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Quasicrystals are characterized by quasi-periodic arrangements of atoms. The description of their mechanics involves deformation and a (so called phason) vector field accounting at macroscopic scale of local phase changes, due to atomic…
In this paper we analyze a virtual element method for the two dimensional elasticity problem allowing small edges. With this approach, the classic assumptions on the geometrical features of the polygonal meshes can be relaxed. In…
In this paper we analyze a virtual element method for the two dimensional elasticity spectral problem allowing small edges. Under this approach, and with the aid of the theory of compact operators, we prove convergence of the proposed VEM…
The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which…
Monopole-like electrostatic interactions are ubiquitous in biology and condensed matter, but they are often screened by counter-ions and cannot be switched from attractive to repulsive. In colloidal science, where the prime goal is to…
By mapping the interactions of colloidal particles onto the problem of minimizing areas, the physics of foams can be used to understand the phase diagrams of both charged and fuzzy colloids. We extend this analogy to study the elastic…
A model (further referred to as the enhanced vector-based model or EVM) for elastic bonds in solids, composed of bonded particles is presented. The model can be applied for a description of elastic deformation of rocks, ceramics, concrete,…
Searches for permanent electric-dipole moments (EDM) of atoms provide important constraints on competing extensions to the standard model of elementary particles. Recently proposed experiment with liquid $^{129}$Xe [M.V. Romalis and M.P.…
To begin with, we identify the equations of elastostatics in a Riemannian manifold, which generalize those of classical elasticity in the three-dimensional Euclidean space. Our approach relies on the principle of least energy, which asserts…
Elasticity of soft materials can be greatly influenced by the presence of air bubbles. Such a capillary effect is expected for a wide range of materials, from polymer gels to concentrated emulsions and colloidal suspensions. Whereas…
We consider quantum mechanics on constrained surfaces which have non-Euclidean metrics and variable Gaussian curvature. The old controversy about the ambiguities involving terms in the Hamiltonian of order hbar^2 multiplying the Gaussian…
We consider a set of electrostatic problems relevant for determining the real-space structure and the ground-state energy of a two-dimensional electron liquid subject to smooth external potentials. Three fundamental geometries are…
We propose a protocol to model accurately the electromechanical behavior of dielectric elastomer membranes using experimental data of stress-stretch and voltage-stretch tests. We show how the relationship between electric displacement and…
Viscoelastic fluids are a subclass of complex fluids used in widespread applications ranging from biological to large-scale industrial settings. These fluids are often associated with various complex flow phenomena due to the presence of…
Molecular-dynamics simulation can give atomistic information on the processes occurring in nanoindentation experiments. In particular, the nucleation of dislocation loops, their growth, interaction and motion can be studied. We investigate…
Besides being one of the most fundamental basic issues of plasma physics, the stability analysis of an electron beam-plasma system is of critical relevance in many areas of physics. Surprisingly, decades of extensive investigation had not…
The stability of multielectron bubbles (MEBs) in liquid helium is investigated using the liquid-drop model for fissioning nuclei. Whereas a critical positive pressure can make the bubble unstable against fissioning, a small negative…
We analyse the Virtual Element Methods (VEM) on a simple elliptic model problem, allowing for more general meshes than the one typically considered in the VEM literature. For instance, meshes with arbitrarily small edges (with respect to…
Consider a stochastic nonlinear system controlled over a possibly noisy communication channel. An important problem is to characterize the largest class of channels for which there exist coding and control policies so that the closed-loop…
We use recent theoretical advances to develop a new functional form for interatomic forces in bulk silicon. The theoretical results underlying the model include a novel analysis of elastic properties for the diamond and graphitic structures…