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Commability is the finest equivalence relation between locally compact groups such that $G$ and $H$ are equivalent whenever there is a continuous proper homomorphism $G \to H$ with cocompact image. Answering a question of Cornulier, we show…
Similar to Poisson's effect, mechanical coupling is a directional indirect response by a directional input loading. With the advance in manufacturing techniques of 3D complex geometry, architected materials with unit cells of finite volume…
In this article, we mainly give the strictly copositive conditions of a special class of third order three dimensional symmetric tensors. More specifically, by means of the polynomial decomposition method, the analytic sufficient and…
Despite the recent progress on two-dimensional multilayer materials (2DMM) with weak interlayer interactions, the investigation on 2DMM with strong interlayer interactions is far from its sufficiency. Here we report on first-principles…
Given the ground state wavefunction for an interacting lattice model, we define a "correlation density matrix"(CDM) for two disjoint, separated clusters $A$ and $B$, to be the density matrix of their union, minus the direct product of their…
We discuss a model for the on-site matrix elements of the sp3d5s* tight-binding hamiltonian of a strained diamond or zinc-blende crystal or nanostructure. This model features on-site, off-diagonal couplings between the s, p and d orbitals,…
We study perfect matchings, or close-packed dimer coverings, of finite sections of the eleven Archimedean lattices and give a constructive proof showing that any two perfect matchings can be transformed into each other using small sets of…
We study the dynamics of a finite chain of diffusively coupled Lorenz oscillators with periodic boundary conditions. Such rings possess infinitely many fixed states, some of which are observed to be stable. It is shown that there exists a…
A wide variety of experimental results and theoretical investigations in recent years have convincingly demonstrated that several transition metal oxides and other materials, have dominant states that are not spatially homogeneous. This…
Jammed packings' mechanical properties depend sensitively on their detailed local structure. Here we provide a complete characterization of the pair correlation close to contact and of the force distribution of jammed frictionless spheres.…
The stability properties of simple element choices for the mixed formulation of the Laplacian are investigated numerically. The element choices studied use vector Lagrange elements, i.e., the space of continuous piecewise polynomial vector…
Cohesive zone models do not consider the lateral contraction of adhesive layers under tensile loads. The constraint of the lateral contraction by the adherents which depends on the geometry of the adhesive layer has a major influence on the…
This paper focuses on the strict copositivity analysis of 4th-order 3-dimensional symmetric tensors. A necessary and sufficient condition is provided for the strict copositivity of a fourth-order symmetric tensor. Subsequently, building…
Exact ground states of interacting electrons on the diamond Hubbard chain in a magnetic field are constructed which exhibit a wide range of properties such as flat-band ferromagnetism and correlation induced metallic, half-metallic or…
We prove that the homology of the mapping class groups of non-orientable surfaces stabilizes with the genus of the surface. Combining our result with recent work of Madsen and Weiss, we obtain that the classifying space of the stable…
The inclusion of rigid elements into elastic composites may lead to superior mechanical properties for the equivalent elastic continuum, such as, for instance, extreme auxeticity. To allow full exploitation of these properties, a tool for…
A number of methods are discussed which may serve for a treatment of electron correlations in solids. When the electron correlations are relatively weak like in semiconductors or a number of ionic crystals one may start from a…
Understanding contact between rough surfaces undergoing plastic deformation is crucial in many applications. We test Persson's multiscale contact mechanics theory for elastoplastic solids, assuming a constant penetration hardness. Using a…
Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…
This article introduces and studies the tight approximation property, a property of algebraic varieties defined over the function field of a complex or real curve that refines the weak approximation property (and the known cohomological…