标题： 通用异常扩散的稳定效应，与瑞利数无关 显示英文标题

标题： Stabilising effect of generic anomalous diffusion independent of the Rayleigh number

摘要： 这项工作研究了通用异常扩散模型对流体饱和多孔介质中质量对流的影响，重点在于超扩散区域。 建立了一个数学模型，并进行了稳定性分析——包括线性和非线性分析。 结果表明，描述异常扩散的时间函数的具体形式显著影响系统稳定性，使得稳定性可以超越经典的瑞利-贝纳德中性阈值。 此外，在某些条件下观察到瞬时扰动增长，随后最终衰减。 本文系统地检查了各种记忆函数，包括幂律、指数和对数形式，突出了它们对扰动动力学的影响。 研究结果强调了异常扩散在调节稳定性中的重要性，并提供了关于非菲克质量传输引起的瞬态行为的新见解。 显示英文摘要

摘要： This work investigates the influence of a generic anomalous diffusion model on mass convection in a fluid-saturated porous medium, focusing on superdiffusive regimes. A mathematical model is developed, and tability analyses - both linear and nonlinear - are performed. Results demonstrate that the specific form of the time function describing anomalous diffusion significantly affects system stability, allowing stability to persist beyond the classical Rayleigh-B\'enard neutral threshold. Furthermore, transient perturbation growth is observed under certain conditions, followed by eventual decay. The paper systematically examines various memory functions, including power-law, exponential, and logarithmic forms, highlighting their impact on the dynamics of disturbances. The findings underscore the importance of anomalous diffusion in modulating stability and provide new insights into the transient behaviours induced by non-Fickian mass transport.