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41.
In this paper we introduce a numerical conjugacy invariant for planar maps with homoclinic points. This invariant can be estimated based on partial information about the location of compact pieces of the stable and unstable manifolds of the system. The invariant is also related to topological entropy, and we indicate a method by which good bounds on the entropy of a system can be obtained. 相似文献
42.
In the present paper we consider interior and exterior mixed boundary value problems of anti-plane shear in the static theory of linear piezoelectricity. Using the boundary integral equation method we reduce the problems to systems of singular integral equations with discontinuous coefficients to which the classical Nöether’s theorems on existence of the solution can be applied. This allows us to establish well-posedness results and to obtain integral solutions of the corresponding mixed boundary value problems for a rather general class of piezoelectric materials.
Mathematics Subject Classifications (2000) 45E05, 45F15, 74F15. 相似文献
43.
Experiments on polymers indicate that large tensile stress can induce cavitation, that is, the appearance of voids that were
not previously evident in the material. This phenomenon can be viewed as either the growth of pre-existing infinitesimal holes
in the material or, alternatively, as the spontaneous creation of new holes in an initially perfect body. In this paper our
approach is to adopt both views concurrently within the framework of the variational theory of nonlinear elasticity. We model
an elastomer on a macroscale as a void-free material and, on a microscale, as a material containing certain defects that are
the only points at which hole formation can occur. Mathematically, this is accomplished by the use of deformations whose point
singularities are constrained. One consequence of this viewpoint is that cavitation may then take place at a point that is
not energetically optimal. We show that this disparity will generate configurational forces, a type of force identified previously
in dislocations in crystals, in phase transitions in solids, in solidification, and in fracture mechanics.
As an application of this approach we study the energetically optimal point for a solitary hole to form in a homogeneous and
isotropic elastic ball subject to radial boundary displacements. We show, in particular, that the center of the ball is the
unique optimal point. Finally, we speculate that the configurational force generated by cavitation at a non-optimal material
point may be sufficient to result in the onset of fracture. The analysis utilizes the energy-momentum tensor, the asymptotics
of an equilibrium solution with an isolated singularity, and the linear theory of elasticity at the stressed configuration
that the body occupies immediately prior to cavitation.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
44.
Some conclusions about the smooth function classes stability for the basic system of equations of atmospheric motion and instability for Navier-Stokes equation are summarized. On the basis of this, by taking the basic system of equations of atmospheric motion via Boussinesq approximation as example to explain in detail that the instability about some simplified models of the basic system of equations for atmospheric motion is caused by the instability of Navier-Stokes equation, thereby, a principle to guarantee the stability of simplified equation is drawn in simplifying the basic system of equations. 相似文献
45.
46.
利用一维扩展过程的奇点理论并结合能量包络的随机平均法,考查“隐藏在余维2分岔点之后”的同宿分岔系统受参激白噪声影响的分岔行为。 相似文献
47.
AUNIFORMLYDIFFERENCESCHEMEOFSINGULARPERTURBATIONPROBLEMFORASEMILINEARORDINARYDIFFERENTIALEQUATIONWITHMIXEDBOUNDARYVALUECONDIT... 相似文献
48.
Jaume Llibre Paulo R. da Silva Marco A. Teixeira 《Journal of Dynamics and Differential Equations》2007,19(2):309-331
Singular perturbations problems in dimension three which are approximations of discontinuous vector fields are studied in
this paper. The main result states that the regularization process developed by Sotomayor and Teixeira produces a singular
problem for which the discontinuous set is a center manifold. Moreover, the definition of sliding vector field coincides with
the reduced problem of the corresponding singular problem for a class of vector fields.
相似文献
49.
机器人在完成其规划动作时,常可能要通过其运动链的奇点,这时求解其运动学逆问题的通用算法遇到本质的困难,本文给出了一种算法,它可以成功地克服这个困难。文中还给出了计算实例。 相似文献
50.