Constrained Fluctuations

受约束的波动

• 批准号: 0803315
• 负责人: Mehran Kardar
• 金额: $ 39万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-15 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0803315&HistoricalAwards=false
• 关键词: Constrained; Fluctuations

TECHNICAL SUMMARY:This award supports theoretical research and education on the role of fluctuations in various physical contexts. Fluctuations, whether of quantum, thermal, or non-equilibrium origin, are an inherent part of physical matter. Constraining these fluctuations by boundaries, geometry or topology, leads to a myriad of interactions, patterns and phases. This proposal aims at quantifying such phenomena in several contexts.Specific questions that will be addressed by the research include:(i) The forces between neutral objects are due to constrained electromagnetic fluctuations. How do these forces depend on the shapes and orientations of these objects? Can one hold an object in stable equilibrium using only such forces?(ii) How does the confinement of critical thermal fluctuations of the order parameter lead to the thinning of helium films at the onset of superfluidity?(iii) What is the role of rigidity in the melting of double-stranded polymers such as DNA? How do fluctuations soften the elasticity of polymers and sheets? (iv) What governs the distribution of escape times, from a confining interval, in a process that is slower than diffusion? Is there a common description for such processes? (iv) How can we classify and catalog entangled proteins?Fluctuating systems are characterized by probability distribution functions. Statistical physics provides the relative weights of different configurations in equilibrium, and the time evolution of weights away from equilibrium. The methods of statistical field theory are appropriate for handling quantum fluctuations of the electromagnetic field. The Casimir force between different materials and its dependence of geometry can be obtained by constraining the fluctuations on the bodies. Transfer matrix and renormalization group methods will be used to address questions involving semi-flexible polymers. Anomalous dynamics will be studied by a combination of scaling theory, and Monte Carlo and Molecular Dynamics simulations.Education is an important component of this award. This research project is interdisciplinary; methods from statistical physics will be applied to a wide range of scientific problems. The research is closely linked to courses taught by the PI, which through textbooks and dissemination by the web will have impact on broader scientific community. The PI will also be an organizer of a workshop at the Kavli Institute for Theoretical Physics on the subject of fluctuation?induced forces.NONTECHNICAL SUMMARY:This award supports theoretical research and education on the materials and physical consequences of fundamental principles of statistical physics. The research encompasses a wide range of physical systems and phenomena that are connected through the unifying question of how confinement modifies behavior and properties. The effects of confinement are an inherent part of physical systems and the effects of boundaries and geometry lead to a myriad of interactions, patterns and phases. This research quantifies such phenomena in several contexts. Varied research questions are addressed.(i) Theoretical predictions concerning the forces between neutral objects, due to mere proximity, known as Casimir forces, are decades old, but have only recently been measured and even more recently been the subject of experiments to investigate their application in devices. This research moves from what is known for simple planar geometries to investigating how these forces depend on the shapes and orientations of the objects. Unanswered fundamental questions are taken up, such as can one hold an object in stable arrangement using only such forces?(ii) This thrust focuses on how the confinement of helium films alters their behavior from simple fluids to exhibit a variety of unusual fluid properties. Films of the element helium are essentially two dimensional liquids that exist at very low temperatures and exhibit behavior governed by quantum mechanics.(iii) A related topic is the role of confinement induced in molecules by crowding and interacting with other members of bulk collection. This aspect of the research studies the softening and elasticity of polymers and flexible sheets. In this case, confinement arises through the entanglement of long molecules.Education is an important component of this award. This research project is interdisciplinary; methods from statistical physics will be applied to a wide range of scientific problems. The research is closely linked to courses taught by the PI, which through textbooks and dissemination by the web will have impact on broader scientific community. The PI will also be an organizer of a workshop for the broader theoretical physics community at the Kavli Institute for Theoretical Physics.

技术总结：该奖项支持关于波动在各种物理环境中的作用的理论研究和教育。涨落，无论是量子的、热的还是非平衡的起源，都是物理物质的固有部分。通过边界、几何形状或拓扑结构来约束这些波动，会导致无数的相互作用、模式和阶段。这项建议的目的是在几种情况下量化这种现象，研究将解决的具体问题包括：（一）中性物体之间的力是由于受约束的电磁波动。这些力是如何依赖于这些物体的形状和方向的？仅仅使用这样的力就能使一个物体保持稳定的平衡吗？(ii)如何限制的顺序参数的临界热涨落导致薄的氦膜在超流性的开始？(iii)刚性在双链聚合物（如DNA）的熔化过程中起什么作用？波动如何软化聚合物和片材的弹性？(iv)在一个比扩散慢的过程中，是什么决定了从一个限制区间逃逸时间的分布？是否对这些过程有共同的描述？(iv)我们如何对纠缠蛋白质进行分类和编目？涨落系统的特征是概率分布函数。统计物理学提供了平衡状态下不同构型的相对权重，以及权重偏离平衡状态的时间演化。统计场论的方法适用于处理电磁场的量子涨落。通过约束物体上的涨落，可以得到不同材料之间的Casimir力及其几何依赖性。转移矩阵和重整化群方法将用于解决涉及半柔性聚合物的问题。反常动力学将结合标度理论、蒙特卡罗和分子动力学模拟进行研究。教育是该奖项的重要组成部分。该研究项目是跨学科的;统计物理学的方法将应用于广泛的科学问题。该研究与PI教授的课程密切相关，通过教科书和网络传播将对更广泛的科学界产生影响。PI还将在Kavli理论物理研究所组织一个关于波动问题的研讨会。非技术性总结：该奖项支持统计物理学基本原理的材料和物理后果的理论研究和教育。 该研究涵盖了广泛的物理系统和现象，这些系统和现象通过限制如何改变行为和属性的统一问题联系起来。 限制的影响是物理系统的固有部分，边界和几何形状的影响导致无数的相互作用，模式和阶段。这项研究在几种情况下量化了这种现象。不同的研究问题得到解决。(i)关于中性物体之间的力的理论预测，由于仅仅是接近，被称为卡西米尔力，已经有几十年的历史了，但直到最近才被测量，甚至最近才成为实验的主题，以研究它们在设备中的应用。 这项研究从简单的平面几何形状转移到研究这些力如何取决于物体的形状和方向。未回答的基本问题，如一个可以举行一个物体在稳定的安排只使用这样的力量？(ii)这个推力集中在氦膜的限制如何改变它们的行为，从简单的流体表现出各种不寻常的流体性质。氦元素的薄膜本质上是二维液体，存在于非常低的温度下，并表现出受量子力学控制的行为。（三） 一个相关的主题是限制诱导分子拥挤和相互作用与其他成员的批量收集的作用。这方面的研究主要研究聚合物和柔性片材的软化和弹性。 在这种情况下，限制是通过长分子的纠缠产生的。教育是这个奖项的重要组成部分。该研究项目是跨学科的;统计物理学的方法将应用于广泛的科学问题。该研究与PI教授的课程密切相关，通过教科书和网络传播将对更广泛的科学界产生影响。PI还将在Kavli理论物理研究所为更广泛的理论物理社区组织一个研讨会。