Model for Glass Transition in a Binary fluid from a Mode Coupling approach

We consider the Mode Coupling Theory (MCT) of Glass transition for a Binary fluid. The Equations of Nonlinear Fluctuating Hydrodynamics are obtained with a proper choice of the slow variables corresponding to the conservation laws. The resulting model equations are solved in the long time limit to locate the dynamic transition. The transition point from our model is considerably higher than predicted in existing MCT models for binary systems. This is in agreement with what is seen in Computer Simulation of binary fluids. fluids.Comment: 9 Pages, 3 Figure

Clusters in weighted macroeconomic networks : the EU case. Introducing the overlapping index of GDP/capita fluctuation correlations

GDP/capita correlations are investigated in various time windows (TW), for the time interval 1990-2005. The target group of countries is the set of 25 EU members, 15 till 2004 plus the 10 countries which joined EU later on. The TW-means of the statistical correlation coefficients are taken as the weights (links) of a fully connected network having the countries as nodes. Thereafter we define and introduce the overlapping index of weighted network nodes. A cluster structure of EU countries is derived from the statistically relevant eigenvalues and eigenvectors of the adjacency matrix. This may be considered to yield some information about the structure, stability and evolution of the EU country clusters in a macroeconomic sense.Comment: 6 pages, 8 figures, 1 table, 17 references, submitted to Physica A; proceedings of APFA

Fluctuation-Dissipation relations in Driven Granular Gases

We study the dynamics of a 2d driven inelastic gas, by means of Direct Simulation Monte Carlo (DSMC) techniques, i.e. under the assumption of Molecular Chaos. Under the effect of a uniform stochastic driving in the form of a white noise plus a friction term, the gas is kept in a non-equilibrium Steady State characterized by fractal density correlations and non-Gaussian distributions of velocities; the mean squared velocity, that is the so-called {\em granular temperature}, is lower than the bath temperature. We observe that a modified form of the Kubo relation, which relates the autocorrelation and the linear response for the dynamics of a system {\em at equilibrium}, still holds for the off-equilibrium, though stationary, dynamics of the systems under investigation. Interestingly, the only needed modification to the equilibrium Kubo relation is the replacement of the equilibrium temperature with an effective temperature, which results equal to the global granular temperature. We present two independent numerical experiment, i.e. two different observables are studied: (a) the staggered density current, whose response to an impulsive shear is proportional to its autocorrelation in the unperturbed system and (b) the response of a tracer to a small constant force, switched on at time $t_w$, which is proportional to the mean-square displacement in the unperturbed system. Both measures confirm the validity of Kubo's formula, provided that the granular temperature is used as the proportionality factor between response and autocorrelation, at least for not too large inelasticities.Comment: 11 pages, 7 figures, submitted for publicatio

Density functional theory of phase coexistence in weakly polydisperse fluids

The recently proposed universal relations between the moments of the polydispersity distributions of a phase-separated weakly polydisperse system are analyzed in detail using the numerical results obtained by solving a simple density functional theory of a polydisperse fluid. It is shown that universal properties are the exception rather than the rule.Comment: 10 pages, 2 figures, to appear in PR

Crossover between Equilibrium and Shear-controlled Dynamics in Sheared Liquids

We present a numerical simulation study of a simple monatomic Lennard-Jones liquid under shear flow, as a function of both temperature and shear rate. By investigating different observables we find that i) It exists a line in the (temperature-shear) plane that sharply marks the boarder between an ``equilibrium'' and a ``shear-controlled'' region for both the dynamic and the thermodynamic quantities; and ii) Along this line the structural relaxation time, is proportional to the inverse shear rate, i.e. to the typical time-scale introduced by the shear flow. Above the line the liquid dynamics is unaffected by the shear flow, while below it both temperature and shear rate control the particle motion.Comment: 14 pages, 5 figure

Attractive Interactions Between Rod-like Polyelectrolytes: Polarization, Crystallization, and Packing

We study the attractive interactions between rod-like charged polymers in solution that appear in the presence of multi-valence counterions. The counterions condensed to the rods exhibit both a strong transversal polarization and a longitudinal crystalline arrangement. At short distances between the rods, the fraction of condensed counterions increases, and the majority of these occupy the region between the rods, where they minimize their repulsive interactions by arranging themselves into packing structures. The attractive interaction is strongest for multivalent counterions. Our model takes into account the hard-core volume of the condensed counterions and their angular distribution around the rods. The hard core constraint strongly suppresses longitudinal charge fluctuations.Comment: 4 figures, uses revtex, psfig and epsf. The new version contains a different introduction, and the bibliography has been expande

Charge Fluctuations on Membrane Surfaces in Water

We generalize the predictions for attractions between over-all neutral surfaces induced by charge fluctuations/correlations to non-uniform systems that include dielectric discontinuities, as is the case for mixed charged lipid membranes in an aqueous solution. We show that the induced interactions depend in a non-trivial way on the dielectric constants of membrane and water and show different scaling with distance depending on these properties. The generality of the calculations also allows us to predict under which dielectric conditions the interaction will change sign and become repulsive

Offsprings of a point vortex

The distribution engendered by successive splitting of one point vortex are considered. The process of splitting a vortex in three using a reverse three-point vortex collapse course is analysed in great details and shown to be dissipative. A simple process of successive splitting is then defined and the resulting vorticity distribution and vortex populations are analysed

Shear yielding of amorphous glassy solids: Effect of temperature and strain rate

We study shear yielding and steady state flow of glassy materials with molecular dynamics simulations of two standard models: amorphous polymers and bidisperse Lennard-Jones glasses. For a fixed strain rate, the maximum shear yield stress and the steady state flow stress in simple shear both drop linearly with increasing temperature. The dependence on strain rate can be described by a either a logarithm or a power-law added to a constant. In marked contrast to predictions of traditional thermal activation models, the rate dependence is nearly independent of temperature. The relation to more recent models of plastic deformation and glassy rheology is discussed, and the dynamics of particles and stress in small regions is examined in light of these findings

Scaling properties in off equilibrium dynamical processes

In the present paper, we analyze the consequences of scaling hypotheses on dynamic functions, as two times correlations $C(t,t')$. We show, under general conditions, that $C(t,t')$ must obey the following scaling behavior $C(t,t') = \phi_1(t)^{f(\beta)}{\cal{S}}(\beta)$, where the scaling variable is $\beta=\beta(\phi_1(t')/\phi_1(t))$ and $\phi_1(t')$, $\phi_1(t)$ two undetermined functions. The presence of a non constant exponent $f(\beta)$ signals the appearance of multiscaling properties in the dynamics.Comment: 6 pages, no figure