Froemberg D, Schmidt-Martens H, Sokolov I M, Sagués F
Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, Berlin, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jul;78(1 Pt 1):011128. doi: 10.1103/PhysRevE.78.011128. Epub 2008 Jul 31.
We consider an irreversible autocatalytic conversion reaction A+B-->2A under subdiffusion described by continuous-time random walks. The reactants' transformations take place independently of their motion and are described by constant rates. The analog of this reaction in the case of normal diffusion is described by the Fisher-Kolmogorov-Petrovskii-Piskunov equation leading to the existence of a nonzero minimal front propagation velocity, which is really attained by the front in its stable motion. We show that for subdiffusion, this minimal propagation velocity is zero, which suggests propagation failure.
我们考虑在连续时间随机游走描述的亚扩散条件下，一个不可逆的自催化转化反应A + B→2A。反应物的转化独立于其运动发生，且由恒定速率描述。在正常扩散情况下，该反应的类似情况由Fisher-Kolmogorov-Petrovskii-Piskunov方程描述，导致存在非零的最小前沿传播速度，而前沿在其稳定运动中确实能达到该速度。我们表明，对于亚扩散，这个最小传播速度为零，这意味着传播失败。
