Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

We study quantum classical correspondence in terms of the coherent wave functions of a charged particle in two-dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than h is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 27r-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.

THE ROTATIONALLY PERIODIC SYMMETRY IN BEM

Rotationally periodic symmetry is exploited in 2-D elastostatic calculation using the BEM.It is proved that the coefficient matrices of the global boundary element equations for the rotationally periodic system are block-circulant so long as a kind of symmetry-adapted reference coordinate system is adopted. Furthermore,an efficient algorithm,which partitions the original problem of solving the boundary element equations into a series of subproblems,is proposed.The method permits arbitrary load distribution for stress analysis problems.

Rotationally Symmetric Translating Solutions to Curvature Flows in Image Processing

This paper proves the existence of rotationally symmetric solutions to a curvature flow in image processing. The flow includes the level sets flow and the mean curvature flow projected onto the normal. Sharp estimates are obtained for these solutions..

A NEW METHOD FOR NUMERICAL SIMULATION OF TWO TRAINS PASSING BY EACH OTHER AT THE SAME SPEED

A new method is proposed to numerically simulate problems of trains passing by each other at the same speed, and is implemented in UDF language of commercial software Fluent. Because only a half of the computational domain is required and the dynamic mesh technique is avoided, the computational efficiency is greatly improved. A two-dimensional test case is used for validation, which shows that the flow field and the pressure wave during the train-passing events can be correctly calculated by this new method. This method can be easily extended to three-dimensional simulations, to deal with practical problems.

Classification of gradient steady Ricci solitons with linear curvature decay

In this paper,we study steady Ricci solitons with a linear decay of sectional curvature.In particular,we give a complete classification of 3-dimensional steady Ricci solitons and 4-dimensional K-noncollapsed steady Ricci solitons with non-negative sectional curvature under the linear curvature decay.

Spherical Logistic Distribution

Some of the spherical distributions can be constructed through proper transformation of the densities on plane.Since the logistic density on the Euclidean space has similar behavior to the normal distribution,it is of interest to extend it for spherical data.In this paper,we introduce spherical logistic distribution on the unit sphere and then study relevant statistical inferences including parameters estimation through method of moments and maximum likelihood techniques.It is shown that the spherical logistic distribution is a multimodal distribution with the marginal logistic density function.Proposed density has rotational symmetry property and this plays a key role to drive some important results related to first two moments.To investigate the proposed density in more details,some simulation studies along with analyzing real-life data are also considered.

Qualitative tool for designing natural protected areas and ecological restoration projects

The rotational symmetry connection between the Species-Area Relationship(SAR)and Endemics-Area Relationship(EAR)was discovered in the frame of Species-Area Theory.In this paper,this paired connection was applied into the impact of variation of number of species and area and dynamic change of species-abundance distribution on the curve shape of SAR and EAR,which can be integrated into the assessment of Natural Protected Areas and Ecological Restoration Projects.The results indicate that the underestimate or overestimate of total number of species can lead to the underestimate or overestimate of extinction rate,while the reduction or expansion of area can lead to the increase or decrease in extinction rate.In addition,the species-abundance distribution change of community causes the shape tuning of SAR and EAR,which leads to inconsistent change of extinction rate.Thus,this SAT frame can be used as a qualitative tool in conservation and restoration management.