Chapter 8 **Perturbation Method for Solar/Infrared Radiative Transfer in a Scattering Medium with Vertical Inhomogeneity in Internal Optical Properties 141**

Yi-Ning Shi, Feng Zhang, Jia-Ren Yan, Qiu-Run Yu and Jiangnan Li

Preface

In this book, we aim to present the recent developments and applications of the perturba‐ tion theory for treating problems in applied mathematics, physics and engineering. The eight chapters presented in this book are written by 22 authors from 8 countries: Japan, Chi‐

Each chapter is independent and self-contained, providing a contemporary overview of the perturbation methods that are used in theoretical and applied sciences. The reference list at the end of each chapter provides the reader a selected list of journal papers, books and con‐ ference proceedings. The chapters can be summarized as follows: In the first chapter, a com‐ putational technique is developed to predict the piezoelectric properties of materials using the density functional perturbation theory (DFPT). In the next chapter, the development of a sliding-mode perturbation observer-based control scheme for voltage source converter based high voltage direct current systems is described. In the third chapter, a multiplication operation is introduced and via this operation, it is allowed to give the Carleman operator the form of a multiplication operator. In the same chapter, a formal perturbation theory of Carleman operators is also established. The next chapter is devoted to optimal perturbation techniques and various types of optimal perturbation techniques, namely optimal determin‐ istic perturbation theory, optimal stochastic perturbation and simultaneous stochastic per‐ turbation methods are introduced to demonstrate the efficiency of perturbation methods in predictability of dynamical systems that arise in atmospheric and oceanographic sciences. In the fifth chapter, a discussion of the nonlinear parametric systems is presented and the con‐ ditions of motions of existence in the resonance zones are put forward. In the sixth chapter, mechanical perturbations strategy is applied at the working electrode during one-step elec‐ trodeposition process and the results are compared to the standard one-step electrodeposi‐ tion. In the next chapter, an approximate analytical solution is constructed for the wellbore pressure via the method of matched asymptotic expansions applied to the one-dimensional saturation convection-dispersion equation. The solutions to this type of nonlinear equations is of great importance in fluid mechanics and especially in petroleum engineering. In the last chapter, a new inhomogeneous scheme based on perturbation methods to solve the solar/ infrared radiative transfer (SRT/IRT) problem is developed. This chapter contains significant

The book is intended to reach to researchers, scientists and postgraduate students in aca‐ demia as well as in industry and published as an open access book in order to significantly

**Dr. İlkay Bakırtaş**

Istanbul, Turkey

Istanbul Technical University Department of Mathematics

increase the reach and impact of the information that is contained in the book.

na, Algeria, France, Russia, Mexico, USA and Canada.

and applicable information in meteorological sciences.
