2018/04/30 by F. Le Vot, Carlos Escudero, C. Escudero +2 · 11 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Annihilation #Coalescence (physics) #Diffusion and Search Dynamics #Distribution (mathematics) #Distribution function #Domain (mathematical analysis) #Mathematical analysis #Mathematics #Multiplicity (mathematics) #Physics #Quantum mechanics #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.98.032137
published in Physical review. E 98(3) (American Physical Society) · 40 pages, 10 figures
openalex created_date 2018/04/24 · openalex publication_date 2018/09/26 · arxiv created 2018/10/19 · arxiv updated 2018/10/22 · openalex updated_date 2026/08/05
The kinetics of encounter-controlled processes in growing domains is markedly different from that in a static domain. Here we consider the specific example of diffusion-limited coalescence and annihilation reactions in one-dimensional space. In the static case, such reactions are among the few systems amenable to exact solution, which can be obtained by means of a well-known method of intervals. In the case of a uniformly growing domain, we show that a double transformation in time and space allows one to extend this method to compute the main quantities characterizing the spatial and temporal behavior. We show that a sufficiently fast domain growth brings about drastic changes in the behavior. In this case, the reactions stop prematurely, as a result of which the survival probability of the reacting particles tends to a finite value at long times and their spatial distribution freezes before reaching the fully self-ordered state. We obtain exact results for the survival probability and for key properties characterizing the degree of self-ordering induced by the chemical reactions, i.e., the interparticle distribution function and the pair correlation function. These results are confirmed by numerical simulations.