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Beatty M.F., Hayes M.A. (eds.) Mechanics and Mathematics of Crystals. Selected Papers of J.L. Ericksen

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Beatty M.F., Hayes M.A. (eds.) Mechanics and Mathematics of Crystals. Selected Papers of J.L. Ericksen
New Jersey: World Scientific. – 2005. – 653 p. This book celebrates the 80th birthday of Professor Jerald. L. Ericksen, our esteemed teacher and good friend for nearly 45 years now. The volume presents a selection of research papers by Ericksen on the mechanics and mathematics of crystals published over the past 35 years, just a fraction of his (currently) 145 journal and book articles published since 1948, all of which are listed below in the "Publications of J. L. Ericksen." With the exception of the first paper in this collection, an English version of the original Russian language publication unique to this volume, all others are reproduced entirely as originally published. Moreover, except for this brief Foreword, everything else in this book is written by Jerry Ericksen alone. The papers are arranged by Ericksen into four principal groups, or chapters, each of which is preceded by a summary introduction describing its contents. Unfortunately, we are unable to reprint Ericksen's two most recent papers which are expected to appear in 2005. Nevertheless, useful extended summaries of these works are provided in Chapter
3. This collection of selected works of Ericksen thus provides a splendid corpus of research papers which should prove valuable to a broad group of researchers in the mechanics, applied mathematics, and materials science communities. We are very pleased to have included in this volume a short autobiography of Professor Ericksen, which he very kindly prepared at our request.
Contents:
Foreword (by M. F. Beatty and M. A. Hayes).
J. L. Ericksen's Autobiography.
Publications of J.L. Ericksen.
Crystal Symmetry
On the Symmetry of Crystals // Problems of Mechanics of Deformable Solid Bodies (in Russian), eds. Y. N. Rabotnov and L. I. Sedov, Academy of Sciences USSR, Sudostroenie, Leningrad (St. Petersburg) 1970, pp. 493-496.
Nonlinear Elasticity of Diatomic Crystals // Int. J. Solids Structures, 1970, Vol. 6, pp. 951-957.
On the Symmetry of Deformable Crystals // Archive for Rational Mechanics and Analysis, Vol. 72, Number 1, 1979, P. 1—13.
Changes in Symmetry in Elastic Crystals // Proceedings of the IUTAM Symposium on Finite Elasticity, eds. Carlson D.E. and Shield R.T., Martinus NijhofT Publishers, The Hague/Boston/London, 1981, pp. 167-177.
Crystal Lattices and Sub-Lattices // Rend. Sem. Mat. Univ. Padova, Vol. 68 (1982), pp. 1-9.
On Nonessential Descriptions of Crystal Multilattices // Mathematics and Mechanics of Solids, Vol. 4, pp. 363-392, 1998.
On Groups Occurring in the Theory of Crystal Multi-Lattices // Arch. Rational Mech. Anal., Vol. 148 (1999) pp. 145-178.
Constitutive Theory
Multi-Valued Strain Energy Functions for Crystals // Int. J. Solids Structures, Vol.
18., No. 10, pp. 913-916, 1982.
The Cauchy and Born Hypotheses for Crystals // Phase Transformations and Material Instabilities in Solids, Academic Press Inc., 1984, pp. 61-77.
Constitutive Theory for Some Constrained Elastic Crystals // Int. J. Solids Structures, Vol. 22, No. 9, pp. 951-964, 1986.
Some Constrained Elastic Crystals // Material Instabilities in Continuum Mechanics and Related Mathematical Problems, Oxford University Press, 1988, pp. 119-135.
Equilibrium Theory for X-ray Observations of Crystals // Arch. Rational Mech. Anal., Vol. 139 (1997) pp. 181-200.
A Minimization Problem in the X-ray Theory // Anniversary Volume Krzysztof Wilmanski, 2000, pp. 77-82.
Notes on the X-ray Theory // Journal of Elasticity, Vol. 55, pp. 201-218, 1999.
On Pitteri Neighborhoods Centered at Hexagonal Close-Packed Configurations // Arch. Rational Mech. Anal., Vol. 164 (2002) pp. 103-131.
Defects
Volterra Dislocations in Nonlinearly Elastic Bodies // Analele stiintifice ale Universitatii „Al. I. Cuza" din Iasi, Vol. XXIII, 1977, pp. 423-430.
Twinning of Crystals // Metastability and Incompletely Posed Problems, eds. S. Antman, J.L. Ericksen, D. Kinderlehrer, and I. Milller, Springer, 1987, pp. 77-93.
Thermoelastic Considerations for Continuously Dislocated Crystals // The Mechanics of Dislocations, Proceedings of an International Symposium, 1983, pp. 95-100.
Some Surface Defects in Unstressed Thermoelastic Solids // Archive for Rational Mechanics and Analysis, Vol. 88, Number 4, 1985, pp. 337-345.
Stable Equilibrium Configurations of Elastic Crystals // Archive for Rational Mechanics and Analysis, Vol. 94, Number 1, 1986, pp. 1-14.
On Nonlinear Elasticity Theory for Crystal Defects // International Journal of Plasticity, Vol. 14, Nos. 1-3, pp. 9-24, 1998.
On Correlating Two Theories of Twinning // Arch. Rational Mech. Anal., Vol. 153 (2000) pp. 261-289.
Twinning Analyses in the X-ray Theory // International Journal of Solids and Structures, Vol. 38 (2001) pp. 967-995.
Twinning Theory for Some Pitteri Neighborhoods // Continuum Mech. Thermodyn. (2002) Vol. 14, pp. 249-262.
On the X-ray Theory of Twinning // Mathematics and Mechanics of Solids, Vol. 7, pp. 331-352, 2002.
On the Theory of Rotation Twins in Crystal Multilattices // Journal of Elasticity, Vol. 70, pp. 267-283, 2003.
On the Theory of Growth Twins in Quartz // Mathematics and Mechanics of Solids, Vol. 6, pp. 359-386, 2001.
On the Theory of Cyclic Growth Twins.
Unusual Solutions of Twinning Equations in the X-ray Theory.
Phase Transitions
Some Phase Transitions in Crystals // Archive for Rational Mechanics and Analysis, Vol. 73, 1980, pp. 99-124.
Continuous Martensitic Transitions in Thermoelastic Solids // Journal of Thermal Stresses, Vol. 4, pp. 107-119, 1981.
Weak Martensitic Transformations in Bravais Lattices // Archive for Rational Mechanics and Analysis, Vol. 107, Number 1, 1989, pp. 23-36.
Bifurcation and Martensitic Transformations in Bravais Lattices // Journal of Elasticity, Vol. 28, pp. 55-78, 1992.
Local Bifurcation Theory for Thermoelastic Bravais Lattices // The IMA Volumes in Mathematics
and Its Applications. Vol. 54: Microstructure and Phase Transition, Springer, 1993, pp. 57-84.
Thermal Expansion Involving Phase Transitions in Certain Thermoelastic Crystals // Meccanica, Vol. 31, pp. 473-488, 1996.
On the Possibility of Having Different Bravais Lattices Connected Thermodynamically // Mathematics and Mechanics of Solids, Vol. 1, pp. 5-24, 1996.
On the Theory of alpha-beta Phase Transition in Quartz // Journal of Elasticity, Vol. 63, pp. 61-86, 2001.
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