Stochastic differential equation and random field theory applied to waves in random media

随机微分方程和随机场论应用于随机介质中的波

• 批准号: 312798-2011
• 负责人: Field, Timothy
• 金额: $ 1.6万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=526617
• 关键词: Stochastic; differential; equation; random; field

The focus of the research is the description of waves interacting with random media, throughout space and time. Scattering of waves (far field interaction) has many important physics and engineering applications, including radar, astronomy and wireless communications. The statistical characteristics of a scattering population play a crucial role in descriptions of scattering processes. The population may be realized in different ways depending on the problem - in maritime radar as facets on the ocean surface, in astronomy as the atmosphere, and in wireless as the number of available propagation paths for the microwave. Each case can be described in much the same mathematical terms, however. For populations that interact with each other we apply new mathematical techniques to better understand their dynamics and large time behaviour. The work draws on fundamental techniques in theoretical physics - the Ising model and the path integral method, in tandem with the stochastic calculus, to describe such populations and their interaction with waves of a variety of kinds. These studies are of vital significance in radar applications, especially satellite interferometric synthetic aperture radar (InSAR) with relevance to geothermal imaging and climatology. In wireless communications the techniques have important relevance to time varying channels in non-stationary receiver-transmitter environments with implications for coding and channel capacity calculations. Novel applications in acoustic propagation and speckle phenomena include sonar, in the generation of synthetic images (e.g. of the ocean floor with relevance to tsunami prediction), and ultrasound medical imaging, via stochastic inference techniques. In NMR (near field interaction), the population of interest consists of spins, and the resulting amplitude is spin noise. Chemical studies should have important consequences in imaging applications, particularly in functional magnetic resonance imaging, of key benefit to the Canadian health research community. In summary, the research addresses the behaviour of waves in random environments, and harnesses such description for extraction of useful information in a variety of physical applications.

研究的重点是描述波与随机介质的相互作用，跨越空间和时间。波的散射(远场相互作用)具有许多重要的物理和工程应用，包括雷达、天文学和无线通信。散射总体的统计特性在描述散射过程中起着至关重要的作用。根据问题的不同，人口可能以不同的方式实现--在海洋雷达中作为海洋表面的面，在天文学中作为大气，在无线中作为微波的可用传播路径的数量。然而，每一种情况都可以用大致相同的数学术语来描述。对于相互作用的种群，我们应用新的数学技术来更好地理解它们的动态和长时间行为。这项工作利用了理论物理中的基本技术--伊辛模型和路径积分法，并结合随机微积分，描述了这种群体及其与各种波的相互作用。这些研究对雷达应用，特别是与地热成像和气候学相关的卫星干涉合成孔径雷达(InSAR)具有重要意义。在无线通信中，这些技术对于非平稳接收器-发射器环境中的时变信道具有重要的相关性，并且对编码和信道容量计算具有影响。声学传播和散斑现象方面的新应用包括声纳、合成图像(例如，与海啸预报相关的海底图像)的生成，以及通过随机推断技术的超声医学成像。在核磁共振(近场相互作用)中，感兴趣的布居由自旋组成，由此产生的幅度是自旋噪声。化学研究应该在成像应用方面产生重要影响，特别是在功能磁共振成像方面，这对加拿大卫生研究界来说是关键的好处。总而言之，这项研究解决了随机环境中波的行为，并利用这种描述在各种物理应用中提取有用的信息。