Effect of hydrophobic solutes on the liquid-liquid critical point

Jagla ramp particles, interacting through a ramp potential with two characteristic length scales, are known to show in their bulk phase thermodynamic and dynamic anomalies, similar to what is found in water. Jagla particles also exhibit a line of phase transitions separating a low density liquid phase and a high density liquid phase, terminating in a liquid-liquid critical point in a region of the phase diagram that can be studied by simulations. Employing molecular dynamics computer simulations, we study the thermodynamics and the dynamics of solutions of hard spheres (HS) in a solvent formed by Jagla ramp particles. We consider the cases of HS mole fraction x = 0.10, 0.15 and 0.20, and also the case x = 0.50 (a 1:1 mixture of HS and Jagla particles). We find a liquid-liquid critical point, up to the highest HS mole fraction; its position shifts to higher pressures and lower temperatures upon increasing x. We also find that the diffusion coefficient anomalies appear to be preserved for all the mole fractions studied.Comment: 8 pages, 7 figures, 1 table. In press (Phys. Rev. E

Multifractal Properties of the Random Resistor Network

We study the multifractal spectrum of the current in the two-dimensional random resistor network at the percolation threshold. We consider two ways of applying the voltage difference: (i) two parallel bars, and (ii) two points. Our numerical results suggest that in the infinite system limit, the probability distribution behaves for small current i as P(i) ~ 1/i. As a consequence, the moments of i of order q less than q_c=0 do not exist and all current of value below the most probable one have the fractal dimension of the backbone. The backbone can thus be described in terms of only (i) blobs of fractal dimension d_B and (ii) high current carrying bonds of fractal dimension going from $1/\nu$ to d_B.Comment: 4 pages, 6 figures; 1 reference added; to appear in Phys. Rev. E (Rapid Comm

Aging in short-ranged attractive colloids: A numerical study

We study the aging dynamics in a model for dense simple liquids, in which particles interact through a hard-core repulsion complemented by a short-ranged attractive potential, of the kind found in colloidal suspensions. In this system, at large packing fractions, kinetically arrested disordered states can be created both on cooling (attractive glass) and on heating (repulsive glass). The possibility of having two distinct glasses, at the same packing fraction, with two different dynamics offers the unique possibility of comparing -- within the same model -- the differences in aging dynamics. We find that, while the aging dynamics of the repulsive glass is similar to the one observed in atomic and molecular systems, the aging dynamics of the attractive glass shows novel unexpected features.Comment: 8 pages, 11 figures, submited to Journal of Chemical Physic

Dynamics of Surface Roughening with Quenched Disorder

We study the dynamical exponent $z$ for the directed percolation depinning (DPD) class of models for surface roughening in the presence of quenched disorder. We argue that $z$ for $(d+1)$ dimensions is equal to the exponent $d_{\rm min}$ characterizing the shortest path between two sites in an isotropic percolation cluster in $d$ dimensions. To test the argument, we perform simulations and calculate $z$ for DPD, and $d_{\rm min}$ for percolation, from $d = 1$ to $d = 6$.Comment: RevTex manuscript 3 pages + 6 figures (obtained upon request via email [email protected]

Phase diagram of a two-dimensional system with anomalous liquid properties

Using Monte Carlo simulation techniques, we calculate the phase diagram for a square shoulder-square well potential in two dimensions that has been previously shown to exhibit liquid anomalies consistent with a metastable liquid-liquid critical point. We consider the liquid, gas and five crystal phases, and find that all the melting lines are first order, despite a small range of metastability. One melting line exhibits a temperature maximum, as well as a pressure maximum that implies inverse melting over a small range in pressure.Comment: 11 pages, 13 figure

Statistical Properties of Business Firms Structure and Growth

We analyze a database comprising quarterly sales of 55624 pharmaceutical products commercialized by 3939 pharmaceutical firms in the period 1992--2001. We study the probability density function (PDF) of growth in firms and product sales and find that the width of the PDF of growth decays with the sales as a power law with exponent $\beta = 0.20 \pm 0.01$. We also find that the average sales of products scales with the firm sales as a power law with exponent $\alpha = 0.57 \pm 0.02$. And that the average number products of a firm scales with the firm sales as a power law with exponent $\gamma = 0.42 \pm 0.02$. We compare these findings with the predictions of models proposed till date on growth of business firms