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This book serves as a self-contained reference source for engineers, materials scientists, and physicists with an interest in relaxation phenomena. It is made accessible to students and those new to the field by the inclusion of both elementary and advanced math techniques, as well as chapter opening summaries that cover relevant background information and enhance the book's pedagogical value. These summaries cover a wide gamut from elementary to advanced topics.
The book is divided into three parts. The opening part, on mathematics, presents the core techniques and approaches. Parts II and III then apply the mathematics to electrical relaxation and structural relaxation, respectively. Part II discusses relaxation of polarization at both constant electric field (dielectric relaxation) and constant displacement (conductivity relaxation), topics that are not often discussed together. Part III primarily discusses enthalpy relaxation of amorphous materials within and below the glass transition temperature range. It takes a practical approach inspired by applied mathematics in which detailed rigorous proofs are eschewed in favor of describing practical tools that are useful to scientists and engineers. Derivations are however given when these provide physical insight and/or connections to other material.
A self-contained reference on relaxation phenomena
Details both the mathematical basis and applications
For engineers, materials scientists, and physicists

### Chapter 1. Mathematical Functions and Techniques

This chapter summarizes many of the mathematical functions and techniques required to analyze relaxation phenomena quantitatively. Elementary mathematical results are given in Appendix B, and additional specialized results are presented in Chaps. 2, 3 and 5. Elementary statistics is briefly summarized in Chap. 4.
Ian M. Hodge

### Chapter 2. Complex Variables and Functions

Complex numbers and functions are discussed. This material lays the groundwork for fundamental relaxation results.
Ian M. Hodge

### Chapter 3. Other Functions and Relations

This chapter describes mathematics that are specifically applicable to relaxation phenomena but not restricted to the frequency domain. In particular Sect. 3.7 gives fundamental derivations of relations between frequency domain functions and relaxation time distributions.
Ian M. Hodge

### Chapter 4. Elementary Statistics

This chapter describes elementary statistical functions and techniques that apply to the analyses of experimental data. Statistics is probably second in subtlety only to thermodynamics (Chap. 10).
Ian M. Hodge

### Chapter 5. Relaxation Functions

This Chapter mainly reviews specific (and with one exception empirical) complex relaxation functions and distributions of relaxation times used to analyze experimental relaxation data. The Chapter also summarizes basic relaxation concepts such as Boltzmann superposition and thermorheologucal complexity (temperature dependent relaxation parameters).
Ian M. Hodge

### Chapter 6. Introduction to Electrical Relaxation

This Chapter reviews basic elements of electromagnetism.
Ian M. Hodge

### Chapter 7. Dielectric Relaxation

Relaxation of electrical polarization at constant electric field is discussed.
Ian M. Hodge

### Chapter 8. Conductivity Relaxation

Relaxation of electrical polarization at constant displacement is discussed.
Ian M. Hodge

### Chapter 9. Examples

Applications of electrical relaxation phenomenologies to several materials are reviewed. The materials include various forms of water and several solid electrolytes.
Ian M. Hodge

### Chapter 10. Thermodynamics

The basic elements of thermodynamics are discussed.
Ian M. Hodge

### Chapter 11. Structural Relaxation

Relaxation of dynamic and thermodynamic properties in amorphous materials is discussed for temperatures above, within, and below the glass transition temperature range.
Ian M. Hodge