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 and mathematical analysis play a vital role.

By providing an overview of the quest of mathematics for the oscillator, we had to make choices, as is evident in the selection of the first three chapters:


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 discuss these themes:


Technology, Dalian, China. He is interested in reducing vibrations of civil structures under harmonic or wind excitations.

Authors and coauthors cover various areas of oscillator research throughout this book. The common thread of the chapters in this book is to conduct investigations in the field of oscillators. This book will certainly be useful for students, engineers, and researchers who want to keep up with the latest developments in oscillators through chosen examples. We assume that the original approach of this book consists in the possibility offered to the reader to realize the diversity of the field covered by oscillators and their relevance in research today.

Patrice Salzenstein

Senior Research Engineer, Centre National de la Recherche Scientifique (CNRS), Franche-Comté Electronique Mécanique Thermique et Optique—Sciences et Technologies (FEMTO-ST) institute, mixed research unit associated with CNRS (UMR 6174), Besançon, France

### References

[1] Salzenstein P, Kuna A, Sojdr L, Chauvin J. Significant step in ultra high stability quartz crystal oscillators. Electronics Letters. 2010;46(21): 1433-1434

[2] Volyanskiy K, Salzenstein P, Tavernier H, Pogurmirskiy M, Chembo YK, Larger L. Compact optoelectronic microwave oscillators using ultra-high q whispering gallery mode disk-resonators and phase modulation. Optics Express. 2010; 18(21):22358-22363

[3] Curie J, Curie P. Développement par pression, de l'électricité polaire dans les cristaux hémièdres à faces inclinées. Comptes Rendus. 1880;91:294

[4] Salzenstein P. Recent progress in the performances of ultrastable Quartz resonators and oscillators. International Journal for Simulation and Multidisciplinary Design Optimization. 2016;7:A8(6)

Section 1

From Mathematics to

Oscillators

1

Section 1
