BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Developing PDE-compartment hybrid frameworks for modeling stochast
 ic reaction-diffusion processes - Kit Yates (University of Bath)
DTSTART:20160622T100000Z
DTEND:20160622T104500Z
UID:TALK66543@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span> <span>Co-author: Mark Flegg (University of Monash) <br>
 </span></span><span><br>Spatial reaction-diffusion models have been employ
 ed to describe many  emergent phenomena in biology. The modelling techniqu
 e most commonly adopted is  systems of partial differential equations (PDE
 s)\, which assumes there are  sufficient densities of particles that a con
 tinuum approximation is valid.  However\, the simulation of computationall
 y intensive individual-based models has  become a popular way to investiga
 te the effects of noise in reaction-diffusion  systems. <br> <br>The speci
 fic stochastic models with which we shall be concerned in this talk  are r
 eferred to as `compartment-based&#39\; or `on-lattice&#39\;. These models 
 are  characterised by a discretisation of the computational domain into a 
  grid/lattice of `compartments&#39\;. Within each compartment particles ar
 e assumed to  be well-mixed and are permitted to react with other particle
 s within their  compartment or to transfer between neighbouring compartmen
 ts. <br> <br>In this work we develop two hybrid algorithms in which a PDE 
 in one region of  the domain is coupled to a compartment-based model in th
 e other. Rather than  attempting to balance average fluxes\, our algorithm
 s answer a more fundamental  question: `how are individual particles trans
 ported between the vastly different  model descriptions?&#39\; First\, we 
 present an algorithm derived by carefully  re-defining the continuous PDE 
 concentration as a probability distribution.  Whilst this first algorithm 
 shows very strong convergence to analytic solutions  of test problems\, it
  can be cumbersome to simulate. Our second algorithm is a  simplified and 
 more efficient implementation of the first\, it is derived in the  continu
 um limit over the PDE region alone. We test our hybrid methods for  functi
 onality and accuracy in a variety of different scenarios by comparing the 
  averaged simulations to analytic solutions of PDEs for mean concentration
 s. <br><br>Related Links <ul> <li><a target="_blank" rel="nofollow">http:/
 /rsif.royalsocietypublishing.org/content/12/106/20150141</a>  - First pape
 r associated with this talk&nbsp\;</li></ul></span>
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR