From kinetic models to hydrodynamics : some novel results / / Matteo Colangeli

• Record Nr.: UNINA9910437877203321
• Autore: Colangeli Matteo
• Pubbl/distr/stampa: New York, : Springer, 2013
• ISBN: 1-4614-6306-8
• Edizione: [1st ed. 2013.]
• Descrizione fisica: 1 online resource (xii, 96 pages) : illustrations (some color)
• Collana: SpringerBriefs in Mathematics, , 2191-8198
• Classificazione: UG 1300
• Disciplina: 621.89
• Soggetti: Dynamics; Hydrodynamics - Mathematical models
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "ISSN: 2191-8198."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: 1. Introduction -- 2. From the Phase Space to the Boltzmann Equation -- 3. Methods of Reduced Description -- 4. Hydrodynamic Spectrum of Simple Fluids -- 5. Hydrodynamic Fluctuations from the Boltzmann Equation -- 6. 13 Moment Grad System -- 7. Conclusions -- References. .
• Sommario/riassunto: From Kinetic Models to Hydrodynamics serves as an introduction to the asymptotic methods necessary to obtain hydrodynamic equations from a fundamental description using kinetic theory models and the Boltzmann equation. The work is a survey of an active research area, which aims to bridge time and length scales from the particle-like description inherent in Boltzmann equation theory to a fully established “continuum” approach typical of macroscopic laws of physics. The author sheds light on a new method—using invariant manifolds—which addresses a functional equation for the nonequilibrium single-particle distribution function. This method allows one to find exact and thermodynamically consistent expressions for: hydrodynamic modes; transport coefficient expressions for hydrodynamic modes; and transport coefficients of a fluid beyond the traditional hydrodynamic limit. The invariant manifold method paves the way to establish a needed bridge between Boltzmann equation theory and a particle-based theory of hydrodynamics. Finally, the author explores the ambitious and longstanding task of obtaining hydrodynamic constitutive equations from their kinetic counterparts. ; The work is intended for specialists in kinetic theory—or more generally statistical mechanics—and will provide a bridge between a physical and mathematical approach to solve real-world problems.