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SUMMARY:A journey from kinetic transport models to fractional-diffusion-ad
 vection equations - Pedro Aceves Sanchez (University of Vienna)
DTSTART:20150929T150000Z
DTEND:20150929T160000Z
UID:TALK61221@talks.cam.ac.uk
CONTACT:Adam Kashlak
DESCRIPTION:In recent years the concept of superdiffusion has been found t
 o be a useful tool to describe many phenomenon appearing in nature. In par
 ticular\, it has been recently discovered that the bacteria E. coli may ex
 hibit a superdiffusive behaviour under certain circumstances. E. coli is a
  microorganism that swims towards regions of higher chemoatractants\, and 
 away from unfavourable environments. This type of behaviour is known as ch
 emotaxis. The movement of E. coli is characterized by a series of run-and-
 tumble events\, which can be modelled via a velocity-jump process. Hence\,
  a possible way to describe it is through kinetic transport equations.\n\n
 Due to the fact that E. coli was found to have a superdiffusive behaviour\
 , the Keller-Segel model\, which is commonly used to describe the movement
  of E. coli\, fails in describing the behaviour of it under this setting. 
 In this talk we shall introduce some kinetic models with a given chemoatra
 ctant concentration\, and perform the rigorous passage to the macroscopic 
 limit\, obtaining fractional-diffusion-advection equations. The coefficien
 ts of the latter equations depend on the microscopic quantities governing 
 the movement of the agents.\n
LOCATION:MR14\, Centre for Mathematical Sciences
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