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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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From the propagation of phase-transition fronts to the evolution of the growth plate in long bones; pp. 72–78

(Full article in PDF format) doi: 10.3176/proc.2010.2.03


Authors

Gérard A. Maugin

Abstract

The various methodologies exploited in the study of the propagation of phase transition fronts in crystalline substances (inert matter) are examined and compared with a view to identifying mathematical tools useful in a scientific mechanobiological approach to the critical problem of the growth of long bones in mammals.

Keywords

mechanobiology, phase transition, nonlinear waves, solitons, long bones.

References

  1. Maugin , G. A. Multiscale approach to a basic problem of materials mechanics (Propagation of phase-transition fronts). In Multifield Problems: State of the Art (Proc. Int. Conf. Multifield Problems , Stuttgart , Oct. 1999) (Sandig , A. , Schielen , W. , and Wendland , W. L. , eds). Springer , Berlin , 2000 , 11–22.

  2. Carter , D. R. and Beaupré , G. S. Skeleton Function and Form (Mechanobiology of Skeleton Development , Aging , and Regeneration). Cambridge University Press , UK , 2001.

  3. Engelbrecht , J. Nonlinear Wave Dynamics (Complexity and Simplicity). Kluwer , Dordrecht , The Netherlands , 1997.

  4. Maugin , G. A. Nonlinear waves in elastic bodies in strong gravitational fields. In Nonlinear Deformation Waves (Proc. Int. Symp. Tallinn , 1978) (Nigul , U. and Engelbrecht , J. , eds). Publ. Estonian Acad. Sci. , Tallinn , 1978 , Vol. 2 , 123–126.

  5. Falk , F. Ginzburg-Landau theory of static domain walls in shape-memory alloys. Zeit. Phys. C. Cond. Matter , 1983 , 51 , 177–185.
doi:10.1007/BF01308772

  6. Pouget , J. Nonlinear dynamics of lattice models for elastic continua. In NATO Summer School on Physical Properties and Thermodynamical Behavior of Minerals , Oxford , 1988 (Saljé , K. , ed.). Reidel , Dordrecht , 1988 , 359–402.

  7. Maugin , G. A. and Cadet , S. Existence of solitary waves in martensitic alloys. Int. J. Eng. Sci. , 1991 , 29 , 243–255.
doi:10.1016/0020-7225(91)90021-T

  8. Maugin , G. A. and Trimarco , C. The dynamics of configurational forces at phase-transition fronts. Meccanica , 1995 , 30 , 605–619.
doi:10.1007/BF01557088

  9. Maugin , G. A. Thermomechanics of inhomogeneous–heterogeneous systems: application to the irreversible progress of two- and three-dimensional defects. ARI (Springer-Verlag) , 1997 , 50 , 41–56.

10. Maugin , G. A. On shock waves and phase-transition fronts in continua. ARI (Springer-Verlag) , 1998 , 50 , 141–150.

11. Maugin , G. A. Material Inhomogeneities in Elasticity. Chapman and Hall , London , 1993.

12. Truskinovsky , L. M. About the normal growth approximation in the dynamical theory of phase transitions. Cont. Mech. Thermodyn. , 1994 , 6 , 185–208.
doi:10.1007/BF01135253

13. Maugin , G. A. and Christov , C. I. Nonlinear duality between elastic waves and quasi-particles. In Selected Topics in Nonlinear Wave Mechanics (Christov , C. I. and Guran , A. , eds). Birkhäuser , Boston , 2002 , 101–145.

14. Berezovski , A. and Maugin , G. A. Simulation of thermoelastic wave propagation by means of a composite wave-propagation algorithm. J. Comp. Phys. , 2001 , 168 , 249–264.
doi:10.1006/jcph.2001.6697

15. Muschik , W. Aspects of Non-Equilibrium Thermodynamics. World Scientific , Singapore , New York , 1990.

16. Berezovski , A. , Engelbrecht , J. , and Maugin , G. A. Numerical Simulations of Wave and Fronts in Inhomogeneous Solids. World Scientific , Singapore , 2008.
doi:10.1142/9789812832689

17. Sharipova , L. , Maugin , G. A. , and Freidin , A. B. Modelling the influence of mechanical factors on the growth plate. In Abstracts of International Conference on Applied Mathematics: Modeling , Analysis and Computation , June 1–5 , 2008 , City University of Hong Kong , 51–52.

18. Radhakrishnan , P. , Lewis , N. T. , and Mao , J. J. Zone-specific micromechanical properties of the extracellular matrices of growth plate cartilage. Ann. Biomed. Eng. , 2004 , 32 , 284–291.
doi:10.1023/B:ABME.0000012748.41851.b4

19. Epstein , M. and Maugin , G. A. Thermomechanics of volumetric growth in uniform bodies. Int. J. Plasticity , 2000 , 16 , 951–978.
doi:10.1016/S0749-6419(99)00081-9

20. Ambrosi , D. and Guillou , A. Growth and dissipation in biological tissues. Cont. Mech. Thermodyn. , 2007 , 19 , 245–251.
doi:10.1007/s00161-007-0052-y
 
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Current Issue: Vol. 68, Issue 4, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December