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SUMMARY:Bifurcation Analysis of Active Filament Models - Bethany Clarke
DTSTART:20230615T120000Z
DTEND:20230615T130000Z
UID:TALK202324@talks.cam.ac.uk
CONTACT:Marco Vona
DESCRIPTION:Slender filaments such as microtubules are ubiquitous in natur
 e\, driving fluid flow at the microscopic scale. Molecular motors like dyn
 ein and kinesin translocate along microtubules\, causing a range of both s
 teady and time-dependent behaviours. The coordinated motion of microtubule
 s can lead to phenomena like cytoplasmic streaming and ciliary beating\, g
 enerating fluid flows on larger scales. In this talk we provide a comprehe
 nsive overview of the emerging dynamics of the most fundamental model that
  captures the effect of molecular motors on a single filament\; the follow
 er force model\, whereby a compressive force is imposed at the filament ti
 p. We vary both the strength of this force and the slenderness of the fila
 ment to explore the resulting state space\, using a filament model built o
 n Kirchoff’s rod theory and which employs unit quaternions and implicit 
 time integration to handle the development of the filament’s local frame
  over time [1]. Employing a Jacobian-Free Newton-Krylov method\, we establ
 ish both steady and time-periodic solutions to the model\, as well as new\
 , quasi-periodic solutions. We classify and fully characterize the bifurca
 tions yielding different states and analyse their stability. In doing so\,
  we provide a clear picture of the full bifurcation diagram for the fundam
 ental model of microtubule-motor protein complexes.
LOCATION:CMS MR14
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