Dynamical symmetry of screened Coulomb potential and isotropic harmonic oscillator

It is shown that for the screened Coulomb potential and isotropic harmonic oscillator, there exists an infinite number of closed orbits for suitable angular momentum values. At the aphelion (perihelion) points of classical orbits, an extended Runge-Lenz vector for the screened Coulomb potential and an extended quadrupole tensor for the screened isotropic harmonic oscillator are still conserved. For the screened two-dimensional (2D) Coulomb potential and isotropic harmonic oscillator, the dynamical symmetries SO3 and SU(2) are still preserved at the aphelion (perihelion) points of classical orbits, respectively. For the screened 3D Coulomb potential, the dynamical symmetry SO4 is also preserved at the aphelion (perihelion) points of classical orbits. But for the screened 3D isotropic harmonic oscillator, the dynamical symmetry SU(2) is only preserved at the aphelion (perihelion) points of classical orbits in the eigencoordinate system. For the screened Coulomb potential and isotropic harmonic oscillator, only the energy (but not angular momentum) raising and lowering operators can be constructed from a factorization of the radial Schrodinger equation.

The vector fields admitting one-parameter spatial symmetry group and their reduction

For a n-dimensional vector fields preserving some n-form, the following conclusion is reached by the method of Lie group. That is, if it admits an one-parameter, n-form preserving symmetry group, a transformation independent of the vector field is constructed explicitly, which can reduce not only dimesion of the vector field by one, but also make the reduced vector field preserve the corresponding ( n - 1)-form. In partic ular, while n = 3, an important result can be directly got which is given by Me,ie and Wiggins in 1994.

Symmetry of chaotic attractors and kink-antikink structures in CMLs

In this paper the symmetries of coupled map lattices (CMLs) and their attractors are investigated by group and dynamical system theory, as well as numerical simulation, by means of which the kink-antikink patterns of CMLs in space-amplitude plots are discussed.

Receptivity to free-stream disturbance waves for blunt cone axial symmetry hypersonic boundary layer

Based on high-order compact upwind scheme, a high-order shock-fitting finite difference scheme is studied to simulate the generation of boundary layer disturbance waves due to free-stream waves. Both steady and unsteady flow solutions of the receptivity problem are obtained by resolving the full Navier-Stokes equations. The interactions of bow-shock and free-stream disturbance are researched. Direct numerical simulation (DNS) of receptivity to free-stream disturbances for blunt cone hypersonic boundary layers is performed.

Quantum interference in laser-induced nonsequential double ionization in diatomic molecules: Role of alignment and orbital symmetry

We address the influence of the orbital symmetry and the molecular alignment with respect to the laser-field polarization on laser-induced nonsequential double ionization of diatomic molecules, in the length and velocity gauges. We work within the strong-field approximation and assume that the second electron is dislodged by electron-impact ionization, and also consider the classical limit of this model. We show that the electron-momentum distributions exhibit interference maxima and minima due to electron emission at spatially separated centers. The interference patterns survive integration over the transverse momenta for a small range of alignment angles, and are sharpest for parallel-aligned molecules. Due to the contributions of the transverse-momentum components, these patterns become less defined as the alignment angle increases, until they disappear for perpendicular alignment. This behavior influences the shapes and the peaks of the electron-momentum distributions.

Symmetry of the Talbot effect and its applications

The Talbot effect is one of the most basic optical phenomena that has received extensive investigations both because its new results provide us more understanding of the fundamental Fresnel diffraction and also because of its wide applications. We summarize our recent results on this subject. Symmetry of the Talbot effect, which was reported in Optics Communications in 1995, is now realized as the key to reveal other rules for explanation of the Talbot effect for array illumination. The regularly rearranged-neighboring-phase-differences (RRNPD) rule, a completely new set of analytic phase equations (Applied Optics, 1999), and the prime-number decomposing rule (Applied Optics, 2001) are the newly obtained results that reflect the symmetry of the Talbot effect in essence. We also reported our results on the applications of the Talbot effect. Talbot phase codes are the orthogonal codes that can be used for phase coding of holographic storage. A new optical scanner based on the phase codes for Talbot array illumination has unique advantages. Furthermore, a novel two-layered multifunctional computer-generated hologram based on the fractional Talbot effect was proposed and implemented (Optics Letters, 2003). We believe that these new results should bring us more new understanding of the Talbot effect and help us to design novel optical devices that should benefit practical applications. (C) 2004 Society of Photo-Optical Instrumentation Engineers.

A novel method for measuring the coma of a lithographic projection system by use of mirror-symmetry marks

A novel method for measuring the coma of a lithographic projection system is proposed and the principle of the method is described. By utilizing mirror-symmetry marks, the adverse effects of axial aberrations on the coma measurement are avoided. Experimental results demonstrated that the method has high accuracy. Compared with TAMIS, the conventional technique used for coma measurement, the method is more reliable because the influences of the process factors on the lateral displacements have been considered. (c) 2006 Elsevier Ltd. All rights reserved.

Numerical simulation of wavefronts diffracted by apertures with circular symmetry

The numerical simulation of the wavefronts diffracted by apertures with circular symmetry is realized by a numerical method. It is based on the angular spectrum of plane waves, which ignored the vector nature of light. The on-axial irradiance distributions of plane wavefront and Gauss wavefront diffracted by the circular aperture have been calculated along the propagation direction. Comparisons of the simulation results with the analytical results and the experimental results tell us that it is a feasible method to calculate the diffraction of apertures. (c) 2006 Published by Elsevier GmbH.

Evolution of the black muntjac (Muntiacus crinifrons) karyotype revealed by comparative chromosome painting

The black muntjac (Muntiacus crinifrons) has an unusual karyotype of 2n = 8 in females and 2n = 9 in males. We have studied the evolution of this karyotype by hybridising chromosome-specific paints derived from flow-sorted chromosomes of the Chinese muntjac (M. reevesi, 2n = 46) to chromosomes of the black muntjac. The hybridisation pattern allowed us to infer chromosomal homologies between these two species. Tandem and centromeric fusions, reciprocal translocations, and insertions are involved in the reduction of the diploid number from 2n = 46 to 2n = 8, 9. The painting patterns further show complex chromosomal rearrangements in the male black muntjac which involve more than half the karyotype, including both sex chromosomes. Since early meiosis is reported to be normal without any visible inversion loops of the synaptonemal complex, the observed chromosomal rearrangements would lead to heterosynapsis and, therefore, leave a large fraction of the male black muntjac karyotype balanced between the two sexes.

Reciprocal chromosome painting among human, aardvark, and elephant (superorder Afrotheria) reveals the likely eutherian ancestral karyotype

The Afrotheria, a supraordinal grouping of mammals whose radiation is rooted in Africa, is strongly supported by DNA sequence data but not by their disparate anatomical features. We have used flow-sorted human, aardvark, and African elephant chromosome painting probes and applied reciprocal painting schemes to representatives of two of the Afrotherian orders, the Tubulidentata (aardvark) and Proboscidea (elephants), in an attempt to shed additional light on the evolutionary affinities of this enigmatic group of mammals. Although we have not yet found any unique cytogenetic signatures that support the monophyly of the Afrotheria, embedded within the aardvark genome we find the strongest evidence yet of a mammalian ancestral karyotype comprising 2n = 44. This karyotype includes nine chromosomes that show complete conserved synteny to those of man, six that show conservation as single chromosome arms or blocks in the human karyotype but that occur on two different chromosomes in the ancestor, and seven neighbor-joining combinations (i.e., the synteny is maintained in the majority of species of the orders studied so far, but which corresponds to two chromosomes in humans). The comparative chromosome maps presented between human and these Afrotherian species provide further insight into mammalian genome organization and comparative genomic data for the Afrotheria, one of the four major evolutionary clades postulated for the Eutheria.

Chromosome painting in the long-tailed field mouse provides insights into the ancestral murid karyotype

We report on the hybridization of mouse chromosomal paints to Apodemus sylvaticus, the long-tailed field mouse. The mouse paints detected 38 conserved segments in the Apodemus karyotype. Together with the species reported here there are now six species of rodents mapped with Mus musculus painting probes. A parsimony analysis indicated that the syntenies of nine M. musculus chromosomes were most likely already formed in the muroid ancestor: 3, 4, 7, 9, 14, 18, 19, X and Y. The widespread occurrence of syntenic segment associations of mouse chromosomes 1/17, 2/13, 7/19, 10/17, 11/16, 12/17 and 13/15 suggests that these associations were ancestral syntenies for muroid rodents. The muroid ancestral karyotype probably had a diploid number of about 2n = 54. It would be desirable to have a richer phylogenetic array of species before any final conclusions are drawn about the Muridae ancestral karyotype. The ancestral karyotype presented here should be considered as a working hypothesis. Copyright (C) 2004 S. Karger AG, Basel.

Karyotype relationships of six bat species (Chiroptera, Vespertilionidae) from China revealed by chromosome painting and G-banding comparison

The Vespertilionidae is the largest family in the order Chiroptera and has a worldwide distribution in the temperate and tropical regions. In order to further clarify the karyotype relationships at the lower taxonomic level in Vespertilionidae, genome-wid