End to end distance on contour loops of random gaussian surfaces

A self consistent field theory that describes a part of a contour loop of a random Gaussian surface as a trajectory interacting with itself is constructed. The exponent \nu characterizing the end to end distance is obtained by a Flory argument. The result is compared with different previuos derivations and is found to agree with that of Kondev and Henley over most of the range of the roughening exponent of the random surface.Comment: 7 page

Force correlations and arches formation in granular assemblies

In the context of a simple microscopic schematic scalar model we study the effects of spatial correlations in force transmission in granular assemblies. We show that the parameters of the normalized weights distribution function, $P(v)\sim v^{\alpha}\exp(-v/\phi)$, strongly depend on the spatial extensions, $\xi_V$, of such correlations. We show, then, the connections between measurable macroscopic quantities and microscopic mechanisms enhancing correlations. In particular we evaluate how the exponential cut-off, $\phi(\xi_V)$, and the small forces power law exponent, $\alpha(\xi_V)$, depend on the correlation length, $\xi_V$. If correlations go to infinity, weights are power law distributed.Comment: 6 page

Angoricity and compactivity describe the jamming transition in soft particulate matter

The application of concepts from equilibrium statistical mechanics to out-of-equilibrium systems has a long history of describing diverse systems ranging from glasses to granular materials. For dissipative jammed systems-- particulate grains or droplets-- a key concept is to replace the energy ensemble describing conservative systems by the volume-stress ensemble. Here, we test the applicability of the volume-stress ensemble to describe the jamming transition by comparing the jammed configurations obtained by dynamics with those averaged over the ensemble as a probe of ergodicity. Agreement between both methods suggests the idea of "thermalization" at a given angoricity and compactivity. We elucidate the thermodynamic order of the jamming transition by showing the absence of critical fluctuations in static observables like pressure and volume. The approach allows to calculate observables such as the entropy, volume, pressure, coordination number and distribution of forces to characterize the scaling laws near the jamming transition from a statistical mechanics viewpoint.Comment: 27 pages, 13 figure

Force balance in canonical ensembles of static granular packings

We investigate the role of local force balance in the transition from a microcanonical ensemble of static granular packings, characterized by an invariant stress, to a canonical ensemble. Packings in two dimensions admit a reciprocal tiling, and a collective effect of force balance is that the area of this tiling is also invariant in a microcanonical ensemble. We present analytical relations between stress, tiling area and tiling area fluctuations, and show that a canonical ensemble can be characterized by an intensive thermodynamic parameter conjugate to one or the other. We test the equivalence of different ensembles through the first canonical simulations of the force network ensemble, a model system.Comment: 9 pages, 9 figures, submitted to JSTA

Glassy dynamics in granular compaction

Two models are presented to study the influence of slow dynamics on granular compaction. It is found in both cases that high values of packing fraction are achieved only by the slow relaxation of cooperative structures. Ongoing work to study the full implications of these results is discussed.Comment: 12 pages, 9 figures; accepted in J. Phys: Condensed Matter, proceedings of the Trieste workshop on 'Unifying concepts in glass physics

A variant approach to the overlap action

I describe an implementation of the overlap action, which is built from an action which is itself an approximate overlap action. It appears to be about a factor of 15-20 less expensive to use, than the usual overlap action with the Wilson fermion action as its kernel. Ingredients include a fat link to suppress coupling to dislocations and a free field action with a spectrum which resembles an overlap; much of the gain comes from the use of eigenmodes of the approximate action to begin the overlap calculation. As a physics example, I compute the quark condensate in finite volume in the quenched approximation.Comment: 15 pages, Revtex, postscript figures. COLO-HEP-44

Surface Polymer Network Model and Effective Membrane Curvature Elasticity

A microscopic model of a surface polymer network - membrane system is introduced, with contact polymer surface interactions that can be either repulsive or attractive and sliplinks of functionality four randomly distributed over the supporting membrane surface anchoring the polymers to it. For the supporting surface perturbed from a planar configuration and a small relative number of surface sliplinks, we investigate an expansion of the free energy in terms of the local curvatures of the surface and the surface density of sliplinks, obtained through the application of the Balian - Bloch - Duplantier multiple surface scattering method. As a result, the dependence of the curvature elastic modulus, the Gaussian modulus as well as of the spontaneous curvature of the "dressed" membrane, ~{\sl i.e.} polymer network plus membrane matrix, is obtained on the mean polymer bulk end to end separation and the surface density of sliplinks.Comment: 15 pages with one included compressed uuencoded figure

Emergence of macroscopic temperatures in systems that are not thermodynamical microscopically: towards a thermodynamical description of slow granular rheology

A scenario for systems with slow dynamics is characterised by stating that there are several temperatures coexisting in the sample, with a single temperature shared by all observables at each (widely separate) time-scale. In preparation for the study of granular rheology, we show within this framework that glassy systems with driving and friction that are generic and do not correspond to a thermal bath --- and whose microscopic `fast' motion is hence not thermal --- have a well-defined macroscopic temperature associated to the slow degrees of freedom. This temperature is what a thermometer coupled to the system will measure if tuned to respond to low frequencies, and since it can be related to the number of stationary configurations, it is the formalisation of Edwards' `compactivity' ideas.Comment: Revised version: treatment of `tapping' deferre

Dynamical response functions in models of vibrated granular media

In recently introduced schematic lattice gas models for vibrated dry granular media, we study the dynamical response of the system to small perturbations of shaking amplitudes and its relations with the characteristic fluctuations. Strong off equilibrium features appear and a generalized version of the fluctuation dissipation theorem is introduced. The relations with thermal glassy systems and the role of Edwards' compactivity are discussed.Comment: 12 pages, 2 postscript figure