Don Jones studies partial differential equations (PDEs) associated with geophysical fluids. That is, equations resulting from the modeling of the atmosphere, ocean, and interiors of planets. The primary mathematical tools employed come from a branch of mathematics called functional analysis. The analysis is used, in part, to validate, rigorously, the models possess the physical properties engineers and physicists expect. This approach often yields surprising properties of the solutions to the equations and suggests new algorithms for approximating the models.
Education
Ph.D. University of California-Irvine 1992
Publications
D Jones, H. Smith, H. Thieme. Spread of Viral Infection of Immobilized Bacteria. Networks and Heterogeneous Media (2013).
Jones, H Smith, H. Thieme, G, Rost. Spread of Phage infection of Bacteria in a Petri Dish. SIAM Journal on Applied Mathematics, Vol 72, No.2, 670-688 (2012) (2012).
D Jones and Hal Smith. Bacteriophage and Bacteria in a Flow Reactor. Bulletin of Mathematical Biology (2011).
Ballyk, M, Jones, Donald, Smith, H. The Biofilm Model of Freter: A Review, a chapter in Structured Population Models in Biology and Epidemiology. Springer-Verlag (2007).
M Imran, Donald Jones, H Smith. Biofilms and the Plasmid Maintenance Question. Mathematical Biosciences, 193 (2005).
Donald Jones, Hristo Kojouharo. Microbial Competition for Nutrient in a 3-D Flow Reactor. Dynamics of Continuous, Discrete, and Implusive Dyanmical Systems,Series B: Applications and Algorithm (2003).
Donald Jones, Hristo Kojouharov, Dung Le, H Smith. Bacterial wall attachment in a flow reactor: mixed culture. Canadian. Appl. Math. Quart (2003).
Donald Jones, Hristo Kojouharov, Dung Le, H Smith. The Freter Model: a simple model of biofilm formatio. Journal of Mathematical Biolog (2003).
Donald Jones. Mathematical analysis of geophysical balance models. J. Diff. Eqs (2002).
Donald Jones, A Poje, L Margolin. Accuracy and Non-Oscillatory Properties of Enslaved Difference Schemes. Comp. Phys (2002).
Donald Jones, Hristo Kojouharov, Le Dung, H Smith. Bacterial wall attachment in a flow reactor. SIAM Applied Math (2002).
M Ballyk, Donald Jones, H Smith. Microbial competition in reactors with wall attachment: a comparison of chemostat and plug flow models. Microbial Ecology (2001).
Donald Jones, H Smith. Microbial competition for nutrient and wall sites in plug flow. SIAM Applied Math (2000).
Research Activity
Kostelich,Eric John*, Armbruster,Hans Dieter, Crook,Sharon Marie, Crook,Sharon Marie, Gardner,Carl L, Gelb,Anne, Jackiewicz,Zdzislaw, Jones,Donald, Lopez,Juan Manuel, Mahalov,Alex, Renaut,Rosemary Anne, Ringhofer,Christian, Welfert,Bruno Denis. CSUMS: Undergraduate research Experiences for Computational Math Science Majors at ASU. NSF-MPS-DMS(9/15/2007 - 8/31/2014).
