Alan Elcrat

Family

TaeKwonDo

Kim's 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. Elcrat , Bengt Fornberg, and K. Miller, Steady axisymmetric vortex flows with swirl and shear, J.Fluid Mechanics vol 613 (2008), pp. 395-410.
• "T. DeLillo, T. A. Driscoll, A. Elcrat and J. A. Pfaltzgraff, Radial and circular slit maps of unbounded multiply connected circle domains, Proceedings of The Royal Society A (2008), 464, 1719-1737.
• "T.DeLillo, T. Driscoll, A.Elcrat, and J. Pfaltzgraff, Computation of Multiply Connected Schwarz-Christoffel Maps for Exterior Domains, Comp.Meth. and Function Th. 6 (2) (2006) 301-315.
• "A. Elcrat and R. Treinen, Floating Drops and functions of bounded variation, to appear in Complex Analysis and Operator Theory.
• "A.R.Elcrat and R.Treinen, Numerical results for floating drops, Discrete and Continuous Dynamical Systems,Suppl.Vol.(2005)241-249.
• "A.R.Elcrat, B.Fornberg, and K.Miller, Stability of Vortices in Equilibrium With a Cylinder, J.Fluid Mechanics,(2005),vol.544,53-68.
• "Equilibrium configurations for a floating drop" with R.Neel and D.Siegel, Journal of Mathematical Fluid  Mechanics 6 (2004), pp. 405-429
• "Schwarz-Christoffel mappings of multiply connected domains" with T.K.Delillo and J.A.Pfaltzgraff, Journal d'Analyse, 94 (2004), pp. 17-47.
• "A monotone iteration  for axisymmetric vortices with swirl"  with K.G.Miller, Differential Equations and Integral Equations  16 (2003), pp. 949-968.
• "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 Books:

Breakthrough in Conformal Mapping

Recent talks:

Courses:

Mathematical Theory of Fluid Mechanics

In the spring semester of 2010 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 Complex Analysis II, M845 the course will follow the of Ahlfors with additional topics in conformal mapping including the Schwarz-Christoffel transformation.