Extended corresponding-states behavior for particles with variable range attractions

We propose an extension of the law of corresponding states that can be applied to systems - such as colloidal suspensions - that have widely different ranges of attractive interactions. We argue that, for such systems, the ``reduced'' second virial coefficient is a convenient parameter to quantify the effective range of attraction. This procedure allows us to give a simple definition of the effective range of attraction of potentials with different functional forms. The advantage of the present approach is that it allows us to estimate the relative location of the liquid-vapor and solid-fluid coexistence curves exclusively on basis of the knowledge of the pair-potential.Comment: REVTeX, 5 pages, 2 figure

The Structure of Langevin's Memory Kernel From Lagrangian Dynamics

We obtain the memory kernel of the generalized Langevin equation, describing a particle interacting with longitudinal phonons in a liquid. The kernel is obtained analytically at T=0 Kelvin and numerically at T>0 Kelvin. We find that it shows some non-trivial structural features like negative correlations for some range of time separations. The system is shown to have three characteristic time scales, that control the shape of the kernel, and the transition between quadratic and linear behavior of the mean squared distance (MSD). Although the derivation of the structure in the memory kernel is obtained within a specific dynamical model, the phenomenon is shown to be quite generic.Comment: 8 pages, 5 figures, latex, include europhys.sty and euromacr.te

The role of long-range forces in the phase behavior of colloids and proteins

The phase behavior of colloid-polymer mixtures, and of solutions of globular proteins, is often interpreted in terms of a simple model of hard spheres with short-ranged attraction. While such a model yields a qualitative understanding of the generic phase diagrams of both colloids and proteins, it fails to capture one important difference: the model predicts fluid-fluid phase separation in the metastable regime below the freezing curve. Such demixing has been observed for globular proteins, but for colloids it appears to be pre-empted by the appearance of a gel. In this paper, we study the effect of additional long-range attractions on the phase behavior of spheres with short-ranged attraction. We find that such attractions can shift the (metastable) fluid-fluid critical point out of the gel region. As this metastable critical point may be important for crystal nucleation, our results suggest that long-ranged attractive forces may play an important role in the crystallization of globular proteins. However, in colloids, where refractive index matching is often used to switch off long-ranged dispersion forces, gelation is likely to inhibit phase separation.Comment: EURO-LATEX, 6 pages, 2 figure

Constructing quantum vertex algebras

This is a sequel to \cite{li-qva}. In this paper, we focus on the construction of quantum vertex algebras over \C, whose notion was formulated in \cite{li-qva} with Etingof and Kazhdan's notion of quantum vertex operator algebra (over \C[[h]]) as one of the main motivations. As one of the main steps in constructing quantum vertex algebras, we prove that every countable-dimensional nonlocal (namely noncommutative) vertex algebra over \C, which either is irreducible or has a basis of PBW type, is nondegenerate in the sense of Etingof and Kazhdan. Using this result, we establish the nondegeneracy of better known vertex operator algebras and some nonlocal vertex algebras. We then construct a family of quantum vertex algebras closely related to Zamolodchikov-Faddeev algebras.Comment: 37 page

A Generalization of Metropolis and Heat-Bath Sampling for Monte Carlo Simulations

For a wide class of applications of the Monte Carlo method, we describe a general sampling methodology that is guaranteed to converge to a specified equilibrium distribution function. The method is distinct from that of Metropolis in that it is sometimes possible to arrange for unconditional acceptance of trial moves. It involves sampling states in a local region of phase space with probability equal to, in the first approximation, the square root of the desired global probability density function. The validity of this choice is derived from the Chapman-Kolmogorov equation, and the utility of the method is illustrated by a prototypical numerical experiment.Comment: RevTeX, 7 pages, 2 table

Boundary Friction on Molecular Lubricants: Rolling Mode?

A theoretical model is proposed for low temperature friction between two smooth rigid solid surfaces separated by lubricant molecules, admitting their deformations and rotations. Appearance of different modes of energy dissipation (by ''rocking'' or ''rolling'' of lubricants) at slow relative displacement of the surfaces is shown to be accompanied by the stick-and-slip features and reveals a non-monotonic (mean) friction force {\it vs} external loadComment: revtex4, 4 pages, 5 figure