Meet the editor

Patrice Salzenstein holds a Masters and engineering diploma (University of Lille, 1993) and a PhD degree in Electronics (University of Lille, 1996). Between 1996 and 2001, he worked near Paris successively as a technology research engineer at THOM-SON-CSF-LCR (Thales-TRT), microwave engineer at ALCATEL, and head of the RF and Time & Frequency Group at LCIE private research laboratories. Since 2001, he has been working with

oscillators for the Centre National de la Recherche Scientifique (CNRS) at FEM-TO-ST institute in Besançon, France. In 2010, one of his articles was featured in Electronics Letters for his participation with Czech and Swiss colleagues regarding the best frequency stability ever measured on a quartz-crystal oscillator: 2.5×10-14 at 5MHz. His fields of interest in research were for optoelectronic resonators and oscillators (2010–2017) and now on Brillouin light-scattering and instrumentation as a CNRS senior research engineer. He is author or coauthor of more than 22 high-impact factors papers.

Contents

Section 1

Preface III

From Mathematics to Oscillators 1

Chapter 1 3

Chapter 2 23

Chapter 3 47

From the Atomic Scale to the Vibration of a Building 75

Chapter 4 77

Chapter 5 99

Mathematical Models of Oscillators with Memory

Oscillation Criteria of Two-Dimensional Time-Scale Systems

Time-Domain Simulation of Microstrip-Connected Solid-State

Oscillators for Close-Range Noise Radar Applications

by Vladimir Yurchenko and Lidiya Yurchenko

Oscillator Dampers in Civil Structures

by Roman Ivanovich Parovik

Quantum Harmonic Oscillator

by Coşkun Deniz

by Ozkan Ozturk

by Yonggang Tan

Section 2

## Contents


Preface

An oscillator is dedicated to the generation of signals. It is used in computers, telecoms, watchmaking, astronomy, and metrology. It can be a pendulum, an electronic oscillator based on quartz technology [1], an optoelectronic oscillator [2], or an atomic clock, depending on its application. Since water clocks of antiquity, mechanical clocks invented during the thirteenth century, and the discovery of piezoelectricity by Jacques and Pierre Curie in 1880 [3], oscillators have made great progress [4]. This book does not attempt to tell the story of oscillators, but rather to provide an overview of particular oscillator structures through examples from mathematics to oscillators, and from the millimeter scale to the vibration of a building, focusing on recent developments, as we live in a time when technology

By providing an overview of the quest of mathematics for the oscillator, we had to

• It all starts with the need to have the best mathematical models to understand what an oscillator is. This is why we became interested in the work of Roman Parovik, researcher at the Institute of Cosmophysical Research and Radio Wave Propagation at Vitus Bering Kamchatka State University, Petropavlovsk-Kamchatskiy, Russia. He investigates mathematical models of oscillators with

• Then we focused our attention on the research of Coskun Deniz, working as Lecturer in Department of Electrical-Electronics Engineering in the Aydin Adnan Menderes University, Aydin, Turkey. He has worked on the quantum harmonic oscillator (QHO) and two conventional semi-classical approximation

• Ozkan Ozturk from the American University of the Middle East in Kuwait is interested in theories of time-scale systems to acquire information about the long-time behavior of nonlinear systems. Therefore he is interested in the

We have chosen to emphasize the place of oscillators in our word. The oscillation problem begins at the micrometer scale with microstrip oscillators and extends to the macroscopic scales with civil structures such as bridges. Two following chapters

• Time-domain simulation of microstrip-connected solid-state oscillators for radar applications is a hot topic investigated by Vladimir Yurchenko and Lidiya Yurchenko at the O.Ya. Usikov Institute for Radiophysics and Electronics,

• Yonggang Tan, awarded by the Chinese construction Enterprise Management

engineering at the faculty of infrastructure engineering, Dalian University of

Association of Science and Technology, works on bridge and tunnel

oscillation criteria of two-dimensional time-scale systems.

make choices, as is evident in the selection of the first three chapters:

and mathematical analysis play a vital role.

memory.

discuss these themes:

Kharkov, Ukraine.

methods to solve QHO.
