This collection contains selected publications and research by WPI Mathematical Sciences faculty.

WPI faculty can submit their publications and research to be archived in Digital WPI by emailing digitalwpi@wpi.edu.

#### Submissions from 2017

Conformality and Q-harmonicity in sub-Riemannian manifolds, Luca Capogna, Giovanna Citti, Enrico Le Donne, and Alessandro Ottazzi

Conformal equivalence of visual metrics in pseudoconvex domains, Luca Capogna and Enrico Le Donne

Strong Comparison Principle for $p-$harmonic functions in Carnot-Caratheodory spaces, Luca Capogna and Xiaodan Zhou

#### Submissions from 2016

Regularity for subelliptic PDE through uniform estimates in multi-scale geometries, Luca Capogna and Giovanna Citti

Smoothness of subRiemannian isometries, Luca Capogna and Enrico Le Donne

#### Submissions from 2015

Regularity of mean curvature flow of graphs on Lie groups free up to step 2, Luca Capogna, Giovanna Citti, and Maria Manfredini

#### Submissions from 2014

Harnack estimates for degenerate parabolic equations modeled on the subelliptic p-Laplacian, Benny Avelin, Luca Capogna, Giovanna Citti, and Kaj Nystrom

L ∞-Extremal Mappings in AMLE and Teichmüller Theory, Luca Capogna

#### Submissions from 2013

Sub-Riemannian heat kernels and mean curvature flow of graphs, Luca Capogna, Giovanna Citti, and Cosimo Magnani

Uniform Gaussian bounds for subelliptic heat kernels and an application to the total variation flow of graphs over Carnot groups, Luca Capogna, Giovanna Citti, and Maria Manfredini

A subelliptic analogue of Aronson-Serrin’s Harnack inequality, Luca Capogna, Giovanna Citti, and Garrett Rea

Portfolio Optimization under Convex Incentive Schemes, Stephan Sturm and Maxim Bichuch

#### Submissions from 2012

An Aronsson type approach to extremal quasiconformal mappings, Luca Capogna and Andrew Raich

From Smile Asymptotics to Market Risk Measures, Stephan Sturm and Ronnie Sircar

Geometry-Driven Charge Accumulation in Electrokinetic Flows Between Thin, Closely Spaced Laminates, Burt S. Tilley, Bogdan M. Vernescu, and J. D. Plummer

#### Submissions from 2011

On refined volatility smile expansion in the Heston model, Peter K. Friz, Stefan Gerhold, Archil Gulisashvili, and Stephan Sturm

Arbitrage-Free Models in Markets with Transaction Costs, Hasanjan Sayit and Frederi Viens

Is the Minimum Value of an Option on Variance Generated by Local Volatility?, Stephan Sturm, Mathias Beiglöck, and Peter K. Friz

Impact of Flow Rates in a Cardiac Cycle on Correlations Between Advanced Human Carotid Plaque Progression and Mechanical Flow Shear Stress and Plaque Wall Stress, Chun Yang, Gador Canton, Chun Yuan, Marina Ferguson, Thomas S. Hatsukami, and Dalin Tang

#### Submissions from 2010

Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups Hn, n > 1, Luca Capogna, Giovanna Citti, and Maria Manfredini

Convexity and horizontal second fundamental forms for hypersurfaces in Carnot groups, Luca Capogna, Scott Pauls, and Jeremy Tyson

Intraplaque Hemorrhage is Associated with Higher Structural Stresses in Human Atherosclerotic Plaques: An In Vivo MRI-Based 3D Fluid-Structure Interaction Study, Xueying Huang, Zongzhao Teng, Gador Canton, Marina Ferguson, Chun Yuan, and Dalin Tong

Assessing Local Turbulence Strength from a Time Series, Mayer Humi

The Effect of Shear on the Generation of Gravity Waves, Mayer Humi

On the Equivalence Between Real Mutually Unbiased Bases and a Certain Class of Association Schemes, Nicholas LeCompte, William J. Martin, and William Owens

Analysis of Block Parareal Preconditioners for Parabolic Optimal Control Problems, Tarek P. Mathew, Marcus Sarkis, and C. E. Schaerer

#### Submissions from 2009

Generalized mean curvature flow in Carnot groups, Luca Capogna and Giovanna Citti

Regularity of non-characteristic minimal graphs in the Heisenberg group H1, Luca Capogna, Giovanna Citti, and Maria Manfredini

Existence of Traveling Domain Solutions for a Two-Dimensional Moving Boundary Problem, Y. S. Choi and Roger Lui

Vector-Space Methods and Kirchhoff Graphs for Reaction Networks, Joseph D. Fehribach

Approximating Infinity-Dimensional Stochastic Darcy's Equations without Uniform Ellipticity, J. Galvis and Marcus Sarkis

No Arbitrage without Semimartingales, Robert A. Jarrow, Philip Protter, and Hasanjan Sayit

Local Critical Stress Correlates Better Than Global Maximum Stress with Plaque Morphological Features Linked to Atherosclerotic Plaque Vulnerability: An In Vivo Multi-Patient Study, Dalin Tang, Zongzhao Teng, Gador Canton, Thomas Hatsukami, Li Dong, Xueying Huang, and Chun Yuan

A Double Layer Surface Traction Free Green's Tensor, Darko Volkov

#### Submissions from 2008

On Using Approximate Finite Differences in Matrix-Free Newton-Krylov Methods, Peter N. Brown, Homer F. Walker, Rebecca Wasyk, and Carol S. Woodward

Mutual Absolute Continuity of Harmonic and Surface Measures for Hormander Type Operators, Luca Capogna, Nicola Garofalo, and Duy-Minh Nhieu

Long's Equation in Terrain Following Coordinates, Mayer Humi

The mixed problem in Lp for some two-dimensional Lipschitz domains, Loredana Lanzani, Luca Capogna, and Russell Brown

Inexact Newton Dogleg Methods, Roger P. Pawlowski, Joseph P. Simonis, Homer F. Walker, and John N. Shadid

Exploring the Control Circuit of Cell Migration by Mathematical Modeling, Javier Satulovsky, Roger Lui, and Yu-li Wang

Convergence Analysis for the Numerical Boundary Corrector for Elliptic Equations with Rapidly Oscillating Coefficients, Henrique Versieux and Marcus Sarkis

#### Submissions from 2007

Isoperimetric inequalities in the Heisenberg group and in the plane, Luca Capogna

Linearized Stability of Traveling Cell Solutions Arising from a Moving Boundary Problem, Y. S. Choi and Roger Lui

Density Representation of Long's Equation, Mayer Humi

Uniqueness of Complex Permittivity Reconstruction in a Parallel-Plane Waveguide, Y. V. Shestopalov and Vadim V. Yakovlev

Guided Modes in Periodic Slabs: Existence and Nonexistence, Stephen Shipman and Darko Volkov

Anderson Acceleration for Fixed-Point Iterations, Homer F. Walker and Peng Ni

#### Submissions from 2006

Ahlfors type estimates for perimeter measures in Carnot-Carathéodory spaces, Luca Capogna and Nicola Garofalo

On the Solution of Long's Equation with Shear, Mayer Humi

Steady States of Self-Gravitating Incompressible Fluid in Two Dimensions, Mayer Humi

Globalization Techniques for Newton-Krylov Methods and Applications to the Fully Coupled Solution of the Navier-Stokes Equations, Roger P. Pawlowski, John N. Shadid, Joseph P. Simonis, and Homer F. Walker

Stochastic Galerkin Method for Elliptic Spdes: A White Noise Approach, Luis J. Roman and Marcus Sarkis

Permeability Hysteresis in Gravity Counterflow Segregation, C. E. Schaerer, Marcus Sarkis, D. Marchiesin, and P. Bedrikovetsky

#### Submissions from 2005

Darboux Transformations for Schrodinger Equations in Two Variables, Mayer Humi

#### Submissions from 2004

Estimation of the Atmospheric Structure Constants from Airplane Data, Mayer Humi

Simultaneous Concentration Bands for Continuous Random Samples, Balgobin Nandram and Jai Won Choi

#### Submissions from 2003

Restricted Additive Schwarz Preconditioners with Harmonic Overlap for Symmetric Positive Definite Linear Systems, Xiao-Chuan Cai, Maksymilian Dryja, and Marcus Sarkis

Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type, Luca Capogna and Nicola Garofalo

Using Numerical Experiments to Discover Theorems in Differential Equations, Joseph D. Fehribach

#### Submissions from 2001

Diffusion-Reaction-Conduction Processes in Porous Electrodes: The Electrolyte Wedge Problem, Joseph D. Fehribach

Estimates for Polarization Losses in Molten Carbonate Fuel Cell Cathodes, Joseph D. Fehribach and Kas Hemmes

#### Submissions from 2000

Maximum Norm Analysis of Overlapping Nonmatching Grid Discretizations of Elliptic Equations, Xiao-Chuan Cai, Tarek P. Mathew, and Marcus Sarkis

On the Representation of Effective Energy Densities, Christopher J. Larsen

A Free Moving Boundary Model and Boundary Iteration Method for Unsteady Viscous Flow in Stenotic Elastic Tubes, Dalin Tang and Jun Yang

#### Submissions from 1999

Overlapping Nonmatching Grid Mortar Element Methods for Elliptic Problems, Xiao-Chuan Cai, Maksymilian Dryja, and Marcus Sarkis

A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems, Xiao-Chuan Cai and Marcus Sarkis

An Empirical Bayes Prediction Interval for the Finite Population Mean of a Small Area, Balgobin Nandram

Constraining Plane Configurations in Computer-Aided Design: Combinatorics of Directions and Lengths, Brigitte Servatius and Walter Whiteley

An Adaptation of Krylov Subspace Methods to Path Following Problems, Homer F. Walker

#### Submissions from 1997

An Integro-Differential Equation Arising from an Electrochemistry Model, Y. S. Choi and Roger Lui

#### Submissions from 1996

Critical Radius, Size Effects and Inverse Problems for Composites with Imperfect Interface, Robert Lipton and Bogdan M. Vernescu

A Three-Phase Homogeneous Model for Porous Electrodes in Molten-Carbonate Fuel Cells, J. A. Prins-Jansen, Joseph D. Fehribach, Kas Hemmes, and J. H. W. de Wit

#### Submissions from 1994

Existence and Stability of Traveling-Wave Solutions for a Population Genetic Model via Singular Perturbations, Jack D. Dockery and Roger Lui

Homogenization of 2-Phase Emulsions, Robert Lipton and Bogdan M. Vernescu

#### Submissions from 1993

Analysis and Application of a Continuation Method for a Self-Similar Coupled Stefan System, Joseph D. Fehribach

Numerical and Asymptotic Solutions for Peristaltic Motion of Nonlinear Viscous Flows with Elastic Free Boundaries, Dalin Tang and Samuel Rankin

#### Submissions from 1992

Existence of Traveling-Wave Solutions for a Bistable Evolutionary Ecology Model, Jack D. Dockery and Roger Lui

Rotating Chemical Waves in the Gray-Scott Model, William W. Farr and M. Golubitsky

#### Submissions from 1990

An Analysis of Polarization Mixing Errors in Distance Measuring Interferometers, Walter Augustyn and Paul Davis

Optimal Large Eddy Simulation in One Dimension, Mayer Humi

Existence and Stability of Traveling-Wave Solutions for an Evolutionary Ecology Model, Roger Lui

The Extension of Optimization Problems Containing Controls in the Coefficients, Konstantin A. Lurie

#### Submissions from 1989

Asymptotic Behavior of Solutions to An Evolutionary Ecology Model with Diffusion, Roger Lui

Surface Subgroups of Graph Groups, Herman J. Servatius, Carl Droms, and Brigitte Servatius

#### Submissions from 1987

Finite-Dimensional Lorentz Covariant Bifurcations, Mayer Humi

Representations and Invariant Equations of E(3), Mayer Humi

#### Submissions from 1986

Factorization of Systems of Differential-Equations, Mayer Humi

A Nonlinear Integral Operator Arising from a Model in Population-Genetics .4. Clines, Roger Lui

#### Submissions from 1985

Summary Abstract - Quantitative Phase-Analysis of Partially Stabilized Zirconia-8.5-Percent Yttria by a Random Fitting Least Chi-Squared Method, Ichiro Sone, Richard D. Sisson Jr., and Ronald R. Biederman

#### Submissions from 1984

Interior Solutions to Einstein-Maxwell-Equations in Spherical and Plane Symmetry When p=np, Mayer Humi and J. Mansour

#### Submissions from 1983

The Group of Automorphisms of a Distributively Generated Near Ring, J. J. Malone

#### Submissions from 1980

A Non-Abelian 2-Group Whose Endomorphisms Generate a Ring, and other Examples of E-Groups, J. J. Malone

On a Best Choice Problem with Partial Information, Joseph D. Petruccelli