An Unbounded Experience In Random Walks With Applications - Hardcover

Michael F Shlesinger

Hardcover

ISBN 10: 9811232806 ISBN 13: 9789811232800

Publisher: World Scientific Publishing, 2021

Synopsis

This volume comprises the author's account of the development of novel results in random walk theory and its applications during the fractal and chaos revolutions. The early history of probability is presented in an engaging manner, and peppered with pitfalls and paradoxes. Readers will find the introduction of Paul Lévy's work via Mandelbrot's Lévy flights which are featured uniquely as Weierstrass and Riemann random walks.

Generalizations to coupled memories, internal states and fractal time are introduced at the level for graduate students. Mathematical developments are explained including Green's functions, inverse Mellin transforms, Jacobians, and matrix methods. Applications are made to anomalous diffusion and conductivity in amorphous semiconductors and supercooled liquids. The glass transition is discussed especially for pressure effects.

All along the way, personal stories are recounted and special appreciations are made to Elliott Montroll and Harvey Scher for their ever-expanding influence on the field of non-equilibrium anomalous processes that now are found in topics including disordered materials, water table processes, animal foraging, blinking quantum dots, rotating flows, optical lattices, dynamical strange attractors and strange kinetics.

About this title

About the Author

Dr Michael F Shlesinger has worked in universities, a non-profit research company, and for the last 37 years in the Office of Naval Research. There he has headed the physics division and worked as a chief scientist and as a member of the senior executive service. With the Presidential Rank Award and the Outstanding Lifetime Achievement Award, he held the Kinnear Professorship at the USNA. He is a fellow of the American Physical Society with their Outstanding Referee award and has published works on stochastic processes including cover articles in Physics Today. In another field he has patents on protein design. He co-founded the World Scientific journal Fractals and was a divisional associate editor of Physical Review Letters. He co-founded the Experimental Chaos Conference. He has given invited talks including the Michelson Lecture at the USNA and the Regents Lecture at UCSD.

Edition details

• Publisher: World Scientific Publishing
• Publication date: 2021
• Language: English
• ISBN 10: 9811232806
• ISBN 13: 9789811232800
• Binding: Hardcover
• Number of pages: 216