BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Growth of thin fingers in Laplacian and Poisson fi
elds - Robb McDonald (University College London)
DTSTART;TZID=Europe/London:20191031T143000
DTEND;TZID=Europe/London:20191031T153000
UID:TALK133522AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/133522
DESCRIPTION:(i) The Laplacian growth of thin two-dimensional p
rotrusions in the form of either straight needles
or curved fingers satisfying Loewner'\;s equati
on is studied using the Schwarz-Christoffel (SC) m
ap. Particular use is made of Driscoll'\;s nume
rical procedure\, the SC Toolbox\, for computing t
he SC map from a half-plane to a slit half-plane\,
where the slits represent the needles or fingers.
Since the SC map applies only to polygonal region
s\, in the Loewner case\, the growth of curved fin
gers is approximated by an increasing number of sh
ort straight line segments. The growth rate of the
fingers is given by a fixed power of the harmonic
measure at the finger or needle tips and so inclu
des the possibility of &lsquo\;screening&rsquo\; a
s they interact with themselves and with boundarie
s. The method is illustrated by examples of needle
and finger growth in half-plane and channel geo
metries. Bifurcating fingers are also studied and
application to branching stream networks discussed
. (ii) Solutions are found for the growth of infi
nitesimally thin\, two-dimensional fingers governe
d by Poisson'\;s equation in a long strip. The
analytical results determine the asymptotic paths
selected by the fingers which compare well with th
e recent numerical results of Cohen and Rothman (2
017) for the case of two and three fingers. The ge
neralisation of the method to an arbitrary number
of fingers is presented and further results for fo
ur finger evolution given. The relation to the ana
logous problem of finger growth in a Laplacian fie
ld is also discussed.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
END:VEVENT
END:VCALENDAR