BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Growth of thin fingers in Laplacian and Poisson fields - Robb McDo
 nald (University College London)
DTSTART:20191031T143000Z
DTEND:20191031T153000Z
UID:TALK133528@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:(i) The Laplacian growth of thin two-dimensional protrusions i
 n the form of either straight needles or curved fingers satisfying Loewner
 &#39\;s equation is studied using the Schwarz-Christoffel (SC) map. Partic
 ular use is made of Driscoll&#39\;s numerical procedure\, the SC Toolbox\,
  for computing the SC map from a half-plane to a slit half-plane\, where t
 he slits represent the needles or fingers. Since the SC map applies only t
 o polygonal regions\, in the Loewner case\, the growth of curved fingers i
 s approximated by an increasing number of short straight line segments. Th
 e growth rate of the fingers is given by a fixed power of the harmonic mea
 sure at the finger or needle tips and so includes the possibility of &lsqu
 o\;screening&rsquo\; as they interact with themselves and with boundaries.
  The method is illustrated by examples of needle and finger growth  in  ha
 lf-plane and channel geometries. Bifurcating fingers are also studied and 
 application to branching stream networks discussed.<br><br>(ii) Solutions 
 are found for the growth of infinitesimally thin\, two-dimensional fingers
  governed by Poisson&#39\;s equation in a long strip. The analytical resul
 ts determine the asymptotic paths selected by the fingers which compare we
 ll with the recent numerical results of Cohen and Rothman (2017) for the c
 ase of two and three fingers. The generalisation of the method to an arbit
 rary number of fingers is presented and further results for four finger ev
 olution given. The relation to the analogous problem of finger growth in a
  Laplacian field is also discussed.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR