Campos Daniel, Fedotov Sergei, Méndez Vicenç
School of Mathematics, University of Manchester, Manchester, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jun;77(6 Pt 1):061130. doi: 10.1103/PhysRevE.77.061130. Epub 2008 Jun 20.
In this paper we reconsider the mass action law (MAL) for the anomalous reversible reaction A <==> B with diffusion. We provide a mesoscopic description of this reaction when the transitions between two states A and B are governed by anomalous (heavy-tailed) waiting-time distributions. We derive the set of mesoscopic integro-differential equations for the mean densities of reacting and diffusing particles in both states. We show that the effective reaction rate memory kernels in these equations and the uniform asymptotic states depend on transport characteristics such as jumping rates. This is in contradiction with the classical picture of MAL. We find that transport can even induce an extinction of the particles such that the density of particles A or B tends asymptotically to zero. We verify analytical results by Monte Carlo simulations and show that the mesoscopic densities exhibit a transient growth before decay.
在本文中，我们重新考虑了具有扩散的异常可逆反应A⇌B的质量作用定律（MAL）。当两个状态A和B之间的转变由异常（重尾）等待时间分布控制时，我们给出了该反应的介观描述。我们推导了两个状态下反应和扩散粒子平均密度的介观积分 - 微分方程组。我们表明，这些方程中的有效反应速率记忆核以及均匀渐近状态取决于诸如跳跃率等传输特性。这与质量作用定律的经典图景相矛盾。我们发现传输甚至可以导致粒子灭绝，使得粒子A或B的密度渐近趋于零。我们通过蒙特卡罗模拟验证了分析结果，并表明介观密度在衰减之前呈现出瞬态增长。
