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

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

Using Administrative Data to Count Local Populations

There is growing evidence that official population statistics based on the decennial census are inaccurate at the local authority level—the fundamental administrative unit of the UK. This paper investigates the use of locally available administrative data sets for counting populations. The method uses truth tables for combining different data sources with different population coverage according to a defined and therefore replicable set of rules. The result is timelier and geographically more flexible data which is more cost-effective to produce than a survey-based census. Associated techniques for linking diverse data sources at individual and household level are briefly discussed. The methodology is then applied to administrative data from a London borough with about 170,000 people. The results are evaluated and compared with other population sources. The paper concludes by discussing potential improvements including scaling up the work to cover multiple local authorities. The practicalities of using alternative central government data sets are briefly considered. A sequel paper in this journal provides examples of key applications of this approach at local level

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

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 $R^3$

Weak-strong uniqueness property for the full Navier-Stokes-Fourier system

The Navier-Stokes-Fourier system describing the motion of a compressible, viscous, and heat conducting fluid is known to possess global-in-time weak solutions for any initial data of finite energy. We show that a weak solution coincides with the strong solution, emanating from the same initial data, as long as the latter exists. In particular, strong solutions are unique within the class of weak solutions

Disorder-Driven Pretransitional Tweed in Martensitic Transformations

Defying the conventional wisdom regarding first--order transitions, {\it solid--solid displacive transformations} are often accompanied by pronounced pretransitional phenomena. Generally, these phenomena are indicative of some mesoscopic lattice deformation that ``anticipates'' the upcoming phase transition. Among these precursive effects is the observation of the so-called ``tweed'' pattern in transmission electron microscopy in a wide variety of materials. We have investigated the tweed deformation in a two dimensional model system, and found that it arises because the compositional disorder intrinsic to any alloy conspires with the natural geometric constraints of the lattice to produce a frustrated, glassy phase. The predicted phase diagram and glassy behavior have been verified by numerical simulations, and diffraction patterns of simulated systems are found to compare well with experimental data. Analytically comparing to alternative models of strain-disorder coupling, we show that the present model best accounts for experimental observations.Comment: 43 pages in TeX, plus figures. Most figures supplied separately in uuencoded format. Three other figures available via anonymous ftp

Controllable motions of compressible simple materials of various types

It is shown that a motion is possible in every compressible homogeneous isotropic simple solid having a certain range of memory, in the presence of a constant body force field, if and only if it is homogeneous and uniformly accelerated after a certain time. In the class of solids having perfect memory, the only motion of this kind which can be smoothly initiated in a body at rest is a rigid one. For the class of solids having finite memory of duration T and initially at rest, the motions of the type considered need be homogeneous and uniformly accelerated only after time T . For those solids having fading memory, the motion must reduce to a fixed homogeneous deformation. Similar results are developed for simple fluids and anisotropic simple solids. Es wird gezeigt, daß in jedem kompressiblen, homogenen und isotropen einfachen Festkörper mit einem gewissen Erinnerungsbereich und in Gegenwart eines konstanten Massenkraftfeldes eine Bewegung dann und nur dann möglich ist, wenn sie homogen und nach einer gewissen Zeit gleichmäßig beschleunigt ist. Bei Festkörpern mit vollkommener Erinnerung ist die einzige Bewegung dieser Art, die bei einem ruhenden Körper glatt eingeleitet werden kann, eine starre. Bei Festkörpern mit begrenzter Erinnerungsdauer T , die anfangs in Ruhe waren, müssen die Bewegungen der betrachteten Art homogen und nur nach der Zeit T gleichmäßig beschleunigt sein. Für Festkörper mit schwindendem Gedächtnis reduziert sich die Bewegung auf eien feste homogene Verformung. Ähnliche Ergebnisse werden für einfache Flüssigkeiten und anisotrope einfache Festkörper entwickelt.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41721/1/707_2005_Article_BF01204714.pd