Dynamics and scattering of vortices and vortex rings

涡流和涡环的动力学和散射

基本信息

  • 批准号:
    2206016
  • 负责人:
  • 金额:
    $ 30万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2022
  • 资助国家:
    美国
  • 起止时间:
    2022-08-15 至 2025-07-31
  • 项目状态:
    未结题

项目摘要

This project focuses on a classical subject that has found new relevance due to recent experimental results. Nineteenth century researchers including Helmholtz and Kirchhoff wrote down a system of equations describing how point vortices---infinitesimal whirlpools---induce motion in a fluid, which in turn affects the motion of the vortices. A similar system exists that describes the more complex problem of vortex rings. Both Bose-Einstein Condensates (BEC), an exotic phase of matter first produced experimentally in the 1990s, and superfluids including liquid helium, can support point vortices and vortex rings. Recent experimental work has imaged interacting point vortices in a BEC, showing strong agreement with mathematical predictions. This project will mathematically investigate a number of phenomena in the interactions of point vortices, and in the closely-related problem of interacting vortex rings. In particular, there is a motion called the leapfrogging orbit in which a pair of vortex rings propagate along a line, periodically expanding and contracting while moving through each other (this is a well-known trick performed by cigar smokers with smoke rings). This is well understood in the case of two vortex rings, and computer simulations have generalized this phenomenon to three or more rings, but have not performed a full mathematical study. This project will perform the first detailed mathematical study of the generalized problem. It is likely impossible to write down exact formulas for these solutions, so numerical techniques will be essential, especially numerical continuation and bifurcation methods and a recently-developed method called Lagrangian descriptors, which allows us to see structure in otherwise opaque chaotic systems. A second problem will study a phenomenon called chaotic scattering of point vortices: A pair of vortices can be made to propagate at a constant speed along a straight line. Collisions between such pairs can lead to extremely complex dynamics which will be investigated using dynamical systems methods.This project will apply techniques from dynamical systems to two classes of problems in the classical subject of the dynamics of interacting point vortices or vortex rings. The first is several generalizations of the problem of leapfrogging vortices, in which two pairs of vortices travel along a straight line while repeatedly and periodically widening, then narrowing, with one pair passing through the other, and the lead changing. This has been very well-studied for point vortices, but less well for vortex rings. The study aims to generalize this system to systems of three or more pairs of vortices (or three or more vortex rings), and to leapfrogging orbits in other geometries such as on the surface of a sphere. While limited numerical studies exist of such orbits, they remain unexplored mathematically. Hamiltonian reduction is the technique at the center of our understanding of the four-vortex system, leading two a two-degree-of-freedom Hamiltonian that is amenable to further analytical simplification. With larger sets of vortices, Hamiltonian reduction does not lead to systems of small enough dimension for the method to provide much insight, and other methods are required, including numerical continuation and bifurcation methods. The project will also make use of the newly-developed method of Lagrangian descriptors, although the size of the system means that choices need to be made about how to find surfaces in initial-condition space that will lead allow insight into the dynamics. The second class of problems is the chaotic scattering of colliding point vortex pairs. This system has some features in common with chaotic scattering studied in earlier NSF-sponsored research: a two degree-of-freedom system consisting of a slow dynamical system with a separatrix coupled to a fast dynamical system. However, the dynamics in this case are far more complex: there is no small parameter. Instead, the separation of time scales arises due to the dynamics but may not hold for all time. In the previous system, a separatrix describes how solutions escape to infinity, while the mechanism of escape here is still unknown.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
该项目的重点是一个经典主题,该主题由于最近的实验结果而发现了新的相关性。包括Helmholtz和Kirchhoff在内的十九世纪研究人员写下了一个方程式系统,描述了点涡流如何 - 无穷小旋转 - - 诱导流体运动,这反过来影响涡流的运动。存在类似的系统,描述了涡旋环的更复杂问题。 两种Bose-Einstein冷凝物(BEC)是1990年代首次通过实验生产的物质的外来阶段,包括液氦在内的超氟可以支持点涡流和涡旋环。最近的实验工作已在BEC中成像相互作用的点涡旋,显示出与数学预测的强烈一致性。该项目将在数学上研究点涡流的相互作用中的许多现象,以及在相互作用的涡流环的密切相关问题中。特别是,有一个名为“跨越轨道”的动作,其中一对涡流环沿线传播,在彼此之间进行定期扩展和收缩(这是烟烟烟雾戒烟者表现出的众所周知的技巧)。在两个涡旋环的情况下,这是可以很好地理解的,并且计算机模拟将此现象概括为三个或更多环,但没有进行完整的数学研究。该项目将对广义问题进行首次详细的数学研究。可能不可能为这些解决方案写下确切的公式,因此数值技术将是必不可少的,尤其是数值延续和分叉方法,以及最近开发的称为Lagrangian描述符的方法,这使我们可以在其他不透明的混乱系统中看到结构。第二个问题将研究一种称为点涡流的混沌散射的现象:可以使一对涡流沿直线以恒定的速度传播。这种对之间的碰撞可能会导致极其复杂的动力学,这些动力学将使用动态系统方法进行研究。该项目将从动态系统应用到相互作用点涡流或涡旋环动态的经典主题中的两类问题。第一个是跨越涡流的问题的几个概括,其中两对涡流沿着一条直线传播,同时反复并定期扩大,然后变窄,一对穿过另一对,而铅则变化。对于点涡流而言,这是很好的研究,但对于涡旋环而言,这是不太好的。该研究旨在将该系统概括为三对涡流(或三个或三个或更多涡度环)的系统,并越过其他几何形状(例如在球体表面)中的轨道。尽管存在有限的数值研究,但它们在数学上仍未得到探索。汉密尔顿的还原是我们对四涡式系统的理解的中心技术,领导了两位两度自由的哈密顿量,可以进一步简化分析。借助较大的涡旋,汉密尔顿的还原并不会导致足够小的尺寸系统,以便提供大量洞察力,并且需要其他方法,包括数值延续和分叉方法。该项目还将利用新开发的Lagrangian描述符的方法,尽管系统的大小意味着需要选择如何在初始条件空间中找到表面,这将导致洞悉动力学。第二类问题是碰撞点涡流对的混乱散射。该系统具有一些共同的特征,与早期NSF赞助的研究中研究的混乱散射:一个两种自由度系统,该系统由慢速动力学系统组成,该系统具有分离型系统,并与快速动力学系统耦合。但是,在这种情况下的动力学要复杂得多:没有小参数。取而代之的是,时间尺度的分离是由于动态而产生的,但可能一直保持不变。在上一个系统中,分隔质描述了解决方案如何逃脱到无穷大,而这里的逃生机制仍然未知。该奖项反映了NSF的法定任务,并认为使用基金会的知识分子和更广泛的影响审查标准,认为值得通过评估来支持。

项目成果

期刊论文数量(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Transition to instability of the leapfrogging vortex quartet
跨越式涡四重奏向不稳定的转变
  • DOI:
    10.1016/j.mechrescom.2023.104068
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    2.4
  • 作者:
    Goodman, Roy H.;Behring, Brandon M.
  • 通讯作者:
    Behring, Brandon M.
{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ monograph.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ sciAawards.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ conferencePapers.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ patent.updateTime }}

Roy Goodman其他文献

Comparison of clinic, home, and deferred language treatment for aphasia. A Veterans Administration Cooperative Study.
失语症的诊所、家庭和延期语言治疗的比较。
  • DOI:
  • 发表时间:
    1986
  • 期刊:
  • 影响因子:
    0
  • 作者:
    R. Wertz;D. Weiss;J. Aten;R. Brookshire;L. Garcia;A. Holland;J. Kurtzke;L. Lapointe;F. Milianti;R. Brannegan;Howard Greenbaum;R. Marshall;D. Vogel;John E. Carter;Norman S. Barnes;Roy Goodman
  • 通讯作者:
    Roy Goodman

Roy Goodman的其他文献

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

{{ truncateString('Roy Goodman', 18)}}的其他基金

Nonlinear Waves and Dynamical Systems
非线性波和动力系统
  • 批准号:
    0807284
  • 财政年份:
    2008
  • 资助金额:
    $ 30万
  • 项目类别:
    Standard Grant
Mathematical methods for nonlinear wave interactions
非线性波相互作用的数学方法
  • 批准号:
    0506495
  • 财政年份:
    2005
  • 资助金额:
    $ 30万
  • 项目类别:
    Standard Grant
Pulse Propagation and Capture in Bragg Grating Optical Fibers
布拉格光栅光纤中的脉冲传播和捕获
  • 批准号:
    0204881
  • 财政年份:
    2002
  • 资助金额:
    $ 30万
  • 项目类别:
    Standard Grant

相似国自然基金

小角X射线/中子散射解析共轭高分子材料及其共混物的溶液态聚集结构
  • 批准号:
    22375143
  • 批准年份:
    2023
  • 资助金额:
    50 万元
  • 项目类别:
    面上项目
全固态锂电池硫化物固体电解质的合成、调控及多尺度中子散射研究
  • 批准号:
    12375301
  • 批准年份:
    2023
  • 资助金额:
    53 万元
  • 项目类别:
    面上项目
飞鸟动态电磁散射特性建模及运动特征提取研究
  • 批准号:
    62361006
  • 批准年份:
    2023
  • 资助金额:
    32 万元
  • 项目类别:
    地区科学基金项目
受激拉曼散射成像方法用于细胞类型特异的肿瘤代谢研究
  • 批准号:
    22377016
  • 批准年份:
    2023
  • 资助金额:
    50 万元
  • 项目类别:
    面上项目
随机时变相位低相干宽带激光抑制受激拉曼散射的动理学研究
  • 批准号:
    12305265
  • 批准年份:
    2023
  • 资助金额:
    30 万元
  • 项目类别:
    青年科学基金项目

相似海外基金

In-situ X-ray Scattering Studies of Oxide Epitaxial Growth Kinetics and Dynamics
氧化物外延生长动力学和动力学的原位 X 射线散射研究
  • 批准号:
    2336506
  • 财政年份:
    2024
  • 资助金额:
    $ 30万
  • 项目类别:
    Continuing Grant
Unveiling magnetic structure of long-range ordered quasicrystals and approximant crystals via X-ray Resonant Magnetic Scattering method
通过X射线共振磁散射法揭示长程有序准晶和近似晶体的磁结构
  • 批准号:
    24K17016
  • 财政年份:
    2024
  • 资助金额:
    $ 30万
  • 项目类别:
    Grant-in-Aid for Early-Career Scientists
Spectroscopic Detection of Magnetic Scattering and Quasiparticles at Atomic Resolution in the Electron Microscope
电子显微镜中原子分辨率的磁散射和准粒子的光谱检测
  • 批准号:
    EP/Z531194/1
  • 财政年份:
    2024
  • 资助金额:
    $ 30万
  • 项目类别:
    Research Grant
CAREER: Neural Computational Imaging - A Path Towards Seeing Through Scattering
职业:神经计算成像——透视散射的途径
  • 批准号:
    2339616
  • 财政年份:
    2024
  • 资助金额:
    $ 30万
  • 项目类别:
    Continuing Grant
Advanced Raman Spectroscopy for Exhaled Breath Analysis for Lung Cancer Detection
用于肺癌检测的呼出气体分析的先进拉曼光谱
  • 批准号:
    494958
  • 财政年份:
    2023
  • 资助金额:
    $ 30万
  • 项目类别:
    Operating Grants
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了