The 11th Annual GGAM Mini-Conference convenes on Saturday, February 20, 2016. The conference is a coming together between the group's faculty and its students in order to facilitate fruitful collaborations. In an informal forum, faculty will describe their research interests, giving students an opportunity to experience the broad directions available to them in applied mathematics. And though the conference is called "GGAM", our Math students are certainly encouraged to attend as well.
All first and second year graduate students in Applied Mathematics are strongly encouraged to register for the GGAM Mini-Conference. By doing so, registered students will earn one unit of credit. The CRN number to register in Winter 2016 is available from student services.
The GGAM Mini-Conference is an all-day event held in room 1147 of Mathematical Science Building.
Update: Photos from the mini-conference.
|9:30–10:00||Welcome and Introduction|
|10:00–10:50||Prof. James Sharpnack||Signal processing over graphs|
|11:30–12:00||Dr. Ying He||A Discontinuous Galerkin Method with a Bound Preserving Limiter for Stable Advection of non-Diusive Fields in Computational Geodynamics|
|1:00–1:50||Prof. Qinglan Xia||Ramified optimal transportation and its applications|
|2:00–2:50||Prof. Bob Guy||Mechanisms of Elastic Enhancement and Hindrance for Swimmers in Viscoelastic Fluids|
|3:30–4:20||Dr. Andrew Sornborger||Information Processing with Neural Assemblies|
|4:30–5:00||Dr. Mimi Tsuruga||Random Discrete Morse|
The social part of the event, consisting of a conference reception and a dinner, will be held beginning at 5:00p in room 1147 of the Mathematical Sciences Building. Significant others and family members are welcome to join. RSVP is required; please indicate, with number of guests, to firstname.lastname@example.org no later than 4:00p by MONDAY, February 15, 2016.
- Prof. Bob Guy, Mechanisms of Elastic Enhancement and Hindrance for Swimmers in Viscoelastic Fluids (50 minutes talk)
Abstract: Low Reynolds number swimming of microorganisms in Newtonian fluids is an extensively studied classical problem. However, many biological fluids such as mucus are mixtures of water and polymers and are more appropriately described as viscoelastic fluids. Recently, there have been many studies on locomotion in complex fluids. Both experiments and theory have exhibited that viscoelasticity can lead to either an enhancement or retardation of swimming, but a complete understanding of this problem is lacking.
A computational model of finite-length undulatory swimmers is used to examine the physical origin of the effect of elasticity on swimming speed. We reproduce conflicting results from the literature simply by changing relevant physical parameters. Additionally, we examine an oscillatory bending beam in a viscoelastic fluid to provide a mechanistic understanding of how elasticity affects swimming and to identify a threshold in amplitude related to the development of large elastic stresses. We relate this transition to previously studied bifurcations in steady extensional flows of complex fluids. This reduced model sheds light on properties of swimmer gaits and body mechanics that lead to either elastic enhancement or hindrance.
- Dr. Ying He, A Discontinuous Galerkin Method with a Bound Preserving Limiter for Stable Advection of non-Diusive Fields in Computational Geodynamics (30 minutes talk)
Abstract: Flow in the Earth’s mantle is driven by thermo-chemical convection in which the properties and geochemical signatures of rocks vary depending on their origin and composition. Therefore, tracking of active or passive fields with distinct compositional, geochemical or rheologic properties is important for incorporating physical realism into mantle convection simulation. The difficulty in numerically advecting fields arises because they are non-diffusive and have sharp boundaries, and therefore require different methods than usually used for temperature. Previous methods for tracking fields include the marker-chain, tracer particle, and field-correction (e.g., the Lenardic Filter) methods: each of these has different advantages or disadvantages, trading off computational speed with accuracy in tracking feature boundaries. Here we present a method for modeling active fields in mantle dynamics simulations using a new solver implemented in the deal.II package that underlies the ASPECT software. The new solver for the advection-diffusion equation uses a Discontinuous Galerkin (DG) algorithm, which combines features of both finite element and finite volume methods, and is particularly suitable for problems with a dominant first-order term and discontinuities. Furthermore, we have applied a post-processing technique to insure that the solution satisfies a global maximum/minimum. To demonstrate the capabilities of this new method we present results for a benchmark used previously: a falling cube with distinct buoyancy and viscosity. To evaluate the trade-offs in computational speed and solution accuracy we present results for the same benchmark using the standard Finite Element Method.
- Prof. James Sharpnack, Signal processing over graphs (50 minute talk)
Abstract: We will survey methodology for recovering a signal over a graph in white noise. We focus on signals generated by the Potts model and piecewise polynomial variants. This includes synthesis methods, such as graph wavelets, and analysis regularization, such as trend filtering. We will focus on the relationship between the graph topology and approximate signal recovery, which manifests itself through algebraic properties of graph differential operators. Specifically, the entropy numbers of the Laplacian, and its higher order variants, plays a central role and these properties for various graph models will be discussed. I will talk about the remaining open problems, and promising future directions.
- Dr. Andrew Sornborger, Information Processing with Neural Assemblies (50 minute talk)
Abstract: Cognitive tasks are associated with the dynamic excitation of neural assemblies. When we consider how quickly and flexibly such collectives may be formed and incorporated in a task, a persistent question has been: how can the brain rapidly evoke and involve different neural assemblies in a computation when synaptic coupling changes only slowly? In this talk, I will present mechanisms whereby information may be rapidly and selectively routed through a neural circuit, and sub-circuits may be turned on and off. The resulting information processing framework achieves the goal that has been pursued, but until now largely not attained, of achieving faithful, flexible information transfer and processing across many synapses and dynamic excitation of neural assemblies with fixed connectivities.
- Dr. Mimi Tsuruga, Random Discrete Morse (30 minutes talk)
Abstract: We will give a mini-intro to computational topology by way of example. We will examine Benedetti and Lutz's algorithm, random discrete Morse theory, which will help to introduce some basic vocabulary, some tools that are available (or in development), and more importantly, the types of questions a computational topologist may ask.
- Prof. Qinglan Xia, Ramified optimal transportation and its applications (50 minutes talk)Abstract: The optimal transportation problem aims at finding a cost efficient transport from sources to targets. In mathematics, there are at least two very important types of optimal transportation: Monge-Kantorovich problem and ramified optimal transportation. In this talk, I will give a brief introduction to the theory of ramified optimal transportation. One motivation of the theory comes from the study of the branching structures found in nature. Many living systems such as trees, the veins on a leaf, as well as animal cardiovascular/circulatory systems exhibit branching structures, as do many non-living systems such as river channel networks, railways, airline networks, electric power supply and communication networks. Why do nature and engineers both prefer these ramifying structures? What are the advantages of these branching structures over non-branching structures? These questions partially motivates us to explore the mathematics behind them. In this talk, I will talk about how to set up a mathematical theory for this general phenomenon in terms of optimal transport paths. An optimal transport path between two probability measures can be viewed as a geodesic in the space of probability measures. In this talk, I will also survey some applications of the theory in multidisciplinary areas such as mathematical biology (e.g. the dynamical formation of tree leaves), metric geometry (e.g. the geodesic problems in quasimetric spaces), fractal geometry (e.g. the modified diffusion-limited aggregation), geometric analysis (e.g. transport dimension of measures) and mathematical economics (e.g. ramified optimal allocation problem).