Alan Elcrat
Home
address 
2825 W. 17

Phone 
316  943 9702

Office 
351 Jabara
Wichita State University
316  978 3965
elcrat@math.wichita.edu

Research
Interests 
vortex dynamics,
computational complex
analysis

Personal
Interests 
Tae Kwon Do, home
brewing

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
Current Research:
"SchwarzChristoffel
Mapping of Multiply
Connected Domains"
"On detecting emerging
surface cracks from
boundary measurements."
"Some steady
axisymmetric vortex flows
past a sphere."
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. 395410.
 "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, 17191737.
 "T.DeLillo, T. Driscoll, A.Elcrat, and J. Pfaltzgraff, Computation of Multiply Connected SchwarzChristoffel Maps for Exterior Domains, Comp.Meth. and Function Th. 6 (2) (2006) 301315.
 "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)241249.
 "A.R.Elcrat, B.Fornberg, and K.Miller, Stability of Vortices in Equilibrium With a Cylinder, J.Fluid Mechanics,(2005),vol.544,5368.
 "Equilibrium configurations for a floating drop" with R.Neel and D.Siegel, Journal of Mathematical Fluid Mechanics 6 (2004), pp. 405429
 "SchwarzChristoffel mappings of multiply connected domains" with T.K.Delillo and J.A.Pfaltzgraff, Journal d'Analyse, 94 (2004), pp. 1747.
 "A monotone iteration for axisymmetric vortices with swirl" with K.G.Miller, Differential Equations and Integral Equations 16 (2003), pp.
949968.
 "Some Steady Vortex Flows Past a Sphere" with B. Fornberg and K.G. Miller, J. Fluid Mechanics, 433(2001),315328..
 "On Detecting Emerging Surface Cracks From Boundary Measurements" with B. Bunck and T. Hrycak, Inverse Problems, 17(2001),13911400.
 "SchwarzChristoffel Mapping of the Annulus" with T.K. DeLillo and J.A. Pfaltzgraff, Siam Review, 43(3)(2001),469477.
 "A Monotone Iteration For Concentrated Vortices" with K.G. Miller, Nonlinear Analysis, 44(2001),777789.
 "Some Steady Vortex Flows Past a Circular Cylinder" with B.
Fornberg, M. Horn, and K.G. Miller, J. Fluid
Mechanics,409(2000),1327.
 "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), 277292 (1997).
 "On the Inverse Problem of a Fourth Order Selfadjoint
Binomial
Operator" with V.G. Papanicolaou, SIAM J. Math. Anal. 28 (4) (1997),
pp. 886896.
 "Numerical Conformal Mapping Methods Based on Faber Series"
with
T.K. DeLillo and J.A. Pfaltzgraff, J.Comp. and
Appl. Math. 83 (1997), pp. 205236.
 "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), 14811490 (1995).
 "Variational Formulas on Lipshitz Domains" with K.G.
Miller,
Transactions of the AMS 347 (7), 26692678 (1995).
 "On Finding a surface crack from boundary measurements"
with V.
Isakov and 0. Neculoiu, Inverse Problems 11,
343351 (1995).
 "An Iteration for steady vortices in rearrangement classes"
with
0. Neculoiu, Nonlinear Analysis, Theory, Methods,
and Applications 24(3), 419432 (1995).
Recently Published Books:
"Mathematical Theory of Electromagnetism"
with
Piero Bassanini, Simai electure Notes
"Theory and Applications of Partial Differential Equations"
with
Piero Bassanini, Plenum Press
Recent talks:
Traveling vortex pairs
Applications of multiply connected SchwarzChristoffel transformations
Swirling vortices
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 SchwarzChristoffel transformation.