A Discrete Convolution Model¶for Phase Transitions
A Discrete Convolution Model¶for Phase Transitions
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DOI：
10.1007/s002050050189
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发表时间：
1999-12
影响因子：
2.5
通讯作者：
P. Bates;Adam J. J. Chmaj-Adam-J.-J.-Chmaj-1997508
中科院分区：
文献类型：
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作者：
P. Bates;Adam J. J. Chmaj-Adam-J.-J.-Chmaj-1997508
我们研究了类伊辛相变的离散卷积模型。对于具有一般长程相互作用的亥姆霍兹自由能泛函，这个非局域模型被导出为12-梯度流。我们构造了行波和定常解，并研究了它们的唯一性和稳定性。特别是，我们找到了一些“传播”和“钉扎”的判据，并将我们的结果与以前研究的一个连续统卷积模型的结果进行了比较。
We study a discrete convolution model for Ising-like phase transitions. This nonlocal model is derived as anl2-gradient flow for a Helmholtz free energy functional with general long range interactions. We construct traveling waves and stationary solutions, and study their uniqueness and stability. In particular, we find some criteria for “propagation” and “pinning”, and compare our results with those for a previously studied continuum convolution model.