CURRICULUM VITAE

Donald A. Jones

Arizona State University
Department of Mathematics
Tempe, AZ 85287-1804
Phone: (480) 965-0083
Fax:     (480) 965-8119
E-mail : dajones@asu.edu

• Ph.D. Mathematics, February 1992,
  University of California, Irvine
  Ph.D. Dissertation: Determining Nodes and Long-Time Approximations
  to the Navier-Stokes Equations
  Ph.D. Advisor: Edriss S. Titi
  
• M.S. Mathematics, Georgia Institute of Technology, Atlanta, Georgia
  
• B.S. Physics, Georgia Institute of Technology, Atlanta Georgia, Highest Honor

RESEARCH INTERESTS:

• Navier-Stokes Equations
• Mathematical Physics
• Partial Differential Equations
• Scientific Computation
• Mathematical Biology

PROFESSIONAL EXPERIENCE:

• Arizona State University Fall 1996-present
  Associate Professor, Department of Mathematics.
• Los Alamos National Laboratory, Los Alamos, NM, 9/93 -12/96
  Postdoctoral Fellow at the Center for Nonlinear Studies/Institute for Geophysics and Planetary Physics.
• Stanford University, Fall 1992-Fall 93
  Postdoctoral Fellow at the Center for Turbulence Research/Department of Mathematics.

VISITING POSITIONS:

• University of California, Davis, Davis, CA 8/1/00-7/31/01,
  Department of Mathematics.
  
• Los Alamos National Laboratory, Los Alamos, NM, 5/30/99-7/1/99, 7/1/98-8/8/98, 7/1/97-8/5/98,
  Center for Nonlinear Studies/Institute for Geophysics and Planetary Physics.

PUBLISHED WORK:

1. On the number of determining nodes for the 2D Navier-Stokes equations, (with E.S. Titi), J. Math. Anal. Appl., 168, (1992), 72-88.

2. Determination of the solutions of the Navier-Stokes equations by finite volume elements , (with E.S. Titi), Physica D60, (1992), 165-174.

3. An approximate inertial manifold for computing Burgers' equation , (with L.G. Margolin), Physica D60, (1992), 175-184.

4. Upper bounds on the number of determining modes, nodes, and volume elements for the Navier-Stokes equations, (with E.S. Titi), Indiana Univ Math. J., 42, (1993), 875-887.

5. A remark on quasi-stationary approximate inertial manifolds for the 2D Navier-Stokes equations (with E.S. Titi) SIAM J. Math. Anal., 25 , (1994), 894-914.

6. On the effectiveness of the approximate inertial manifold- a computational study, (with L. G. Margolin, E. S. Titi), Theor. Comp. Fluid Dyn., 7, (1995), 243-260.

7. Determining degrees of freedom for nonlinear dissipative equations , (with E.S. Titi, B. Cockburn), C.R. Acad. Sci Paris Se'r I, 321, (1995), 563-568.

8. Attractive invariant manifolds under approximation: Inertial manifolds, (with A.M. Stuart), J. Diff. Eq., 123, (1995), 588-637.

9. On the behavior of attractors under finite difference approximations , Num. Funt. Anal. and Opt., 16, (1995), 1155-1180.

10. Enslaved finite difference schemes for nonlinear dissipative PDEs, (with A.C. Poje, L.G. Margolin), Num. Meth. for PDEs, 12, (1996), 13-40.

11. C^1 approximations of inertial manifolds for dissipative nonlinear equations, (with E. S. Titi), J. Diff. Eq., 127, (1996), 54-86.

12. Enslaved finite difference schemes for quasigeostrophic shallow flows, (with A.C. Poje, L.G. Margolin), Physica D98, (1996), 559-573.

13. Local existence results for the generalized inverse of the vorticity equation in the plane, (with C. R. Hagelberg, A.F. Bennett), Inverse Problems, 12, (1996), 437-454.

14. Estimating the asymptotic degrees of freedom for nonlinear dissipative PDEs, (with E.S. Titi, B. Cockburn), Math. Comp., 66, (1997), 1073-1087.

15. Resolution effects and Enslaved finite difference schemes for a double gyre, shallow water model, (with A. C. Poje, L.G. Margolin), J. Theor. Comp Fluid Dynamics., 9, (1997), 269-280.

16. Persistence of invariant sets for dissipative evolution equations, (with A. M. Stuart, E.S. Titi), J. Math. Anal. Appl., 219, (1998), 479-502.

17. Persistence of invariant manifolds for nonlinear PDEs, (with Steve Shkoller), Studies in Applied Math., 102, (1999), 27-67.

18. An operator splitting for the shallow-water equations with large ageostrophic initial data, (with A. Mahalov, B. Nicolaenko). J. Theor. Comp Fluid Dynamics., 13, (1999), 263.

19. Effects of random motility on micobial growth and competition in a flow reactor, (with M. Ballyk, H. Smith, L. Dung), SIAM J. Appl. Math., 59, (1999), 573-596.

20. Microbial competition for nutrient and wall sites in plug flow, (with Hal L. Smith), SIAM Applied Math., 60, (2000), 1576-1600.

21. Microbial competition in reactors with wall attachment: a comparison of chemostat and plug flow models, (with M. Ballyk, H.L. Smith), Microbial Ecology, 41, (2001).

22. Don A. Jones, Mathematical analysis of geophysical balance models, J. Diff. Eq, 179, (2002), 1-26.

23. Accuracy and Non-Oscillatory Properties of Enslaved Difference Schemes , (with L.G. Margolin, A.C. Poje), Comp. Phys., 181, (2002), 705-728.

24. Bacterial wall attachment in a flow reactor, (with Hristo V. Kojouharov, Dung Le, Hal Smith), SIAM Applied Math., 62, (2002), 195-222.

25. Microbial Competition for Nutrient in a 3D Flow Reactor, , (with Hristo V. Kojouharov, Dung Le, Hal Smith), Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Applications and Algorithms, 10:1 (2003) 57-68.

26. Bacterial Wall Attachment in a Flow Reactor: mixed culture, , (with Hristo V. Kojouharov, Dung Le, Hal Smith), SIAM Journal on Applied Mathematics, 62:5 (2002) 1728-1771.

27. The Freter Model: a Simple Model of Biofilm Formation, (with Hristo V. Kojouharov, Dung Le, Hal Smith), Journal of Mathematical Biology, 47:2 (2003) 137-152.

28. Biofilms and the plasmid maintenance question, (with Mudassar Imran, H.L. Smith}, Mathematical Biosciences, 193, (2005), 183-204.

29. Modified truncation error finite difference schemes, Comp. Phys., 209, (2005), 322-339.

30. Bacteriophage and Bacteria in a Flow Reactor, (with Hal L. Smith), Bulletin Bulletin of Mathematical Biology: 73, Issue 10 (2011), 2357-2383.

31. Spread of Phage infection of Bacteria in a Petri Dish, (with Hal L. Smith, Horst Thieme, Gergely Rost), SIAM Journal on Applied Mathematics, 72, No.2, (2012) 670-688.

32. Modified-truncation finite difference schemes for geophysical flows, (submitted).