相关论文: A crystallization result in two dimensions for a s…
We devise a new technique to prove two-dimensional crystallization results in the square lattice for finite particle systems. We apply this strategy to energy minimizers of configurational energies featuring two-body short-ranged particle…
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 investigate two-dimensional crystallization phenomena, i.e. minimality of a lattice's patch for interaction energies, with pair potentials of type $(x,y)\mapsto V(\|x-y\|)$ where $\|\cdot\|$ is an arbitrary norm on $\mathbb{R}^2$ and…
Using concepts from classical density functional theory (DFT) we investigate the freezing of a two-dimensional (2D) system of ultra-soft particles in a one-dimensional (1D) external potential; a phenomenon often called laser-induced…
We show that the emerging field of discrete differential geometry can be usefully brought to bear on crystallization problems. In particular, we give a simplified proof of the Heitmann-Radin crystallization theorem (R. C. Heitmann, C.…
We investigate the formation of cluster crystals with multiply occupied lattice sites on a spherical surface in systems of ultra-soft particles interacting via repulsive, bounded pair potentials. Not all interactions of this kind lead to…
We use numerical simulations to study the crystallization of monodisperse systems of hard aspherical particles. We find that particle shape and crystallizability can be easily related to each other when particles are characterized in terms…
We investigate ground state configurations of atomic systems in two dimensions interacting via short range pair potentials. As the number of particles tends to infinity, we show that low-energy configurations converge to a macroscopic…
A free-energy functional for a crystal proposed by Singh and Singh (Europhys. Lett. {\bf {88}}, 16005 (2009)) and which contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function has been used to…
We simulate a two dimensional model of self-propelled particles confined by a deformable boundary. The particles tend to accumulate near the boundary and the shape of the boundary deforms upon the collisions. We find that there are two…
This work is a continuation of our papers from the last couple of years on the Casimir friction for a pair of particles at low relative velocity. The new element in the present analysis is to allow the media to be dense. Then the situation…
It has been found in numerical experiments that when one removes a sector from an elastic sheet and glues the edges of the sector back together, the resulting configuration is radially symmetric and nearly conical. We make a rigorous…
We consider a variant of the sticky disk energy where distances between particles are evaluated through the sup norm $\lVert\cdot\rVert_\infty$ in the plane. We first prove crystallization of minimizers in the square lattice, for any fixed…
We perform extensive monomer-resolved computer simulations of suitably-designed amphiphilic dendritic macromolecules over a broad range of densities, proving the existence and stability of cluster crystals formed in these systems, as…
The present paper - a continuation of our recent series of papers on Casimir friction for a pair of particles at low relative particle velocity - extends the analysis so as to include dense media. The situation becomes in this case more…
We address the question of whether three-dimensional crystals are minimizers of classical many-body energies. This problem is of conceptual relevance as it presents a significant milestone towards understanding, on the atomistic level,…
The study of singular perturbations of the Dirichlet energy is at the core of the phenomenological-description paradigm in soft condensed matter. Being able to pass to the limit plays a crucial role in the understanding of the…
Systems of soft-core particles interacting via a two-scale potential are studied. The potential is responsible for peaks in the structure factor of the liquid state at two different but comparable length scales, and a similar bimodal…
We describe a family of circular, and elliptical, finite disks with a disk potential that is a power of the radius. These are all flattened ellipsoids, obtained by squashing finite spheres with a power-law density distribution, and cutoff…
We consider a two-dimensional atomic mass spring system and show that in the small displacement regime the corresponding discrete energies can be related to a continuum Griffith energy functional in the sense of Gamma-convergence. We also…