相关论文: The square sticky disk: crystallization and Gamma-…

Starting from a particle system with short-range interactions, we derive a continuum model for the bending, torsion, and brittle fracture of inextensible rods moving in three-dimensional space. As the number of particles tends to infinity,…

Surface/edge energy is typically modeled as a continuous function of orientation, $\gamma({\bf n})$. We put forward a simple geometric argument that suggests this picture is inadequate for crystals with a non-Bravais lattice structure. In…

We have studied a class of marginally jammed states in a system of hard disks confined in a narrow channel---a quasi-one-dimensional system---whose exponents are not those predicted by theories valid in the infinite dimensional limit. The…

An analytic solution is presented to the three-dimensional problem of steady axisymmetric fluid flow through an accretion disk. The solution has been obtained through a systematic expansion in the small parameter epsilon =H/R (the ratio of…

We consider a variant of Gamow's liquid drop model with an anisotropic surface energy. Under suitable regularity and ellipticity assumptions on the surface tension, Wulff shapes are minimizers in this problem if and only if the surface…

For the contact of two finite portions of interacting rigid crystalline surfaces, we compute the dependence of the pinning energy barrier on the misfit angle and contact area. The resulting data are used to investigate the distribution of…

We consider the axial compression of a thin elastic cylinder placed about a hard cylindrical core. Treating the core as an obstacle, we prove upper and lower bounds on the minimum energy of the cylinder that depend on its relative thickness…

We study wrinkling patterns in a thin elastic annulus subjected to radial stretching within the framework of the F\"oppl--von K\'arm\'an theory. Building on the analysis of the Lam\'e problem in Bella and Kohn, we investigate the asymptotic…

We explore the behavior of two-dimensional patchy colloidal particles with 8 or 10 symmetrically arranged patches by employing Monte-Carlo simulations. The particles interact according to an isotropic pair potential that possesses only one…

A granular-matter model is exactly solved, where disks of two sizes and weights in alternating sequence are confined to a narrow channel. The axis of the channel is horizontal and its plane vertical. Disk sizes and channel width are such…

We derive von-K\'arm\'an plate theory from three dimensional, purely atomistic models with classical particle interaction. This derivation is established as a $\Gamma$-limit when considering the limit where the interatomic distance…

In this paper we derive, by means of $\Gamma$-convergence, the periodically wrinkled plate model starting from three dimensional nonlinear elasticity. We assume that the thickness of the plate is $h^2$ and that the mid-surface of the plate…

Let A be a compact set in the right-half plane and $\Gamma(A)$ the set in $\mathbb{R}^{3}$ obtained by rotating A about the vertical axis. We investigate the support of the limit distribution of minimal energy point charges on $\Gamma(A)$…

The dispersion relation of the high energy optical \pi-plasmons of simple hexagonal intrinsic graphite was calculated within the self-consistent-field approximation. The plasmon frequency \omega_p is determined as functions of the…

We report our theoretical results on the emergence of rectangular- and square-shaped magnetic skyrmion crystals on a centrosymmetric square lattice with magnetic anisotropy. By performing the simulated annealing for a frustrated spin model…

A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. According to the relation between the softness parameter and the size of the microstructure, three different limit models are…

The postulate of the existence of a jamming phase diagram (Liu and Nagel, Nature 396, 21 EP (1998aa)) provides a theoretical basis for the classification of a wide range of amorphous solids (colloidal, molecular and emulsion glasses,…

Particles interacting through long-range attraction and short-range repulsion given by power-laws have been widely used to model physical and biological systems, and to predict or explain many of the patterns they display. Apart from rare…

We focus on the probability distribution function (pdf) $P(\Delta \gamma; \gamma)$ where $\Delta \gamma$ are the {\em measured} strain intervals between plastic events in an athermal strained amorphous solids, and $\gamma$ measures the…

Disks of two sizes and weights in alternating sequence are confined to a long and narrow channel. The axis of the channel is horizontal and its plane vertical. The channel is closed off by pistons that freeze jammed microstates out of loose…