Abstract
We consider the model proposed earlier by us for explaining the phenomenon of jumps on creep curves[1]. The model consists of three types of dislocations namely the mobile, the immobile and those with clouds of solute atoms and some transformations between them, leading to a coupled set of nonlinear differential equations for the densities of the dislocations. The model reproduces a large number of experimentally observed features [1,2]. The mathematical mechanism has been shown to be Hopf-bifurcation with respect to several physically relevant drive parameters. The earlier analysis had demonstrated the existence of a pair of complex conjugate slow modes and a fast mode [2]. Here, we present a mathematical analysis of adiabatic elimination of the fast mode and obtaining a Ginzburg-Landau form representation of the order parameter beyond the Hopf bifurcation point upto quintic terms
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References
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© 1994 Springer-Verlag
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Bekele, M., Ananthakrishna, G. (1994). Ginzburg-Landau form description for steps on creep curves. In: Bardhan, K.K., Chakrabarti, B.K., Hansen, A. (eds) Non-Linearity and Breakdown in Soft Condensed Matter. Lecture Notes in Physics, vol 437. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58652-0_38
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DOI: https://doi.org/10.1007/3-540-58652-0_38
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