5,117 research outputs found
Double cosets in free groups
In this paper we study double cosets of finite rank free groups. We focus our
attention on cancellation types in double cosets and their formal language
properties.Comment: Minor change
Inferring bulk self-assembly properties from simulations of small systems with multiple constituent species and small systems in the grand canonical ensemble
In this paper we generalize a methodology [T. E. Ouldridge, A. A. Louis, and
J. P. K. Doye, J. Phys.: Condens. Matter {\bf 22}, 104102 (2010)] for dealing
with the inference of bulk properties from small simulations of self-assembling
systems of characteristic finite size. In particular, schemes for extrapolating
the results of simulations of a single self-assembling object to the bulk limit
are established in three cases: for assembly involving multiple particle
species, for systems with one species localized in space and for simulations in
the grand canonical ensemble. Furthermore, methodologies are introduced for
evaluating the accuracy of these extrapolations. Example systems demonstrate
that differences in cluster concentrations between simulations of a single
self-assembling structure and bulk studies of the same model under identical
conditions can be large, and that convergence on bulk results as system size is
increased can be slow and non-trivial.Comment: Accepted by J. Chem. Phy
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
Crystal growth from a supersaturated melt: relaxation of the solid-liquid dynamic stiffness
We discuss the growth process of a crystalline phase out of a metastable
over-compressed liquid that is brought into contact with a crystalline
substrate. The process is modeled by means of molecular dynamics. The particles
interact via the Lennard-Jones potential and their motion is locally
thermalized by Langevin dynamics. We characterize the relaxation process of the
solid-liquid interface, showing that the growth speed is maximal for liquid
densities above the solid coexistence density, and that the structural
properties of the interface rapidly converge to equilibrium-like properties. In
particular, we show that the off-equilibrium dynamic stiffness can be extracted
using capillary wave theory arguments, even if the growth front moves fast
compared to the typical diffusion time of the compressed liquid, and that the
dynamic stiffness converges to the equilibrium stiffness in times much shorter
than the diffusion time
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