The Department of Applied Mathematics is pleased to host this series of colloquium lectures, funded in part by a generous gift from the Boeing Company. This series will bring to campus prominent applied mathematicians from around the world.
The talks should be of general interest to researchers and students in the mathematical sciences and related fields. All are welcome to attend. There will be three talks in this series each quarter, on Thursday afternoons at 4:00pm. Each talk will be followed by a reception.
For a list of all previous Boeing Colloquia, see our Boeing Colloquia Archive.
April 13, 2017
Title: Surprises in the Fluid Dynamics of Flows in Simple Geometries
Abstract:The flow of particle-laden fluids occurs widely, including bulk flows at low or high Reynolds numbers, which arise in all manners of applications. We give a few examples of our current work in this area. First we consider flow in a T-junction, which is perhaps the most common element in many piping systems. The flows are laminar but have high Reynolds numbers, typically Re=100-1000. It seems obvious that any particles in the fluid that enter the T-junction will leave following the one of the two main outlet flow channels. Nevertheless, we report experiments that document that bubbles and other low density objects can be trapped at the bifurcation. The trapping leads to the steady accumulation of bubbles that can form stable chain-like aggregates in the presence, for example, of surfactants, or give rise to growth due to coalescence. Our three-dimensional numerical simulations rationalize the mechanism behind this surprising phenomenon. Second, we consider low Reynolds number flows in channels and porous systems with dead-end pores. We document how salt gradients, via a mechanism referred to as diffusiophoresis, can remove particles from dead-end pores or deliver particles into such pores. The transport can be size dependent and we explore the phenomenon using experiments and modeling. We suggest how the mechanistic ideas can be used to design processes for cleaning water in energy efficient ways.
February 2, 2017
Title: Mean Field Games: theory and applications
Abstract: We review the Mean Field Game paradigm introduced independently by Caines-Huang-Malhame and Lasry-Lyons ten years ago, and we illustrate their relevance to applications with a couple of examples (bird flocking and room exit). We then review the probabilistic approach based on Forward-Backward Stochastic Differential Equations, and we derive the Master Equation from a version of the chain rule (Ito’s formula) for functions over flows of probability measures. Finally, motivated by the literature on economic models of bank runs, we introduce mean field games of timing and discuss new results, and some of the many remaining challenges.
January 12, 2017
Title: Collective Behavior of Large Networks of Simple Dynamical Units
Abstract: Large systems of many coupled dynamical units are of crucial interest in a host of physical, biological and technological settings. Often the dynamical units that are coupled exhibit oscillatory behavior. The understanding and analysis of these large, complex systems offers many challenges. In this talk I will introduce this topic, give some examples, and describe a technique for analyzing a large class of problems of this type. The results I will discuss will reduce the complicated, high dimensional, microscopic dynamics of the full system to that or a low dimensional system governing the macroscopic evolution of certain ‘order parameters’. This reduction is exact in the limit of large systems, i.e., N going to infinity, where N is the number of coupled units, and can be employed to discover and study all the macroscopic attractors and bifurcations of the system. [Refs.: E.Ott and T.M.Antonsen, Chaos (2008, 2009).]
November 17, 2016
Title: The Emerging Roles and Computational Challenges of Stochasticity in Biological Systems
Abstract: In recent years it has become increasingly clear that stochasticity plays an important role in many biological processes. Examples include bistable genetic switches, noise enhanced robustness of oscillations, and fluctuation enhanced sensitivity or “stochastic focusing”. Numerous cellular systems rely on spatial stochastic noise for robust performance. We examine the need for stochastic models, report on the state of the art of algorithms and software for modeling and simulation of stochastic biochemical systems, and identify some computational challenges.
November 10, 2016
Title: From a model network of 10,000 neurons to a smartphone app with 175,000 users: novel approaches to study daily timekeeping
Abstract: I will briefly describe mathematical models of networks of neurons and biochemical reactions within neurons that generate daily (circadian) timekeeping. The numerical and analytical challenges of these models as well as the benefits in terms of biological predications will be highlighted. I will then explain how models can be used to find schedules that decrease the time needed to adjust to a new timezone by a factor of 2 or more. These optimal schedules have been implemented into a smartphone app, ENTRAIN, which collects data from users and in return helps them avoid jet-lag. We will use the data from this app to determine how the world sleeps. This presents a new paradigm in mathematical biology research where large-scale computing bridges the gap between basic mechanisms and human behavior and yields hypotheses that can be rapidly tested using mobile technology.
October 27, 2016
Title: Approximating Matrices: One Picture and One Thousand Words
Abstract: Matrix approximation is a well-studied area of mathematics, but despite the attention it has received, many open questions remain involving existence, uniqueness, extensions to tensors, and efficient computation. The focus in this talk is on matrix approximation problems constrained in rank, sparsity, and nonnegativity, including a novel approach to uncertainty in matrix entries. Applications to deblurring pictures (images) and to article summarization and classification will be discussed.
October 6, 2016
Title: Modeling the Melt: What Math Tells Us About the Shrinking Polar Ice Caps
Abstract: The precipitous loss of Arctic sea ice has outpaced expert predictions. We will explore how mathematical models of composite materials and statistical physics are being developed to study key sea ice structures and processes and advance how sea ice is represented in climate models. Our composite material models for sea ice are developed in conjunction with field experiments that we have conducted in both the Arctic and Antarctic. This work is helping to improve projections of the fate of Earth’s sea ice packs, and the response of the polar ecosystems they support. The lecture is intended for a wide, interdisciplinary audience.
May 12, 2016
Title: Matrix iterative methods from the historical, analytic, application, and computational perspective
Abstract: Modern matrix iterative methods represented, in particular, by Krylov subspace methods, are fascinating mathematical objects that integrate many lines of thought and are linked with hard theoretical problems.
Krylov subspace methods can be seen as highly nonlinear model reduction that can be very efficient in some cases and not easy to handle in others. Convergence behaviour is well understood for the self-adjoint and normal operators (matrices), where we can conveniently rely on the spectral decomposition. That does not have a parallel in non-normal cases. Theoretical analysis of efficient preconditioners is therefore complicated and it is often based on a simplified view to Krylov subspace methods as linear contractions. In numerical solution of boundary value problems, e.g., the infinite dimensional formulation, discretization, and algebraic iteration (including preconditioning) should be tightly linked to each other. Computational efficiency requires accurate, reliable and cheap a posteriori error estimators that relate the discretization and algebraic errors in order to construct an appropriate (problem dependent) stopping criteria. Understanding numerical stability issues is crucial and this becomes even more urgent with increased parallelism where the communication cost becomes a prohibitive factor.
The presentation will concentrate on ideas and connections between them with emphasizing the historical perspective. Technical details will be kept at minimum so that the lecture is accessible to a wide audience.
April 28, 2016
Title: Linear and Nonlinear Waves in Gas Dynamics
Abstract: This talk explores some puzzles of multidimensional conservation laws (quasilinear hyperbolic partial differential equations) by looking at two types of characteristic families in a model system: the Euler equations of compressible fluid flow. There is as yet no existence theory for such systems, and a considerable amount of recent activity raises questions of whether these equations, and others like them, are even well-posed. The
classical theory of characteristics provides a framework that unifies some observations, and suggestions directions for further study.
March 31, 2016
Title: Complex oscillations: mixed modes and bursting in dynamical systems with multiple time scales
Abstract: Multiple time scales have a profound impact on dynamical systems. The generic behaviors found in this setting include bursting, chaotic relaxation oscillations and mixed mode oscillations. Recent advances in theory and accompanying computational methods have dramatically improved our understanding of these complex temporal behaviors. A natural classification of different types of bursting and mixed modes is developed and used as a foundation for computational methods that analyze multiple time scale models. This lecture will present examples of biological, geophysical, engineering and chemical systems that illustrate recent discoveries.