Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): I. Mathematical Framework

This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5th-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.

Exponential-fraction trial function method to the 5th-order mKdV equation

This paper obtains some solutions of the 5th-order mKdV equation by using the exponential-fraction trial function method, such as solitary wave solutions, shock wave solutions and the hopping wave solutions. It successfully shows that this method may be valid for solving other nonlinear partial differential equations.

Asymptotic Property of Solutions in a 4th-Order Parabolic Model for Epitaxial Growth of Thin Film

This paper deals with a homogeneous Neumann initial-boundary problem of a 4th-order parabolic equation modeling epitaxial growth of thin film. We determine the classification of initial energy on the existence of blow-up, global existence and extinction of solutions by using the potential well method and the auxiliary function method.Moreover, asymptotic estimates on global solution and extinction solution are studied,respectively.

Numerical Simulation of Two-Dimensional Dendritic Growth Using Phase-Field Model

In this article, we study the phase-field model of solidification for numerical simulation of dendritic crystal growth that occurs during the casting of metals and alloys. Phase-field model of solidification describes the physics of dendritic growth in any material during the process of under cooling. The numerical procedure in this work is based on finite difference scheme for space and the 4th-order Runge-Kutta method for time discretization. The effect of each physical parameter on the shape and growth of dendritic crystal is studied and visualized in detail.

Periodic Solutions for the Higher Order Differential Equations with Multiple Delays

By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalization of the results developed by W. Layton to the case of multiple delays.

An Innovative State-of-charge Estimation Method of Lithium-ion Battery Based on 5th-order Cubature Kalman Filter

The lithium-ion batteries have drawn much attention as the major energy storage system.However,the battery state estimation still suffers from inaccuracy under dynamic operational conditions,with the unstable environmental noise influencing the robustness of estimation.This paper presents a 5th-order cubature Kalman filter with improvements on adaptivity for real-time state-of-charge estimation.The second-order equivalent circuit model is developed for describing the characteristics of battery,and parameter identification is carried out according to particle swarm optimization.The developed method is validated in stable and dynamic conditions,and simulation results show a satisfactory consistency with the experimental results.The maximum estimation error under static conditions is less than 3%and the maximum error under dynamic conditions is 5%.Numerical analysis indicates that the method has better convergence and robustness than the traditional method under the disturbances of initial error,which demonstrates the potential for EV applications in harsh environments.The proposed method shows application potential for both online estimations and cloud-computing system,indicating its diverse application prospect in electric vehicles.

NumericalAnalysis of theMixed 4th-OrderRunge-Kutta Scheme of Conditional Nonlinear Optimal Perturbation Approach for the EI Nino-Southern OscillationModel

In this paper,we proposes and analyzes the mixed 4th-order Runge-Kutta scheme of conditional nonlinear perturbation(CNOP)approach for the EI Ni˜no-Southern Oscillation(ENSO)model.This method consists of solving the ENSO model by using a mixed 4th-order Runge-Kutta method.Convergence,the local and global truncation error of this mixed 4th-order Runge-Kutta method are proved.Furthermore,optimal control problem is developed and the gradient of the cost function is determined.

H_∞ Control of a 5th- order Model of Synchronous Generators

：This paper deals with H∞ control of a 5th-order model of synchronous generators. First,byusing the method of exact linearization, we transform the 5th-order model into a linear one. Then we assignthe pole of the linearized model in the open left half plane. Finally, we apply the design method of linear H∞control to get a state feedback controller.