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SUMMARY:The role of exponential asymptotics and complex singularities in s
 elf-similarity\, transitions\, and branch merging of nonlinear dynamics - 
 Jonathan Chapman (University of Oxford)
DTSTART:20230724T103000Z
DTEND:20230724T113000Z
UID:TALK202759@talks.cam.ac.uk
DESCRIPTION:We study a prototypical example in nonlinear dynamics where tr
 ansition to self-similarity in a singular limit is fundamentally changed a
 s a parameter is varied. We focus on the complicated dynamics that occur i
 n a generalised unstable thin-film equation that yields finite-time ruptur
 e. A parameter\, n\, is introduced to model more general disjoining pressu
 res. For the standard case of van der Waals intermolecular forces\, n = 3\
 , it was previously established that a countably infinite number of self-s
 imilar solutions exist leading to rupture. However\, recent numerical resu
 lts have demonstrated the surprising complexity that exists for general va
 lues of n. In particular\, the bifurcation structure of self-similar solut
 ions now exhibits branch merging as n is varied. We shall present key idea
 s of how branch merging can be interpreted via exponential asymptotics.
LOCATION:Seminar Room 1\, Newton Institute
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