• G Ananthakrishna

      Articles written in Bulletin of Materials Science

    • Repeated yield drop phenomena as a cooperative effect

      G Ananthakrishna

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      We present a theoretical model of repeated yielding (ry) which reproduces many experimentally observed features, apart from showing how the temporal behaviour of the phenomenon emerges as a consequence of the cooperative behaviour of defects. We first consider the case of step-like creep curves. Our model leads to a coupled set of nonlinear differential equations which admit limit cycle solutions, and thence jumps on the creep curve. Approximate closed form solutions for the limit cycles and the steps on the creep curve are obtained. The model is then extended to the constant strain rate experiment by including the machine equation. The temporal ordering ofry is shown to follow, as well as several other features characteristic ofry. Chaotic flow is also exhibited: the model has a sequence of period-doubling bifurcations with an exponent equal to that of the quadratic map. Finally, we have analysed the fluctuations during the onset ofry using nonlinear Langevin equations. Fluctuations in the periodic (ry) phase are also investigated. We conclude thatry is another example of a dissipative structure.

    • Random walk on a fibonacci chain

      G Ananthakrishna T Balasubramanian

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      Random walk on a Fibonacci chain is studied both numerically and analytically. We demonstrate that the long-time behaviour is diffusive.

    • Formation and propagation of bands in jerky flow: a coupled lattice map description

      G Ananthakrishna

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      There has been revival of interest in Jerky flow from the point of view of dynamical systems. The earliest attempt in this direction was from our group. One of the predictions of the theory is that Jerky flow could be chaotic. This has been recently verified by us. We have recently extended the earlier model to account for the spatial aspect as well. Both these models are in the form of coupled set of nonlinear differential equations and hence, they are complicated in their structure. For this reason we wish to devise a model based on the results of these two theories in the form of coupled lattice map for the description of the formation and propagation of dislocation bands. We report here one such model and its results.

    • Monte Carlo simulation of nucleation and growth of thin films

      J Goswami G Ananthakrishna S A Shivashankar

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      We study thin film growth using a lattice-gas, solid-on-solid model employing the Monte Carlo technique. The model is applied to chemical vapour deposition (CVD) by including the rate of arrival of the precursor molecules and their dissociation. We include several types of migration energies including the edge migration energy which allows the diffusive movement of the monomer along the interface of the growing film, as well as a migration energy which allows for motion transverse to the interface. Several well-known features of thin film growth are mimicked by this model, including some features of thin copper films growth by CVD. Other features reproduced are—compact clusters, fractal-like clusters, Frank-van der Merwe layer-by-layer growth and Volmer-Weber island growth. This method is applicable to film growth both by CVD and by physical vapour deposition (PVD).

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