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Chinese Physics B 2012年第4期21卷 67-73页

作者：辛俊丽梁九卿 Institute of Theoretical Physics Shanxi UniversityTaiyuan 030006China Department of Physics and Electronic Engineering Yuncheng CollegeYuncheng 044000China

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.

关键词： quantum-classical correspondence anyon rotational symmetry arbitrary quantization of angular momentum

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

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Journal of Hydrodynamics 2010年第5期22卷 697-702页

作者： ZHAO Xiao-li SUN Zhen-xu School of Aerospace Tsinghua University Beijing China State Key Laboratory for Turbulence and Complex Systems College of Engineering Peking University Beijing China

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.

关键词： trains passing by each other rotational symmetry dynamic mesh pressure wave

Multi-Band Absorption Properties and Near-Field Enhancement in Mid-Infrared Based on the Interference Theory

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Chinese Physics Letters 2014年第5期31卷 56-60页

作者：衡航杨理 Department of Physics Nanjing Normal University Nanjing 210097 Center for Analysis and Testing Nanjing Normal University Nanjing 210097

We numerically study the multi-band absorption properties and near-field enhancement inside the microcavity based on the interference theory. The compact single unit cell consists of a gold square patch placed on the top of a metallic ground plane, separated by a dielectric layer. At the normal incidence of electromagnetic radiation, four bands of a maximum absorption of 98% are accomplished by appropriate sizes of the square patch. Furthermore, we demonstrate that the four bands, which are corresponding to the fundamental mode and higher modes of the standing wave, can be readily tuned in the mid-infrared region and associated with the near-field enhancement in the cuboid mierocavity. Since chemical and biological fingerprints of the common functional groups can be found in the mid-infrared region, we may readily tune the multi-bands of interest in the mid-infrared range and identify the molecular stretches of groups. Moreover, the proposed structure is insensitive to the polarization of the incident wave due to the complete rotational symmetry （C4 symmetry）. The unique properties of the optical metamaterial indicate that this approach is a promising strategy for surface-enhanced infrared absorption spectroscopy and for the tracking of characteristic molecular vibrational modes

关键词： INFRARED absorption RADIATION absorption NEAR field communication ELECTRIC interference STANDING waves rotational symmetry

Classification of gradient steady Ricci solitons with linear curvature decay

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Science China Mathematics 2020年第1期63卷 135-154页

作者： Yuxing Deng Xiaohua Zhu School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China School of Mathematical Sciences and BICMR Peking UniversityBeijing 100871China

In this paper,we study steady Ricci solitons with a linear decay of sectional *** particular,we give a complete classification of 3-dimensional steady Ricci solitons and 4-dimensional K-noncollapsed steady Ricci solit... 详细信息

关键词： Ricci flow steady Ricci solitons rotational symmetry

Nematic Ferromagnetism on the Lieb Lattice

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Chinese Physics Letters 2014年第11期31卷 14-17页

作者：陈科技张威 Department of Physics Renmin University of China Beijing 100872 Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices Renmin University of China Beijing 100872

We discuss the properties of ferromagnetic orders on the Lieb lattice and show that a symmetry protected quadratic-fiat band crossing point will dramatically affect the magnetic ordering. In the presence of a weak on-site repulsive interaction, the ground state is a nematic ferromagnetic order with simultaneously broken time-reversal and rotational symmetries. When the interaction strength increases, the rotational symmetry will restore at a critical value, and the system enters a conventional ferromagnetic regime. The mean-field transition temperatures for both the nematic and conventional ferromagnetic phases are in the order of interaction. This observation suggests that these magnetic orders have the potential to be realized and detected in cold atomic systems within realistic experimental conditions.

关键词： FERROMAGNETISM CONDENSED matter physics LATTICE theory rotational symmetry NEMATOCIDES

Weighted polyharmonic equation with Navier boundary conditions in a half space

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Science China Mathematics 2017年第3期60卷 491-510页

作者： ZHUO Ran Department of Mathematical Sciences Huanghuai University Zhumadian 463000 China Department of Mathematical Sciences Yeshiva UniversityNew York NY 10033 USA

We study positive solutions of the following polyharmonic equation with Hardy weights associated to Navier boundary conditions on a half space：where rn is any positive integer satisfying 0 〈 2m 〈 n. We first prove that the positive solutions of （0.1） are super polyharmonic, i.e.,where x＊ = （x1,... ,Xn-1, --Xn） is the reflection of the point x about the plane Rn-1. Then, we use the method of moving planes in integral forms to derive rotational symmetry and monotonicity for the positive solution of （0.3）, in which α can be any real number between 0 and n. By some Pohozaev type identities in integral forms, we prove a Liouville type theorem--the non-existence of positive solutions for （0.1）.

关键词： Navier boundary conditions half space super polyharmonic equivalence integral equation rotational symmetry non-existence

Liouville type theorems for Schrdinger systems

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Science China Mathematics 2015年第1期58卷 179-196页

作者： ZHUO Ran LI Feng Quan Department of Mathematical Sciences Yeshiva University School of Mathematical Sciences Dalian University of Technology

We study positive solutions to the following higher order SchrSdinger system with Dirichlet boundary conditions on a half space： where a is any even number between 0 and n. This PDE system is closely related to the integral system where G is the corresponding Green＇s function on the half space. More precisely, we show that every solution to （0.2） satisfies （0.1）, and we believe that the converse is also true. We establish a Liouville type theorem the non-existence of positive solutions to （0.2） under a very weak condition that u and v are only locally integrable. Some new ideas are involved in the proof, which can be applied to a system of more equations.

关键词： Schrodinger systems poly-harmonic operators Dirichlet boundary conditions method of movingplanes in integral forms Kelvin transforms monotonicity rotational symmetry non-existence

A Zernike-moment-based non-local denoising filter for cryo-EM images

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Science China(Life Sciences) 2013年第4期56卷 384-390页

作者： WANG Jia YIN ChangCheng Department of Biophysics School of Basic Medical Sciences Peking University

Cryo-electron microscopy (cryo-EM) plays an important role in determining the structure of proteins, viruses, and even the whole cell. It can capture dynamic structural changes of large protein complexes, which other methods such as X-ray crystallography and nuclear magnetic resonance analysis find difficult. The signal-to-noise ratio of cryo-EM images is low and the contrast is very weak, and therefore, the images are very noisy and require filtering. In this paper, a filtering method based on non-local means and Zernike moments is proposed. The method takes into account the rotational symmetry of some biological molecules to enhance the signal-to-noise ratio of cryo-EM images. The method may be useful in cryo-EM image processing such as the automatic selection of particles, orientation determination, and the building of initial models.

关键词： cryo-electron microscopy non-local means Zernike moments rotational symmetry

Spherical Logistic Distribution

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Communications in Mathematics and Statistics 2020年第2期8卷 151-166页

作者： M.Moghimbeygi M.Golalizadeh Department of Statistics Tarbiat Modares UniversityTehranIran

Some of the spherical distributions can be constructed through proper transformation of the densities on *** the logistic density on the Euclidean space has similar behavior to the normal distribution,it is of interest to extend it for spherical *** 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 *** is shown that the spherical logistic distribution is a multimodal distribution with the marginal logistic density *** density has rotational symmetry property and this plays a key role to drive some important results related to first two *** investigate the proposed density in more details,some simulation studies along with analyzing real-life data are also considered.

关键词： Bessel function Logistic density Bimodality Spherical distribution rotational symmetry

Qualitative tool for designing natural protected areas and ecological restoration projects

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Ecosystem Health and Sustainability 2019年第1期5卷 181-184,I0018页

作者： Xubin Pan Institute of Plant Quarantine Chinese Academy of Inspection and QuarantineBeijingChina

The rotational symmetry connection between the Species-Area Relationship(SAR)and Endemics-Area Relationship(EAR)was discovered in the frame of Species-Area *** 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 *** 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 *** addition,the species-abundance distribution change of community causes the shape tuning of SAR and EAR,which leads to inconsistent change of extinction ***,this SAT frame can be used as a qualitative tool in conservation and restoration management.

关键词： rotational symmetry extinction rate speciesabundance distribution Pan effect disturbance