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Research Seminars: Applied and Computational Mathematics


Past: Applied and Computational Mathematics

Fall 2018

Time & Location: Typically talks will be on Fridays in Gibson Hall 310 at 3:30 PM.
Organizers: Glatt-Holtz, Nathan and Zhao, Kun

September 14

Topic

SpeakerInstitution

Abstract: TBA


September 28

Fluid-structure interactions within marine phenomena

Shilpa KhatriTulane university

Abstract:

To understand the fluid dynamics of marine phenomena fluid-structure interaction problems must be solved. Challenges exist in developing analytical and numerical techniques to solve these complex flow problems with boundary conditions at fluid-structure interfaces. I will present details of two different problems where these challenges are handled: (1) modeling of marine aggregates settling in density stratified fluids and (2) accurate evaluation of layer potentials near boundaries and interfaces. The first problem of modeling marine aggregates will be motivated by field and experimental work. I will discuss the related data and provide comparisons with the modeling. For the second problem of accurate evaluation of layer potentials, I will show how classical numerical methods are problematic for evaluations close to boundaries and how newly developed asymptotic methods can be used to remove the error. To demonstrate this method, I will consider the interior Laplace problem.


October 5

How to deduce a physical dynamical model from expectation values

Denys BondarTulane University

Abstract:

In this talk, we will provide an answer to the question: "What kind of observations (i.e., expectation values) and assumptions are minimally needed to formulate a physical model?" Our answer to this question leads to the new systematic approach of Operational Dynamical Modeling (ODM), which allows deducing equations of motions from time evolution of observables. Using ODM, we are not only able to re-derive well-known physical theories, but also solve open problems in quantum non-equilibrium statistical dynamics. Furthermore, ODM has revealed unexplored flexibility of nonlinear optics: A shaped laser pulse can drive a quantum system to emit light as if it were a different system (e.g., making lead look like gold).

Time 4:10


October 12

Fall Break



October 19

Topic

SpeakerInstitution

Abstract: TBA


October 26

A bundled approach for high-dimensional informatics problems

Reginald McGeeCollege of the Holy Cross

Abstract:


As biotechnologies for data collection become more efficient and mathematical modeling becomes more ubiquitous in the life sciences, analyzing both high-dimensional experimental measurements and high-dimensional spaces for model parameters is of the utmost importance. We present a perspective inspired by differential geometry that allows for the exploration of complex datasets such as these. In the case of single-cell leukemia data we present a novel statistic for testing differential biomarker correlations across patients and within specific cell phenotypes. A key innovation here is that the statistic is agnostic to the clustering of single cells and can be used in a wide variety of situations. Finally, we consider a case in which the data of interest are parameter sets for a nonlinear model of signal transduction and present an approach for clustering the model dynamics. We motivate how the aforementioned perspective can be used to avoid global bifurcation analysis and consider how parameter sets with distinct dynamic clusters contrast.

 


November 2

An Overview of Model Reduction

Christopher BeattieVirginia Polytechnic Institute and State University

Abstract: Dynamical systems form the basic modeling framework for a large variety of complex systems.  Direct numerical simulation of these dynamical systems is one of few means available for accurate prediction of the associated physical phenomena.  However, ever increasing needs for improved accuracy require the inclusion of ever more detail in the modeling stage, leading inevitably to ever larger-scale, ever more complex dynamical systems that must be simulated.   Simulations in such large-scale settings can be overwhelming and may create unmanageably large demands on computational resources; this is the main motivation for model reduction, which has as its goal the extraction simpler dynamical systems that retain essential features of the original systems, especially high fidelity emulation of input/output response and conserved quantities.   I will give a brief overview of the objectives and methodology of system theoretic approaches to model reduction, focussing eventually on projection methods that are both simple and capable of providing nearly optimal reduced models in some circumstances.  These methods provide a framework for model reduction that allows retention of special model structure such as parametric dependence, passivity/dissipativity, and port-Hamiltonian structure.


November 9

A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Nonlinear Turbulent Dynamical Systems

Nan ChenUniversity of Wisconsin, Madison

Abstract:

A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of complex 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. The other related topics such as parameter estimation and causality analysis will also be briefly discussed.

November 16

Taming turbulence via nudging

Patricio ClarkUniveristy of Rome

Abstract:

 

The technique of nudging is commonly used to incorporate empirical data into a simulation in order to control its chaotic evolution and reproduce a given dynamical benchmark. We show how to do this in fully developed three dimensional turbulence using data both in configuration and Fourier space. Our results show that given enough data, nudging is successful in reconstructing the whole turbulent field. We give physical arguments for the choice of optimal parameters and the amount and quality of data needed to do this. Nudging thus serves as a way to probe for key degrees of freedom in a flow. We also turn the algorithm on its head and show how it can be used to infer the values of parameters and the presence of unknown physical mechanisms in the data.


November 23

Thanksgiving 


November 29

Special Day and Time

Asymptotic approximations of near fields in scattering problems

Camille CarvalhoUC-Merced

Abstract:

Accurate evaluations of near fields can is crucial in a wide range of applications, like for the modeling of micro-organisms swimming in Stokes flow, or for the light enhancement in plasmonic structures. Plasmonic structures are in particular made of dielectrics, and metals (or metamaterials) for which the electromagnetic properties enable the propgation of highly-oscillating (sub-wavelength) surface waves at the interface of the two materials. Boundary integral equation methods can approximate the solution of such problems with high-accuarcy using Nystöm methods, however this accuracy is lost for evaluation points close (but not on) the boundary. In this presentation we present some technique based on asymptotic approximations to address the close evaluation problem for acoustic scattering (Helmholtz), and we will discuss the case of scattering in plasmonic structures at the end.

Location: Stanley Thomas 316


Time:
11:00

 


November 29

Special Day

Cell migration from birth to death: Modeling and analyzing the motion of cells in tissues and tumors

Tracy StepienUniversity of Arizona

Abstract:

 

Beginning momentarily after we are conceived through to our final days, cells migrate within our bodies. From embryonic development to the progression of many diseases including cancer, cell migration plays an essential role in maintaining our health. To understand the mechanisms and forces involved in migration related to early embryonic development, eye and retina development, wound healing, and cancer growth, I have developed continuum mechanical models with free boundaries and reaction-diffusion equation models of the spread of tissues and tumors.  Mathematical analysis and numerical simulations of the models indicate conditions for traveling wave and similarity under scaling solutions, and data and image analysis of experimental data has facilitated the estimation of model parameter values that are physically relevant.  In this talk, I will give examples of biological cell migration problems that I work on as well as an in-depth look at some of the mathematical analysis that has arisen from the model equations.

Location: Gibson Hall 325

Time: 2:30


November 30

Special Colloquium



December 7

Improving Model Selection Using Geometric Data Characterization

Brandilyn StiglerSouthern Methodist University

Abstract: Inferring models from experimental data is an important problem in systems biology.  While there are many classes of functions that can fit data from an underlying network, under certain conditions all functions fitting discretized data are polynomials.  A useful consequence is that polynomial models of discretized data can be written in terms of a monomial basis, where each choice of basis provides a different prediction regarding network structure.</p>                          <p>In this work, we use affine transformations to partition data sets into equivalences classes with the same sets of monomial bases.  This partition reveals a geometric property of data sets that have unique models associated with them.  Implications of this work are guidelines for designing experiments which maximize information content and for determining data sets which yield unambiguous predictions.

 






Spring 2019

January 25

Clifford


February 1

Topic

Andrei TarfuleaUniversity of Chicago

Abstract: TBA


February 8

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Zach BradshawTulane University

Abstract: TBA


February 15

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February 15

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February 22

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Zhuolin QuTulane University

Abstract: TBA


March 1

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March 8

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March 15

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March 22

Topic

Nicole BeisiegelUniversity College Dublin

Abstract: TBA


March 29

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April 5

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April 12

Topic

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April 19

Good Friday


April 26

Jazz Fest

Friday, April 26 - May 5


Mathematics Department, 424 Gibson Hall, New Orleans, LA 70118 504-865-5727 math@math.tulane.edu