Related papers: Lamination exact relations and their stability und…
The main result of this work is a homogenization theorem via variational convergence for elastic materials with stiff checkerboard-type heterogeneities under the assumptions of physical growth and non-self-interpenetration. While the…
Recently, the first-named author gave a classification of 3D consistent 6-tuples of quad-equations with the tetrahedron property; several novel asymmetric 6-tuples have been found. Due to 3D consistency, these 6-tuples can be extended to…
We derive exact density functionals for systems of hard rods with first-neighbor interactions of arbitrary shape but limited range on a one-dimensional lattice. The size of all rods is the same integer unit of the lattice constant. The…
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant…
The presence of flat bands is a source of localization in lattice systems. While flat bands are often unstable with respect to interactions between the particles, they can persist in certain cases. We consider a diamond ladder with…
Fourth-rank tensors of complete Voigt's symmetry, that embody the elastic properties of crystalline anisotropic substances, were constructed for all 2D crystal systems. Using them we obtained explicit expressions for inverse of Young's…
The paper gathers and unifies mechanical stability conditions for all symmetry classes of 3D and 2D materials under arbitrary load. The methodology is based on the spectral decomposition of the fourth-order stiffness tensors mapped to…
When interacting electrons are confined to low-dimensions, the electron-electron correlation effect is enhanced dramatically, which often drives the system into exhibiting behaviors that are otherwise highly improbable. Superconductivity…
In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d N=2 theory. The Lagrangians of some theories with the desired properties can be constructed with…
Networks of flexible filaments often involve regions of tight contact. Predictively understanding the equilibrium configurations of these systems is challenging due to intricate couplings between topology, geometry, large nonlinear…
Many biological and engineering materials have nonperiodic microstructures for which classical periodic homogenization results do not apply. Certain nonperiodic microstructures may be approximated by locally periodic microstructures for…
We consider the statistical mechanics of a system of topologically linked polymers, such as for instance a dense solution of polymer rings. If the possible topological states of the system are distinguished using the Gauss linking number as…
Term "asymmetrical pseudoelasticity" refers to the theory, in which a symmetrical stress tensor and a symmetrical strain tensor are connected by means of an asymmetrical material tensor. An 6-dimensional asymmetrical matrix of elasticity…
Polymer composites are ideal candidates for next generation biomimetic soft materials because of their exquisite bottom-up designability. However, the richness of behaviours comes at a price: the need for precise and extensive…
We give a detailed account of the methods introduced in [1] to calculate holographic four-point correlators in IIB supergravity on $AdS_5 \times S^5$. Our approach relies entirely on general consistency conditions and maximal supersymmetry.…
The aim of this paper is two-fold. Firstly we provide necessary and sufficient criteria for the existence of a strict deformation quantization of algebraic tensor products of Poisson algebras, and secondly, we discuss the existence of…
In this paper we investigate numerically an instance of the problem of G-closure for two-dimensional periodic metamaterials. Specifically, we consider composites with isotropic homogenized elasticity tensor, obtained as a mixture of two…
While intersection cohomology is stable under small resolutions, both ordinary and intersection cohomology are unstable under smooth deformation of singularities. For complex projective algebraic hypersurfaces with an isolated singularity,…
We review theoretical concepts and models for materials with strongly correlated d- or f electrons. We discuss low-energy effective models and the renormalized band method for Ce-based Kondo lattice systems. They are applied to the analysis…
An initial-boundary value problem for the multidimensional type III thermoelaticity for a nonsimple material with a center of symmetry is considered. In the linear case, the well-posedness with and without Kelvin-Voigt and/or frictional…