Space—times admitting Killing—Yano tensors. II

1982 ◽  
Vol 381 (1781) ◽  
pp. 315-322 ◽  
Keyword(s):  
Angular Momentum ◽  
Vector Field ◽  
Equatorial Plane ◽  
Kepler Problem ◽  
Three Dimensional ◽  
Position Vector ◽  
Line Elements ◽  
Tangent Field

In this paper we derive canonical line elements admitting a simple KillingYano tensor f* ab. There exist three distinct cases according to the character o f f* ab (spacelike, timelike, null). We reveal several close analogies between the vector field la = f * arp r along a geodesic with tangent field p r and the angular momentum l = rxpin the case of a spacelike Killing-Yano tensor. In particular, we show that, in consequence of the Killing-Yano tensor equations, there exists an analogue of the three-dimensional position vector field in certain hypersurfaces and th at la can be written in the form (r x p )a. Furthermore, an analogue of the ‘ equatorial plane ’ of the classical Kepler problem can be constructed intrinsically.

Dynamics and Regularization of the Kepler Problem on Surfaces of Constant Curvature

2017 ◽  
Vol 69 (5) ◽  
pp. 961-991 ◽  
Author(s):  
Jaime Andrade ◽  
Nestor Dàvila ◽  
Ernesto Pérez-Chavela ◽  
Claudio Vidal
Keyword(s):  
Angular Momentum ◽  
Vector Field ◽  
Constant Curvature ◽  
Kepler Problem ◽  
Phase Portraits ◽  
Problem Of Time

AbstractWe classify and analyze the orbits of the Kepler problemon surfaces of constant curvature (both positive and negative, 𝕊2and ℍ2, respectively) as functions of the angular momentum and the energy. Hill's regions are characterized, and the problem of time-collision is studied. We also regularize the problem in Cartesian and intrinsic coordinates, depending on the constant angular momentum, and we describe the orbits of the regularized vector field. The phase portraits both for 𝕊2and ℍ2are pointed out.

scholarly journals Closedness of orbits in a space with SU(2) Poisson structure

2014 ◽  
Vol 29 (17) ◽  
pp. 1450081 ◽  
Author(s):  
Amir H. Fatollahi ◽  
Ahmad Shariati ◽  
Mohammad Khorrami
Keyword(s):  
Angular Momentum ◽  
Poisson Structure ◽  
Kepler Problem ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Spherically Symmetric ◽  
Symmetric Potential ◽  
Ordinary Space ◽  
Three Dimensional Space ◽  
Central Forces

The closedness of orbits of central forces is addressed in a three-dimensional space in which the Poisson bracket among the coordinates is that of the SU(2) Lie algebra. In particular it is shown that among problems with spherically symmetric potential energies, it is only the Kepler problem for which all bounded orbits are closed. In analogy with the case of the ordinary space, a conserved vector (apart from the angular momentum) is explicitly constructed, which is responsible for the orbits being closed. This is the analog of the Laplace–Runge–Lenz vector. The algebra of the constants of the motion is also worked out.

scholarly journals Vortex states in an acoustic Weyl crystal with a topological lattice defect

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qiang Wang ◽  
Yong Ge ◽  
Hong-xiang Sun ◽  
Haoran Xue ◽  
Ding Jia ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Lattice Defect ◽  
Three Dimensional ◽  
Surface States ◽  
Real Space ◽  
Lattice Defects ◽  
One Dimensional ◽  
Topological Features ◽  
Topological Lattice

AbstractCrystalline materials can host topological lattice defects that are robust against local deformations, and such defects can interact in interesting ways with the topological features of the underlying band structure. We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital angular momentum locked to the direction of propagation. They span a range of axial wavenumbers defined by the projections of two bulk Weyl points to a one-dimensional subspace, in a manner analogous to the formation of Fermi arc surface states. We use acoustic experiments to probe their dispersion relation, orbital angular momentum locked waveguiding, and ability to emit acoustic vortices into free space. These results point to new possibilities for creating and exploiting topological modes in three-dimensional structures through the interplay between band topology in momentum space and topological lattice defects in real space.

Kinematical evolution of Globular Clusters

2019 ◽  
Vol 14 (S351) ◽  
pp. 524-527
Author(s):  
Maria A. Tiongco ◽  
Enrico Vesperini ◽  
Anna Lisa Varri
Keyword(s):  
Angular Momentum ◽  
Structural Properties ◽  
Globular Clusters ◽  
Velocity Dispersion ◽  
Three Dimensional ◽  
Stellar Populations ◽  
Velocity Space ◽  
Fundamental Understanding

AbstractWe present several results of the study of the evolution of globular clusters’ internal kinematics, as driven by two-body relaxation and the interplay between internal angular momentum and the external Galactic tidal field. Via a large suite of N-body simulations, we explored the three-dimensional velocity space of tidally perturbed clusters, by characterizing their degree of velocity dispersion anisotropy and their rotational properties. These studies have shown that a cluster’s kinematical properties contain distinct imprints of the cluster’s initial structural properties, dynamical history, and tidal environment. Building on this fundamental understanding, we then studied the dynamics of multiple stellar populations in globular clusters, with attention to the largely unexplored role of angular momentum.

scholarly journals Dynamical and Physical Processes Leading to Tropical Cyclone Intensification under Upper-Level Trough Forcing

2013 ◽  
Vol 70 (8) ◽  
pp. 2547-2565 ◽  
Author(s):  
Marie-Dominique Leroux ◽  
Matthieu Plu ◽  
David Barbary ◽  
Frank Roux ◽  
Philippe Arbogast
Keyword(s):  
Angular Momentum ◽  
Tropical Cyclone ◽  
Potential Vorticity ◽  
Weather Prediction ◽  
Three Dimensional ◽  
Vertical Wind Shear ◽  
Thick Layer ◽  
Limited Area ◽  
Southwest Indian Ocean ◽  
Upper Level

Abstract The rapid intensification of Tropical Cyclone (TC) Dora (2007, southwest Indian Ocean) under upper-level trough forcing is investigated. TC–trough interaction is simulated using a limited-area operational numerical weather prediction model. The interaction between the storm and the trough involves a coupled evolution of vertical wind shear and binary vortex interaction in the horizontal and vertical dimensions. The three-dimensional potential vorticity structure associated with the trough undergoes strong deformation as it approaches the storm. Potential vorticity (PV) is advected toward the tropical cyclone core over a thick layer from 200 to 500 hPa while the TC upper-level flow turns cyclonic from the continuous import of angular momentum. It is found that vortex intensification first occurs inside the eyewall and results from PV superposition in the thick aforementioned layer. The main pathway to further storm intensification is associated with secondary eyewall formation triggered by external forcing. Eddy angular momentum convergence and eddy PV fluxes are responsible for spinning up an outer eyewall over the entire troposphere, while spindown is observed within the primary eyewall. The 8-km-resolution model is able to reproduce the main features of the eyewall replacement cycle observed for TC Dora. The outer eyewall intensifies further through mean vertical advection under dynamically forced upward motion. The processes are illustrated and quantified using various diagnostics.

Spectral Sensitivity of Photoreceptors and Colour Vision in the Solitary Bee, Osmia Rufa

1988 ◽  
Vol 136 (1) ◽  
pp. 35-52
Author(s):  
R. MENZEL ◽  
E. STEINMANN ◽  
J. DE SOUZA ◽  
W. BACKHAUS
Keyword(s):  
Spectral Sensitivity ◽  
Colour Vision ◽  
Three Dimensional ◽  
Just Noticeable Difference ◽  
Species Discrimination ◽  
Colour Space ◽  
Absorption Function ◽  
Perceptual Distance ◽  
Line Elements ◽  
Colour Signals

The spectral sensitivity of single photoreceptors of Osmia rufa was determined by a fast voltage-clamp technique. Three receptor types were found whose spectral sensitivity functions followed a rhodopsin-like photopigment absorption function with λmax values at 348nm (ultraviolet receptor), 436nm (blue receptor) and 572nm (green receptor). The λmax of the green receptor in Osmia rufa is shifted to much longer wavelengths compared with other insect species. Discrimination of colour signals was tested after training a bee at the entrance to its nest. The colour signals were filter discs (70 mm in diameter) with a hole (10 mm in diameter) in the centre and the bees quickly learned to use the coloured disc as a marker of the nest entrance. Tests were dual forced-choice tests with two coloured discs closely positioned next to each other. 94 different tests were each repeated 5–15 times and were performed after training to 12 different colour signals. A photoreceptor model was used to calculate the loci of the colour signals in a three-dimensional colour space and in a chromaticity diagram. The perceptual distance between the colour loci was calculated as line elements (minimum number of just noticeable difference, jnd-steps), which were based on the noiseproperties of the photoreceptors. The discrimination determined by the behavioural tests correlated very well with the jnd-steps. The correlation was better for the line elements in the colour plane than in the colour space. Osmia rufa was compared with the honeybee Apis mellifera and the stingless bee Melipona quadrifasciata. There is no difference in colour selection between Osmia and Apis, whereas Melipona discriminates less well in the violet-blue region. The model calculation was used to compare the chromaticity diagrams and the spectral discrimination functions of the three species. It is concluded that the receptor model used in this study predicts the discrimination behaviour of the three bee species very well. Therefore, comparative studies on colour vision in flowervisiting insects may be based on spectral measurements of the photoreceptors, and in many cases this reduces the extent of laborious behavioural studies.

AGN torus threaded by large scale magnetic field

2018 ◽  
Vol 27 (10) ◽  
pp. 1844006
Author(s):  
A. Dorodnitsyn ◽  
T. Kallman
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Accretion Disk ◽  
Large Scale ◽  
Three Dimensional ◽  
X Ray ◽  
Radiative Feedback ◽  
Large Scale Magnetic Field ◽  
Three Dimensional Simulations

Large scale magnetic field can be easily dragged from galactic scales toward AGN along with accreting gas. There, it can contribute to both the formation of AGN “torus” and help to remove angular momentum from the gas which fuels AGN accretion disk. However the dynamics of such gas is also strongly influenced by the radiative feedback from the inner accretion disk. Here we present results from the three-dimensional simulations of pc-scale accretion which is exposed to intense X-ray heating.

Short Helical Combustor: Flow Control in a Combustion System With Angular Air Supply

2017 ◽  
Author(s):  
Behdad Ariatabar ◽  
Rainer Koch ◽  
Hans-Jörg Bauer
Keyword(s):  
Temperature Field ◽  
Angular Momentum ◽  
Three Dimensional ◽  
The Novel ◽  
Combustion System ◽  
Flow Angle ◽  
Air Supply ◽  
Inhomogeneous Flow ◽  
Generic Design ◽  
Industrial Optimization

The concept of the novel Short Helical Combustor (SHC) was investigated in our previous work [1, 2]. Based on the insight gained from these previous investigations, we propose a generic design improvement to address the tremendous loss of initial angular momentum as well as inhomogeneous flow and temperature field at the outlet of the SHC. In the present paper, the main features of this design are introduced. It is shown that a three-dimensional shaping of the sidewalls, the dome, and the liners can effectively counteract the suboptimal interaction of the swirl flames with these surrounding walls. As a result, the flow at the outlet of the combustor features a high angular momentum and exhibits a uniform flow angle and temperature field. The insight gained from these generic investigations, and the resulting design optimization provides a useful framework for further industrial optimization of the SHC.

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