论文标题
污染物在大气中的湍流扩散的变形衍生化模型
A deformed derivative model for turbulent diffusion of contaminants in the atmosphere
论文作者
论文摘要
在目前的工作中，我们提出了一个带有Hausdorff变形衍生物的对流扩散方程，以探讨大气中污染物的湍流扩散。我们将模型的性能与具有经典和Caputo分数衍生物的模型进行比较，以拟合实验数据。我们发现，拟合实验数据时，Hausdorff方程比传统对流扩散方程提供了更好的结果。最重要的是，我们表明我们的模型和Caputo分数导数模型在所有实验中都表现出非常相似的性能。最后的结果表明，无论我们使用的非经典衍生物种类，具有非经典衍生物的对流扩散方程比具有经典衍生物的模型比具有污染物在大气中的扩散更为足以描述大气中污染物的扩散。此外，由于Hausdorff衍生物可能与几个变形的操作员有关，并且由于具有Hausdorff衍生物的微分方程比具有Caputo和其他非本地分数衍生物的方程式更容易求解，因此我们的结果突出了变形的衍生模型的潜力，以描述大气中污染物的扩散。
In the present work, we propose an advection-diffusion equation with Hausdorff deformed derivatives to stud the turbulent diffusion of contaminants in the atmosphere. We compare the performance of our model to fit experimental data against models with classical and Caputo fractional derivatives. We found that the Hausdorff equation gives better results than the tradition advection-diffusion equation when fitting experimental data. Most importantly, we show that our model and the Caputo fractional derivative model display a very similar performance for all experiments. This last result indicates that regardless of the kind of non-classical derivative we use, an advection-diffusion equation with non-classical derivative displaying power-law mean square displacement is more adequate to describe the diffusion of contaminants in the atmosphere than a model with classical derivatives. Furthermore, since Hausdorff derivatives can be related to several deformed operators, and since differential equations with the Hausdorff derivatives are easier to solve than equations with Caputo and other non-local fractional derivatives, our result highlights the potential of deformed derivative models to describe the diffusion of contaminants in the atmosphere.
