Projects per year
Abstract
We consider an extension of the zerorange process to the case where the hop rate depends on the state of both departure and arrival sites. We recover the misanthrope and the target process as special cases for which the probability of the steady state factorizes over sites. We discuss conditions which lead to the condensation of particles and show that although two different hop rates can lead to the same steady state, they do so with sharply contrasting dynamics. The first case resembles the dynamics of the zerorange process, whereas the second case, in which the hop rate increases with the occupation number of both sites, is similar to instantaneous gelation models. This new 'explosive' condensation reveals surprisingly rich behaviour, in which the process of the condensate's formation goes through a series of collisions between clusters of particles moving through the system at increasing speed. We perform a detailed numerical and analytical study of the dynamics of condensation: we find the speed of the moving clusters, their scattering amplitude, and their growth time. We finally show that the time to reach steady state decreases with the size of the system.
Original language  English 

Article number  095001 
Number of pages  27 
Journal  Journal of physics aMathematical and theoretical 
Volume  47 
Issue number  9 
DOIs  
Publication status  Published  17 Feb 2014 
Keywords
 zerorange process
 condensation
 migration process
 misanthrope process
 driven diffusive systems
 BACKGAMMON MODEL
 DYNAMICS
 UNIVERSE
 SYSTEMS
Projects
 2 Finished


Design Principles for New Soft Materials
Cates, M., Allen, R., Clegg, P., Evans, M., MacPhee, C., Marenduzzo, D. & Poon, W.
7/12/11 → 6/06/17
Project: Research
Profiles

Martin Evans
 School of Physics and Astronomy  Personal Chair in Statistical Physics
Person: Academic: Research Active

Bartlomiej Waclaw
Person: Academic: Research Active