Functionalized Cahn-Hillard

Analysis

Competitive Geometric Evolution of Amphiphilic Interfaces, S. Dai and K. Promislow, submitted 2013.
Meander and Pearling of Single-Curvature Bilayer interfaces, A. Doelman, G. Hayrapetyan, K. Promislow, and B. Wetton, submitted 2013.
Spectra of Functionalized Operators arising from hypersurfaces, G. Hayrapetyan and K. Promislow submitted 2013.
Existence of compressible bilayers in the functionalized Cahn-Hilliard equation, K. Promislow and L. Yi, submitted 2013.
Geometric Evolution of Bilayers under the Functionalized Cahn-Hilliard equation, S. Dai and K. Promislow Proc. Roy. Soc. London, Series A 469 20120505, 2013.
Critical points of Functionalized Lagrangians, H. Zhang and K. Promislow Discrete and Continuous Dynamical Systems, A 33 1-16, 2013.
Curvature driven flow of bi-layer interfaces, N. Gavish, G. Hayrapetyan, K. Promislow, L. Yang, Physica D 240 675-693, 2011.

Modeling, Numerical, and Experimental Results

High accuracy solutions to energy gradient flows from material science models A. Christlieb, J. Jones, K. Promislow, B. Wetton, and M. Willoughby, submitted 2013.
Variational Models of Pore Networks in Ionomer Membranes: the Role of Electrostatics K. Promislow, J. Jones, Z. Xu, N. Gavish, A. Christlieb, Electrochemical Society Transactions, A 50 161-173, 2013.
Variational Models of Network Formation and Ion Transport: Applications to Perfluorosulfonate Ionomer Membranes, N.Gavish, J. Jones, Z. Xu, A. Christlieb, K. Promislow, Polymers 4 630-655, 2012.
PEM fuel cells: A Mathematical Overview K. Promislow and B. Wetton, SIAM Applied Math. 70 369-409, 2009.
Spatial and Temporal Mapping of Water Content across Nafion Membranes under Wetting and Drying Conditions, Z. Zhang, A. Marble, B. MacMillian, K. Promislow, J. Martin, H. Wang, B. Balcom, J. Magnetic Resonance 194 245-253, 2008.

Renormalization Group Methods

Adiabatic Stability of Semi-Strong Interactions in an Activator-Inhibitor system: The Weakly Damped Regime, T. Bellksy, A. Doelman, T. Kaper, K. Promislow, Indiana U. Math. Journal to appear.
Front interactions in a three-component system P. van Heijster, A. Doelman, T. Kapper, and K. Promislow, SIAM J. Applied Dynamical Systems 9 2010.
The semi-strong limit of multipulse interaction in a thermally driven optical system, R. Moore and K. Promislow J. Diff. Eqns. 245 1616-1655, 2008.
Nonlinear stability of oscillatory pulses in the parametric nonlinear Schrodinger equation, P.A.C. Chang and K. Promislow Nonlinearity 20 743-763, 2007.
Nonlinear asymptotic stability of the semi-strong pulse dynamics in a regularized Gierer-Meinhardt model, A. Doelman and T. Kapper, SIAM Math. Analysis , 38 1760-1787, 2007
Renormalization group reduction of pulse dynamics in thermally loaded optical parametric oscillators, Physica D 206 (2005) 62-81, with R. Moore.
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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 Cell Device Level Models

A simple, analytic model of polymer electrolyte membrane fuel cell anode recirculation at operating power including nitrogen crossover, K. Promislow, J. St. Pierre, B. Wetton, J. Power Sources 196 10050-10056, 2011.
Bi-modal water transport behavior across a simple Nafion membrane, Z. Zhang, K. Promislow, J. Martin, H. Wang, B. J. Balcom, J. Power Sources 196 8525-8530, 2011.
A Two Phase Unit Cell Model for Slow Transients in Polymer Electrolyte Membrane Fuel Cells K. Promislow, P. Chang, H. Haas, and B. Wetton, J. Electrochem. Soc. 155 A494-504, 2008.
The impact of membrane constraint on PEM fuel cell water management, I. Nazarov and K. Promislow, J. Electrochem. Soc. 154 B623-630 2007.
Reduced dimensional computational models of polymer electrolyte membrane fuel cell stacks , P.A.C. Chang, G.S. Kim, K. Promislow, and B. Wetton J. Comp. Physics 223> 797-821, 2007.
The effects of water and microstructure on the performance of polymer electrolyte fuel cells, A. Shah, G.S Kim, W. Gervais, A. Young, J. Li, K. Promislow, and S. Ye J. Power Sources , 160 2006, 1251-1268.
Analysis of a Cathode Catalyst layer model for a Polymer Electrolyte Fuel Cell, P. Berg, A. Novruzi, and K. Promislow, Chemical Engineering Science 61 (13) (2006), 4316-4331.
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, I. Nazarov and K. Promislow, Chemical Engineering Science 61 (2006) 3198-3209.
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.