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.

Crystal structure and phase transition studies in perovskite-type oxides using powder-diffraction techniques and symmetry-mode analysis : SrLnMRuO6 (Ln=La,Pr,Nd; M=Zn,Co,Mg,Ni,Fe) and ALn2CuTi2O9 (A=Ca,Ba; Ln=La,Pr,Nd,Sm)

La tesis se ha centrado en la síntesis y caracterización estructural de materiales tipo perovskita: SrLnMRuO6 (Ln=La,Pr,Nd; M=Zn,Co,Mg,Ni,Fe) y ALn2CuTi2O9 (A=Ca,Ba; Ln=La,Pr,Nd,Sm). El estudio de las estructuras de los materiales se ha realizado mediante el análisis de los patrones de difracción en polvo de rayos-X, sincrotrón y/o neutrones. En el refinamiento por el método de Rietveld de las estructuras se han sustituido las coordenadas atómicas (el método más común), por coordenadas colectivas: las amplitudes de los modos que describen la distorsión de la fase prototipo. Los resultados generales para la serie SrLnMRuO6 (Ln=La,Pr,Nd; M=Zn,Co,Mg,Ni) a temperatura ambiente se ha recogido en un diagrama en el que se han indicado las amplitudes de los modos que transforman de acuerdo a las irreps en función del factor de tolerancia, ya que todos ellos cristalizan en la misma fase monoclínica (P21/n); y a temperaturas altas se ha construido un diagrama de fase. Los materiales SrLnFeRuO6 ( Ln=La,Pr,Nd) y CaLn2CuTi2O9 cristalizan en la fase ortorrómbica Pbnm a temperatura ambiente; mientras que BaLn2CuTi2O9 tienen una estructura más simétrica, I4/mcm. A altas temperaturas se han identificado las transiciones de fase inducidas por el cambio de temperatura.A temperaturas bajas se han analizado las estructuras magnéticas de algunos de los compuestos mediante difracción de neutrones.

Relative mirror symmetry and ramifications of a formula for Gromov-Witten invariants

For a toric Del Pezzo surface S, a new instance of mirror symmetry, said relative, is introduced and developed. On the A-model, this relative mirror symmetry conjecture concerns genus 0 relative Gromov-Witten of maximal tangency of S. These correspond, on the B-model, to relative periods of the mirror to S. Furthermore, for S not necessarily toric, two conjectures for BPS state counts are related. It is proven that the integrality of BPS state counts of the total space of the canonical bundle on S implies the integrality for the relative BPS state counts of S. Finally, a prediction of homological mirror symmetry for the open complement is explored. The B-model prediction is calculated in all cases and matches the known A-model computation for the projective plane.