Fields of Interest:

• Mathematical theory of defects

• G-structures, frame bundles, theory of connections

• Hyperbolic waves, shock waves in non-linear elasticity

• Cavitations in non-linear elasticity

• Thermodynamics

Books, Notes:

• (with M. Epstein) Material Inhomogeneities and Their Evolution, A Geometric Approach, Springer-Verlag, 2007, http://www.springer.com/978-3-540-72372-1

· Mathematical Theory of Uniform Elastic Structures, Kielce University of Technology Press, Kielce, 1995. (PDF)

· An Introduction to Applied Partial Differential Equations (draft). (PDF)

Selected Research Articles:

1. (with S. Preston) Material Uniformity and the Concept of the Stress Space, in: Continuous Media with Microstructure, ed. B. Alberts, Springer-Verlag (2010) 91-101. (PDF), http://www.springer.com/engineering/book/978-3-642-11444-1

2. (with S. Preston) A Model of the Self-Driven Evolution of a Defective Continuum, Mathematics and Mechanics of Solids, 12 (2007) 450-465. (PDF)

3. (with G. P. Parry)  Material Symmetry in a Theory of Continuously Defective Crystals, Journal of Elasticity, 74 (2004) 215-237. (PDF)

4. (with M. Epstein )  A Model of the Evolution of a Two-dimensional Defective Structure, Journal of Elasticity, 70 (2003) 255-265. (PDF)

5. (with E. Binz) Another Look at the Evolution of Material Structures, Mathematics and Mechanics of Solids, 7(2) (2002) 203-214. (PDF)

6. About Non-Spherically Symmetric Deformations of an Incompressible Neo-Hookean Sphere, in: Contributions to Continuum Theories (Anniversary Volume for Krzysztof Wilmanski) WIAS, (2000) 68-72 .  (PDF)

7. (with S. Preston) On Non-Holonomic Second Order Connections, with Applications to Continua with Microstructure, Extracta Mathematicae 11(1) (1996) 51-58. (PDF)

8. (with S. Prishepionok)   Connections on Higher Order Frame Bundles in: New Developments in Differential Geometry, eds. L.Tamassy  and J.Szenthe, Kluwer Acad. Publishers (1996) 131- 142.  (PDF)

9. (with S. Prishepionok)  Higher Grade Material Structures, Proceedings of the IUTAM & ISIMM Symposium on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics, University of Nottingham, August/September 1994, Kluwer (1995) 63-68.

10. Some New Ideas in the Theory of Continuous Distributions of Defects, in: Characterization of Mechanical Properties of Materials, eds. W.-Y. Lu, C.-S. Man, ASME-MD, 33 (1992) 75-82.

11. (with S. Prishepionok) Locally Homogeneous Configurations of Uniform Elastic Bodies, Reports on Mathematical Physics 31(3), (1992) 229-240.

12. (with M. Epstein) The Symmetry Group of Second Grade Materials, International J. Non- linear Mechanics, 27(4), (1992) 635-638.

13. (with M. Epstein) The Interplay of Uniformity and Constrained Elasticity, Stability and Applied Analysis of Continuous Media, 1, (1991) 95-107.

14. (with M. Epstein and J.  Sniatycki) G-structures and  Material Homogeneity, Journal of Elasticity, 23(2-3), (1990) 167-180.

15. (with M. Epstein) The Decay and Formation of One-Dimensional Nonconservative Shocks, Applied Mathematical Modelling 12(3), (1988), 280-284.

16. (with M. Epstein) Attenuation of Shocks by Viscoelastic Support, ASCE Journal of Engineering Mechanics, 112(6), (1986), 587-592.

17. (with M. Epstein) Decay of Strong Shocks in Nonlinear Elasticity, Journal of Sound and Vibration, 103(3), (1985), 371-378.

18. (with M. Epstein), Geometric Characterization of Hyperelastic Uniformity, Archive for Rational Mechanics and Analysis, 88, (1985), 347-357.

19. Thermodynamic Stability of Continuous Body, Journal of Mathematical Analysis and Applications 108(2), (1985), 303-315

20. On the Necessary Conditions for Stability in Thermodynamics, Bull.Acad.Polon.Sci. (Ser.Sci.Techn.) 28, (1980), 77-83.

 April 24, 2010