Preface

**Chapter 7 113**

**Chapter 8 131**

The Possibilities of Modeling Petri Nets and Their Extensions

Line Impedance Emulator: Modeling, Control Design, Simulation

*by Marwa Ben Saïd-Romdhane, Sondes Skander-Mustapha*

*by Goharik Petrosyan*

and Experimental Validation

*and Ilhem Slama-Belkhodja*

**II**

Information technologies have changed people's lives to a great extent, and now it is almost impossible to imagine any activity that does not depend on computers in some way. Since the invention of first computer systems, people have been trying to avail computers in order to solve complex problems in various areas. The need for computer systems in the calculation of different building and automotive constructions has appeared with the development of industry. Traditional methods of calculation have been replaced by computer programs that have the ability to predict the behavior of structures under different loading conditions. Hence, expensive experiments, tests and examinations had been replaced by cheaper and more powerful computational methods that do not require the destruction of structure in order to determine its capacity.

Computer simulation or a computer model has the task to simulate the behavior of an abstract model of a particular system. Computer simulations have become a useful part of mathematical modeling of many natural systems in physics, quantum mechanics, chemistry and biology, then in economic systems, psychology and social sciences, as well as in the engineering process of new technologies, in order to gain a better insight into their way of working and behaving.

In comparison to classical modeling (model making, prototyping, etc.), mathematical and numerical modeling is more cost-effective and model itself can be checked and examined much faster and in a more efficient way, therefore one does not need to use considerable material resources - money, raw materials for modeling, energy, etc. Mathematical modeling provides more freedom for engineers to utilize different variations of components, elements and parameters of conceived technical solutions. The advantage of this type of modeling is the fact that only important and poorly tested elements of the system can be submitted to modeling.

Any kind of previously mentioned process of modeling requires the engineers' excellent knowledge in the field one is considering, as well as the methods used for solving the required task. The attained knowledge through permanent education has the significant influence on the quality of designed model.

Computer simulations are different from computer programs. Contrary to computer programs that run for a few minutes, simulations can be run on the local network and can last for hours or even for days. It can be said that the simulations exceeded many methods that use pencil and paper for solving any kind of mathematical problems.

The first chapter of this book illustrates the usage of pilot Fortran software library for the solution of Laplace's Equation by the boundary element method (BEM). The second chapter describes the optimal control of thermal pollution emitted by power plants. In the third chapter, the authors present the finite difference solution of conjugate heat transfer in double pipe with trapezoidal fins. The fourth chapter deals with a photovoltaic system integrated into the buildings. The fifth chapter presents the way in which computer simulation affect the practice of diagnosis in

the field of oral medicine and radiology. In the sixth chapter, the authors write about the simulation and parametric inference of a mixed effects model with stochastic differential equations using the Fokker – Planck equation solution. The seventh chapter illustrates the possibilities of modeling Petri nets and their extensions. Finally, the eighth chapter presents modeling, control design, simulation and experimental validation of the line impedance emulator.

We would like to express our sincere gratitude to all the authors and coauthors for their contribution. The successful completion of the book *Numerical Modeling and Computer Simulation* has been the result of the cooperation between many people. We would especially like to thank the Publishing Process Manager Ms. Dajana Pemac for her support during the publishing process.

> **Dragan M. Cvetković** Singidunum University, Faculty of Informatics and Computing, Belgrade, Republic of Serbia

> > Section 1

Numerical Modeling

**1**

**Gunvant A. Birajdar** Tata Institute of Social Sciences, School of Rural Development, Tuljapur, District - Osmanabad, Maharashtra Section 1
