Numerical solution of the nonlinear Klein–Gordon equation using radial basis functions

The nonlinear Klein–Gordon equation is used to model many nonlinear phenomena. In this paper, we propose a numerical scheme to solve the one-dimensional nonlinear Klein–Gordon equation with quadratic and cubic nonlinearity. Our scheme uses the collocation points and approximates the solution using Thin Plate Splines (TPS) radial basis functions (RBF). The implementation of the method is simple as finite difference methods. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme.     

Some remarks on the two-level DEA model

The two-level DEA model was introduced to increase the discriminational power of Data Envelopment Analysis (DEA) models. This nonlinear model was presented by Meng et al. (2008) [3], and then converted into a linear model by Kao (2008) [4].In this paper two subjects will be discussed: first, we show that the two-level DEA model is a special case of DEA models where weight restrictions are applied. Then, we express that the nonlinear model is equivalent to the conventional DEA model.     

Wave solitons in a coupled left-handed nonlinear transmission line: Effect of the coupling parameter

In this work, we investigate the dynamics of modulated waves in a discrete coupled Left-Handed nonlinear transmission line, assuming a one-dimensional (1-D) propagation variation. A nonlinear Schrödinger equation (NLSE) is derived, analytical solitons are found and the instability region is presented for this model.     

Adaptive Strategy for the Damping Parameters in an Iteratively Regularized Gauss–Newton Method

In this paper, a convergence analysis of an adaptive choice of the sequence of damping parameters in the iteratively regularized Gauss–Newton method for solving nonlinear ill-posed operator equations is presented. The selection criterion is motivated from the damping parameter choice criteria, which are used for the efficient solution of nonlinear least-square problems. The performance of this selection criterion is tested for the solution of nonlinear ill-posed model problems.     

On the calculation of Topological Derivatives considering an exemplary nonlinear material model

In this contribution, a new approach for dealing with material nonlinearities in structural optimization is presented. The method combines the advantage of the calculation of the Topological Derivatives in elasticity problems with the use of meta-modelling for capturing complex correlations. For an exemplary nonlinear material model, the calculation of the Topological Derivative and the resulting difference to the linear elastic material model is shown. An academic example shows the difference between the linear and the nonlinear material model. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

非线性测量误差模型的影响分析

本文对非线性测量误差模型给出了统一的诊断方法,并证明了数据删除模型与均值漂移模型的等价性,由此出发得到了Cook距离、残差、杠杆值等诊断统计量.本文还讨论了非线性测量误差模型的局部影响分析,并给出了一个具体应用实例.推广了Zhao & Lee(1995)的结果.     

Stabilizer control design for nonlinear systems based on the hyperbolic modelling

In this paper, a new approach to design a stabilizer control for nonlinear systems is presented. First, the general form of the nonlinear control systems is approximated with a hyperbolic model. Then, by a feedback technique, a stabilizer control for the hyperbolic system is obtained. It is shown that this control can stabilize the original nonlinear control system. Finally, by some illustrative examples, the efficiency of the presented approach is demonstrated.     

A Simulation-free Nonlinear Model Order-reduction Approach and Comparison Study

In this paper, a new approach to the model order reduction of nonlinear systems is presented. This approach does not need a simulation of the original system, and therefore, it is suitable for large systems. By separating the linear and nonlinear parts of the original nonlinear model, the idea is to consider the nonlinearities of the resulting system as additional inputs. Based on the linear system from the last step, a known order-reduction method can be applied to find the coefficients of the nonlinear and the linear parts of a reduced-order model. Two different methods from linear-order reduction (balancing and truncation and Eitelberg's method with some modification) are used for this purpose, and their advantages and disadvantages are discussed. For comparison with some known methods in order reduction of nonlinear systems, three other methods are discussed briefly. Finally, a technical nonlinear system is reduced, and different methods are compared.     

A semiparametric method for estimating nonlinear autoregressive model with dependent errors

The first-order nonlinear autoregressive model is considered and a semiparametric method is proposed to estimate regression function. In the presented model, dependent errors are defined as first-order autoregressive AR(1). The conditional least squares method is used for parametric estimation and the nonparametric kernel approach is applied to estimate regression adjustment. In this case, some asymptotic behaviors and simulated results for the semiparametric method are presented. Furthermore, the method is applied for the financial data in Iran’s Tejarat-Bank.     

Existence and Blow-up for a Parabolic System from?Combustion Theory

We study the stability of the Solid Fuel Model, which represents a thermal reaction of a solid material. This model corresponds to a nonlinear eigenvalue problem of two strongly coupled nonlinear reaction–diffusion equations, with different boundary conditions on each unknown. We obtain a strong bifurcation criterion for the steady problem and estimates for the blow-up time in the unsteady case. In addition, numerical solutions of both the steady and unsteady problem are presented to illustrate the results.     

Homotopy perturbation based linearization of nonlinear heat transfer dynamic

In this paper a new linearization procedure based on Homotopy Perturbation Method (HPM) will be presented. The procedure begins with solving nonlinear differential equation by HPM. This will be done by evaluation of the time response of a nonlinear dynamic. An equivalent Laplace transform of the time response will be obtained. In the preceding, the effect of an external excitation i.e. input, will be removed from the model to find an approximate linear model for the nonlinear dynamic. The effectiveness of the procedure is verified using a heat transfer nonlinear equation. Ultimately, both HPM based linear model and that of nonlinear have been controlled via a closed loop PID controller. The simulation result shows the significance of the proposed technique.     

An implicit finite difference scheme for the nonlinear size-structured population model

In this paper we consider the "fully nonlinear" size structured population model. We develop an implicit finite difference scheme to approximate the solution of this nonlinear partial differential equation. The convergence of this approximation to a unique bounded variation solution of this model is obtained. Numerical results to an example problem are presented.     

A new nonlinear dynamic analysis method of rotor system supported by oil-film journal bearings

The strong nonlinear behavior usually exists in rotor systems supported by oil-film journal bearings. In this paper, the partial derivative method is extended to the second-order approximate extent to predict the nonlinear dynamic stiffness and damping coefficients of finite-long journal bearings. And the nonlinear oil-film forces approximately represented by dynamic coefficients are used to analyze nonlinear dynamic performance of a symmetrical flexible rotor-bearing system via the journal orbit, phase portrait and Poincaré map. The effects of mass eccentricity on dynamic behaviors of rotor system are mainly investigated. Moreover, the computational method of nonlinear dynamic coefficients of infinite-short bearing is presented. The nonlinear oil-film forces model of finite-long bearing is validated by comparing the numerical results with those obtained by an infinite-short bearing-rotor system model. The results show that the representation method of nonlinear oil-film forces by dynamic coefficients has universal applicability and allows one easily to conduct the nonlinear dynamic analysis of rotor systems.     

Lead with closed-loop system compensation of a radically rotating elastic rod attached to a rigid body part II: Nonlinear system simulation and control

As was stated in Part I, the linear control models of a radically rotating elastic rod in all the analysis and design procedures for lead with closed-loop system compensation is presented. For a given linear system model, if the model is accurate, it will be accurate only over a very limit range of operation of the system. However, all the effort of design comes to be meaningful until it is tested using the nonlinear system model. On the other hand, the response of the nonlinear system model will not be as good as that of the linear model. In fact, some iterations on the design and on improving the design based-model are often needed before there is even a resemblance between the linear model response and the nonlinear system response. The present paper is a continuation of [1] and nonlinear control system simulation and a tuning process are presented. While almost all design procedures for physical system contain some tuning process, the development of an analytic design procedure for models of distributed-parameter control system can be evidently shown through this paper.     

Constitutive modeling and FEM for a nonlinear Cosserat continuum

The choice of non-standard material parameters in the presented micropolar continuum model leads to a highly nonlinear problem which calls also for a nonlinear numerical treatment. The model benefits in describing length scale effects as really non-linear effects. The numerical torsion test is one example for the possibilities of our model. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An improvement to multiple criteria ABC inventory classification

In this paper we presented an extended version of the Ng-modelg [W.L. Ng, A simple classifier for multiple criteria ABC analysis, European Journal of Operational Research 177 (2007) 344–353] for multi-criteria inventory classification. The proposed model is a nonlinear programming model which determines a common set of weights for all the items. Our model not only incorporates multiple criteria for ABC classification, but also maintains the effects of weights in the final solution, an improvement over the model proposed by Ng. An illustrative example is presented to compare our model and the Ng-model.     

Numerical solution of a thermomechanical coupled model governing glacier evolution

In this paper the numerical solution of a highly nonlinear model for the thermomechanical behavior of polythermal glaciers is presented. The modeling follows the shallow ice approximation (SIA) for glaciers introduced in Fowler (1997) [13]. The model has been extended to incorporate additional moving boundaries and other nonlinear features. Moreover, a fixed domain formulation is proposed to avoid the computational drawbacks of a time-dependent domain in the numerical simulation with front tracking methods. In this setting, the coupled problem is decomposed into different nonlinear problems which allow one to obtain sequentially the profile evolution, the velocity field, the glacier surface and atmospheric temperatures, basal magnitudes and the temperature distribution inside the ice mass. A fixed point iteration algorithm converges to the solution of the nonlinear coupled problem. Among different numerical methods involved in the solution of the subproblems, characteristic schemes for time discretization, finite elements for spatial discretization, duality methods for the nonlinearities associated to maximal monotone operators and a Newton scheme for the nonlinear viscous term are proposed. Several numerical simulation examples illustrate the performance of the numerical methods and the behavior of the involved physical magnitudes.     

Constitutive modeling of ferromagnetic and ferroelectric behaviors and application to multiferroic composites

In this paper, the constitutive modeling of nonlinear multifield behavior as well as the finite element implementation are presented. Nonlinear material models describing the magneto-ferroelectric or electro-ferromagnetic behaviors are presented. Both physically and phenomenologically motivated constitutive models have been developed for the numerical calculation of principally different nonlinear magnetostrictive behaviors. Further, the nonlinear ferroelectric behavior is based on a physically motivated constitutive model. On this basis, the polarization in the ferroelectric and magnetization in the ferromagnetic and magnetostrictive phases, respectively, are simulated and the resulting effects analyzed. Numerical simulations focus on the calculation of magnetoelectric coupling and on the prediction of local domain orientations going along with the poling process, thus supplying information on favorable electric-magnetic loading sequences. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Calculation of Fiber Orientation in Three-Dimensional Arterial Walls

In this contribution an approach for the fiber reorientation in three-dimensional arterial walls is presented. In detail the load-bearing capacity of the tissue is increased by re orienting the fibers with respect to the principal stresses, cf. [1]. The improved fiber reorientation algorithm is combined with the polyconvex nonlinear anisotropic material model presented in [3]. The results of a three-dimensional finite element simulation, where the reorientation approach is applied to a short segment of a patient-specific arterial geometry, are presented. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)