相关论文: Moving frames applied to shell elasticity
We derive a new set of kinematic equations for front motion in two-dimensional bistable media. The equations generalize the geometric approach by complementing the equation for the front curvature with an order parameter equation associated…
Fluid mechanics can be formulated on dynamical surfaces of arbitrary co-dimension embedded in a background space-time. This has been the main object of study of the blackfold approach in which the emphasis has primarily been on stationary…
The present work pursues the aim to draw attention to unique possibilities of the skew-symmetric differential forms. At present the theory of skew-symmetric exterior differential forms that possess invariant properties has been developed.…
Although fully elastic when static, granular media become transiently elastic when being slowly sheared -- during which both the elastic energy and stress relax. Starting from this observation, we cogently derive the framework for granular…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
A system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed…
Although infinite cylinders are not astrophysical entities, it is possible to learn a great deal about the basic qualitative features of generation of gravitational waves and the behavior of the matter conforming such shells in the limits…
We develop a framework to understand the mechanics of metamaterial sheets on curved surfaces. Here we have constructed a continuum elastic theory of mechanical metamaterials by introducing an auxiliary, scalar gauge-like field that absorbs…
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
The method of moving frames (rep\`ere mobile) was used by Elie Cartan as a way of organizing the identification of differential invariants and solving equivalence problems. In this expository paper, we discuss how moving frames are used to…
A continuum field theory approach is presented for modeling elastic and plastic deformation, free surfaces and multiple crystal orientations in non-equilibrium processing phenomena. Many basic properties of the model are calculated…
A number of simplified dynamical problems is studied in an attempt to clarify some of the mechanisms leading to turbulence and the existing proposals to control this transition. A simplified set of boundary layer equations displays a…
We have adapted classical molecular dynamics to study the structural and dynamical properties of amorphous silica surfaces. Concerning the structure, the density profile exhibits oscillations perpendicularly to the surface as observed in…
The mechanical properties of a solid, which relate its deformation to external applied forces, are key factors in enabling or disabling the use of an otherwise optimal material in any application, strongly influencing also its service…
The system of Lama's equations is investigated, describing the motion of the elastic media under subsonic, transonic and supersonic velocities of the moving source of distributions, and its decisions in space of generalized…
To go beyond the simple model for the fold as two flexible surfaces or faces linked by a crease that behaves as an elastic hinge, we carefully shape and anneal a crease within a polymer sheet and study its mechanical response. First, we…
The dynamical analysis of vibrational systems of masses interconnected by restitution elements each with a single degree of freedom, and different configurations between masses and spring constants, is presented. Finite circular and linear…
We develop some basic facts on deformations of exterior differential ideals on a smooth complex algebraic variety. With these tools we study deformations of several types of differential ideals, leading to several irreducible components of…
In this article, we introduce a moving-frame approach to the geophysical equation of two-dimensional uniformly stratified rotational fluid in oceans and find a family of exact solutions containing ten arbitrary parameter functions.
A survey of some recent and important results which have to do with integrable equations and their relationship with the theory of surfaces is given. Some new results are also presented. The concept of the moving frame is examined, and it…