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

Waiting and Residence Times of Brownian Interface Fluctuations

We report on the residence times of capillary waves above a given height $h$ and on the typical waiting time in between such fluctuations. The measurements were made on phase separated colloid-polymer systems by laser scanning confocal microscopy. Due to the Brownian character of the process, the stochastics vary with the chosen measurement interval $\Delta t$. In experiments, the discrete scanning times are a practical cutoff and we are able to measure the waiting time as a function of this cutoff. The measurement interval dependence of the observed waiting and residence times turns out to be solely determined by the time dependent height-height correlation function $g(t)$. We find excellent agreement with the theory presented here along with the experiments.Comment: 5 figure

Effects of Transport Memory and Nonlinear Damping in a Generalized Fisher's Equation

Memory effects in transport require, for their incorporation into reaction diffusion investigations, a generalization of traditional equations. The well-known Fisher's equation, which combines diffusion with a logistic nonlinearity, is generalized to include memory effects and traveling wave solutions of the equation are found. Comparison is made with alternate generalization procedures.Comment: 6 pages, 4 figures, RevTeX

Existence and Stability of Steady Fronts in Bistable CML

We prove the existence and we study the stability of the kink-like fixed points in a simple Coupled Map Lattice for which the local dynamics has two stable fixed points. The condition for the existence allows us to define a critical value of the coupling parameter where a (multi) generalized saddle-node bifurcation occurs and destroys these solutions. An extension of the results to other CML's in the same class is also displayed. Finally, we emphasize the property of spatial chaos for small coupling.Comment: 18 pages, uuencoded PostScript file, J. Stat. Phys. (In press

A Potential of Interaction between Two- and Three-Dimensional Solitons

A general method to find an effective potential of interaction between far separated 2D and 3D solitons is elaborated, including the case of 2D vortex solitons. The method is based on explicit calculation of the overlapping term in the full Hamiltonian of the system (_without_ assuming that the ``tail'' of each soliton is not affected by its interaction with the other soliton, and, in fact,_without_ knowing the exact form of the solution for an isolated soliton - the latter problem is circumvented by reducing a bulk integral to a surface one). The result is obtained in an explicit form that does not contain an artificially introduced radius of the overlapping region. The potential applies to spatial and spatiotemporal solitons in nonlinear optics, where it may help to solve various dynamical problems: collisions, formation of bound states (BS's), etc. In particular, an orbiting BS of two solitons is always unstable. In the presence of weak dissipation and gain, the effective potential can also be derived, giving rise to bound states similar to those recently studied in 1D models.Comment: 29 double-spaced pages in the latex format and 1 figure in the ps format. The paper will appear in Phys. Rev.

Localization behavior of vibrational modes in granular packings

We study the localization of vibrational modes of frictionless granular media. We introduce a new method, motivated by earlier work on non-Hermitian quantum problems, which works well both in the localized regime where the localization length $\xi$ is much less than the linear size $L$ and in the regime $\xi$ grater or of order $L$ when modes are extended throughout our finite system. Our very lowest frequency modes show "quasi-localized" resonances away from the jamming point; the spatial extent of these regions increases as the jamming point is approached, as expected theoretically. Throughout the remaining frequency range, our data show no signature of the nearness of the jamming point and collapse well when properly rescaled with the system size. Using Random Matrix Theory we derive the scaling relation $\xi$ ~ $L^{d/2}$ for the regime $\xi$ >> $L$ in $d$ dimensions.Comment: 6 pages, 7 figure

The gas of elastic quantum strings in 2+1 dimensions: finite temperatures

The finite temperature physics of the gas of elastic quantum strings as introduced in J. Zaanen, Phys. Rev. Lett. 84, 753 is investigated. This model is inspired on the stripes in the high Tc superconductors. We analyze in detail how the kinetic interactions of the zero temperature quantum problem crossover into the entropic interactions of the high temperature limit.Comment: 14 pages, 2 figure

Kinks Dynamics in One-Dimensional Coupled Map Lattices

We examine the problem of the dynamics of interfaces in a one-dimensional space-time discrete dynamical system. Two different regimes are studied : the non-propagating and the propagating one. In the first case, after proving the existence of such solutions, we show how they can be described using Taylor expansions. The second situation deals with the assumption of a travelling wave to follow the kink propagation. Then a comparison with the corresponding continuous model is proposed. We find that these methods are useful in simple dynamical situations but their application to complex dynamical behaviour is not yet understood.Comment: 17pages, LaTex,3 fig available on cpt.univ-mrs.fr directory pub/preprints/94/dynamical-systems/94-P.307

Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation

In evolution equations for a complex amplitude, the phase obeys a much more intricate equation than the amplitude. Nevertheless, general methods should be applicable to both variables. On the example of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation (CGL5), we explain how to overcome the difficulties arising in two such methods: (i) the criterium that the sum of residues of an elliptic solution should be zero, (ii) the construction of a first order differential equation admitting the given equation as a differential consequence (subequation method).Comment: 12 pages, no figure, to appear, Theoretical and Mathematical Physic