DMS Applied and Computational Mathematics Seminar
Mar 17, 2023 02:00 PM
328 Parker Hall
Speaker: Yang Yang, Michigan State University
Title: Acoustic Source and Sound Speed Imaging with Application to Photoacoustic Tomography: A Numerical Study
Abstract: We present numerical algorithms to image passive acoustic sources (resp., sound speed) in the absence of sound speed (resp., source) information. The measurement is the boundary wave field and its spatial derivatives. The algorithms are validated with numerical examples. An application scenario is Photoacoustic Tomography, a multi-wave imaging modality where acoustic sources in unknown biological tissue are to be imaged.
The presentation is based on joint work with G. Huang, J. Qian, S. Qin, R. Wang.
DMS Applied and Computational Math
Feb 24, 2023 02:00 PM
328 Parker Hall
Speaker: Professor Alejandro Aceves, Southern Methodist University
Title: On the Fractional Nonlinear Schrödinger Equation
Abstract: The concept of the fractional Laplacian as it relates to Levi flights in comparison to Brownian motion appears in many applications in physics. In this talk we will present our work as it relates to optical physics, in particular in the nonlinear regime.
DMS Applied and Computational Math Seminar
Jan 13, 2023 02:00 PM
328 Parker Hall
Title: Level-set forced mean curvature flow with the Neumann boundary condition
Abstract: In this talk, we consider a level-set forced mean curvature flow with the homogeneous Neumann boundary condition. The well-posedness and the comparison principle for the flow are well established in the theory of viscosity solutions. Our goal is to go beyond the well-posedness theory and understand the large-time behavior of the solution. We first show that the solution is Lipschitz in time and locally Lipschitz in space. Then, under an additional condition on the forcing term, we prove that the solution is globally Lipschitz. Using this, we obtain the large-time behavior of the solution in this setting. Examples demonstrating the sharpness of the additional condition will be provided.
DMS Applied and Computational Mathematics Seminar
Dec 02, 2022 02:00 PM
328 Parker Hall
Speaker: Dr. Tuoc Phan, University of Tennessee Knoxville
Title: On local interior and boundary estimates for Stokes systems with singular measurable coefficients and applications
Abstract: We study non-stationary Stokes systems with measurable coefficients that are allowed to be singular. Interior estimates in Lebesgue mixed norm spaces are proved under a smallness condition on the mean oscillations of the coefficients. As an application, a new epsilon-regularity criterion for Leray-Hopf weak solutions of Navier-Stokes equations is introduced, which in turn implies some borderline cases of the well-known Serrin's regularity criterion. Some results on local boundary estimates are also presented and the optimality of the smallness condition on the mean oscillations of the coefficients will be discussed. The results in the talk are based on my joint papers with Hongjie Dong (Brown University), Juraj Foldes (University of Virginia), and Doyoon Kim (Korea University).
Faculty host: Selim Sukhtaiev
DMS Applied and Computational Mathematics Seminar
Nov 18, 2022 02:00 PM
328 Parker Hall and ZOOM
Speaker: Tan Bui-Thanh, University of Texas at Austin
Title: Enabling approaches for real-time deployment, calibration, and UQ for digital twins.
Abstract: Digital twins (DTs) are digital replicas of systems and processes. At the core of a DT is a physical/mathematical model which captures the behavior of the real system across temporal and spatial scales. One of the key roles of DTs is enabling “what if” scenario testing of hypothetical simulations to understand the implications at any point throughout the life cycle of the process, to monitor the process, and to calibrate parameters to match the actual process. In this talk we will present two real time approaches: (1) mcTangent (a model-constrained tangent slope learning) approach for learning dynamical systems; and (2) TNet (a model-constrained Tikhonov network) approach for learning inverse solutions. Both theoretical and numerical results for various problems including transport, heat, Burgers and Navier-Stokes equations will be presented.
Faculty hosts: Yanzhao Cao and Phuong Hoang
Short bio: Tan Bui-Thanh is an associate professor, and the endowed William J Murray Jr. Fellow in Engineering No. 4, of the Oden Institute for Computational Engineering & Sciences, and the Department of Aerospace Engineering & Engineering mechanics at the University of Texas at Austin. Bui-Thanh obtained his PhD from the Massachusetts Institute of Technology in 2007, Master of Sciences from the Singapore MIT-Alliance in 2003, and Bachelor of Engineering from the Ho Chi Minh City University of Technology (DHBK) in 2001. He has decades of experience and expertise on multidisciplinary research across the boundaries of different branches of computational science, engineering, and mathematics. Bui-Thanh is currently a Co-director of the Center for Scientific Machine Learning at the Oden Institute. He is a former elected vice president of the SIAM Texas-Louisiana Section, and currently the elected secretary of the SIAM SIAG/CSE. Bui-Thanh was an NSF (OAC/DMS) early CAREER recipient, the Oden Institute distinguished research award, and a two-time winner of the Moncrief Faculty Challenging award.
DMS Applied and Computational Mathematics Seminar
Nov 11, 2022 02:00 PM
328 Parker Hall
Speaker: Susmitha Sadhu, Georgia College & State University
Title: A novel mechanism for detecting early warning signals of dramatic population changes and predicting a regime shift in a predator-prey model.
Abstract: A regime shift refers to a significant change in the behavior of an ecosystem after a long period of apparently stable dynamics. Often an abrupt change in the state of an ecosystem may not be necessarily preceded by a noticeable change in the environment and hence the question of identifying an early warning signal and predicting a regime shift is challenging. In this talk, I will discuss a mechanism for detecting an early signal of a sudden dramatic population change as well as predicting a regime shift in a two-trophic ecosystem consisting of two species of predators competing for their common prey. With proper rescaling, the model can be written as a singularly perturbed system of equations, where the prey evolves on a faster timescale than its predators. In a parameter regime near a
singular Hopf bifurcation, chaotic
mixed-mode oscillations (MMOs), featuring concatenation of small and large-amplitude oscillations, are observed as long transients before the system approaches its asymptotic state and experiences a regime shift. To analyze the dynamical cause that initiates a large amplitude oscillation, the model is reduced to a suitable normal form near the singular-Hopf point. Exploiting the separation of timescales and properties of the solutions of the normal form, the transient dynamics are analyzed. The analysis yields a method for detecting the initiation of a large amplitude oscillation and predicting the onset of a transition to the asymptotic state.
Faculty host: Hans-Werner van Wyk
DMS Applied and Computational Mathematics Seminar
Nov 04, 2022 02:00 PM
ZOOM
Speaker: Rongjie Lai, Rensselaer Polytechnic Institute
Title: Computational Methods for Mean-field Games: From Conventional Numerical Methods to Deep Generative Models
Abstract: Mean field game (MFG) problems study how a large number of similar rational agents make strategic movements to minimize their costs. In this talk, I will discuss our recent work on computational methods for MFGs. I will start from a low-dimensional setting using conventional discretization/optimization methods and discuss some convergence results of the proposed method. Then, I will discuss its extension to computing problems on low-dimensional manifolds. After that, I will extend my discussion to high-dimensional problems by bridging the trajectory representation of MFG with a special type of deep generative model, normalizing flows. This connection does not only help solve high-dimensional MFGs, but also provides a way to improve the robustness of normalizing flows.
Faculty host: Yimin Zhong
DMS Applied and Computational Mathematics Seminar
Oct 28, 2022 02:00 PM
328 Parker Hall
Speaker: Dr. Paul Zhang, Auburn University
Title: Regularity of Hele-Shaw flow with source and drift: Flat free boundaries are Lipschitz
Abstract: The classical Hele-Shaw flow describes the motion of incompressible viscous fluid, which occupies part of the space between two parallel, nearby plates. With source and drift, the equation is used in models of tumor growth where cells evolve with contact inhibition, and congested population dynamics. We consider the flow with Hölder continuous source and Lipschitz continuous drift. We show that if the free boundary of the solution is locally close to a Lipschitz graph, then it is indeed Lipschitz, given that the Lipschitz constant is small. This is joint work with Inwon Kim.
DMS Applied and Computational Mathematics Seminar
Oct 24, 2022 03:00 PM
ZOOM
Speaker: Dr. Christopher Strickland, University of Tennessee
Title: Using mechanistic models to advance theory in opioid use disorder epidemiology
Abstract: Opioid use disorder has been a national health crisis in recent years, with high economic costs and opioid involvement in over 70% of all drug overdose deaths in 2019. Widespread opioid use has its roots in prescription medication – a fact which greatly increases the population’s exposure and mathematically suggests non-contact-based routes of addiction. In this talk, I will describe two recent mathematical models for opioid use disorder and treatment, including dynamics involving heroin and fentanyl in the context of data for the state of Tennessee. I will also show how these models, as well as population models for alcohol use disorder, exhibit fundamentally different dynamics from infectious disease models and therefore require a different approach to analysis. Finally, I will present an agent-based, social-network approach we are working on that complements our population-level modeling and shows promise for teasing out certain micro-level, heterogeneous dynamics related to the social spread of opioid use disorder.
DMS Applied and Computational Mathematics Seminar
Oct 21, 2022 02:00 PM
328 Parker Hall ZOOM
Speaker: Raymond Chu, UCLA
Title: Stiffness Limit of Porous Medium Type Equations
Abstract: The Porous Medium Equation (PME) is a PDE that is used to model biological aggregation, population dynamics, crowd motion, and tumor growth. The PME model represents the tumor as an evolving density function, while some models of tumor growth represent the tumor as an evolving region. By the stiffness limit, we can bridge these two types of models.
In this talk we will discuss the PME and Hele-Shaw flow. Then we introduce our work that generalizes the classical stiffness limit by allowing the limiting density to be bounded above by a spatial and time varying upper bound.
Faculty host: Paul Zhang
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