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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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