• February 6, 2015
    Wenxian Shen
    Department of Mathematics and Statistics, Auburn University
    Location and Time: Parker 328, 2pm-3pm
    Title: On Nonlocal Dispersal Evolution Equations
    Abstract: The current talk is concerned with some dynamical issues in nonlocal dispersal evolution equations. First, I will present some spectral theory for nonlocal dispersal operators with time periodic dependence. I will then consider the asymptotic dynamics of nonlocal dispersal evolution equations/systems in bounded media. Finally, I will give some discussion on the front propagation dynamics of nonlocal dispersal evolution equations in unbounded media.

  • February 20, 2015
    Dawit Denu
    Department of Mathematics and Statistics, Auburn University
    Location and Time: Parker 328, 2pm-3pm
    Title: Analysis of Vector-host epidemic model
    Abstract: Vector-borne diseases, among all infectious diseases of humans have constituted a major cause of human mortality. Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic. In this talk, we shall discuss the dynamics of a vector-host SIS epidemic model and the associated nonlinear system of differential equation. In addition, we will show that the global and local dynamics is completely determined by the basic reproduction number R0.

  • February 27, 2014 (special applied math seminar)
    Shari Moskow
    Department of Mathematics, Drexel University
    Location and Time: Parker Hall 250, 2:30pm-3:30pm
    Title: Inverse Born series for the Calderon problem and related inverse problems
    Abstract: We propose a direct reconstruction method for the Calderon problem and other related inverse problems based on inversion of the Born series. We characterize the convergence, stability and approximation error of the method and illustrate its use in numerical reconstructions.

  • March 6, 2015
    Yanzhao Cao
    Department of Mathematics and Statistics, Auburn University
    Location and Time: Parker 328, 2pm-3pm
    Title: PDF method for nonlinear filtering problem: from Fokker Planck equation to Zakai equation and backward SDES
    Abstract: In the talk, I will use the Fokker Planck equation, whose solution is the PDF of a stochastic differential equation, as a motivation to derive the stochastic partial differential equations and backward stochastic differential equations related to nonlinear filtering problems. Numerical methods of solving these equations will be discussed.

  • March 13, 2015
    Kbenesh W. Blayneh
    Department of Mathematics, Florida A &M University
    Location and Time: Parker 328, 2pm-3pm
    Title: Vertically transmitted vector-borne diseases and the effects of climate conditions on disease dynamic
    Abstract: The transmission dynamics of vector-borne diseases which are vertically transmitted in the vector as well as in the host population is analyzed using a system of nonlinear differential equations. It is assumed that some proportions of immigrants are already exposed to the disease. Results show the impacts of vertical transmission, extrinsic incubation period and the disease-induced death rates of hosts on the epidemic level and persistence of vector-borne diseases. Further, the assessment of these and the effectiveness of interventions are carried out using analytical and numerical techniques. Related results on vector-borne diseases where vertical transmissions are not included will also be presented.

  • April 3, 2015
    Dmitry Glotov
    Department of Mathematics and Statistics, Auburn University
    Location and Time: Parker 328, 2pm-3pm
    Title: On an inverse coefficient problem with application in geology
    Abstract: The distribution of radiogenic $^{40}$Ar formed from decay of $^{40}$K provides a record of the temperature and duration of geologic processes. We present results of numerical (forward) modeling of accumulation and diffusion of argon in micas. The inverse problem of determining the temperature as a function of time is not uniquely solvable. Motivated by data available in geology literature, we introduce an additional integral constraint, incorporate it in a numerical scheme, and address well-posedness of the problem with additional data.

  • April 10, 2015
    Xiaoying Han
    Department of Mathematics and Statistics, Auburn University
    Location and Time: Parker 328, 2pm-3pm
    Title: Asymptotic Dynamics of chemostat in temporally varying environments
    Abstract: Chemostat models have a long history in the biological sciences as well as in biomathematics. Hitherto most investigations have focused on autonomous systems, that is, with constant parameters, inputs and outputs. In many realistic situations these quantities can vary in time, either deterministically (e.g., periodically) or randomly. They are then non-autonomous dynamical systems for which the usual concepts of autonomous systems do not apply or are too restrictive. The newly developing theory of non-autonomous dynamical systems provides the necessary concepts, in particular that of a non-autonomous pullback attractor. These will be used here to analyze the dynamical behavior of non-autonomous chemostat models with or without wall growth, time dependent delays, variable inputs and outputs. The possibility of over-yielding in non-autonomous chemostats will also be discussed.

  • April 17, 2015
    Zhu Wang
    Department of Mathematics, University of South Carolina
    Location and Time: Parker 328, 2pm-3pm
    Title: Reduced-Order Modeling of Complex Fluid Flows
    Abstract: In many scientific and engineering applications of complex fluid flows such as the flow control and optimization problem, computational efficiency is of paramount importance. Thus, model reduction techniques are frequently used. To achieve a balance between the low computational cost required by a reduced-order model and the complexity of the target turbulent flows, appropriate closure modeling strategies need to be employed. In this talk, we present reduced-order modeling strategies synthesizing ideas originating from proper orthogonal decomposition and large eddy simulation, and design efficient algorithms for the new reduced-order models.