• Jan. 22, 2016
    Chunyou Sun
    Department of Mathematics, Lanzhou University, China
    Location and Time: Parker Hall 352, 1pm-2pm
    Title: Dynamics for a 2D generalized incompressible Navier-Stokes 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 Navier-Stokes equations.

  • Jan. 29, 2016
    Jeff Borggaard
    Department of Mathematics, Virginia Tech
    Location and Time: Parker Hall 352, 1pm-2pm
    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 steady-state flow, use interpolation-based model reduction on the resulting linear model to generate a low-dimensional model of the input-output system with input-independent error bounds, then use this reduced model to design the feedback control law. Closed-loop simulations of the Navier-Stokes 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, 1pm-2pm
    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, 1pm-2pm
    Title: Global Small solution to the 2D MHD System with a Velocity Damping Term

    Abstract: In this talk, I will show a global well-posedness 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 large-time 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, 1pm-2pm
    Title: Semi-Kolmogorov type of predation models in varying environments

    Abstract: In this talk I will introduce several semi-kolmogorov 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 continuous-time 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, 1pm-2pm
    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 Fokker-Planck 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, 1pm-2pm
    Title: Numerical Solution of Diffraction Problems: A High-Order 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. High-Order 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 high-order accuracy one can achieve with an implementation of this algorithm.

  • March 25, 2016
    Sanjeev Baskiyar and Tin-Yau Tam
    Department of Computer Science and Software Engineering, and Department of Mathematics and Statistics, Auburn University
    Location and Time: Parker Hall 352, 1pm-2pm
    Title: Minimum Energy Consumption for Rate Monotonic Algorithm in a Hard Real-Time Environment

    Abstract: Limited battery power is a typical constraint in stand-alone 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 real-time embedded environment (especially hard real-time), timing constraints are critical. We focus on dynamic energy reduction of tasks scheduled by Rate Monotonic (RM) algorithm in a hard real-time 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 worst-case 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, 1pm-2pm
    Title: Rothe's method for time-dependent 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 time-dependent, 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, 4pm-5pm
    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 functions--which 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 non-linear Partial Differential Equations in complex three dimensional geometries, including general solution of PDEs in the time domain such as the fluid-dynamics and elastic wave equations (where virtual dispersionlessness is demonstrated) and, using integral equation methods and related fast highly-accurate 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, 1pm-2pm
    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.