Stochastic effects at ripple formation processes in anisotropic systems with multiplicative noise

Abstract

We study pattern formation processes in anisotropic system governed by the Kuramoto-Sivashinsky equation with multiplicative noise as a generalization of the Bradley-Harper model for ripple formation induced by ion bombardment. For both linear and nonlinear systems we study noise-induced effects at ripple formation and discuss scaling behavior of the surface growth and roughness characteristics. It was found that the secondary parameters of the ion beam (beam profile and variations of an incidence angle) can crucially change the topology of patterns and the corresponding dynamics.

Statistical properties of nanosized clusters on a surface in overdamped stochastic reaction-Cattaneo systems

“…In other words it is responsible for processes realized at low hierarchical level. This approach was well exploited to study pattern selection processes in one-component crystalline systems subjected to particle irradiation [33] and binary systems undergoing phase decomposition [34][35][36]. If we take the memory kernel in an decaying exponential form, then instead of the ordinary model of reaction-diffusion system with f ≠ 0 we obtain a generalized model incorporating time derivative of the second order, i.e., τ J ∂ tt…”

Modeling microstructure evolution of binary systems subjected to irradiation and mechanical loading

“…This model was exploited to study phase decomposition and patterning processes under irradiation (see [8,9,[33][34][35][36][37]). It is known that a generation of point defects due to irradiation produces structural disorder and results in emergence of uncompensated deformation fields.…”

“…This model of the ballistic mixing was proposed in Ref. [32] and effectively used to study pattern formation in crystalline one-component systems and phase separation processes in binary systems under sustained irradiation [8,9,[33][34][35][36][37]. In our study we consider two cases of constant rate mechanical loading: (i) shear strain and (ii) cyclic loading.…”

“…A particle irradiation producing structural disorder and point defects rearrangement leads to hardening, swelling and embrittlement of materials. Understanding microstructure evolution and mechanisms governing rearrangement of defects generated at irradiation remains an actual problem in modern material science and, generally, in physics of nonequilibrium phenomena [2][3][4][5][6][7][8][9].…”

Formation of Nanosize Structures of Adsorbate in Processes of Condensation of a Gas Phase with Due Regard for Temperature Effects

“…Використовуючи різні методи для осадження, можна ефективно залучати різні механізми вирощування нанороз-мірного острова (адсорбція/десорбція, дифузія, взаємодія адато-мів), що веде до утворення різних типів поверхневих структур: пе-ріодичного розташування вакансійних структур [5], витягнутих островів адсорбату в напівпровідниках Ge/Si і Si/Si [6,7] і металах Cu/Pd, Ag/Cu [8,9]. Упродовж останніх десятиліть рівновісні та видовжені нанорозмірні структури спостерігалися в реальних екс-периментах та при числовому моделюванні при осадженні з газової фази та з використанням електронного пучка [10][11][12][13], йонно-променевому розпорошенні [14][15][16][17][18][19], імпульсному лазерному опро-міненні [20][21][22], молекулярно-променевій епітаксії [23][24][25][26][27][28][29].…”