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Theory of Zipf's Law and Beyond
Zipf’s law is one of the few quantitative reproducible regularities found in e- nomics. It states that, for most countries, the size distributions of cities and of rms (with additional examples found in many other scienti c elds) are power laws with a speci c exponent: the number of cities and rms with a size greater thanS is inversely proportional toS. Most explanations start with Gibrat’s law of proportional growth but need to incorporate additional constraints and ingredients introducing deviations from it. Here, we present a general theoretical derivation of Zipf’s law, providing a synthesis and extension of previous approaches. First, we show that combining Gibrat’s law at all r...
Electron Impact Ionization
It is perhaps surprising that a process which was one of the first to be studied on an atomic scale, and a process which first received attention over seven decades ago, continues to be the object of diverse and intense research efforts. Such is the case with the (seemingly) conceptually simple and familiar mechanism of electron impact ionization of atoms, molecules, and ions. Not only has the multi-body nature of the collision given ground to theoretical effort only grudgingly, but also the variety and subtlety of processes contributing to ionization have helped insure that progress has come only with commensurate work: no pain - no gain. Modern experimental methods have made it possible to effectively measure and explore threshold laws, differential cross sections, partial cross sections, inner-shell ionization, and the ionization of unstable species such as radicals and ions. In most instances the availability of experimental data has provided impetus and guidance for further theoretical progress.
Electron-Molecule Interactions and Their Applications
Electron-Molecule Interactions and Their Applications, Volume 1 presents a comprehensive account of electron-molecule interactions in high- and ultra-high-pressure gases and liquids. Topics covered include elastic scattering of electrons by molecules; excitation, ionization, and dissociation of molecules by electron impact; electron-molecule resonances; and electron attachment and detachment processes. This volume is comprised of seven chapters and begins with a discussion on non-resonant elastic scattering and rotational excitation of molecules by electrons, followed by a review of non-resonant vibrational and electronic excitation. The reader is then introduced to resonance effects in elec...
Human Behavior and the Principle of Least Effort
This classic is arranged as follows: Preface 1. The Question of Practical Application. 2. The Question of Natural Science. 1. Introduction and Orientation I. The Selection of a Path II. The “Singleness of the Superlative” III. The Principle of Least Effort IV. The Scope of the Principle: “Tools-and-Jobs” V. Previous Studies VI. Prospectus 2. On the Economy of Words I. In Medias Res: Vocabulary Usage, and the Forces of Unification and Diversification II. The Question of Vocabulary Balance III. The Orderly Distribution of Meanings IV. The Integrality of Frequencies V. The Integrality of Rank VI. The Length of Intervals Between Repetitions VII. The Problem of Spreading Work Over Time (T...
Photoionization And Photodetachment (In 2 Parts)
Owing to the advances of vacuum ultraviolet and ultrafast lasers and third generation synchrotron sources, the research on photoionization, photoelectrons, and photodetachment has gained much vitality in recent years. These new light sources, together with ingenious experimental techniques, such as the coincidence imaging, molecular beam, pulsed field ionization photoelectron, mass-analyzed threshold ion, and pulsed field ion pair schemes, have allowed spectroscopic, dynamic, and energetic studies of gaseous species to a new level of detail and accuracy. Profitable applications of these methods to liquids are emerging.This invaluable two-volume review consists of twenty-two chapters, focusing on recent developments in photoionization and photodetachment studies of atoms; molecules, transient species, clusters, and liquids.
Atomic and Molecular Processes in Fusion Edge Plasmas
This well-illustrated resource provides vital cross-section information for the atomic and molecular collision processes taking place in the boundary region of magnetically confined fusion plasmas and in other laboratory and astrophysical low-temperature plasmas. The expertly assessed information in this noteworthy volume includes the most recent experimental and theoretical results presented in a convenient format. Coverage includes the processes of electron-impact excitation and ionization of plasma edge atoms, electron-ion recombination, dissociative collision processes involving electrons and much more.
