Alternative Mathematical Theory of Non-equilibrium Phenomena

Alternative Mathematical Theory of Non-equilibrium Phenomena presents an entirely new theoretical approach to complex non-equilibrium phenomena, especially Gibbs/Falk thermodynamics and fluid mechanics. This innovative new theory allows for inclusion of all state variables and introduces a new vector-dissipation velocity-which leads to useful restatements of momentum, the Second Law, and tensors for the laws of motion, friction, and heat conduction. This application-oriented text is relatively self-contained and is an excellent guide-book for engineers with a strong interest in fundamentals, or for professionals using applied mathematics and physics in engineering applications.

This book emphasizes macroscopic phenomena, focusing specifically on gaseous states, though relations to liquid and crystalline states are also considered. The author presents a new Alternative Continuum Theory of Compressible Fluids (AT) which providesa qualitative description of the subject in predominantly physical terms, minimizing the mathematical premises. The methodology discussed has applications in a wide range of fields outside of physics in areas including General System Theory, TheoreticalEconomics, and Biophysics and Medicine.

Presents the first theory capable of handling non-equilibria phenomenaOffers a unified theory of all branches of macroscopic physicsConsiders a consistent and uniform view of reality, supported by modern mathematics, leading to results different than those produced by classical theoriesResults in a change of paradigms in physics, engineering, and natural philosophy

Physics Today--Perspectives: Motivation. Origin and Importance of Non-equilibrium Phenomena. Today's Mechanical World View: A Historical Outline. Continuum Theories of Mass-point Fluids. Gibbsian Thermostatics? FalkianDynamics--An Introduction: Falk's Principle. Gibbs Fundamental Equation and System Modeling. Equilibria and Criteria of Stability. Mathematical Foundation of Falk's Dynamics I: Mappings. Mathematical Foundation of Falk's Dynamics II: Systems. Motion and Matter: Basic Equations. Callen's Principle. Energy-Momentum Transport and Matter Model. Realistic Concept of Real Matter. Systems and Symmetry: An Approach to Implant Space and Time in Physics. Falk's Dynamics of Hamiltonian Systems. Review of the Noether Theorem. Phases, Heating, and Power as Interaction Phenomena. Barriers and Balances: Body-Field Systems. Multi-component Multi-phase Properties. Time Parameters in Thermodynamics of Fluid Systems. Balance Equations. Non-equilibrium Processes: Dissipation Velocity. Kinetic Equilibrium in Fields. Three Additional Theorems Concerning Non-Equilibrium. Hypothetical State at Rest. Constitutive Properties of Matter. General Equation of Motion and its Approximations: ElementaryPicture of Dissipation. General Equation of Motion. Some Remarks on Turbulent Flows. Conservation of Angular Momentum. Nacier-Stokes-Fourier Fluids. Simplified Models of Dissipative Flows. "Paradigmata are the Winner's Dogmata": Selection of Paragons. Vorticity-Influenced Flows. Basic Applications of Gasdynamics. Complex Flow Phenomena. Gibbs-Falkian Electromagnetism: A Quandary Concerning Electromagnetic Field Variables. Perspectives and Electromagnetic Units. Falk's Dynamics of Electromagnetic Phenomena. Maxwell's Equations. Non-Equilibrium Flows in Polarized Fluids. Sundry Remarks on an Electromagnetic Dilemma. Appendices. List of Frequently Used Symbols. References. Author Index. Subject Index.