Geodesic
Nonlocal model for the formation of ripple topography induced by ion bombardment. Nonhomogeneous nanostructures
Matematičeskoe modelirovanie, Tome 28 (2016) no. 3, pp. 33-50.

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А mathematical model for the formation of a non-homogeneous thopography on the surface under ionic bombardment is considered. The principal part of this model is any nonlinear functional-differential equation. The possibility of ripple topography formation is demonstrated by means of the bifurcation theory. Asymptotic formulas for the nanostructures are obtained. In particular, it was shown that the set of these solutions forms the local attractor. But all solutions belonging to this attractor are unstable in the sense of Lyapunov definition.
Keywords: nonlocal model of erosion, ionic bombardment, boundary value problems, stability, attractor.
Mots-clés : bifurcations 
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A. N. Kulikov; D. A. Kulikov. Nonlocal model for the formation of ripple topography induced by ion bombardment. Nonhomogeneous nanostructures. Matematičeskoe modelirovanie, Tome 28 (2016) no. 3, pp. 33-50. http://geodesic.mathdoc.fr/item/MM_2016_28_3_a2/

[1] A. S. Rudy, V. I. Bachurin, “Spatially nonlocal model of surface erosion by ion bombardment”, Bulletin of the Russian Academy of Sciences Physics, 72:5 (2008), 586–591 | DOI

[2] A. S. Rudyi, A. N. Kulikov, D. A. Kulikov, A. V. Metlitskaya, “High-mode wave relief in a spatially nonlocal erosion model”, Russian Microelectronics, 43:4 (2014), 277–283 | DOI | DOI

[3] A. S. Rudyi, A. N. Kulikov, A. V. Metlitskaya, “Simulation of formation of nanostructures during sputtering of the surface by ion bombardment”, Russian Microelectronics, 40:2 (2011), 98–108 | DOI

[4] D. A. Kulikov, “Neodnorodnye dissipativnye structury v zadache o formirovanii nanorelefa”, Dinamicheskie sistemy, 2(30):3–4 (2012), 259–272

[5] D. A. Kulikov, A. S. Rudyi, “Formirovanie volnovogo nanorelefa pri raspylenii poverhnosti ionnoy bombardirovkoy”, Modelir. i analiz inform. system, 19:5 (2012), 82–91 | Zbl

[6] D. A. Kulikov, “Spatially ingomogeneous dissipative structures in a periodic boundaryvalue problem for a nonlocal erosion equation”, Journal of Mathematical Sciences, 205:6 (2015), 791–805 | DOI | MR | Zbl

[7] P. Sigmund, “Theory of sputtering yield of amorphous and polycrystalline targets”, Phys. Rev., 184:2 (1969), 383–416 | DOI

[8] R. M. Bradley, J. M. E. Harper, “Theory of ripple topography induced by ion bombardment”, J. Vac. Sci. Technol. A, 6 (1988), 2390–2395 | DOI

[9] S. G. Krein, Lineinye differentsialnye uravnenia v banakhovom prostranstve, Nauka, M., 1967, 464 pp.

[10] P. E. Sobolevskiy, “Ob uravneniach parabolicheskogo tipa v banachovom prostranstve”, Trudy Mosk. matem. ob-va, 10, 1961, 297–350 | MR | Zbl

[11] J. E. Marsden, M. McCraken, The Hopf bifurcation and its applications, Springer-Verlag, New York–Heidelberg–Berlin, 1976, 408 pp. | MR | Zbl

[12] A. N. Kulikov, “O gladkikh invariantnykh mnogoobraziyach nelineynich operatorov v banachovom prostranstve”, Issledovanie po ustoychivosti i teorii kolebaniy, Isd-vo IarGU, 1976, 114–129

[13] A. N. Kulikov, “Inertsialnye mnogoobrasia nelineinych avtonomnych differentsialnych uravneniy v gilbertovom prostranstve”, Keldysh Institute preprints, 1991, 085, 22 pp.

[14] A. N. Kulikov, D. A. Kulikov, “Formation of wavy nanostructures on the surface of flat substrates by ion bombardment”, Comp. Math. and Math. Physics, 52:5 (2012), 800–814 | DOI | MR | Zbl

[15] G. Iooss, D. D. Joseph, Elementary stability and bifurcation theory, Springer-Verlag, New York–Heidelberg–Berlin, 2014, 304 pp. | MR

[16] J. Guckenheimer, P. Holmes, Nonlinear oscillations, dynamical systems and bifurcations of vector fields, Springer-Verlag, New York–Heidelberg–Berlin, 1983, 462 pp. | MR | Zbl

[17] D. A. Kulikov, “Mechanism formirovania volnovych dissipativnych structur v odnoi is zadach nanotechnologiy”, Vestnik RAEN, 13:4 (2013), 23–31 | MR

[18] N. A. Kudriashov, P. N. Ryabov, M. N. Strichanov, “Chislennoe modelirovanie formirovania nanostructur na poverchnosti ploskich podlozhek pri ionnoi bombardirovke”, Iadernaia fizika i inginiring, 1:2 (2010), 151–158

[19] N. A. Kudriashov, P. N. Ryabov, T. E. Fedianin, “Osobennosti samoorganizatsii nanostructur na poverchnosti poluprovodnikov pri ionnoi bombardirovke”, Matem. model., 24:12 (2012), 23–28 | Zbl

[20] A. N. Kulikov, D. A. Kulikov, “Bifurkatsii prostranstvenno neodnorodnych resheniy v dvuch kraevyich zadachakh dlya obobshchennogo uravnenia Kuramoto–Sivashinskogo”, Vestnik MIFI, 3:4 (2014), 408–415 | DOI | Zbl