Alan Elcrat

Alan Elcrat, Professor

Partial Differential Equations; PhD, Indiana University, 1967

Contact

Awards

Excellence in Research WSU 2000

PhD Students

Trenton Albrecht, (current)

German Vargas, "Steady Solution of th Navier-Stokes Equations for a Viscous Flow Past a Circular Cylinder, PhD thesis, 2009

Ray Treinen, "A Study of Floating Drops", PhD thesis, 2004

Tae-Eun Kim, "Cappilary Surface Interfaces in Annular Domains", PhD thesis, 2001

Chenglie Hu, "Applications of Computational Complex Analysis to Some Free Boundary and Vortex Flows", PhD thesis, 1995

Octavian Nicolio, "Steady Vortex Flows Past Obstacles", PhD thesis, 1994

Research

It has been said that vortices are the sinews of fluid flows, and the study of these fascinating structures has been a central theme in Elcrat's recent research. See the research summary of Professor Miller for more about our joint work. This work combines mathematical analysis with related computations, and this follows a style in applied mathematics that we hold in high regard. In recent work with DeLillo and Pfaltzgraff a generalization of the Schwarz-Christoffel formula to arbitrary connectivity has been discovered. The use of this for computing conformal maps, inverse problems, and non destructive testing is an active area of current research. A third area of active research is in capillarity. A prototype of this work is the floating drop problem. Think of a drop of Guiness floating on surface of Czech lager.

Selected Publications

  • T.Albrecht, A.Elcrat, and K. Miller, Steady Vortex Dipoles with General Profile Functions, Journal of Fluid Mechanics, Oct. 22, 2010.
  • A. R. Elcrat & K. G. Miller, Steady axisymmertic vortex flow with swirl and shear, Journal of Fluid Mechanics 613 (2008), 395-410
  • T. K. DeLillo, A. R. Elcrat & J. A. Pfaltzgraff, Radial & circular slit maps of unbound multiply connected circle domains. Proc.R.Soc. A 464 (2008), 1719-1737
  • A. R. Elcrat, B. Fornberg, and K. Miller, Stability of Vortices in Equilibrium with a Cylinder, J. Fluid Mechanics, 544 (2005), 53-68.
  • A. R. Elcrat and K. Miller, Free Surface Waves in Equilibrium with a Vortex, European J. Mech. B., 25 (2006), 255-266.
  • T. K. DeLillo, A. R. Elcrat, and J. A. Pfaltzgraff, Schwarz-Christoffel Mapping of Multiply Connected Domains, Journal d'Analyse, 94 (2004), 17-47.