1,570 research outputs found
Critical jamming of frictional grains in the generalized isostaticity picture
While frictionless spheres at jamming are isostatic, frictional spheres at
jamming are not. As a result, frictional spheres near jamming do not
necessarily exhibit an excess of soft modes. However, a generalized form of
isostaticity can be introduced if fully mobilized contacts at the Coulomb
friction threshold are considered as slipping contacts. We show here that, in
this framework, the vibrational density of states (DOS) of frictional discs
exhibits a plateau when the generalized isostaticity line is approached. The
crossover frequency to elastic behavior scales linearly with the distance from
this line. Moreover, we show that the frictionless limit, which appears
singular when fully mobilized contacts are treated elastically, becomes smooth
when fully mobilized contacts are allowed to slip.Comment: 4 pages, 4 figures, submitted to PR
Gauss Sums and Quantum Mechanics
By adapting Feynman's sum over paths method to a quantum mechanical system
whose phase space is a torus, a new proof of the Landsberg-Schaar identity for
quadratic Gauss sums is given. In contrast to existing non-elementary proofs,
which use infinite sums and a limiting process or contour integration, only
finite sums are involved. The toroidal nature of the classical phase space
leads to discrete position and momentum, and hence discrete time. The
corresponding `path integrals' are finite sums whose normalisations are derived
and which are shown to intertwine cyclicity and discreteness to give a finite
version of Kelvin's method of images.Comment: 14 pages, LaTe
Annular electroconvection with shear
We report experiments on convection driven by a radial electrical force in
suspended annular smectic A liquid crystal films. In the absence of an
externally imposed azimuthal shear, a stationary one-dimensional (1D) pattern
consisting of symmetric vortex pairs is formed via a supercritical transition
at the onset of convection. Shearing reduces the symmetries of the base state
and produces a traveling 1D pattern whose basic periodic unit is a pair of
asymmetric vortices. For a sufficiently large shear, the primary bifurcation
changes from supercritical to subcritical. We describe measurements of the
resulting hysteresis as a function of the shear at radius ratio . This simple pattern forming system has an unusual combination of
symmetries and control parameters and should be amenable to quantitative
theoretical analysis.Comment: 12 preprint pages, 3 figures in 2 parts each. For more info, see
http://mobydick.physics.utoronto.c
On elliptic solutions of the cubic complex one-dimensional Ginzburg-Landau equation
The cubic complex one-dimensional Ginzburg-Landau equation is considered.
Using the Hone's method, based on the use of the Laurent-series solutions and
the residue theorem, we have proved that this equation has neither elliptic
standing wave nor elliptic travelling wave solutions. This result amplifies the
Hone's result, that this equation has no elliptic travelling wave solutions.Comment: LaTeX, 12 page
Density of states in random lattices with translational invariance
We propose a random matrix approach to describe vibrational excitations in
disordered systems. The dynamical matrix M is taken in the form M=AA^T where A
is some real (not generally symmetric) random matrix. It guaranties that M is a
positive definite matrix which is necessary for mechanical stability of the
system. We built matrix A on a simple cubic lattice with translational
invariance and interaction between nearest neighbors. We found that for certain
type of disorder phonons cannot propagate through the lattice and the density
of states g(w) is a constant at small w. The reason is a breakdown of affine
assumptions and inapplicability of the elasticity theory. Young modulus goes to
zero in the thermodynamic limit. It strongly reminds of the properties of a
granular matter at the jamming transition point. Most of the vibrations are
delocalized and similar to diffusons introduced by Allen, Feldman et al., Phil.
Mag. B v.79, 1715 (1999).Comment: 4 pages, 5 figure
Doppler Effect of Nonlinear Waves and Superspirals in Oscillatory Media
Nonlinear waves emitted from a moving source are studied. A meandering spiral
in a reaction-diffusion medium provides an example, where waves originate from
a source exhibiting a back-and-forth movement in radial direction. The periodic
motion of the source induces a Doppler effect that causes a modulation in
wavelength and amplitude of the waves (``superspiral''). Using the complex
Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus
instability can exhibit monotonous growth or decay as well as saturation of
these modulations away from the source depending on the perturbation frequency.
Our findings allow a consistent interpretation of recent experimental
observations concerning superspirals and their decay to spatio-temporal chaos.Comment: 4 pages, 4 figure
Dynamics of localized structures in vector waves
Dynamical properties of topological defects in a twodimensional complex
vector field are considered. These objects naturally arise in the study of
polarized transverse light waves. Dynamics is modeled by a Vector Complex
Ginzburg-Landau Equation with parameter values appropriate for linearly
polarized laser emission. Creation and annihilation processes, and
selforganization of defects in lattice structures, are described. We find
"glassy" configurations dominated by vectorial defects and a melting process
associated to topological-charge unbinding.Comment: 4 pages, 5 figures included in the text. To appear in Phys. Rev.
Lett. (2000). Related material at http://www.imedea.uib.es/Nonlinear and
http://www.imedea.uib.es/Photonics . In this new version, Fig. 3 has been
replaced by a better on
Phase chaos in the anisotropic complex Ginzburg-Landau Equation
Of the various interesting solutions found in the two-dimensional complex
Ginzburg-Landau equation for anisotropic systems, the phase-chaotic states show
particularly novel features. They exist in a broader parameter range than in
the isotropic case, and often even broader than in one dimension. They
typically represent the global attractor of the system. There exist two
variants of phase chaos: a quasi-one dimensional and a two-dimensional
solution. The transition to defect chaos is of intermittent type.Comment: 4 pages RevTeX, 5 figures, little changes in figures and references,
typos removed, accepted as Rapid Commun. in Phys. Rev.
Sparse random matrices and vibrational spectra of amorphous solids
A random matrix approach is used to analyze the vibrational properties of
amorphous solids. We investigated a dynamical matrix M=AA^T with non-negative
eigenvalues. The matrix A is an arbitrary real NxN sparse random matrix with n
independent non-zero elements in each row. The average values =0 and
dispersion =V^2 for all non-zero elements. The density of vibrational
states g(w) of the matrix M for N,n >> 1 is given by the Wigner quarter circle
law with radius independent of N. We argue that for n^2 << N this model can be
used to describe the interaction of atoms in amorphous solids. The level
statistics of matrix M is well described by the Wigner surmise and corresponds
to repulsion of eigenfrequencies. The participation ratio for the major part of
vibrational modes in three dimensional system is about 0.2 - 0.3 and
independent of N. Together with term repulsion it indicates clearly to the
delocalization of vibrational excitations. We show that these vibrations spread
in space by means of diffusion. In this respect they are similar to diffusons
introduced by Allen, Feldman, et al., Phil. Mag. B 79, 1715 (1999) in amorphous
silicon. Our results are in a qualitative and sometimes in a quantitative
agreement with molecular dynamic simulations of real and model glasses.Comment: 24 pages, 7 figure
Examine the species and beam-energy dependence of particle spectra using Tsallis Statistics
Tsallis Statistics was used to investigate the non-Boltzmann distribution of
particle spectra and their dependence on particle species and beam energy in
the relativistic heavy-ion collisions at SPS and RHIC. Produced particles are
assumed to acquire radial flow and be of non-extensive statistics at
freeze-out. J/psi and the particles containing strangeness were examined
separately to study their radial flow and freeze-out. We found that the strange
hadrons approach equilibrium quickly from peripheral to central A+A collisions
and they tend to decouple earlier from the system than the light hadrons but
with the same final radial flow. These results provide an alternative picture
of freeze-outs: a thermalized system is produced at partonic phase; the
hadronic scattering at later stage is not enough to maintain the system in
equilibrium and does not increase the radial flow of the copiously produced
light hadrons. The J/psi in Pb+Pb collisions at SPS is consistent with early
decoupling and obtains little radial flow. The J/psi spectra at RHIC are also
inconsistent with the bulk flow profile.Comment: 12 pages, 4 figures, added several references and some clarifications
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