Related papers: Korn type Inequalities for Objective Structures
We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a characterization of what finitely presentable groups may admit a…
Korn's inequality has been at the heart of much exciting research since its first appearance in the beginning of the 20th century. Many are the applications of this inequality to the analysis and construction of discretizations of a large…
Non-uniform structures of nuclear matter are studied in a wide density-range. Using the density functional theory with a relativistic mean-field model, we examine non-uniform structures at sub-nuclear densities (nuclear ``pastas'') and at…
A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…
In this paper, we study the weighted Korn inequality on some irregular domains, e.g., $s$-John domains and domains satisfying quasi-hyperbolic boundary conditions. Examples regarding sharpness of the Korn inequality on these domains are…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
The main goal of this note is to begin a systematic study on conic-line arrangements in the complex projective plane. We show a de Bruijn-Erd\H{o}s-type inequality and Hirzebruch-type inequality for a certain class of conic-line…
We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the way we introduce a new class of combinatorial matroids and associated linear…
We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…
The generalized transport equations for a consistent description of kinetic and hydrodynamic processes in dense gases and liquids are considered. The inner structure of the generalized transport kernels for these equations is established.…
We examine a two-dimensional nonequilibrium lattice model where particles adsorb at empty sites and desorb when the number of neighbouring particles is greater than a given threshold. In a certain range of parameters the model exhibits…
Crystal structures are indispensable across various domains, from batteries to solar cells, and extensive research has been dedicated to predicting their properties based on their atomic configurations. However, prevailing Crystal Structure…
A continuum density-field formulation with particle-scale resolution is constructed to simultaneously incorporate the orientation dependence of interparticle interactions and the rotational invariance of the system, a fundamental but…
We consider shells with zero Gaussian curvature, namely shells with one principal curvature zero and the other one having a constant sign. Our particular interests are shells that are diffeomorphic to a circular cylindrical shell with zero…
We prove a Korn-type inequality for tensor fields without gradient structure, which generalizes Korn's first inequality.
We prove generalized Gaffney inequalities and the discrete compactness for finite element differential forms on $s$-regular domains, including general Lipschitz domains. In computational electromagnetism, special cases of these results have…
The inhomogeneity of the media or the external forces usually destroy the integrability of a system. We propose a systematic construction of a class of quantum models, which retains their exact integrability inspite of their explicit…
We establish sharp trace- and Korn-type inequalities that involve vectorial differential operators, the focus being on situations where global singular integral estimates are not available. Starting from a novel approach to sharp Besov…
We give a new, simpler proof of the fractional Korn's inequality for subsets of $\mathbb{R}^d$. We also show a framework for obtaining Korn's inequality directly from the appropriate Hardy-type inequality.
Many physical systems are well modeled as collections of interacting particles. Nevertheless, a general approach to quantifying the absolute degree of order immediately surrounding a particle has yet to be described. Motivated thus, we…