EXACT SOLUTION AND ITS BEHAVIOR CHARACTERISTIC OF NONLINEAR DUAL-POROSITY MODEL

A nonlinear dual-porosity model considering a quadratic gradient term is presented. Assuming the pressure difference between matrix and fractures as a primary unknown, to avoid solving the simultaneous system of equations, decoupling of fluid pressures in the blocks from the fractures was furnished with a quasi-steady-state flow in the blocks. Analytical solutions were obtained in a radial flow domain using generalized Hankel transform. The real value cannot be gotten because the analytical solutions were infinite series. The real pressure value was obtained by numerical solving the eigenvalue problem. The change law of pressure was studied while the nonlinear parameters and dual-porosity parameters changed, and the plots of typical curves are given. All these result can be applied in well test analysis.

Remaining useful lifetime prediction for equipment based on nonlinear implicit degradation modeling

Nonlinearity and implicitness are common degradation features of the stochastic degradation equipment for prognostics.These features have an uncertain effect on the remaining useful life(RUL)prediction of the equipment.The current data-driven RUL prediction method has not systematically studied the nonlinear hidden degradation modeling and the RUL distribution function.This paper uses the nonlinear Wiener process to build a dual nonlinear implicit degradation model.Based on the historical measured data of similar equipment,the maximum likelihood estimation algorithm is used to estimate the fixed coefficients and the prior distribution of a random coefficient.Using the on-site measured data of the target equipment,the posterior distribution of a random coefficient and actual degradation state are step-by-step updated based on Bayesian inference and the extended Kalman filtering algorithm.The analytical form of the RUL distribution function is derived based on the first hitting time distribution.Combined with the two case studies,the proposed method is verified to have certain advantages over the existing methods in the accuracy of prediction.

Langrangian formulation and solitary wave solutions of a generalized Zakharov–Kuznetsov equation with dual power-law nonlinearity in physical sciences and engineering

This paper presents analytical studies carried out explicitly on a higher-dimensional generalized Zakharov–Kuznetsov equation with dual power-law nonlinearity arising in engineering and nonlinear science.We obtain analytic solutions for the underlying equation via Lie group approach as well as direct integration method.Moreover,we engage the extended Jacobi elliptic cosine and sine amplitude functions expansion technique to seek more exact travelling wave solutions of the equation for some particular cases.Consequently,we secure,singular and nonsingular(periodic)soliton solutions,cnoidal,snoidal as well as dnoidal wave solutions.Besides,we depict the dynamics of the solutions using suitable graphs.The application of obtained results in various fields of sciences and engineering are presented.In conclusion,we construct conserved currents of the aforementioned equation via Noether’s theorem(with Helmholtz criteria)and standard multiplier technique through the homotopy formula.

EQ^(rot)_1 Nonconforming Finite Element Method for Nonlinear Dual Phase Lagging Heat Conduction Equations

EQrot nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O（h2） one order higher than its interpolation error O（h）, the superclose results of order O（h2） in broken Hi-norm are obtained. At the same time, the global superconvergence in broken Hi-norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O（h4） is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQrot element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.