PACS. 68.35Bs -Surface structure and topography. PACS. 61.43Dq -Amorphous alloys.Abstract. -Experimental results on amorphous ZrAlCu thin film growth and the dynamics of the surface morphology as predicted from a minimal nonlinear stochastic deposition equation are analysed and compared. Key points of this study are (i) an estimation procedure for coefficients entering into the growth equation and (ii) a detailed analysis and interpretation of the time evolution of the correlation length and the surface roughness. The results corroborate the usefulness of the deposition equation as a tool for studying amorphous growth processes.Typeset using EURO-L A T E X
A nonlinear stochastic growth equation is derived from (i) the symmetry principles relevant for the growth of vapor deposited amorphous films, (ii) no excess velocity, and (iii) a low-order expansion in the gradients of the surface profile. A growth instability in the equation is attributed to the deflection of the initially perpendicular incident particles due to attractive forces between the surface atoms and the incident particles. The stationary solutions of the deterministic limit of the equation and their stability are analyzed. The growth of the surface roughness and the correlation length of the moundlike surface structure arising from the stochastic growth equation is investigated.
Third-order explicit autonomous differential equations in one scalar variable or, mechanically interpreted, jerky dynamics constitute an interesting subclass of dynamical systems that can exhibit many major features of regular and irregular or chaotic dynamical behavior. In this paper, we investigate the circumstances under which three dimensional autonomous dynamical systems possess at least one equivalent jerky dynamics. In particular, we determine a wide class of three-dimensional vector fields with polynomial and non-polynomial nonlinearities that possess this property. Taking advantage of this general result, we focus on the jerky dynamics of Sprott's minimal chaotic dynamical systems and Rössler's toroidal chaos model. Based on the interrelation between the jerky dynamics of these models, we classify them according to their increasing polynomial complexity. Finally, we also provide a simple criterion that excludes chaotic dynamics for some classes of jerky dynamics and, therefore, also for some classes of three-dimensional dynamical systems.
The phenomenon of effective phase synchronization in stochastic oscillatory systems can be quantified by an average frequency and a phase diffusion coefficient. A different approach to compute the noise-averaged frequency is put forward. The method is based on a threshold crossing rate pioneered by Rice. After the introduction of the Rice frequency for noisy systems we compare this quantifier with those obtained in the context of other phase concepts, such as the natural and the Hilbert phase, respectively. It is demonstrated that the average Rice frequency R typically supersedes the Hilbert frequency H, i.e. R > or = H. We investigate next the Rice frequency for the harmonic and the damped, bistable Kramers oscillator, both without and with external periodic driving. Exact and approximative analytic results are corroborated by numerical simulation results. Our results complement and extend previous findings for the case of noise-driven inertial systems.
We investigate the connection between one-dimensional Newtonian jerky dynamics and nonlinear dynamical systems in a three-dimensional phase space. With exact transformations, we show that the Rössler model, as well as the Lorenz model, can be interpreted as jerky motion and discuss whether they are Newtonian or not. Moreover, Sprott’s model R is identified as one of the simplest Newtonian jerky dynamics that can lead to chaos. Using a wide class of jerk functions, we derive a criterion for being Newtonian jerky.
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