical experiments are performed studying the realignment of the director field when applying a voltage difference over the liquid crystal cell. In particular, we study how the relative strength of dissipative versus inertial forces influence the time scales of the transition between the initial configuration and the electrostatic equilibrium state.

Optical vibrations in alkali halide crystals

We consider long-wave phonon–polaritons and longitudinal optical phonons in alkali–halide ionic crystals. The model of point charges that are polarized in the self-consistent electromagnetic field in a dielectric environment is used. The standard dispersion laws for both branches of phonon–polaritons and longitudinal optical phonons are obtained. The transversal optical phonon frequency is found from the electrostatic equilibrium condition. It is proved by comparison with tabular data that the found frequency coincides with the ion plasma frequency multiplied on the relation [Formula: see text] where ε∞ and ε0 are the high-frequency dielectric and static constants, respectively.

The Arc-Length Method from Controlling Load to Controlling Electric Potential

This paper generalizes the arc-length method, and proposes a new scheme of controlling equilibrium path including static equilibrium and electrostatic equilibrium. To take example for the thin plate electrode posing on the electrostatic field force, whose governing equations are the two fold nonlinear coupling equation, the method to compute the incremental factor is give in detain. The result is to show that not only the approximate critical voltage is obtained but also the trace after losing stability is found stably.