Spatially nonlocal model of surface erosion by ion bombardment

Rudy, Alexander; Бачурин, В. И.

doi:10.3103/s1062873808050043

Cited by 6 publications

(2 citation statements)

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“…Indeed, in numerous cases, the Bradley-Harper equation can be reduced to the Kuramoto-Sivashinsky equation, which is widely known as a mathematical model for a series of problems of chemical kinetics and hydrodynamics. In the present paper, we consider the equation introduced in [5] for a more precise description of some aspects of the formation of inhomogeneous surface topographies. It was repeatedly emphasized that the Bradley-Harper equation cannot be used for the description of perturbations of the order of nanometers ( ⇠ 10 9 m).…”

Section: Introductionmentioning

confidence: 99%

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Spatially Inhomogeneous Dissipative Structures in a Periodic Boundary-value Problem for a Nonlocal Erosion Equation

Kulikov

2015

J Math Sci

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We consider a nonlinear partial differential equation with deviating (transformed) space variable. This equation serves as a mathematical model of formation of the surface patterns on a plate as a result of ionic bombardment. We study a periodic boundary-value problem and propose a mechanism of formation of ripple nanopatterns due to the loss of stability of the flat surface topography. The ripple topography is found as the solution of bifurcation problems studied by using the theory of normal forms and the method of invariant manifolds. For the solutions that describe ripple nanopatterns, we give asymptotic formulas.

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Section: Introductionmentioning

confidence: 99%

“…It was repeatedly emphasized that the Bradley-Harper equation cannot be used for the description of perturbations of the order of nanometers ( ⇠ 10 9 m). The present paper is devoted to the investigation of a boundary-value problem for an alternative model, which is called a nonlocal erosion equation [5][6][7].…”

Section: Introductionmentioning

confidence: 99%