2,161 research outputs found
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
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