Related papers: A proof of finite crystallization via stratificati…

The rigorous simulation of stratified turbulence remains challenging due to pronounced flow anisotropy, suppressed vertical transport, and high sensitivity to numerical dissipation. This study systematically evaluates the predictive…

Let $z\in \mathbb{H}:=\{z= x+ i y\in\mathbb{C}: y>0\}$ and $\mathcal{K}(\alpha;z):=\sum_{ (m,n)\in \mathbb{Z} ^2 }\frac{{\left| mz+n \right|}^2}{{{\Im}(z)}}e^{-\pi\alpha\frac{ \left|mz+n\right|^2}{\Im(z)}}.$ In this paper, we characterize…

The use of multidimensional entanglement opens new perspectives for quantum information processing. However, an important challenge in practice is to certify and characterize multidimensional entanglement from measurement data that are…

A static variational model for shape formation in heteroepitaxial crystal growth is considered. The energy functional takes into account surface energy, elastic misfit-energy and nucleation energy of dislocations. A scaling law for the…

We present the status of our formalism for extracting three-particle scattering observables from lattice QCD (LQCD). The method relies on relating the discrete finite-volume spectrum of a quantum field theory with its scattering amplitudes.…

The crystallization of electrons in quasi low-dimensional solids is studied in a model which retains the full three-dimensional nature of the Coulomb interactions. We show that restricting the electron motion to layers (or chains) gives…

We present a quantization condition for the spectrum of a system composed of three identical bosons in a finite volume with periodic boundary conditions. This condition gives a relation between the finite volume spectrum and infinite volume…

In the case where the charge of the particle is small compared to its mass, we describe the asymptotics of the Lorentz-Maxwell equation for any finite-energy data. As time goes to infinity, we prove that the speed of the particle converges…

We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…

We unravel the existence and nonequilibrium response of one-dimensional harmonically trapped droplet configurations in the presence of a central potential barrier or well. For fixed negative chemical potentials, it is shown that droplets…

In this paper, based on the analysis of the formula (2.2) for calculating the elastic scattering diagrams of microparticles on a multilayer crystal surface, derived by the author in the article [3], it is shown that the stochastic approach…

We extend a previously studied lattice model of particles with infinite repulsions to the case of finite energy interactions. The phase diagram is studied using grand canonical Monte Carlo simulation. Simulations of dynamical phenomena are…

We develop a general stability analysis for objective structures, which constitute a far reaching generalization of crystal lattice systems. We show that these particle systems, although in general neither periodic nor space filling, allow…

We study a $(1+1)$-dimensional semi-discrete random variational problem that can be interpreted as the geometrically linearized version of the critical $2$-dimensional random field Ising model. The scaling of the correlation length of the…

We explore whether the topology of energy landscapes in chemical systems obeys any rules and what these rules are. To answer this and related questions we use several tools: (i)Reduced energy surface and its density of states, (ii)…

We provide a rigorous justification of the classical linearization approach in plasticity. By taking the small-deformations limit, we prove via \Gamma-convergence for rate-independent processes that energetic solutions of the quasi-static…

We discuss effective field theory treatments of the problem of three particles interacting via short-range forces (range R >> a_2, with a_2 the two-body scattering length). We show that forming a once-subtracted scattering equation yields a…

The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground state magnetization with an external magnetic field for two different…

Controlling a state of material between its crystalline and glassy phase has fostered many real-world applications. Nevertheless, design rules for crystallization and vitrification kinetics still lack predictive power. Here, we identify…

We consider a system of spherical particles interacting by means of a pair potential equal to a finite constant for interparticle distances smaller than the sphere diameter and zero outside. The model may be a prototype for the interaction…