PUBLICATIONS OF DARREN CROWDY

Below is a list of publications (since 1997) together with links to PDF files of the papers.

Review articles (no links to files):

D.G. Crowdy, "Quadrature domains and fluid dynamics", in "Quadrature domains and applications", a Harold Shapiro Anniversary volume (Eds. Ebenfelt, Gustafsson, Khavinson, Putinar), Birkhauser, (2005).

M.Z. Bazant & D.G. Crowdy, "Conformal mapping methods for interfacial dynamics", Handbook of Materials Modelling, Vol I, 4.10 (Ed. S. Yip), Springer, (2005).

S. Boatto & D.G. Crowdy, "Point vortex dynamics", Encyclopedia of Mathematical Physics, Springer-Verlag, (2006).

Papers/articles (including links to PDF files):

D.G. Crowdy
“Schwarz-Christoffel mappings to unbounded multiply connected polygonal regions",
Math. Proc. Camb. Phil. Soc. , 142, 319-339
, (2007).

D.G. Crowdy and J.S. Marshall
“Green's functions for Laplace's equation in multiply connected domains",
IMA. J. Appl. Math, doi:10.1093/imamat/hxm007,
(2007).

D.G. Crowdy and J.S. Marshall
“Computing the Schottky-Klein prime function on the Schottky double of planar domains",
Comput. Methods Funct. Theory, 7(1),
293-308, (2007).

D.G. Crowdy, A. Surana & K-Y Yick
“The irrotational flow generated by two planar stirrers in inviscid fluid",
Phys. Fluids, 19, 018103,
(2007).

D.G. Crowdy
“Exact solutions to the unsteady two-phase Hele-Shaw problem",
Quart. J. Mech. Appl. Math. , 59, 475-485,
(2006).

D.G. Crowdy
“Analytical solutions for uniform potential flow past multiple cylinders",
Eur. J. Mech. B/Fluids , 25(4), 459-470,
(2006).

D.G. Crowdy
“Point vortex motion on the surface of a sphere with impenetrable boundaries",
Phys. Fluids, 18, 036602,
(2006).

D.G. Crowdy and J.S. Marshall
“Conformal mappings between canonical multiply connected domains",
Comput. Methods Funct. Theory, 6(1),
59--76, (2006).

D.G. Crowdy
“Calculating the lift on a finite stack of cylindrical aerofoils",
Proc. Roy. Soc. A., 462, 1387--1407,
(2006).

D.G. Crowdy and J.S. Marshall
“The motion of a point vortex through gaps in walls",
J. Fluid Mech., 551, 31--48,
(2006).

D.G. Crowdy
“Genus N algebraic reductions of the Benney hierarchy within a Schottky model ",
J. Phys. A: Math. Gen., 38, 10917--10934,
(2005).

D.G. Crowdy, S Tanveer & G. Vasconcelos
“On a pair of interacting bubbles in planar Stokes flow”
J. Fluid Mech., 541, 231--261, (2005).

D.G. Crowdy
“The Schwarz-Christoffel mapping to bounded multiply connected polygonal domains ",
Proc. Roy. Soc. A., 461, 2653--2678,
(2005).

D.G. Crowdy
“The Benney hierarchy and the Dirichlet boundary problem in two dimensions”
Phys. Lett A, 343(4), 319-329, (2005).

D.G. Crowdy & J. Marshall
“Analytical formulae for the Kirchhoff-Routh path function in multiply connected domains",
Proc. Roy. Soc. A., 461, 2477--2501,
(2005).

D.G. Crowdy
“Exact solutions for uniform vortex layers attached to corners and wedges"
Eur. J. Appl. Math., 15, 643--650, (2005).

D.G. Crowdy & L. Duchemin
“The effect of solid boundaries on pore shrinkage in Stokes flow”
J. Fluid Mech., 531, 359-379, (2005).

D.G. Crowdy & J.S. Marshall
“The motion of a point vortex around multiple circular islands”
Phys. Fluids, 17, 056602, (2005).

D.G. Crowdy
Quadrature domains and fluid dynamics”
Operator theory: advances and applications
(a Harold Shapiro anniversary volume), 156, 113--129, Birkhauser, (2005)
.

D.G. Crowdy & J.S. Marshall
“Analytical solutions for rotating vortex arrays involving multiple vortex patches”
J. Fluid Mech., 523, 307-338, (2005).

D.G. Crowdy & M. Siegel
Exact solutions for the evolution of a bubble in Stokes flow: a Cauchy transform approach”
SIAM J. Appl. Math., 65, 941-963, (2005)
.

D.G. Crowdy
“Explicit solutions for a vortex-wave interaction”
J. Fluid Mech., 513, 161-170, (2004).

D.G. Crowdy & J.S. Marshall
“On the construction of multiply connected quadrature domains”
SIAM J. Appl. Math., 64, 1334-1359, (2004)
.

D.G. Crowdy & J.S. Marshall
"Growing vortex patches'',
Phys. Fluids, 16, 3122-3129, (2004).

D.G. Crowdy & S. Tanveer
“The effect of finiteness in the Saffman-Taylor viscous fingering problem ”
J. Stat. Phys., 114, 1501-1536, (2004).

D.G. Crowdy & A.S. Fokas
"Explicit integral solutions for the plane elastostatic semi-strip”
Proc. Roy. Soc. A, 460, 1285-1310, (2004).

D.G. Crowdy
“Stuart vortices on a sphere”
J. Fluid Mech., 498, 381-402, (2004).

D.G. Crowdy
“Polygonal N-Vortex arrays: a Stuart model”
Phys. Fluids, 15(12), 3710-3717, (2003).

D.G. Crowdy
“An elliptical-pore model of late-stage planar viscous sintering”
J. Fluid Mech., 501, 251-277, (2004).

D.G. Crowdy
“Viscous sintering of unimodal and bimodal cylindrical packings with shrinking pores”
Eur. J. Appl. Math., 14, 421-225, (2003).

D.G. Crowdy
“Compressible bubbles in Stokes flow”
J. Fluid Mech., 476, 345-356, (2003).

D.G. Crowdy & M. Cloke
“Analytical solutions for distributed multipolar vortex equilibria on a sphere”
Phys. Fluids, 15(1), 22-34, (2002).

D.G. Crowdy
“Exact solutions for two steady inviscid bubbles in the flow-field generated by a four-roller mill”
J. Eng. Math. 44, 311-330, (2002).

D.G. Crowdy
“Exact solutions for rotating vortex arrays with finite-area cores”
J. Fluid Mech., 469, 209-235, (2002).

D.G. Crowdy
“Exact solutions for the viscous sintering of multiply connected fluid domains”
J. Eng. Math., 42, 225-242, (2002).

D.G. Crowdy & M. Cloke
“Stability analysis of a class of two-dimensional multipolar vortex equilibria”
Phys. Fluids, 14(6), 1862-1876, (2002).

D.G. Crowdy
“Multipolar vortices and algebraic curves”
Proc. Roy. Soc. A, 457, 2337-2359, (2001).

D.G. Crowdy & H. Kang
“Squeeze flow of multiply connected fluid domains in a Hele-Shaw cell”
J. Nonlinear Sci., 11(4), 279-304, (2001).

D.G. Crowdy
“Steady nonlinear capillary waves on curved sheets”
Eur. J. Appl. Math., 12, 689-708, (2001).

D.G. Crowdy
“On the construction of exact multipolar equilibria of the 2D Euler equations”
Phys. Fluids, 14(1), 257-267, (2002).

R.Wegmann & D.G. Crowdy
"Shapes of two-dimensional bubbles deformed by circulation"
Nonlinearity, 13, 2131-2141, (2000).

D.G. Crowdy
“A theory of exact solutions for the evolution of an annular blob in a rotating Hele-Shaw cell”
Q. Appl. Math., LX(1), 11-36, (2002).

D.G. Crowdy
“On a class of geometry-driven free boundary problems”
SIAM. J. Appl. Math., 62(2), 945-954, (2002).

D.G. Crowdy
“A new approach to free surface Euler flows with capillarity”
Stud. Appl. Math., 105, 35-58, (2000).

D.G. Crowdy
“Circulation-induced shape deformations of drops and bubbles: exact two-dimensional models”
Phys. Fluids, 11(10), 2836-2845, (1999).

D.G. Crowdy
“A note on viscous sintering and quadrature identities”
Eur. J. Appl. Math., 10, 623-634, (1999).

D.G. Crowdy
“A class of exact multipolar vortices”
Phys. Fluids, 11(9), 2556-2564, (1999).

D.G. Crowdy
“Hele-Shaw flows and water waves”
J. Fluid Mech., 409, 223-242, (2000).

D.G. Crowdy
“Exact solutions for capillary waves on a fluid annulus”
J. Nonlinear Sci., 9, 615-640, (1999).

D.G. Crowdy & S. Tanveer
“A theory of exact solutions for plane viscous blobs”
J. Nonlinear Sci., 8(3), 261-279, (1998).

D.G. Crowdy & S. Tanveer
“A theory of exact solutions for annular viscous blobs”
J. Nonlinear Sci., 8(4), 375-400, (1998).

D.G. Crowdy
“A note on the linear stability of Burgers' vortex”
Stud. Appl. Math., 100, 107-126, (1998).

D.G. Crowdy
“General solutions of the 2D Liouville equation”
Int. J. Engng Sci., 35(2), 141-153, (1997).