Motivated by problems arising in the applied sciences, I will tell the story
of what might reasonably be called a "forgotten function". It was discovered
in the late 1800s, but has hardly ever been used in the physical sciences even
though, as I will show, its applications in science and engineering turn out
to be many and varied.
In particular, I will survey a new theoretical approach to solving problems in what mathematicians call "multiply connected" domains.
The behaviour of elastic liquids does not follow simply from our understanding of both elastic solids and viscous liquids. Four anomalous behaviours will be discussed :-- (i) long wakes at low Reynolds numbers, (ii) large vortices upstream of a constriction, (iii) long times for capillary forces to squeeze a filament, and (iv) different devices measuring wildly different values of `the' extensional viscosity for the international standard liquid M1.
Tao Tang, Department of Mathematics, Hong Kong Baptist University and South University of Science and Technology, China
Uncertainty quantification (UQ) has been a hot research topic recently. UQ has a variety of applications, including hydrology, fluid mechanics, data assimilation, and weather forecasting. Among a large number of approaches, the high order numerical methods have become one of the important tools; and the relevant computational techniques and their mathematical theory have attracted great attention in recent years. This talk begins with a brief introduction to recent developments of high order numerical methods including Galerkin projection methods and stochastic collocation methods.
Predicting the behaviour of a structure when subjected to an earthquake is an important problem from Civil Engineering. Here, we consider a planar post-tensioned frame, which can be modelled as a two-degree-of-freedom system that is equivalent to the analytical model of a tied rocking block on an elastic foundation. The frame remains structurally sound as long as the tilt angle of the frame does not exceed a certain maximal angle.
Aircraft are designed to fly but also need to operate efficiently and safely as vehicles on the ground. The tricycle configuration of commercial aircraft presents challenges for manoeuvres, such as high-speed turns off a runway. The talk will present results of a collaboration with Airbus into the stability of ground manoeuvres, whose central idea is to employ tools from bifurcation analysis to relevant industry-validated aircraft models. Compared to standard extensive numerical simulations, this approach has been demonstrated to have potential efficiency benefits during the design stage.
I will present the results of our recent work on epithelial morphogenesis, a highly conserved set of processes that transform two-dimensional sheets of cells into complex three-dimensional structures. Such transformations play key roles during embryogenesis and their understanding is important both from a purely scientific standpoint and for the design of man-made tissues and organs. Our laboratory is using the eggshell morphogenesis in the fruit fly Drosophila melanogaster as a model for studying epithelial morphogenesis in a relatively simple setting, with a constant number of cells.
Data assimilation is the process of systematically including (often noisy) data into a forecast. It is now widely used in numerical weather prediction and its positive impact on the accuracy of weather forecasts is unquestionable. Indeed improvements in our ability to forecast the weather over the last decade are a reflection on the increasing volume of data available, improved computational methods and (significantly) much improved algorithms for incorporating this data into the forecast.
Daniel Hammer, Bioengineering and Chemical and Biomolecular Engineering, University of Pennsylvania
Adhesive Dynamics is a method to simulate the dynamics of cell adhesion to surfaces. Adhesion receptors are modeled as reactive mechanical entities with adhesive tips, and the formation and breakage of adhesion molecules with cognate ligands is simulated using random number sampling. Once the bonds form, the contact points they make with surfaces are tracked, and a force balance is used to calculate the motion of the cell.