

Jan. 22, 2016
Chunyou Sun
Department of Mathematics, Lanzhou University, China
Location and Time: Parker Hall 352, 1pm2pm
Title: Dynamics for a 2D generalized incompressible NavierStokes equations
Abstract: In this talk, I will present our recent results about the zero viscosity limit of long time averages of solutions and the existence and finite dimensionality of global attractor for a 2D damped generalized incompressible NavierStokes equations.

Jan. 29, 2016
Jeff Borggaard
Department of Mathematics, Virginia Tech
Location and Time: Parker Hall 352, 1pm2pm
Title: Rotational Stabilization of Cylinder Wakes Using Linear Feedback Control
Abstract: We demonstrate the feasibility of linear feedback control to stabilize vortex shedding behind twin cylinders using the cylinder rotations. Our approach isto linearize the flow about a desired steadystate flow, use interpolationbased model reduction on the resulting linear model to generate a lowdimensional model of the inputoutput system with inputindependent error bounds, then use this reduced model to design the feedback control law. Closedloop simulations of the NavierStokes equations demonstrate the effectiveness of this control strategy.

February 12, 2016
Wayne M. Lawton
Department of Mathematics, Mahidol University, Thailand
Location and Time: Parker Hall 352, 1pm2pm
Title: Matrices and Recursive Algorithms
Abstract: The Euclidean algorithm of antiquity proceeds by recursively multiplying a column vector [a1 b1]^T on the left by a 2 x 2 matrix to give [a2 b2=a1]^T where a2 is the remainder of b1 upon division by a1. This algorithm terminates when an = 0 and then bn is the greatest common divisor of a1 and b1. The formula for the inverse of a product of matrices explicitly represents bn as an integral linear combination of a1 and b1. Our talk discussed similar recursions arising in continued fractions, filter design, wave propagation in layered media, and quantum physics.

February 19, 2016
Xiaojing Xu
Department of Mathematics, Beijing Normal University, China
Location and Time: Parker Hall 352, 1pm2pm
Title: Global Small solution to the 2D MHD System with a Velocity Damping Term
Abstract: In this talk, I will show a global wellposedness result of the incompressible magnetohydrodynamic (MHD) system with a velocity damping term. We establish the global existence and uniqueness of smooth solutions when the initial data is close to an equilibrium state. In addition, explicit largetime decay rates for various Sobolev norms of the solutions are also given.

February 26, 2016
Xiaoying Han
Department of Mathematics and Statistics, Auburn University
Location and Time: Parker Hall 352, 1pm2pm
Title: SemiKolmogorov type of predation models in varying environments
Abstract: In this talk I will introduce several semikolmogorov type of predation models, including a nonautonomous model with periodic forcing, a random model with real bounded noise, a stochastic model with white noise, and a stochastic model with continuoustime Markov chain. In particular I will talk about the long term behavior of these systems.

March 4, 2016
Yanzhao Cao
Department of Mathematics and Statistics, Auburn University
Location and Time: Parker Hall 352, 1pm2pm
Title: Backward SDE methods for nonlinear filtering problems
Abstract: A nonlinear filtering problem can be classified as a stochastic Bayesian optimization problem of identifying the state of a system with a noise perturbation given noisy observations of the system. Well known numerical simulation methods include unscented Karlman filters and particle filters. In this talk, we attempt to construct efficient numerical methods using forward backward stochastic differential equations. The backward SDEs for the nonlinear filtering problems are the counter parts of FokkerPlanck equations for SDEs with no observation constraints. In this talk we will describe the process of deriving such backward SDEs as well as the corresponding high order numerical algorithms for nonlinear filtering problems.

March 11, 2016
David Nicholls
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago
Location and Time: Parker Hall 352, 1pm2pm
Title: Numerical Solution of Diffraction Problems: A HighOrder Perturbation of Surfaces/Asymptotic Waveform Evaluation Method
Abstract: The rapid and robust simulation of linear waves interacting with layered periodic media is a crucial capability
in many areas of scientific and engineering interest. HighOrder Perturbation of Surfaces (HOPS) algorithms are interfacial methods which recursively
estimate scattering quantities via perturbation in the interface shape
heights/slopes. For a single incidence wavelength such methods are the
most efficient available in the parameterized setting we consider
here. In this talk we describe a generalization of one of these HOPS
schemes by incorporating a further expansion in the wavelength about a
base configuration which constitutes an "Asymptotic Waveform
Evaluation" (AWE). We not only provide a detailed specification of the
algorithm, but also verify the scheme and point out its benefits and
shortcomings. With numerical experiments we show the remarkable
efficiency, fidelity, and highorder accuracy one can achieve with an
implementation of this algorithm.

March 25, 2016
Sanjeev Baskiyar and TinYau Tam
Department of Computer Science and Software Engineering,
and Department of Mathematics and Statistics, Auburn University
Location and Time: Parker Hall 352, 1pm2pm
Title: Minimum Energy Consumption for Rate Monotonic Algorithm in a Hard RealTime Environment
Abstract: Limited battery power is a typical constraint in standalone embedded systems. One way to extend the battery lifetime is by reducing CPU power consumption. Because of the quadratic relationship between power consumption in CMOS circuits and CPU voltage, power reduction can be obtained by scaling down supply voltage, or Dynamic Voltage Scaling. However, reducing supply voltage slows down CPU speed since supply voltage has a proportional relationship with CPU frequency. On the other hand, in any realtime embedded environment (especially hard realtime), timing constraints are critical. We focus on dynamic energy reduction of tasks scheduled by Rate Monotonic (RM) algorithm in a hard realtime embedded environment. The RM algorithm preemptively schedules any set of periodic tasks by assigning higher priorities to frequent tasks. For any periodic task set that satisfies the CPU utilization bound, we determine the provably optimal scaling of the worstcase execution time of each task that consumes minimum dynamic energy while satisfying the utilization bound. As RM algorithm is widely used, we expect this work can lead to better energy reduction management and expectations. In this talk we will give the background, formulation, solution, and algorithm of the problem. The talk is based on our paper that appears in the journal Computing.

April 1, 2016
Sedar Ngoma
Department of Mathematics and Statistics, Auburn University
Location and Time: Parker Hall 352, 1pm2pm
Title: Rothe's method for timedependent inverse source / coefficient problems arising in geochronology
Abstract: We investigate a problem arising in geochronology, the study of dating of rock formations and geological events, and in particular the reconstruction of temperature histories of rocks, and dating the cooling of rocks through exhumation. Reconstructing the temperature history amounts to solving a timedependent, inverse coefficient problem for an integral constrained PDE. Using Rothe's method and an energy argument, we show the existence and uniqueness of weak solutions to the related inverse source problem. We describe numerical schemes which can be used to approximate solutions of the inverse problems and report on the errors and convergence rates. We also present the existence and uniqueness of a classical solution to the inverse source problem using the semigroup approach.

Apri 8, 2016 ( special seminar)
Oscar Bruno
Department of Computing and Mathematical Sciences, Caltech
Location and Time: Parker Hall 352, 4pm5pm
Title: Fourier Continuation, resolution of the Gibbs phenomenon, and application to numerical analysis and computation.
Abstract: Fourier expansions possess excellent properties of approximation of smooth and periodic functionswhich make them ideal elements for simulation of periodic systems. This talk presents a new approach which extends use of rapidly convergent Fourier series to general problems in computational science. We will demonstrate these ideas with results of recent applications to numerical solution of linear and nonlinear Partial Differential Equations in complex three dimensional geometries, including general solution of PDEs in the time domain such as the fluiddynamics and elastic wave equations (where virtual dispersionlessness is demonstrated) and, using integral equation methods and related fast highlyaccurate algorithms, solution of Laplace eigenvalue problems and problems of acoustics and electromagnetism at high frequencies.

April 15, 2016
John Schotland
Department of Mathematics, University of Michigan
Location and Time: Parker Hall 352, 1pm2pm
Title: Optical Tomography
Abstract: There is considerable interest in the development of optical methods for
biomedical imaging. The physical problem consists of recovering the
optical properties of a medium in which light propagates by multiple
scattering. This talk will review recent work on related inverse
scattering problems for the radiative transport equation and fast image
reconstruction algorithms for large data sets. Numerical simulations and
experimental data from model systems are used to illustrate the results.
