DPhil in the use of asymptotic techniques in modelling glass manufacture

玻璃加工通常涉及粘性液体在薄区域中的流动，该粘性液体的粘度是温度的强函数。我们特别感兴趣的是在建模的几何形状是复杂的和未知的提前和/或过程中可能会受到不稳定的情况。在这个项目中，我们将专注于薄玻璃板的绘制，以制造电视，平板电脑和智能手机的屏幕。已知压缩区域可导致这些片材弯曲，从而在最终产品中产生局部波纹。然而，目前还没有一个很好的完整的理论，解释如何的振幅的扰动饱和，由于弱非线性效应，或如何波纹成为“冻结”的玻璃冷却。在该项目中，也有可能解决玻璃制造过程中出现的相关和相关的工业问题。这项研究的新奇是由于还没有一个完全已知的粘性薄板屈曲理论-这将在研究过程中进行探索。它还来自于利用应用数学的技术来选择与工业相关的新问题，如果解决，制造的质量和效率将得到提高。虽然属于数学科学主题，但该项目将具体属于EPSRC的研究领域：连续介质力学，流体动力学和空气动力学，制造未来主题和数学分析。它福尔斯连续介质力学领域，因为玻璃的粘度严重依赖于温度，因此可以表现出固体和流体行为。由于玻璃在制造过程中表现为粘性液体，因此该研究与流体动力学和空气动力学有关。由于该项目旨在提高工业生产玻璃的能力，由于重点是了解过程中的不稳定性，从而有助于限制程序的缺陷，因此该研究也福尔斯制造未来的主题。该项目也属于数学分析领域的研究，因为渐近技术将被用来利用的事实，即几何形状的研究往往是薄福尔斯。在分析所得方程时，还将使用常微分方程和偏微分方程中的技术。如果从分析中得不到明确的解决办法，则将使用数值模拟和模型来捕捉系统的行为。

Glass processing typically involves the flow of a viscous liquid, whose viscosity is a strong function of temperature, in a thin domain. We are particularly interested in modelling situations where the geometry is complicated and unknown in advance and/or where the process may be subject to instabilities. In this project, we will focus on the drawing of thin glass sheets to make screens for TVs, tablets and smartphones. It is known that regions of compression can cause these sheets to buckle, resulting in local ripples in the final product. However, there is currently no good complete theory of viscous sheet buckling that explains how the amplitude of the disturbance saturates, due to weakly nonlinear effects, or how the ripples become "frozen in" as the glass cools. Within the project there is also the potential to tackle relevant and pertinent industrial problems on the modelling of glass manufacture should such problems arise within the course of study.The novelty of the research is as a result of there not yet being a fully known theory of viscous sheet buckling - which will explore during the course of the study. It also comes from utilizing techniques from applied mathematics on a selection of new problems relevant to the industry, where if solved, the quality and efficiency of manufacture will be improved.While coming under the mathematical sciences theme, this project will specifically fall under the EPSRC research areas of: continuum mechanics, fluid dynamics and aerodynamics, manufacturing the future theme and mathematical analysis. It falls under the area of continuum mechanics because the viscosity of glass is heavily dependent on temperature, so can exhibit both solid and fluid behaviour. As glass behaves as a viscous liquid in the manufacturing process, the research is linked to fluid dynamics and aerodynamics. Because the project aims to improve the ability of the industry to manufacture glass, due to the focus on understanding the instabilities in the process and so helping to limit the defects of the procedure, the research also falls under the manufacturing the future theme. The project also falls under the mathematical analysis area of research because asymptotic techniques will be used to exploit the fact that the geometries studies will often be thin. Techniques in ordinary and partial differential equations will also be used when analysing the resulting equations. Numerical simulations and models will then be used to capture the behaviour of the systems if explicit solutions are not tractable from the analysis.