一类具两条不连续相交线的平面系统的闭轨

研究了一类具两条不连续相交线的平面系统的闭轨.利用微分包含理论和点变换的方法,获得了一些有趣的结果,包括滑模解,同宿解和闭轨的存在性.同时给出了闭轨存在的必要条件.     

Time-Domain Mapping of Electromagnetic Ray Movement Inside Anisotropic Spherical Resonator

This paper presents the analytical proof of Time-Domain Mapping Method for the spherical resonator made up of uniaxial crystal. In this way, the main types of caustics inside the spherical resonator made up of uniaxial crystal, which were investigated numerically before, are confirmed analytically. It is engraved that the problem of the ray flow inside the spherical resonator can be reduced to the problem of the ray flow inside metal cavity shaped as spheroid.     

Multi-separation, centrifugality and centripetality imply chaos

Let be an interval. need not be compact or bounded. Let be a continuous map, and be a trajectory of with or . Then there is a point such that . A point is called a centripetal point of relative to if or , and is centrifugal if or . In this paper we prove that if there exist centripetal points of in , then has periodic points of some odd () period . In addition, we also prove that if ) is multi-separated by Fix(), or there exists a centrifugal point of in , then is turbulent and hence has periodic points of all periods.

     

Existence and Limiting Behavior of Trajectories Associated with P0-equations

Given a continuous P₀-function F : Rⁿ Rⁿ, we describe a method of constructing trajectories associated with the P₀-equation F(x) = 0. Various well known equation-based reformulations of the nonlinear complementarity problem and the box variational inequality problem corresponding to a continuous P₀-function lead to P₀-equations. In particular, reformulations via (a) the Fischer function for the NCP, (b) the min function for the NCP, (c) the fixed point map for a BVI, and (d) the normal map for a BVI give raise to P₀-equations when the underlying function is P₀. To generate the trajectories, we perturb the given P₀-function F to a P-function F(x, ); unique solutions of F(x, ) = 0 as varies over an interval in (0, ) then define the trajectory. We prove general results on the existence and limiting behavior of such trajectories. As special cases we study the interior point trajectory, trajectories based on the fixed point map of a BVI, trajectories based on the normal map of a BVI, and a trajectory based on the aggregate function of a vertical nonlinear complementarity problem.     

Cooling efficiency in collisions between Pd and He,Ne, Ar and Kr

The cooling of the metal cluster Pd₁₃ in an atmosphere of rare gas has been studied by means of computer simulation. By simulation, the average energy transfer in collisions between one cluster and one gas atom has been obtained. Emphasis has been placed on conditions when the temperatures of the colliding species are almost equal. All modes of motion, inclusive the translation, must be considered in order to obtain vanishing energy transfer at equilibrium. A simulation scheme is presented by which the energy transfer is zero to the cluster when the gas and the cluster temperatures are equal. At equilibrium the energy transfer does however not vanish for all impact parameters. In the collisions with Pd₁₃, the cluster is heated by collisions with a small impact parameter but equally cooled by collisions with a large impact parameter. Argon and krypton are found to cool Pd₁₃ equally efficiently while neon and helium are less efficient cooling agents. Received 28 September 2001 / Received in final form 8 August 2002 Published online 12 November 2002 RID="a" ID="a"e-mail: JanW@phc.gu.se     

Non-adiabatic transitions at a continuum edge

We consider interaction of a single level with a broad, tending to semi-infinite continuum. In an example of two exactly solvable problems, we show that for time dependent quantum systems the probability of the irreversible transition from a discrete level to a continuum is strongly inhibited or even completely suppressed by the presence of a discrete adiabatic level near the continuum edge. Received 10 October 2002 Published online 4 March 2003 RID="a" ID="a"e-mail: Alain.Sarfati@lac.u-psud.fr     

Charge exchange collisions of H<Superscript>+</Superscript>/D<Superscript>+</Superscript> ions with alkaline Earth atoms (Ca,Mg)

The Classical Trajectory Monte Carlo (CTMC) Method has been used to calculate the differential, partial and total single electron capture cross sections for the collision of H⁺/D⁺ with Ca and Mg atoms in the energy range of 1–100 keV. The differential cross sections at angles near the diffraction limit (<0.1^○) in both systems show a forward peak followed by an asymptotic fall at higher angles. Total and partial capture cross sections are found to be in good agreement with the experimental observations. Oscillations in the partial capture cross sections have been explained due to the swapping of the field electron. Isotope effect in the electron transfer is reported to be negligible.     

Electron scattering from an assembly of point scatterers in the presence of a quantizing magnetic field

Summary We have studied the scattering of electrons by a structured target in the presence of a quantizing static magnetic field, under the assumption that the presence of the field does not affect the behaviour of the massive target nuclei, but it influences only the motion of the incident electrons. In this case, the electron motion in the plane perpendicular to the magnetic field is confined within a typical distance given by the cyclotron radius ρ₀=(cℏ/|e|B)^1/2, that for particular values of the intensity of the magnetic field can be comparable with the distance between two scattering centres. The known field-free interference conditions are modified, depending both on the energy of the incident particle and on the intensity and the direction of the magnetic field. The general case of a three-dimensional scattering array has been derived in detail. Numerical results are given for the case of two scattering centres in perpendicular geometry. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

On the metric properties of the Feigenbaum attractor

The two standard literature definitions of the function associated with the Feigenbaum attractor are not equivalent. The method due to Vulet al. and Feigenbaum is used to calculate the Haussdorff dimension of the Feigenbaum attractor, using as input the trajectory scaling functions. The two calculations yield the same Hausdorff dimensionD=0.5380451435 to within the accuracy of the computation.