Particle dynamics in a mass-conserving coalescence process

摘要: We consider a fully asymmetric one-dimensional diffusion model with mass- conserving coalescence. Particles of unit mass enter at one edge the chain and coalesce while performing biased random walk towards other where they exit. The conserved particle acts as passive scalar in reaction process A +A! A, allows an exact mapping to restricted ballistic surface deposition for which results exist. In particular, mass-mass correlation function is exactly known. These complement earlier without mass. introduce comprehensive scaling theory this process. analytical numerical confirm its validity. Diffusion-limited chemical processes are focus recent research. dynamic systems timescales short compared those controlling spatial fluctuations concentration. latter dominate kinetics, low dimensions. Such display scale invariance properties that robust, tend be universal, not sensitive many details actual dynamics microscopic level. Simplified models therefore able catch essence Moreover, some these accessible solutions dimension. An example one-species coalescence process, (1-5). Exact were obtained recently using so-called inter-particle distribution (IPDF) method, also known method empty intervals (6). This includes several versions model, external input particles presence or absence bias along (7, 8). Coagulation localized like have been studied analytically (7) context potential applications, such stars (9) cluster distributions reactions (10). letter we address version chain, when meet each other, driven (8). enhance by assigning particle, preserved during merging event (7). Our motivation generalization it derive physical quantities through our onto growth (namely (11)) describing inhomogeneously growing surfaces. Consider linear L sites. left boundary x D 1, diffuse right meet, ultimately exit xD L. totally biased. Choose