(UC Berkeley)

Complex dynamics underlying industrial manufacturing depend in part on multiphase multiphysics, in which fluids and materials interact across orders of magnitude variations in time and space. In this talk, we will discuss the development and application of a host of numerical methods for these problems, including Level Set Methods, Voronoi Implicit Interface Methods, implicit adaptive representations, and multiphase discontinuous Galerkin Methods.  Applications for industrial problems will include modeling how foams evolve, how electro-fluid jetting devices work, and the physics and dynamics of rotary bell spray painting across the automotive industry.

In this talk, I will discuss a wide range of mechanical systems,
including Hoberman’s sphere, Euler’s disk, a sliding cylinder, the
Dynabee, BB-8, and Littlewood’s hoop, and the research they inspired.
Studies of the dynamics of the cylinder ultimately led to a startup
company while studying Euler’s disk led to sponsored research with a
well-known motorcycle company.

This talk is primarily based on research performed with a number of
former students over the past three decades. including Prithvi Akella,
Antonio Bronars, Christopher Daily-Diamond, Evan Hemingway, Theresa
Honein, Patrick Kessler, Nathaniel Goldberg, Christine Gregg, Alyssa
Novelia, and Peter Varadi over the past three decades.

The tree amplituhedron A(n, k, m) is a geometric object generalizing the positive Grassmannian, which was introduced by Arkani-Hamed and Trnka in 2013 in order to give a geometric basis for the computation of scattering amplitudes in N=4 supersymmetric Yang-Mills theory. I will give a gentle introduction to the amplituhedron, and then describe what it looks like in various special cases. For example, one can use the theory of sign variation and matroids to show that the amplituhedron A(n, k, 1) can be identified with the complex of bounded faces of a cyclic hyperplane arrangement. I will also present some conjectures relating the amplituhedron A(n, k, m) to combinatorial objects such as non-intersecting lattice paths and plane partitions. This is joint work with Steven Karp, and part of it is additionally joint work with Yan Zhang.