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Publications

Selected Journal Papers:

  1. *One-dimensional stability of parallel shock layers in isentropic magnetohydrodynamics. Submitted 2009 (with Blake Barker and Kevin Zumbrun).
  2. *Stability of isentropic viscous shock profiles in the high mach number limit. Communications in Mathematical Physics, to appear 2009 (with Olivier Lafitte and Kevin Zumbrun).
  3. *Spectral stability of ideal-gas shock layers. Archive for Rational Mechanics and Analysis, 194(3):1029-1079, 2009 (with Gregory Lyng and Kevin Zumbrun).
  4. *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).
  5. *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).
  6. *On the shock wave spectrum for isentropic gas dynamics with capillarity. Journal of Differential Equations 246(7):2938--2957, 2009.
  7. *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).
  8. An efficient shooting algorithm for Evans function calculations in large systems. Physica D. 220(2):116--126, 2006 (with Kevin Zumbrun).
  9. 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).
  10. Admissibility of viscous-dispersive systems. Journal of Hyperbolic Differential Equations 2(4):963--974, 2005.
  11. Stability of Jin-Xin relaxation shocks. Quarterly of Applied Mathematics 61(2):251--263, 2003.
  12. 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).
  13. Nonmonotonic twist maps. Physica D. 80(3):256--276, 1995 (with James E. Howard).

Other Journal Papers:

  1. 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).
  2. *Stability of isentropic Navier--Stokes shocks. Applied Mathematics Letters 21(7):742--747, 2008 (with Blake Barker, Olivier Lafitte, Keith Rudd, and Kevin Zumbrun).
  3. Comment on "Signature of classical chaos in quantum tunneling". Physical Review E. 51(6):6313--6315, 1995 (with David Farrelly).

Refereed Proceedings:

  1. *Dynamic input consensus using integrators. Submitted 2009 (with Randal W. Beard and Clark N. Taylor).
  2. *Pricing of American retail options. Submitted 2009 (with Tina Benhaim, McKay Heasley, and Jialin Li).
  3. *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).
  4. *Option pricing for inventory management and control. Proceedings of the American Controls Conference, St. Louis, MO, June 2009 (with Bryant Angelos and McKay Heasley).
  5. 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).
  6. On the stability of viscous-dispersive fronts. Hyperbolic Problems: Theory, Numerics and Applications, Vol II., 2004. Proceedings of the 10th International Conference, Yokohama Publishers.
  7. 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.