Professor of Mathematical Sciences; Member, Faculty of Information Technology
Ph.D., Johns Hopkins University
Professor Herron’s research is in one of the richest areas of applied mathematics: the theory of the stability of fluid flows. Common applications are to phenomena in the atmosphere, the oceans, to problems of the motion of ships and aircraft and to internal machinery. Modern approaches involve new techniques in operator theory, energy methods and dynamical systems. Current research interests are in (i) stability of rotating magneto-hydrodynamic flows, (ii) more complicated geophysical flows such as groundwater, for which mathematical models are still being developed.
Some Recent Publications:
“Improved bounds on linear instability of barotropic zonal flow within the shallow water equations,”
Geophysical & Astrophysical Fluid Dynamics, Volume 107, Issue 3, June 2013, pp. 328352 (with Antwan Clark).
“Exchange of stabilities in Couette flow between cylinders with Navier-slip conditions”
Quarterly Of Applied Mathematics Vol. LXX, Number 4, Dec. 2012, pp. 743758 (with Pablo Suárez).
"Gauging magnetorotational instability" Journal of Applied Mathematics and Physics (Z. Angew. Math. Phys.) Vol. 61, Number 4, pp. 663-672, 2010 (with Jeremy Goodman).
"On the Principle of Exchange of Stabilities in Rayleigh-Benard Convection" SIAM J. Appl.Math. 61, No.4, December 2000, p.1362-1368.
2002 MAA-NAM David Blackwell Lecture: "Random Walk, Diffusion, and Energy Decay"
"The Principle of Exchange of Stabilities for Couette Flow", Quarterly of Applied Mathematics, Volume 61, Number 2, June 2003, pp. 279-293 (with Halima N. Ali).
"On the Principle of Exchange of Stabilities in Rayleigh-Benard Convection, II - No-slip Boundary Conditions", Ann. Univ. Ferrara-Sez. VII-Sc. Nat. Vol. 49, pp. 169-182, December 2003.
"Onset of Instability in Hydromagnetic Couette Flow", Analysis and Applications, Vol. 2, No. 2, April 2004, pp.145-159.
"The stability of Couette flow in a toroidal magnetic field", Applied Mathematics Letters, 19, 1113-1117 (2006) (with Fritzner Soliman).
“The small Prandtl number approximation suppresses magnetorotational instability”, Journal of Applied Mathematics and Physics (Z. Angew. Math. Phys.) 57, 615-622 (2006) (with Jeremy Goodman).
“Partial Differential Equations in Fluid Dynamics”, Cambridge University Press, 2008 (Textbook with Michael R. Foster).