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Applied Nonlinear Mathematics: Making it Real

应用非线性数学：让它成为现实

基本信息

批准号：
EP/E032249/1
负责人：
Stephen Hogan
金额：
$ 225.61万
依托单位：
University of Bristol
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2007
资助国家：
英国
起止时间：
2007 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FE032249%2F1
关键词：
Applied Nonlinear Mathematics Making Real

项目摘要

Many problems of practical importance give rise to very similarunderlying applied mathematics problems. The proposed research willaddress four real-world challenges in the Life Sciences and inEngineering. They have in common the presence of delays due to thecoupling between different components and of nonsmoothness due tofreeplay and friction. Furthermore, we must address their spatial extentand the overarching question of robustness of mathematical models.The first real-world challenge we address is the neurophysiology of thehuman brain. Specifically, we will develop models of differentcomplexity with both local and distributed components. Delays enternaturally due to electro-chemical signalling. A major focus of this workis the prediction of the onset of epilepsy, which causes more than 2000deaths annually in the UK. More generally, the question is: how does thecontrol of microscopic neuronal parameters (e.g. via drug delivery orelectrical stimulation) affect the overall macroscopic behaviour?Biomechanical systems frequently perform far better than any man-madedevice. Examples include the detection of sounds by mammals and insects,as well as the locomotion of land animals (from the cheetah to thecockroach) that can travel over rough terrain at amazing speed andefficiency. Our second real-world challenge is to understand how thisreally works, and to help construct better communication systems or fast,legged robots. An important element is impact, for example of the legswith the ground, which gives rise to nonsmoothness in the mathematicalmodels.Our third real-world challenge is hybrid testing. This new method offersthe opportunity to test a full-scale individual component, such as anaircraft engine, bridge cable or floor of a skyscraper, as if it werepart of the entire engineering structure. Apart from potentially givinghuge cost savings over conventional tests, hybrid testing also allowsone to perform tests that are currently impossible. To make hybridtesting an engineering reality we need to close in real-time the controlloop involving sensors and actuators between the test specimen and acomputer model of the remainder of the structure. Both specimen andmodel are generally of large spatial extent and subject to externalinfluences such as periodic forcing. We will study the interplay betweenthese different effects in the presence of delays in the control loop.Even in our increasingly electronic world the performance of manyengineering systems depends crucially on an efficient mechanicaltransmission of energy. Our fourth real-world challenge concerns cleverways of avoiding noise and vibrations in mechanical transmissionsystems. Freeplay and impacts are the major concerns affecting theoverall performance. While in the car industry the goal is to reducenoise and achieve driver comfort, large vibrations may lead tocatastrophic failure of wind turbines. Another important application ispower scavenging at microscales, which could be used to drive pacemakersor even mobile phones. The parameter and phase spaces of mechanicaltransmission systems are very large, so that the issue of modelrobustness is crucial.The grant involves the collaboration of eight investigators, fourpostdoctoral researchers, and eight postgraduate students withengineering and life sciences colleagues at Bristol, and industrialpartners and visiting researchers from around the world.

许多具有实际意义的问题产生了非常相似的基本应用数学问题。这项拟议的研究将解决生命科学和工程学中的四个现实挑战。它们的共同之处是由于不同部件之间的耦合而存在延迟，以及由于自由发挥和摩擦而产生的不平顺。此外，我们必须解决它们的空间范围和数学模型的稳健性这一首要问题。我们解决的第一个现实世界挑战是人脑的神经生理学。具体地说，我们将开发具有不同复杂性的模型，包括本地组件和分布式组件。由于电化学信号的原因，自然会延误进入。这项工作的一个主要焦点是癫痫发作的预测，在英国，癫痫每年导致2000多人死亡。更广泛地说，问题是：微观神经元参数的控制(例如，通过药物输送或电刺激)如何影响整体宏观行为？生物力学系统经常比任何人造设备表现得更好。例如哺乳动物和昆虫对声音的探测，以及陆地动物(从猎豹到蟑螂)的移动，它们可以惊人的速度和效率在崎岖的地形上移动。我们在现实世界中的第二个挑战是了解这是如何真正工作的，并帮助构建更好的通信系统或快速、有腿的机器人。一个重要的因素是影响，例如腿部与地面的碰撞，这会导致数学模型中的非光滑。我们在现实世界中的第三个挑战是混合测试。这种新方法提供了测试完整尺寸的单个部件的机会，例如飞机发动机、桥梁电缆或摩天大楼的楼板，就像它是整个工程结构的一部分一样。除了潜在地比传统测试节省大量成本外，混合测试还允许One进行目前不可能进行的测试。为了使混合测试成为工程上的现实，我们需要在测试样本和结构剩余部分的计算机模型之间实时闭合涉及传感器和执行器的控制回路。试件和模型一般都具有较大的空间范围，并受到周期性强迫等外部影响。我们将研究在控制回路存在延迟的情况下这些不同影响之间的相互作用。即使在我们日益电子化的世界中，许多工程系统的性能也关键取决于有效的机械能量传输。我们在现实世界中的第四个挑战是关于如何巧妙地避免机械传动系统中的噪音和振动。自由发挥和影响是影响整体表现的主要因素。虽然汽车行业的目标是减少噪音并实现驾驶舒适性，但大幅振动可能会导致风力涡轮机的灾难性故障。另一个重要的应用是微米级的能量回收，可以用来驱动起搏器，甚至手机。机械传动系统的参数和相空间非常大，因此模型的稳健性问题至关重要。拨款涉及8名研究人员、4名博士后研究人员和8名研究生与布里斯托尔的工程和生命科学同事，以及来自世界各地的工业合作伙伴和访问研究人员。