Proposal on Pulse Shaping for Waves in Multiscale Media

关于多尺度介质中波的脉冲整形的建议

• 批准号: 0093992
• 负责人: Knut Solna
• 金额: $ 8.85万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-15 至 2004-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0093992&HistoricalAwards=false
• 关键词: Proposal; Pulse; Shaping; Waves; Multiscale

Solna0093992 The investigator analyzes how a propagating wave pulsebehave in a medium with rough variations. Predicting theevolution of the wave pulse from information about the`roughness' of the medium is a problem of deep mathematical andpractical interest, as is the inverse problem of deducinginformation about the medium from measurements of a transmittedpulse. Most often a detailed description of the (fine scale)variations of the medium is not possible, only a description oftheir statistical character. Hence, the investigator considersthe fine scale medium variations as a realization of a stochasticprocess. This entails analysis of differential equations withrandomly varying coefficients. The project has three specificobjectives: First, obtain a characterization of thetransformation of sound pulses propagating in a medium with acontinuum of length scales, a medium defined in terms of a randomfractal. Second, extend and use theory about the transformationof a wave pulse in some specific inverse problems, in particular,high contrast seismic imaging and time reversal mirrors. Third,derive strict bounds for how an electromagnetic pulse can beaffected by the medium heterogeneity without knowing the detailsof these variations. The main question the investigator addresses is: How does apropagating wave behave in a medium that varies when thevariations are not small? For instance, when a laser beampropagates through the turbulent atmosphere how is it affected byintense, turbulent, variations in the local speed of propagation?When such medium variations are smooth, say with a constantspeed of propagation, the problem is well understood. For roughmedium variations, as in the above example, the interaction of awave pulse with the medium heterogeneities is a fundamental yetlargely open question. This problem, predicting the evolution ofsignal or wave pulse that propagates in a rough medium, is ofdeep mathematical and practical interest. In addition to wavepropagation in the turbulent atmosphere there are many otherapplications. In reflection seismology the earth's crust isprobed with a wave pulse and the reflected pulses are used toinfer knowledge about macroscale variations in the medium. It isthen important to know how the rough microscale variations in themedium affect the probing pulse. Remote sensing, ocean acoustics,and medical imaging provide similar examples. In communicationsystems, it is important to be able to describe how mediumimperfections and variations affect the propagating signal. Inthe theory of composite materials, it is important to optimallyconstruct a complex material so that it has some desiredpropagation properties.

研究者分析了传播波脉冲在具有粗糙变化的介质中的行为。从介质的“粗糙度”信息中预测波脉冲的演变是一个深刻的数学和实际兴趣问题，正如从传输脉冲的测量中推断介质信息的反问题一样。大多数情况下，不可能详细描述（精细尺度）介质的变化，只能描述其统计特征。因此，研究者认为细尺度的介质变化是一个随机过程的实现。这就需要对系数随机变化的微分方程进行分析。该项目有三个具体目标：首先，获得声音脉冲在具有长度尺度连续体的介质中传播的变换特征，这种介质是根据随机分形定义的。第二，将波脉冲变换理论推广应用于一些具体的反演问题，特别是高对比地震成像和时间反演镜。第三，在不知道这些变化的细节的情况下，推导出电磁脉冲如何受到介质非均质性影响的严格界限。研究者解决的主要问题是：当变化不小时，传播波在变化介质中的表现如何？例如，当激光束在湍流大气中传播时，它是如何受到本地传播速度的剧烈、湍流变化的影响的？当这种介质的变化是平滑的，比如以恒定的传播速度，这个问题就很好理解了。对于粗糙介质的变化，如在上面的例子中，波脉冲与介质非均质性的相互作用是一个基本的但很大程度上尚未解决的问题。这个问题预测在粗糙介质中传播的信号或波脉冲的演变，具有深刻的数学和实际意义。除了湍流大气中的波传播外，还有许多其他应用。在反射地震学中，用波脉冲探测地壳，用反射脉冲推断出介质宏观尺度变化的知识。因此，了解介质中粗糙的微尺度变化如何影响探测脉冲是很重要的。遥感、海洋声学和医学成像也提供了类似的例子。在通信系统中，能够描述介质缺陷和变化如何影响传播信号是很重要的。在复合材料理论中，重要的是优化构造复杂材料，使其具有某些期望的传播特性。