Comment on "Dynamic Scaling of Non-Euclidean Interfaces" [arXiv:0804.1898]

This is the revised version of a Comment on a paper by C. Escudero (Phys. Rev. Lett. 100, 116101, 2008; arXiv:0804.1898)

Anti-Coarsening and Complex Dynamics of Step Bunches on Vicinal Surfaces during Sublimation

A sublimating vicinal crystal surface can undergo a step bunching instability when the attachment-detachment kinetics is asymmetric, in the sense of a normal Ehrlich-Schwoebel effect. Here we investigate this instability in a model that takes into account the subtle interplay between sublimation and step-step interactions, which breaks the volume-conserving character of the dynamics assumed in previous work. On the basis of a systematically derived continuum equation for the surface profile, we argue that the non-conservative terms pose a limitation on the size of emerging step bunches. This conclusion is supported by extensive simulations of the discrete step dynamics, which show breakup of large bunches into smaller ones as well as arrested coarsening and periodic oscillations between states with different numbers of bunches.Comment: 26 pages, 11 figure

Dynamic phase transitions in electromigration-induced step bunching

Electromigration-induced step bunching in the presence of sublimation or deposition is studied theoretically in the attachment-limited regime. We predict a phase transition as a function of the relative strength of kinetic asymmetry and step drift. For weak asymmetry the number of steps between bunches grows logarithmically with bunch size, whereas for strong asymmetry at most a single step crosses between two bunches. In the latter phase the emission and absorption of steps is a collective process which sets in only above a critical bunch size and/or step interaction strength.Comment: 4 pages, 4 figure

Persistence of Kardar-Parisi-Zhang Interfaces

The probabilities $P_\pm(t_0,t)$ that a growing Kardar-Parisi-Zhang interface remains above or below the mean height in the time interval $(t_0, t)$ are shown numerically to decay as $P_\pm \sim (t_0/t)^{\theta_\pm}$ with $\theta_+ = 1.18 \pm 0.08$ and $\theta_- = 1.64 \pm 0.08$. Bounds on $\theta_\pm$ are derived from the height autocorrelation function under the assumption of Gaussian statistics. The autocorrelation exponent $\bar \lambda$ for a $d$--dimensional interface with roughness and dynamic exponents $\beta$ and $z$ is conjectured to be $\bar \lambda = \beta + d/z$. For a recently proposed discretization of the KPZ equation we find oscillatory persistence probabilities, indicating hidden temporal correlations.Comment: 4 pages, 3 figures, uses revtex and psfi

Kinetics of step bunching during growth: A minimal model

We study a minimal stochastic model of step bunching during growth on a one-dimensional vicinal surface. The formation of bunches is controlled by the preferential attachment of atoms to descending steps (inverse Ehrlich-Schwoebel effect) and the ratio $d$ of the attachment rate to the terrace diffusion coefficient. For generic parameters ($d > 0$) the model exhibits a very slow crossover to a nontrivial asymptotic coarsening exponent $\beta \simeq 0.38$. In the limit of infinitely fast terrace diffusion ($d=0$) linear coarsening ($\beta$ = 1) is observed instead. The different coarsening behaviors are related to the fact that bunches attain a finite speed in the limit of large size when $d=0$, whereas the speed vanishes with increasing size when $d > 0$. For $d=0$ an analytic description of the speed and profile of stationary bunches is developed.Comment: 8 pages, 10 figure

Scaling properties of step bunches induced by sublimation and related mechanisms: A unified perspective

This work provides a ground for a quantitative interpretation of experiments on step bunching during sublimation of crystals with a pronounced Ehrlich-Schwoebel (ES) barrier in the regime of weak desorption. A strong step bunching instability takes place when the kinetic length is larger than the average distance between the steps on the vicinal surface. In the opposite limit the instability is weak and step bunching can occur only when the magnitude of step-step repulsion is small. The central result are power law relations of the between the width, the height, and the minimum interstep distance of a bunch. These relations are obtained from a continuum evolution equation for the surface profile, which is derived from the discrete step dynamical equations for. The analysis of the continuum equation reveals the existence of two types of stationary bunch profiles with different scaling properties. Through a mathematical equivalence on the level of the discrete step equations as well as on the continuum level, our results carry over to the problems of step bunching induced by growth with a strong inverse ES effect, and by electromigration in the attachment/detachment limited regime. Thus our work provides support for the existence of universality classes of step bunching instabilities [A. Pimpinelli et al., Phys. Rev. Lett. 88, 206103 (2002)], but some aspects of the universality scenario need to be revised.Comment: 21 pages, 8 figure

Breakdown of step-flow growth in unstable homoepitaxy

Two mechanisms for the breakdown of step flow growth, in the sense of the appearance of steps of opposite sign to the original vicinality, are studied by kinetic Monte Carlo simulations and scaling arguments. The first mechanism is the nucleation of islands on the terraces, which leads to mound formation if interlayer transport is sufficiently inhibited. The second mechanism is the formation of vacancy islands due to the self-crossing of strongly meandering steps. The competing roles of the growth of the meander amplitude and the synchronization of the meander phase are emphasized. The distance between vacancy islands along the step direction appears to be proportional to the square of the meander wavelengthComment: 7 pages, 9 figure

Entrepreneurship by Alliance

Recent years have seen the introduction of markets and a system of private property rights in China with a view to changing the composition of production and demand and enhancing welfare. Central to the success of these reforms is the rise of entrepreneurship with its potential to set the economy on a higher growth path by supplying the products which consumers need and want, creating new employment opportunities, and introducing new and more efficient technologies of production. But to what extent can we expect to see entrepreneurs in China behaving like their counterparts in the advanced industrial economies of Western Europe, Japan, and the United States? This is the question we address in this chapter. In our view, the reform programme has, indeed, opened up new opportunities for private enterprise activity; but idiosyncrasies of the business environment are at the same time generating novel institutional arrangements in support of entrepreneurs' investments. We agree, therefore, with Herrick and Kindleberger when they assert that "Development ought not to be viewed as a monotonic, stylized path, ever onward and upward, historically established and invariably repeated" (1983, p.62).entrepreneurship;economic growth;economic development;business networking;Western economies