1997/05/31 by M. J. E. Richardson · 1 citation
Mathematics · Physics and Astronomy · #Annihilation #Elementary particle #Exact solutions in general relativity #Generalization #Line (geometry) #Particle (ecology) #Product (mathematics) #Stochastic process #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1007/bf02765544
published as J. Stat. Phys. 89 (1997) 777 · 22 pages, 2 figures, typos corrected
openalex publication_date 1997/11/01 · arxiv created 1998/01/05 · openalex created_date 2016/06/24 · arxiv updated 2016/08/31 · openalex updated_date 2026/08/05
The reaction process A+B->C is modelled for ballistic reactants on an infinite line with particle velocities vA=c and vB=-c and initially segregated conditions, i.e. all A particles to the left and all B particles to the right of the origin. Previous, models of ballistic annihilation have particles that always react on contact, i.e. pair-reaction probability p=1. The evolution of such systems are wholly determined by the initial distribution of particles and therefore do not have a stochastic dynamics. However, in this paper the generalisation is made to p<1, allowing particles to pass through each other without necessarily reacting. In this way, the A and B particle domains overlap to form a fluctuating, finite-sized reaction zone where the product C is created. Fluctuations are also included in the currents of A and B particles entering the overlap region, thereby inducing a stochastic motion of the reaction zone as a whole. These two types of fluctuations, in the reactions and particle currents, are characterised by the `intrinsic reaction rate', seen in a single system, and the `extrinsic reaction rate', seen in an average over many systems. The intrinsic and extrinsic behaviours are examined and compared to the case of isotropically diffusing reactants.