Abelian-Higgs-Navier-Stokes Hydrodynamics for Nematic Films with Defects

A new theory of hydrodynamics of uniaxial nematic liquid crystal films in the presence of defects is developed. A gauge field incorporating screening is introduced, resulting in the static elastic free energy having the form of a two-dimensional Abelian-Higgs model. Hydrodynamic equations are derived via the standard methods of de~Groot and Mazur. By working in the vicinity of the Bogomol'nyi equations consequences for defect centre motion are outlined.Comment: 12 page

A scheme for parameterizing cirrus cloud ice water content in general circulation models

Clouds strongly influence th earth's energy budget. They control th amount of solar radiative energy absorbed by the climate system, partitioning the energy between the atmosphere and the earth's surface. They also control the loss of energy to space by their effect on thermal emission. Cirrus and altostratus are the most frequent cloud types, having an annual average global coverage of 35 and 40 percent, respectively. Cirrus is composed almost entirely of ice crystals and the same is frequently true of the upper portions of altostratus since they are often formed by the thickening of cirrostratus and by the spreading of the middle or upper portions of thunderstorms. Thus, since ice clouds cover such a large portion of the earth's surface, they almost certainly have an important effect on climate. With this recognition, researchers developing climate models are seeking largely unavailable methods for specifying the conditions for ice cloud formation, and quantifying the spatial distribution of ice water content, IWC, a necessary step in deriving their radiative characteristics since radiative properties are apparently related to IWC. A method is developed for specifying IWC in climate models, based on theory and measurements in cirrus during FIRE and other experiments

Continuum elasticity theory of edge excitations in a two-dimensional electron liquid with finite range interactions

We make use of continuum elasticity theory to investigate the collective modes that propagate along the edge of a two-dimensional electron liquid or crystal in a magnetic field. An exact solution of the equations of motion is obtained with the following simplifying assumptions: (i) The system is {\it macroscopically} homogeneous and isotropic in the half-plane delimited by the edge (ii) The electron-electron interaction is of finite range due to screening by external electrodes (iii) The system is nearly incompressible. At sufficiently small wave vector $q$ we find a universal dispersion curve $\omega \sim q$ independent of the shear modulus. At larger wave vectors the dispersion can change its form in a manner dependent on the comparison of various length scales. We obtain analytical formulas for the dispersion and damping of the modes in various physical regimes.Comment: 3 figure

On the accuracy of the melting curves drawn from modelling a solid as an elastic medium

An ongoing problem in the study of a classical many-body system is the characterization of its equilibrium behaviour by theory or numerical simulation. For purely repulsive particles, locating the melting line in the pressure-temperature plane can be especially hard if the interparticle potential has a softened core or contains some adjustable parameters. A method is hereby presented that yields reliable melting-curve topologies with negligible computational effort. It is obtained by combining the Lindemann melting criterion with a description of the solid phase as an elastic continuum. A number of examples are given in order to illustrate the scope of the method and possible shortcomings. For a two-body repulsion of Gaussian shape, the outcome of the present approach compares favourably with the more accurate but also more computationally demanding self-consistent harmonic approximation.Comment: 25 pages, 7 figure

Magnetoelasticity theory of incompressible quantum Hall liquids

A simple and physically transparent magnetoelasticity theory is proposed to describe linear dynamics of incompressible fractional quantum Hall states. The theory manifestly satisfies the Kohn theorem and the $f$-sum rule, and predicts a gaped intra-Landau level collective mode with a roton minimum. In the limit of vanishing bare mass $m$ the correct form of the static structure factor, $s(q)\sim q^4$, is recovered. We establish a connection of the present approach to the fermionic Chern-Simons theory, and discuss further extensions and applications. We also make an interesting analogy of the present theory to the theory of visco-elastic fluids.Comment: RevTeX 4, 6 pages; expanded version to appear in PRB; more technical details, and discussions of the physics adde