Beltrami operators and their application to constrained diffusion in Beltrami fields
Beltrami operators and their application to constrained diffusion in Beltrami fields
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Beltrami算子及其在Beltrami油田约束扩散中的应用
DOI：
10.1088/1751-8121/ab1cdc
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Sato N
中科院分区：
文献类型：
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作者：
Sato N
贝尔特拉米场作为流体流动欧拉方程的固定解以及磁流体动力学中的无力磁场出现。在本文中，我们讨论了贝尔特拉米场被视为作用于哈密顿函数以生成粒子动力学的算子时的作用。贝尔特拉米算子（包括作为特殊子类的泊松算子）出现在非哈密顿系统中拓扑约束扩散的描述中。扩展之前的结果（Sato and Yoshida 2018 Phys. Rev. E 97 022145），我们表明由 Beltrami 算子生成的随机运动满足 H 定理，从而在 Beltrami 条件成立的坐标系上产生广义玻尔兹曼分布。当违反贝尔特拉米条件时，随机波动不再起作用以均匀化它们所应用的坐标系中的粒子分布。由此产生的分布变得异质。异质性取决于测量操作员离开贝尔特拉米场的“场电荷”。给出了三维和四维实数维度的贝尔特拉米算子和非贝尔特拉米算子的例子以及相应的平衡分布函数。
Beltrami fields occur as stationary solutions of the Euler equations of fluid flow and as force free magnetic fields in magnetohydrodynamics. In this paper we discuss the role of Beltrami fields when considered as operators acting on a Hamiltonian function to generate particle dynamics. Beltrami operators, which include Poisson operators as a special subclass, arise in the description of topologically constrained diffusion in non-Hamiltonian systems. Extending previous results (Sato and Yoshida 2018 Phys. Rev. E 97 022145), we show that random motion generated by a Beltrami operator satisfies an H-theorem, leading to a generalized Boltzmann distribution on the coordinate system where the Beltrami condition holds. When the Beltrami condition is violated, random fluctuations do not work anymore to homogenize the particle distribution in the coordinate system where they are applied. The resulting distribution becomes heterogeneous. The heterogeneity depends on the'field charge'measuring the departure of the operator from a Beltrami field. Examples of both Beltrami and non-Beltrami operators in three and four real dimensions together with the corresponding equilibrium distribution functions are given.