Related papers: A group theoretical approach to elasticity under c…

We develop an invariant deformation theory, in a form accessible to practice, for affine schemes $W$ equipped with an action of a reductive algebraic group $G$. Given the defining equations of a $G$-invariant subscheme $X \subset W$, we…

This article discusses the modular representation theory of finite groups of Lie type from the viewpoint of Broue's abelian defect group conjecture. We discuss both the defining characteristic case, the inspiration for Alperin's weight…

This is a largely expository paper about how groups arise or are of interest in model theory. Included are the following topics: classifying groups definable in specific structures or theories and the relation to algebraic groups, groups…

We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…

Many materials of contemporary interest, such as gels, biological tissues and elastomers, are easily deformed but essentially incompressible. Traditional linear theory of elasticity implements incompressibility only to first order and thus…

In this article we show how Gr\"un's results in group theory can be used for studying the structure of class groups in normal extensions.

We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1+1)-dimensional nonlinear…

The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…

In the present work, the overall nonlinear elastic behavior of a 1D multi-modular structure incorporating possible imperfections at the discrete (micro-scale) level, is derived with respect to both tensile and compressive applied loads. The…

The discrete modeling of a large class of mechanical structures can be based on a stick-and-spring concept. We here present a stick-and-spring theory with potential application to the statics and the dynamics of such nanostructures as…

We show that the deformation theory of a perfect complex and that of its determinant are related by the trace map, in a general setting of sheaves on a site. The key technical step, in passing from the setting of modules over a ring where…

We develop a global bifurcation theory for two classes of nonlinear elastic materials. It is supposed that they are subjected to anti-plane shear deformation and occupy an infinite cylinder in the reference configuration. Curves of…

We derive continuum limits of atomistic models in the realm of nonlinear elasticity theory rigorously as the interatomic distances tend to zero. In particular we obtain an integral functional acting on the deformation gradient in the…

Topology is an important determinant of the behavior of a great number of condensed-matter systems, but until recently has played a minor role in elasticity. We develop a theory for the deformations of a class of twisted non-Euclidean…

Usual introductions of the concept of motion are not well adapted to a subsequent, strictly tensorial, theory of elasticity. The consideration of arbitrary coordinate systems for the representation of both, the points in the laboratory, and…

We present a novel derivation of the elastic theory of shells. We use the language of Geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools…

We present a general approach to the bifurcation analysis of elastic frameworks with symmetry. While group-theoretic methods for bifurcation problems with symmetry are well known, their actual implementation in the context of elastic…

We present a model for the dynamics of elastic or poroelastic bodies with monopolar repulsive long-range (electrostatic) interactions at large strains. Our model respects (only) locally the non-self-interpenetration condition but can cope…

Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…

It is known that a finite-size homogeneous granular fluid develops an hydrodynamic-like instability when dissipation crosses a threshold value. This instability is analyzed in terms of modified hydrodynamic equations: first, a source term…