ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
Proceeding cover
proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2022): 0.9
From the propagation of phase-transition fronts to the evolution of the growth plate in long bones; pp. 72–78
PDF | doi: 10.3176/proc.2010.2.03

Author
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.
References

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

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  7. Maugin, G. A. and Cadet, S. Existence of solitary waves in martensitic alloys. Int. J. Eng. Sci., 1991, 29, 243–255.
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  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.

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

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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.

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doi:10.1016/S0749-6419(99)00081-9

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doi:10.1007/s00161-007-0052-y
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