caa a22 4500 467892067 CHVBK 20180406152752.0 cr unu---uuuuu 170328e20060501xx s 000 0 eng 10.1007/s10955-006-9083-1 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9083-1 Nanoscale Spontaneous Patterning [Elektronische Daten] [Z. Feng, Y. Li] 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. Springer Science+Business Media, Inc., 2006 Nanoscale rippling nationallicence SMB equation nationallicence energy principle nationallicence Feng Z. Department of Mechanical and Aerospace Engineering, University of Missouri, 65211, Columbia, MO, USA aut Li Y. Department of Mathematics, University of Missouri, 65211, Columbia, MO, USA aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/4(2006-05-01), 741-751 0022-4715 123:4<741 2006 123 10955 https://doi.org/10.1007/s10955-006-9083-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9083-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Feng Z. Department of Mechanical and Aerospace Engineering, University of Missouri, 65211, Columbia, MO, USA aut NATIONALLICENCE 700 1- Li Y. Department of Mathematics, University of Missouri, 65211, Columbia, MO, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/4(2006-05-01), 741-751 0022-4715 123:4<741 2006 123 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer