论文标题
两种种类反应 - 灌注系统的生存：重新归一化组的治疗和数值模拟
Survival in two-species reaction-superdiffusion system: Renormalization group treatment and numerical simulations
论文作者
论文摘要
我们分析了两个物种反应扩散系统，包括捕获反应$ a + b \ to a $以及凝血/an灭反应$ a + a \ to（a，0）$，其中这两个物种的粒子都以控制参数$ 0 <σ<2 $执行lévy飞行，已知会导致超级产物行为。众所周知，在此类系统中，目标粒子$ b $的密度以及相关函数在空间维度下以非平凡的通用指数进行扩展。应用重新归一化组形式主义，我们在临界尺寸以下的超扩散$ d_c =σ$的情况下计算这些指数。在一维情况下的数值模拟也进行了。与我们的分析结果相吻合，对生存颗粒密度的衰减指数的定量估计值非常吻合。特别是，发现超级放射状态中目标颗粒的存活概率高于普通扩散系统中的目标颗粒。
We analyze the two-species reaction-diffusion system including trapping reaction $A + B \to A$ as well as coagulation/annihilation reactions $A + A \to (A,0)$ where particles of both species are performing Lévy flights with control parameter $0 < σ< 2$, known to lead to superdiffusive behaviour. The density, as well as the correlation function for target particles $B$ in such systems, are known to scale with nontrivial universal exponents at space dimension $d \leq d_{c}$. Applying the renormalization group formalism we calculate these exponents in a case of superdiffusion below the critical dimension $d_c=σ$. The numerical simulations in one-dimensional case are performed as well. The quantitative estimates for the decay exponent of the density of survived particles $B$ are in good agreement with our analytical results. In particular, it is found that the surviving probability of the target particles in a superdiffusive regime is higher than that in a system with ordinary diffusion.
