Fokker

One of the central problems synergetics is concerned with consists in the study of macroscopic qualitative changes of systems belonging to various disciplines such as physics, chemistry, or electrical engineering. When such transitions from one state to another take place, fluctuations, i.e., random processes, may play an im portant role. Over the past decades it has turned out that the Fokker-Planck equation pro vides a powerful tool with which the effects of fluctuations close to transition points can be adequately treated and that the approaches based on the Fokker Planck equation are superior to other approaches, e.g., based on Langevin equa tions. Quite generally, the Fokker-Planck equation plays an important role in problems which involve noise, e.g., in electrical circuits. For these reasons I am sure that this book will find a broad audience. It pro vides the reader with a sound basis for the study of the Fokker-Planck equation and gives an excellent survey of the methods of its solution. The author of this book, Hannes Risken, has made substantial contributions to the development and application of such methods, e.g., to laser physics, diffusion in periodic potentials, and other problems. Therefore this book is written by an experienced practitioner, who has had in mind explicit applications to important problems in the natural sciences and electrical engineering.

This is an analysis of multidimensional nonlinear dissipative Hamiltonian dynamical systems subjected to parametric and external stochastic excitations by the Fokker-Planck equation method.The author answers three types of questions concerning this area. First, what probabilistic tools are necessary for constructing a stochastic model and deriving the FKP equation for nonlinear stochastic dynamical systems? Secondly, what are the main results concerning the existence and uniqueness of an invariant measure and its associated stationary response? Finally, what is the class of multidimensional dynamical systems that have an explicit invariant measure and what are the fundamental examples for applications?

There has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations, and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not self-adjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction, this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart, the global Weyl-Hörmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schrödinger-type operators, the Witten complexes, and the Morse inequalities.

Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems in which noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the Itô calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.

Vol. 1.

Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and nonlinear Fokker-Planck equations that describe the evolution of distribution functions. It emphasizes principles and notions of the theory (e.g. self-organization, stochastic feedback, free energy, and Markov processes), while also illustrating the wide applicability (e.g. collective behavior, multistability, front dynamics, and quantum particle distribution). The focus is on relaxation processes in homogeneous many-body systems describable by nonlinear Fokker-Planck equations. Also treated are Langevin equations and correlation functions. Since these phenomena are exhibited by a diverse spectrum of systems, examples and applications span the fields of physics, biology and neurophysics, mathematics, psychology, and biomechanics.

Comprehensive biography of Anthony Fokker, the famed Dutch pilot and daredevil aviator Anthony Fokker: The Flying Dutchman Who Shaped American Aviation tells the larger-than-life true story of maverick pilot and aircraft manufacturer Anthony Fokker. Fokker came from an affluent Dutch family and developed a gift for tinkering with mechanics. Despite not receiving a traditional education, he stumbled his way into aviation as a young stunt pilot in Germany in 1910. He survived a series of spectacular airplane crashes and rose to fame within a few years. A combination of industrial espionage, luck, and deception then propelled him to become Germany's leading aircraft manufacturer during World War I, making him a multimillionaire by his midtwenties. When the German Revolution swept the country in 1918 and 1919, Fokker made a spectacular escape to the United States. He set up business in New York and New Jersey in 1921, and shortly thereafter became the world's largest aircraft manufacturer. The U.S. Army and Navy acquired his machines, and his factories equipped legendary carriers such as Pan American and TWA at the dawn of commercial air transport. Yet despite his astounding success, his empire collapsed in the late 1920s after a series of ill-conceived business decisions and deeply upsetting personal dramas. In 1927, aviator Richard Byrd solicited a Fokker three-engine plane to be the first to fly non-stop across the Atlantic. The plane was damaged on a test flight and Charles Lindbergh beat him to it. Lindbergh's solo adventure in the Spirit of St. Louis earned him--and cost Fokker--a lasting place in the history books. Using previously undiscovered records and primary sources, Marc Dierikx traces Fokker's extraordinary life and celebrates his spectacular achievements.

The appearance in July 1915 of the Fokker E I heralded a reign of terror over the Western Front that the Allies called the 'Fokker Scourge'. The French Nieuport 11 was one type desperately thrown into action to counter the Fokkers. The swirling dogfights between this fighter – and its more powerful but more unwieldy stablemate, the Nieuport 16 – and a succession of improved Fokkers, the E II, E III and E IV, came to symbolise air combat in World War I. This book gives a detailed look at the developmental history of the fighters, contrasting the interrupter gear-equipped Fokker with the more improvised solution incorporated in the Nieuport – a machine gun fitted to the upper wing to avoid the propeller entirely. The Germans went on to abandon the monoplane in favour of a new and deadly generation of biplane fighters, based on the lessons learned from these vicious engagements and influenced by the success of the French Nieuport.