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Anomalous dimensions and the renormalization group in a nonlinear diffusion process

热1 yhhuang 添加于 2010-4-16 09:21 | 2114 次阅读 | 0 个评论

作者
Goldenfeld N, Martin O, Oono Y, Liu F
摘要
We present a renormalization-group (RG) approach to the nonlinear diffusion process ∂_tu=D ∂_x²u, with D=1/2 for ∂_x²u>0 and D=(1+ε)/2 for ∂_x²u<0, which describes the pressure during the filtration of an elastic fluid in an elastoplastic porous medium. Our approach recovers Barenblatt’s long-time result that, for a localized initial pressure distribution, u(x,t)∼t^-(α+1/2)f(x/ √t, ε), where f is a scaling function and α=ε(2πe)^1/2+O(ε²) is an anomalous dimension, which we compute perturbatively using the RG. This is the first application of the RG to a nonlinear partial differential equation in the absence of noise.
详细资料
- 文献种类: Journal Article
- 期刊名称: Physical Review Letters
- 期刊缩写: Phys. Rev. Lett.
- 期卷页: 1990年第64卷第12期 1361-1364页
- ISBN: 0031-9007
学科领域自然科学 » 数学
标签

renormalization group
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