L6

The collapse of granular columns in a viscous fluid is a common model case for submarine geophysical flows. In immersed granular collapses, dense packings result in slow dynamics and short runout distances, while loose packings are associated with fast dynamics and long runout distances. However, the underlying mechanisms of the triggering and runout, particularly regarding the complex fluid-particle interactions at the pore-scale, are yet to be fully understood. In this study, a three-dimensional approach coupling the Lattice Boltzmann Method and the Discrete Element Method is adopted to investigate the influence of packing density on the collapsing dynamics. The direct numerical simulation of fluid-particle interactions provides evidence of the pore pressure feedback mechanism. In dense cases, a strong arborescent contact force network can form to prevent particles from sliding, resulting in a creeping failure behavior. In contrast, the granular phase is liquefied substantially in loose cases, leading to a rapid and catastrophic failure. Furthermore, hydroplaning can take place in loose cases due to the fast-moving surge front, which reduces the frictional resistance dramatically and thereby results in a longer runout distance. More quantitatively, we are able to linearly correlate the normalized runout distance and the densimetric Froude number across a wide range of length scales, including small-scale numerical/experimental data and large-scale field data.

Arctic sea ice is one of the most sensitive components of the Earth’s climate system. The underlying ocean plays an important role in the evolution of the ice cover through its heat flux at the ice-ocean interface. Despite its importance, the spatio-temporal variations of this heat flux are not well understood. In this talk, I will take the following approach to study the variations in the heat flux. First, I will consider the problem of classical Rayleigh-Bénard convection and systematically explore the effects of fractal boundaries on heat transport using direct numerical simulations. And second, I will analyze time-series data from the Surface Heat Budget of the Arctic Ocean (SHEBA) program using Multifractal Detrended Fluctuation Analysis (MFDFA) to understand the nature of fluctuations in the heat flux. I will also discuss developing simple stochastic ODEs using results from these studies.

The homological monodromy of the universal family of cubic threefolds defines a representation of a certain Artin-type group into the symplectic group Sp(10;\Z). We use Thurston’s classification of surface automorphisms to prove this does not factor through the genus five mapping class group.  This gives a geometric group theory perspective on the well-known irrationality of cubic threefolds, as established by Clemens and Griffiths.