Series:

Nonlinear Physical Science

2 total works

Cover of Fractional Derivatives for Physicists and Engineers

The first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. Fractional Derivatives for Physicists and Engineers— The first volume contains a clear introduction into such a modern branch of analysis as the fractional calculus. The second develops a wide panorama of applications of the fractional calculus to various physical problems. This book recovers new perspectives in front of the reader dealing with turbulence and semiconductors, plasma and thermodynamics, mechanics and quantum optics, nanophysics and astrophysics. 

The book is addressed to students, engineers and physicists, specialists in theory of probability and statistics, in mathematical modeling and numerical simulations, to everybody who doesn't wish to stay apart from the new mathematical methods becoming more and more popular.

Prof. Vladimir V. UCHAIKIN is a known Russian scientist and pedagogue, a Honored Worker of Russian High School, a member of the Russian Academy of Natural Sciences. He is the author of about three hundreds articles and more than a dozen books (mostly in Russian)  in Cosmic ray physics, Mathematical physics, Levy stable statistics, Monte Carlo methods with applications to anomalous processes in complex systems of various levels: from quantum dots to the Milky Way galaxy.

Cover of Electron-Photon Cascades
This book demonstrates the practical application of an alternative approach to current problems in high-energy astrophysics. In high-energy astrophysical processes, single collisions are accompanied by the appearance of many secondary particles with different properties. To describe the infinitesimal evolution of such a system at a measurement instant, as is commonly done when deriving the kinetic equation for the system with conserved number of particles, one must know either its prehistory or the infinite family of many-particle distributions. An alternative to this approach is to use an adjoint (in the sense of Lagrange) mathematical formalism, where the independent active variable is the phase position of a primary particle generating the cascade, and the dependent variable has the form of a functional of the cascade as a whole, interpreted as the reading of some not necessarily linear (additive) detector. This approach is characterized by mathematical efficiency: no matter how many particles are formed in a cascade, the active argument of the desired functional always remains one particle. The second advantage is its generality: the formalization of the readings of the detector, which performs real measurements through the functionality of a random implementation of the cascade, allows it to be applied to a wide range of actually used devices and installations.
Readers will be able to master the fundamentals of particle astrophysics in the context of the latest developments in the field. It will benefit graduate students and established researchers alike, equipping them with the knowledge and tools necessary to design and interpret their own experiments and, ultimately, to address a number of questions about the nature and origin of cosmic particles that have arisen in recent research.