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Mathematics Department

Applied Math Seminar

Spring 2018

All talks are from 12:00-1:00 p.m. in the Seminar Room CH351, unless otherwise specified.

  • May
    04
  • Engineering in an Imperfect World
    Dylan Poulson
    Washington College

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    Stability theory lies at the heart of engineering. If an engineer wants a system to behave a certain way, stability theory can be used to design the system to tend naturally to the desired behavior. Therefore, stability theory is a standard topic in the engineering curriculum. This beautiful theory relies on an assumption that the timing of the engineering system is uniform in nature. Unfortunately, in many engineering systems, especially those that span large distances or rely on network connectivity, the condition of uniform timing cannot be met without significant monetary costs. The mathematical theory of dynamic equations on time scales can help engineers design reliable systems even in an imperfect world.
  • Apr
    13
  • Andrew Dorsett
    Wolfram Mathematica
    Location: CH 110 (Note the room change)

    View Abstract

    This technical talk will show live calculations in Mathematica 11 and other Wolfram technologies relevant to courses and research. Specific topics include: * Enter calculations in everyday English, or using the flexible Wolfram Language * Visualize data, functions, surfaces, and more in 2D or 3D * Store and share documents locally or in the Wolfram Cloud * Use the Predictive Interface to get suggestions for the next useful calculation or function options * Access trillions of bits of on-demand data * Use semantic import to enrich your data using Wolfram curated data * Easily turn static examples into mouse-driven, dynamic applications * Access 10,000 free course-ready applications * Utilize the Wolfram Language's wide scope of built-in functions, or create your own * Get deep support for specialized areas including machine learning, time series, image processing, parallelization, and control systems, with no add-ons required Current users will benefit from seeing the many improvements and new features of Mathematica 11 (https://www.wolfram.com/mathematica/new-in-11/), but prior knowledge of Mathematica is not required.
  • Apr
    06
  • A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Nonlinear Turbulent Dynamical Systems
    Nan Chen
    New York University

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    A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction. This talk will include three applications of such conditional Gaussian framework. The first part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the second part, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high-dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions. In the last part of this talk, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features.
  • Mar
    30
  • From Medical Diagnostic Instruments to Therapeutic Proteins
    Ryan Evans
    National Institute of Standards and Technology
  • Mar
    23
  • Modeling Sound Scattering from Subsea buried Targets using in-air Laboratory Measurements
    Earl Williams
    Naval Research Laboratory

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    Identification of unexploded ordinance (UXO) buried in the sediment in the littoral waters throughout the world is a problem of great concern. An estimated 200 million pounds of dangerous bombs, missiles, projectiles and other ordnance exists in the world’s waterways. An approach developed at the Naval Research Laboratory aims to help in the identification by capitalizing on acoustic resonances of the UXO target. When illuminated by low-frequency sonar many of these targets exhibit a unique vibration pattern that can be used to identify them. This vibration behavior is embodied and identified by a quantity called the in vacuo structural admittance matrix Ys, a relationship between the sonar-induced forces f and resulting vibration v of its surface, given by the simple linear algebra equation v=Ys f. Nearly impossible to measure in situ, Ys can be measured in air in a simple, acoustically unaltered laboratory space using an array of loudspeakers and the cross-correlations of velocity and pressure measurements made on the target’s surface. When coupled with computed matrices that describe the subsea sediment, one can predict the dominant directions and intensity of the sound scattered off the UXO as a function of frequency (called the acoustic color). This scattered field is picked up by surface ships or unmanned undersea vehicles and complex algorithms are used to identify the UXO from the acoustic color. The objective of this seminar is to demonstrate the range and type of mathematical principles at play, and how they lead to a solution of a naval problem of significant practical importance. The need for a strong and varied mathematical background is crucial to success. Furthermore, a physical experiment is critical and serves as a proof of the approach for mathematicians and acousticians alike. Mathematical theories meet their ultimate test in the cross hairs of experimentation. Work supported by the Office of Naval Research.
  • Mar
    09
  • Stochastic Modeling of Multiscale Biochemical Networks
    Hye Won Kang
    University of Maryland Baltimore County

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    Stochastic effects may play an important role in mathematical modeling of biological and chemical processes in case the copy number of some component involved in the system is small. This talk will present the recent work on stochastic modeling of biochemical networks. First, I will introduce a continuous-time Markov chain model for chemical reaction networks when the systems are well stirred. The relationship between the stochastic and deterministic models will be considered. This model is extended to describe reaction and diffusion in the spatially distributed systems. Next, multiscale algorithms for stochastic simulation of reaction-diffusion processes will be introduced, that couple different modeling schemes for better efficiency of the simulation. The algorithms apply to the systems including the region with a few molecules where a continuous-time Markov chain model is used and the region with a large number of molecules where stochastic partial differential equations (SPDEs) are applied. Short Bio: Hye-Won Kang is an Assistant Professor in the Department of Mathematics and Statistics at the University of Maryland at Baltimore County since 2013. She finished her Ph.D. in Mathematics (Probability) at the University of Wisconsin, Madison under the supervision of Thomas G. Kurtz with the dissertation on "Multiple scaling methods in chemical reaction networks." She was a postdoctoral researcher at the University of Minnesota during 2008-2011 and in the Mathematical Biosciences Institute at the Ohio State University during 2011-2013. Her research interest lies in stochastic modeling, analysis, and simulation of reaction-diffusion systems in biology and chemistry.
  • Mar
    02
  • Flutter: The Waltz of the Wave and Plate Equations
    Justin Webster
    University of Maryland Baltimore County
    Time: 12:00 PM

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    When a thin elastic structure is immersed in a fluid flow, certain conditions may bring about structural excitations. That is, the dynamic loading of the fluid feeds back with the natural oscillatory modes of the structure. In this case we have a bounded-response instability, and the oscillatory behavior may persist until the flow parameters change or energy is adequately dissipated from the structure. This onset of this interactive phenomenon is referred to as flutter. Beyond the obvious applications in aeroscience (projectile paneling and flaps, flags, and airfoils), the flutter phenomenon arises in: (i) the biomedical realm (in treating sleep apnea), and (ii) sustainable energies (in providing a low-cost power generating mechanisms). Modeling, predicting, and controlling flutter (as well as understanding post flutter nonlinear dynamics) has been a foremost problems in engineering for nearly 70 years. In this talk we describe the basics of modeling a flow-structure interaction in the simplest configuration (an aircraft panel) using differential equations and dynamical systems. After discussing the partial differential equation model, we will discuss theorems that can be proved about solutions to these equations using modern analysis (e.g., nonlinear functional analysis, semigroups, monotone operator theory, the theory of global attractors). We will relate these dynamical systems results back to experimental observations in engineering and recent numerical work. We will also describe very recent (and very open) problems in the analysis of "flag-like" configurations, where a portion of the structure is unsupported.
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