分形无标度网络上两种群反应扩散过程湮灭中的分凝
Segregation in the annihilation of two-species reaction-diffusion processes on fractal scale-free networks
摘要：
在度指数为$γ$的随机无标度网络上的反应扩散过程$A+B \to \varnothing$中，当初始粒子密度相同时，粒子密度随时间按指数为$α$的幂律衰减.指数$α$对于$2 < γ< 3$是$α> 1$，对于$γ\ge 3$是$α=1$。在这里，我们研究了分形SF网络上的反应过程，发现即使对于$2 < γ< 3$，$α< 1$也是如此。这种缓慢衰减的行为源于隔离效应：分形SF网络包含彼此排斥的局部枢纽。这些枢纽吸引粒子并加速反应，然后创建包含相同种类粒子的域。因此，反应发生在这些区域之间的非中心边界处，因此颗粒密度缓慢衰减。由于许多真实的SF网络是分形的，因此在非均匀颗粒之间的反应动力学中必须考虑偏析效应。
英文摘要：
In the reaction-diffusion process $A+B \to \varnothing$ on random scale-free (SF) networks with the degree exponent $γ$, the particle density decays with time in a power law with an exponent $α$ when initial densities of each species are the same. The exponent $α$ is $α> 1$ for $2 < γ< 3$ and $α=1$ for $γ\ge 3$. Here, we examine the reaction process on fractal SF networks, finding that $α< 1$ even for $2 < γ< 3$. This slowly decaying behavior originates from the segregation effect: Fractal SF networks contain local hubs, which are repulsive to each other. Those hubs attract particles and accelerate the reaction, and then create domains containing the same species of particles. It follows that the reaction takes place at the non-hub boundaries between those domains and thus the particle density decays slowly. Since many real SF networks are fractal, the segregation effect has to be taken into account in the reaction kinetics among heterogeneous particles.
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