Nonlinear Dynamics with Applications in Physical Systems

非线性动力学在物理系统中的应用

基本信息

  • 批准号:
    9704554
  • 负责人:
  • 金额:
    $ 10.8万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    1997
  • 资助国家:
    美国
  • 起止时间:
    1997-07-15 至 1999-11-30
  • 项目状态:
    已结题

项目摘要

9704554 Levi The first part of the project part deals with the study of mathematical aspects of Josephson junctions. It was discovered recently that the junctions occur naturally in certain crystals where superconducting layers interlace with insulating layers. It is proposed to derive and to study a mathematical model of such crystals and to develop theory of traveling waves in discrete media. In the second part of the project it is proposed to produce the qualitative analysis of systems of relaxation oscillators of a recently discovered type. The third part of the project deals with various applications of the investigator's recent observation on the role of curvature in high- frequency averaging. These applications include the study of the motion of rigid bodies (such as particles embedded in fluid) or coupled systems of particles, such as molecules subjected to rapidly varying force fields. Another application includes the behavior of a resonant medium subjected to an electromagnetic pulse. Finally, the last part of the project deals with establishing a connection between two classes of systems: the geodesic motion on a surface on the one hand and the billiard motion inside that surface on the other. The first of the four parts of the project deals with the study of Josephson junctions -- superconducting devices whose properties offer great potential for applications. The advantages of Josephson junctions lie in their small size and in low energy consumption, which allow for a great reduction of the circuit size, but the disadvantage is the low power output. To overcome that disadvantage, the junctions can be put in arrays. Remarkably, such arrays occur naturally: some crystals were discovered to consist of stacked Josephson junction layers. This recent discovery offers potential new applications, notably for use in interfaces between ultrafast optical communication lines and electric circuits as well as for generation of high frequency oscillations for use in communications and radio-astronomical observations. Understanding the behavior of such arrays takes on a crucial importance. The project proposed here aims at such understanding. The second part of the project addresses relaxation oscillators - these occur in biological and electronic systems whose oscillations consist of slow drifts punctuated by fast jumps. A large class of such oscillators exhibiting chaotic behavior was discovered recently, and an isolated oscillator analyzed. Understanding systems of coupled oscillators (the goal of this project) offers great challenges and is of importance in some biological and electric systems. In the third part of this effort, the dynamical effects of high-frequency oscillations will be explored. Such effects underlie the operation of the Paul trap (the inventor was awarded a Nobel prize) and the more recent "laser tweezers" which allow to move objects inside the cell without damaging it. This research will extend mathematical analysis of these phenomena with the aim of possible applications which include vibrational control as well as environmental applications such as separation processes (removing particles from the air, etc.) In the fourth part of the project it is proposed to establish a connection between two century-old geometry problems which were developed in parallel but without a direct connection, by showing that one is a limiting case of another. Both of these problems played a central role in the development of the theory of dynamical systems, and thus indirectly but crucially in the development of particle accelerators, in astronomy and in optics.
项目的第一部分涉及Josephson结的数学方面的研究。最近发现,在某些晶体中,超导层与绝缘层相互交错时,结是自然发生的。提出推导和研究这类晶体的数学模型,发展离散介质中的行波理论。在项目的第二部分,提出了对最近发现的一类弛豫振荡系统进行定性分析。该项目的第三部分涉及研究者最近对曲率在高频平均中的作用的观察的各种应用。这些应用包括研究刚体(如嵌入流体中的粒子)或粒子耦合系统(如受快速变化力场影响的分子)的运动。另一应用包括受电磁脉冲作用的谐振介质的行为。最后,项目的最后一部分涉及建立两类系统之间的连接:一方面是表面上的测地线运动,另一方面是表面内的台球运动。该项目四个部分的第一部分涉及约瑟夫森结的研究——超导器件,其特性具有巨大的应用潜力。约瑟夫森结的优点在于其体积小,能耗低,这使得电路尺寸大大减小,但缺点是输出功率低。为了克服这个缺点,连接点可以排列起来。值得注意的是,这样的阵列是自然发生的:一些晶体被发现是由堆叠的约瑟夫森结层组成的。这一最新发现提供了潜在的新应用,特别是用于超高速光通信线路和电路之间的接口,以及用于通信和射电天文观测的高频振荡的产生。理解这类数组的行为具有至关重要的意义。这里提出的项目就是为了这样的理解。该项目的第二部分涉及弛豫振荡-这些振荡发生在生物和电子系统中,其振荡由缓慢漂移和快速跳跃组成。最近发现了一类具有混沌行为的振子,并对一个孤立振子进行了分析。理解耦合振荡器系统(本项目的目标)提供了巨大的挑战,并且在一些生物和电气系统中很重要。在本文的第三部分,我们将探讨高频振荡的动力学效应。这种效应是保罗陷阱(保罗陷阱的发明者获得了诺贝尔奖)和最近的“激光镊子”的基础,后者可以在不损坏细胞的情况下移动细胞内的物体。这项研究将扩展这些现象的数学分析,目的是可能的应用,包括振动控制以及环境应用,如分离过程(从空气中去除颗粒等)。在项目的第四部分,建议建立两个百年历史的几何问题之间的联系,这两个问题是并行发展的,但没有直接联系,通过表明一个是另一个的极限情况。这两个问题在动力系统理论的发展中发挥了核心作用,因此间接地但至关重要地影响了粒子加速器、天文学和光学的发展。

项目成果

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Mark Levi其他文献

Nonchaotic behavior in the Josephson junction.

Mark Levi的其他文献

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{{ truncateString('Mark Levi', 18)}}的其他基金

Nonlinear Dynamics with Applications to Physical Systems
非线性动力学及其在物理系统中的应用
  • 批准号:
    2206500
  • 财政年份:
    2022
  • 资助金额:
    $ 10.8万
  • 项目类别:
    Standard Grant
Nonlinear Dynamics with Applications to Physical Systems
非线性动力学及其在物理系统中的应用
  • 批准号:
    1909200
  • 财政年份:
    2019
  • 资助金额:
    $ 10.8万
  • 项目类别:
    Standard Grant
Nonlinear dynamics with applications to physical systems
非线性动力学及其在物理系统中的应用
  • 批准号:
    1412542
  • 财政年份:
    2014
  • 资助金额:
    $ 10.8万
  • 项目类别:
    Continuing Grant
Nonlinear Dynamics with Applications to Physical Systems
非线性动力学及其在物理系统中的应用
  • 批准号:
    1009130
  • 财政年份:
    2010
  • 资助金额:
    $ 10.8万
  • 项目类别:
    Standard Grant
Nonlinear Dynamics with Applications to Physical Systems
非线性动力学及其在物理系统中的应用
  • 批准号:
    0605878
  • 财政年份:
    2006
  • 资助金额:
    $ 10.8万
  • 项目类别:
    Continuing Grant
Nonlinear Dynamics with Applications to Physical Systems
非线性动力学及其在物理系统中的应用
  • 批准号:
    0205128
  • 财政年份:
    2002
  • 资助金额:
    $ 10.8万
  • 项目类别:
    Continuing Grant
U.S.-Mexico Collaborative Research: Dynamics of Extended Systems and Coupled Map Lattices
美国-墨西哥合作研究:扩展系统动力学和耦合地图格子
  • 批准号:
    0104675
  • 财政年份:
    2001
  • 资助金额:
    $ 10.8万
  • 项目类别:
    Standard Grant
Nonlinear Dynamics with Applications in Physical Systems
非线性动力学在物理系统中的应用
  • 批准号:
    0096172
  • 财政年份:
    1999
  • 资助金额:
    $ 10.8万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Nonlinear Dynamics and its Application in Physical Systems
数学科学:非线性动力学及其在物理系统中的应用
  • 批准号:
    9406022
  • 财政年份:
    1994
  • 资助金额:
    $ 10.8万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Qualitative Analysis of Nonlinear Dynamical Systems
数学科学:非线性动力系统的定性分析
  • 批准号:
    9113139
  • 财政年份:
    1991
  • 资助金额:
    $ 10.8万
  • 项目类别:
    Standard Grant

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