737 research outputs found
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
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
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 , and 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
, where 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
On the epistemic view of quantum states
We investigate the strengths and limitations of the Spekkens toy model, which
is a local hidden variable model that replicates many important properties of
quantum dynamics. First, we present a set of five axioms that fully encapsulate
Spekkens' toy model. We then test whether these axioms can be extended to
capture more quantum phenomena, by allowing operations on epistemic as well as
ontic states. We discover that the resulting group of operations is isomorphic
to the projective extended Clifford Group for two qubits. This larger group of
operations results in a physically unreasonable model; consequently, we claim
that a relaxed definition of valid operations in Spekkens' toy model cannot
produce an equivalence with the Clifford Group for two qubits. However, the new
operations do serve as tests for correlation in a two toy bit model, analogous
to the well known Horodecki criterion for the separability of quantum states.Comment: 16 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
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
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 at metal and metal-overlayer
surfaces. Here, the theory is developed linking 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(11) 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
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
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