**(Names of students are listed in bold.)**

2017

Report | Author(s) | Description | Link | Date |
---|

TR-MATH 17-03 | O. Oyekole, M. Bukač and C. Trenchea | A second-order in time approximation of fluid-structure interaction problem | October 2017 | |

TR-MATH 17-02 |
| The Williams step increases the stability and accuracy of the hoRA time filter | October 2017 | |

TR-MATH 17-01 | V. Ervin, | Partitioned penalty methods for the evolutionary Stokes-Darcy-transport problem | August 2017 |

2016

Report | Author(s) | Description | Link | Date |
---|

TR-MATH 16-03 |
| Existence and ergodicity for the two-dimensional Boussinesq equation | December 2016 | |

TR-MATH 16-01 | A. Vainchtein, Y. Starosvetsky, J. D. Wright, and R. Perline | Solitary waves in diatomic chains | March 2016 | |

TR-MATH 16-02 | L. Liu, G. James, P. Kevrekidis, and A. Vainchtein | Breathers in a locally resonant granular chain with precompression | March 2016 |

### 2015

Report | Author(s) | Description | Link | Date |
---|

TR-MATH 15-10 | V.J. Ervin, | On limiting behavior of contaminant transport models in coupled surface and groundwater flows | October 2015 | |

TR-MATH 15-05 | L. Liu, G. James, P. Kevrekidis and A. Vainchtein | Nonlinear waves in a strongly nonlinear resonant granular chain | June 2015 | |

TR-MATH 15-04 | A. Vainchtein, E. S. Van Vleck and A. Zhang | Propagation of periodic patterns in a discrete system with competing interactions | May 2015 | |

TR-MATH 15-03 | and C. TrencheaY. Li | Partitioned second order method for magnetohydrodynamics in Elsasser fields | February 2015 | |

TR-MATH 15-02 | N. Jiang, M. Mohebujjaman, L.G.Rebholz, C.Trenchea | Analysis of a family of regularization methods for Navier-Stokes equations | January 2015 | |

TR-MATH 15-01 | Y. Li and C. Trenchea | Analysis of time filters used with the leapfrog scheme | January 2015 |

2014

Report | Author(s) | Description | Link | Date |
---|

TR-MATH 14-11 | H.A. Tran, C. Trenchea and C.G Webster | A convergence analysis of stochastic collocation method for Navier-Stokes equations with random input data | October 2014 | |

TR-MATH 14-10 | L. Truskinovsky and A. Vainchtein | Solitary waves in a non-integrable FPU chain | September 2014 | |

TR-MATH 14-09 | N. Jiang, S. Kaya and W. Layton | Analysis of Model Variance for Ensemble Based Turbulence Modeling | May 2014 | |

TR-MATH 14-08 | N. Wilson, A. Labovsky, C. Trenchea | High accuracy method for magnetohydrodynamics system in Elsasser variables | May 2014 | |

TR-MATH 14-07 | W. Layton | The 1877 Boussinesq Conjecture: Turbulent Fluctuations are Dissipative on the Mean Flow | March 2014 | |

TR-MATH 14-06 | W. Layton | 2D Decaying Turbulence does not have Exponential Seperation of Trajectories | March 2014 | |

TR-MATH 14-05 | C. Brucato | The Traveling Salesman Problem | January 2014 | |

TR-MATH 14-04 | S. Jayasuriyay, S. Reichy and J. Wheeler | On the Iinverse Erdos-Heilbronn Problem for Restricted Set Addition in Finite Groups | January 2014 | |

TR-MATH 14-03 | N. Jiang | A Higher Order Ensemble Simulation Algorithm for Fluid Flows | January 2014 | |

TR-MATH 14-02 | andN. Jiang H. Tran | Analysis of a stabilized CNLF method with fast slow wave splittings for flow problems | January 2014 | |

TR-MATH 14-01 | and P.D.WilliamsY. Li | Analysis of the RAW Filter in Composite-Tendency Leapfrog Integrations | January 2014 |

### 2013

Report | Author(s) | Description | Link | Date |
---|

TR-MATH 13-01 | N. Hurl, W. Layton, Y. Li and C. Trenchea | Stability Analysis of the Crank-Nicolson-Leap-Frog Method with the Robert-Asselin-Williams Time Filter | January 2013 | |

TR-MATH 13-02 | W. Layton, H. Tran and C. Trenchea | Numerical Analysis of two Partitioned Methods for Uncoupling Evolutionary MHD Flows | January 2013 | |

TR-MATH 13-03 | M. Kubacki and M. Moraiti | Analysis of a Second Order, Unconditionally Stable, Partitioned Method for the Evolutionary Stokes-Darcy Problem | January 2013 | |

TR-MATH 13-04 | C. Lupu | Mean value theorems of Flett type for a Volterra operator | February 2013 | |

TR-MATH 13-05 | L. Liu, A. Vainchtein, Y. Wang | Kinetics of a Twinning Step | March 2013 | |

TR-MATH 13-06 | N. Jiang and W. Layton | An Algorithm for Fast Calculation of Flow Ensembles | April 2013 | |

TR-MATH 13-15 | W. Layton and L.G. Rebholz | On Relaxation Times in the Navier-Stokes-Voigt Model | April 2013 | |

TR-MATH 13-07 | B. Espinoza, P. Gartside and | n-Arc Connected Spaces | May 2013 | |

TR-MATH 13-08 | S. P. Hastings and J. B McLeod | Uniqueness of Relaxation Oscillations: A Classical Approach | June 2013 | |

TR-MATH 13-09 |
| Numerical Analysis of two Ensemble Eddy Viscosity Models of Fluid Motion | July 2013 | |

TR-MATH 13-10 |
| The Unstable Mode in the Crank-Nicolson Leap-Frog Method is Stable | August 2013 | |

TR-MATH 13-11 | W. Layton and | Energy Stability Of A First Order Partitioned Method For Systems With General Coupling
| August 2013 | |

TR-MATH 13-12 |
| Further Numerical Tests of Ensemble Eddy Viscosity Methods
| August 2013 | |

TR-MATH 13-13 | W. Layton, | Instability of Crank-Nicolson Leap-Frog for Nonautonomous Systems | August 2013 | |

TR-MATH 13-14 |
| Exact Solution of the Stochastic Navier-Stokes Equations | August 2013 | |

TR-MATH 13-15 |
and M. Moraiti H. Tran | A Crank-Nicolson Leap-Frog stabilization: | September 2013 | |

TR-MATH 13-16 |
| A higher-order Robert-Asselin type time filter | September 2013 | |

TR-MATH 13-17 | M. Bukač, W. Layton, | Analysis of partitioned methods for Biot system | October 2013 |

### 2012

Report | Author(s) | Description | Link | Date |
---|---|---|---|---|

TR-MATH 12-01 | W. Layton | The Interior Error of Van Cittert Deconcolution of Differential Filters is Optimal | January 2012 | |

TR-MATH 12-02 | W. Layton | Introduction to the Transfer theory of Turbulence | Januray 2012 | |

TR-MATH 12-03 | M. Moraiti | On the Quasistatic Approximation in the Stokes-Darcy Model of Groundwater-Surface Water Flows | March 2012 | |

TR-MATH 12-04 | C. Trenchea | Stability of Partitioned Imex Methods for Systems of Evolution Equations with Skew-Symmetric Coupling | April 2012 | |

TR-MATH 12-05
| C. Trenchea | Unconditional Stability of a Partitioned Imex Method for Magnetohydrodynamic Flows | April 2012 | |

TR-MATH 12-06 | V. Girault, D. Vassilev and I. Yotov | Mortar Multiscale Finite Element Methods for Stokes-Darcy Flows | April 2012 | |

TR-MATH 12-07 | M. Kubacki | Uncoupling Evolutionary Groundwater-Surface Water Flows Using the Crank-Nicolson Leapfrog Method | April 2012 | |

TR-MATH 12-08 | P. Rosakis and A. Vainchtein | New Solutions for Slow Moving Kinks in a Forced Frenkel-Kontorova Chain | May 2012 | |

TR-MATH 12-09 | A. Jorgenson | Unconditional Stability of a Crank-Nicolson Adams-Bashforth 2 Implicit-Explicit Numerical Method | May 2012 | |

TR-MATH 12-10 | C. Trenchea | Second Order Implicit for Local Effects and Explicit for Nonlocal Effects is Unconditionally Stable | May 2012 | |

TR-MATH 12-11 | W. Layton and A. Takhirov | A Test of a Modular, Wall Adapted Nonlinear Filter Model for Underresolved Flows | June 2012 | |

TR-MATH 12-8 | and V. MateiC. Lupu | Arithmetic Functions, Prime Counting Function and Polynomials | July 2012 | |

TR-MATH 12-14 | N. Hurl | Energy Stability of the Crank-Nicolson Leap Frog Method with Time Filters | October 2012 | |

TR-MATH 12-15 | X. Xiong | Analysis of a Multi-Rate Splitting Method for Uncoupling Evolutionary Groundwater-Surfacewater Flows | October 2012 | |

TR-MATH 12-16 | A. Takhirov | Stokes-Brinkman Lagrange Multiplier/Fictitious Domain Method for Flows in Pebble Bed Geometries | October 2012 | |

TR-MATH 12-19 | N. Costea, D. A. Ion and C. Lupu | Variational-like Inequality Problems Involving Set-Valued Maps and Generalized Monotonicity | October 2012 | |

TR-MATH 12-17 | P.G. Kevrekidis, A. Vainchtein, M. Serra Garcia, and C. Daraio | Interaction of Traveling Waves with Mass-With-Mass Defects within a Hertzian Chain | December 2012 |

### 2011

Report | Author(s) | Description | Link | Date |
---|---|---|---|---|

TR-MATH 11-01 | L. Shan, H. Zheng and W. Layton | Decoupled scheme with different time step sizes for the evolutionary Stokes-Darcy model | January 2011 | |

TR-MATH 11-02 | W. Layton, C. Trenchea | Stability of two IMEX methods, CNLF and BDF2-AB2, for uncoupling systems of evolution equations | February 2011 | |

TR-MATH 11-03 | L. Shan, H. Zheng and W. Layton | A Non-Iterative, Domain Decomposition Method with Different Time Step Sizes for the Evolutionary Stokes-Darcy Model | May 2011 | |

TR-MATH 11-04 | L. Shan and H. Zheng | Partitioned Time Stepping Method for Fully Evolutionary Stokes-Darcy Flow with Beavers-Joseph Interface | May 2011 | |

TR-MATH 11-05 | W. Layton, H. Tran and C. Trenchea | Analysis of Long Time Stability and Errors of Two Partitioned Methods for Uncoupling Evolutionary Groundwater - Surface Water Flows | May 2011 | |

TR-MATH 11-06 | G. Yuksel and R. Ingram | Numerical Analysis of a Finite Element, Crank-Nicolson Discretization for MHD Flows at Small Magnetic Reynolds Numbers | May 2011 | |

TR-MATH 11-07 | R. Ingram | A New Linearly Extrapolated Crank-Nicolson Time-Stepping Scheme for the NSE | July 2011 | |

TR-MATH 11-08 | A. Vainchtein and P. G. Kevrekidis | Dynamics of phase transitions in a piecewise linear diatomic chain | September 2011 | |

TR-MATH 11-09 | A. Bowers, L. Rebholz, A. Takhirov, and C. Trenchea | Improved Accuracy in Regularization Models of Iincompressible Flow Via Adaptive Nonlinear Filtering | October 2011 | |

TR-MATH 11-10 | W. Layton, N. Mays, M. Neda and C. Trenchea | Numerical Analysis of Modular Regularization Methods for the BDF2 Time Discretization of the Navier-Stokes Equations | November 2011 | |

TR-MATH 11-11 | W. Layton, H. Tran and X. Xiong | Long Time Stability of Four Methods for Splitting the Evolutionary Stokes-Darcy Problem into Stokes and Darcy Subproblems | November 2011 |

### 2010

Report | Author(s) | Description | Link | Date |
---|---|---|---|---|

TR-MATH 10-01 | V. Ervin, W. Layton and M. Neda | Numerical Analysis of Filter Based Stabilization for Evolution Equations | January 2010 | |

TR-MATH 10-02 | J. Arciero, G. Ermentrout, J. Upperman, Y. Vodovotz, J. Rubin | Using a Mathematical Model to Analyze the Role of Probiotics and Inflammation in Necrotizing Enterocolitis | January 2010 | |

TR-MATH 10-03 | E. Manica, G. Medvedev and J. Rubin | First Return Maps for the Dynamics of Synaptically Coupled Conditional Bursters | January 2010 | |

TR-MATH 10-04 | H. Tran | On the Estimates of Determining Modes for NS-alpha and NS-omega Models | January 2010 | |

TR-MATH 10-05 | E. Trofimov and A. Vainchtein | Shocks versus kinks in a discrete model of displacive phase transitions | February 2010 | |

TR-MATH 10-06 | B. Ganis, I. Yotov and M. Zhong | A Stochastic Mortar Mixed Finite Element Method for Flow in Porous Media with Multiple Rock Types | April 2010 | |

TR-MATH 10-07 | A. Labovschii and C. Trenchea | Approximate Deconvolution Models for Magnetohydrodynamics | April 2010 | |

TR-MATH 10-08 | S. Hritz | Phenomenology and Computations of a Regularization of the Navier-Stokes Equations Related to a Non-Newtonian Fluid Flow Model | May 2010 | |

TR-MATH 10-09 | R. Ingram | Unconditional convergence of high-order extrapolations of the Crank-Nicolson, nite element method for the Navier-Stokes equations | July 2010 | |

TR-MATH 10-10 | W. Layton, L. Rebholz and C. Trenchea | Modular Nonlinear Filter Stabilization of Methods for Higher Reynolds Numbers Flow | September 2010 | |

TR-MATH 10-11 | W. Layton, M. Neda and | A Transfer Theory Analysis of Approximate Deconvolution Models of Turbulence | October 2010 | |

TR-MATH 10-12 | W. Layton, L. Roehe and H. Tran | Explicitly Uncoupled VMS Stabilization of Fluid Flow | November 2010 | |

TR-MATH 10-13 | M. Sussman | A Stability Examble | November 2010 | |

TR-MATH 10-14 | K. Lipnikov, D. Vassilev and I. Yotov | Discontinuous Galerkin and Mimetic Finite Difference Methods for Coupled Stokes-Darcy Flows on Polygonal and Polyhedral Grids | November 2010 | |

TR-MATH 10-15 | M. Wheeler, G. Xue and I. Yotov | A Multiscale Mortar Multipoint Flux Mixed Finite Element Method | December 2010 | |

TR-MATH 10-16 | M. Wheeler, G. Xue and I. Yotov | A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra | December 2010 | |

TR-MATH 10-17 | W. Layton, L. Shan and H. Zheng | Numerical Analysis of Modular VMS Methods with Nonlinear Eddy Viscosity for the Naiver-Stokes Equations | December 2010 |

### 2009

Report | Author(s) | Description | Link | Date |
---|---|---|---|---|

TR-MATH 09-01 | J. Connors | Convergence analysis and computational testing of the finite element discretization of the Navier-Stokes-alpha model | January 2009 | |

TR-MATH 09-02 | X. Hu AND D. Wang | Low Mach Number Limit of Viscous Compressible Magnetohydrodynamic Flows | February 2009 | |

TR-MATH 09-03 | C. Manica and I. Stanculescu | Numerical Analysis of Leray-Tikhonov Deconvolution Models of Fluid Motion | Feburary 2009 | |

TR-MATH 09-04 | J. Connors and A. Labovsky | High Accuracy Semi-implicit Spectral Deffered Correction Decoupling Methods for a Parabolic Two Domain Problem | February 2009 | |

TR-MATH 09-05 | B. Doubrov,J. Holland and G. Sparling | Space-time and G2 | February 2009 | |

TR-MATH 09-06 | A. Lozovskiy | Numerical Analysis of the Semidiscrete Finite Element Method for Computing the Noise Generated by Turbulent Flows | February 2009 | |

TR-MATH 09-07 | S. Verduzco-Flores, M. Bodner, G.B. Ermentrout, J. M. Fuster, YD.Zhou | Working memory cells’ behavior may be explained by crossregional networks with synaptic facilitation | February 2009 | |

TR-MATH 09-08 | S. Verduzco-Flores, B. Ermentrout and M. Bodner | From working memory to epilepsy: Dynamics of facilitation and inhibition in a cortical network | February 2009 | |

TR-MATH 09-10 | P. Hajlasz and Z. Liu | A Compact Embedding of a Sobolev Space is Equivalent to an Embedding into a Better Space | March 2009 | |

TR-MATH 09-11 | A. Vainchtein and E. Van Vleck | Nucleation and propagation of phase mixtures in a bistable chain | March 2009 | |

TR-MATH 09-12 | B. Ganis and I. Yotov | Implementation of a Mortar Mixed Finite Element Method using a Multiscale Flux Basis | March 2009 | |

TR-MATH 09-13 | B Layton and A Novoyny | On Lighthill's acoustic analogy for low Mach number flows | April 2009 | |

TR-MATH 09-14 | J. Day, J. Rubin and C. Chow | Competition Between Transients in the Rate of Approach to a Fixed Point | April 2009 | |

TR-MATH 09-15 | G. Chen, M. Slemrod and D. Wang | Weak Continuity of the Gauss-Codazzi-Ricci System for Isometric Embedding | May 2009 | |

TR-MATH 09-16 | X. Hu and D. Wang | Global Strong Solution to the Density-Dependent Incompressible Viscoelastic Fluids | May 2009 | |

TR-MATH 09-17 | L. Truskinovsky and A. Vaninchtein | Beyond Kinetic Relations | May 2009 | |

TR-MATH 09-18 | S. Kubota, J. Rubin and T. Kitajima | Modulation of LTP/LTD balance in STDP by activity-dependent feedback mechanism | May 2009 | |

TR-MATH 09-19 | A. Vainchtein | The Role of Spinodal Region in the Kinetics of Lattice Phase Transitions | May 2009 | |

TR-MATH 09-20 | T. Stepien | Tubuloglomerular Feedback-Mediated Dynamics in Three Coupled Nephrons | May 2009 | |

TR-MATH 09-21 | S. Bayrama, T. Stepien, and E. Pitman | TGF-Mediated Dynamics in a System of Many Coupled Nephrons | May 2009 | |

TR-MATH 09-22 | R. Ingram | A Mixed Finite Element Approximation of Stokes-Brinkman and NS-Brinkman Equation for Non-Darcian Flows | July 2009 | |

TR-MATH 09-23 | W. Layton and C. Trenchea | The Das-Moser Commutator Closure for Filtering Through a Boundary is Well Posed | July 2009 | |

TR-MATH 09-24 | R. Ingram, M. Wheeler and I. Yotov | A multipoint flux mixed finite element method on hexahedra'' by Ross Ingram, Mary F. Wheeler | July 2009 | |

TR-MATH 09-25 | M. Garvie, P. Maini and C Trenchea | A Methodology for Parameter Identification in Turing Systems | August 2009 | |

TR-MATH 09-26 | M. F. Wheeler, T. Wildey, and I. Yotov | A multiscale preconditioner for stochastic mortar mixed finite elements | August 2009 | |

TR-MATH 09-27 | W. Layton | On Taylor/Eddy Solutions of Approximate Deconvolution Models of Turbulence | August 2009 | |

TR-MATH 09-28 | A. Vainchtein | Effect of nonlinearity on the steady motion of a twinning dislocation | September 2009 | |

TR-MATH 09-29 | W. Layton, C. Pruett and L. Rebholz | Temporally Regularized Direct Numerical Simulation | October 2009 | |

TR-MATH 09-30 | W. Layton | Fluid-Porous Interface Conditions with the "Inertia Term" 1/2 |UFLUID|2 are not Galilean Invariant | October 2009 | |

TR-MATH 09-31 | A. Lozovskiy | Numerical Analysis of the Fully Discrete Finite Element Scheme for the Lighthill Acoustic Analogy and Estimating the Errorin the Sound Power | October 2009 | |

TR-MATH 09-32 | G. Ermentrout, J. Jalics and J. Rubin | Stimulus-driven traveling solutions in continuum neuronal models with a general smooth firing rate function | December 2009 | |

TR-MATH 09-33 | J. Dunmyre and J. Rubin | Optimal Intrinsic Dynamics for Bursting in a Three-Cell Network | December 2009 | |

TR-MATH 09-34 | C. Frias | Comparison of turbulence models using OPENFOAM
| December 2009 |

### 2008

Report | Author(s) | Description | Link | Date |
---|---|---|---|---|

TR-MATH 08-01 | W. Layton, C. Manica, M. Neda and L. Rebholz | Numerical Analysis and Computational comparisons of the NS-alpha and NS-omegaregularizations | January 2008 | |

TR-MATH 08-02 | W. Layton and I. Stanculescu | Chebychev optimized approximate deconvolution models of turbulence | January 2008 | |

TR-MATH 08-03 | X. Hu and D. Wang | Global existence and large-time behavior of solutions to the three-dimensional equations of compressible magnetohydrodynamics flows | January 2008 | |

TR-MATH 08-04 | X. Hu and D. Wang | Global solutions to the three-dimensional full compressible magnetohydrodynamics flows | January 2008 | |

TR-MATH 08-05 | X. Hu and D. Wang | Compactness of weak solutions to the three-dimensional compressible magnetohydrodynamics flows | January 2008 | |

TR-MATH 08-06 | A. Reynolds, J. Rubin, G. Clermont, J. Day, Y. Vodovotz, G. B. Ermentrout | A reduced mathematical model of the acute inflammatory response: | February 2008 | |

TR-MATH 08-07 | J. Day, J. Rubin, Y. Vodovotz, C. Chow,A. Reynolds, G. Clermont | A reduced mathematical model of the acute inflammatory response II. Capturing scenarios of repeated endotoxin administration | February 2008 | |

TR-MATH 08-08 | K. Lipnikov, M. Shashkov, and I. Yotov | Local flux mimetic finite difference methods | February 2008 | |

TR-MATH 08-09 | B. Ganis, H. Klie, M. F. Wheeler, T. Wildey, I. Yotov, and D. Zhang | Stochastic collocation and mixed finite elements for flow in porous media | February 2008 | |

TR-MATH 08-10 | V. Girault, S. Sun, M. Wheeler, And I. Yotov | Coupling discontinuous Galerkin and mixed finite element discretizations using mortar finite elements | February 2008 | |

TR-MATH 08-11 | G. Pencheva and I. Yotov | Interior superconvergence in mortar and non-mortar mixed finite element methods on non-matching grids | March 2008 | |

TR-MATH 08-12 | J. Day, J. Rubin and C. Chow | Competition Between Transients in the Rate of Approach to a Fixed Point | March 2008 | |

TR-MATH 08-13 | W. Layton, L. Rebholz and M. Sussman | Energy and Helicity Dissipation Rates of the NS-Alpha and NS-Alpha-Deconvolution Models | March 2008 | |

TR-MATH 08-14 | S. P. Hastings and J. B. McLeod | An Elementary Approach to a Model Problem of Lagerstrom | April 2008 | |

TR-MATH 08-15 | B. Ermentrout and S.P. Hastings | Steady state analysis of a continuum model for super-infection. | April 2008 | |

TR-MATH 08-16 | S. Dauna, J. Rubin, Y. Vodovotz, A. Roye, R. Parkere and G. Clermont | An Ensemble of Models of the Acute Inflammatory Response to Bacterial Lipopolysaccharide in Rats: Results from Parameter Space Reduction | April 2008 | |

TR-MATH 08-17 | A. Cesmelioglu and B. Riviere | Analysis of Time-Dependent Navier-Stokes Flow Coupled with Darcy Flow | May 2008 | |

TR-MATH 08-18 | W. Layton, I. Stanculescu and C. Trenchea | Theory of the NS-omega model: A Compliment to the NS-alpha Model | June 2008 | |

TR-MATH 08-19 | J. Connors and W. Layton | On the Accuracy of the Finite Element Method Plus Time Relaxation | June 2008 | |

TR-MATH 08-20 | W. Layton, C. Manica, M. Neda, M. Olshanskii and L. Rebholz | On the Accurate of the Rotation form in Simulations of the Navier- Stokes Equations | June 2008 | |

TR-MATH 08-21 | S. Daun, J. Rubin and I. Rybak | Control of Oscillation Periods and Phase Durations in Half-Central Pattern Generators: a Comparative Mechanistic Analysis | July 2008 | |

TR-MATH 08-27 | P. Gartside and Z. Feng | Spaces with a Finite Family of Basic Functions | July 2008 | |

TR-MATH 08-22 | D. Vassilev and I. Yotov | Coupling Stokes-Darcy Flow with Transport | August 2008 | |

TR-MATH 08-23 | R. Ingram, W. Layton and N. Mays | Analysis of Iterated Tikhonov: Defect Correction for Ill-Posed Problems | August 2008 | |

TR-MATH 08-28 | L. Chism, X. He, L. Huang, A. Ibrahim,C. Jones, Y. Shu, C. Wah Wu, Z. Fu | Performance study of peer-to-peer video streaming on complex networks | August 2008 | |

TR-MATH 08-24 | M. Garvie and C. Trenchea | The Identification of Space Time Distributed Parameters in Reaction-Diffusion Systems | September 2008 | |

TR-MATH 08-25 | W. Layton | Existence of Smooth Attractors for the Navier-Stokes-Omega Model of Turbulence: Expanded Version | December 2008 | |

TR-MATH 08-26 | J. Conners, J. Howell and W. Layton | Partitioned Timestepping For a Parabolic Two Domain Problem | December 2008 |

### 2007

Report | Author(s) | Description | Link | Date |
---|---|---|---|---|

TR-MATH 07-01 | W. Layton and R. Lewandowski | A high accuracy Leray-deconvolution model of turbulence and its limiting behavior | January 2007 | |

TR-MATH 07-02 | W. Layton and I. Stanculescu | K-41 optimized approximate deconvolution models | January 2007 | |

TR-MATH 07-03 | P. Lindqvist and J.J. Manfredi | Viscosity supersolutions of the evolutionary p-Laplace equation | February 2007 | |

TR-MATH 07-04 | S. Zenker, J. Rubin, and G. Clermont | Towards a model based medicine: a clinically meaningful approach to ill-posed inverse problems in quantitative physiology | February 2007 | |

TR-MATH 07-05 | W. Layton | A remark on regularity of an elliptic-elliptic singular perturbation problem | February 2007 | |

TR-MATH 07-06 | B. Lal Sharma and A. Vainchtein | Quasistatic propagation of steps along a phase boundary | March 2007 | |

TR-MATH 07-07 | Y. Zhen and A. Vainchtein | Dynamics of steps along a martensitic phase boundary I: semi-analytical solution | March 2007 | |

TR-MATH 07-08 | Y. Zhen and A. Vainchtein | Dynamics of steps along a martensitic phase boundary II: numerical simulations | March 2007 | |

TR-MATH 07-09 | V. Girault and B. Riviere | DG approximation of coupled Navier-Stokes and Darcy equations by Beaver-Joseph-Saffman interface condition | March 2007 | |

TR-MATH 07-10 | S. Chanillo and J. J. Manfredi | Sharp global bounds for the Hessian on pseudo-hermitian manifolds | April 2007 | |

TR-MATH 07-11 | A. Borisov, M. Dickinson and S. Hastings | A congruence problem for polyhedra | PDF Code | April 2007 |

TR-MATH 07-12 | S. Hastings, D. Kinderlehrer, J.B. McLeod | Diffusion mediated transport in multiple state systems | April 2007 | |

TR-MATH 07-21 | P. Gartside and Z. Feng | More stratifiable function spaces | April 2007 | |

TR-MATH 07-22 | Z. Feng and R. Heath | Metrizability of Topological Semigroups on Linearly Ordered Topological Spaces | April 2007 | |

TR-MATH 07-13 | P.Chidyagwai and B. Riviere | A weak solution and a multinumerics solution of the coupled Navier-Stokes and Darcy equations | August 2007 | |

TR-MATH 07-14 | A. Labovschii | A Defect Correction Method for the Time-Dependent Navier-Stokes Equations | August 2007 | |

TR-MATH 07-15 | A. Labovschii, W. Layton, C. Manica, M. Neda, L. Rebholz | The Stabilized, Extrapolated Trapezoidal Finite Element Method for the Navier-Stokes Equations | August 2007 | |

TR-MATH 07-16 | A. Labovschii, C. Trenchea | Large Eddy Simulation for MHD Flows | August 2007 | |

TR-MATH 07-17 |
| Existence Theory of Abstract Approximate Deconvolution Models of Turbulence | August 2007 | |

TR-MATH 07-18 |
| Mathematical Architecture of Approximate Deconvolution Models of Turbulence | September 2007 | |

TR-MATH 07-19 | L. Truskinovsky, A. Vainchtein | Dynamics of martensitic phase boundaries: discreteness, dissipation and inertia | October 2007 | |

TR-MATH 07-20 | A. Labovschii | A Defect Correction Method for the Evolutionary Convection Diffusion Problem with Increased Time Accuracy | October 2007 |

### 2006

Report | Author(s) | Description | Link | Date |
---|---|---|---|---|

TR-MATH 06-01 | Y. Epshteyn, T. Khan, and B. Riviere | Inverse problem in optical tomography using discontinuous Galerkin method | January 2006 | |

TR-MATH 06-02 | L. Rebholz | An energy and helicity conserving finite element scheme for the Navier-Stokes equations | January 2006 | |

TR-MATH 06-03 | J. Rubin and A. Bose | The geometry of neuronal recruitment | February 2006 | |

TR-MATH 06-04 | V. John, W. Layton, and C. Manica | Convergence of time averaged statistics of finite element approximations of the Navier-Stokes equations | February 2006 | |

TR-MATH 06-05 | Y. Epshteyn and B. Riviere | Symmetric interior penalty Galerkin methods for elliptic problems | February 2006 | |

TR-MATH 06-06 | V. Ervin, W. Layton, and M. Neda | Numerical analysis of a higher order time relaxation model of fluids | February 2006 | |

TR-MATH 06-07 | J. Proft and B. Riviere | Analytical and numerical study of diffusive fluxes for transport equations with near-degenerate coefficients | April 2006 | |

TR-MATH 06-08 | J. Rubin | Bursting induced by excitatory synaptic coupling in non-identical conditional relaxation oscillators or square-wave bursters | April 2006 | |

TR-MATH 06-09 | W. Layton and M. Neda | A similarity theory of approximate deconvolution models of turbulence | May 2006 | |

TR-MATH 06-10 | W. Layton, C. Manica, M. Neda, and L. Rebholz | The joint helicity-energy cascade for homogeneous, isotropic turbulence generated by approximate deconvolution models | May 2006 | |

TR-MATH 06-11 | C. Manica and S. Kaya Merdan | New discretizations of turbulent flow problems | May 2006 | |

TR-MATH 06-12 | C. Manica and S. Kaya Merdan | Convergence analysis of the finite element method for a fundamental model in turbulence | May 2006 | |

TR-MATH 06-13 | W. Layton | Bounds on energy and helicity dissipation rates of approximate deconvolution models of turbulence | June 2006 | |

TR-MATH 06-14 | P. Lindqvist and J. Manfredi | Note on a remarkable superposition for a nonlinear equation | July 2006 | |

TR-MATH 06-15 | T. Arbogast, G. Pencheva, M.F. Wheeler, and I. Yotov | A multiscale mortar mixed finite element method | July 2006 | |

TR-MATH 06-16 | W. Layton | Superconvergence of finite element discretization of time relaxation models of advection | August 2006 | |

TR-MATH 06-17 | Y. Epshteyn and B. Riviere | Analysis of hp discontinuous Galerkin methods for incompressible two-phase flow | September 2006 | |

TR-MATH 06-18 | M. Neda and B. Riviere | Discontinuous finite elements for solving the Stolz-Adams approximate deconvolution model for turbulent flows | October 2006 | |

TR-MATH 06-19 | L. Rebholz | A family of new high order NS-alpha models arising from helicity correction in Leray turbulence models | November 2006 | |

TR-MATH 06-20 | J. Rubin and M. Wechselberger | Giant squid-hidden canard: the 3D geometry of the Hodkin-Huxley model | November 2006 | |

TR-MATH 06-21 | W. Layton, C. Manica, M. Neda, and L. Rebholz | Numerical analysis and computational testing of a high accuracy Leray-deconvolution model of turbulence | November 2006 |

### 2005

Report | Author(s) | Description | Link | Date |
---|---|---|---|---|

TR-MATH 05-01 | S. Kaya, W. Layton, and B. Riviere | Subgrid stabilized defect correction methods for the Navier-Stokes equations | February 2005 | |

TR-MATH 05-02 | V. John, S. Kaya, and W. Layton | A two-level variational multiscale method for convection-diffusion equations | February 2005 | |

TR-MATH 05-03 | W. Layton and R. Lewandowski | An exposition on the time-averaged accuracy of approximate de-convolution, large eddy simulation models of turbulence | February 2005 | |

TR-MATH 05-04 | J. Best, A. Borisyuk, J. Rubin, D. Terman, and M. Wechselberger | The dynamic range of bursting in a network of synaptically coupled square-wave bursting respiratory pacemaker cells | February 2005 | |

TR-MATH 05-05 | W. Layton and R. Lewandowski | Residual stress of approximate deconvolution models of turbulence | April 2005 | |

TR-MATH 05-06 | M.F. Wheeler and I. Yotov | A multipoint flux mixed finite element method | July 2005 | |

TR-MATH 05-07 | Y. Epshteyn and B. Riviere | Fully implicit discontinuous Galerkin schemes for multiphase flow | June 2005 | |

TR-MATH 05-08 | L. Truskinovsky and A. Vainchtein | Quasicontinuum models of dynamic phase transitions | July 2005 | |

TR-MATH 05-09 | L. Rebholz | A multiscale V-P discretization for flow problems | September 2005 | |

TR-MATH 05-10 | W. Klieber and B. Riviere | Adaptive simulations of two-phase flow by discontinuous Galerkin methods | October 2005 | |

TR-MATH 05-11 | L. Rebholz | Conservation laws of turbulence models | October 2005 | |

TR-MATH 05-12 | G. Pencheva | On some numerical convergence studies of mixed finite element methods for flow in porous media | November 2005 | |

TR-MATH 05-13 | K. Lipnikov, M. Shashkov, and I. Yotov | Local flux mimetic finite difference methods | November 2005 | |

TR-MATH 05-14 | I. Aavatsmark, G.T. Eigestad, R.A. Klausen, M.F. Wheeler, and I. Yotov | Convergence of a symmetric MPFA method on quadrilateral grids | November 2005 | |

TR-MATH 05-15 | W. Layton and M. Neda | Truncation of scales by time relaxation | November 2005 | |

TR-MATH 05-16 | J. Rubin and K. Josic | The firing of an excitable neuron in the presence of stochastic trains of strong synaptic inputs | November 2005 | |

TR-MATH 05-17 | G. Pencheva and I. Yotov | Changes in UTPRODJ3D: a three-dimension multiblock mixed-hybrid finite element code | November 2005 | |

TR-MATH 05-18 | T. Russel, M.F. Wheeler, and I. Yotov | Superconvergence for control-volume mixed finite element methods on rectangular grids | Nov. 2005 | |

TR-MATH 05-19 | M.F. Wheeler and I. Yotov | A cell-centered finite difference method on quadrilaterals | November 2005 |

### 2004

Report | Author(s) | Description | Link | Date |
---|---|---|---|---|

TR-MATH 04-01 | J. Rubin and A. Bose | Localized activity pattern in excitatory neuronal networks | February 2004 | |

TR-MATH 04-02 | B. Riviere | Numerical study of a discontinuous Galerkin method for incompressible two-phase flow | March 2004 | |

TR-MATH 04-03 | L. Truskinovsky and A. Vainchtein | Quasicontinuum modeling of short-wave instabilities in crystal lattices | April 2004 | |

TR-MATH 04-04 | K. Josic and J. Rubin | Deriving information about architecture from activity patterns in coupled cell systems | April 2004 | |

TR-MATH 04-05 | W. Layton and R. Lewandowski | On a well-posed turbulence model | August 2004 | |

TR-MATH 04-06 | S. Kaya and B. Riviere | A two-grid stabilization method for solving the steady-state Navier-Stokes equations | August 2004 | |

TR-MATH 04-07 | W. Layton and R. Lewandowski | Consistency and feasibility of approximate deconvolution models of turbulence | August 2004 | |

TR-MATH 04-08 | V. Girault, B. Riviere, and M. Wheeler | A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations | September 2004 | |

TR-MATH 04-09 | L. Truskinovsky and A. Vainchtein | Kinetics of martensitic phase transitions: lattice model | October 2004 |

### 2003

Report | Author(s) | Description | Link | Date |
---|---|---|---|---|

TR-MATH 03-01 | J. Su, J. Rubin, and D. Terman | Effects of noise on elliptic bursters | January 2003 | |

TR-MATH 03-02 | W. Layton | Model reduction by constraints, discretization of flow problems and an induced pressure stabilization | January 2003 | |

TR-MATH 03-03 | W. Layton | A mathematical introduction to large Eddy simulation | January 2003 | |

TR-MATH 03-04 | S. Kaya | Numerical analysis of a subgrid scale Eddy viscosity method for higher Reynolds number flow problems | January 2003 | |

TR-MATH 03-05 | S. Kaya and W. Layton | Subgrid-scale eddy viscosity methods are variational multiscale methods | January 2003 | |

TR-MATH 03-06 | V. John, W. Layton, and N. Sahin | Derivation and analysis of near wall models for channel and recirculating flows | February 2003 | |

TR-MATH 03-07 | L. Truskinovsky and A. Vainchtein | About the origin of the nucleation peak in transformational plasticity | April 2003 | |

TR-MATH 03-08 | B. Riviere and I. Yotov | Locally conservative coupling of Stokes and Darcy flows | May 2003 | |

TR-MATH 03-09 | M. Kaya | Existence of weak solutions for a scale-similarity model of the motion of large eddies in turbulent flow | July 2003 | |

TR-MATH 03-10 | J. Drover, J. Rubin, J. Su, and B. Ermentrout | Analysis of a canard mechanism by which excitatory synaptic coupling can synchronize neurons at low firing frequencies | July 2003 | |

TR-MATH 03-11 | B. Riviere | Analysis of a discontinuous finite element method for the coupled Stokes and Darcy problems | July 2003 | |

TR-MATH 03-12 | L. Truskinovsky and A. Vainchtein | Explicit kinetic relation from "first principles" | August 2003 | |

TR-MATH 03-13 | G.M. Constantine | On the partial orthogonality of faithful characters | August 2003 | |

TR-MATH 03-14 | S. Kaya and B. Riviere | Analysis of a discontinuous Galerkin and eddy viscosity method for Navier-Stokes | September 2003 | |

TR-MATH 03-15 | Y.B. Altundas and G. Caginalp | Computations of dendrites in 3-D and comparison with microgravity experiments | September 2003 | |

TR-MATH 03-16 | R.C. Read and E.G. Whitehead Jr. | A note on chain lengths and the Tutte polynomial | October 2003 | |

TR-MATH 03-17 | M. Anitescu, W.J. Layton, and F. Pahlevani | Implicit for local effects and explicit for nonlocal effects is unconditionally stable | October 2003 | |

TR-MATH 03-18 | A. Dunca and Y. Epshteyn | On the Adams-Stolz deconvolution LES models | October 2003 |

### 2002

Report | Author(s) | Description | Link | Date |
---|---|---|---|---|

TR-MATH 02-01 | P. Bastian and B. Riviere | Superconvergence and H(div) projection for discontinuous Galerkin methods | September 2002 | |

TR-MATH 02-02 | G. Pencheva and I. Yotov | Balancing domain decomposition for mortar mixed finite element methods | October 2002 | |

TR-MATH 02-03 | T.C. Hales | The honeycomb problem on the sphere | November 2002 | |

TR-MATH 02-04 | J. Gordon and T.C. Hales | Virtual transfer factors | November 2002 | |

TR-MATH 02-05 | A. Caglar | Weak imposition of boundary conditions for the Navier-Stokes equations | November 2002 | |

TR-MATH 02-06 | L. Truskinovsky and A. Vainchtein | Peierls-Nabarro landscape for martensitic phase transitions | December 2002 | |

TR-MATH 02-07 | T.C. Hales | Orbital integrals are motivic | December 2002 |

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