Browsing by Author "Pierre Gremaud, Member"
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- A Robust and Efficient Finite Volume method for Compressible Two-Phase Flows at All Speeds on Unstructured Grids.(2018-08-13) Pandare, Aditya Kiran; Hong Luo, Chair; Jack Edwards, Member; Pramod Subbareddy, Member; Pierre Gremaud, Member
- Active Subspace Techniques, Bayesian Inference and Uncertainty Propagation for Nuclear Neutronics and Chemistry Models.(2019-07-25) Coleman, Kayla Danielle; Ralph Smith, Chair; Stephen Campbell, Member; Pierre Gremaud, Member; Brian Reich, Member
- An Analytical and Numerical Study of a Class of Nonlinear Evolutionary PDEs.(2013-08-20) Pendleton, Terrance Lamar; Alina Chertock, Chair; Roby Sawyers, Graduate School Representative; Michael Shearer, Member; Pierre Gremaud, Member; Mark Hoefer, Member
- Computational approaches for maximum likelihood estimation for nonlinearmixed models.(2000-07-19) Hartford, Alan Hughes; Marie Davidian, Co-Chair; John Monahan, Co-Chair; Pierre Gremaud, Member; Sastry Pantula, Member; Carla Savage, MemberThe nonlinear mixed model is an important tool for analyzingpharmacokinetic and other repeated-measures data.In particular, these models are used when the measured response for anindividual,,has a nonlinear relationship with unknown, random, individual-specificparameters,.Ideally, the method of maximum likelihood is used to find estimates forthe parameters ofthe model after integrating out the random effects in the conditionallikelihood. However, closed form solutions tothe integral are generally not available. As a result, methods have beenpreviously developed to find approximatemaximum likelihood estimates for the parameters in the nonlinear mixedmodel. These approximate methods include FirstOrder linearization, Laplace's approximation, importance sampling, andGaussian quadrature. The methods are availabletoday in several software packages for models of limited sophistication;constant conditional error variance is requiredfor proper utilization of most software. In addition, distributionalassumptions are needed. This work investigates howrobust two of these methods, First Order linearization and Laplace'sapproximation, are to these assumptions. The findingis that Laplace's approximation performs well, resulting in betterestimation than first order linearization when bothmodels converge to a solution. A method must provide good estimates of the likelihood at points inthe parameter space near the solution. This workcompares this ability among the numerical integration techniques,Gaussian quadrature, importance sampling, and Laplace'sapproximation. A new "scaled" and "centered" version of Gaussianquadrature is found to be the most accurate technique.In addition, the technique requires evaluation of the integrand at onlya few abscissas. Laplace's method also performs well; it is more accurate than importance sampling with even 100importance samples over two dimensions. Even so, Laplace's method still does not perform as well as Gaussian quadrature.Overall, Laplace's approximation performs better than expected, and is shown to be a reliable method while stillcomputationally less demanding. This work also introduces a new method to maximize the likelihood.This method can be sharpened to any desired levelof accuracy. Stochastic approximation is incorporated to continuesampling until enough information is gathered to resultin accurate estimation. This new method is shown to work well for linear mixed models, but is not yet successful for thenonlinear mixed model.
- Design and Sensitivity Analysis of Inverse Problems Governed by Partial Differential Equations.(2022-03-22) Sunseri, Isaac Paul; Alen Alexanderian, Chair; Pierre Gremaud, Member; Arvind Krishna Saibaba, Member; Bart Van Bloemen Waanders, External; Murthy Guddati, Member
- Efficient Dimension Reduction and Uncertainty Quantification for Complex Physical and Biological Systems.(2020-03-20) Guy, Hayley; Alen Alexanderian, Chair; Pierre Gremaud, Member; Ralph Smith, Member; John Mattingly, Member
- Exact Sums-of-Squares Certificates in Numeric Algebraic Geometry.(2011-05-24) Hutton, Sharon; Erich Kaltofen, Chair; Hoon Hong, Member; Agnes Szanto, Member; Pierre Gremaud, Member; Lihong Zhi, External; James Crisp, Graduate School Representative
- Fabrication of Flexible Metal Hollow Microneedles using Microsecond Pulsing of Single Mode Fiber Laser.(2012-11-28) Reeves, Nicholas Beamer; Juei Tu, Chair; Lawrence Silverberg, Member; Pierre Gremaud, Member
- Global Sensitivity Analysis and Reduced Order Modeling for High-dimensional Systems.(2021-03-26) Cleaves, Helen Larrabee; Alen Alexanderian, Chair; Ralph Smith, Member; Richard Longland, Member; Pierre Gremaud, Member
- High-Order Accurate Solutions to the Helmholtz Equation in the Presence of Boundary Singularities.(2015-02-27) Britt, Darrell Steven; Semyon Tsynkov, Chair; Moody Chu, Member; Alina Chertock, Member; Dmitriy Anistratov, Graduate School Representative; Pierre Gremaud, Member
- Hyperbolic Navier-Stokes Method Based on Reconstructed-Discontinuous-Galerkin or Reconstructed-Finite-Volume Formulation with Variational Reconstruction.(2019-10-25) Li, Lingquan; Hong Luo, Chair; Hiroaki Nishikawa, External; Pierre Gremaud, Member; Jack Edwards, Member; Pramod Subbareddy, Member
- Interface Problems and Binary Electromagnetic Cloaking Designs in Computational Electromagnetics.(2020-05-12) Vogt, Ryan; Zhilin Li, Chair; David Aspnes, Member; Pierre Gremaud, Member; Alen Alexanderian, Member; Sven Leyffer, External
- Mathematical Analysis of Autonomic Control of Blood Pressure and Heart Rate.(2019-07-05) Randall, Eric Benjamin; Mette Olufsen, Chair; Carl Kelley, Member; Jesper Mehlsen, External; Pierre Gremaud, Member; Paul Mozdziak, Minor
- Modeling Cerebral Autoregulation During Orthostatic Stress in the Presence of Aging and Hypertension.(2016-11-04) Mader, Gregory Charles; Mette Olufsen, Chair; Adam Mahdi, Member; Hien Tran, Member; Pierre Gremaud, Member
- A Numerical Investigation into the Expansion of a Plasma Plume due to Ablation of a Graphite Target by a Nano-second Laser Pulse.(2011-05-19) Cohen, Sean; Alina Chertock, Chair; Pierre Gremaud, Member; Zhilin Li, Member; Michael Shearer, Member
- Pair-instability Supernova Explosions in 1D, 2D, and 3D and Their Observational Signatures.(2018-03-22) Gilmer, Matthew Stonecipher; Carla Frohlich, Chair; James Kneller, Member; Stephen Reynolds, Member; Pierre Gremaud, Member
- Parameter Estimation in Groundwater Models Using Proper Orthogonal Decomposition.(2012-07-23) Winton, Corey Wayne; Carl Kelley, Chair; Pierre Gremaud, Member; Ralph Smith, Member; HOWINGTON, STACEY E. (E), External; MILLER, CASEY TIMOTHY (UNC-CH), Inter-Institutional; Heather Cheshire, Graduate School Representative
- Parameter Estimation of Viscoelastic Models in a 1-D Circulatory Network(2015-08-18) Battista, Christina; Mette Olufsen, Co-Chair; Mansoor Haider, Co-Chair; Pierre Gremaud, Member; Brooke Steele, External; Sharon Lubkin, Member
- Parameter Subset Selection and Subspace Analysis Techniques Applied to a Polydomain Ferroelectric Material Phase-Field Energy Model.(2018-08-17) Leon, Lider Steven; Ralph Smith, Chair; Pierre Gremaud, Member; Mansoor Haider, Member; Elizabeth Dickey, Member
- Patterns of air flow and particle deposition in the diseased human lung(2001-07-05) Segal, Rebecca Anne; Michael Shearer, Chair; Ted Martonen, Member; Sharon Lubkin, Member; Pierre Gremaud, MemberIn this work, we investigate particle deposition and air flow in thehuman lung. In particular we are interested in how the motion ofparticulate matter and air is affected by the presence of lungdisease. Patients with compromised lung function are more sensitiveto air pollution; understanding the extent of that sensitivity canlead to more effective air quality standards. Also, understanding ofair flow andparticle trajectories could lead to the development of better aerosoldrugs to treat the lung diseases.We focus our efforts on twodiseases: chronic obstructive pulmonary disease (COPD) and bronchialtumors. Because COPD affects the majority of airways in a patientwith the disease, we are able to take a more global approach toanalyzing the effects of the disease. Using a FORTRAN codewhich computes total deposition in the lung over the course of onebreath, we modified the pre-existing code to account forthe difference between healthy subjects and patients with COPD. Usingthe model, itwas possible to isolate the different disease components of COPD andsimulate their effects separately. It was determined thatthe chronic bronchitis component of COPD was responsible for the increaseddeposition seen in COPD patients.While COPD affects the whole lung, tumors tend to belocalized to one or several airways. This led us to investigate theeffects of bronchial tumors in detail within these individualairways. Using a computational fluid dynamics package, FIDAP, wedefined a Weibel type branching network of airways.In particular, we modeled theairways of a four-year-old child.In the work with the tumors, we ran numerous simulations with variousinitial velocities and tumor locations. It was determined that tumorslocated on the carinal ridge had the dominant effect on the flow. Athigher initial velocities, areas of circulation developed downstream from the tumors. Extensive simulations were run with a 2-D model. Theresults from the 2-D model were then compared with some initial 3-Dsimulations.In the development of the FIDAP model, we avoided thecomplications of flow past the larynx, by limiting the model togenerations 2-5 of the Weibel lung. We developed a realistic inletvelocity profile to be used as the input into the model. The skewednature ofthis inlet profile led to thequestion of boundary layer development and the determination of theentrance length needed to achieve fully developed parabolicflow. Simple scale analysis of the Navier-Stokes equations did notcapture the results we were seeing with the CFD simulations.We turned to a more quantitative, energy correctionanalysis to determine the theoretical entrance length.In conclusion, the presence of disease in the lunghas a large effect both on global deposition patterns and on localizedairflow patterns. This indicates the need for different protocolsregarding susceptibility of people to airborne pollutants that take intoaccount lung disease. It also suggests that treatment should accountfor changes in airflow in the diseased lung.