Selected Journal Papers:
- Stability of viscous detonations for Majda's model, submitted, 2012 (with Gregory Lyng and Kevin Zumbrun).
- Spectral behavior of combustion fronts with high exothermicity. SIAM Journal on Applied Mathematics, to appear 2013 (with Anna Ghazaryan and Joshua Lytle).
- A fresh look at the Kalman filter. SIAM Review, 54(4): 801-823, 2012 (with Preston Redd, and Jeremy M. West).
- Efficient numerical stability analysis of detonation waves in ZND. Quarterly of Applied Mathematics, 70(4):685-703, 2012 (with Kevin Zumbrun).
- Kalman filtering with Newton’s method. IEEE Control Systems Magazine, 30(6):101--106, 2010 (with Jeremy West).
- One-dimensional stability of parallel shock layers in isentropic magnetohydrodynamics. Journal of Differential Equations, 249(9):2175–2213, 2010 (with Blake Barker and Kevin Zumbrun).
- Stability of isentropic viscous shock profiles in the high mach number limit. Communications in Mathematical Physics, 293(1):1-36, 2010 (with Olivier Lafitte and Kevin Zumbrun).
- Spectral stability of ideal-gas shock layers. Archive for Rational Mechanics and Analysis, 194(3):1029-1079, 2009 (with Gregory Lyng and Kevin Zumbrun).
- Computing expected transition events in reducible Markov chains, SIAM Journal on Matrix Analysis and Applications (SIMAX) 31(3):1040-1054, 2009 (with Brian D. Ewald and Jeremy West) (download source code).
- Spectral stability of compressive noncharacteristic boundary layers. Archive for Rational Mechanics and Analysis 192(3):537-587, 2009 (with Nicola Costanzino, Toan Nguyen, and Kevin Zumbrun).
- On the shock wave spectrum for isentropic gas dynamics with capillarity. Journal of Differential Equations 246(7):2938-2957, 2009.
- Stability of viscous shocks in isentropic gas dynamics. Communications in Mathematical Physics 281(1):231-249, 2008 (with Blake Barker, Keith Rudd, and Kevin Zumbrun).
- An efficient shooting algorithm for Evans function calculations in large systems. Physica D. 220(2):116-126, 2006 (with Kevin Zumbrun).
- Efficient computation of analytic bases in Evans function analysis of large systems. Numerische Mathematik 103(4):631-642, 2006 (with Björn Sandstede and Kevin Zumbrun).
- Admissibility of viscous-dispersive systems. Journal of Hyperbolic Differential Equations 2(4):963-974, 2005.
- Stability of Jin-Xin relaxation shocks. Quarterly of Applied Mathematics 61(2):251-263, 2003.
- Spectral stability of small-amplitude shock profiles for dissipative symmetric hyperbolic-parabolic systems. Zeitschrift für angewandte Mathematik und Physik (ZAMP) 53(1):20-34, 2002 (with Kevin Zumbrun).
- Nonmonotonic twist maps. Physica D. 80(3):256-276, 1995 (with James E. Howard).
Other Journal Papers:
- A dynamic workflow framework for mass customization using web service and autonomous agent techniques. Journal of Intelligent Manufacturing 19(5):537-552, 2008 (with Daniel Karpowitz, Jordan Cox, and Sean Warnick).
- Stability of isentropic Navier--Stokes shocks. Applied Mathematics Letters 21(7):742-747, 2008 (with Blake Barker, Olivier Lafitte, Keith Rudd, and Kevin Zumbrun).
- Comment on "Signature of classical chaos in quantum tunneling". Physical Review E. 51(6):6313-6315, 1995 (with David Farrelly).
- Following Straight Line and Orbital Paths with Input Constraints. Proceedings of the American Controls Conference, San Fransisco, CA, 2011 (with Randal W. Beard).
- Dynamic input consensus using integrators. Proceedings of the American Controls Conference, San Fransisco, CA, 2011 (with Randal W. Beard and Clark N. Taylor).
- Pricing of American retail options. Proceedings of the American Controls Conference, Baltimore, MD, July 2010 (with Tina Burton, McKay Heasley, and Jialin Li).
- The Analysis of Discrete Transient Events in Markov Games. Proceedings of the American Controls Conference, St. Louis, MO, June 2009 (with Brian D. Ewald and Jeremy West).
- Option pricing for inventory management and control. Proceedings of the American Controls Conference, St. Louis, MO, June 2009 (with Bryant Angelos and McKay Heasley).
- Competition dynamics in a virtual fund management system. Proceedings of the American Controls Conference, New York City, NY, July 2007 (with Casey Dougal, David Merriman, Sean Warnick).
- On the stability of viscous-dispersive fronts. Hyperbolic Problems: Theory, Numerics and Applications, Vol II., 2004. Proceedings of the 10th International Conference, Yokohama Publishers.
- Normalization of resonant Hamiltonians. Hamiltonian mechanics (Toru\'n, 1993), 237-244, NATO Advanced Science Institutes Series B: Physics, 331, Plenum, New York, 1994 (with David Farrelly and T. Uzer).
- Spectral energy methods and the stability of shock waves. Ph.D. dissertation, Indiana University, Bloomington, IN, 2002.
Work supported in part by the National Science Foundation, Grant numbers DMS-0607721, DMS-0639328, and DMS-CAREER-0847074.