Modern achievements in the intensively developing field of applied mathematics are presented in this monograph. In particular, it proposes a new approach to extremal problem theory for nonlinear operators, differential-operator equations and inclusions, and for variational inequalities in Banach spaces. An axiomatic study of nonlinear maps (including multi-valued ones) is given, and the properties of resolving operators for systems, consisting of operator and differential-operator equations, are stated in nonlinear-map terms. The solvability conditions and the properties of extremal problem solutions are obtained, while their weak expansions and necessary conditions of optimality in variational inequality form are formulated. In addition. the monograph proposes regularization methods and approximation schemes. This book is adressed to scientists, graduates and undergraduates who are interested in nonlinear analysis, control theory, system analysis and differential equations.

A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.

The Advanced Study Institute on Strongly Coupled Plasmas was held on the campus of the Universite d'Orleans, Orleans-la-Source, France, from July 6th through July 23rd, 1977. 15 invited lecturers and 50 other participants attended the Institute. The present Volume contains the texts of most of the lectures and of some of the numerous seminars presented at the Institute. The topic of strongly coupled coulomb-systems has been an area of vigorous activities over the last few years. Such systems occur in a great variety of physical situations: stellar and planetary interiors, solid and liquid metals, semiconductors, laser compressed plasmas and gas discharges are some of the most important examples. All these systems have the common feature that for one or more of their constituent charged particle liquids the potential energy to kinetic energy ratio is not small, and therefore the application of the traditional plasma perturbation techniques is not feasible. Many ingenious theoretical schemes have been worked out in order to attack both the related equilibrium and nonequilibrium problems, and also various methods have been borrowed from areas where problems not dissimilar to the ones arising in coulomb-systems had already been tackled. At the same time, computer simulations have led to a probably unparalleled accumulation of data on the behavior of an ensemble of classical charged particles. For the first time, the Institute assembled workers from various disciplines who had been involved with diverse aspects of the strongly coupled plasma problem.

Ever since Einstein s special relativity in 1905, the principle of invariant light speed in vacuum has been attracting attention from a wide range of disciplines. How to interpret the principle of light speed? Is light referred to continuous light, or light pulse with definite boundaries? Recent discovery of superluminal medium triggered vigorous discussion within the Physics community. Can communication via such superluminal channel break the speed limit and thus violate causality principle? Or, will a single photon, which is not governed by classical laws of Physics, tend to break the speed limit? To solve these problems, this Brief brings in Optical Precursors, the theoretical works for which started as early as 1914. This is a typical optical phenomenon combining wave propagation theory and light-wave interaction. Both theory and experimental works are covered in this Brief. The study of precursor verifies that the effective information carried by light pulses can never exceed the speed of light in vacuum- c. Further, through observation from nonclassical single photon source, the precursor rules out the probability of a single photon traveling with the speed, breaking the classical limit.

The ionization of atoms and molecules in strong laser fields is an active field in modern physics and has versatile applications in such as attosecond physics, X-ray generation, inertial confined fusion (ICF), medical science and so on. "Classical Trajectory Perspective of Atomic Ionization in Strong Laser Fields" covers the basic concepts in this field and discusses many interesting topics using the semiclassical model of classical trajectory ensemble simulation, which is one of the most successful ionization models and has the advantages of a clear picture, feasible computing and accounting for many exquisite experiments quantitatively. The book also presents many applications of the model in such topics as the single ionization, double ionization, neutral atom acceleration and other timely issues in strong field physics, and delivers useful messages to readers with presenting the classical trajectory perspective on the strong field atomic ionization. The book is intended for graduate students and researchers in the field of laser physics, atom molecule physics and theoretical physics. Dr. Jie Liu is a professor of Institute of Applied Physics and Computational Mathematics, China and Peking University.

Space plasma is so hot that the atoms break up into charged particles which then become trapped and stored in magnetic fields. When critical conditions are reached the magnetic field breaks up, releasing a large amount of energy and causing dramatic phenomena. The largest space plasma activity events observed in the solar system occur on the Sun, when coronal mass ejections expel several billion tons of plasma mass into space. This book provides a coherent and detailed treatment of the physical background of large plasma eruptions in space. It provides the background necessary for dealing with space plasma activity, and allows the reader to reach a deeper understanding of this fascinating natural event. The book employs both fluid and kinetic models, and discusses the applications to magnetospheric and solar activity. This will form an interesting reference for graduate students and academic researchers in the fields of astrophysics and plasma physics.

An outgrowth of the first Asia-Pacific Regional School on the International Heliophysical Year (IHY), this volume contains a collection of review articles describing the universal physical processes in the heliospace influenced by solar electromagnetic and mass emissions. The Sun affects the heliosphere in the short term (space weather) and in the long term (space climate) through numerous physical processes that exhibit similarities in various spatial domains of the heliosphere. The articles take into account various aspects of the Sun-heliosphere connection under a systems approach.

This volume will serve as a ready reference work for research in the emerging field of heliophysics, which describes the physical processes taking place in the physical space controlled by the Sun out to the local interstellar medium.

The inner magnetosphere plasma is a very unique composition of different plasma particles and waves. It covers a huge energy plasma range with spatial and time variations of many orders of magnitude. In such a situation, the kinetic approach is the key element, and the starting point of the theoretical description of this plasma phenomena which requires a dedicated book to this particular area of research.

Nuclear fusion research is entering a new phase, in which power exhaust will play a vital role. This book presents a complete and up-to-date summary of this emerging field of research in fusion plasmas, focusing on the leading tokamak concept. Emphasis is placed on rigorous theoretical development, supplemented by numerical simulations, which are used to explain and quantify a range of experimental observations. The text offers a self-contained introduction to power exhaust, and deals in detail with both edge plasma turbulence and edge localized modes, providing the necessary background to understand these important, yet complicated phenomena. Combining an in-depth overview with an instructive development of concepts, this is an invaluable resource for academic researchers and graduate students in plasma physics.

Non-thermal (cold) plasmas at atmospheric pressure have recently found many breakthrough applications in biology, medicine, and food security. Plasmas can efficiently kill bacteria, yeasts, moulds, spores, biofilms and other hazardous microorganisms, including potential bio-terrorism agents. They can be employed for bio-decontamination and sterilization of surfaces, medical instruments, water, air, food, even of living tissues without causing their damage. Direct or indirect plasma interaction with living cells of microorganisms or even humans enables novel bio-medical applications, e.g. treatment of skin diseases and ulcers. Plasma-enhanced blood coagulation coupled with its antiseptic properties proved success in wound healing and opens new possibilities in surgery, emergency medicine and military applications. Plasma treatment allows cell manipulations, their removal and targeted transfer into the injured area, which can accelerate wound healing. Plasma induced apoptosis (programmed cell death) of tumor cells brings forth a great potential for cancer treatment. Besides, plasma enables painless treatment of dental caries, root canal disinfection, and other dentistry applications. This book is a selection of reviewed manuscripts issuing from the NATO Advanced Research Workshop Plasma for bio-decontamination, medicine and food security held in Jasna, Slovakia, on 15-18 March 2011. It provides a comprehensive overview of the current knowledge and research activities focused at the plasma applications in areas such as bio-decontamination, water chemistry, effects on cells; biofilm inactivation, UV sterilization, and medicine, especially tissue treatment and wound healing, as well as dentistry and food security.

Complex plasmas differ from traditional plasmas in many ways: these are low-temperature high pressure systems containing nanometer to micrometer size particles which may be highly charged and strongly interacting. The particles may be chemically reacting or be in contact with solid surfaces, and the electrons may show quantum behaviour. These interesting properties have led to many applications of complex plasmas in technology, medicine and science. Yet complex plasmas are extremely complicated, both experimentally and theoretically, and require a variety of new approaches which go beyond standard plasma physics courses. This book fills this gap presenting an introduction to theory, experiment and computer simulation in this field. Based on tutorial lectures at a very successful recent Summer Institute, the presentation is ideally suited for graduate students, plasma physicists and experienced undergraduates.

In June of 1996, at the idyllic seaside resort of Guaruja, Brazil, a renowned group of researchers in space and astrophysical plasmas met to provide a forum on Advanced Topics on Astrophysical and Space Plasmas at a school consisting of some 60 students and teachers, mainly from Brazil and Argentina, but also from all the other parts of the globe. The purpose was to provide an update on the latest theories, observations, and simulations of space-astrophysical plasma phenomena. The topics covered included space plasma mechanisms for particle acceleration, nonthermal emission in cosmic plasma, magnetohydrodynamic instabilities in solar, interstellar, and other cosmic objects, magnetic field line reconnection and merging, the nonlinear and often chaotic structure of astrophysical plasmas, and the advances in high performance supercomputing resources to replicate the observed phenomena. The lectures were presented by Professor Mark Birkinshaw of the Harvard-Smithsonian Center for Astrophysics and the University of Bristol; Dr Anthony Peratt, Los Alamos National Laboratory Scientific Advisor to the United States Department of Energy; Dr Dieter Biskamp of the Max Planck Institute for Plasma Physics, Garching, Germany; Professor Donald Melrose, Director, Centre for Theoretical Astrophysics, University of Sydney, Australia; Professor Abraham Chian of the National Institute for Space Research, Brazil; and Professor Nelson Fiedler-Ferrara of the University of Sao Paulo, Brazil. As summarized by Professor Reuven Opher, Institute of Astronomy and Geophysics, University of Sao Paulo, the advanced or interested student of space and astrophysical plasmas will find reference to nearly all modern aspects in the field of Plasma Astrophysics and Cosmology in the presented lectures.

Les deuxiernes "Rencontres de l'Observatoire", qui ont eu lieu a l'Observatoire de Paris a Meudon du 10 au 14 Janvier 2000, ont reuni autour du theme "Problernes ernergents en physique de I'espace" 120 physiciens et astrophysiciens venus d'une vingtaine de pays differents. Nous avons voulu honorer a cette occasion Jean-Louis Steinberg pour ses con- tributions majeures a la recherche spatiale, ala radioastronomie et a la physique de I'espace. L'approche explicitement pluridisciplinaire de ce colloque, qui ne s'est pas laisse confiner dans les limites etroites de la physique spatiale ni dans celles imposees par certains programmes officiels, suit l'esprit de sa carriere scientifique: sortir des limites des sujets deja etudies ou sur Ie point de l'etre, et appliquer les connaissances acquises pour explorer de nouveaux domaines. Ce dernier quart de siecle a vu une croissance vertigineuse des performances spatiales. La technologie moderne ne perrnet pas encore de jongler avec les univers comme Ie prestidigitateur de Grandville (Grandville, Un autre monde, ed. H. Four- nier, Paris, 1844); mais quelques decades ont suffi pour voir des instruments soph- istiques explorer les frontieres du systerne solaire, et la cornmunaute de la recher- che spatiale a depasse rapidement Ie sujet etroit de I'environnement soleil-terre pour s'interesser a I'ensemble de l'heliosphere, OU les memes processus physiques sont a I'ceuvre.

Nuclear Fusion describes the state and ultimate goals of nuclear fusion research. The book concentrates on the energy problem in the near future, the role of nuclear fusion reactions for a solution of the energy problem, the requirements for releasing fusion energy and the methods likely to lead to fusion reactions. The book is organised into four sections. In turn these cover the fundamentals of nuclear fusion, methods of magnetic confinement, methods of innertial confinement and the fusion reactor itself. The book has a strong theoretical content, covering those areas of plasma physics which are necessary for an understanding of the confinement problem. This book was first published in Japanese. This edition in English has been thoroughly revised by Keishiro Niu.

The book is devoted to the theory describing the interaction of ultra-short electromagnetic pulses (USP) with matter, including both classical and quantum cases. This theme is a hot topic in modern physics because of the great achievements in generating USP. Special attention is given to the peculiarities of UPS-matter interaction. One of the important items of this book is the derivation and applications of a new formula which describes the total photo-process probability under the action of USP in the framework of perturbation theory. Strong field-matter interaction is also considered with the use of the Bloch formalism in a two-level approximation for UPS with variable characteristics.

Intended for advanced students of physics, chemistry and related disciplines, this text treats the quantum theory of atoms and ions within the framework of self-consistent fields. Data needed for the analysis of collisions and other atomic processes are also included.

Emphasis is placed on the analysis of translational, rotational, vibrational and electronically excited state kinetics, coupled to the electron Boltzmann equation.

The electric probe has long been used as a fundamental diagnostic tool for measuring the local properties of a plasma. Since Langmuir first developed the electric-probe technique in 1924, probes have been used to measure electron densities and temperatures in a wide variety of gaseous ionized media, such as electric discharges, afterglows, ionizing shock waves, flames, MHD, and plasma-jet flows, reentry vehicle flow fields, and atmospheric and space plasmas. The first systematic account of modern theories of electriC-probe behavior was given by Chen (1965), who also provided practical information on experimental techniques. A subsequent survey by Swift and Schwar (1970), which was representative of results contained in the literature through 1969, included additional information on some of the modern theories and on practical details of probe utilization. The purpose of this volume is to supplement the previously mentioned two works by providing an account of a large body of the up-to-date informa tion available on electric probes, particularly in the areas of transitional and continuum-flow phenomena, and by offering, for all domains of probe appli cation, a critical appraisal of the more significant probe theories and experi mental investigations in the literature."

The laser as a radiation source with temporal and spatial coherence has made a tremendous impact in the different fields of science. As a result, new and exciting research has been developing allover the world. Laser spectro scopy shares a large fraction of this research, and in the last decade nu merous books and monographs have been published on this subject. Most of these books and monographs contain the work done in the physics community. Very few books represent the advances made in laser chemistry, a field that is flourishing and whose future is indeed very exciting. It was felt that a meeting that focused on the important questions being asked in the chemistry community, and on new and possible directions in laser chemistry, was needed. This three-day conference, held at the California Institute of Technology, Pasadena, California, on March 20-22, 1978, covered five important areas in laser chemistry: Laser-induced chemistry, picosecond processes and techniques, nonlinear optical spectroscopy and dephasing processes, multiphoton exci tation in molecules, and molecular dynamics by molecular beams."

This book aims to give a comprehensive view on the present status of a tremendously fast-developing field - the quantum dynamics of fragmenting many-particle Coulomb systems. In striking contrast to the profound theo retical knowledge, achieved from extremely precise experimental results on the static atomic and molecular structure, it was only three years ago when the three-body fundamental dynamical problem of breaking up the hydro gen atom by electron impact was claimed to be solved in a mathematically consistent way. Until now, more "complicated," though still fundamental scenarios, ad dressing the complete fragmentation of the "simplest" many-electron system, the helium atom, under the action of a time-dependent external force, have withstood any consistent theoretical description. Exceptions are the most "trivial" situations where the breakup is induced by the impact of a single real photon or of a virtual photon under a perturbation caused by fast, low charged particle impact. Similarly, the dissociation of the "simplest" molecu lar systems like Ht or HD+, fragmentating in collisions with slow electrons, or the H3 molecule breaking apart into two or three" pieces" as a result of a single laser-photon excitation, establish a major challenge for state-of-the-art theoretical approaches."

We arepleasedtopresentthesixthvolumeofProgressinUltrafastIntenseLaserS- ence. As the frontiers of ultrafast intense laser science rapidly expand ever outward, there continues to be a growing demand for an introduction to this interdisciplinary research?eldthatisatoncewidelyaccessibleandcapableofdeliveringcutting-edge developments. Our series aims to respond to this call by providing a compilation of concise review-style articles written by researchers at the forefront of this research ?eld, so that researcherswith differentbackgroundsas well as graduatestudentscan easily grasp the essential aspects. As in previousvolumesof PUILS, each chapterof this bookbeginswith an int- ductory part, in which a clear and concise overview of the topic and its signi?cance is given, and moves onto a description of the authors' most recent research results. All the chapters are peer-reviewed. The articles of this sixth volume cover a diverse rangeoftheinterdisciplinaryresearch?eld,andthetopicsmaybegroupedintothree categories: responses of molecules to ultrashort intense laser pulses (Chaps. 1 - 4), generation and characterization of attosecond pulses and high-order harmonics (Chaps. 5 - 8), and?lamentationand laser-plasma interactionand their applications (Chaps. 9 - 11).

This textbook treats Hydro- and Fluid Dynamics, the engineering science dealing with forces and energies generated by fluids in motion, playing a vital role in everyday life. Practical examples include the flow motion in the kitchen sink, the exhaust fan above the stove, and the air conditioning system in our home. When driving a car, the air flow around the vehicle body induces some drag which increases with the square of the car speed and contributes to excess fuel consumption. Engineering applications encompass fluid transport in pipes and canals, energy generation, environmental processes and transportation (cars, ships, aircrafts). This book deals with the topic of applied hydrodynamics. The lecture material is grouped into two complementary sections: ideal fluid flow and real fluid flow. The former deals with two- and possibly three-dimensional fluid motions that are not subject to boundary friction effects, while the latter considers the flow regions affected by boundary friction and turbulent shear. The lecture material is designed as an intermediate course in fluid dynamics for senior undergraduate and postgraduate students in Civil, Environmental, Hydraulic and Mechanical Engineering. It is supported by notes, applications, remarks and discussions in each chapter. Moreover a series of appendices is added, while some major homework assignments are developed at the end of the book, before the bibliographic references.

This second volume of the Charged Particle Traps deals with the rapidly expanding body of research exploiting the electromagnetic con?nement of ions, whose principles and techniques were the subject of volume I. These applications include revolutionary advances in diverse ?elds, ranging from such practical ?elds as mass spectrometry, to the establishment of an ult- stable standard of frequency and the emergent ?eld of quantum computing made possible by the observation of the quantum behavior of laser-cooled con?nedions. Bothexperimentalandtheoreticalactivity intheseapplications has proliferated widely, and the number of diverse articles in the literature on its many facets has reached the point where it is useful to distill and organize the published work in a uni?ed volume that de?nes the current status of the ?eld. As explained in volume I, the technique of con?ning charged particles in suitable electromagnetic ?elds was initially conceived by W. Paul as a thr- dimensional version of his rf quadrupole mass ?lter. Its ?rst application to rf spectroscopy on atomic ions was completed in H. G. Dehmelt's laboratory where notable work was later done on the free electron using the Penning trap. The further exploitation of these devices has followed more or less - dependently along the two initial broad areas: mass spectrometry and high resolution spectroscopy. In volume I a detailed account is given of the theory of operation and experimental techniques of the various forms of Paul and Penning ion traps.