CAREER: Solitary Waves and Wavetrains in Dispersive Media

职业：色散介质中的孤立波和波列

• 批准号: 1255422
• 负责人: Mark Hoefer
• 金额: $ 42万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-06-01 至 2015-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1255422&HistoricalAwards=false
• 关键词: CAREER; Solitary; Waves; Wavetrains; Dispersive

This interdisciplinary project examines solitary wave and wavetrain solutions of certain nonlinear, dispersive partial differential equations utilizing a combination of analytical, numerical, and experimental approaches. The aim is to provide an accurate, practical, detailed description of these coherent wave structures that is useful for applications in nanomagnetism and the fluid dynamics of dissipationless, dispersive media. Motivated by recent experiments, time-periodic, localized solutions of a modified Landau-Lifshitz equation that incorporates a spin transfer torque forcing term to compensate damping will be computed and studied analytically using asymptotic methods. These magnetic droplet solitons and their generalizations have potential for technological applications. Another research front will be developed involving modulated nonlinear wavetrains or dispersive shock waves (DSWs). The generation of DSWs represents a universal mechanism to resolve hydrodynamic singularities in dispersive media such as water waves, plasma, optics, interfacial fluids, Bose-Einstein condensates, and two-phase, viscously deformable fluids. Theoretical studies will focus upon central questions of modern DSW theory including loss of genuine nonlinearity/strict hyperbolicity in the modulation equations, multi-dimensional DSWs, and stability. In collaboration with undergraduate and graduate students, the principal investigator will undertake experiments involving a viscous fluid conduit system in order to make quantitative measurements of DSW properties for comparison with theory.When wave properties intrinsically depend upon the wave amplitude, novel physical behavior can arise. With a view toward applications, this project encompasses two classes of these nonlinear waves: solitary waves in nanomagnetism and shock waves in dispersive media. Spintronics encompasses the effort to develop information transport, processing, and storage using the electron's spin in addition to its charge, for example, to continue Moore's Law (the doubling of the number of transistors per unit area every eighteen months) beyond present technological limitations. The spatially localized spin excitations in a nanomagnet to be studied in this project possess features that hold great promise for future spintronic applications. Viscous shock waves that form when a projectile exceeds the speed of sound in air are commonly understood. The dispersive shock waves studied in this project are of a very different type, lacking dissipation and realized as expanding, oscillatory wavetrains. A fluid experiment will be developed to carefully measure these shock properties while also being used as an educational, outreach, and demonstration tool, providing young mathematicians direct experience with nonlinear waves. Presentations at the North Carolina Museum of Natural Sciences will provide the general public with exposure to this fascinating field.

该跨学科项目研究了通过分析，数值和实验方法组合的某些非线性，分散部分微分方程的孤立波和波动溶液。 目的是为这些连贯的波结构提供准确，实用，详细的描述，该结构可用于纳米磁性的应用和无耗散，分散介质的流体动力学。 通过最近的实验，将使用渐近方法分析和分析研究并研究了一个经过修改的Landau-Lifshitz方程的时间周期性的局部解决方案，该方程融合了自旋传递扭矩强迫术语以补偿阻尼。 这些磁性液滴孤子及其概括具有技术应用的潜力。将开发另一个研究方面，涉及调制的非线性波浪形或色散冲击波（DSW）。 DSW的产生代表了一种通用机制，可以解决分散培养基（例如水波，等离子体，光学，界面流体，Bose-Einstein冷凝物和两相，可粘性的流体）中的流体动力奇异性。 理论研究将重点介绍现代DSW理论的中心问题，包括在调制方程，多维DSW和稳定性中失去真正的非线性/严格的双曲线。 与本科生和研究生合作，首席研究者将进行涉及粘性流体导管系统的实验，以便对DSW属性进行定量测量以与理论进行比较。当波浪特性本质上取决于波幅度时，可以出现新的身体行为。 从对应用的看法，该项目包括这些非线性波的两个类别：纳米磁性中的孤立波和分散介质中的冲击波。 Spintronics除了电荷外，还涵盖了使用电子旋转来开发信息传输，处理和存储的努力，例如，超出了当前技术限制，以继续摩尔定律（每18个月的每个单位区域每18个月的晶体管数量加倍）。 该项目中要研究的纳米磁体中的空间局部旋转激发具有对未来的自旋应用程序的巨大希望。 通常了解弹丸超过空气中声音速度时形成的粘性冲击波。该项目中研究的分散性冲击波具有非常不同的类型，缺乏耗散，并且被认为是扩展的振荡波动。 将开发一个流体实验，以仔细测量这些冲击特性，同时也被用作一种教育，外展和演示工具，从而为年轻的数学家提供了非线性波的直接经验。 北卡罗来纳州自然科学博物馆的演讲将为公众提供这个迷人的领域。