Nanoscale Spontaneous Patterning |
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Authors: | Z C Feng Y Charles Li |
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Institution: | (1) Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA;(2) Department of Mathematics, University of Missouri, Columbia, MO 65211, USA |
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Abstract: | The SMB equation describing nanoscale spontaneous patterning is studied both analytically and numerically. In contradiction to the claim in the original SMB paper D. Srolovitz, A. Mazor, B.
Bukiet, J. Vac. Sci. Technol. A6(4) (1988), 2371--2380.] that some steady states are stable, we found that all the steady states are unstable. A dynamical system reason for this is given. We also
found that typical small initial data solutions undergo an exponential growth followed by an almost linear growth. Such a feature is consistent with the experimental data in the paper J. Erlebacher et al., J. Vac. Sci. Technol., A18(1) (2000), 115--120, Figure 3]. On the other hand, we never observed the decay portion of the numerical solution reported in this paper. We invent an elegant energy principle which supports our findings. |
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Keywords: | Nanoscale rippling SMB equation energy principle |
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