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SUMMARY:Modelling Chemical Kinetics in a non-Markovian environment - Kevin
  Burrage (Queensland University of Technology)
DTSTART:20231107T103000Z
DTEND:20231107T110000Z
UID:TALK203218@talks.cam.ac.uk
DESCRIPTION:This presentation is joint work with Pamela Burrage.&nbsp\;\nT
 he standard approach to simulating chemical kinetics is to assume a well-s
 tirred homeogeneous environment and this leads to the use of the stochasti
 c simulation algorithm (in which the waiting time to the next reaction is 
 exponentially distributed)\, the chemical master equation (descrbing its p
 df)\, the chemical langevin equation and the use of the Law of Mass Action
  to derive a system of ordinary differential equations.&nbsp\; However\, i
 f the chemical kinetics operate in a spatially crowded heterogeneous envir
 onment then the modelling and simulation becomes more complex.&nbsp\;\nIf 
 a parameter alpha between 0 and 1 captures the broad features of this hete
 rogeneity\, then we must deal with the so-called Mittag-Leffler (heavy tai
 led function) in all of the above settings along with the concept of time 
 change.&nbsp\; We briefly discuss these issues.&nbsp\; We also show how to
  adapt the approach of Jahnke and Huisinga\, who have given the exact solu
 tion of the CME for unimolecular reactions\, in terms of convolutions of m
 ultinomial and Poisson distributions in the homogeneous setting\, together
  with the use of iterated Brownian path algorithms when alpha takes the fo
 rm of (1/2)^k to accuately simulate the fractional kinetics of some simple
  systems.
LOCATION:Seminar Room 1\, Newton Institute
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