Nonlinear hydroelastic waves with applications to ice sheets

自由边界问题是一个具有挑战性的数学问题，它涉及到解决非线性问题的区域，其形状必须找到作为解决方案的一部分。它们出现在许多工业、环境和生物应用中。例如涂层问题、海浪和肿瘤。在这个建议中，我们集中在水弹性波，特别是对冰盖的应用。这项研究的动机是了解人造大型浮动结构（特别是机场）和南极探险，在南极探险中，重型设备通常会在浮冰上行驶，飞机将在浮动的冰盖跑道上运行。冰盖下的波浪最近也引起了人们的关注，因为它们是需要考虑的影响气候变化的许多因素之一。水弹性波的数学表述涉及复杂的非线性积分微分方程系统，其中大多数研究都局限于线性模型。虽然线性近似通常是足够的，但在许多情况下，冰盖的非线性和大的缺陷是不能忽略的。因此，我们建议发展完全非线性数值理论和弱非线性渐近模型来解决这些问题。孤立波、暗孤子、内波和三维波是其中的研究课题。PI，CI和访问研究员在非线性波方面的经验将对项目的成功非常有用。预期的RA是列奥纳多Xavier Epsin博士。他在建模，渐近和数值模拟方面的强大背景使他非常适合研究所提出的问题。如果他不能接受这个职位，其他合格的候选人是已知的PI和CI。

Free boundary problems are challenging mathematical problems which involve solving nonlinear problems in domains whose shapes have to be found as part of the solution. They occur in many industrial, environmental and biological applications. Examples are coating problems, ocean waves and tumors. In this proposal we concentrate on hydroelastic waves and in particular on applications to ice sheets. The research is motivated by the understanding of man-made large floating structures (especially airports) and by Antarctic exploration where often heavy equipment will travel over roads on floating ice and aircraft will operate on floating ice-sheet runways. Waves under ice sheets have also recently attracted attention because they are one of the many factors that need to be considered as having an impact in climate change. The mathematical formulation of hydroelastic waves involve complicated systems of nonlinear integro-differential equations for which most studies have been restricted to linear models. Although linear approximations are often adequate, there are many situations in which nonlinearities and large defections of the ice sheet cannot be neglected. Therefore we propose to develop fully nonlinear numerical theories and weakly nonlinear asymptotic models to tackle these problems. Solitary waves, dark solitons, internal waves and three dimensional waves are among the topics to be studied. The previous experience of the PI, CIs and visiting researcher with nonlinear waves will be very instrumental for the success of the project. The intended RA is Dr Leonardo Xavier Epsin. His strong background in modelling, asymptotics and numerical simulationsmakes him very well suited to work on the proposed problems. In case he were not able to take the position, other qualified candidates are known to the Pi and CIs.