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Publications

Journal Papers:

  1. Multidimensional stability of large-amplitude Navier-Stokes shocks. Preprint, 2016 (with Gregory Lyng and Kevin Zumbrun).
  2. Root following in Evans function computation. SIAM Journal on Numerical Analysis (SINUM), 53(5), 2329–2346, 2015 (with Joshua Lytle).
  3. Stability of viscous weak detonation waves for Majda's model. Journal of Dynamics and Differential Equations, 27(2):237--260, 2015 (with Jeffrey Hendricks, Gregory Lyng and Kevin Zumbrun).
  4. Viscous hyperstabilization of detonation waves in one space dimension. SIAM Journal on Applied Mathematics (SIAP), 75(3):885-906, 2015 (with Blake Barker, Gregory Lyng and Kevin Zumbrun).
  5. Fixed Wing UAV Path Following in Wind with Input Constraints. IEEE Transactions on Control Systems Technology, 22(6):2103-2117, 2014 (with Randal W. Beard with Jeff Ferrin).
  6. Stability of viscous detonations for Majda's model. Physica D, 259:63-80, 2013 (with Gregory Lyng and Kevin Zumbrun).
  7. Spectral behavior of combustion fronts with high exothermicity. SIAM Journal on Applied Mathematics (SIAP), 73(1):422-437, 2013 (with Anna Ghazaryan and Joshua Lytle).
  8. A fresh look at the Kalman filter. SIAM Review (SIREV), 54(4): 801-823, 2012 (with Preston Redd, and Jeremy M. West).
  9. Efficient numerical stability analysis of detonation waves in ZND. Quarterly of Applied Mathematics, 70(4):685-703, 2012 (with Kevin Zumbrun).
  10. Kalman filtering with Newton's method. IEEE Control Systems Magazine, 30(6):101--106, 2010 (with Jeremy West).
  11. 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).
  12. 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).
  13. Spectral stability of ideal-gas shock layers. Archive for Rational Mechanics and Analysis, 194(3):1029-1079, 2009 (with Gregory Lyng and Kevin Zumbrun).
  14. 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).
  15. 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).
  16. On the shock wave spectrum for isentropic gas dynamics with capillarity. Journal of Differential Equations 246(7):2938-2957, 2009.
  17. 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).
  18. 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).
  19. Stability of isentropic Navier--Stokes shocks. Applied Mathematics Letters 21(7):742-747, 2008 (with Blake Barker, Olivier Lafitte, Keith Rudd, and Kevin Zumbrun).
  20. An efficient shooting algorithm for Evans function calculations in large systems. Physica D. 220(2):116-126, 2006 (with Kevin Zumbrun).
  21. 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).
  22. Admissibility of viscous-dispersive systems. Journal of Hyperbolic Differential Equations 2(4):963-974, 2005.
  23. Stability of Jin-Xin relaxation shocks. Quarterly of Applied Mathematics 61(2):251-263, 2003.
  24. 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).
  25. Nonmonotonic twist maps. Physica D. 80(3):256-276, 1995 (with James E. Howard).
  26. Comment on "Signature of classical chaos in quantum tunneling". Physical Review E. 51(6):6313-6315, 1995 (with David Farrelly).

Refereed Proceedings:

  1. Following Straight Line and Orbital Paths with Input Constraints. Proceedings of the American Controls Conference, San Fransisco, CA, 2011 (with Randal W. Beard).
  2. Dynamic input consensus using integrators. Proceedings of the American Controls Conference, San Fransisco, CA, 2011 (with Randal W. Beard and Clark N. Taylor).
  3. Pricing of American retail options. Proceedings of the American Controls Conference, Baltimore, MD, July 2010 (with Tina Burton, McKay Heasley, and Jialin Li).
  4. 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).
  5. Option pricing for inventory management and control. Proceedings of the American Controls Conference, St. Louis, MO, June 2009 (with Bryant Angelos and McKay Heasley).
  6. 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).
  7. On the stability of viscous-dispersive fronts. Hyperbolic Problems: Theory, Numerics and Applications, Vol II., 2004. Proceedings of the 10th International Conference, Yokohama Publishers.
  8. 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).

Non-Refereed Papers:

  1. 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.