Multiple Bifurcation Types and the Linear Dynamics of Ion Sputtered Surfaces

Molecular dynamics of single-particle impacts predicts phase diagrams for large scale pattern formation

“…Hence, it is important to be able to predict the expected behaviour within a given environment. Unfortunately, precisely which physical effects cause observed transitions between different regimes 9,10 has remained a matter of speculation 11 .…”

Linear dynamics of ion sputtered surfaces: instability, stability and bifurcations

“…stability to perpendicular modes) at some intervals of the slope b, unlike the case for response functions discussed in the previous section [35]. In particular, one can find parameter regimes where β < β * (thus the yield curve retains its characteristic shape) and S [14] and [27]. This result demonstrates a very significant conclusion: small changes in the shape of the surface response of a single ion can completely change the stability characteristics of a flat surface from BH predictions, but yet lead to an experimentally indistinguishable sputter yield curve.…”

“…Therefore, it is impossible to confirm or rule out their existence from sputter yield measurements. Second, although surface currents cannot be represented by local response of the form (3) or (6) Although this mechanism could be related to the observation of flat surfaces in experiments [26], stability of flat surfaces at a range of intermediate beam angles, reported in [14] and [27] seems to imply other mechanisms not included in this approach, such as response functions that are not everywhere erosive (discussed in the beginning of this section) and possibly other processes as described in the following sections.…”

“…While it is hard to draw general conclusions from few existing results, there is a substantial evidence that at least some bifurcation points in the dynamics of ion-sputtered surfaces are characterized by finite rather than diverging wavelength [27][28][29].…”

“…exponential growth and temperature dependence of pattern amplitude [25]) a growing number of experimental observations [14,[26][27][28][29] show that, although they can potentially explain some of these observations, such theories do not suffice to explain all deviations from the BH predictions in the linear regime. In Section IV we explain why experimental observations imply terms that must be added to the BH equations, and point out two examples of these terms containing linear integral operators, hinting on the nonlocal nature of the physical mechanisms that they represent.…”