Related papers: Classifying minimum energy states for interacting …
We study one-dimensional hardcore lattice gases, with nearest-neighbor interactions, in the presence of an external potential barrier, that moves on the periodic lattice with a constant speed. We investigate how the nature of the…
Motivated by applications to cell biology, we study the constrained minimization of the Helfrich energy among closed surfaces confined to a container. We show existence of minimizers in the class of bubble trees of spherical weak branched…
We report on self-assemblies formed from spherical patchy particles interacting by a long-range attraction through a patch region in a two-dimensional system. We performed Monte Carlo simulations to find stable structures in a system with…
The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional in the class of $\mathbb{S}^2$-valued maps defined in cylindrical surfaces. The model naturally arises as a curved thin-film limit in the theories of…
In this paper we look for minimizers of the energy functional for isotropic compressible elasticity taking into consideration the effect of a gravitational field induced by the body itself. We consider the displacement problem in which the…
3D kinetic-scale turbulence is studied numerically in the regime where electrons are strongly magnetized (the ratio of plasma species pressure to magnetic pressure is $\beta_e=0.1$ for electrons and $\beta_i=1$ for ions). Such a regime is…
We consider the dynamics of particle systems where the particles are confined by impenetrable barriers to a bounded, possibly non-convex domain $\Omega$. When particles hit the boundary, we consider an instant change in velocity, which…
This paper is motivated by the complex blister patterns sometimes seen in thin elastic films on thick, compliant substrates. These patterns are often induced by an elastic misfit which compresses the film. Blistering permits the film to…
We study a quantum mechanical system consisting of up to three identical dipoles confined to move along a helical shaped trap. The long-range interactions between particles confined to move in this one dimension leads to an interesting…
We report on a study of a classical, finite system of confined particles in two dimensions with a two-body repulsive interaction. We first develop a simple analytical method to obtain equilibrium configurations and energies for few…
In biomimetic and biological systems, interactions between surfaces are often mediated by adhesive molecules, nanoparticles, or colloids dispersed in the surrounding solution. We present here a general, statistical-mechanical model for two…
Collective behavior is all around us, from flocks of birds to schools of fish. These systems are immensely complex, which makes it pertinent to study their behavior through minimal models. We introduce such a minimal model for cohesive and…
We consider a classical system of point particles interacting by means of a short range potential. We prove that, in the low--density (Boltzmann--Grad) limit, the system behaves, for short times, as predicted by the associated Boltzmann…
We prove the existence of minimisers for a family of models related to the single-slip-to-single-plane relaxation of single-crystal, strain-gradient elastoplasticity with $L^p$-hardening penalty. In these relaxed models, where only one…
A model for a MEMS device, consisting of a fixed bottom plate and an elastic plate, is studied. It was derived in a previous work as a reinforced limit when the thickness of the insulating layer covering the bottom plate tends to zero. This…
In this paper, we investigate nonlocal interaction equations with repulsive-attractive radial potentials. Such equations describe the evolution of a continuum density of particles in which they repulse each other in the short range and…
We study the quantum self-organization of a few interacting particles with strong short-range interactions. The physical system is modeled via a 2D Hubbard square lattice model, with a nearest-neighbor interaction term of strength U and a…
We investigate lattice energies for radially symmetric, spatially extended particles interacting via a radial potential and arranged on the sites of a two-dimensional Bravais lattice. We show the global minimality of the triangular lattice…
We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model used is characterized by a finite-strain hyperelastic membrane energy perturbed by small…
In analytical models of structure formation, protohalos are routinely assumed to be peaks of the smoothed initial density field, with the smoothing filter being spherically symmetric. This works reasonably well for identifying a protohalo's…