757 resultados para Invariants de Riemann


Relevância:

10.00% 10.00%

Publicador:

Resumo:

Duración (en horas): Más de 50 horas. Destinatario: Estudiante y Docente

Relevância:

10.00% 10.00%

Publicador:

Resumo:

der="0" alt="" hspace="0" width="300" height="300" align="left" />《计算流体力学》是为高等院校和科研单位研究生撰写的“计算流体力学”课程的教科书。全书共分九章。前五章讲述了计算流体力学中的基本概念和基本方法。包括流体动力学的诸方程和模型方程及其数学性质、数值解的理论依据、基本计算方法和数值解的行为分析等。计算方法包含有空间离散方法、代数方程和非定常方程(包括时间离散)的求解方法。这里涉及到的离散方法有有限差分方法、有限体积方法、有限元方法和谱方法。这些都是已经成熟和具有普适性的方法。书中描述了构造这些方法的基本思想,重点是有限差分方法。书中的后四章是针对各种物理问题讲述计算方法。这里包含低速不可压和高速可压缩流体运动数值模拟的计算方法和网格生成技术。着重阐述了针对不同物理问题的特征对计算方法精度的要求,及构造不同计算方法的基本思想,且给出了一些简单物理问题的数值模拟结果,以证实计算方法的有效性。

目录

主要符号表
第一章 引论
1.1 计算流体力学及其特征
1.2 计算流体力学的发展
1.3 本书的目的和内容
参考文献
习题

第二章 流体力学方程及模型方程
2.1 流体力学基本方程
2.2 模型方程及其数学性质
2.3 双曲型方程组的初边值问题
2.4 Riemann间断解
参考文献
习题

第三章 偏微分方程的数值解法
3.1 有限差分法
3.2 偏微分方程的全离散
3.3 有限体积法
3.4 有限元方法
3.5 谱方法
参考文献
习题

第四章 高精度有限差分法及数值解的行为分析
4.1 模型方程及半离散化方程
4.2 高精度差分逼近式
4.3 数值解的精度及分辨率分析
4.4 数值解中的耗散效应与色散效应
4.5 数值解的群速度
4.6 数值解行为的进一步分析
4.7 时间离散的色散与耗散效应
参考文献
习题

第五章 代数方程的求解
5.1 Gauss消去法
5.2 标量追赶法
5.3 矩阵追赶法及LU分解法
5.4 迭代法求解代数方程
5.5 交替方向追赶法
5.6 非线性方程的求解
5.7 时间关系法及局部时间步长法
参考文献
习题

第六章 可压缩流体力学方程组的离散
6.1 一维流体力学方程及Jacobian系数矩阵的分裂
6.2 一维Euler方程的离散
6.3 Godunov间断分解法
6.4 Roe格式与Roe分解
6.5 多维问题的差分逼近
6.6 粘性项的差分逼近
参考文献
习题

第七章激波高分辨率差分格式
7.1 数值解中的非物理振荡
7.2 一阶TVD格式
7.3 二阶TVD格式
7.4 TVD格式在流体力学中的应用
7.5 MUSCL格式
7.6 其他类型的高分辨率格式
参考文献
习题

第八章 不可压Navier-Stokes方程的差分逼近
8.1 控制方程
8.2 求解定常N-S方程的人工压缩性方法
8.3 非定常原始变量N-S方程的求解
8.4 涡量-流函数法
参考文献
习题

第九章 网格技术
9.1 网格生成技术
9.2 非结构网格
9.3 基于非等距网格的有限差分法
习题
专业名词索引
外国人名译名对照表
Synopsis
Contents
作者简介

Relevância:

10.00% 10.00%

Publicador:

Resumo:

A new high-order finite volume method based on local reconstruction is presented in this paper. The method, so-called the multi-moment constrained finite volume (MCV) method, uses the point values defined within single cell at equally spaced points as the model variables (or unknowns). The time evolution equations used to update the unknowns are derived from a set of constraint conditions imposed on multi kinds of moments, i.e. the cell-averaged value and the point-wise value of the state variable and its derivatives. The finite volume constraint on the cell-average guarantees the numerical conservativeness of the method. Most constraint conditions are imposed on the cell boundaries, where the numerical flux and its derivatives are solved as general Riemann problems. A multi-moment constrained Lagrange interpolation reconstruction for the demanded order of accuracy is constructed over single cell and converts the evolution equations of the moments to those of the unknowns. The presented method provides a general framework to construct efficient schemes of high orders. The basic formulations for hyperbolic conservation laws in 1- and 2D structured grids are detailed with the numerical results of widely used benchmark tests. (C) 2009 Elsevier Inc. All rights reserved.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

In Part I a class of linear boundary value problems is considered which is a simple model of boundary layer theory. The effect of zeros and singularities of the coefficients of the equations at the point where the boundary layer occurs is considered. The usual boundary layer techniques are still applicable in some cases and are used to derive uniform asymptotic expansions. In other cases it is shown that the inner and outer expansions do not overlap due to the presence of a turning point outside the boundary layer. The region near the turning point is described by a two-variable expansion. In these cases a related initial value problem is solved and then used to show formally that for the boundary value problem either a solution exists, except for a discrete set of eigenvalues, whose asymptotic behaviour is found, or the solution is non-unique. A proof is given of the validity of the two-variable expansion; in a special case this proof also demonstrates the validity of the inner and outer expansions.

Nonlinear dispersive wave equations which are governed by variational principles are considered in Part II. It is shown that the averaged Lagrangian variational principle is in fact exact. This result is used to construct perturbation schemes to enable higher order terms in the equations for the slowly varying quantities to be calculated. A simple scheme applicable to linear or near-linear equations is first derived. The specific form of the first order correction terms is derived for several examples. The stability of constant solutions to these equations is considered and it is shown that the correction terms lead to the instability cut-off found by Benjamin. A general stability criterion is given which explicitly demonstrates the conditions under which this cut-off occurs. The corrected set of equations are nonlinear dispersive equations and their stationary solutions are investigated. A more sophisticated scheme is developed for fully nonlinear equations by using an extension of the Hamiltonian formalism recently introduced by Whitham. Finally the averaged Lagrangian technique is extended to treat slowly varying multiply-periodic solutions. The adiabatic invariants for a separable mechanical system are derived by this method.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

The primary focus of this thesis is on the interplay of descriptive set theory and the ergodic theory of group actions. This incorporates the study of turbulence and Borel reducibility on the one hand, and the theory of orbit equivalence and weak equivalence on the other. Chapter 2 is joint work with Clinton Conley and Alexander Kechris; we study measurable graph combinatorial invariants of group actions and employ the ultraproduct construction as a way of constructing various measure preserving actions with desirable properties. Chapter 3 is joint work with Lewis Bowen; we study the property MD of residually finite groups, and we prove a conjecture of Kechris by showing that under general hypotheses property MD is inherited by a group from one of its co-amenable subgroups. Chapter 4 is a study of weak equivalence. One of the main results answers a question of Abért and Elek by showing that within any free weak equivalence class the isomorphism relation does not admit classification by countable structures. The proof relies on affirming a conjecture of Ioana by showing that the product of a free action with a Bernoulli shift is weakly equivalent to the original action. Chapter 5 studies the relationship between mixing and freeness properties of measure preserving actions. Chapter 6 studies how approximation properties of ergodic actions and unitary representations are reflected group theoretically and also operator algebraically via a group's reduced C*-algebra. Chapter 7 is an appendix which includes various results on mixing via filters and on Gaussian actions.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

In this thesis, we discuss 3d-3d correspondence between Chern-Simons theory and three-dimensional N = 2 superconformal field theory. In the 3d-3d correspondence proposed by Dimofte-Gaiotto-Gukov information of abelian flat connection in Chern-Simons theory was not captured. However, considering M-theory configuration giving the 3d-3d correspondence and also other several developments, the abelian flat connection should be taken into account in 3d-3d correspondence. With help of the homological knot invariants, we construct 3d N = 2 theories on knot complement in 3-sphere for several simple knots. Previous theories obtained by Dimofte-Gaiotto-Gukov can be obtained by Higgsing of the full theories. We also discuss the importance of all flat connections in the 3d-3d correspondence by considering boundary conditions in 3d N = 2 theories and 3-manifold.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

This thesis consists of two parts. In Part I, we develop a multipole moment formalism in general relativity and use it to analyze the motion and precession of compact bodies. More specifically, the generic, vacuum, dynamical gravitational field of the exterior universe in the vicinity of a freely moving body is expanded in positive powers of the distance r away from the body's spatial origin (i.e., in the distance r from its timelike-geodesic world line). The expansion coefficients, called "external multipole moments,'' are defined covariantly in terms of the Riemann curvature tensor and its spatial derivatives evaluated on the body's central world line. In a carefully chosen class of de Donder coordinates, the expansion of the external field involves only integral powers of r ; no logarithmic terms occur. The expansion is used to derive higher-order corrections to previously known laws of motion and precession for black holes and other bodies. The resulting laws of motion and precession are expressed in terms of couplings of the time derivatives of the body's quadrupole and octopole moments to the external moments, i.e., to the external curvature and its gradient.

In part II, we study the interaction of magnetohydrodynamic (MHD) waves in a black-hole magnetosphere with the "dragging of inertial frames" effect of the hole's rotation - i.e., with the hole's "gravitomagnetic field." More specifically: we first rewrite the laws of perfect general relativistic magnetohydrodynamics (GRMHD) in 3+1 language in a general spacetime, in terms of quantities (magnetic field, flow velocity, ...) that would be measured by the ''fiducial observers” whose world lines are orthogonal to (arbitrarily chosen) hypersurfaces of constant time. We then specialize to a stationary spacetime and MHD flow with one arbitrary spatial symmetry (e.g., the stationary magnetosphere of a Kerr black hole); and for this spacetime we reduce the GRMHD equations to a set of algebraic equations. The general features of the resulting stationary, symmetric GRMHD magnetospheric solutions are discussed, including the Blandford-Znajek effect in which the gravitomagnetic field interacts with the magnetosphere to produce an outflowing jet. Then in a specific model spacetime with two spatial symmetries, which captures the key features of the Kerr geometry, we derive the GRMHD equations which govern weak, linealized perturbations of a stationary magnetosphere with outflowing jet. These perturbation equations are then Fourier analyzed in time t and in the symmetry coordinate x, and subsequently solved numerically. The numerical solutions describe the interaction of MHD waves with the gravitomagnetic field. It is found that, among other features, when an oscillatory external force is applied to the region of the magnetosphere where plasma (e+e-) is being created, the magnetosphere responds especially strongly at a particular, resonant, driving frequency. The resonant frequency is that for which the perturbations appear to be stationary (time independent) in the common rest frame of the freshly created plasma and the rotating magnetic field lines. The magnetosphere of a rotating black hole, when buffeted by nonaxisymmetric magnetic fields anchored in a surrounding accretion disk, might exhibit an analogous resonance. If so then the hole's outflowing jet might be modulated at resonant frequencies ω=(m/2) ΩH where m is an integer and ΩH is the hole's angular velocity.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

In this thesis, we consider two main subjects: refined, composite invariants and exceptional knot homologies of torus knots. The main technical tools are double affine Hecke algebras ("DAHA") and various insights from topological string theory.

In particular, we define and study the composite DAHA-superpolynomials of torus knots, which depend on pairs of Young diagrams and generalize the composite HOMFLY-PT polynomials from the full HOMFLY-PT skein of the annulus. We also describe a rich structure of differentials that act on homological knot invariants for exceptional groups. These follow from the physics of BPS states and the adjacencies/spectra of singularities associated with Landau-Ginzburg potentials. At the end, we construct two DAHA-hyperpolynomials which are closely related to the Deligne-Gross exceptional series of root systems.

In addition to these main themes, we also provide new results connecting DAHA-Jones polynomials to quantum torus knot invariants for Cartan types A and D, as well as the first appearance of quantum E6 knot invariants in the literature.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

O objetivo deste trabalho é tratar da simulação do fenômeno de propagação de ondas em uma haste heterogênea elástico, composta por dois materiais distintos (um linear e um não-linear), cada um deles com a sua própria velocidade de propagação da onda. Na interface entre estes materiais existe uma descontinuidade, um choque estacionário, devido ao salto das propriedades físicas. Empregando uma abordagem na configuração de referência, um sistema não-linear hiperbólico de equações diferenciais parciais, cujas incógnitas são a velocidade e a deformação, descrevendo a resposta dinâmica da haste heterogénea. A solução analítica completa do problema de Riemann associado são apresentados e discutidos.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

170 p.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

Uma forma de generalizar a teoria de Einstein da gravitação é incorporar na lagrangiana termos que dependem de escalares formados com os tensores de Ricci e Riemann, tais como (Ricci)2, ou (Riemann)2. Estas teorias tem sido estudadas intensamente nos últimos anos, já que elas podem ser usadas para descrever a expansão acelerada do universo no modelo cosmológico standard. Entre os desfios de modificar a teoria de Einstein, se encontra o de limitar a ambiguidade na escolha da dependência da lagrangiana com os escalares antes mencionados. A proposta desta dissertação é a de colocar limites sobre as possíveis lagrangianas impondo que as ondas (isto é, perturbações lineares) se propaguem no vácuo sem que apareça, shocks.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

Neste trabalho é apresentada uma nova modelagem matemática para a descrição do escoamento de um líquido incompressível através de um meio poroso rígido homogêneo e isotrópico, a partir do ponto de vista da Teoria Contínua de Misturas. O fenômeno é tratado como o movimento de uma mistura composta por três constituintes contínuos: o primeiro representando a matriz porosa, o segundo representando o líquido e o terceiro representando um gás de baixíssima densidade. O modelo proposto possibilita uma descrição matemática realista do fenômeno de transição insaturado/saturado a partir de uma combinação entre um sistema de equações diferenciais parciais e uma desigualdade. A desigualdade representa uma limitação geométrica oriunda da incompressibilidade do líquido e da rigidez do meio poroso. Alguns casos particulares são simulados e os resultados comparados com resultados clássicos, mostrando as consequências de não levar em conta as restrições inerentes ao problema.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

Esse texto trata do problema de um fluido contaminado escoando por um meio poroso, tratando os componentes na mistura como meios contínuos. Na primeira parte, desenvolvemos a teoria de misturas de meios contínuos e discutimos equações da continuidade, momento linear e momento angular. A seguir, descrevemos o problema em detalhe e fazemos hipóteses para simplificar o escoamento. Aplicamos as equações encontradas anteriormente para encontrarmos um sistema de equações diferenciais parciais. Desse ponto em diante, o problema se torna quase puramente matemático. Discutimos o caso insaturado, e depois a saturação do meio poroso. Finalmente, adicionamos um contaminante à mistura e, em seguida, N contaminantes.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

A teoria magneto-hidrodinâmicos permite a estruturação de modelos computacionais, designados modelos MHDs, que são uma extensão da dinâmica dos fluidos para lidar com fluidos eletricamente carregados, tais como os plasmas, em que se precisa considerar os efeitos de forças eletromagnéticas. Tais modelos são especialmente úteis quando o movimento exato de uma partícula não é de interesse, sendo que as equações descrevem as evoluções de quantidades macroscópicas. Várias formas de modelos MHD têm sido amplamente utilizadas na Física Espacial para descrever muitos tipos diferentes de fenômenos de plasma, tais como reconexão magnética e interações de ventos estelares com diferentes objetos celestiais. Neste trabalho, o objetivo é analisar o comportamento de diversos fluxos numéricos em uma discretização de volumes finitos de um modelo numérico de MHD usando um esquema de malha entrelaçada sem separação direcional considerando alguns casos testes. Para as simulações, utiliza-se o código Flash, desenvolvido pela Universidade de Chicago, por ser um código de amplo interesse nas simulações astrofísicas e de fenômenos no espaço próximo à Terra. A metodologia consiste na inclusão de um fluxo numérico, permitindo melhoria com respeito ao esquema HLL.