SFB 1173: Wave phenomena: analysis and numerics

波使一般的科学家特别是数学家着迷。我们的两种感官--视觉和听觉--是基于光和声波的传播，人类的心跳是由去极化波驱动的，而大多数现代通信是基于电磁波的。波浪无处不在，了解它们的行为会让我们了解自然。对于数学家来说，研究波还有第二个原因：相关数学本身的美丽和多样性。波的传播是由许多有趣的方程描述的，这些方程具有美丽的性质，这些方程的数学运算带来了许多著名的结果。该合作研究中心（CRC）的目标是通过交织分析和数值来分析理解，数值模拟并最终操纵现实场景下的波传播。我们的研究重点是典型的波现象，如驻波和行波或波前的出现，振荡和共振，波的色散，反射，折射和散射。我们CRC的巨大潜力在于分析和数值专家的密切合作。来自光学和光子学、生物医学工程和应用物理学的五位项目负责人提供了应用程序的接口。这种独特的跨学科研究环境已经导致了大量的成果，推动了该领域的知识。此外，还出现了大量令人兴奋的研究问题，这些问题将在未来的资助期内得到解答。综合研究培训小组使有前途的博士和博士后研究人员从这种有利的合作中受益，并促进了新一代数学家的早期职业生涯。

Waves fascinate scientists in general and mathematicians in particular. Two of our senses – seeing and hearing – are based on the propagation of light and sound waves, the human heartbeat is driven by depolarization waves, and most modern communication is based on electromagnetic waves. Waves are everywhere, and understanding their behavior leads us to understand nature. For mathematicians there is a second reason to study waves: The beauty and diversity of the related mathematics itself. Wave propagation is described by a number of intriguing equations with beautiful properties, and the mathematics of these equations has brought about many celebrated results. The goal of this Collaborative Research Centre (CRC) is to analytically understand, numerically simulate, and eventually manipulate wave propagation under realistic scenarios by intertwining analysis and numerics. Our research focuses on typical wave phenomena such as the emergence of standing and traveling waves or wave fronts, oscillations and resonances, dispersion, reflection, refraction and scattering of waves. The outstanding potential of our CRC lies in the close cooperation of specialists from analysis and numerics. Five project leaders from optics and photonics, biomedical engineering, and applied geophysics provide an interface to applications. This unique interdisciplinary research environment has already led to substantial results that have advanced the knowledge in the field. In addition, a wealth of exciting research questions has emerged which will be answered in the coming funding period. The integrated Research Training Group enables promising doctoral and postdoctoral researchers to benefit from this advantageous cooperation, and it fosters the early career of a new generation of mathematicians.