Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection

Patterns forming spontaneously in extended, three-dimensional, dissipative systems are likely to excite several homogeneous soft modes (approximate to hydrodynamic modes) of the underlying physical system, much more than quasi-one- (1D) and two-dimensional (2D) patterns are. The reason is the lack of damping boundaries. This paper compares two analytic techniques to derive the pattern dynamics from hydrodynamics, which are usually equivalent but lead to different results when applied to multiple homogeneous soft modes. Dielectric electroconvection in nematic liquid crystals is introduced as a model for 3D pattern formation. The 3D pattern dynamics including soft modes are derived. For slabs of large but finite thickness the description is reduced further to a 2D one. It is argued that the range of validity of 2D descriptions is limited to a very small region above threshold. The transition from 2D to 3D pattern dynamics is discussed. Experimentally testable predictions for the stable range of ideal patterns and the electric Nusselt numbers are made. For most results analytic approximations in terms of material parameters are given. [S1063-651X(00)09512-X].

Pattern formation of chevrons in the conduction regime in homeotropically aligned liquid crystals

We report on chevrons (herringbonelike patterns) observed in homeotropically aligned liquid crystals with high electric conductivity. We focus our attention on two types of chevrons observed in the conduction regime. The threshold voltage and the characteristic double periodicity of chevrons (i.e., the short wavelength lambda(1) of the striated rolls and the long wavelength lambda(2) Of the chevron bands) have been measured as functions of the applied electric frequency f. With the aid of a crossed polarizer set, we have, in addition, determined the director field which shows a periodic in-plane rotation for our chevrons (with a wavelength lambda(2)) We arrived at the types of chevrons after qualitatively different bifurcation sequences with increasing voltage. The frequency dependence of lambda(2) also shows a qualitatively different behavior with respect to the two types of chevrons. The experimental results are discussed in terms of recent theoretical investigations.

A Description of the Stationary Wave Pattern of a Marine Craft in Shallow and Intermediate Water Depths

A stationary phase model is used to study supercritical waves generated by high speed ferries. Some general relationships in terms of wave angle, propagation direction, dispersion relationship and depth wavelength relationship are explored and discussed. In particular, it is shown that the wave pattern generated by high speed craft at supercritical speeds depends mainly on the relationship of water depth and ship speed and that the wave patterns are similar in terms of location of crests and troughs for a given depth Froude number. In addition it is found that the far field wave pattern can be described adequately using a single moving point source. The theoretical model compares well with towing tank measurements and full scale data over a range of parameters and hull shapes. The paper also demonstrates that the far field wave pattern at supercritical speeds should be non-dimensionalised by water depth and not hull length unlike it is usually done for subcritical speeds.

Artificial Impedance Surfaces for Reduced Dispersion in Antenna Feeding Systems

An impedance surface is presented that reduces the dispersion experienced upon propagation of broadband pulses within rectangular waveguides. The surface impedance is selected so that, within a frequency range, the transverse resonance condition is satisfied for longitudinal wavenumber that varies linearly with frequency. A synthesis procedure for practical surface topologies consisting of periodic dipole arrays is described. An example involving a finite structure is employed to illustrate the reduced dispersion. Numerical simulation results obtained from in-house mode-matching method as well as HFSS are presented. A prototype is fabricated and tested experimentally validating the theoretical predictions.