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摘要翻译：
最近，我们考虑了一个描述细胞前沿侵入伤口的随机离散模型\cite{KSS}。在模型中，细胞可以运动，增殖，并经历细胞间的粘附。在本工作中，我们用一个带有扩散项的广义Cahn-Hilliard方程(GCH)对这一现象进行了连续描述。在离散模型中，有两个有趣的制度。对于亚临界粘着，存在着与Fisher-Kolmogorov方程类似的传播“拉”锋。研究了前沿速度的选择问题，我们的理论预测与GCH方程的数值解符合得很好。对于超临界粘附，存在一个非平凡的瞬态行为，其中密度分布呈现出一个次峰。为了分析这种情况，我们研究了无增殖的Cahn-Hilliard方程的弛豫动力学。我们发现弛豫过程表现出自相似行为。对于我们所分析的不同制度，连续模型和离散模型的结果是一致的。
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英文标题：
《A generalized Cahn-Hilliard equation for biological applications》
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作者：
Evgeniy Khain and Leonard M. Sander
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
Recently we considered a stochastic discrete model which describes fronts of cells invading a wound \cite{KSS}. In the model cells can move, proliferate, and experience cell-cell adhesion. In this work we focus on a continuum description of this phenomenon by means of a generalized Cahn-Hilliard equation (GCH) with a proliferation term. As in the discrete model, there are two interesting regimes. For subcritical adhesion, there are propagating "pulled" fronts, similarly to those of Fisher-Kolmogorov equation. The problem of front velocity selection is examined, and our theoretical predictions are in a good agreement with a numerical solution of the GCH equation. For supercritical adhesion, there is a nontrivial transient behavior, where density profile exhibits a secondary peak. To analyze this regime, we investigated relaxation dynamics for the Cahn-Hilliard equation without proliferation. We found that the relaxation process exhibits self-similar behavior. The results of continuum and discrete models are in a good agreement with each other for the different regimes we analyzed.
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PDF链接：
https://arxiv.org/pdf/801.2574
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