Bifurcation analysis of the twist-Freedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions

Motivated by a recent investigation of Millar and McKay [Mol. Cryst. Liq. Cryst., 435, 277/[937]-286/[946] (2005)], we study the magnetic field twist-Fr´eedericksz transition for a nematic liquid crystal of positive diamagnetic anisotropy with strong anchoring and pre- twist boundary conditions. Despite the pre-twist, the system still possesses Z2 symmetry and a symmetry-breaking pitchfork bifurcation, which occurs at a critical magnetic-field strength that, as we prove, is above the threshold for the classical twist-Fr´eedericksz tran- sition (which has no pre-twist). It was observed numerically by Millar and McKay that this instability occurs precisely at the point at which the ground-state solution loses its monotonicity (with respect to the position coordinate across the cell gap). We explain this surprising observation using a rigorous phase-space analysis

Critical Behavior of a Three-State Potts Model on a Voronoi Lattice

We use the single-histogram technique to study the critical behavior of the three-state Potts model on a (random) Voronoi-Delaunay lattice with size ranging from 250 to 8000 sites. We consider the effect of an exponential decay of the interactions with the distance,$J(r)=J_0\exp(-ar)$, with $a>0$, and observe that this system seems to have critical exponents $\gamma$ and $\nu$ which are different from the respective exponents of the three-state Potts model on a regular square lattice. However, the ratio $\gamma/\nu$ remains essentially the same. We find numerical evidences (although not conclusive, due to the small range of system size) that the specific heat on this random system behaves as a power-law for $a=0$ and as a logarithmic divergence for $a=0.5$ and $a=1.0$Comment: 3 pages, 5 figure

A Novel Approach for Designing Omnidirectional Slotted-Waveguide Antenna Array

This paper presents a novel design of a high-gain omnidirectional slotted-waveguide antenna array for 5G mm-wave applications. The structure is based on a circular waveguide filled with teflon for manipulating its dimension. It provides 12,1 dBi gain and omnidirectional coverage in the azimuth plane with only 1.3 dB deviation, which is ensured by making use of a twisting technique for proper placing the slots into the waveguide walls. A bandwidth of 1.61 GHz centered at 26.2 GHz has been numerically demonstrated

Millimeter Wave Beam Steerable/Reconfigurable Liquid Metal Array Antenna

This paper presents a mm-wave beam steerable/reconfigurable phased array antenna incorporating Eutectic Gallium Indium Alloy (EGaIn) liquid metal switches. The antenna operates at 26.2 GHz and has a scan range of ±58° which yields a ±40° improvement in scan range over a conventional dipole phased array antenna at a side lobe level of or better than 8.8 dB. Moreover the beam scanning approach proposed here supports continuous beam steering over a much wider scan angle range than is possible with conventional techniques

The tikhonov regularization method in elastoplasticity

The numeric simulation of the mechanical behaviour of industrial materials is widely used in the companies for viability verification, improvement and optimization of designs. The eslastoplastic models have been used for forecast of the mechanical behaviour of materials of the most several natures (see [1]). The numerical analysis from this models come across ill-conditioning matrix problems, as for the case to finite or infinitesimal deformations. A complete investigation of the non linear behaviour of structures it follows from the equilibrium path of the body, in which come the singular (limit) points and/or bifurcation points. Several techniques to solve the numerical problems associated to these points have been disposed in the specialized literature, as for instance the call Load controlled Newton-Raphson method and displacement controlled techniques. Although most of these methods fail (due to problems convergence for ill-conditioning) in the neighbour of the limit points, mainly in the structures analysis that possess a snapthrough or snap-back equilibrium path shape (see [2]). This work presents the main ideas formalities of Tikhonov Regularization Method (for example see [12]) applied to dynamic elastoplasticity problems (J2 model with damage and isotropic-kinetic hardening) for the treatment of these limit points, besides some mathematical rigour associated to the formulation (well-posed/existence and uniqueness) of the dynamic elastoplasticity problem. The numeric problems of this approach are discussed and some strategies are suggested to solve these misfortunes satisfactorily. The numerical technique for the physical problem is by classical Gelerkin method