Scaling behavior of the time-fractional equations for molecular-beam epitaxy growth: scaling analysis versus numerical stimulations |
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| Authors: | H Xia G Tang K Han D Hao and Z Xun |
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| Institution: | (1) Department of Land, Air and Water Resources, University of California, Davis, CA 95616, USA;(2) School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW, 2052, Australia |
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| Abstract: | The scaling behavior of the time-fractional molecular-beam epitaxy (TFMBE) equations in 1+1 dimensions is investigated by
numerical simulations and scaling analysis, respectively. The growth equations studied include the time-fractional linear
molecular-beam epitaxy (TFLMBE) and the time-fractional Lai-Das Sarma-Villain (TFLDV). Growth exponents are obtained using
the two methods. The analytical results are consistent with the corresponding numerical solutions based on Caputo-type fractional
derivative. |
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