Related papers: Rigorous Probabilistic Analysis of Equilibrium Cry…
A continuum model of crystalline solid equilibrium is presented in which the underlying periodic lattice structure is taken explicitly into account. This model also allows for both point and line defects in the bulk of the lattice and at…
We present two-dimensional crystallization results in the square lattice for finite particle systems consisting of two different atomic types. We identify energy minimizers of configurational energies featuring two-body short-ranged…
We address finite crystallization in two dimensions in the presence of a flat crystalline substrate. Particles interact through short-range two- and three-body potentials favoring local square-lattice arrangements. An additional interaction…
We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air- or fluid-liquid crystal interfaces…
An equilibrium theory of classical fluids based on the space distribution among the particles is derived in the framework of the energy minimization method. This study is motivated by current difficulties of evaluation of optical properties…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
A generalised Wulf-Kaishew theorem is given describing the equilibrium shape (ES) of an isolated 3D crystal A deposited coherently onto a lattice mismatched planar substrate. For this purpose a free polyhedral crystal is formed then…
We use surface tension to distinguish between phases with isotropic internal structure from phases which are microscopically anisotropic. There are many interesting open problems, especially in two dimensions, and in phase coexistence.
The present work revisits the classical Wulff problem restricted to crystalline integrands, a class of surface energies that gives rise to finitely faceted crystals. The general proof of the Wulff theorem was given by J.E. Taylor (1978) by…
A critical examination of some basic conceptual issues in classical statistical mechanics is attempted, with a view to understanding the origins, structure and statuts of that discipline. Due attention is given to the interplay between…
Strong correlation effects in classical and quantum plasmas are discussed. In particular, Coulomb (Wigner) crystallization phenomena are reviewed focusing on one-component non-neutral plasmas in traps and on macroscopic two-component…
Ultrastable glasses have risen to prominence due to their potentially useful material properties and the tantalizing possibility of a general method of preparation via vapor deposition. Despite the importance of this novel class of…
We consider a system of $N$ hard spheres sitting on the nodes of either the $\mathrm{FCC}$ or $\mathrm{HCP}$ lattice and interacting via a sticky-disk potential. As $N$ tends to infinity (continuum limit), assuming the interaction energy…
Relevant and fundamental concepts of the statistical mechanical theory of classical liquids are ordinarily introduced in the context of the description of thermodynamic equilibrium states. This makes explicit reference to probability…
Molecular crystals often exist in multiple competing polymorphs, showing significantly different physico-chemical properties. Computational crystal structure prediction is key to interpret and guide the search for the most stable or useful…
In self-gravitating stars, two dimensional or geophysical flows and in plasmas, long range interactions imply a lack of additivity for the energy; as a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with…
Statistical equilibrium models of coherent structures in two-dimensional and barotropic quasi-geostrophic turbulence are formulated using canonical and microcanonical ensembles, and the equivalence or nonequivalence of ensembles is…
The local equilibrium approach previously developed by the Authors [J. Mabillard and P. Gaspard, J. Stat. Mech. (2020) 103203] for matter with broken symmetries is applied to crystalline solids. The macroscopic hydrodynamics of crystals and…
We investigate the dynamics of $N$ point vortices in the plane, in the limit of large $N$. We consider {\em relative equilibria}, which are rigidly rotating lattice-like configurations of vortices. These configurations were observed in…
We develop a rigorous framework for modelling the geometry equilibration of crystalline defects. We formulate the equilibration of crystal defects as a variational problems on a discrete energy space and establish qualitatively sharp…