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.

非相对论Chern-Simons多涡旋解的拓扑结构(英文)

运用规范势分解理论研究了Jackiw-Pi模型中的自对偶方程,得到一个新的自对偶方程,发现了Chern-Simons多涡旋解与拓扑荷之间的联系。为了研究Jackiw-Pi模型多涡旋解的拓扑性质,构造了一个新的静态自对偶Chern-Simons多涡旋解,每个涡旋由5个实参数描述。2个实参量用来描述涡旋的位置,2个实参量用来描述涡旋的尺度和相位,还有一个实参量描述涡旋的荷。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。另外还研究了该涡旋解的磁通量的拓扑量子化。

SU(2)Chern-Simons涡旋解的拓扑结构

运用规范势分解理论研究了Dunne-Jackiw-Pi-Trugenberger模型中的自对偶方程,得到一个静态的自对偶Chern-Simons多涡旋解,每个涡旋由5个参数描述。发现了自对偶解与拓扑数之间的关系,而拓扑数由Brouwer度与Hopf指标确定。同时,也研究了该涡旋解的磁通量的拓扑量子化。

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

Jackiw-Pi模型的新涡旋解

运用映射拓扑流理论研究了Jackiw-Pi模型中的自对偶方程,得到一个静态的自对偶解满足带有δ函数项的刘维尔方程,从而得到了一个完整的带有拓扑信息的涡旋解,自然给出了磁通量子化.

Topological structure of the many vortices solution in Jackiw-Pi model

By using the gauge potential decomposition, we discuss the self-dual equation and its solution in Jackiw-Pi model. We obtain a new concrete self-dual equation and find relationship between Chern-Simons vortices solution and topological number which is determined by Hopf indices and Brouwer degrees of Psi-mapping. To show the meaning of topological number we give several figures with different topological numbers. In order to investigate the topological properties of many vortices, we use five parameters (two positions, one scale, one phase per vortex and one charge of each vortex) to describe each vortex in many vortices solutions in Jackiw-Pi model. For many vortices, we give three figures with different topological numbers to show the effect of the charge on the many vortices solutions. We also study the quantization of flux of those vortices related to the topological numbers in this case.

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.

Topological structure of vortex solution in Jackiw-Pi model

By using phi-mapping method, we discuss the topological structure of the self-duality solution in Jackiw-Pi model in terms of gauge potential decomposition. We set up relationship between Chern-Simons vortex solution and topological number, which is determined by Hopf index and Brouwer degree. We also give the quantization of flux in this case. Then, we study the angular momentum of the vortex, which can be expressed in terms of the flux.

Topological structure of the solitons solution in SU(3) Dunne-Jackiw-Pi-Trugenberger model

By using phi-mapping topological current theory and gauge potential decomposition, we discuss the self-dual equation and its solution in the SU(N) Dunne-Jackiw-Pi-Trugenberger model and obtain a new concrete self-dual equation with a 6 function. For the SU(3) case, we obtain a new self-duality solution and find the relationship between the soliton solution and topological number which is determined by the Hopf index and Brouwer degree of phi-mapping. In our solution, the flux of this soliton is naturally quantized.

Holographic dual of linear dilaton black hole in Einstein-Maxwell-dilaton-axion gravity

Motivated by the recently proposed Kerr/CFT correspondence, we investigate the holographic dual of the extremal and non-extremal rotating linear dilaton black hole in Einstein-Maxwell-Dilaton-Axion Gravity. For the case of extremal black hole, by imposing the appropriate boundary condition at spatial infinity of the near horizon extremal geometry, the Virasoro algebra of conserved charges associated with the asymptotic symmetry group is obtained. It is shown that the microscopic entropy of the dual conformal field given by Cardy formula exactly agrees with Bekenstein-Hawking entropy of extremal black hole. Then, by rewriting the wave equation of massless scalar field with sufficient low energy as the SLL(2, R) x SLR(2, R) Casimir operator, we find the hidden conformal symmetry of the non-extremal linear dilaton black hole, which implies that the non-extremal rotating linear dilaton black hole is holographically dual to a two dimensional conformal field theory with the non-zero left and right temperatures. Furthermore, it is shown that the entropy of non-extremal black hole can be reproduced by using Cardy formula.

Saltation in wind blown sand

The Boltzmann equation of the sand particle velocity distribution function in wind-blown sand two-phase flow is established based on the motion equation of single particle in air. And then, the generalized balance law of particle property in single phase granular flow is extended to gas-particle two-phase flow. The velocity distribution function of particle phase is expanded into an infinite series by means of Grad's method and the Gauss distribution is used to replace Maxwell distribution. In the case of truncation at the third-order terms, a closed third-order moment dynamical equation system is constructed. The theory is further simplified according to the measurement results obtained by stroboscopic photography in wind tunnel tests.

粘弹性体中裂纹演化的细观力学分析

根据Eshelby等效夹杂理论研究含钱币形裂纹的粘弹体中裂纹张开位移随时间的缓慢增大以及含裂纹粘弹体的等效模量的变化。对于Maxwell粘弹性材料给出了模量随时间变化的显式表达式,结果表明裂纹的缓慢张开使材料模量减小更快。

风沙两相流中的跃移运动

从单个跃移沙粒在气流中的运动方程出发导出了风沙两相流中沙粒相速度分布函数的Ｂoltzmann方程；并以此将单相颗粒流理论中的广义平衡方程推广到气固两相流的情形。提出用Grad方法将粒子相速度分布函数展成无穷级数，并引入Gauss分布取代单相颗粒流中传统的Maxwell分布。在保留到3次项的情况下，建立了气体－颗粒两相湍流边界层三阶矩封闭理论的动力学方程组。并在风洞频闪摄影实验的基础上，对理论进行简化，得到便于工程应用的简化方程。

粘弹流体的定常等温纺丝

本文考虑了粘弹流体的定常等温纺丝的流动问题,采用的本构方程是修改的Maxwell模型。得到了纺线方程的数值解和分析(近似)解,上述二种方法所得到的结果符合得很好。这就证明了我们采用的摄动法有较好的准确性。

球形粒子的热致迁移及各跳跃系数对适应系数的依赖关系

本文讨论有温度梯度场的稀薄气体(K_n(?)1时)中圆球所受的热泳力问题。在内区设分子在壁面作Maxwell类型反射求解B-K-W方程,与外区的Stokes方程和Laplace方程的解匹配。滑移系数C_m,热蠕动系数C_s和温度跳跃系数C_t,做为待定量在内区解的一阶近似中定出。所得的热泳力与实验相符,计算所得的C_m,C_s和C_t之值及对适应系数α的依赖关系与用变分等方法对平板问题所得结果相符。