Noise from metallic surfaces -- effects of charge diffusion

Non-local electrodynamic models are developed for describing metallic surfaces for a diffusive metal. The electric field noise at a distance z_0 from the surface is evaluated and compared with data from ion chips that show anomalous heating with a noise power decaying as z_0^{-4}. We find that high surface diffusion can account for the latter result.Comment: 16 pages, 2 figures. Revised version focusing on charge diffusing and anomalous heatin

Shear-induced crystallization of a dense rapid granular flow: hydrodynamics beyond the melting point?

We investigate shear-induced crystallization in a very dense flow of mono-disperse inelastic hard spheres. We consider a steady plane Couette flow under constant pressure and neglect gravity. We assume that the granular density is greater than the melting point of the equilibrium phase diagram of elastic hard spheres. We employ a Navier-Stokes hydrodynamics with constitutive relations all of which (except the shear viscosity) diverge at the crystal packing density, while the shear viscosity diverges at a smaller density. The phase diagram of the steady flow is described by three parameters: an effective Mach number, a scaled energy loss parameter, and an integer number m: the number of half-oscillations in a mechanical analogy that appears in this problem. In a steady shear flow the viscous heating is balanced by energy dissipation via inelastic collisions. This balance can have different forms, producing either a uniform shear flow or a variety of more complicated, nonlinear density, velocity and temperature profiles. In particular, the model predicts a variety of multi-layer two-phase steady shear flows with sharp interphase boundaries. Such a flow may include a few zero-shear (solid-like) layers, each of which moving as a whole, separated by fluid-like regions. As we are dealing with a hard sphere model, the granulate is fluidized within the "solid" layers: the granular temperature is non-zero there, and there is energy flow through the boundaries of the "solid" layers. A linear stability analysis of the uniform steady shear flow is performed, and a plausible bifurcation diagram of the system, for a fixed m, is suggested. The problem of selection of m remains open.Comment: 11 pages, 7 eps figures, to appear in PR

Strong contraction of the representations of the three dimensional Lie algebras

For any Inonu-Wigner contraction of a three dimensional Lie algebra we construct the corresponding contractions of representations. Our method is quite canonical in the sense that in all cases we deal with realizations of the representations on some spaces of functions; we contract the differential operators on those spaces along with the representation spaces themselves by taking certain pointwise limit of functions. We call such contractions strong contractions. We show that this pointwise limit gives rise to a direct limit space. Many of these contractions are new and in other examples we give a different proof

Singular solutions of the L^2-supercritical biharmonic Nonlinear Schrodinger equation

We use asymptotic analysis and numerical simulations to study peak-type singular solutions of the supercritical biharmonic NLS. These solutions have a quartic-root blowup rate, and collapse with a quasi self-similar universal profile, which is a zero-Hamiltonian solution of a fourth-order nonlinear eigenvalue problem

Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation

We present new singular solutions of the biharmonic nonlinear Schrodinger equation in dimension d and nonlinearity exponent 2\sigma+1. These solutions collapse with the quasi self-similar ring profile, with ring width L(t) that vanishes at singularity, and radius proportional to L^\alpha, where \alpha=(4-\sigma)/(\sigma(d-1)). The blowup rate of these solutions is 1/(3+\alpha) for 4/d\le\sigma<4, and slightly faster than 1/4 for \sigma=4. These solutions are analogous to the ring-type solutions of the nonlinear Schrodinger equation.Comment: 21 pages, 13 figures, research articl

Interference in presence of Dissipation

We study a particle on a ring in presence of various dissipative environments. We develop and solve a variational scheme assuming low frequency dominance. We analyze our solution within a renormalization group (RG) scheme to all orders which reproduces a 2 loop RG for the Caldeira-Legget environment. In the latter case the Aharonov-Bohm (AB) oscillation amplitude is exponential in -R^2 where R is the ring's radius. For either a charge or an electric dipole coupled to a dirty metal we find that the metal induces dissipation, however the AB amplitude is ~ R^{-2} for large R, as for free particles. Cold atoms with a large electric dipole may show a crossover between these two behaviors.Comment: 5 pages, added motivations and reference

Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas

We employ Navier-Stokes granular hydrodynamics to investigate the long-time behavior of clustering instability in a freely cooling dilute granular gas in two dimensions. We find that, in circular containers, the homogeneous cooling state (HCS) of the gas loses its stability via a sub-critical pitchfork bifurcation. There are no time-independent solutions for the gas density in the supercritical region, and we present analytical and numerical evidence that the gas develops thermal collapse unarrested by heat diffusion. To get more insight, we switch to a simpler geometry of a narrow-sector-shaped container. Here the HCS loses its stability via a transcritical bifurcation. For some initial conditions a time-independent inhomogeneous density profile sets in, qualitatively similar to that previously found in a narrow-channel geometry. For other initial conditions, however, the dilute gas develops thermal collapse unarrested by heat diffusion. We determine the dynamic scalings of the flow close to collapse analytically and verify them in hydrodynamic simulations. The results of this work imply that, in dimension higher than one, Navier-Stokes hydrodynamics of a dilute granular gas is prone to finite-time density blowups. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.Comment: 18 pages, 19 figure