Phase transformations in the TiO2–SiO2 system at high pressures and temperatures

In situ X-ray diffraction study of a sol–gel-produced SiO₂–TiO₂ glass and intimately mixed ultrafine powders of SiO₂ and TiO₂ was used to investigate the effect of TiO₂ on the high-pressure phase transformations of SiO₂ and specifically on the change in the p,T-conditions of the formation of coesite and stishovite. Our findings have shown that at pressures to 7.5?GPa and temperatures up to 1300?K the presence of TiO₂ does not favor the formation of stishovite.     

Some identities for Moore–Penrose inverses of matrix products

A group of identities are established for the Moore–Penrose inverses and the weighted Moore–Penrose inverses of matrix products AB and ABC. Some consequences and applications are also presented.     

On the Free Boundary Conditions for a Dynamic Shell Model Based on Intrinsic Differential Geometry

The mathematical theory behind the modeling of shells is a crucial issue in many engineering problems. Here, the authors derive the free boundary conditions and associated strong form of a dynamic shallow Kirchhoff shell model based on the intrinsic geometry methods of Michael Delfour and Jean-Paul Zolésio. This model relies on the oriented distance function which describes the geometry. This is an extension of the work done in [J. Cagnol, I. Lasiecka, C. Lebiedzik and J.-P. Zolésio (2002). Uniform stability in structural acoustic models with flexible curved walls. J. Differential Equation, 186(1), 88–121.], where the model was derived for clamped boundary conditions only. In the current article, manipulations with the model result in a cleaner form where the displacement of the shell and shell boundary is written explicitly in terms of standard tangential operators.     

Drift-diffusion in electrochemistry: thresholds for boundary flux and discontinuous optical generation

We consider an extension of the classical drift-diffusion model, which incorporates thermodynamic switching rules for generation and boundary flux. The motivation is the important case of the splitting of water molecules upon photonic irradiation of a semiconductor electrode located in an electrochemical cell. The solid state electrode forms the spatial domain of the model. The rules are motivated by the fact that the valence band of the semiconductor, which supplies positive charge to solution, has to be located at a lower energy level than the electrochemical potential of O₂ evolution in solution, and the conduction band, which supplies electrons to solution, has to be positioned at a higher energy level than the electrochemical potential of H₂ evolution. This defines thresholds in terms of electrochemical potentials before boundary flux is activated. The optical generation rate is affected, due to the increased carrier relaxation time, when these thresholds are crossed, and may be discontinuous. We thus consider a self-consistent model, in which ‘switching’ occurs only in principal variables. The steady-state model is considered, and trapping regions are derived for the solutions.     

On a class of nonlinear variational–hemivariational inequalities

A three critical points theorem for nondifferentiable functions is pointed out and an existence result of multiple solutions for a Neumann elliptic variational–hemivariational inequality involving the p-laplacian is established. As an application, a Neumann problem for elliptic equations with discontinuous nonlinearities is studied.     

Nuclear Superfluidity. Pairing in Finite Systems,by D.M. Brink and R.A. Broglia

Introduction to High Energy Physics. By D. H. Perkins. (Addison-Wesley, 1972.) [Pp. xiii + 353.] £4.30. Scope: Textbook. Level: Postgraduate. undergraduate.

Fundamentals of Aeronomy. By R. C. Whitten and I. G. Poppoff. (John Wiley, 1971). [Pp. xiv+446.] £7.00. Scope: Treatise/textbook. Level: Specialist/postgradute; undergraduate (3rd year).

Statistical Physics. By F. Mandl. (John Wiley &; Sons Ltd., 1971.) [Pp. xiii+379.] £2.75 (paper only). Scope: Textbook. Level: Undergraduate.

Basic Theory of Lasers and Masers. By J. Vanier. (Gorden &; Breach, 1971.) [Pp. xii+115.] Cloth £4.75; paper £2.25. Scope: Treatise. Level: For specialists only; specialist/postgraduate.

Concepts of Classical Mechanics. By L. R. B. Elton. (McGraw-Hill, 1971.) [Pp. xvii+177.] £2.60. Scope: Textbook. Level: Undergraduate.

College Physics. By E. Gillam and R. M. King. (Macdonald &; Evans Ltd., 1971.) Volume 1. [Pp. xvii+ 390.] £1.15. Volume 2. [Pp. xvii+404.] £1.25. Scope: Textbook. Level: Undergraduate.

Physical Science for Liberal Arts Students. By Hugo N. Swenson and J. E. Woods. (John Wiley &; Sons Ltd., 1971.) [Pp. viii+361.] £5.00. Scope: Textbook. Level: Undergraduate.

Natural Philosophy Through the Eighteenth Century. Edited by Allan Ferguson. (Taylor and Francis, 1972.) [Pp. vii+164.] £5.00.

Recent Advances in Plasma Diagnostics. Vol 1. Edited by V. T. Tolok. (Consultants Bureau, 1971.) [Vol. 1: vi+130.] $25.20. [Vol. 2: vi+105.] $25.20. [Vol. 3. vi+73.] Level: For specialists only.

Astronomy. By E. G. Ebbighusen. (Prentice Hall International, 1971.) [Pp. vii+ 150.] £1.00. Scope: Textbook. Level: Undergraduate; school.

Solid State Electronics. Edited by Edwin R. Jones. (Intertext Group of Publishers, 1971.) [Pp. x+398.] £5.50. Scope: Textbook. Level: Undergraduate.

Electronic Energy Bands in Solids. By L. Pincherle. (Macdonald, 1971.) [Pp. vi+196.] £4.00. Scope: Textbook. Level: postgraduate.

Advances in Nuclear Physics. Edited by Michel Baranger and Erich Vogt. (Plenum Press. 1971.) [Pp. xvi+448.] $2040. Scope: Survey. Level: Specialist/postgraduate.

Photophysics of Arowmtic Molecules. By J. B. Birks. (Wiley-Interscience, London). [Pp. xiii+704.] £10.50. Scope: Treatise. Level: Postgraduate.

Quench Hardening in Metals. By H. Kimura and R. Maddin. (North-Holland Publishing Company., 1971.) [Pp. ix+124.] $10.00. Scope: Treatise. Level: Specialist/postgraduate; undergraduate.

Thermodynamic Diagrams for High Temperature Plasmas of Air, Air-Carbon, Carbo-Hydrogen Mixtures, and Argon. By H. Kroepelin, K-K Neumann, K-U. Hoffmann and R. Kuthe. (Pergamon, 1971.) [Pp. xii+184.] £7.30. Scope: Library. Level: For specialists only.

The Plasma State. By Juda Leon Shohet. (Academic Press, 1971.) [Pp. viii+333.] £6.30. Scope: Treatise/textbook. Level: Specialist/postgraduate.

Kinetic Equations. Edited by R. L. Liboff and N. Rostoker. (Gordon and Breach, 1971.) [Pp. xv+346.] £8.16. Scope: Conference proceedings. Level: Specialist/postgraduate.

Hadronic Interactions of Electrons and Photons. Edited by J. Cummwa and H. Osbobn. Academic Press 1971.) [Pp. xvi+653.] £10.50. Scope: Conference Proceedings. Level: Postgraduate.

Concepts in Hadron Physics. Edited by P. Urbau. (Vienna and New York: Springer-Verlag, 1971.) [Pp. xv+424.] $26.40. Scope: Conference proceedings. Level: Specialist/postgraduate.

Certificate Physics. (SI Edition.) By C. W. Kearsey. (Longman, 1971.) [Pp. 383.] £1.16. Scope: Textbook. Level: School (O Level plus).

Force in Newton's Physics. By R. S. Westfall. (Macdonald, London; American Elsevier, New York, 1971.) [Pp. xii+579.] £10. Scope: Survey. Level: Specialist/post-graduate.

Elementary Quantum Mechanics. ByN. F. Mott. (Wykeham Publications (London) Ltd., 1972.) [Pp. viii+ 122.] Cloth £2.75; Paper £2. Scope: Textbook. Level: Undergraduate.

Electron Optics and Electron Microscopy. By P. W. Hawkes. (Taylor and Francis, London, 1972.) [Pp. xv+244.] £5. Scope: Textbook. Level: Specialist/postgraduate.

Selected Papers by Cecil Frank Powell. Edited by E. H. S. Burhop, W. O. Look and M. G. K. Menon. (North-Holland, 1972.) [Pp. xiii+455.] Dft 80.00, $25.00. Scope: Library. Level: General reader.

Rare Earths and Actinidea. (Conference Digest No. 3.) (The Institute of Physics, 1971.) [Pp. viii+ 252.] Scope: Conference proceedings. Level: Specialist/postgraduate.     

A Hamilton–Jacobi type equation for computing minimum potential energy paths

A new method for computing minimum-energy reaction paths is presented. Unlike existing approaches (e.g. intrinsic reaction coordinate methods), our approach works for any reactant configuration: the structure of the transition state, reactive intermediates and product will be determined by the algorithm, and so need not be known beforehand. The method we have developed is based on solving a Hamilton–Jacobi type equation. Specifically, we introduce a speed function so that the ‘first arrival times’ from the Hamilton–Jacobi equation correspond to least-potentials. Then, adopting a back-tracing method, we can use the first arrival times to determine the minimum-energy path between any classically allowed molecular conformation and the initial (reactant) conformation. The method is illustrated by applying it to six different systems: (1) a model system with four different minima in the potential energy surface, (2) a model Muller–Brown potential, (3) the isomerization reaction of malonaldehyde using a fitting potential energy surface, (4) a model Minyaev–Quapp potential representative of con- and dis-rotations of two BH₂ groups in the BH₂–CH₂–BH₂ molecule, (5) the F?+?H₂→FH?+?H reaction and (6) the H?+?FH?→?HF?+?H reaction. Our results demonstrate that the proposed method represents a robust alternative to existing techniques for finding chemical reaction paths.     

Temperature dependence of liquid viscosity

Least squares programs were used to evaluate the correlation between recent experimental results and theoretical, semi-theoretical, or empirical relations between liquid viscosity and temperature. It was found that none of these describes the experimental dependence in the whole range of temperature. A new dependence based on the free volume concept and cell-hole liquid theory is proposed. The theory permits linearization of the viscosity-temperature data in the range (T_i, T_i+1), where the T_i's are the liquid-liquid transition temperatures. It was demonstrated that these transitions, both in small molecular and in polymeric liquids, occur in discrete steps: T_i = a_iT_g, where T_g is the glass transition temperature and the a_i's are numerical parameters. Not all the transitions T_i were apparent in all liquids. Transition T₂ = 1.26T_g was observed for most polymeric liquids. On the basis of thermal analysis it was demonstrated that the T_i's coincide with the temperatures at which small changes in the apparent specific heat were detected. These temperatures can be assigned to the maximum rate of crystallization and melting temperatures of the metastable and stable crystalline forms.     

An Expedient Large-Scale Preparation of a Dibenz[b,e]oxepinone Derivative

A convenient, large-scale synthesis of a dibenz[b,e]oxepinone derivative is described. The dibenz[b, e]oxepinone ring system is constructed using an iron chloride catalyzed intramolecular Friedel-Crafts cyclization of an appropriate phenoxymethylbenzoic acid chloride in toluene, reagents and conditions that are economically and environmentally compatible with large-scale preparation.