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Understanding Physics and Physical Chemistry Using Formal Graphs

By Eric Vieil

CRC Press – 2012 – 815 pages

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  • Add to CartHardback: $169.95
    978-1-42-008612-6
    February 23rd 2012

Description

The subject of this book is truly original. By encoding of algebraic equations into graphs—originally a purely pedagogical technique—the exploration of physics and physical chemistry reveals common pictures through all disciplines. The hidden structure of the scientific formalism that appears is a source of astonishment and provides efficient simplifications of the representation of physical laws.

Understanding Physics and Physical Chemistry Using Formal Graphs is organized according to the structures emerging from formal graphs, from simple to elaborate, providing after each series of case studies the theoretical elements necessary for understanding their common features. More than 80 case studies are tackled in domains ranging from translational mechanics to Newtonian gravitation to chemical reactions.

With the help of this new tool, the modeling of physical phenomena becomes a fascinating cross-disciplinary exploration. The graphs encourage a visual, unified comprehension of the relationships between physical concepts and variables, properties, and operators. Out-of-the-box and thought provoking, this book inspires lively discussions and fruitful thinking about the connections between mechanics, chemical reactivity, electrodynamics, thermodynamics, and more.

Reviews

Vieil presents a universal toolkit—Formal Graphs—for understanding a wide range of scientific domains. … mainly for graduate students, researchers and specialists, and engineers; the process itself would even be accessible to undergraduate students … . The disk contains all the graphs, in color bitmap files, and software for building simple electric circuits and translating them into Formal Graphs.

—SciTech News, Vol. 66, September 2012

Vieil (French Atomic Energy Agency) discusses the use of formal graphs in physics and chemistry to facilitate an understanding of these subjects. This method has four primary purposes. First, pedagogically, students can benefit from considering theoretical systems in a non-algebraic way. With pictorial representations, students can more easily see relationships between elements of a theory and the similarities of formal graph structures among theories. Second, since formal graphs are neural networks, it is much easier to translate the science into algorithms if one starts with the graphs. Third, scientists already familiar with one area can more easily learn and gain insight into a new area that is using the same formal graph. Finally, researchers can benefit by examining the work of researchers in other disciplines that are considering the same formal graphs. This is an intriguing way to represent the science. The author provides more than 80 case studies to illustrate this method. A companion CD-ROM includes all of the book's formal graphs as well as software for translating simple examples into formal graphs. The related website contains a variety of supplementary materials. Recommended.

—E. Kincanon, Gonzaga University, CHOICE, August 2012

Contents

Introduction

Aim of this Book

An Imperfect State of Science

Improvement through Graphs

Nodes of Graphs

Energy and State Variables

Links and Organization

System Constitutive Properties

Formal Objects and Organization Levels

Poles

The Pole as Elementary Collection

Formal Graph Representation of a Pole

Composition of Poles

Definition of a Pole and Its Variables

Space Distributed Poles

The Role of Space

Formal Graph Representation of a Space Distributed Pole

Space Operators

Translation Problems and Generalization

Dipoles

The Dipole

Formal Graph Representation of a Dipole

Interaction through Exchange between Poles

Dipole Properties

Common Features Result in New Ideas

Influence between Poles

Interaction between Poles

Poles–Dipole Constitutive Properties

Influence Theory

In Short

Multipoles

The Multipole

Decomposition into Dipoles

Decomposition into Poles

Theory of Conduction

Dipole Assemblies

The Dipole Assembly

Evolution and Time

Formal Graph Representation of a Dipole Assembly

Temporal Oscillator

Spatial Oscillator

Spatiotemporal Oscillator

Transfers

Definition of Transfer

Comparison between Energy Varieties

Energy Behaviors

Convection

Assemblies and Circuits

Assemblies and Dissipation

Dissipation and Conversion

Basic Processes Involving Dissipation

Relaxation Models

Damped Oscillator (Temporal)

Spatially Damped Oscillator

Attenuated Propagation

Coupling between Energy Varieties

Passages of Energy

Energetic Equivalence

Energetic Coupling

Properties of Coupling

Multiple Couplings

Ideal Gas

The Energy of Coupling

The Scaling Chemical Potential

Map of Energetic Couplings

Conclusion and Perspectives

Characteristics of the Theory

Perspectives

Conclusion

Appendices

Glossary

Symbol List

Graph Coding

List of Case Studies

CD-ROM content

References

Index

Author Bio

Dr. Eric Vieil is a researcher in physical chemistry at the French Atomic Energy Agency (CEA) in Grenoble, France. He is a specialist with more than 80 publications in theoretical and experimental studies on the electrochemical mechanisms of conducting materials.

Name: Understanding Physics and Physical Chemistry Using Formal Graphs (Hardback)CRC Press 
Description: By Eric Vieil. The subject of this book is truly original. By encoding of algebraic equations into graphs—originally a purely pedagogical technique—the exploration of physics and physical chemistry reveals common pictures through all disciplines...
Categories: Chemistry, Combinatorics, Mathematical Physics