Renormalization Group Methods

Nonlinear stability of oscillatory pulses in the parametric nonlinear Schrodinger equation, with P.A.C. Chang, submitted to Nonlinearity August 2006.
Nonlinear asymptotic stability of the semi-strong pulse dynamics in a regularized Gierer-Meinhardt model, to appear in SIAM Math. Analysis , with A. Doelman and T. Kapper.
Renormalization group reduction of pulse dynamics in thermally loaded optical parametric oscillators, Physica D 206 (2005) 62-81, with R. Moore.
Copy and Paste: doi:10.1016/j.physd.2005.04.015
A renormalization method for modulational stability of quasi-steady patterns in dispersive systems , SIAM J. Math. Analysis 33 No. 6 (2002), 1455-1482.
Bifurcation and Asymptotic Stability in the Large Detuning Limit of the Optical Parametric Oscillator, Nonlinearity 13 (2000), 675-698, with J. Nathan Kutz

PEM Fuel Cells

The impact of membrane constraint on PEM fuel cell water management, with I. Nazarov, submitted to J. Electrochem. Soc.
Reduced dimensional computational models of polymer electrolyte membrane fuel cell stacks , to appear in J. Comp. Physics , with P.A.C. Chang, G.S. Kim, and B. Wetton
The effects of water and microstructure on the performance of polymer electrolyte fuel cells, J. Power Sources , 160 2006, 1251-1268, with A. Shah, G.S Kim, W. Gervais, A. Young, J. Li, and S. Ye
Analysis of a Dry 1D Catalyst layer model for a Polymer Electrolyte Fuel Cell, Chemical Engineering Science 61 (13) (2006), 4316-4331, with P. Berg and A. Novruzi. Copy and Paste: doi:10.1016/j.ces.2006.01.033
A Sharp Interface Reduction for Multiphase flow in a Porous PEM Fuel Cell Electrode, Proc. Roy. Soc. London: Series A 462 (2006), 789-816. with J. Stockie and B. Wetton.
Electrical coupling in Proton Exchange Membrane fuel cell stacks: mathematical and computational modelling, IMA J. Applied Math. 71 (2006) 241-261, with P. Berg, A. Calgar, J. St. Pierre, and B. Wetton.
Ignition Bifurcations in a Stirred Tank PEM Fuel Cell, Chemical Engineering Science 61 (2006) 3198-3209, with I. Nazarov.
Copy and paste: doi:10.1016/j.ces.2005.11.068
A Simple Mathematical Model of Thermal Coupling in Fuel Cell Stacks, Journal Power Sources , 150 (2005) 129-135, with B. Wetton.
Electrical Coupling in Proton Exchange Membrane Fuel Cell Stacks, Journal of Power Sources, 152 (2005) 210-217, with G.S. Kim, J. St. Pierre, and B. Wetton.
Discharge of a Segmented Polymer Electrolyte Membrane Fuel Cell, Journal of Fuel Cell Science and Technology 2 (May 2005), 111-120, with P. Berg, J. Stumper, and B. Wetton.
Water management in PEM fuel cells, J. Electrochem. Soc. 151 (No. 3) (2004) A341-A354, with P. Berg, J. St. Pierre, J. Stumper, and B. Wetton.
A Computational Study of Multicomponent Gas Transport in a Porous Fuel Cell Electrode, International J. Numerical Methods in Fluids, 41, (2003), 577-599, with J. Stockie and B. Wetton.
Transport phenomena in the porous cathode of a proton exchange membrane fuel cell, Numerical Heat Transfer, Part A, 42 (2002) 1-18, with R. Bradean and B. Wetton.
Adiabatic Relaxation of Convective-Diffusive Gas Transport in a Porous Fuel Cell Electrode, SIAM J. Appl. Math. 62 No. 1 (2001), 180-205, with J. Stockie.

Nonlinear Optics and Nonlinear Waves

Localized breathing solutions for Bose-Einstein condensates in periodic traps, Phys. Rev. A. 66 Sept 033610 (2002), with R. Carretero-Gonzalez.
Stability of Attractive Bose-Einstein Condensates in a Periodic Potential, Phys. Rev. E 64 Nov. 056615 (2001), with J. Bronski, L. Carr, R. Carretero-Gonzalez, B. Deconinck, J. Kutz.
Repulsive Bose-Einstein condensate in Period Potentials: Wells Barriers, and Standing Waves, Phys. Rev. E 63 Mar. 036612 (2001), with J. Bronski, L. Carr, B. Deconinck, J. Kutz.
The Mechanism of the Polarizational Mode Instability in Birefringent Fiber Optics, SIAM Journal on Math. Anal., 31 (2000), 1351-1373, with Yi A. Li.
Structural Stability of non-ground state traveling wave of a Nonlinear Schr\"odinger System, Physica D 137 (1998), 137-165, with Yi A. Li.
Fourier Splitting and Dissipation of Nonlinear Dispersive Waves, Proc. Roy. Soc. Edingburg, Series A , 129 (1999), 477-502, with J. Bona and F. Demengel.
Higher Order Asymptotics of Decay for Nonlinear, Dispersive, Dissipative Waves, Nonlinearity 37 (1994) 265-277, with J. Bona and Gene Wayne.
On the Asymptotic Behavior of Solutions to Nonlinear, Dispersive, Dissipative Wave Equations, J. Math and Comput. in Simul. 37, (1994) 265-277, with J. Bona and Gene Wayne.