School of Mathematical Sciences

Computing scaling functions for two-dimensional vesicle models: from generating functions to coalescing saddle point asymptotics. menu

Computing scaling functions for two-dimensional vesicle models: from generating functions to coalescing saddle point asymptotics.

Speaker: 
Thomas Prellberg (QMUL)
Date/Time: 
Mon, 08/11/2010 - 16:30
Room: 
M103
Seminar series: 


A large class of area-perimeter generating functions of vesicle models
satisfy q-deformed algebraic functional equations. In several instances
these functional equations can be solved in terms of quotients of basic
hypergeometric functions. The singular limit as q approaches 1 is of
fundamental importance in the phase diagram of the model. A rigorous
derivation of the scaling function at the critical point is based on
a particular contour integral representation of the associated basic
hypergeometric series.