...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Discrete and continuous dynamical systems >SUB-RIEMANNIAN GEOMETRY AND FINITE TIME THERMODYNAMICS PART 1: THE STOCHASTIC OSCILLATOR
【24h】

SUB-RIEMANNIAN GEOMETRY AND FINITE TIME THERMODYNAMICS PART 1: THE STOCHASTIC OSCILLATOR

机译：子riemannian几何和有限时间热力学第1部分：随机振荡器

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

The field of sub-Riemannian geometry has ourished in the past four decades through the strong interactions between problems arising in applied science (in areas such as robotics) and questions of a pure mathematical character about the nature of space. Methods of control theory, such as controllability properties determined by Lie brackets of vector fields, the Hamilton equations associated to the Maximum Principle of optimal control, Hamilton- Jacobi-Bellman equation etc. have all been found to be basic tools for answering such questions. In this paper, we find a useful role for the vantage point of sub-Riemannian geometry in attacking a problem of interest in nonequilibrium statistical mechanics: how does one create rules for operation of micro- and nano-scale systems (heat engines) that are subject to uctuations from the surroundings, so as to be able to do useful things such as converting heat into work over a cycle of operation? We exploit geometric optimal control theory to produce such rules selected for maximal efficiency. This is done by working concretely with a model problem, the stochastic oscillator. Essential to our work is a separation of time scales used with great efficacy by physicists and justified in the linear response regime.
机译：通过在应用科学（如机器人等地区）中出现的问题之间存在的强烈相互作用以及关于空间性质的纯数学特征的问题之间的强烈相互作用，在过去的四十年中占据了近十年的田地。控制理论的方法，例如由矢量场的李括号确定的可控性特性，所有与最佳控制原则相关的汉密尔顿方程都被发现是回答这些问题的基本工具。在本文中，我们为攻击统计力学兴趣问题的次黎曼几何中的有用点找到了一个有用的作用：如何创造用于操作的微型和纳米级系统（热电引擎）的规则受周围环境的uctuations的影响，以便能够在操作循环上进行有用的东西，例如将热量转换为工作？我们利用几何最优控制理论来生产用于最大效率的这些规则。这是通过具体实施模型问题，随机振荡器来完成的。对于我们的工作至关重要是以物理学家的效力很大的时间尺度分离，并在线性响应制度证明。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号