COMMODITY POLICY ISSUES FOR THE 1980S

Agricultural and Food Policy,

Remarks on explicit strong ellipticity conditions for anisotropic or pre-stressed incompressible solids

We present a set of explicit conditions, involving the components of the elastic stiffness tensor, which are necessary and sufficient to ensure the strong ellipticity of an orthorhombic incompressible medium. The derivation is based on the procedure developed by Zee & Sternberg (Arch. Rat. Mech. Anal., 83, 53-90 (1983)) and, consequently, is also applicable to the case of the homogeneously pre-stressed incompressible isotropic solids. This allows us to reformulate the results by Zee & Sternberg in terms of components of the incremental stiffness tensor. In addition, the resulting conditions are specialized to higher symmetry classes and compared with strong ellipticity conditions for plane strain, commonly used in the literature.The first author’s work and the second author’s visit to Brunel University were partly supported by Brunel University’s ‘BRIEF’ award scheme

Design of blended rolled edges for compact range main reflectors

A procedure to design blended rolled edge terminations for arbitrary rim shape compact range main reflectors is presented. The reflector may be center-fed or offset-fed. The design procedure leads to a reflector which has a continuous and smooth surface. This procedure also ensures small diffracted fields from the junction between the paraboloid and the blended rolled edge while satisfying certain constraints regarding the maximum height of the reflector and minimum operating frequency of the system. The prescribed procedure is used to design several reflectors and the performance of these reflectors is presented

Flow-Induced Twist-Compression in a Twisted Nematic Cell

Lizhen Ruan and J. Roy Sambles, Physical Review Letters, Vol. 90, article 168701 (2003). "Copyright © 2003 by the American Physical Society."An optical convergent-beam guided-wave technique is used to explore in detail the dynamic flow effects in a twisted nematic cell. During switch-on it is found that the dynamic flow compresses the director twist to regions close to the cell walls. For high fields this twist compression takes the cell far beyond the Mauguin limit and it no longer effectively guides the polarization of the light through the cell. This results in a very fast switch to a transient dark state

Combinatorial Trigonometry with Chebyshev Polynomials

We provide a combinatorial proof of the trigonometric identity cos(nθ) = Tncos(θ),where Tn is the Chebyshev polynomial of the first kind. We also provide combinatorial proofs of other trigonometric identities, including those involving Chebyshev polynomials of the second kind

Thermodynamical Consistent Modeling and Analysis of Nematic Liquid Crystal Flows

The general Ericksen-Leslie system for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal model is then investigated analytically. A fairly complete dynamic theory is developed by analyzing these systems as quasilinear parabolic evolution equations in an $L^p-L^q$-setting. First, the existence of a unique, local strong solution is proved. It is then shown that this solution extends to a global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the natural norm of the underlying state space. In these cases, the solution converges exponentially to an equilibrium in the natural state manifold

Lattice Boltzmann Simulations of Liquid Crystal Hydrodynamics

We describe a lattice Boltzmann algorithm to simulate liquid crystal hydrodynamics. The equations of motion are written in terms of a tensor order parameter. This allows both the isotropic and the nematic phases to be considered. Backflow effects and the hydrodynamics of topological defects are naturally included in the simulations, as are viscoelastic properties such as shear-thinning and shear-banding.Comment: 14 pages, 5 figures, Revte

Asymptotic Behavior for a Nematic Liquid Crystal Model with Different Kinematic Transport Properties

We study the asymptotic behavior of global solutions to hydrodynamical systems modeling the nematic liquid crystal flows under kinematic transports for molecules of different shapes. The coupling system consists of Navier-Stokes equations and kinematic transport equations for the molecular orientations. We prove the convergence of global strong solutions to single steady states as time tends to infinity as well as estimates on the convergence rate both in 2D for arbitrary regular initial data and in 3D for certain particular cases

Two-phase densification of cohesive granular aggregates

When poured into a container, cohesive granular materials form low-density, open granular aggregates. If pressed upon with a ram, these aggregates densify by particle rearrangement. Here we introduce experimental evidence to the effect that particle rearrangement is a spatially heterogeneous phenomenon, which occurs in the form of a phase transformation between two configurational phases of the granular aggregate. We then show that the energy landscape associated with particle rearrangement is consistent with our interpretation of the experimental results. Besides affording insight into the physics of the granular state, our conclusions are relevant to many engineering processes and natural phenomena.Comment: 7 pages, 3 figure

Global Weak Solutions to a General Liquid Crystals System

We prove the global existence of finite energy weak solutions to the general liquid crystals system. The problem is studied in bounded domain of $R^3$ with Dirichlet boundary conditions and the whole space $R^3$