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:DAMTP Friday GR Seminar
SUMMARY:Numerical renormalization group-based approach to
secular perturbation theory - Jose Tomas Galvez Gh
ersi (CITA)
DTSTART;TZID=Europe/London:20220128T130000
DTEND;TZID=Europe/London:20220128T140000
UID:TALK167171AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/167171
DESCRIPTION:Perturbation theory is a crucial tool for many phy
sical systems\, when exact solutions are not avail
able\, or nonperturbative numerical solutions are
intractable. Naive perturbation theory often fails
on long timescales\, leading to secularly growing
solutions. These divergences have been treated wi
th a variety of techniques\, including the powerfu
l dynamical renormalization group (DRG). Most of t
he existing DRG approaches rely on having analytic
solutions up to some order in perturbation theory
. However\, sometimes the equations can only be so
lved numerically. We reformulate the DRG in the la
nguage of differential geometry\, which allows us
to apply it to numerical solutions of the backgrou
nd and perturbation equations. This formulation al
so enables us to use the DRG in systems with backg
round parameter flows\, and therefore\, extend our
results to any order in perturbation theory. As a
n example\, we apply this method to calculate the
soliton-like solutions of the Korteweg-de Vries eq
uation deformed by adding a small damping term. We
numerically construct DRG solutions which are val
id on secular time scales\, long after naive pertu
rbation theory has broken down.
LOCATION:Zoom
CONTACT:Justin Ripley
END:VEVENT
END:VCALENDAR