Technical Reports

(Names of students are listed in bold.)

2023

Report

 Author(s) Description Link

Date
TR-MATH 23-02 G. Sosa Jones and C. Trenchea Discrete energy balance equation via a symplectic second-order method for two-phase flow in porous media PDF October 2023
TR-MATH 23-01 M. Edwards, M. Bukač, and C. Trenchea

A second-order partitioned method for bioconvective flows with concentration dependent viscosity

 PDF June 2023

2022

Report Author(s) Description Link Date
TR-MATH 22-04 W. Layton, W. Pei and C. Trenchea Time step adaptivity in the method of Dahlquist, Liniger and Nevanlinna PDF September 2022
TR-MATH 22-03 F. Siddiqua and C. Trenchea

A second-order symplectic method for an advection-diffusion-reaction problem in bioseparation

PDF

 August 2022
TR-MATH 22-02 M. Bukač, G. Fu, A. Seboldt and C. Trenchea

Time-adaptive partitioned method for fluid-structure interaction problems with thick structures

 PDF April 2022
TR-MATH 22-01 A. Takhirov and C. Trenchea

Efficient nonlinear filter stabilizationof the Leray-alpha model

 PDF March 2022

2021

Report Author(s) Description Link Date
TR-MATH 21-01 M. Bukač and C. Trenchea Adaptive, second-order, unconditionally stable partitioned method for fluid-structure interaction PDF March 2021
TR-MATH 21-02 J. Burkardt, W. Pei, and C. Trenchea A stress test for the midpoint time-stepping method PDF September 2021
TR-MATH 21-03 W. Layton, W. Pei, and C. Trenchea Refactorization of a variable step, unconditionally stable method of Dahlquist, Liniger and Nevanlinna PDF October 2021
TR-MATH 21-04 A. Takhirov, C. Trenchea, and J. Waters

Second-order efficient nonlinear filter stabilization for high Reynolds number flows

PDF

 December 2021

2020

Report Author(s) Description Link Date
TR-MATH 20-03 M. Bukač, A. Seboldt and C. Trenchea Refactorization of Cauchy’s method: a second– order partitioned method for fluid–thick structure interaction problems PDF August 2020
TR-MATH 20-02 J. Burkardt and C. Trenchea Refactorization of the midpoint rule PDF January 2020
TR-MATH 20-01 W. Layton, W. Pei, Y. Qin and C. Trenchea Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow PDF January 2020

2018

Report Author(s) Description Link Date
TR-MATH 18-05
 Y. Rong, W. Layton and H. Zhao Extension of a simplified Baldwin-Lomax model of non-equilibrium turbulence: model, analysis and algorithms PDF December 2018
TR-MATH 18-04 M.Bukač and C. Trenchea
BOundary Update via Resolvent for fluid-structure interaction
 PDF October 2018
TR-MATH 18-03 F. Diele, M. Garvie and C. Trenchea Analysis of a second-order in time implicit-symplectic scheme for predator-prey systems PDF August 2018
TR-MATH 18-02
A. Guzel and W. Layton
 Analysis of the time filters on the implicit method increased accuracy and improved stability PDF January 2018
TR-MATH 18-01
O. Oyekole, M.Bukač and C. Trenchea
 A second-order in time approximation of fluid structure interaction problem  PDF  January 2018

2017

Report Author(s) Description Link Date

TR-MATH 17-02
A. Guzel and C. Trenchea
 The Williams step increases the stability and accuracy of the hoRA time filter PDF October 2017

TR-MATH 17-01
V. Ervin, M. Kubacki, W. Layton, M. Moraiti, Z. Si, C. Trenchea
 Partitioned penalty methods for the evolutionary Stokes-Darcy-transport problem  PDF  August 2017

2016

Report Author(s) Description Link Date

TR-MATH 16-03
Yong Li, Catalin Trenchea
 Existence and ergodicity for the two-dimensional Boussinesq equation  PDF December 2016
TR-MATH 16-04 Roxana Tanase, Catalin Trenchea, and Ivan Yotov Optimal Control of Systems Governed by PDEs with Random Parameter Fields


PDF

 April 2016

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

TR-MATH 16-02

   L. Liu, G. James, P. Kevrekidis, and A. Vainchtein Breathers in a locally resonant granular chain with precompression PDF March 2016

2015

Report Author(s) Description Link Date

TR-MATH 15-10

V.J. Ervin, M. Kubacki, W. Layton, M. Moraiti, Z. Si, C. Trenchea

 On limiting behavior of contaminant transport models in coupled surface and groundwater flows  PDF October 2015

TR-MATH 15-05

   L. Liu, G. James, P. Kevrekidis and A. Vainchtein Nonlinear waves in a strongly nonlinear resonant granular chain PDF 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 PDF May 2015

TR-MATH 15-03

 Y. Li and C. Trenchea  Partitioned second order method for magnetohydrodynamics in Elsasser fields PDF 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 PDF January 2015

TR-MATH 15-01

 Y. Li and C. Trenchea Analysis of time filters used with the leapfrog scheme PDF 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 PDF October 2014

TR-MATH 14-10

 L. Truskinovsky and A. Vainchtein Solitary waves in a non-integrable FPU chain PDF September 2014

TR-MATH 14-09

 N. Jiang, S. Kaya and W. Layton Analysis of Model Variance for Ensemble Based Turbulence Modeling PDF May 2014

TR-MATH 14-08

 N. Wilson, A. Labovsky, C. Trenchea High accuracy method for magnetohydrodynamics system in Elsasser variables PDF May 2014

TR-MATH 14-07

 W. Layton The 1877 Boussinesq Conjecture: Turbulent Fluctuations are Dissipative on the Mean Flow PDF March 2014
TR-MATH 14-06 W. Layton 2D Decaying Turbulence does not have Exponential Seperation of Trajectories PDF March 2014
TR-MATH 14-05 C. Brucato The Traveling Salesman Problem PDF 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 PDF January 2014
TR-MATH 14-03 N. Jiang A Higher Order Ensemble Simulation Algorithm for Fluid Flows PDF January 2014
TR-MATH 14-02 N. Jiang and H. Tran Analysis of a stabilized CNLF method with fast slow wave splittings for flow problems PDF January 2014
TR-MATH 14-01 Y. Li and P.D.Williams  Analysis of the RAW Filter in Composite-Tendency Leapfrog Integrations PDF 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 PDF January 2013
TR-MATH 13-02 W. Layton, H. Tran and C. Trenchea Numerical Analysis of two Partitioned Methods for Uncoupling Evolutionary MHD Flows PDF 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 PDF January 2013
TR-MATH 13-04 C. Lupu Mean value theorems of Flett type for a Volterra operator PDF February 2013
TR-MATH 13-05 L. Liu, A. Vainchtein, Y. Wang Kinetics of a Twinning Step PDF March 2013
TR-MATH 13-06 N. Jiang and W. Layton An Algorithm for Fast Calculation of Flow Ensembles PDF April 2013
TR-MATH 13-15 W. Layton and L.G. Rebholz

On Relaxation Times in the Navier-Stokes-Voigt Model

 PDF April 2013
TR-MATH 13-07

B. Espinoza, P. Gartside and A. Mametelashvili

 n-Arc Connected Spaces PDF May 2013
TR-MATH 13-08

S. P. Hastings and J. B McLeod 

 Uniqueness of Relaxation Oscillations: A Classical Approach  PDF June 2013
TR-MATH 13-09

N. Jiang and W. Layton

 Numerical Analysis of two Ensemble Eddy Viscosity Models of Fluid Motion PDF July 2013
TR-MATH 13-10

N. Hurl, W. Layton, Y. Li and M. Moraiti

The Unstable Mode in the Crank-Nicolson Leap-Frog Method is Stable

 PDF August 2013
TR-MATH 13-11

W. Layton and A. Takhirov

Energy Stability Of A First Order Partitioned Method For Systems With General Coupling

 

 PDF August 2013
TR-MATH 13-12

N. Jiang and W. Layton

Further Numerical Tests of Ensemble Eddy Viscosity Methods

 

 PDF August 2013
TR-MATH 13-13

W. Layton, A. Takhirov and M. Sussman

Instability of Crank-Nicolson Leap-Frog for Nonautonomous Systems

 PDF August 2013
TR-MATH 13-14

A. Takhirov

Exact Solution of the Stochastic Navier-Stokes Equations

 PDF August 2013
TR-MATH 13-15

N. Jiang, M. Kubacki, W. Layton, M. Moraiti and H. Tran

A Crank-Nicolson Leap-Frog stabilization:
unconditional stability and two applications

 PDF September 2013
TR-MATH 13-16

Y. Li and C. Trenchea 

A higher-order Robert-Asselin type time filter

 PDF September 2013
TR-MATH 13-17

M. Bukač, W. Layton, M. Moraiti, H. Tran and C. Trenchea 

Analysis of partitioned methods for Biot system

 PDF 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 PDF January 2012
TR-MATH 12-02

W. Layton

 Introduction to the Transfer theory of Turbulence PDF Januray 2012
TR-MATH 12-03 M. Moraiti On the Quasistatic Approximation in the Stokes-Darcy Model of
Groundwater-Surface Water Flows		 PDF March 2012
TR-MATH 12-04 C. Trenchea Stability of Partitioned Imex Methods for Systems of Evolution Equations with Skew-Symmetric Coupling PDF April 2012

TR-MATH 12-05

 

 C. Trenchea Unconditional Stability of a Partitioned Imex Method for Magnetohydrodynamic Flows PDF April 2012
TR-MATH 12-06

V. Girault, D. Vassilev and I. Yotov

 Mortar Multiscale Finite Element Methods for
Stokes-Darcy Flows		 PDF April 2012
TR-MATH 12-07 M. Kubacki Uncoupling Evolutionary Groundwater-Surface Water Flows Using the Crank-Nicolson Leapfrog Method PDF April 2012
TR-MATH 12-08 P. Rosakis and A. Vainchtein New Solutions for Slow Moving Kinks in a Forced Frenkel-Kontorova Chain PDF May 2012
TR-MATH 12-09 A. Jorgenson Unconditional Stability of a Crank-Nicolson Adams-Bashforth 2 Implicit-Explicit Numerical Method PDF May 2012
TR-MATH 12-10 C. Trenchea  Second Order Implicit for Local Effects and Explicit for Nonlocal Effects is Unconditionally Stable PDF May 2012
TR-MATH 12-11 W. Layton and A. Takhirov A Test of a Modular, Wall Adapted Nonlinear Filter Model for Underresolved Flows PDF June 2012
TR-MATH 12-8 C. Lupu and V. Matei  Arithmetic Functions, Prime Counting Function and Polynomials PDF July 2012
TR-MATH 12-14 N. Hurl Energy Stability of the Crank-Nicolson Leap
Frog Method with Time Filters		 PDF October 2012
TR-MATH 12-15 X. Xiong Analysis of a Multi-Rate Splitting Method for Uncoupling Evolutionary Groundwater-Surfacewater Flows PDF October 2012
TR-MATH 12-16 A. Takhirov Stokes-Brinkman Lagrange Multiplier/Fictitious Domain Method for Flows in Pebble Bed Geometries PDF 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 PDF 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 PDF 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 PDF 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 PDF 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 PDF 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		 PDF 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		 PDF 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		 PDF May 2011
TR-MATH 11-07 R. Ingram A New Linearly Extrapolated Crank-Nicolson Time-Stepping Scheme for the NSE PDF July 2011
TR-MATH 11-08 A. Vainchtein and P. G.  Kevrekidis Dynamics of phase transitions in a piecewise linear diatomic chain PDF 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		 PDF 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		 PDF 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 PDF 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 PDF 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 PDF January 2010

TR-MATH 10-03

 E. Manica, G. Medvedev and J. Rubin First Return Maps for the Dynamics of
Synaptically Coupled Conditional Bursters		 PDF January 2010
TR-MATH 10-04 H. Tran On the Estimates of Determining Modes for NS-alpha and
NS-omega Models		 PDF January 2010
TR-MATH 10-05 E. Trofimov and A. Vainchtein Shocks versus kinks in a discrete model of displacive phase transitions PDF 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		 PDF April 2010
TR-MATH 10-07 A. Labovschii and C. Trenchea Approximate Deconvolution Models for Magnetohydrodynamics PDF 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 PDF 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		 PDF July 2010
TR-MATH 10-10 W. Layton, L. Rebholz and C. Trenchea Modular Nonlinear Filter Stabilization of Methods for Higher Reynolds Numbers Flow PDF September 2010
TR-MATH 10-11

W. Layton,  M. Neda and K. Wyss

A Transfer Theory Analysis of Approximate Deconvolution Models of Turbulence

 PDF October 2010
TR-MATH 10-12 W. Layton, L. Roehe and H. Tran Explicitly Uncoupled VMS Stabilization of Fluid Flow PDF November 2010
TR-MATH 10-13 M. Sussman A Stability Examble PDF 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 PDF November 2010
TR-MATH 10-15 M. Wheeler, G. Xue and I. Yotov A Multiscale Mortar Multipoint Flux Mixed Finite Element Method PDF 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 PDF 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

 PDF 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 PDF January 2009
TR-MATH 09-02 X. Hu AND D. Wang Low Mach Number Limit of Viscous Compressible
Magnetohydrodynamic Flows		 PDF February 2009
TR-MATH 09-03 C. Manica and I. Stanculescu Numerical Analysis of Leray-Tikhonov Deconvolution Models
of Fluid Motion		 PDF 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 PDF February 2009
TR-MATH 09-05 B. Doubrov,
J. Holland and G. Sparling		 Space-time and G2 PDF February 2009
TR-MATH 09-06 A. Lozovskiy Numerical Analysis of the Semidiscrete Finite
Element Method for Computing the Noise
Generated by Turbulent Flows		 PDF 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		 PDF 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		 PDF 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		 PDF March 2009
TR-MATH 09-11 A. Vainchtein and E. Van Vleck Nucleation and propagation of phase mixtures in a bistable chain PDF March 2009
TR-MATH 09-12 B. Ganis and I. Yotov Implementation of a Mortar Mixed Finite Element Method using a Multiscale Flux Basis PDF March 2009
TR-MATH 09-13 B Layton and A Novoyny On Lighthill's acoustic analogy for low Mach number flows PDF 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

PDF
(sup)

 April 2009
TR-MATH 09-15 G. Chen, M. Slemrod and D. Wang Weak Continuity of the Gauss-Codazzi-Ricci System for Isometric Embedding PDF May 2009
TR-MATH 09-16 X. Hu and D. Wang Global Strong Solution to the Density-Dependent
Incompressible Viscoelastic Fluids		 PDF May 2009
TR-MATH 09-17 L. Truskinovsky and A. Vaninchtein Beyond Kinetic Relations PDF 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		 PDF May 2009
TR-MATH 09-19 A. Vainchtein The Role of Spinodal Region in the Kinetics of Lattice Phase Transitions PDF May 2009
TR-MATH 09-20 T. Stepien Tubuloglomerular Feedback-Mediated Dynamics in Three
Coupled Nephrons		 PDF May 2009
TR-MATH 09-21 S. Bayrama, T. Stepien, and E. Pitman TGF-Mediated Dynamics in a System of Many Coupled
Nephrons		 PDF May 2009
TR-MATH 09-22 R. Ingram A Mixed Finite Element Approximation of Stokes-Brinkman and NS-Brinkman Equation for Non-Darcian Flows PDF July 2009
TR-MATH 09-23 W. Layton and C. Trenchea The Das-Moser Commutator Closure for Filtering Through a Boundary is Well Posed PDF 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 PDF July 2009
TR-MATH 09-25 M. Garvie, P. Maini and C Trenchea A Methodology for Parameter Identification in
Turing Systems		 PDF August 2009
TR-MATH 09-26 M. F. Wheeler, T. Wildey, and I. Yotov A multiscale preconditioner for stochastic mortar mixed finite elements PDF August 2009
TR-MATH 09-27 W. Layton On Taylor/Eddy Solutions of Approximate Deconvolution Models of Turbulence PDF August 2009
TR-MATH 09-28 A. Vainchtein Effect of nonlinearity on the steady motion of a twinning dislocation PDF September 2009
TR-MATH 09-29 W. Layton, C. Pruett and L. Rebholz Temporally Regularized Direct Numerical
Simulation		 PDF October 2009
TR-MATH 09-30 W. Layton Fluid-Porous Interface Conditions with the "Inertia Term" 1/2 |UFLUID|2 are not Galilean Invariant PDF 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		 PDF 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		 PDF December 2009
TR-MATH 09-33 J. Dunmyre and J. Rubin Optimal Intrinsic Dynamics for Bursting in a Three-Cell Network PDF December 2009
TR-MATH 09-34 C. Frias Comparison of turbulence models using OPENFOAM

 

 PDF 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 PDF January 2008
TR-MATH 08-02 W. Layton and I. Stanculescu Chebychev optimized approximate deconvolution models of turbulence PDF 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 PDF January 2008
TR-MATH 08-04 X. Hu and D. Wang Global solutions to the three-dimensional full compressible magnetohydrodynamics flows PDF January 2008
TR-MATH 08-05 X. Hu and D. Wang Compactness of weak solutions to the three-dimensional compressible magnetohydrodynamics flows PDF 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:
I. Derivation of model and analysis of anti-inflammation

 PDF 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		 PDF February 2008
TR-MATH 08-08 K. Lipnikov, M. Shashkov, and I. Yotov Local flux mimetic finite difference methods PDF 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 PDF 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 PDF 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 PDF 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 PDF 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 PDF March 2008
TR-MATH 08-14 S. P. Hastings and J. B. McLeod An Elementary Approach to a Model Problem of
Lagerstrom		 PDF April 2008
TR-MATH 08-15 B. Ermentrout and S.P. Hastings Steady state analysis of a continuum model for super-infection. PDF 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 PDF April 2008
TR-MATH 08-17 A. Cesmelioglu and B. Riviere Analysis of Time-Dependent Navier-Stokes Flow Coupled with Darcy Flow PDF 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 PDF June 2008
TR-MATH 08-19 J. Connors and W. Layton On the Accuracy of the Finite Element Method Plus Time Relaxation PDF 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 PDF 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 PDF July 2008
TR-MATH 08-27 P. Gartside and Z. Feng Spaces with a Finite Family of Basic Functions PDF July 2008
TR-MATH 08-22 D. Vassilev and I. Yotov Coupling Stokes-Darcy Flow with Transport PDF August 2008
TR-MATH 08-23 R. Ingram, W. Layton and N. Mays Analysis of Iterated Tikhonov: Defect Correction for Ill-Posed Problems PDF 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		 PDF August 2008
TR-MATH 08-24 M. Garvie and C. Trenchea The Identification of Space Time Distributed Parameters in Reaction-Diffusion Systems PDF September 2008
TR-MATH 08-25 W. Layton Existence of Smooth Attractors for the
Navier-Stokes-Omega Model of Turbulence: Expanded Version		 PDF December 2008
TR-MATH 08-26 J. Conners, J. Howell and W. Layton Partitioned Timestepping For a Parabolic Two Domain Problem PDF 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 PDF January 2007
TR-MATH 07-02 W. Layton and I. Stanculescu K-41 optimized approximate deconvolution models PDF January 2007
TR-MATH 07-03 P. Lindqvist and J.J. Manfredi Viscosity supersolutions of the evolutionary p-Laplace equation PDF 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 PDF February 2007
TR-MATH 07-05 W. Layton A remark on regularity of an elliptic-elliptic singular perturbation problem PDF February 2007
TR-MATH 07-06 B. Lal Sharma and A. Vainchtein Quasistatic propagation of steps along a phase boundary PDF March 2007
TR-MATH 07-07 Y. Zhen and A. Vainchtein Dynamics of steps along a martensitic phase boundary I: semi-analytical solution PDF March 2007
TR-MATH 07-08 Y. Zhen and A. Vainchtein Dynamics of steps along a martensitic phase boundary II: numerical simulations PDF 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 PDF March 2007
TR-MATH 07-10 S. Chanillo and J. J. Manfredi Sharp global bounds for the Hessian on pseudo-hermitian manifolds PDF April
2007
TR-MATH 07-11 A. Borisov, M. Dickinson and S. Hastings A congruence problem for polyhedra PDF April
2007
TR-MATH 07-12 S. Hastings, D. Kinderlehrer, J.B. McLeod Diffusion mediated transport in multiple state systems PDF April
2007
TR-MATH 07-21 P. Gartside and Z. Feng More stratifiable function spaces PDF April 2007
TR-MATH 07-22 Z. Feng and R. Heath Metrizability of Topological Semigroups on Linearly Ordered Topological Spaces PDF 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 PDF August 2007
TR-MATH 07-14 A. Labovschii A Defect Correction Method for the Time-Dependent Navier-Stokes Equations PDF 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 PDF August 2007
TR-MATH 07-16 A. Labovschii, C. Trenchea Large Eddy Simulation for MHD Flows PDF August 2007
TR-MATH 07-17

I. Stanculescu

 

 Existence Theory of Abstract Approximate Deconvolution Models of Turbulence PDF August 2007
TR-MATH 07-18

A. Labovschii,
W. Layton, C. Manica, M. Neda, L. Rebholz,
I. Stanculescu, C. Trenchea

 Mathematical Architecture of Approximate Deconvolution Models of Turbulence PDF September 2007
TR-MATH 07-19 L. Truskinovsky, A. Vainchtein Dynamics of martensitic phase boundaries: discreteness,
dissipation and inertia		 PDF October 2007
TR-MATH 07-20 A. Labovschii A Defect Correction Method for the Evolutionary
Convection Diffusion Problem with Increased Time Accuracy		 PDF October 2007

2006

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TR-MATH 06-01 Y. Epshteyn, T. Khan, and B. Riviere Inverse problem in optical tomography using discontinuous Galerkin method PDF January 2006
TR-MATH 06-02 L. Rebholz An energy and helicity conserving finite element scheme for the Navier-Stokes equations PDF January 2006
TR-MATH 06-03 J. Rubin and A. Bose The geometry of neuronal recruitment PDF 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 PDF February 2006
TR-MATH 06-05 Y. Epshteyn and B. Riviere Symmetric interior penalty Galerkin methods for elliptic problems PDF February 2006
TR-MATH 06-06 V. Ervin, W. Layton, and M. Neda Numerical analysis of a higher order time relaxation model of fluids PDF 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 PDF April 2006
TR-MATH 06-08 J. Rubin Bursting induced by excitatory synaptic coupling in non-identical conditional relaxation oscillators or square-wave bursters PDF April 2006
TR-MATH 06-09 W. Layton and M. Neda A similarity theory of approximate deconvolution models of turbulence PDF 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 PDF May 2006
TR-MATH 06-11 C. Manica and S. Kaya Merdan New discretizations of turbulent flow problems PDF 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 PDF May 2006
TR-MATH 06-13 W. Layton Bounds on energy and helicity dissipation rates of approximate deconvolution models of turbulence PDF June 2006
TR-MATH 06-14 P. Lindqvist and J. Manfredi Note on a remarkable superposition for a nonlinear equation PDF July 2006
TR-MATH 06-15 T. Arbogast, G. Pencheva, M.F. Wheeler, and I. Yotov A multiscale mortar mixed finite element method PDF July 2006
TR-MATH 06-16 W. Layton Superconvergence of finite element discretization of time relaxation models of advection PDF August 2006
TR-MATH 06-17 Y. Epshteyn and B. Riviere Analysis of hp discontinuous Galerkin methods for incompressible two-phase flow PDF 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 PDF 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 PDF November 2006
TR-MATH 06-20 J. Rubin and M. Wechselberger Giant squid-hidden canard: the 3D geometry of the Hodkin-Huxley model PDF 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 PDF November 2006

2005

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TR-MATH 05-01 S. Kaya, W. Layton, and B. Riviere Subgrid stabilized defect correction methods for the Navier-Stokes equations PDF February 2005
TR-MATH 05-02 V. John, S. Kaya, and W. Layton A two-level variational multiscale method for convection-diffusion equations PDF 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 PDF 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 PDF February 2005
TR-MATH 05-05 W. Layton and R. Lewandowski Residual stress of approximate deconvolution models of turbulence PDF April 2005
TR-MATH 05-06 M.F. Wheeler and I. Yotov A multipoint flux mixed finite element method PDF July 2005
TR-MATH 05-07 Y. Epshteyn and B. Riviere Fully implicit discontinuous Galerkin schemes for multiphase flow PDF June 2005
TR-MATH 05-08 L. Truskinovsky and A. Vainchtein Quasicontinuum models of dynamic phase transitions PDF July 2005
TR-MATH 05-09 L. Rebholz A multiscale V-P discretization for flow problems PDF September 2005
TR-MATH 05-10 W. Klieber and B. Riviere Adaptive simulations of two-phase flow by discontinuous Galerkin methods PDF October 2005
TR-MATH 05-11 L. Rebholz Conservation laws of turbulence models PDF October 2005
TR-MATH 05-12 G. Pencheva On some numerical convergence studies of mixed finite element methods for flow in porous media PDF November 2005
TR-MATH 05-13 K. Lipnikov, M. Shashkov, and I. Yotov Local flux mimetic finite difference methods PDF 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 PDF November 2005
TR-MATH 05-15 W. Layton and M. Neda Truncation of scales by time relaxation PDF 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 PDF November 2005
TR-MATH 05-17 G. Pencheva and I. Yotov Changes in UTPRODJ3D: a three-dimension multiblock mixed-hybrid finite element code PDF 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 PDF Nov. 2005
TR-MATH 05-19 M.F. Wheeler and I. Yotov A cell-centered finite difference method on quadrilaterals PDF November 2005

2004

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TR-MATH 04-01 J. Rubin and A. Bose Localized activity pattern in excitatory neuronal networks PDF February 2004
TR-MATH 04-02 B. Riviere Numerical study of a discontinuous Galerkin method for incompressible two-phase flow PDF March 2004
TR-MATH 04-03 L. Truskinovsky and A. Vainchtein Quasicontinuum modeling of short-wave instabilities in crystal lattices PDF April 2004
TR-MATH 04-04 K. Josic and J. Rubin Deriving information about architecture from activity patterns in coupled cell systems PDF April 2004
TR-MATH 04-05 W. Layton and R. Lewandowski On a well-posed turbulence model PDF August 2004
TR-MATH 04-06 S. Kaya and B. Riviere A two-grid stabilization method for solving the steady-state Navier-Stokes equations PDF August 2004
TR-MATH 04-07 W. Layton and R. Lewandowski Consistency and feasibility of approximate deconvolution models of turbulence PDF 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 PDF September 2004
TR-MATH 04-09 L. Truskinovsky and A. Vainchtein Kinetics of martensitic phase transitions: lattice model PDF October 2004

2003

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TR-MATH 03-01 J. Su, J. Rubin, and D. Terman Effects of noise on elliptic bursters PDF January 2003
TR-MATH 03-02 W. Layton Model reduction by constraints, discretization of flow problems and an induced pressure stabilization PDF January 2003
TR-MATH 03-03 W. Layton A mathematical introduction to large Eddy simulation PDF January 2003
TR-MATH 03-04 S. Kaya Numerical analysis of a subgrid scale Eddy viscosity method for higher Reynolds number flow problems PDF January 2003
TR-MATH 03-05 S. Kaya and W. Layton Subgrid-scale eddy viscosity methods are variational multiscale methods PDF 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 PDF February 2003
TR-MATH 03-07 L. Truskinovsky and A. Vainchtein About the origin of the nucleation peak in transformational plasticity PDF April 2003
TR-MATH 03-08 B. Riviere and I. Yotov Locally conservative coupling of Stokes and Darcy flows PDF 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 PDF 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 PDF July 2003
TR-MATH 03-11 B. Riviere Analysis of a discontinuous finite element method for the coupled Stokes and Darcy problems PDF July 2003
TR-MATH 03-12 L. Truskinovsky and A. Vainchtein Explicit kinetic relation from "first principles" PDF August 2003
TR-MATH 03-13 G.M. Constantine On the partial orthogonality of faithful characters PDF August 2003
TR-MATH 03-14 S. Kaya and B. Riviere Analysis of a discontinuous Galerkin and eddy viscosity method for Navier-Stokes PDF September 2003
TR-MATH 03-15 Y.B. Altundas and G. Caginalp Computations of dendrites in 3-D and comparison with microgravity experiments PDF September 2003
TR-MATH 03-16 R.C. Read and E.G. Whitehead Jr. A note on chain lengths and the Tutte polynomial PDF 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 PDF October 2003
TR-MATH 03-18 A. Dunca and Y. Epshteyn On the Adams-Stolz deconvolution LES models PDF October 2003

2002

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TR-MATH 02-01 P. Bastian and B. Riviere Superconvergence and H(div) projection for discontinuous Galerkin methods PDF September 2002
TR-MATH 02-02 G. Pencheva and I. Yotov Balancing domain decomposition for mortar mixed finite element methods PDF October 2002
TR-MATH 02-03 T.C. Hales The honeycomb problem on the sphere PDF November 2002
TR-MATH 02-04 J. Gordon and T.C. Hales Virtual transfer factors PDF November 2002
TR-MATH 02-05 A. Caglar Weak imposition of boundary conditions for the Navier-Stokes equations PDF November 2002
TR-MATH 02-06 L. Truskinovsky and A. Vainchtein Peierls-Nabarro landscape for martensitic phase transitions PDF December 2002
TR-MATH 02-07 T.C. Hales Orbital integrals are motivic PDF December 2002
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TR-MATH 21-01 M. Bukač and C. Trenchea Adaptive, second-order, unconditionally stable partitioned method for fluid-structure interaction PDF March 2021
TR-MATH 21-02 J. Burkardt, W. Pei, and C. Trenchea A stress test for the midpoint time-stepping method PDF September 2021
TR-MATH 21-03 W. Layton, W. Pei, and C. Trenchea Refactorization of a variable step, unconditionally stable method of Dahlquist, Liniger and Nevanlinna PDF October 2021
TR-MATH 21-04 A. Takhirov, C. Trenchea, and J. Waters

Second-order efficient nonlinear filter stabilization for high Reynolds number flows

PDF

 December 2021