Shift in the velocity of a front due to a cutoff
Shift in the velocity of a front due to a cutoff
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DOI：
10.1103/physreve.56.2597
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发表时间：
1997-09-01
影响因子：
2.4
通讯作者：
Derrida, B
中科院分区：
文献类型：
--
作者：
Brunet, E;Derrida, B
我们考虑了小截止子对一维行波速度的影响。超过十个数量级的模拟以及一个简单的理论论证表明，截止ε的作用是选择一个当ε-->；0时收敛于边际稳定性论证所预测的速度的单一速度。对于小epsilon，速度漂移的形式为K(Ln Epsilon)(-2)，我们对常数K的预测与我们的模拟结果非常吻合。在更复杂的情况下，特别是在一些微观随机系统的有限大小效应中，出现了非常类似的对数漂移。我们的理论方法还可以推广到给出一种简单的方法来推导由于Fisher-Kolmogorov方程或类似方程中的初始条件而引起的位置移动。
We consider the effect of a small cutoff epsilon on the velocity of a traveling wave in one dimension. Simulations done over more than ten orders of magnitude as well as a simple theoretical argument indicate that the effect of the cutoff epsilon is to select a single velocity that converges when epsilon-->0 to the one predicted by the marginal stability argument. For small epsilon, the shift in velocity has the form K(ln epsilon)(-2) and our prediction for the constant K agrees very well with the results of our simulations. A very similar logarithmic shift appears in more complicated situations, in particular in finite-size effects of some microscopic stochastic systems. Our theoretical approach can also be extended to give a simple way of deriving the shift in position due to initial conditions in the Fisher-Kolmogorov or similar equations.