Related papers: Mechanics of plates
Introducing the deformation theory of holomorphic Cartan geometries, we compute infinitesimal automorphisms and infinitesimal deformations. We also prove the existence of a semi-universal deformation of a holomorphic Cartan geometry.
An algebraic deformation theory of coalgebra morphisms is constructed.
This paper is concerned with the study of the rolling without slipping of a dynamically symmetric (in particular, homogeneous) heavy ball on a cone which rotates uniformly about its symmetry axis. The equations of motion of the system are…
The generalization of Bertrand's theorem to the case of the motion of point particle on the surface of a cone is presented. The superintegrability of such models is discussed. The additional integrals of motion are analyzed for the case of…
In this paper we develop a generalization of foliated manifolds in the context of metric spaces. In particular we study dendritations of surfaces that are defined as maximal atlases of compatible upper semicontinuous local decompositions…
This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.
We give a bird's-eye view of the plastic deformation of crystals aimed at the statistical physics community, and a broad introduction into the statistical theories of forced rigid systems aimed at the plasticity community. Memory effects in…
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…
Examples are given of q-deformed systems that may be interpreted by the standard rules of quantum theory in terms of new degrees of freedom and supplementary quantum numbers.
A multilayered plate theory which takes into account transverse shear and normal stretching is presented. The theory is based on a seven-unknowns kinematic field with five warping functions. Four warping functions are related to the…
A fluid droplet in general deforms, if subject to active driving, such as a finite slip velocity or active tractions on its interface. We show that these deformations and their dynamics can be computed analytically in a perturbation theory…
Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…
Various properties of fluids consisting of platelike particles differ from the corresponding ones of fluids consisting of spherical particles because interactions between platelets depend on their mutual orientations. One of the main issues…
The bending of bilayer plates is a mechanism which allows for large deformations via small externally induced lattice mismatches of the underlying materials. Its mathematical modeling, discussed herein, consists of a nonlinear fourth order…
The dynamics and thermodynamics of dislocated crystals are studied within the framework of the nonlinear theory of elastic and plastic deformations.
The theory of surfaces in Euclidean space can be naturally formulated in the more general context of Legendre surfaces into the space of contact elements. We address the question of deformability of Legendre surfaces with respect to the…
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
We survey the salient features and problems of conformal and superconformal mechanics and portray some of its developments over the past decade. Both classical and quantum issues of single- and multiparticle systems are covered.
According to the experimentally observed theory of the static Casimir effect, two metal, uncharged, conductive and flat plates attract each other in vacuum >.Herein, equations of motion of the plates which are influenced by Casimir…
An overview of the cosmological models with expansion, shear and rotation is presented. Problems of the rotating models are discussed, their general kinematic properties and dynamical realizations are described. A particular attention is…