论文标题
奇异的旋转模型和耗散流体的复杂性
Singular cotangent models and complexity in fluids with dissipation
论文作者
论文摘要
在本文中，我们分析了几种具有奇异性的数学模型，在这些模型中，经典的cotangent模型被$ b $ cotangengent模型取代。我们提供了$ b $ odangangengent Bundles的奇异符号几何形状的物理解释，该捆绑包具有两个模型：规范（或非扭转）模型和扭曲的模型。带有边界的流动性上的第一个模型系统，扭曲模型代表了哈密顿系统，其中系统的奇异性位于束的纤维中。扭曲的Cotangent模型包括（对于线性电势）耗散的流体情况。我们将流体的复杂性与雷诺数和（无）升力动力学的（非）存在有关。我们还讨论了对扭曲和非扭曲$ b $ symplectic模型的更一般的物理解释。这些模型为耗散性的系统提供了一种汉密尔顿的配方，扩展了哈密顿动力学的视野，并为研究非保守系统的新方法提供了新的方法。
In this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a $b$-cotangent model. We provide physical interpretations of the singular symplectic geometry underlying in $b$-cotangent bundles featuring two models: the canonical (or non-twisted) model and the twisted one. The first one models systems on manifolds with boundary and the twisted model represents Hamiltonian systems where the singularity of the system is in the fiber of the bundle. The twisted cotangent model includes (for linear potentials) the case of fluids with dissipation. We relate the complexity of the fluids in terms of the Reynolds number and the (non)-existence of cotangent lift dynamics. We also discuss more general physical interpretations of the twisted and non-twisted $b$-symplectic models. These models offer a Hamiltonian formulation for systems which are dissipative, extending the horizons of Hamiltonian dynamics and opening a new approach to study non-conservative systems.
