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Mathematics Department

Applied Math Seminar

Spring 2019

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

  • May
    06
  • Enabling Storm Surge Prediction for High-Resolution Forecasts and Climate Scenarios
    Kyle Mandli
    Columbia University

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    Coastal hazards related to strong storms are one of the most frequently recurring and wide spread hazards to coastal communities today. In particular storm surge, the rise of the sea surface in response to wind and pressure forcing from these storms, can have a devastating effect on the coastline. Furthermore, with the addition of climate change related effects, the ability to predict these events quickly and accurately is critical to the protection and sustainability of these coastal areas. Computational approaches to this problem must be able to handle its multi-scale nature while remaining computationally tractable and physically relevant. This has commonly been accomplished by solving a depth-averaged set of fluid equations and by employing non-uniform and unstructured grids. These approaches, however, have often had shortcomings due to computational expense, the need for involved model tuning, and missing physics. In this talk, I will outline some of the approaches we have developed to address several of these shortcomings through the use of advanced computational techniques. These include adaptive mesh refinement, higher levels of parallelism including many-core technologies, and more accurate model equations such as the two-layer shallow water equations. Combining these new approaches promises to address some of the problems in current state-of-the-art models while continuing to decrease the computational overhead needed to calculate a forecast or climate scenario.
  • Apr
    26
  • The Nonlinear Dynamics of Phyllotaxis
    Matt Pennybacker
    National Aeronautics and Space Administration (NASA)

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    Phyllotaxis, the arrangement of organs (e.g. leaves, bracts, petals, seeds) on the surface of a plant, has long been a target of scientific and mathematical inquiry. Perhaps the best example of this phenomenon is found among the seeds on the head of a sunflower. Counting the number of spirals in the clockwise and anti-clockwise directions at the outer edge of the head often yields two consecutive members of the Fibonacci sequence, and moving inward, a transition to smaller Fibonacci numbers. Starting with a model for the biochemical and mechanical processes of plant growth, I will demonstrate how plant patterns may be realized as a family of nonlinear front solutions to the governing equations near the onset of a pattern-forming instability. This will include analytical and numerical verification of the transition rule that gives Fibonacci and Fibonacci-like progressions. I will also compare these results to those of classical models of phyllotaxis, which explain the observed patterns as the optimization of some quantity (e.g. packing efficiency, contact pressure, entropy) by the plant in order to be best suited for survival. Finally, I will discuss a few open questions, including the circumstances under which plant patterns may be considered universal.
  • Apr
    19
  • From Numerical Analysis to the Analysis of the Numerics
    Sonia Garcia
    United States Naval Academy

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    This is a presentation of my work over the years, between "pure" numerical analysis and all the contrasts that were unveiled over the years with necessary changes of vision of what my research could produce.
  • Apr
    16
  • Geospatial machine learning in the geosciences
    Warren T. Wood
    U.S. Naval Research Laboratory
    Location: [Note the Room: CH110]

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    Within the earth sciences community there is a need to evolve from a paradigm of stand-alone field and modeling efforts, to one of a more unified, multi-scale, consistent regional/global analyses, leading eventually to forecasts supported by consistent measurement and modeling - analogous to that performed in the meteorological and oceanographic communities. Such a paradigm shift does not necessarily impact the number or type of field and/or modeling efforts, but rather puts them in a unifying context. To meet this need, NRL has developed a Global Predictive Seafloor Model (GPSM), which relies heavily on a type of artificial intelligence known as machine learning (ML). Specifically, we show here how ML can find correlations in large, extensive, data sets, (e.g. seafloor porosity, heat flux, and total organic carbon) and use those correlations to predict, with uncertainty, values at geospatial locations where no direct measurements have been made. This is particularly useful when making estimation in difficult-to-access areas such as the Arctic, and/or when global estimates of the land surface or seafloor are desired. Further, a byproduct of the ML analysis is a quantitative measure of what are the important predictors, and where sampling them would be most advantageous for the overall prediction, i.e. a map of where best to sample next.
  • Mar
    29
  • Data-informed stochastic model reduction for complex dynamics
    Fei Lu
    Johns Hopkins University

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    The need to develop reduced nonlinear statistical-dynamical models for complex dynamical systems arises in many applications such as geophysics, biology and engineering. The challenges come from memory effects due to the nonlinear interactions between resolved and unresolved scales, and from the difficulty in inference from discrete partial data. We address these challenges by learning stochastic reduced models, in forms of nonlinear time series, that can account for the memory effects due to truncation/coarse-graining and the numerical errors due to large time-stepping. We show by examples that the stochastic reduced models can capture the key statistical and dynamical properties and can improve the performance of ensemble prediction in data assimilation. The examples include dissipative chaotic/stochastic ODEs and PDEs. We will discuss related open questions in inference and in theoretical understanding of the model reduction.
  • Mar
    22
  • A Crash Course in Basic Single-Scan Target Tracking
    David F. Crouse
    U.S. Naval Research Laboratory

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    This talk goes through the components in generic single-scan target tracking algorithms from filtering to data association, track initiation, and termination. In many areas, reference is made to functions in the open-source copyleft-free Tracker Component Library (available online) so that attendees can rapidly apply the algorithms that are discussed. An extended version of the presentation slides containing additional derivations will be made available.
  • Jan
    23
  • On the existence and uniqueness of the 3D compressible primitive equations of atmospheric dynamics
    Leon Li
    Texas A&M University
    Time: 12:00 PM

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    The vertical scale in the atmosphere is relatively much smaller than the relevant horizontal scales. Capitalizing on this small aspect ratio, formal asymptotic analysis yields the compressible primitive equations for the atmospheric dynamics, which are obtained by replacing the vertical momentum equation in the compressible Navier-Stokes equations by the hydrostatic balance equation. In this talk, we report about recent advances concerning the well-posedness of the 3D compressible primitive equations, in particular, of how to overcome the difficulty caused by the absence of an evolutionary equation for the vertical momentum. This is joint work with Edriss S. Titi, Texas A&M.
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