Alternative Mathematical Theory of Non-equilibrium Phenomena
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Table of contents
- Cover
- Contentsvii
- Prefacexi
- Acknowledgmentsxiv
- Chapter 1. Physics Today: Perspectives1
- 1.1 Motivation1
- 1.2 Origin and Importance of Non-equilibrium Phenomena2
- 1.3 Today's Mechanical Worldview: A Short Historical Outline5
- 1.4 Continuum Theories of Mass-Point Fluids12
- 1.5 Gibbsian Thermostatics?19
- Chapter 2. Falkian Dynamics: An Introduction25
- 2.1 Falk's Principle25
- 2.2 Gibbs' Fundamental Equation and System Modeling31
- 2.3 Equilibria and Criteria of Stability39
- 2.4 Mathematical Foundation of Falk's Dynamics I: Mappings48
- 2.5 Mathematical Foundation of Falk's Dynamics II: Systems57
- Chapter 3. Motion and Matter69
- 3.1 Basic Questions69
- 3.2 Callen's Principle70
- 3.3 Energy–Momentum Transport and Matter Model78
- 3.4 Realistic Concept of Real Matter87
- Chapter 4. Systems and Symmetries96
- 4.1 An Approach to Implant Space and Time in Physics96
- 4.2 Falk's Dynamics of Hamiltonian Systems97
- 4.3 Review of the Noether Theorem103
- 4.4 Phases, Heating, and Power as Interacting Phenomena114
- Chapters 5. Barriers and Balances127
- 5.1 Body-Field Systems127
- 5.2 Multicomponent Single-Phase and Multiphase Properties131
- 5.3 Time Parameters in Thermodynamics of Fluid Systems138
- 5.4 Balance Equations150
- Chapter 6. Non-equilibrium Processes161
- 6.1 Dissipation Velocity161
- 6.2 Kinetic Equilibrium in Fields166
- 6.3 Three Additional Theorems Concerning Non-equilibrium168
- 6.4 Hypothetical State at Rest183
- 6.5 Constitutive Properties of Matter188
- Chapter 7. General Equation of Motion and Its Approximations195
- 7.1 Elementary Picture of Dissipation195
- 7.2 General Equation of Motion197
- 7.3 Some Remarks on Turbulent Flows205
- 7.4 Conservation of Angular Momentum210
- 7.5 Navier–Stokes–Fourier Fluids214
- 7.6 Simplified Models of Dissipative Flows220
- Chapter 8. Paradigmata Are the Winners' Dogmata226
- 8.1 Selection of Paragons226
- 8.2 Vorticity-influenced Flows229
- 8.3 Basic Applications of Gasdynamics246
- 8.4 Complex Flow Phenomena266
- Chapter 9. Gibbs–Falkian Electromagnetism280
- 9.1 A Quandary Concerning Electromagnetic Field Variables280
- 9.2 Perspectives and Electromagnetic Units283
- 9.3 Falk's Dynamics of Electromagnetic Phenomena286
- 9.4 Maxwell's Equations293
- 9.5 Non-equilibrium Flows in Polarized Fluids297
- 9.6 Sundry Remarks on an Electromagnetic Dilemma305
- Appendix 1. Atomism or The Art of Honest Dissimulation314
- A1.1 Motivation314
- A1.2 Pre-Socratic Atomism and its Tradition in the Ancient World315
- A1.3 Atomism in the Dark Middle Ages319
- A1.4 The Galilei Affair325
- A1.5 On the Early History of the Eulerian Mass-Point333
- Appendix 2. Mathematical Supplements339
- A2.1 Supplements to the Noether Theorem339
- A2.2 Some Useful Tensor Rules343
- A2.3 On Vorticity in Navier–Stokes Flows344
- Appendix 3. Computation Scheme for a One-Component Single-Phase Body-Field System347
- List of Relevant Symbols350
- References353
- Name Index363
- Subject Index367
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.
Key Features
* Presents the first theory capable of handling non-equilibria phenomena
* Offers a unified theory of all branches of macroscopic physics
* Considers a consistent and uniform view of reality, supported by modern mathematics, leading to results different than those produced by classical theories
* Results in a change of paradigms in physics, engineering, and natural philosophy
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.
Key Features
* Presents the first theory capable of handling non-equilibria phenomena
* Offers a unified theory of all branches of macroscopic physics
* Considers a consistent and uniform view of reality, supported by modern mathematics, leading to results different than those produced by classical theories
* Results in a change of paradigms in physics, engineering, and natural philosophy