变形量子力学和流体动力学

粒子场理论家关于超对称、非阿贝尔流体力学和d-膜的讲座

A Particle Field Theorist's Lectures on Supersymmetric, Non-Abelian Fluid Mechanics and d-Branes

这本专着是来自一系列的六个讲座，我在中心数学研究在蒙特利尔，在2000年3月和6月，而名义上的艾森施塔特主席。

超对称流体力学

Supersymmetric Fluid Mechanics

当反对易格拉斯曼变量被引入到无旋速度和无涡的流体动力学模型中时，速度获得非零旋度，由此产生的涡度由格拉斯曼变量形成的高斯势描述。在添加进一步的与格拉斯曼自由度的特定相互作用后，模型变得超对称。

从超弦可积超对称流体力学

Integrable Supersymmetric Fluid Mechanics from Superstrings

在建立了平面超对称Chaubergin气体模型的基础上，从（2+1）维光锥参数化的Nambu-Goto超弦得到了（1+1）维超对称流体力学.线性模型是完全可积的，可以用黎曼坐标巧妙地表达出来。展示了守恒电荷和超荷的无限塔。它们形成了一个动力学（隐藏）SO（2，1）对称群的不可约表示。

从玻尔兹曼方程到流形上的流体力学

From the Boltzmann equation to fluid mechanics on a manifold

我们应用Chapman-Enskog程序推导流体动力学方程的任意表面上的玻尔兹曼方程的表面。

Remarks on the principles of statistical fluid mechanics

This is an idiosyncratic survey of statistical fluid mechanics centering on the Hopf functional differential equation. Using the Burgers equation for illustration we review several functional integration approaches to theory of turbulence. We notice in particular that some important contributions have been brought about by researchers working on wave propagation in random media, among which Uriel Frisch is not an exception. We also discuss a particular finite-dimensional approximation for the Burgers equation.

三维模糊流体力学

Fuzzy Fluid Mechanics in Three Dimensions

通过要求动量取球面值，在三维空间的理想流体理论中引入了一个旋转不变的短程截断。这导致位置空间中的函数代数是非交换的。尽管如此，还是有可能找到理想流体的欧拉方程的适当的类似物。该系统仍然具有哈密顿结构。希望这将有助于研究三维Euler（或Navier-Stokes）方程演化过程中可能出现的奇点。

流体动力学的随机几何力学

Stochastic Geometric Mechanics for Fluid Dynamics

本研究介绍了可在全球气候建模中量化不确定性且保留理想流体平流输运特性的随机几何力学（SGM）框架，阐述了其基于李群不变变分原理、面向流体流动与波动动力学的数学构建内容。

流体力学中的非相对论共形对称性

Non-relativistic conformal symmetries in fluid mechanics

自由不可压缩流体的对称性跨越伽利略群，并伴随着空间和时间的独立膨胀。当流体是可压缩的，对称性被扩大到扩展的薛定谔群，这也涉及到，此外，薛定谔扩展。虽然不可压缩的流体动力学可以推导出一个适当的非相对论性限制的共形不变的相对论性理论，最近讨论的共形伽利略群，从相对论共形群收缩，是不是一个对称。这可以用非相对论极限的微妙之处来解释。

量子流体力学与轨迹的表述

A Formulation of Quantum Fluid Mechanics and Trajectories

本文提出了一种量子力学含时多体态的经典力学形式论，推导出与含时薛定谔方程等价的能量与连续性方程，并得到质点轨迹与流体力学方程，揭示了可变质量在量子流体描述中的关键作用。

Classical and relativistic fluids as intermediate integrals of finite dimensional mechanical systems

We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of solutions of a finite dimensional mechanical system (a second order differential equation) are simultaneously Euler's equations of fluids and conversely. This will be done both in the classical and relativistic context. A direct relationship will be established by means of the so-called time constraint (classical unsteady case, static or not) and the relativis…

流体力学和量子场论中一类奇异积分算子的精确半经典方法

Exact and semiclassical approach to a class of singular integral operators arising in fluid mechanics and quantum field theory

介绍并分析了一类奇异积分算子，包括微扰QCD和经典流体动力学中两种物理相关的情形。结果表明，三个特殊值的参数允许一个确切的本征函数的扩展，这些可以与黎曼对称空间的秩为一，正，负或消失的曲率。对于所有其他情况下，一个准确的半经典近似的基础上，识别的运营商与一个奇特的薛定谔的运营商。

流体力学中广义(2+1)维Hirota-Satsuma-Ito方程的Painleve分析、Backlund变换、Lax对及周期波解

Painleve analysis, Backlund transformation, Lax pair and periodic wave solutions for a generalized (2+1)-dimensional Hirota-Satsuma-Ito equation in fluid mechanics

本文针对流体力学中的广义(2+1)维HSI方程，通过Painleve分析证实其特定条件下的可积性，构造双线性形式等关键数学结构，还推导并展示了周期波解。

A complexity perspective on fluid mechanics

This article attempts to use the ideas from the field of complexity sciences to revisit the classical field of fluid mechanics. For almost a century, the mathematical self-consistency of Navier-Stokes equations has remained elusive to the community of functional analysts, who posed the Navier-Stokes problem as one of the seven millennium problems in the dawn of 21st century. This article attempts to trace back the historical developments of fluid mechanics as a discipline and explain the consequences of not rationalising one of the commonly agreed upon tenets - continuum hypothesis - in the co…