Fluctuation, Dissipation and Inversion

波动、耗散和反转

• 批准号: 2008610
• 负责人: Fernando Guevara Vasquez
• 金额: $ 26.2万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-08-01 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2008610&HistoricalAwards=false
• 关键词: Fluctuation; Dissipation; Inversion

Most of us have experienced thermal noise as that undesirable static hiss we get when we turn up the volume of a sound amplifier. Thermal noise is present in any voltage measurement of an electrical circuit and the intensity of the noise increases with both the temperature and the resistance of the circuit elements. One goal of this project is to develop a method to estimate the electrical properties of a circuit from thermal noise measured while heating some circuit elements. One practical application would be to monitor laser welding. We expect that the laser hot spot generates noticeably higher thermal noise with intensity depending mostly on the nearby electric properties. But a defective weld that does not bridge two parts does not conduct electricity well, so one should be able to distinguish a good weld from a bad one based on thermal noise alone. The same principle may also be used in Atomic Force Microscopy to measure the conductivity of a sample. This project will explore these new uses of thermal noise, using mathematical tools to extract valuable information from a usually undesirable andignored quantity. In particular we anticipate to answer questions such as what electric properties can be recovered from thermal noise? How can these be recovered? We will use simulations to illustrate our ideas, with an eye on applications. Another goal of this project is to control heat using small heat pumps called Peltier devices. We use mathematical tools to show that an idealization of these devices can be used to thermally isolate an object, that is, making the temperature surrounding the devices and the object indistinguishable from the ambient temperature. The mathematical framework we will develop could be used for heat control in electronics and to design devices for slow release of drugs. This project provides research training opportunities for graduate and undergraduate students. This project has two main thrusts. The first thrust is about harnessing ubiquitous thermal fluctuations to image the properties of a body and the second thrust concerns active thermal cloaking. An example for the first thrust is Johnson-Nyquist noise, that is, the random currents or voltages that can be measured at the terminals of any resistive electrical component. The voltage variance is proportional to the temperature and the resistance. Thus the resistance can be found from the temperature and the voltage variance. We will consider a similar problem on conducting bodies where the problem is to find the electrical properties (impedance) of a body from the voltage or current covariance measured at a few electrodes (which may be placed either inside the body or on its boundary) all while locally heating the body. A discrete analogue of this problem will be considered for finding the impedance of elements in electric circuits. Johnson-Nyquist noise is a manifestation of the Fluctuation Dissipation Theorem, a fundamental statistical physics result relating the fluctuations about an equilibrium of a system to the dissipation in thesystem. Thus the inverse problems that we plan to study may have applications to other linear systems subject to random externalfluctuations, e.g. thermo-elastic fluctuations. For the second thrust, we will study cloaking strategies for the heat equation that rely on active surfaces to dissimulate objects or heat sources/sinks and are grounded on potential theory (Green identities) for the heat equation.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.

我们中的大多数人都经历过热噪声，当我们打开声音放大器的音量时，我们会听到不受欢迎的静态嘶嘶声。热噪声存在于电路的任何电压测量中，并且噪声的强度随着电路元件的温度和电阻而增加。该项目的一个目标是开发一种方法来估计电路的电性能，从加热一些电路元件时测量的热噪声。一个实际应用是监控激光焊接。我们预计，激光热点会产生明显更高的热噪声，其强度主要取决于附近的电学性质。但是，没有桥接两个部件的有缺陷的焊接不会很好地导电，因此应该能够仅根据热噪声来区分好的焊接和坏的焊接。同样的原理也可以用在原子力显微镜中来测量样品的电导率。这个项目将探索热噪声的这些新用途，使用数学工具从通常不受欢迎和忽视的数量中提取有价值的信息。特别是，我们期望回答的问题，如什么电性能可以从热噪声恢复？如何恢复这些？我们将使用模拟来说明我们的想法，着眼于应用。该项目的另一个目标是使用称为Peltier设备的小型热泵来控制热量。我们使用数学工具来表明，这些设备的理想化可以用来热隔离的对象，也就是说，使周围的设备和对象的温度与环境温度无法区分。我们将开发的数学框架可用于电子学中的热控制和设计药物缓释装置。该项目为研究生和本科生提供研究培训机会。该项目有两个主要目标。第一个推力是关于利用无处不在的热波动来成像物体的特性，第二个推力涉及主动热隐身。第一推力的一个例子是约翰逊-奈奎斯特噪声，也就是说，可以在任何电阻性电子元件的端子处测量的随机电流或电压。电压变化与温度和电阻成比例。因此，电阻可以从温度和电压变化中找到。我们将考虑导体上的类似问题，其中问题是从在局部加热身体的同时在几个电极（可以放置在身体内部或其边界上）处测量的电压或电流协方差中找到身体的电特性（阻抗）。这个问题的一个离散的模拟将被认为是寻找电路中元件的阻抗。约翰逊-奈奎斯特噪声是涨落耗散定理的一种表现形式，涨落耗散定理是一个基本的统计物理结果，将系统平衡点附近的涨落与系统中的耗散联系起来。因此，我们计划研究的逆问题可能会应用到其他线性系统受到随机externalfluctuations，例如热弹性波动。对于第二个推力，我们将研究热方程的隐身策略，该策略依赖于活动表面来隐藏物体或热源/散热器，并基于热方程的潜在理论（绿色恒等式）。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Measuring and Simulating the Local Packing Density Resulting From Ultrasound-Directed Self-Assembly of Spherical Microparticles into Specific Patterns

测量和模拟球形微粒超声引导自组装成特定图案所产生的局部堆积密度

• DOI: 10.1103/physrevapplied.19.064087
• 发表时间: 2023
• 期刊: Physical Review Applied
• 影响因子: 4.6
• 作者: Noparast, Soheyl;Guevara Vasquez, Fernando;Francoeur, Mathieu;Raeymaekers, Bart
• 通讯作者: Raeymaekers, Bart

Active exterior cloaking for the two-dimensional Helmholtz equation with complex wavenumbers and application to thermal cloaking

• DOI: 10.1098/rsta.2022.0073
• 发表时间: 2022-10
• 期刊: Philosophical Transactions of the Royal Society A
• 作者: M. Cassier;T. DeGiovanni;S. Guenneau;F. Guevara Vasquez