Exactly satisfying initial conditions neural network models for numerical treatment of first Painlevé equation

In this paper, novel computing approach using three different models of feed-forward artificial neural networks (ANNs) are presented for the solution of initial value problem (IVP) based on first Painlevé equation. These mathematical models of ANNs are developed in an unsupervised manner with capability to satisfy the initial conditions exactly using log-sigmoid, radial basis and tan-sigmoid transfer functions in hidden layers to approximate the solution of the problem. The training of design parameters in each model is performed with sequential quadratic programming technique. The accuracy, convergence and effectiveness of the proposed schemes are evaluated on the basis of the results of statistical analyses through sufficient large number of independent runs with different number of neurons in each model as well. The comparisons of these results of proposed schemes with standard numerical and analytical solutions validate the correctness of the design models.     

Collapse load of composite laminates: Lower bound evaluation by stress field analytical approximation

The paper proposes a limit analysis approach to define the ultimate load capacity of orthotropic composite laminates under biaxial loading and plane stress conditions. A lower bound to the collapse load multiplier is computed by solving a maximization nonlinear problem, according to the static theorem of limit analysis. To set up the optimization problem a stress field distribution is hypothesized at lamina level, moreover inter-lamina stresses are also considered. The effectiveness and validity of the proposed approach is shown by comparing the obtained numerical predictions both with available experimental data and with other numerical results carried out by means of a different numerical lower bound approach.     

Third order optical nonlinearities characteristics of Disperse Red1 organic dye molecules inside of polymeric nanocapsules

Measuring nonlinear optical response of a specific material in a mixture, not only leads to investigate the behavior of a particular component in various circumstances, but also can be a way to select suitable combination and optimum concentration of additives and therefore obtaining the maximum nonlinear optical signals. In this work, by using dual-arm Z-scan technique, the nonlinear refractive index of Disperse Red1 (DR1) organic dye molecules inside the core of prepared polymeric nanocapsules was measured among various materials which prepared nanocapsules were made of them. Then the measured value was compared with nonlinear refractive index of DR1 solved in dichloromethane.     

Second harmonic generation from a ferroelectric film

We derive an expression for transmittivity (T_SHG) of second harmonic generation (SHG) signals from a ferroelectric (FE) film. Intensities of up and down fields in the medium are investigated in relation to T_SHG. The derivations are made based on undepletion of input fields and nonlinear wave equation derived from the Maxwell equations. We present two cases: film without mirrors and with partial mirrors. Expressions for the newly derived nonlinear susceptibility coefficients of SHG for real crystal symmetry [J. Opt. Soc. Am. B 19 (2002) 2007] are used to get more realistic results. Variations in T_SHG with respect to film thickness are illustrated.     

Profiling Voids Embedded in a Slab by a Non-Linear Model

In this paper, by applying a non linear model for the electromagnetic inverse scattering, a technique for the dielectric profiling of a planarly layered medium is investigated and applied to void localization and diagnostics inside a homogeneous lossless slab (one-dimensional geometry). Data are collected under plane wave multifrequency normal incidence. Suitable finite dimensional representations for the unknown functions are introduced and their influence on the model is discussed. The resulting functional equation is solved by the method of weighted residuals and the solution algorithm amounts to minimizing a non quadratic function, where particular attention is devoted to reduce the occurrence of local minima. Finally, the inversion algorithm is validated by applications to both simulated and experimental data.     

Multi-input,multi-output flight control system design for the YF-16 using nonlinear QFT and pilot compensation

Nonlinear quantitative feedback theory (QFT) and pilot compensation techniques are used to design a 2 × 2 flight control system for the YF-16 aircraft over a large range of plant uncertainty. The design is based on numerical input-output time histories generated with a FORTRAN implemented nonlinear simulation of the YF-16. The first step of the design process is the generation of a set of equivalent linear time-invariant (LTI) plant models to represent the actual nonlinear plant. It has been proven that the solution to the equivalent plant problem is guaranteed to solve the original nonlinear problem. Standard QFT techniques are then used in the design synthesis based on the equivalent plant models. A detailed mathematical development of the method used to develop these equivalent LTI plant models is provided. After this inner-loop design, pilot compensation is developed to reduce the pilot's workload. This outer-loop design is also based on a set of equivalent LTI plant models. This is accomplished by modelling the pilot with parameters that result in good handling qualities ratings, and developing the necessary compensation to force the desired system responses.     

An explicit finite difference method for finite-time observers

In this paper we present a numerical method for estimating the current state of a nonlinear control system. We use finite differences to discretize a modified version of the finite-time observer equations in James. The discretized equations are simple and easily programmed. The convergence and accuracy of the scheme is proved, and the scheme enjoys a number of important properties: availability of rate of convergence estimates, good robustness characteristics, and the ability to handle certain types of discontinuities in the observations. The major disadvantage is that the number of grid points required increases exponentially with the number of state dimensions.     

双轴晶体主平面上倍频的相位匹配

从折射率椭球方程和折射率椭球面出发，讨论光束在双轴晶体中传播及偏振的特性、主平面倍频共线相位匹配（PM）问题，得到了双轴晶体主平面内激光所有可能PM倍频的8种偏振组合及其相应的PM角公式、有效非线性（NL）系数deff的一般表达式。结果表明：得到的公式简单，可大大简化PM参数计算及优化设计；折射率椭球面是单层曲面，比双层的折射率面简单；基于折射率椭球面寻找所有可能PM的类型、偏振组合的方法物理图像简明，易于理解，大大降低了双轴晶体PM问题分析的难度。     

A continuum-based modeling of MEMS devices for estimating their resonant frequencies

A continuum-based modeling of coupled electrostatics-structure interactions is presented for the frequency computations of MEMS devices. The present general formulation of electrostatics accounting for free space is validated first by specializing it to one-dimensional uniform motion of conducting surfaces and comparing the resulting electrostatics to conventional lumped models. The general coupled electrostatics-structure interactions are then applied for the prediction of resonant frequencies of MEMS devices due to bias-voltage changes and temperature variations. Comparisons of predicted resonant frequencies obtained by the present coupled electrostatics-structure interaction models with experimental results available in the literature demonstrate that the proposed continuum-based interaction modeling yields high-confidence predictions of resonant frequencies of MEMS devices.     

DESIGN AND IMPLEMENTATION OF STATE OBSERVERS IN REACTIVE DISTILLATION

This study demonstrates that state observers can be developed and applied to infer the composition profiles of reactive distillation columns from noise-contaminated temperature measurements. The design and implementation of a Kalman filter (KF) and a Luenberger observer (LO) are carried out, and their performances are quantitatively assessed. The reliability, accuracy, and robustness of the two designs method are examined and compared quantitatively. The design and implementation of a Luenberger observer are simpler and easier to carry out than those of a Kalman filter. On the other hand, a Kalman filter is found to be more robust to a noisy measurements, erroneous initial estimates, and model uncertainties. A Luenberger observer could be used for composition estimation of reactive distillation when an ideal model of the system can reasonably approximate the real system; otherwise, a Kalman filter is recommended to be applied in more practical situations.