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Non-equilibrium thermodynamics
Book Reviews Pasterla and Puskerla on p. 105, and Christenson is spelt consistently with an additional “i” throughout the final article. Nevertheless, the book is to be recommended as a convenient starting point for the graduate student entering the field. It covers quite a wide range of mesonic phenomena and of interaction processes, from discussions of baryonic resonances to the CP-violating weak interactions of the neutral K-mesons, and this conjunction of articles will help to broaden the knowledge of any research worker who dips into this book, even if he begins with the sections on his own topic. R. H. DALITZ Department of Theoretical Physics Oxford University Oxford, England
ROTATIONAL STRUCTUREIN THE SPECTRA OF DI_T~MIC MOLECULES, by Istvan Kovacs (Hungarian Academy of Sciences). 320 pages, diagrams, 6+x 9+ in. New York, American Elsevier, 1970. Price, $16.75. Here is a very useful compilation of multiplet-term as well as intensity distribution formulas for a great variety of molecular rotational band types. The reviewer has long felt the need for such a compilation in his studies of stellar molecular spectra. The book should therefore become a standard reference for research workers in this field. It can be used as a text in a specialized course for graduate students. After a short introduction of the observed rotational bands, the author then derives a general wave equation which is solved with matrix mechanics. The subject is developed very well and the notation is consistent throughout. The second chapter gives the solutions of the general secular equation for the multiplet-term formulas in each of the various spin multiplet and L multiplet cases, and in each of Hund’s cases and intermediate cases. These derivations include the effects of lambda doubling; development from the general theory to the special cases is excellent.
146
The third chapter discusses the intensity distribution in the rotational bands. In the beginning of the chapter the author discusses the computations of the dipole matrix elements generally and subsequently he gives the intensity distribution formulas for the various spin and L multiplet transitions. The fourth chapter is a study of perturbation theory with a comparison to observations. This chapter includes a very clear discussion of predissociation in the context of perturbation theory. As in the previous chapter, the formulas for the perturbation matrix elements for each of the various multiplet transitions are listed without derivation, but are extensively referenced. Much of this excellent work has been derived by the author himself. The last section of the chapter discusses new methods for determining the constants of perturbed molecular terms. This is of great current interest. THEODORE D. FAY Bartol Research ~ountion of The l%anklin Institute Swarthrnore, Pennsylvania
NON-EQUILIBRIUM THERMODYNAMICS, by Istvan Gyarmati (English translation by Eve Gyarmati and Wolfgang F. Heinz). 184 pages, diagrams, 59 x 8 in. Springer-Verlag, Berlin and Heidelberg, 1970. Edited by Istvan Szabo, the scope of this little monograph is substantially greater than is indicated by its title; at the same time, it is somewhat less than is indicated by its subtitle: “Field Theory and Variational Principles”. The author, I. Gyarmati, has a keen sense of generalizing and extending the principles of irreversible thermodynamics as pioneered by Onsager and developed by Meixner, Prigogine and de Groot. Cognizance of the contributions to continuum mechanics by Truesdell and Noll has been acknowledged, which conveys partially the generality of the author’s treatment of his subject. The presentation is subtle, and more general than is immediately apparent, and the style is formal, axiomatic and concise. For a reader familiar
Journal of The FranklinInstitute
Rook Reviews with the literature citations, and knowledgeable as to typical practical examples (which are largely omitted), the beauty of Gyarmati’s text will be perceived and appreciated. He has pointed out the extent to which the validity of the theory of irreversible thermodynamics has been demonstrated, and also how this depends on the applicability of the hypothesis of local (cellular) equilibrium. Here and elsewhere in the monograph, Gyarmati points out various pitfalls without going into details merely by citing pertinent literature references. As the text is very formal, the reader is somewhat inconvenienced by the lack of an index in reviewing key statements and definitions, and because of certain irregularities in the translation this is especially noticeable. Although the text is competently translated, it has been inadequately edited. For example, instead of unreal, jictitious, illusory, term and interior, we find respectively irreal, $ctive, illusoric, denomination and internal. The reader can easily take those examples in stride, but he can be left in doubt in a few other cases. But, they are all minor editorial questions which could be resolved in a second printing. B. R. GOSSICK Physics Department University of Kentucky Lexington, Kentucky
TO OPTIMAL CONTROL, by Ian McCausland. 258 pages, diagrams, 6 x 9 in. New York, John Wiley, 1969. Price, $12.00.
INTRODUCTION
It would seem almost impossible to write a 25%page textbook for readers completely unfamiliar with optimal control, covering most of the major aspects of the subject, without being completely superficial. Yet, Professor McCausland has carefully balanced mathematical rigor and intuitive arguments to write an excellent introductory text. The book is intended for advanced undergraduates or beginning graduate students. The material could be covered in one semester by students at that level, and probably stimulate those students
Vol.291,No. 2,February 1971
seriously interested in optimal control into a deeper and more rigorous study of the subject. Practicing engineers unfamiliar with the subject should also tid the book to be an excellent self-teaching text. The style is quite lucid and informal, the examples are simple and to the point, and answers are provided for all problems. In short, the book is easy to read. The material is outlined in Chapter I. The next chapter introduces the concept of optimal control by describing in detail the minimization of the integral-squarederror in a position control system. Chapter III is concerned with stochastic systems. (Since the remainder of the book is concerned with deterministic processes, this part could easily be skipped without loss of continuity.) A brief but excellent presentation of correlation functions and power spectra is given, along with a derivation of the Weiner-Hopf equation and its solution using spectrum factorization. Unfortunately, the extension to Kalman filtering is not quite so clear. Next, a presentation of state variables, coordinate transformations and transition matrices is made. Excellent descriptions of the concepts of controllability and observability are given. The state representation of sampled-data systems is also derived and time-varying and nonlinear systems are mentioned. Chapter V is concerned with the calculus of variations and begins with a derivation of the Euler-Lagrange equation. Isoperimetric constraints are covered, as are fixed and free end-point problems. Transversality conditions are given but unfortunately not derived, thus tending to lend them an unnecessarily mysterious quality. In keeping with the introductory nature of the text, such concepts as corner conditions and second variations are not mentioned. The Hamiltonian is then introduced, and the continuity limitations of the calculus of variations are emphasized; thus leading to the formulation of the maximum principle where detailed examples of minimum-time control of the double integrator and linear oscillator for both point and region target sets are given, along with a minimum fuel application. Dynamic programming is introduced
147
ROTATIONAL STRUCTUREIN THE SPECTRA OF DI_T~MIC MOLECULES, by Istvan Kovacs (Hungarian Academy of Sciences). 320 pages, diagrams, 6+x 9+ in. New York, American Elsevier, 1970. Price, $16.75. Here is a very useful compilation of multiplet-term as well as intensity distribution formulas for a great variety of molecular rotational band types. The reviewer has long felt the need for such a compilation in his studies of stellar molecular spectra. The book should therefore become a standard reference for research workers in this field. It can be used as a text in a specialized course for graduate students. After a short introduction of the observed rotational bands, the author then derives a general wave equation which is solved with matrix mechanics. The subject is developed very well and the notation is consistent throughout. The second chapter gives the solutions of the general secular equation for the multiplet-term formulas in each of the various spin multiplet and L multiplet cases, and in each of Hund’s cases and intermediate cases. These derivations include the effects of lambda doubling; development from the general theory to the special cases is excellent.
146
The third chapter discusses the intensity distribution in the rotational bands. In the beginning of the chapter the author discusses the computations of the dipole matrix elements generally and subsequently he gives the intensity distribution formulas for the various spin and L multiplet transitions. The fourth chapter is a study of perturbation theory with a comparison to observations. This chapter includes a very clear discussion of predissociation in the context of perturbation theory. As in the previous chapter, the formulas for the perturbation matrix elements for each of the various multiplet transitions are listed without derivation, but are extensively referenced. Much of this excellent work has been derived by the author himself. The last section of the chapter discusses new methods for determining the constants of perturbed molecular terms. This is of great current interest. THEODORE D. FAY Bartol Research ~ountion of The l%anklin Institute Swarthrnore, Pennsylvania
NON-EQUILIBRIUM THERMODYNAMICS, by Istvan Gyarmati (English translation by Eve Gyarmati and Wolfgang F. Heinz). 184 pages, diagrams, 59 x 8 in. Springer-Verlag, Berlin and Heidelberg, 1970. Edited by Istvan Szabo, the scope of this little monograph is substantially greater than is indicated by its title; at the same time, it is somewhat less than is indicated by its subtitle: “Field Theory and Variational Principles”. The author, I. Gyarmati, has a keen sense of generalizing and extending the principles of irreversible thermodynamics as pioneered by Onsager and developed by Meixner, Prigogine and de Groot. Cognizance of the contributions to continuum mechanics by Truesdell and Noll has been acknowledged, which conveys partially the generality of the author’s treatment of his subject. The presentation is subtle, and more general than is immediately apparent, and the style is formal, axiomatic and concise. For a reader familiar
Journal of The FranklinInstitute
Rook Reviews with the literature citations, and knowledgeable as to typical practical examples (which are largely omitted), the beauty of Gyarmati’s text will be perceived and appreciated. He has pointed out the extent to which the validity of the theory of irreversible thermodynamics has been demonstrated, and also how this depends on the applicability of the hypothesis of local (cellular) equilibrium. Here and elsewhere in the monograph, Gyarmati points out various pitfalls without going into details merely by citing pertinent literature references. As the text is very formal, the reader is somewhat inconvenienced by the lack of an index in reviewing key statements and definitions, and because of certain irregularities in the translation this is especially noticeable. Although the text is competently translated, it has been inadequately edited. For example, instead of unreal, jictitious, illusory, term and interior, we find respectively irreal, $ctive, illusoric, denomination and internal. The reader can easily take those examples in stride, but he can be left in doubt in a few other cases. But, they are all minor editorial questions which could be resolved in a second printing. B. R. GOSSICK Physics Department University of Kentucky Lexington, Kentucky
TO OPTIMAL CONTROL, by Ian McCausland. 258 pages, diagrams, 6 x 9 in. New York, John Wiley, 1969. Price, $12.00.
INTRODUCTION
It would seem almost impossible to write a 25%page textbook for readers completely unfamiliar with optimal control, covering most of the major aspects of the subject, without being completely superficial. Yet, Professor McCausland has carefully balanced mathematical rigor and intuitive arguments to write an excellent introductory text. The book is intended for advanced undergraduates or beginning graduate students. The material could be covered in one semester by students at that level, and probably stimulate those students
Vol.291,No. 2,February 1971
seriously interested in optimal control into a deeper and more rigorous study of the subject. Practicing engineers unfamiliar with the subject should also tid the book to be an excellent self-teaching text. The style is quite lucid and informal, the examples are simple and to the point, and answers are provided for all problems. In short, the book is easy to read. The material is outlined in Chapter I. The next chapter introduces the concept of optimal control by describing in detail the minimization of the integral-squarederror in a position control system. Chapter III is concerned with stochastic systems. (Since the remainder of the book is concerned with deterministic processes, this part could easily be skipped without loss of continuity.) A brief but excellent presentation of correlation functions and power spectra is given, along with a derivation of the Weiner-Hopf equation and its solution using spectrum factorization. Unfortunately, the extension to Kalman filtering is not quite so clear. Next, a presentation of state variables, coordinate transformations and transition matrices is made. Excellent descriptions of the concepts of controllability and observability are given. The state representation of sampled-data systems is also derived and time-varying and nonlinear systems are mentioned. Chapter V is concerned with the calculus of variations and begins with a derivation of the Euler-Lagrange equation. Isoperimetric constraints are covered, as are fixed and free end-point problems. Transversality conditions are given but unfortunately not derived, thus tending to lend them an unnecessarily mysterious quality. In keeping with the introductory nature of the text, such concepts as corner conditions and second variations are not mentioned. The Hamiltonian is then introduced, and the continuity limitations of the calculus of variations are emphasized; thus leading to the formulation of the maximum principle where detailed examples of minimum-time control of the double integrator and linear oscillator for both point and region target sets are given, along with a minimum fuel application. Dynamic programming is introduced
147