Stochastic interacting particle systems models for reaction-diffusion systems: Non-linear kinetics, steady-state bifurcations (phase transitions), reaction fronts

Wednesday, April 1, 2009 - 11:15am - 12:15pm
Lind 409
James Evans (Iowa State University)
Traditionally, non-linear reaction kinetics and associated spatiotemporal reaction-diffusion behavior have been analyzed with mean-field rate and reaction-diffusion equations. This formulation assumes that the reactants are well-mixed, ignoring spatial correlations and fluctuations. This is akin to the mean-field Van der Waals equation of state for a fluid which has long since been surpassed by statistical mechanical treatments of phase transitions and critical phenomena. The recent USDOE Basic Science Grand Challenges report proposes an analogous sophisticated treatment of such far-from-equilibrium systems (such as chemical reactions), where the thermodynamic framework available for equilibrium systems does not apply. Here, we investigate a statistical mechanical lattice-gas or interacting particle systems (IPS) realization of Schloegl's 2nd model for autocatalysis. The mean-field model displays bistability between a reactive and a poisoned state. In contrast, the IPS realization exhibits a discontinuous phase transition between these states with associated metastability and nucleation phenomena. This is mostly analogous to behavior in equilibrium fluid systems. However, the IPS realization also exhibits generic two-phase coexistence, behavior never seen in an equilibrium system.

References: Phys. Rev. Lett. 98 (2007) 050601; Phys. Rev. E 75 (2007); Physica A 387 (2008); J Stat. Phys. (2009); J. Chem. Phys. 130 (2009) 074106.