The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe,including the accelerated expansion.The ...The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe,including the accelerated expansion.The analogy is manifested by the inclusion in the traditional Lagrangian of general relativity of an additional term accounting for the strain induced in the manifold(i.e.in space-time)by the curvature,be it induced by the presence of a texture defect or by a matter/energy distribution.The additional term is su?cient to account for various observed features of the universe and to give a simple interpretation for the so called dark energy.Then,we show how the same approach can be adopted back in three dimensions to obtain the equilibrium configuration of a given solid subject to strain induced by defects or applied forces.Finally,it is shown how concepts coming from the familiar elasticity theory can inspire new approaches to cosmology and in return how methods appropriated to General Relativity can be applied back to classical problems of elastic deformations in three dimensions.展开更多
Abstract. In this paper the cubic homogeneous parameterized vector fields aJre studied.The classification of the phase portrait near the critical point is presented. This classifica- tion is an extension of the result...Abstract. In this paper the cubic homogeneous parameterized vector fields aJre studied.The classification of the phase portrait near the critical point is presented. This classifica- tion is an extension of the result given by Takens to the cubic homogeneous parameterizedvector fields with six parameters.展开更多
文摘The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe,including the accelerated expansion.The analogy is manifested by the inclusion in the traditional Lagrangian of general relativity of an additional term accounting for the strain induced in the manifold(i.e.in space-time)by the curvature,be it induced by the presence of a texture defect or by a matter/energy distribution.The additional term is su?cient to account for various observed features of the universe and to give a simple interpretation for the so called dark energy.Then,we show how the same approach can be adopted back in three dimensions to obtain the equilibrium configuration of a given solid subject to strain induced by defects or applied forces.Finally,it is shown how concepts coming from the familiar elasticity theory can inspire new approaches to cosmology and in return how methods appropriated to General Relativity can be applied back to classical problems of elastic deformations in three dimensions.
基金National Key Basic Research Special Fund(No.1998020307) National Natural Science Foundation of China(No.19990510).
文摘Abstract. In this paper the cubic homogeneous parameterized vector fields aJre studied.The classification of the phase portrait near the critical point is presented. This classifica- tion is an extension of the result given by Takens to the cubic homogeneous parameterizedvector fields with six parameters.
