Dynamics on Differential One-Forms - Tapa dura

Story, Troy L.

 
9780595744718: Dynamics on Differential One-Forms
Tapa dura
ISBN 10: 0595744710 ISBN 13: 9780595744718
Editorial: iUniverse, 2002

Sinopsis

Book by Story Troy L

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Reseña del editor

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.

Biografía del autor

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.

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Editorial
iUniverse
Año de publicación
2002
Idioma
Inglés
ISBN 10 
0595744710
ISBN 13 
9780595744718
Encuadernación
Tapa dura
Número de páginas
128
Contacto del fabricante
no disponible
Persona responsable
no disponible

Otras ediciones populares con el mismo título

9780595221073: Dynamics on Differential One-Forms

Edición Destacada

ISBN 10:  0595221076 ISBN 13:  9780595221073
Editorial: iUniverse, 2002
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