Applied Mathematics and Computation Seminar 2008-2009

Organizers: Malgorzata Peszynska, Ralph E. Showalter

The AMC seminar is devoted to general topics in applied mathematics and computation. Each year, we select a focus theme, with the proportion of general to specific topics about 1-1. We welcome speakers and audience of faculty, researchers, and graduate students from mathematics, geosciences, computer science, engineering, atmospheric sciences, and all other disciplines.

This year's focused theme is on modeling, analysis, and simulation of nonlinear coupled phenomena of physical, chemical and bio-chemical transformations including solid-liquid-gas phase transitions and reaction-diffusion equations at the many relevant scales.

Attendees are encouraged to join the mailing lists: student mailing list and faculty mailing list.

Graduate students can sign up for credit as MTH 607, Spring CRN 54474.

Schedule 2004-2005
Schedule 2005-2006
Schedule 2006-2007
Schedule 2007-2008
Current schedule

Schedule Fall 2008:

  • Oct 3, 2008 ( Applied Mathematics and Computation Seminar) Ralph E. Showalter, The Stefan Problem

    We consider a model of heat diffusion in the situation where there is a phase change arising from the freezing or thawing of the medium at a fixed temperature. After describing the phase relation between energy and temperature, we formulate the Stefan free-boundary problem which describes heat conduction subject to such constitutive assumptions on the phase relation between energy and temperature. The well-posedness as an evolution equation is briefly discussed.

  • Oct 6, 2008 (Applied Mathematics and Computation Seminar) Clint Dawson and Marco Iglesias, The University of Texas at Austin, (Note unusual day and location) An Iterative Representer Based Scheme for Parameter Estimation

    The representer method was originally proposed for data assimilation in oceanography.  The method solves the Euler-Lagrange equations arising from minimizing the data misfit subject to model constraints, by reducing the problem to the computation of "representer" functions and an expansion of the solution in terms of a forward model solution and the representers.  For linear problems, the method is exact.  For nonlinear problems such as those arising in parameter estimation, we propose an iterative representer based scheme, whereby the representer method is applied to the Euler-Lagrange equations arising from the minimization of the data misfit subject to the constraints imposed by the first order conditions applied to the nonlinear model.  We also describe the combination of the representer method for determining geologically consistent representations of the unknown permeability, described using a Karhunen-Loeve expansion.  Theoretical results for single phase flow problems will be described and numerical results for single and two phase flow will be given.

  • Oct 10, 2008 (Applied Mathematics and Computation Seminar) Vrushali Bokil, Size and Class-Age Structured Shrimp Biomass and Viral Infection Models for Production of Biological Countermeasures

    We consider a novel approach for developing a stable operational platform for the rapid production of large quantities of therapeutic and preventive countermeasures. This approach involves recruiting the biochemical machinery in shrimp for the production of a vaccine or antibody by infection, using the Taura Syndrome Virus (TSV) carrying a passenger gene for the desired countermeasure. We develop a hybrid model of the shrimp biomass/countermeasure production system, which has two components: biomass production and production of countermeasure (antibody/vaccine). Shrimp have size-dependent characteristics and responses to the external environment. We consider a model based on the classic McKendrick-von-Foerster/Sinko-Streifer size-structured population equations with mass (size) as the structure variable. Moreover, experimental results suggest that the mortality rate in acutely infected shrimp as well as the residency times in the latent phase depend on the length of time that individual shrimp remain acute or latent, respectively. We record the variable residency times in the different stages by introducing a new variable, the class-age of an individual, which in a given stage represents the length of time that the individual spends in that stage. Combining size and class-age we make a first attempt at a size and class-age structured mathematical model to study the progression of TSV infection in shrimp.

  • Oct 17, 2008 (Applied Mathematics and Computation Seminar) No seminar today

  • Oct 24, 2008 (Applied Mathematics and Computation Seminar) Lew Semprini, , School of Chemical, Biological and Environmental Engineering, Laboratory and Modeling Studies of the Anaerobic Transformation of Chlorinated Ethenes as Groundwater Contaminants

    The remediation of subsurface contamination with chlorinated ethenes, such as perchloroethene (PCE) and trichloroethene (TCE), using biological processes is currently being applied in practice. Anaerobic processes are increasingly being used because microbes can grow on the chlorinated ethenes as electron acceptors, where highly chlorinated ethenes, such as PCE and TCE, are successively dechlorinated to dichloroethene (DCE), vinyl chloride (VC), and ethene (ETH) as a non-toxic end product. Engineered remediation usually involves the addition of a substrate (like lactate), that can serve as an electron donor, or that ferment to hydrogen (H2) the ultimate electron donor required for the last steps in the transformation pathway. Development of models that can simulate these complex processed are needed to help design efficient remediation systems.
    Laboratory and modeling studies have been conducted with microbial cultures that have been isolated from sites contaminated with TCE and PCE. One culture, which we kinetically characterized in great detail, was isolated from the Evanite site in Corvallis. Kinetic characterization involved the determination of Monod parameters including the maximum utilization rates (kmax) and half-substrate coefficients (Ks) values for each step of the transformation process. Models were also developed for substrate inhibition with more highly chlorinated ethenes inhibiting the transformation of less chlorinated ethenes. Model simulations require the solution of a series of non-linear differential equations for substrate utilization and microbial growth. Simulations performed with independently derived kinetic parameters provided good matches to the results laboratory batch tests with unlimited electron donor availability.
    Model development is currently being extended for conditions that include substrate fermentation and the competition for the H2 produced between the dehalogenating populations and other populations including homoacetogens and methanogens. The model formulation requires the inclusion of thermodynamic equations (free energy) along with the kinetic equations. The system of equations is being solved using COMSOL®. Kinetic studies are being conducted in chemostat reactors where quasi-steady-state conditions are developed and then perturbed. The responses observed in the chemostats are being simulated with a consistent set of kinetic and thermodynamic parameters. The eventual goal of this work is to incorporate the system of equations into a flow and transport model to simulate the results of porous media columns studies that are being performed.

  • Oct 31, 2008 (Applied Mathematics and Computation Seminar) John W. Lee, Solving Boundary Value Problems by Shooting and Continuation

    An overview of the method, including what it is, will be given for BVPs of the form y’’=f(x,y,y’) plus Dirichlet, Sturm-Liouville, Neumann, or Periodic boundary conditions. The goal will be to justify the shooting procedure theoretically (it must work in principle) and to illustrate how it works in practice (numerical results) under assumptions that include interesting physical cases and where the hypotheses that guarantee unique solvability of the BVPs also guarantee that shooting will work. We will do this in the context of BVPs of Bernstein type. Such problems arise, for example, in the calculus of variations and in steady-state heat conduction in a rod. (If the abstract makes general sense to you the talk should be easy to follow.)

  • Nov 7, 2008 (Applied Mathematics and Computation Seminar) Anne Trehu, OSU College of Oceanic and Atmospheric Sciences, Gas Hydrates in Nature

    Most of the talk will be a description of where and why gas hydrates are present in nature, based on recent remote sensing and direct sampling results. The talk will end with a discussion of some possible opportunities for modeling.

  • Nov 14, 2008 (Applied Mathematics and Computation Seminar) Anne Nolin, OSU Geosciences, Modeling Present-day and Future Snowpack in a Pacific Northwest Watershed

    The snowmelt-dominated Cascade Mountains provide critical water supply for agriculture, ecosystems, and municipalities. The McKenzie River basin, located in the Central Western Cascades of Oregon, exhibits characteristics typical of many river systems in the western United States. In this watershed farmers, fish, hydropower, and municipal users compete for a limited supply ? especially in summer when in-stream flows reach a minimum. Future climate projections anticipate warmer but wetter winters and longer, drier summers but watershed-scale impacts of these regional projections are not well understood. While snowpack has been measured at the local scale for decades, accurate basin-wide measurements of snowpack do not exist. Recent studies address the effects of climate on the hydrology of the upper reaches of the basin but do not incorporate a basin-wide prediction of snowpack, particularly transient snow at mid-elevations. This presentation will cover a physically based and spatially distributed approach to modeling snow water equivalent at a basin scale. In addition, I will present preliminary results from a binary regression tree approach used to identify the physiographic variables that govern the spatial variability of snow water equivalent in the McKenzie River basin.

  • Nov 21, 2008 (Applied Mathematics and Computation Seminar) Malgorzata Peszynska, Modeling liquid-gas phase transitions in an implicit black-oil model

    We consider an isothermal model of flow of hydrocarbons and water in subsurface known as black-oil model. The model accounts for three phases and three components. Due to pressure changes, the gas phase may appear or disappear. Various primary unknowns are considered, and the qualitative and quantitative consequences of a choice of primary unknowns are discussed. In particular, a total compressibility is defined and a local nonlinear problem is studied. We discuss conditions on the data which guarantee a degenerate parabolic/elliptic behavior of the pressure equation as well as unique solvability of the local problem. Numerical results will illustrate the talk.

  • Dec 5, 2008 (Applied Mathematics and Computation Seminar) Yue Zhang, Michelin Research and Development Company, Challenges in Simulating Tire Fabrication Process

    Modeling and simulation of the tire fabrication process is essential to reducing manufacturing defects. In this talk, we present some challenges in applying viscoelastic material models and setting up the finite element numerical framework.  We will also discuss a few examples of fabrication defects and how the corresponding simulation results led to long term solutions. 

Schedule Winter 2009:

  • Jan 9, 2009 (Applied Mathematics and Computation Seminar) Ralph E. Showalter, The Super-Stefan Problem

    The classical Stefan free-boundary problem describes the conduction of heat through a medium in which a phase change occurs at a prescribed temperature. Here is considered the more general case in which the freezing temperature lies strictly below the melting temperature, so the entropy is given by a hysteresis functional which permits super-cooling or super-heating of the medium. The model is developed and formulated as an evolution system in $L^1$, and well-posedness results are described.

  • Jan 16, 2009 (Applied Mathematics and Computation Seminar) Robert Guza, Scripps, UCSD, "please attend Edwards's Lecture: Observations of Southern California Waves and Wave-Driven Processes"

  • Jan 23, 2009 (Applied Mathematics and Computation Seminar) Dacian Daescu, Portland State University, Sensitivity analysis and observation impact estimation in variational data assimilation

    The equations of the forecast sensitivity to observations and to the background estimate in a four dimensional variational data assimilation system (4DVAR DAS) are derived from the first order optimality condition in unconstrained optimization. Estimation of the impact of uncertainties in the specification of the error statistics is considered by evaluating the sensitivity to the observation and background error variances.
    A continuation approach is introduced to analyze and develop adjoint-based methods for observation impact estimation in variational data assimilation. High-order accurate measures consistent to nonlinear 3DVAR/4DVAR analysis schemes are derived and issues related to the practical implementation are discussed. The potential use of the observed-minus-analysis increments to observation impact estimation is further investigated. Results are presented with the NASA/GMAO GEOS-5 DAS and idealized 4DVAR experiments with a shallow-water model.

  • Jan 30, 2009 (Applied Mathematics and Computation Seminar) Ralph E. Showalter, Flow with dynamic capillary pressure over multiple scales

    Recent models of partially saturated flow through porous media include dynamic effects in the capillary pressure curves. These lead to partial differential equations of pseudo-parabolic type with multiple nonlinearity and degeneracy. We describe properties and numerical computation of solutions of appropriate initial-boundary-value problems and the upscaling from various types of heterogeneous media. This is joint work with Malgo Peszynska and Son-Young Yi.

  • Feb 6, 2009 (Applied Mathematics and Computation Seminar) John Selker, OSU Biological & Ecological Engineering, Trying to be a thousand times smarter with large scale simulations: local mesh methods of sub-grid scale parameter estimation.

    A conversation outside the box - How can we simulate The world; Kansas; a corn field; and the soil profile? Getting feedback from people who know on use of nested grid computations for global sub-gridscale parameterization. This will be a conversation rather than a seminar, seeking some new ideas that could crack open new ways to approach simulation of turbulent fields. The leader knows virtually nothing about the subject, but will bring some people who do (from oceanography).

  • Feb 13, 2009 (Applied Mathematics and Computation Seminar) Ronald B. Guenther, The Integral Equations for the Time Dependent Fluid Equations of Stokes and Oseen

    I will outline the potential theoretic approach to solving the boundary value problems for the linearized fluid flow equations. The approach is based on the fundamental solution for these systems and involves deriving integral equations for the solution. The numerical implementation of these methods are now known as boundary integral element methods. I will begin by outlining the general approcah for the simple cases of boundary value problems for the Laplace equation and then the heat equation and then showing how these methods are used in the case of solving fluid mechanical problems.

  • Feb 20, 2009 (Applied Mathematics and Computation Seminar) Carrie Manore, Competition and Disease Dynamics in Multi-Species Interactions

    It has been shown that disease can modulate competition between multiple host species and can be a major factor in invasion by exotic species. We model and analyze the dynamics of multi-host communities using coupled systems of ordinary differential equations to understand how the forces of inter-specific infection and competition between multiple species infected by a single pathogen combine to allow invasion by exotic species. Specifically, we propose and analyze a model with Lotka-Volterra competition and Susceptible-Infected disease dynamics using both numerical and analytical methods. We analyze the case of full competition, which affects birth rates of species, combined with disease between species using both mass action and frequency incidence disease transmission. For the case of two species we analyze the disease free equilibrium for stability and for the case of disease transmission via frequency incidence we consider the stability of the endemic coexistence equilibrium. We also extend some threshold values to the case of multiple species.

  • Feb 27, 2009 (Applied Mathematics and Computation Seminar) Sourabh Apte, Department of Mechanical Engineering, A Hybrid Lagrangian-Eulerian Method (hLE) for Interface Tracking Without Connectivity

    A hybrid Lagrangian-Eulerian (hLE) scheme, combining a particle-based, mesh-free tech- nique with a finite-volume flow solver, is developed for direct simulations of two-phase flows. The approach uses marker points around the interface and advects the signed distance to the interface in a Lagrangian frame. The kernel–based derivative calculations typical of particle methods are used to extract the interface normal and curvature from unordered marker points. This approach allows computation of topological changes in the interface and merges the naturally adaptive nature of particle-based schemes, for efficient represen- tation of the interface between two fluids, with the relative flexibility offered by grid-based solvers for complex flows. The fluid flow equations are solved on a background, fixed mesh using a co-located grid finite volume solver together with balanced force algorithm (Francois et al. JCP, 2006) for surface tension force. The numerical scheme is first validated for stan- dard test cases: (i) parasitic currents in a stationary spherical drop, (ii) capillary waves on droplet surface, and (iii) gravity waves to show good accuracy. Extension of the approach to three-dimensions is conceptually straight forward, however, poses challenges for parallel implementation. A domain-decomposition based on balancing the number of grid points per processor gives rise to load–imbalance due to uneven distribution of the marker points. A dual–constraint partitioning balancing the marker points and the grid control volumes is being investigated.

  • Mar 6, 2009 (Applied Mathematics and Computation Seminar) Viviane Klein, Robust a-posteriori estimators for diffusion-reaction systems

    In this talk we explore robustness of a-posteriori estimators for finite-element solutions of elliptic boundary value problems with respect to coefficients of the problem. First we present an overview of estimators for a scalar reaction-diffusion equation and discuss robustness of a particular class of estimators for a singularly perturbed reaction-diffusion problem developed by R.Verfuerth. Next we give an introduction to modeling physical problems in which reaction-diffusion problems arise and in particular we explain principles of modeling chemically reacting systems using differential equations. These applications motivate our study of a coupled system of reaction-diffusion equations which can be cast in a general abstract form of a system coupled by a monotone operator. Last we propose an a-posteriori estimator of residual type for the steady-state version of the system. The talk will be illustrated by numerical results.

  • Mar 13, 2009 (Applied Mathematics and Computation Seminar) Malgorzata Peszynska, Modeling, analysis, and simulation of adsorption and adsorption hysteresis

    We start with a surprise absorption experiment.
    Then we introduce basic models of transport with adsorption on porous surfaces and review the properties of scalar conservation laws which arise as mathematical models. For some adsorption isotherms called favorable the profiles of concentrations exhibit shocks, while for unfavorable isotherms the profiles are rarefaction waves. Correspondingly, we discuss weak solutions in L_1 and challenges to numerical approximation.
    Next we discuss hysteresis in adsorption which can be modeled using a coupled differential inclusion; we discuss some prior and some current work joint with R. Showalter. The talk will be illustrated with numerical simulations for non-hysteretic case and for a regularized model of hysteresis.

Schedule Spring 2009:

  • Apr 3, 2009 (Applied Mathematics and Computation Seminar) Eugene Zhang, OSU Electrical Engineering and Computer Science, Discrete Morse Decompositions of Vector Fields

    Existing topology-based vector field analysis techniques rely on the ability to extract the individual trajectories such as fixed points, periodic orbits and separatrices which are sensitive to noise and errors introduced by simulation and interpolation. This can make such vector field analysis unsuitable for rigorous interpretations. We advocate the use of Morse decompositions, which are robust with respect to perturbations, to encode the topological structures of a vector field in the form of a directed graph, called a Morse connection graph (MCG).
    While an MCG exists for every vector field, it need not be unique. Previous techniques for computing MCG's, while fast, are overly conservative and usually result in MCG's that are too coarse to be useful for the applications. To address this issue, we present a new technique for performing Morse decomposition based on the concept of tau-maps, which typically provides finer MCG's than existing techniques. Furthermore, the choice of tau provides a natural tradeoff between the fineness of the MCG's and the computational costs.
    We provide efficient implementations of Morse decomposition based on tau-maps, which include the use of forward and backward mapping techniques and an adaptive approach in constructing better approximations of the images of the triangles in the meshes used for simulation. Furthermore, we propose the use of spatial tau-maps in addition to the original temporal tau-maps. These techniques provide additional tradeoffs between the quality of the MCG's and the speed of computation. We demonstrate the utility of our technique with various examples in the plane and on surfaces including engine simulation datasets.

  • Apr 10, 2009 (Applied Mathematics and Computation Seminar) Fernando Morales, The Narrow Fracture Approximation by Channeled Flow

    We describe the exchange of fluid between a porous medium saturated with a viscous fluid coupled to the Stokes flow in a thin adjacent open channel. The asymptotic analysis of this system faces two big difficulties: the difference of scales at which Stokes and Darcy's law are valid and the mixed formulation of the system. This gives rise to two intermediate problems comparing Darcy's flow in both regions; with high permeability in the thin one. The first problem will be formulated in the standard minimization form and the second problem will follow the approach in mixed formulation. The asymptotic analysis will be presented in both cases as well as the convergence of the solutions.

  • Apr 17, 2009 (Applied Mathematics and Computation Seminar) Merrick Haller, Coastal and Ocean Engineering Program, Modeling microwave scattering from breaking waves

  • Apr 22, 2009 (Applied Mathematics and Computation Seminar) Dana Knoll, Idaho National Laboratory, Jacobian-Free Newton-Krylov Methods and Semi-Implicit Methods in Computational Fluid Dynamics

    Historically, Semi-Implicit (SI) methods in CFD have been developed to step over stiff wave time scale in a stable fashion for compressible flow (or MHD), or to handle the elliptic constraint in incompressible flow. SI methods generate a reduce set of scalar implicit systems which are inverted on each time step or within each outer iteration. This is typically achieved via some linearization and time splitting. Both of these can produce additional time integration errors for once through methods, or produce convergence issues for methods which iterate within a time step. In this talk, the concept of using SI methods as preconditioners to Jacobian-Free Newton-Krylov (JFNK) methods is developed. This algorithmic approach results in an implicitly balanced method (no linearization or time splitting). We will provide an overview along with results from all-speed compressible flow, geophysical fluid dynamics (GFD) and magnetohydrodynamics (MHD).

  • Apr 24, 2009 (Applied Mathematics and Computation Seminar) , No seminar this Friday. We hope you attended the seminar last Wednesday.

  • May 1, 2009 (Applied Mathematics and Computation Seminar) , No seminar this Friday. Please attend seminar next Monday !

  • May 4, 2009 (Applied Mathematics and Computation Seminar) Charles Radin, The University of Texas at Austin, Modelling sand

    We discuss probability distributions on packings of spheres and other shapes, as a function of the volume fraction of the packings. We then introduce a simple model of static sand piles and use Monte Carlo simulation to analyze the phenomenon of random loose packing in sand.

  • May 8, 2009 (Applied Mathematics and Computation Seminar) Sangil Kim, Oceanography (OSU), Ensemble-based Data Assimilation for Predicting Ocean Thermohaline Circulation

    The problem of data assimilation is to determine the best estimate of the solution history of a dynamical system given some partial and inaccurate measurements. The filtering problem is defined as that of estimating the present state given prior observations. It is generally accepted that the optimal solution is obtained by calculating the conditional statistical distribution of the state vector of the system given the measurements up to the current time.
    The conditional probability density function (PDF) solves the forward Kolmogorov equation between measurements, and the PDF is updated by Bayes's rule at measurement times. However, sovling the forward Klmogorov equation for multidimensional, many -variable systems is not a practical. One efficient way to circumvent this difficulty is to evolve the statistics by computing an N-sample ensemble of realizations of the system, for example, Sequential Importance Resampling method, Ensemble Kalman Filter, and Maximum Entropy Filter. I'll compare those methods and present results for a simple stochastic PDE model of the ocean thermohaline circulation, which has bimodal statistics associated to two distinct stable states.

  • May 13, 2009 (Applied Mathematics and Computation Seminar) , Attendees are encouraged to attend today's Mathematics Colloquium by Prof. Hoffmann, see Colloquium listing.

  • May 15, 2009 (Applied Mathematics and Computation Seminar) Karl-Heinz Hoffmann, Technische Universitaet Muenchen, Germany, "Mathematical Modelling and Analysis of Nanoparticle Detection Process"

    Nanoparticles promise a wide range of applications from medical drug delivery to coatings, paints etc.. Nanoparticles include carbon nanotubes, metal nanowires, semicoductor quantum dots, and other nanoobjects produced from a large variety of substances. However, little is known about possible health hazards caused by nanoparticles that have been set free in industrial process or during usage of products. Safe development of new materials requires that risks to health and the general environment associated with development, production, usage, and disposal of these materials would be recognized. This is necessary to protect the workers involved in production and use of these materials, the public, and the ecosystem. It also helps to inform the public debate about the development of these new, potentially beneficial, materials.
    The objectives of this lecture is to develop mathematical models that describe parts of the complete process of nanoparticle detection and recognition. the complete model should cover all related problems including particle transport in gases, particle transfer into aqueous solutions, binding of particles to the biomolecular receptors, and processing of electrical output signals to detect a phase shift caused by mass loading. in this lecture we will concentrate on describing the biosensor unit and the particle transport in the medium only.
    More scientific details of this talk are provided at this link.

  • May 22, 2009 (Applied Mathematics and Computation Seminar) Ben Dickinson, Mechanical Engineering (OSU), end{document} end{document} Biologically Inspired Hair Sensor Arrays for Flow Detection and Control

    The flight stability of micro air vehicles (MAV) is challenged by gusts of wind and unsteady low Reynolds number environments. Our research is inspired by the biological hair receptor array as a means of flow detection and control to enhance MAV stability and maneuverability. The first part of this presentation will focus on the hair receptor array for flow detection. Modeling each hair as a viscoelastic Euler-Bernoulli beam, an array of surface mounted hairs were simulated in unsteady flow separation. The collective mechanical response at the base of each hair accurately indicated the onset of unsteady flow separation, the formation and movement of near wall vortices and the location of the point of zero wall shear stress. Optimal hair lengths for boundary layer flows were also computed and in close agreement with the range of measured hair receptor lengths. The second half of the presentation will focus on flow control design with hair receptor arrays. In the design of closed-loop model-based flow controllers, state information is often provided from impractical locations for measurements using generalized sensor models. We mathematically integrate the bioinspired hair sensor array in a linear quadratic Gaussian observer for an unsteady Oseen flow field. Accurate flow field estimation could help realized closed-loop flow control designs where only surface measurements are available, such as in MAV applications.

  • May 29, 2009 (Applied Mathematics and Computation Seminar) Malgorzata Peszynska, Upscaling of inertia terms from porescale to mesoscale and from mesoscale to macroscale

    Traditionally saturated flow in porous media is modeled using Darcy model which is linear in the gradient of pressure; this model can be proven by homogenization to be an average of Stokes flow at porescale. In heterogeneous porous media where the scale of heterogeneity is too small to be handled by practical computational models, one has the need to homogeniza/average further to an upscaled Darcy model at macroscale.
    It is known that at larger velocities the inertia effects become significant and Stokes or Darcy models no longer are accurate. We consider a model including the inertia effects at porescale (Navier-Stokes), the non-Darcy model at mesoscale, and upscaled non-Darcy at macroscale, and show our recently published results concerning computational upscaling from porescale to mesoscale (joint work with Trykozko and Augustson, paper in ICCS, 2009), and from mesoscale to macroscale (joint with Garibotti, paper in TiPM, 2009).

  • Jun 5, 2009 (Applied Mathematics and Computation Seminar) Ben Morin/Ken Kennedy, Limiting Behavior for a Random Rock-Paper-Scissor Game (Morin) and Efficient methods for sensitivity analysis (Kennedy)

    Limiting Behavior for a Random Rock-Paper-Scissor Game (Morin)
    The talk will describe a generalization of Polya's Urn involving Rock- Paper-Scissor rules of competition. Simulation strongly suggests a limiting distribution of a multi-dimensional Dirac distribution centered at (1/3,1/3,1/3). A martingale approach supports the observed simulation behavior. A functional, Stein-like approach is suggested and a condition related to distribution classification is posed. Potential applications to E. coli bacteria and the male side-blotched lizard are presented along side an urn that would more appropriately model these systems are given as avenues for further work.

    Efficient methods for sensitivity analysis (Kennedy)
    Understanding the sensitivity of a model or computational method to perturbations in the parameters is relevant for control of the system and for verifying correctness of the method. We present methods for the efficient computation of sensitivity to parameters in coupled systems of partial differential equations.