Mathematical Modelling of Rare Events in Nanoflows: A Feasibility Study

21世纪预示着流体技术小型化的一场革命，这场革命与20世纪在电子领域取得的成就相当，微流控长度秤的技术现在已经完全商业化(例如3D打印机)。自然，现在的重点已经转向开发纳米尺度(即纳米流体)流动的巨大潜力，在纳米尺度上，巨大的表面积与体积比创造了由表面/界面效应驱动的系统，因此可以以我们在日常生活中观察到的规模无法想象的方式操纵微小的流体。我们这里的重点是纳米级液体体积的分解，这是纳米制造(例如薄膜太阳能电池)、泪膜和眼睛的“干燥”、再生医学的仿生纳米设备和新型纳米颗粒药物等应用的关键。值得注意的是，目前还没有为这些纳米流开发出科学工具，例如：-实验技术只能提供有限的信息，因为动力学发生得太快。-基于传统流体动力学的理论方法在纳米尺度上失败，因为热涨落(噪声或布朗运动)推动了质的新的随机动力学。这项可行性研究将探索一种新的数学方法，以克服这些挑战，该方法基于最初为量子力学开发的罕见事件的新方法。如果成功，这将为更广泛的学科内/学科间研究计划提供一个平台，该计划旨在对实际相关的纳米系统进行数学建模，可能使英国走在这一高科技新兴领域的前沿。

The 21st century has heralded a revolution in the miniaturisation of fluid-based technologies that parallels those achieved in electronics in the 20th century, with technologies on microfluidics length scales now fully commercialised (e.g. 3D printers). Naturally, focus has now turned to exploiting the tremendous potential of flows at the nanoscale (i.e. nanofluidics), where huge surface area to volume ratios create systems that are driven by surface/interfacial effects, so that tiny volumes of fluid can be manipulated in ways that are unimaginable at the scales we observe in our daily lives. Our focus here is on the breakup of liquid volumes at the nanoscale, which are key to applications including nano-manufacturing (e.g. of thin-film solar cells), tear films and 'dry out' of the eye, bionic nano-devices for regenerative medicine and novel nano-particle drugs. Remarkably, at present, no scientific tools have been developed for these nanoflows as: - Experimental techniques can only provide limited information, as the dynamics occur too fast. - Theoretical approaches based on conventional fluid dynamics fail at the nanoscale, as thermal fluctuations ('noise' or 'Brownian motion') drive qualitatively new stochastic dynamics.This feasibility study will explore a new mathematical approach to overcome these challenges based on new methods for rare events that were originally developed for quantum mechanics. If successful, this will provide a platform for a much broader programme of intra-/inter-disciplinary research into the mathematical modelling of practically relevant nano-systems that could put the UK at the forefront of this high-tech emerging area.