为提高小麦条锈病的遥感监测精度,该研究利用分数阶微分能够突出光谱的细微信息以及描述光谱数据间微小差异的优势,在对条锈病胁迫下小麦冠层光谱数据进行分数阶微分处理的基础上,构建了两波段和三波段分数阶微分光谱指数,并将其应用于...为提高小麦条锈病的遥感监测精度,该研究利用分数阶微分能够突出光谱的细微信息以及描述光谱数据间微小差异的优势,在对条锈病胁迫下小麦冠层光谱数据进行分数阶微分处理的基础上,构建了两波段和三波段分数阶微分光谱指数,并将其应用于小麦条锈病的遥感探测。研究结果表明,1.2阶次微分光谱与小麦条锈病冠层病情严重度的相关性最高,较原始反射率光谱、一阶微分光谱和二阶微分光谱分别提高了20.9%、3.9%和20.5%;基于分数阶微分光谱指数的最优分数阶次及其对应波长构建的三波段分数阶微分光谱指数对小麦条锈病的探测能力优于两波段分数阶微分光谱指数,其中分数阶微分光化学指数与冠层病情严重度的相关系数达到0.875;以分数阶微分光谱指数为自变量构建的高斯过程回归(Gaussian Process Regression,GPR)模型对小麦条锈病冠层病情严重度的预测精度优于反射率光谱指数,其训练数据集及验证数据集病情指数(Disease Index,DI)预测值和实测值间的决定系数较反射率光谱指数分别提高了3.8%和19.1%。研究结果可为进一步实现作物健康状况大面积高精度遥感监测提供参考。展开更多
For fractional Volterra integro-differential equations(FVIDEs)with weakly singular kernels,this paper proposes a generalized Jacobi spectral Galerkin method.The basis functions for the provided method are selected gen...For fractional Volterra integro-differential equations(FVIDEs)with weakly singular kernels,this paper proposes a generalized Jacobi spectral Galerkin method.The basis functions for the provided method are selected generalized Jacobi functions(GJFs),which can be utilized as natural basis functions of spectral methods for weakly singular FVIDEs when appropriately constructed.The developed method's spectral rate of convergence is determined using the L^(∞)-norm and the weighted L^(2)-norm.Numerical results indicate the usefulness of the proposed method.展开更多
Equations between the differential order and the maximum of the fractional-order differential for the specified peak signals are developed based on the variation of the maximum of the specified peak signals at differe...Equations between the differential order and the maximum of the fractional-order differential for the specified peak signals are developed based on the variation of the maximum of the specified peak signals at different orders. Also, equations between the differential order and the zero-crossing of the fractional-order differential of the specified peak signals are proposed according to the variation of the zero-crossing of the specified peak signals at different orders. Characteristic paramters of the Gaus- sian peak, Lorentzian peak, and Tsallis peak can be estimated using estimator I and estimator II which are obtained by the equations above. As a result, a new method is presented to resolve the overlapped peaks signal. Firstly, a fractional-order differential of the specified peak signals is obtained with the fractional-order differentiation filter. Then, characteristic paramters of the specified peak signals can be extracted using estimator I and estimator II. Finally, the Tsallis peak is used as a model to assign the overlapping peak signals correctly. Experimental results show that the proposed method is efficient and effective for the simulated overlapping peaks and detected overlapping voltammetric peak signals.展开更多
In this study, a collocation technique is presented for approximate solution of the fractional-order logistic population model. Actually, we develop the Bessel collocation method by using the fractional derivative in ...In this study, a collocation technique is presented for approximate solution of the fractional-order logistic population model. Actually, we develop the Bessel collocation method by using the fractional derivative in the Caputo sense to obtain the approximate solutions of this model problem. By means of the fractional derivative in the Caputo sense, the collocation points, the Bessel functions of the first kind, the method transforms the model problem into a system of nonlinear algebraic equations. Numerical applications are given to demonstrate efficiency and accuracy of the method. In applications, the reliability of the scheme is shown by the error function based on the accuracy of the approximate solution.展开更多
Because charge carriers of many organic semiconductors(OSCs)exhibit fractional drift diffusion(Fr-DD)transport properties,the need to develop a Fr-DD model solver becomes more apparent.However,the current research on ...Because charge carriers of many organic semiconductors(OSCs)exhibit fractional drift diffusion(Fr-DD)transport properties,the need to develop a Fr-DD model solver becomes more apparent.However,the current research on solving the governing equations of the Fr-DD model is practically nonexistent.In this paper,an iterative solver with high precision is developed to solve both the transient and steady-state Fr-DD model for organic semiconductor devices.The Fr-DD model is composed of two fractionalorder carriers(i.e.,electrons and holes)continuity equations coupled with Poisson’s equation.By treating the current density as constants within each pair of consecutive grid nodes,a linear Caputo’s fractional-order ordinary differential equation(FrODE)can be produced,and its analytic solution gives an approximation to the carrier concentration.The convergence of the solver is guaranteed by implementing a successive over-relaxation(SOR)mechanism on each loop of Gummel’s iteration.Based on our derivations,it can be shown that the Scharfetter–Gummel discretization method is essentially a special case of our scheme.In addition,the consistency and convergence of the two core algorithms are proved,with three numerical examples designed to demonstrate the accuracy and computational performance of this solver.Finally,we validate the Fr-DD model for a steady-state organic field effect transistor(OFET)by fitting the simulated transconductance and output curves to the experimental data.展开更多
文摘为提高小麦条锈病的遥感监测精度,该研究利用分数阶微分能够突出光谱的细微信息以及描述光谱数据间微小差异的优势,在对条锈病胁迫下小麦冠层光谱数据进行分数阶微分处理的基础上,构建了两波段和三波段分数阶微分光谱指数,并将其应用于小麦条锈病的遥感探测。研究结果表明,1.2阶次微分光谱与小麦条锈病冠层病情严重度的相关性最高,较原始反射率光谱、一阶微分光谱和二阶微分光谱分别提高了20.9%、3.9%和20.5%;基于分数阶微分光谱指数的最优分数阶次及其对应波长构建的三波段分数阶微分光谱指数对小麦条锈病的探测能力优于两波段分数阶微分光谱指数,其中分数阶微分光化学指数与冠层病情严重度的相关系数达到0.875;以分数阶微分光谱指数为自变量构建的高斯过程回归(Gaussian Process Regression,GPR)模型对小麦条锈病冠层病情严重度的预测精度优于反射率光谱指数,其训练数据集及验证数据集病情指数(Disease Index,DI)预测值和实测值间的决定系数较反射率光谱指数分别提高了3.8%和19.1%。研究结果可为进一步实现作物健康状况大面积高精度遥感监测提供参考。
基金supported by the State Key Program of National Natural Science Foundation of China(Grant No.11931003)by the National Natural Science Foundation of China(Grant Nos.41974133,12126325)by the Postgraduate Scientific Research Innovation Project of Hunan Province(Grant No.CX20200620).
文摘For fractional Volterra integro-differential equations(FVIDEs)with weakly singular kernels,this paper proposes a generalized Jacobi spectral Galerkin method.The basis functions for the provided method are selected generalized Jacobi functions(GJFs),which can be utilized as natural basis functions of spectral methods for weakly singular FVIDEs when appropriately constructed.The developed method's spectral rate of convergence is determined using the L^(∞)-norm and the weighted L^(2)-norm.Numerical results indicate the usefulness of the proposed method.
基金Supported by the Air Science Foundation of China (Grant No. 04D52032)
文摘Equations between the differential order and the maximum of the fractional-order differential for the specified peak signals are developed based on the variation of the maximum of the specified peak signals at different orders. Also, equations between the differential order and the zero-crossing of the fractional-order differential of the specified peak signals are proposed according to the variation of the zero-crossing of the specified peak signals at different orders. Characteristic paramters of the Gaus- sian peak, Lorentzian peak, and Tsallis peak can be estimated using estimator I and estimator II which are obtained by the equations above. As a result, a new method is presented to resolve the overlapped peaks signal. Firstly, a fractional-order differential of the specified peak signals is obtained with the fractional-order differentiation filter. Then, characteristic paramters of the specified peak signals can be extracted using estimator I and estimator II. Finally, the Tsallis peak is used as a model to assign the overlapping peak signals correctly. Experimental results show that the proposed method is efficient and effective for the simulated overlapping peaks and detected overlapping voltammetric peak signals.
文摘In this study, a collocation technique is presented for approximate solution of the fractional-order logistic population model. Actually, we develop the Bessel collocation method by using the fractional derivative in the Caputo sense to obtain the approximate solutions of this model problem. By means of the fractional derivative in the Caputo sense, the collocation points, the Bessel functions of the first kind, the method transforms the model problem into a system of nonlinear algebraic equations. Numerical applications are given to demonstrate efficiency and accuracy of the method. In applications, the reliability of the scheme is shown by the error function based on the accuracy of the approximate solution.
基金This work was supported in part by the National Science Foundation through Grant CNS-1726865by the USDA under Grant 2019-67021-28990.
文摘Because charge carriers of many organic semiconductors(OSCs)exhibit fractional drift diffusion(Fr-DD)transport properties,the need to develop a Fr-DD model solver becomes more apparent.However,the current research on solving the governing equations of the Fr-DD model is practically nonexistent.In this paper,an iterative solver with high precision is developed to solve both the transient and steady-state Fr-DD model for organic semiconductor devices.The Fr-DD model is composed of two fractionalorder carriers(i.e.,electrons and holes)continuity equations coupled with Poisson’s equation.By treating the current density as constants within each pair of consecutive grid nodes,a linear Caputo’s fractional-order ordinary differential equation(FrODE)can be produced,and its analytic solution gives an approximation to the carrier concentration.The convergence of the solver is guaranteed by implementing a successive over-relaxation(SOR)mechanism on each loop of Gummel’s iteration.Based on our derivations,it can be shown that the Scharfetter–Gummel discretization method is essentially a special case of our scheme.In addition,the consistency and convergence of the two core algorithms are proved,with three numerical examples designed to demonstrate the accuracy and computational performance of this solver.Finally,we validate the Fr-DD model for a steady-state organic field effect transistor(OFET)by fitting the simulated transconductance and output curves to the experimental data.
