随机过程的有效扩散常数与空间周期性噪声
Stefano Giordano1, Ralf Blossey2
1University of Lille, CNRS, Centrale Lille, <a href="https://ror.org/02ezch769">Université Polytechnique Hauts-de-France</a>, UMR 8520-IEMN-<a href="https://ror.org/02q4res37">Institut d'Électronique, de Microélectronique et de Nanotechnologie</a>, F-59000 Lille, France.
Physical review. E
|November 20, 2024
概括
我们确定了空间依赖噪声的随机过程的有效扩散常数. 我们的研究结果为有效的扩散系数提供了一个通用公式,适用于各种离散规则和噪声条件.
科学领域:
- 物理 物理学 物理
- 物理化学 物理化学
- 统计力学 统计力学
背景情况:
- 随机过程在具有固有随机性的建模系统中是至关重要的.
- 空间依赖的噪声使扩散现象变得复杂.
- 离散规则 (例如,用α表示) 影响得出的漂移-扩散方程.
研究的目的:
- 为了确定空间依赖噪声的随机过程的有效扩散常数 (D_eff).
- 为了获得D_eff的一般结果,对于任何离散规则 (0≤α≤1) 都有效.
- 概括现有的定理,如Lifson-Jackson定理,用于漂移和空间噪声的扩散.
主要方法:
- 分析兰杰文方程来导出漂移-扩散方程.
- 对周期性异质扩散和周期性阴侧扩散的研究.
- 在漂移和空间噪声的存在下,对一般α的D_eff的导出.
- 使用分析和数值计算进行验证.
主要成果:
- 对于周期性异质扩散,独立于离散规则α,确定有效扩散系数 (D_eff) 的一般结果.
- 对于周期性鼻状扩散的具体情况,发现了与莱根德尔函数的联系.
- 利夫森-杰克逊定理被推广为具有周期空间噪声和漂移术语的扩散.
结论:
- 该研究为计算具有复杂噪声特征的系统中的有效扩散常数提供了全面的框架.
- 对D_eff的推导式提高了对异质介质中的扩散的理解.
- 利夫森-杰克逊定理的概括提供了对漂移和空间噪声的扩散过程的新见解.
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