Geometrical Frustration and Static Correlations in Hard-Sphere Glass Formers

We analytically and numerically characterize the structure of hard-sphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated with increasing fluid packing fraction, but to become increasingly irrelevant with increasing dimension. We also find the growth in structural correlations to be modest in the dynamical regime accessible to computer simulations.Comment: 21 pages; part of the "Special Topic Issue on the Glass Transition

Exploiting classical nucleation theory for reverse self-assembly

In this paper we introduce a new method to design interparticle interactions to target arbitrary crystal structures via the process of self-assembly. We show that it is possible to exploit the curvature of the crystal nucleation free-energy barrier to sample and select optimal interparticle interactions for self-assembly into a desired structure. We apply this method to find interactions to target two simple crystal structures: a crystal with simple cubic symmetry and a two-dimensional plane with square symmetry embedded in a three-dimensional space. Finally, we discuss the potential and limits of our method and propose a general model by which a functionally infinite number of different interaction geometries may be constructed and to which our reverse self-assembly method could in principle be applied.Comment: 7 pages, 6 figures. Published in the Journal of Chemical Physic

Some integrals ocurring in a topology change problem

In a paper presented a few years ago, De Lorenci et al. showed, in the context of canonical quantum cosmology, a model which allowed space topology changes (Phys. Rev. D 56, 3329 (1997)). The purpose of this present work is to go a step further in that model, by performing some calculations only estimated there for several compact manifolds of constant negative curvature, such as the Weeks and Thurston spaces and the icosahedral hyperbolic space (Best space).Comment: RevTeX article, 4 pages, 1 figur

Majority-vote model on hyperbolic lattices

We study the critical properties of a non-equilibrium statistical model, the majority-vote model, on heptagonal and dual heptagonal lattices. Such lattices have the special feature that they only can be embedded in negatively curved surfaces. We find, by using Monte Carlo simulations and finite-size analysis, that the critical exponents $1/\nu$, $\beta/\nu$ and $\gamma/\nu$ are different from those of the majority-vote model on regular lattices with periodic boundary condition, which belongs to the same universality class as the equilibrium Ising model. The exponents are also from those of the Ising model on a hyperbolic lattice. We argue that the disagreement is caused by the effective dimensionality of the hyperbolic lattices. By comparative studies, we find that the critical exponents of the majority-vote model on hyperbolic lattices satisfy the hyperscaling relation $2\beta/\nu+\gamma/\nu=D_{\mathrm{eff}}$, where $D_{\mathrm{eff}}$ is an effective dimension of the lattice. We also investigate the effect of boundary nodes on the ordering process of the model.Comment: 8 pages, 9 figure

Quasi Regular Polyhedra and Their Duals with Coxeter Symmetries Represented by Quaternions I

In two series of papers we construct quasi regular polyhedra and their duals which are similar to the Catalan solids. The group elements as well as the vertices of the polyhedra are represented in terms of quaternions. In the present paper we discuss the quasi regular polygons (isogonal and isotoxal polygons) using 2D Coxeter diagrams. In particular, we discuss the isogonal hexagons, octagons and decagons derived from 2D Coxeter diagrams and obtain aperiodic tilings of the plane with the isogonal polygons along with the regular polygons. We point out that one type of aperiodic tiling of the plane with regular and isogonal hexagons may represent a state of graphene where one carbon atom is bound to three neighboring carbons with two single bonds and one double bond. We also show how the plane can be tiled with two tiles; one of them is the isotoxal polygon, dual of the isogonal polygon. A general method is employed for the constructions of the quasi regular prisms and their duals in 3D dimensions with the use of 3D Coxeter diagrams.Comment: 22 pages, 16 figure

A comment on BCC crystalization in higher dimensions

The result that near the melting point three-dimensional crystals have an octahedronic structure is generalized to higher flat non compact dimensions

Hard Discs on the Hyperbolic Plane

We examine a simple hard disc fluid with no long range interactions on the two dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is frustrated, allowing us to construct a tractable model of disordered monodisperse hard discs. We extend free area theory and the virial expansion to this regime, deriving the equation of state for the system, and compare its predictions with simulation near an isostatic packing in the curved space.Comment: 4 pages, 3 figures, included, final versio

The Electron-Phonon Interaction of Low-Dimensional and Multi-Dimensional Materials from He Atom Scattering

Atom scattering is becoming recognized as a sensitive probe of the electron-phonon interaction parameter $\lambda$ at metal and metal-overlayer surfaces. Here, the theory is developed linking $\lambda$ to the thermal attenuation of atom scattering spectra (in particular, the Debye-Waller factor), to conducting materials of different dimensions, from quasi-one dimensional systems such as W(110):H(1$\times$1) and Bi(114), to quasi-two dimensional layered chalcogenides and high-dimensional surfaces such as quasicrystalline 2ML-Ba(0001)/Cu(001) and d-AlNiCo(00001). Values of $\lambda$ obtained using He atoms compare favorably with known values for the bulk materials. The corresponding analysis indicates in addition the number of layers contributing to the electron-phonon interaction that is measured in an atom surface collision.Comment: 23 pages, 5 figures, 1 tabl

Dynamical Arrest in Attractive Colloids: The Effect of Long-Range Repulsion

We study gelation in suspensions of model colloidal particles with short-ranged attractive and long-ranged repulsive interactions by means of three-dimensional fluorescence confocal microscopy. At low packing fractions, particles form stable equilibrium clusters. Upon increasing the packing fraction the clusters grow in size and become increasingly anisotropic until finally associating into a fully connected network at gelation. We find a surprising order in the gel structure. Analysis of spatial and orientational correlations reveals that the gel is composed of dense chains of particles constructed from face-sharing tetrahedral clusters. Our findings imply that dynamical arrest occurs via cluster growth and association.Comment: Final version: Phys. Rev. Lett. 94, 208301 (2005