Alonso Sergio, Kapral Raymond, Bär Markus
Physikalisch-Technische Bundesanstalt, 10587 Berlin, Germany.
Phys Rev Lett. 2009 Jun 12;102(23):238302. doi: 10.1103/PhysRevLett.102.238302.
A simple effective medium theory is derived for spatially heterogeneous nonlinear reaction-diffusion media. Its validity is tested through comparisons with simulations of front and pulse propagation in systems with spatially varying diffusion coefficients and reaction rates. The theory is able to predict wave speeds if the characteristic front width is much larger than the length scale of the heterogeneities. This condition is violated in media with isolated or weakly connected sites. However, the theory nevertheless provides good results in cases where it correctly predicts the percolation threshold of the medium.
针对空间非均匀非线性反应扩散介质，推导了一种简单的有效介质理论。通过与具有空间变化扩散系数和反应速率的系统中前沿和脉冲传播的模拟结果进行比较，检验了该理论的有效性。如果特征前沿宽度远大于非均匀性的长度尺度，该理论能够预测波速。在具有孤立或弱连接位点的介质中，此条件不成立。然而，在该理论正确预测介质的渗流阈值的情况下，它仍然能给出良好的结果。
