The axiom of determinacy, forcing axioms, and the nonstationary ideal [[electronic resource] /] / W. Hugh Woodin

• Record Nr.: UNINA9910455565203321
• Autore: Woodin W. H (W. Hugh)
• Pubbl/distr/stampa: Berlin ; ; New York, : De Gruyter, c2010
• ISBN: 1-282-72287-5; 9786612722875; 3-11-021317-6
• Edizione: [2nd rev. ed.]
• Descrizione fisica: 1 online resource (858 p.)
• Collana: De Gruyter series in logic and its applications, , 1438-1893 ; ; 1
• Disciplina: 511.3
• Soggetti: Forcing (Model theory); Model theory; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Frontmatter -- Contents -- 1 Introduction -- 2 Preliminaries -- 3 The nonstationary ideal -- 4 The ℙmax-extension -- 5 Applications -- 6 ℙmax variations -- 7 Conditional variations -- 8 ♣ principles for ω 1 -- 9 Extensions of L(Γ, ℝ) -- 10 Further results -- 11 Questions -- Backmatter
• Sommario/riassunto: The starting point for this monograph is the previously unknown connection between the Continuum Hypothesis and the saturation of the non-stationary ideal on ω1; and the principle result of this monograph is the identification of a canonical model in which the Continuum Hypothesis is false. This is the first example of such a model and moreover the model can be characterized in terms of maximality principles concerning the universal-existential theory of all sets of countable ordinals. This model is arguably the long sought goal of the study of forcing axioms and iterated forcing but is obtained by completely different methods, for example no theory of iterated forcing whatsoever is required. The construction of the model reveals a powerful technique for obtaining independence results regarding the combinatorics of the continuum, yielding a number of results which have yet to be obtained by any other method. This monograph is ; directed to researchers and advanced graduate students in Set Theory. The second edition is updated to take into account some of the developments in the decade since the first edition appeared, this includes a revised discussion of Ω-logic and related matters.

Electron and proton kinetics and dynamics in flaring atmospheres [[electronic resource] /] / Valentina Zharkova

• Record Nr.: UNINA9910141448203321
• Autore: Zharkova Valentina
• Pubbl/distr/stampa: Weinheim, : Wiley-VCH, 2012
• ISBN: 3-527-63967-5; 1-280-88144-5; 9786613722751; 3-527-63966-7; 3-527-63968-3
• Descrizione fisica: 1 online resource (460 p.)
• Disciplina: 539.7/2; 539.72
• Soggetti: Electrons; Protons; Atmospheric physics; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Electron and Proton Kinetics and Dynamics in Flaring Atmospheres; Contents; Preface; Color Plates; 1 Observational Phenomena of Solar Flares; 1.1 Observational Constraints; 1.2 Hard X-Ray Light Curves and Spectra; 1.2.1 Light Curves; 1.2.2 Photon and Electron Energy Spectra; 1.2.3 Electron Numbers; 1.3 Light Curves and Energy Spectra of Gamma-Rays; 1.3.1 -Ray Light Curves; 1.3.2 Energy Spectra and Abundances of Ions in Flares; 1.3.3 Ion Numbers; 1.4 Geometry of Hard X-Ray and Gamma-Ray Sources; 1.4.1 Differences in Footpoint Spectral Indices; 1.4.2 Hard X-Ray and Gamma-Ray Source Locations; 1.5 Pre- and Postflare Hard X-Ray and Radio Emission1.6 Magnetic Field Changes Associated with Flares; 1.6.1 Local Magnetic Field Variations; 1.7 UV and Optical Emission; 1.8 Seismic Responses; 1.9 Critical Issues; 2 Particle Acceleration in Flares; 2.1 Models of Particle Acceleration; 2.1.1 Basic Physics; 2.1.2 Magnetic Reconnection Models Associated with Flares; 2.1.3 Particle Acceleration in a Reconnecting Current Sheet; 2.1.4 Particle Acceleration by Shocks and Turbulence; 2.2 Recent Theoretical Developments; 2.2.1 Stochastic Acceleration; 2.2.2 Electron Acceleration in Collapsing Current Sheets2.2.3 Particle Acceleration in a Single 3-D RCS with Complicated Magnetic Topology; 2.2.4 Estimations of Accelerated Particle Parameters; 2.2.5 Comparison of the Parameters of Accelerated Particles; 2.2.6 Particle Acceleration in 3-D MHD Models with Fan and Spine Reconnection; 2.3 Limitations of the Test-Particle Approach; 2.3.1 The Polarization Electric Field; 2.3.2 Turbulent Electric Fields; 2.4 Particle-in-Cell Simulation of Acceleration in a 3-D RCS; 2.4.1 Problem Formulation; 2.4.2 Test-Particle Simulations; 2.4.3 PIC Simulation Results2.5 Particle Acceleration in Collapsing Magnetic Islands; 2.5.1 Tearing-Mode Instability in Current Sheets; 2.5.2 Particle Acceleration in Magnetic Islands - PIC Approach; 2.6 Limitations of the PIC Approach; 2.7 Probing Theories versus Observations; 2.7.1 Interrelation between Acceleration and Transport; 2.7.2 Testing Acceleration Models against Observational Constraints; 3 Electron-Beam Precipitation - Continuity Equation Approach; 3.1 Introduction; 3.2 Particle Energy Losses; 3.2.1 Particle Trajectories at Scattering; 3.2.2 Energy Loss and Momentum Variations; 3.3 Continuity Equation Approach for Electrons: Pure Collisions3.3.1 Solutions of Continuity Equation for Power-Law Beam Electrons; 3.3.2 Beam Electron Densities; 3.3.3 Mean Electron Spectra; 3.3.4 Hard X-Ray Bremsstrahlung Emission by Beam Electrons; 3.3.5 Heating Functions; 3.4 Continuity Equation Approach for Electrons - Pure Electric Field; 3.4.1 Estimation of the Ohmic Loss Effect; 3.4.2 Kinetic Solutions for a Pure Electric Field; 3.4.3 Estimations of Electron-Beam Stability; 4 Electron Beam Precipitation - Fokker-Planck Approach; 4.1 General Comments on Particle and Energy Transport; 4.2 Problem Formulation
• Sommario/riassunto: This timely book presents new research results on high-energy particle physics related to solar flares, covering the theory and applications of the reconnection process in a clear and comprehensible way. It investigates particle kinetics and dynamics in flaring atmospheres and their diagnostics from spectral observations, while providing an analysis of the observation data and techniques and comparing various models.Written by an internationally acclaimed expert, this is vital reading for all solar, astro-, and plasma physicists working in the field.