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Ordering in two dimensions
Mathematicsand Computersin SimulationXXIV (1982) 585-589 North-HollandPublishingCompany
585
BOOK REVIEWS
Edited by P. VAN REMOORTERE
1980
S.K. Sinha (Editor): Ordering in Two Dimensions. Proceedings of the International Conference held at Lake Geneva, Wisconsin, USA, May 28-30, 1980. North-Holland Publishing Company, 1980, 498 pages, $55.00, ISBN 0-444-00581-1. The idea behind the Proceedings of the Conference presented in this book was to cut across disciplinary lines and bring together physicists, chemists, and biologists from several different areas to focus on the universal aspects of ordering in two dimensions. Many of the fields represented here are currently centers of intense activity themselves. The papers represented in this volume, however, deal primarily with the unifying theme running through these fields, namely the question of the nature of the phases and phase transitions in systems of dimensionality two. Over two hundred eminent scientists from many different disciplines and countries attended the Conference and many interesting new results are presented for the first time in this collection of twenty-seven invited and seventy-six contributed papers. Recorded question and answer sessions after the invited papers give the reader a feel for many of the important current issues in this area. Represented are theoretical reviews and accounts of recent developments in lattice gas models, Kosterlitz-Thouless transitions, the relations between bulk and surface phase transitions, phase transitions in membranes and liquid crystals; x-ray neutron and electron diffraction and thermodynamic studies of ordering in physisorbed and chemisorbed monolayers; intercalated graphite, layered compounds, molecular monolayers at gasliquid interfaces, surface magnetism and surface reconstruction; studies of thin-film superconductors and two-dimensional electron lattices on liquid
helium surfaces; studies of commensurate-in-commensurate transitions, and the results of the most recent computer simulation studies of melting in two dimensions, by most of the leading experts in the field. Many important new results are reported here for the first time and many other recent advances are comprehensively reviewed and referenced here, also for the first time.
1981
R. Glowinski, R.J. Lions and R. Tremolieres: Numerical Analysis of Variational Inequations. North-Holland Publishing Company, 1981, 776 pages, $109.75, ISBN 0-444-86199-8. This volume is concerned with the numerical treatment of variational inequalities for partial differential operators. Such inequalities play a fundamental role in the modelling of various phenomena in physics and mechanics, as well as in engineering and applied sciences. A detailed analysis of various iterative methods is given for solving the finite dimensional problems resulting from the above approximations. Emphasis is placed in particular on finite difference and finite element approximations and also on iterative techniques such as relaxation, conjugate gradient and duality methods. A large number of numerical tests are given to illustrate the efficiency of the methods described in the work. The work features a large, updated appendix which contains a section showing how variational inequality concepts and methods may help in the numerical solution of transonic flow problems. The volume is unique in that it gives a complete treatment of variational inequality problems.
0378-4754/82/0000-0000/$02.75 © 1982 North-Holland
585
BOOK REVIEWS
Edited by P. VAN REMOORTERE
1980
S.K. Sinha (Editor): Ordering in Two Dimensions. Proceedings of the International Conference held at Lake Geneva, Wisconsin, USA, May 28-30, 1980. North-Holland Publishing Company, 1980, 498 pages, $55.00, ISBN 0-444-00581-1. The idea behind the Proceedings of the Conference presented in this book was to cut across disciplinary lines and bring together physicists, chemists, and biologists from several different areas to focus on the universal aspects of ordering in two dimensions. Many of the fields represented here are currently centers of intense activity themselves. The papers represented in this volume, however, deal primarily with the unifying theme running through these fields, namely the question of the nature of the phases and phase transitions in systems of dimensionality two. Over two hundred eminent scientists from many different disciplines and countries attended the Conference and many interesting new results are presented for the first time in this collection of twenty-seven invited and seventy-six contributed papers. Recorded question and answer sessions after the invited papers give the reader a feel for many of the important current issues in this area. Represented are theoretical reviews and accounts of recent developments in lattice gas models, Kosterlitz-Thouless transitions, the relations between bulk and surface phase transitions, phase transitions in membranes and liquid crystals; x-ray neutron and electron diffraction and thermodynamic studies of ordering in physisorbed and chemisorbed monolayers; intercalated graphite, layered compounds, molecular monolayers at gasliquid interfaces, surface magnetism and surface reconstruction; studies of thin-film superconductors and two-dimensional electron lattices on liquid
helium surfaces; studies of commensurate-in-commensurate transitions, and the results of the most recent computer simulation studies of melting in two dimensions, by most of the leading experts in the field. Many important new results are reported here for the first time and many other recent advances are comprehensively reviewed and referenced here, also for the first time.
1981
R. Glowinski, R.J. Lions and R. Tremolieres: Numerical Analysis of Variational Inequations. North-Holland Publishing Company, 1981, 776 pages, $109.75, ISBN 0-444-86199-8. This volume is concerned with the numerical treatment of variational inequalities for partial differential operators. Such inequalities play a fundamental role in the modelling of various phenomena in physics and mechanics, as well as in engineering and applied sciences. A detailed analysis of various iterative methods is given for solving the finite dimensional problems resulting from the above approximations. Emphasis is placed in particular on finite difference and finite element approximations and also on iterative techniques such as relaxation, conjugate gradient and duality methods. A large number of numerical tests are given to illustrate the efficiency of the methods described in the work. The work features a large, updated appendix which contains a section showing how variational inequality concepts and methods may help in the numerical solution of transonic flow problems. The volume is unique in that it gives a complete treatment of variational inequality problems.
0378-4754/82/0000-0000/$02.75 © 1982 North-Holland