Alan Elcrat

Family

TaeKwonDo

Kims Academy

A rainbow on the Lolo Trail in Montana, July 1998,
following Lewis and Clark

Snowshoeing in Rocky Mountain National Park

Piazza di Popolo, Roma

Perugia 2002

Current Research:

Computation of a pendent drop hanging from the interface between two fluids computed by my student Ray Treinen. (click on the picture for a lot more.)

Recent Publications:

• "A monotone iteration  for axisymmetric vortices with swirl"  with K.G.Miller, Differential Equations and Integral Equations  16(2003), 949-968.
• "Equilibrium configurations for a floating drop" with R.Neel and D.Siegel, Journal of Mathematical Fluid  Mechanics 6(2004),405-429.
  
• "Schwarz-Christoffel mappings of multiply connected domains" with T.K.Delillo and J.A.Pfaltzgraff, Journal d'Analyse, 94(2004),17-47.
  
• "Some Steady Vortex Flows Past a Sphere" with B. Fornberg and K.G. Miller, J. Fluid Mechanics, 433(2001),315-328..
• "On Detecting Emerging Surface Cracks From Boundary Measurements" with B. Bunck and T. Hrycak, Inverse Problems, 17(2001),1391-1400.
• "Schwarz-Christoffel Mapping of the Annulus" with T.K. DeLillo and J.A. Pfaltzgraff, Siam Review, 43(3)(2001),469-477.
• "A Monotone Iteration For Concentrated Vortices" with K.G. Miller, Nonlinear Analysis, 44(2001),777-789.
• "Some Steady Vortex Flows Past a Circular Cylinder" with B. Fornberg, M. Horn, and K.G. Miller, J. Fluid Mechanics,409(2000),13-27.
• "Equilibrium Configurations of point vortices for channel flows past interior obstacles" with C. Hu and K.G. Miller, European Journal of Mechanics B/Fluids 16(2), 277-292 (1997).
• "On the Inverse Problem of a Fourth Order Self-adjoint Binomial Operator" with V.G. Papanicolaou, SIAM J. Math. Anal. 28 (4) (1997), pp. 886-896.
• "Numerical Conformal Mapping Methods Based on Faber Series" with T.K. DeLillo and J.A. Pfaltzgraff, J.Comp. and Appl. Math. 83 (1997), pp. 205-236.
• "Determination of Surface and interior cracks" with C. Hu, International Journal of Engineering Science 34 (10), 1165 - 1181 (1996).
• "Rearrangements in Steady Multiple Vortex Flows" with K.G. Miller, Communication in Partial Differential Equations (20), 1481-1490 (1995).
• "Variational Formulas on Lipshitz Domains" with K.G. Miller, Transactions of the AMS 347 (7), 2669-2678 (1995).
• "On Finding a surface crack from boundary measurements" with V. Isakov and 0. Neculoiu, Inverse Problems 11, 343-351 (1995).
• "An Iteration for steady vortices in rearrangement classes" with 0. Neculoiu, Nonlinear Analysis, Theory, Methods, and Applications 24(3), 419-432 (1995).

Recently Published Book:

Courses:

Mathematical Theory of Fluid Mechanics

In the spring semester of 2006 I will teach two courses: a second course in differential equations,M655, emphasizing geometrical features including periodic solutions, center manifolds, Hopf bifurcations, and chaos; and a course in numerical methods,M551,which will be MATLAB based using Cleve Moler's new book.

. In the fall next year I will begin a year course in the mathematical theory of fluid mechanics. The core of the course will be built around James Serrin's 1959 article in Handbuch der Physik which is still the benchmark in this subject. After a study of kinematics, constituitive relations will be introduced and the dynamics of viscous fluids, nonviscous fluids and vortex motion will be studied. A number of special solutions of the flow equations which illustrate basic properties of flows will be introoduced. The computational aspects of solving flow problems will also be studied.