Vortices in (Abelian) Chern-Simons gauge theory

The vortex solutions of various classical planar field theories with (Abelian) Chern-Simons term are reviewed. Relativistic vortices, put forward by Paul and Khare, arise when the Abelian Higgs model is augmented with the Chern-Simons term. Adding a suitable sixth-order potential and turning off the Maxwell term provides us with pure Chern-Simons theory, with both topological and non-topological self-dual vortices, as found by Hong-Kim-Pac, and by Jackiw-Lee-Weinberg. The non-relativistic limit of the latter leads to non-topological Jackiw-Pi vortices with a pure fourth-order potential. Explicit solutions are found by solving the Liouville equation. The scalar matter field can be replaced by spinors, leading to fermionic vortices. Alternatively, topological vortices in external field are constructed in the phenomenological model proposed by Zhang-Hansson-Kivelson. Non-relativistic Maxwell-Chern-Simons vortices are also studied. The Schrodinger symmetry of Jackiw-Pi vortices, as well as the construction of some time-dependent vortices, can be explained by the conformal properties of non-relativistic space-time, derived in a Kaluza-Klein-type framework. (c) 2009 Elsevier B.V. All rights reserved.

Inner structure of Spin(c)(4) gauge potential on 4-dimensional manifolds

The decomposition of Spin(c)(4) gauge potential in terms of the Dirac 4-spinor is investigated, where an important characterizing equation Delta A(mu) = -lambda A(mu) has been discovered. Here, lambda is the vacuum expectation value of the spinor field, lambda = parallel to Phi parallel to(2), and A(mu) the twisting U(1) potential. It is found that when), takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg-Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed.

Decomposition of Noncommutative U(1) Gauge Potential

We investigate the decomposition of noncommutative gauge potential (A) over cap (i), and find that it has inner structure, namely, (A) over cap (i) can he decomposed in two parts, (b) over cap (i) and (a) over cap (i), where (b) over cap (i) satisfies gauge transformations while (a) over cap (i) satisfies adjoint transformations, so close the Seiberg-Witten mapping of noncommutative, U(1) gauge potential. By, means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U(1) gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor

New vortex solutions of Jackiw-Pi model

Based on current phi-mapping topological theory, a kind of self-dual equations in Jackiw-Pi model are studied. We first obtain explicit, self-dual solutions that satisfy Liouville equation which contains delta-function. Then we get perfect vortex solutions which reflect the system's internal topological structure, and consequently the quantization of flux.

Knotted wave dislocation with the hopf invariant

We study the wave dislocations with an induced gauge potential. The topological current characterized the wave dislocations is constructed with the dual of Abelian gauge field. And the topological charges and locations of the wave dislocations are determined by the phi-mapping topological current theory. Furthermore, it is shown that the knotted wave dislocations can be described with a Hopf invariant in the wave field. At last we discussed the evolution of the knotted wave dislocations.

Enhancing robustness and immunization in geographical networks

We find that different geographical structures of networks lead to varied percolation thresholds, although these networks may have similar abstract topological structures. Thus, strategies for enhancing robustness and immunization of a geographical network are proposed. Using the generating function formalism, we obtain an explicit form of the percolation threshold q(c) for networks containing arbitrary order cycles. For three-cycles, the dependence of q(c) on the clustering coefficients is ascertained. The analysis substantiates the validity of the strategies with analytical evidence.

Knotlike chi disclinations in the cholesteric liquid crystals

We investigate the topological properties of N(N >= 1) disclination lines in cholesteric liquid crystals. The topological structure of N disclination lines is obtained with the Hopf index and Brouwer degree. Furthermore, the knotted x disclination loops is proposed with the Hopf invariant. And we consider the stability of such configuration based on the higher order interaction. At last, the evolution of the disclinations is discussed.

Observation of charge-dependent azimuthal correlations and possible local strong parity violation in heavy-ion collisions

Parity (P)-odd domains, corresponding to nontrivial topological solutions of the QCD vacuum, might be created during relativistic heavy-ion collisions. These domains are predicted to lead to charge separation of quarks along the orbital momentum of the system created in noncentral collisions. To study this effect, we investigate a three-particle mixed-harmonics azimuthal correlator which is a P-even observable, but directly sensitive to the charge-separation effect. We report measurements of this observable using the STAR detector in Au + Au and Cu + Cu collisions at root s(NN) = 200 and 62 GeV. The results are presented as a function of collision centrality, particle separation in rapidity, and particle transverse momentum. A signal consistent with several of the theoretical expectations is detected in all four data sets. We compare our results to the predictions of existing event generators and discuss in detail possible contributions from other effects that are not related to P violation.

规范势分解与Chern-Simons场中涡旋解的拓扑结构

本论文主要包括两部分内容，一部分简述了规范势的可分解理论，第二部分研究了Chern-Simons涡旋解的拓扑结构。讨论了SU(2)规范势分解的几何意义。提出了非对易规范势的可分解性，求出了非对易 群规范势用单位矢量场的分解以及规范平行条件下的规范场强。利用规范势分解理论和Ф-映射拓扑流理论分别研究了Jackiw-Pi模型和SU(2)Dunne-Jackiw-Pi-Trugenberger模型涡旋的拓扑结构，得到一个新的自对偶方程，发现了Chern-Simons多涡旋解与拓扑数之间的联系。我们构造了一个新的静态的自对偶Chern-Simons多涡旋解，每个涡旋由5个实参数描述。为了研究拓扑数对涡旋形状的影响，给出了具有不同拓扑数的多涡旋解，并绘出了涡旋密度的分布图。我们还研究了该涡旋解的磁通量的拓扑量子化

景观农业研究的兴起及其实际意义

Landscape agriculture is the combination of landscape ecology and agriculture. Its basic idea is from the system theory and landscape ecology. Now landscape agriculture is getting more and more attention because of its multi-functional roles. For example, it can exploit the agricultural ecosystem more rationally, make full use of the self-adjustment function of the natural patches and corridors in the field, as well as the effects from landform types and topological components. It uses regenerative biological energy to a large extent, constitutes beautiful scenic view and protects the diversity of genetics, species, ecosystems and landscapes. Landscape agriculture emphasizes environment improvement, bio-diversity protection and tourism development, thus provides new possibility for the increase of economical benefits and gets the positive feedback loop started. An example from the former Soviet Union is presented as well in this paper

陕北黄土丘陵沟壑区城郊农村土地利用变化定量分析

以典型黄土丘陵沟壑区——延安市赵庄村为例,选取土地利用动态度、土地利用趋势状态指数、土地利用景观指数等指标,对村庄尺度上的土地利用变化进行了定量分析。结果表明,6 a来,研究区土地利用发生了较大的变化,主要以耕地的减少和未利用土地的增加等变化为主;未利用土地、居住及建设用地、林地、灌草地以不同程度增加,其动态度大小依次为43.92%,15.35%,0.33%,0.17%;而耕地、果园、水域则以不同程度减小,动态度大小依次为7.45%,3.79%,0.20%;耕地、果园、水域呈"落势"状态,而未利用土地、居住及建设用地、林地、灌草地呈"涨势",朝着规模增大的趋势发展;斑块数与斑块密度增加,优势度指数与偏离度指数减小,多样性指数、均匀度指数和破碎度指数都有不同程度的增大。

子午岭林区典型植被下土壤结构及稳定性指标分析

运用分形理论,研究了子午岭林区5种天然次生植被(以6 a天然恢复弃耕地为对照)下土壤结构特征,分析了土壤水稳性团聚体分维、孔隙分维、平均重量直径等3个指标在描述土壤结构稳定性方面的差异。研究表明,相对于弃耕地,各个植被群落均能明显改善土壤结构,降低土壤水稳性团聚体分形维数,提高孔隙分形维数,增强土壤结构的稳定性。土壤水稳性团聚体分维、孔隙分维与>0.25 mm水稳性团聚体含量、土壤有机碳、容重的相关系数均达到了极显著水平,均能作为评价土壤结构稳定性的指标;而团聚体平均重量直径与土壤有机碳含量、容重相关性不显著,只与>5 mm团聚体含量和>0.25 mm团聚体含量有极显著正相关关系,因此,仅可作为大团聚体含量的评价指标。

黄土丘陵区农业生态安全评价指标体系初探

以纸坊沟流域为例,构建了黄土丘陵区流域农业生态安全评价指标体系。依据该流域近70 a来的农业生态安全状况,将该流域生态经济系统演变过程划分为4个阶段。从这4个阶段入手分析影响农业生态安全的主要因子,得出了一系列评价指标。结合选取指标的科学性、动态性、实用性等基本原则,参考压力—状态—响应(PSR)模型和多位专家的建议,进一步筛选、分类和确定评价指标,从而建立了一套由生态环境、社会经济、综合功能3大类,20个具体指标构成的适宜于黄土丘陵区的农业生态安全评价指标体系。

陕北黄土丘陵沟壑区土地利用景观格局动态变化特征分析

以位于典型黄土丘陵沟壑区的延安赵庄村为例,选取多样性、优势度、均匀度、破碎度和偏离度等主要指标,对村庄尺度上的土地利用景观格局动态变化进行分析研究。结果表明:1)研究期间,研究区景观斑块数与景观斑块密度增加,而平均斑块面积减少;2)研究区2个时期的景观异质性差异显著,景观指数变化表现为:优势度指数与偏离度指数减小,多样性指数、均匀度指数和破碎度指数都有不同程度的增大;3)6年来,随着退耕还林(草)政策的实施,研究区土地利用景观格局有了较大变化,生态环境整体状况趋于改善,农民收入有所增加,产业结构趋向合理,其中,工副业比例增大与种植业、养殖业、果菜比例减小是研究期间农民收入构成的主要变化特点,农民收入以工副业、果菜为主。

黄土高原降雨空间分布的不均匀性研究

根据黄土高原13条流域的降雨资料，分三种雨型即局地强对流条件引起的小范围、短历时、高强度的局地性暴雨（A型暴雨），峰面型降雨夹有局地雷暴性质的较大范围、中历时、中强度暴雨（B型暴雨），峰面型降雨引起的大面积、长历时、低强度暴雨（C型暴雨）；选用流域面雨量离差系数Cv、流域降雨不均匀系数η和流域最大点与最小点降雨量比值系数α三种指标，分析了次降雨空间分布的不均匀性。