天蓝遏蓝菜根系对镉离子吸收的分数阶模型  

Fractional-Order Model of Cadmium Ion Uptake by the Root System of Noccaea Caerulescens

作　　者：林明芳 王玥 欧忠辉 LIN Mingfang;WANG Yue;OU Zhonghui(School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China;Fujian Key Laboratory of Mathematical Analysis and Applications,Fuzhou 350117,China;Center of Applied Mathematics of Fujian Province,Fuzhou 350117,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117 [2]福建省分析数学及应用重点实验室,福建福州350117 [3]福建省应用数学中心,福建福州350117

出　　处：《青岛农业大学学报(自然科学版)》2025年第1期72-78,共7页Journal of Qingdao Agricultural University(Natural Science)

基　　金：国家自然科学基金(11671085;11771082;12271096);福建省自然科学基金(ZGD1707233;ZGD200872301;2021J01653;2023J01299)。

摘　　要：为模拟非均匀、多孔介质中镉离子(Cd^(2+))的扩散模式,在天蓝遏蓝菜(Noccaea caerulescens)根系吸收自由Cd^(2+)的对流扩散模型基础上,提出时空分数阶模型,用来模拟3种土壤Phytorem、Pierrelaye和M6中天蓝遏蓝菜根系附近的Cd^(2+)扩散模式。结果表明:与Pierrelaye和M6相比,Phytorem的缓冲力小,Cd^(2+)的异常扩散现象出现得较早。分别在Phytorem中模拟60 d、在Pierrelaye和M6中各模拟600 d发现:当时间分数阶α和空间分数阶β满足α/(β+1)>0.5时,Cd^(2+)呈现超扩散;当α/(β+1)<0.5时,Cd^(2+)呈现亚扩散。α和β的敏感性分析表明,β取值不同时,Cd^(2+)浓度曲线会相交:在相交位置附近,β对Cd^(2+)的异常扩散贡献率随距离的增大先减小后增大;在远离相交位置处,3种土壤均有较高的α、β贡献率且两者相近。在Phytorem中模拟60 d,α对Cd^(2+)异常扩散总体贡献率比β高1个量级;在Pierrelaye和M6中模拟200 d,α和β对Cd^(2+)异常扩散总体贡献率相近。对时空分数阶模型的数值模拟可有效地反映土壤的复杂系统特征和重金属的扩散机制。In order to simulate diffusion models of Cadmium ion(Cd^(2+))in heterogeneous and porous media,a spatiotemporal fractional-order model was proposed based on the advection-diffusion model for free Cd^(2+)uptake by the root system of Noccaea caerulescens.It was used to simulate diffusion models of Cd^(2+)near the root of Noccaea caerulescens in three kinds of soil including Phytorem,Pierrelaye and M6.The results showed that compared with Pierrelaye and M6,the soil buffer power of Phytorem was smaller,and the abnormal diffusion of Cd^(2+)appeared earlier.As the simulation time was 60,600 and 600 days respectively in Phytorem,Pierrelaye and M6,the super-diffusion of Cd^(2+)occurred when the temporal fractional orderαand spatial fractional orderβsatisfiedα/(β+1)>0.5;the sub-diffusion of Cd^(2+)happened whenα/(β+1)<0.5.The sensitivity analysis ofαandβshowed that Cd^(2+)concentration curves with differentβvalues would intersect.Near the intersection point,the contribution rate ofβto the Cd^(2+)abnormal diffusion firstly decreased and then increased with the increasing distances.At points far from the intersection,the contribution rates ofαandβwere significant and similar in all three types of soil.When the simulation time was 60 days in Phytorem,the overall contribution rate ofαwas one order of magnitude higher than that ofβ.When the simulation time was 200 days in Pierrelaye and M6,the overall contribution rates ofαandβto Cd^(2+)abnormal diffusion were close.The numerical simulation of the spatiotemporal fractional-order model can effectively reflect the complex soil system and the diffusion mechanism of heavy metals.

关 键 词：天蓝遏蓝菜根系 镉离子吸收 Riemann-Liouville分数阶导数 CAPUTO分数阶导数 双因素方差分析 

分 类 号：O175.2[理学—数学]