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

On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and Stability

In this paper we investigate the role of Parodi's relation in the well-posedness and stability of the general Ericksen-Leslie system modeling nematic liquid crystal flows. First, we give a formal physical derivation of the Ericksen-Leslie system through an appropriate energy variational approach under Parodi's relation, in which we can distinguish the conservative/dissipative parts of the induced elastic stress. Next, we prove global well-posedness and long-time behavior of the Ericksen-Leslie system under the assumption that the viscosity $\mu_4$ is sufficiently large. Finally, under Parodi's relation, we show the global well-posedness and Lyapunov stability for the Ericksen-Leslie system near local energy minimizers. The connection between Parodi's relation and linear stability of the Ericksen-Leslie system is also discussed

Poisson-Bracket Approach to the Dynamics of Nematic Liquid Crystals. The Role of Spin Angular Momentum

Nematic liquid crystals are well modeled as a fluid of rigid rods. Starting from this model, we use a Poisson-bracket formalism to derive the equations governing the dynamics of nematic liquid crystals. We treat the spin angular momentum density arising from the rotation of constituent molecules about their centers of mass as an independent field and derive equations for it, the mass density, the momentum density, and the nematic director. Our equations reduce to the original Leslie-Ericksen equations, including the inertial director term that is neglected in the hydrodynamic limit, only when the moment of inertia for angular momentum parallel to the director vanishes and when a dissipative coefficient favoring locking of the angular frequencies of director rotation and spin angular momentum diverges. Our equations reduce to the equations of nematohydrodynamics in the hydrodynamic limit but with dissipative coefficients that depend on the coefficient that must diverge to produce the Leslie-Ericksen equations.Comment: 10 pages, to be published in Phys. Rev. E 72(5

Placental histopathology in late preterm infants: clinical implications

Background: The etiopathogenesis of late preterm (LPT) birth is undetermined. Placental histopathology, which reflects an adverse intrauterine environment and is reportedly associated with preterm labor and neonatal morbidities, has not been studied in LPT infants. Purpose: We investigated placental pathological lesion as markers of an adverse intrauterine environment during LPT labor. Methods: This retrospective case-control study compared placental histopathological and clinical variables between LPT and term neonates. Placental variables included chorioamnionitis, funisitis, hemorrhage, abruption, infarction, calcification, and syncytial knots. Maternal variables included age, substance abuse, pregnancyassociated diabetes mellitus and hypertension, duration of rupture of membrane, antibiotic use, and magnesium sulfate, whereas, those of neonates included gestational age, birth weight, race, sex, and Apgar scores. Standard statistical proedures were applied to analyze the data. Results:Chorioamnionitis (50% vs. 17.8%, P Conclusion: Placental infection is not a risk factor for LPT births. There is a nonsignificant predominance of vascular anomalies in LPT placentas. Higher maternal age, magnesium sulfate therapy, and maternal hypertension are clinical risk factors for LPT labor

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

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

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 $R^3$

A shift from cattle to camel and goat farming can sustain milk production with lower inputs and emissions in north sub-Saharan Africa’s drylands

Climate change is increasingly putting milk production from cattle-based dairy systems in north sub-Saharan Africa (NSSA) under stress, threatening livelihoods and food security. Here we combine livestock heat stress frequency, dry matter feed production and water accessibility data to understand where environmental changes in NSSA’s drylands are jeopardizing cattle milk production. We show that environmental conditions worsened for ∼17% of the study area. Increasing goat and camel populations by ∼14% (∼7.7 million) and ∼10% (∼1.2 million), respectively, while reducing the dairy cattle population by ∼24% (∼5.9 million), could result in ∼0.14 Mt (+5.7%) higher milk production, lower water (−1,683.6 million m3, −15.3%) and feed resource (−404.3 Mt, −11.2%) demand—and lower dairy emissions by ∼1,224.6 MtCO2e (−7.9%). Shifting herd composition from cattle towards the inclusion of, or replacement with, goats and camels can secure milk production and support NSSA’s dairy production resilience against climate change