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The common notion suggests that metallic glasses (MGs) are a homogeneous solid at the macroscopic scale; however, recent experiments and simulations indicate that MGs contain nano-scale elastic heterogeneities. Despite the fundamental…
We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D PT -symmetric lattices. For each configuration, we develop a dynamical model and examine its…
We produce an explicit parameterization of well-rounded sublattices of the hexagonal lattice in the plane, splitting them into similarity classes. We use this parameterization to study the number, the greatest minimal norm, and the highest…
We model the electronic properties of thin films of binary compounds with stacked layers where each layer is a two-dimensional honeycomb lattice with two atoms per unit cell. The two atoms per cell are assigned different onsite energies in…
We put forward new properties of lattice solitons in materials and geometries where both, the linear refractive index and the nonlinearity are spatially modulated. We show that the interplay between linear and out-of-phase nonlinear…
The three-dimensional elastic-plastic deformation is considered. The catastrophe theory underlies the construction of this process model. It was shown that the variety of stable states consists on elastic states and can be depicted as a…
We construct families of periodic tessellations of the plane with arbitrarily high critical temperature, $T_{\rm c}$, for the classical ferromagnetic Ising model. Our approach is motivated by recently found exact bounds, which imply that…
Atomically thin metallenes have properties attractive for applications, but they are intrinsically unstable and require delicate stabilization in pores or other nano-constrictions. Substrates provide solid support, but metallenes' wanted…
In this paper we review the recent advances which have taken place in the understanding and applications of acoustic/elastic metamaterials. Metamaterials are artificially created composite materials which exhibit unusual properties which…
Lattice {\em Kirigami}, ultra-light metamaterials, poly-disperse aggregates, ceramic nano-lattices, and two-dimensional (2-D) atomic materials share an inherent structural discreteness, and their material properties evolve with their shape.…
We consider the elastic constants of phases with nonspherical nuclei, so-called pasta phases, predicted to occur in the inner crust of a neutron star. First, we treat perfectly ordered phases and give numerical estimates for lasagna and…
Particle based methods such as the Discrete Element Method and the Lattice Spring Method may be used for describing the behaviour of isotropic linear elastic materials. However, the common bond models employed to describe the interaction…
We present a procedure to map the constitutive laws of elasticity (both in the linear and nonlinear regime) onto a discrete atomic lattice and we apply the resulting elastic lattice model to investigate the strain field within an embedded…
We describe size-varying cylindrical particles made from silicone elastomers that can serve as building blocks for robotic granular materials. The particle size variation, which is achieved by inflation, gives rise to changes in stiffness…
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…
A new theoretical approach has been developed to describe the elastic properties of cubic blue phases of cholesteric liquid crystals (LCs). Blue phases are three-dimensional periodic chiral liquids with local anisotropy of the average…
The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent field theory, applied to a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents. Examining the…
We propose a framework to model elastic properties of polycrystals by coupling crystal orientational degrees of freedom with elastic strains. Our model encodes crystal symmetries and takes into account explicitly the strain compatibility…
Let G be a finite dimensional simple complex group equipped with the standard Poisson Lie group structure. We show that all G-homogeneous (holomorphic) Poisson structures on $G/H$, where $H \subset G$ is a Cartan subgroup, come from…
Motivated by problems of hyperbolic stochastic geometry we introduce and study the class of beta-star polytopes. A beta-star polytope is defined as the convex hull of an inhomogeneous Poisson processes on the complement of the unit ball in…