Dynamics on Differential One-Forms - Couverture souple

Story, Troy

 
9780595221073: Dynamics on Differential One-Forms
Couverture souple
ISBN 10 : 0595221076 ISBN 13 : 9780595221073
Editeur : iUniverse, 2002

Synopsis

Dynamics on Differential One-Forms proposes a unifying principle for mathematical models of dynamic systems. In "Thermodynamics on One-Forms (chapter I)", the long-standing problem of deriving irreversibility in thermodynamics from reversibility in Hamiltonian mechanics, is solved. Differential geometric analysis shows thermodynamics and Hamiltonian mechanics are both irreversible on representative extended phase spaces. "Dynamics on Differential One-Forms (II)" generalizes (I) to Hamiltonian mechanics, geometric optics, thermodynamics, black holes, electromagnetic fields and string fields. Mathematical models for these systems are revealed as representations of a unifying principle; namely, description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a tangent vector defining system transformations. Relationships between models using exterior calculus and conventional calculus imply a technical definition of dynamic equilibrium. "Global Analysis of Composite Particles (III)" uses differential topology to develop the theory of large vibration-rotation interactions for composite particles. A global classical Hamiltonian and corresponding quantum Hamiltonian operator are derived, then applied to the molecular vibration-rotation problem."Characteristic Electromagnetic and Yang-Mills Gauge (IV)" uses differential geometry to remove some of the arbitrariness in the gauge, and shows how gauge functions for electromagnetic and Yang-Mills fields follow the same differential equation.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Dynamics on Differential One-Forms proposes a unifying principle for mathematical models of dynamic systems. In "Thermodynamics on One-Forms (chapter I)", the long-standing problem of deriving irreversibility in thermodynamics from reversibility in Hamiltonian mechanics, is solved. Differential geometric analysis shows thermodynamics and Hamiltonian mechanics are both irreversible on representative extended phase spaces. "Dynamics on Differential One-Forms (II)" generalizes (I) to Hamiltonian mechanics, geometric optics, thermodynamics, black holes, electromagnetic fields and string fields. Mathematical models for these systems are revealed as representations of a unifying principle; namely, description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a tangent vector defining system transformations. Relationships between models using exterior calculus and conventional calculus imply a technical definition of dynamic equilibrium. "Global Analysis of Composite Particles (III)" uses differential topology to develop the theory of large vibration-rotation interactions for composite particles. A global classical Hamiltonian and corresponding quantum Hamiltonian operator are derived, then applied to the molecular vibration-rotation problem."Characteristic Electromagnetic and Yang-Mills Gauge (IV)" uses differential geometry to remove some of the arbitrariness in the gauge, and shows how gauge functions for electromagnetic and Yang-Mills fields follow the same differential equation.

Biographie de l'auteur

Troy Story is a Professor at Morehouse College (Atlanta, GA, USA). His research in differential geometry and exterior calculus has produced a new unification principle for mathematical models of dynamic systems (Hamiltonian mechanics, geometric optics, thermodynamics, black holes, electromagnetic fields and string fields), giving him world-wide recognition as an outstanding scientist/applied mathematician.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
iUniverse
Date d'édition
2002
Langue
anglais
ISBN 10 
0595221076
ISBN 13 
9780595221073
Reliure
Broché
Nombre de pages
128
Coordonnées du fabricant
non disponible
Personne responsable
gpsr@libri.de
gpsr@libri.de

Friedensallee 273
Hamburg
22763
Allemagne

Autres éditions populaires du même titre

9780595744718: Dynamics on Differential One-Forms

Edition présentée

ISBN 10 :  0595744710 ISBN 13 :  9780595744718
Editeur : iUniverse, 2002
Couverture rigide