Stefan J. Linz

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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(More)
Using an extensive numerical search for the simplest chaotic non-polynomial autonomous three-dimensional dynamical systems, we identify an elementary third-order diffential equation that contains only one control parameter and only one nonlinearity in the form of the modulus of the dynamical variable. We discuss general properties of this equation and the(More)
– 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(More)
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(More)
Granular systems can compact under the influence of sufficiently strong, successive tapping. Recent experimental investigations show that the packing fraction obeys a very slow relaxation to a final, dense packing fraction that is basically proportional to the inverse of the logarithm of the tap number or time. We provide a simple macromechanical argument(More)
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(More)
Lyapunov exponents represent important quantities to characterize the properties of dynamical systems. We show that the Lyapunov exponents of two di€erent dynamical systems that can be converted to each other by a transformation of variables are identical. Moreover, we derive sucient conditions on the transformation for this invariance property to hold. In(More)
A nonlinear stochastic growth equation for the spatiotemporal evolution of the surface morphology of amorphous thin films in the presence of potential density variations is derived from the relevant physical symmetries and compared to recent experimental results. Numerical simulations of the growth equation exhibit a saturation of the surface morphology for(More)