6,996 research outputs found
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
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