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摘要翻译：
对于跳跃概率非线性依赖于$F(r，t)$的情形，导出了在$r$位置和时间$t$处找到随机行者的概率$F(r，t)$的Fokker-Planck方程。结果是经典福克-普朗克方程的推广形式，其中也考虑了由于破坏详细平衡而引起的漂移和外场的影响。结果表明，在没有漂移和外场的情况下，描述反常扩散的标度解只有在跳变概率中的非线性为幂律型($sim f^{eta}(r,t)$)时才有可能，在这种情况下，广义福克-普朗克方程归结为著名的多孔介质方程。Monte-Carlo模拟验证了理论结果。
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英文标题：
《Generalized Diffusion》
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作者：
James F. Lutsko and Jean Pierre Boon
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最新提交年份：
2007
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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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一级分类：Physics 物理学
二级分类：Materials Science 材料科学
分类描述：Techniques, synthesis, characterization, structure. Structural phase transitions, mechanical properties, phonons. Defects, adsorbates, interfaces
技术，合成，表征，结构。结构相变，力学性质，声子。缺陷，吸附质，界面
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一级分类：Physics 物理学
二级分类：Soft Condensed Matter 软凝聚态物质
分类描述：Membranes, polymers, liquid crystals, glasses, colloids, granular matter
膜，聚合物，液晶，玻璃，胶体，颗粒物质
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英文摘要：
The Fokker-Planck equation for the probability $f(r,t)$ to find a random walker at position $r$ at time $t$ is derived for the case that the the probability to make jumps depends nonlinearly on $f(r,t)$. The result is a generalized form of the classical Fokker-Planck equation where the effects of drift, due to a violation of detailed balance, and of external fields are also considered. It is shown that in the absence of drift and external fields a scaling solution, describing anomalous diffusion, is only possible if the nonlinearity in the jump probability is of the power law type ($\sim f^{\eta }(r,t)$), in which case the generalized Fokker-Planck equation reduces to the well-known Porous Media equation. Monte-Carlo simulations are shown to confirm the theoretical results.
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PDF链接：
https://arxiv.org/pdf/711.4487
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