Comment on "Dynamic properties in a family of competitive growing models"

The article [Phys. Rev. E {\bf 73}, 031111 (2006)] by Horowitz and Albano reports on simulations of competitive surface-growth models RD+X that combine random deposition (RD) with another deposition X that occurs with probability $p$. The claim is made that at saturation the surface width $w(p)$ obeys a power-law scaling $w(p) \propto 1/p^{\delta}$, where $\delta$ is only either $\delta =1/2$ or $\delta=1$, which is illustrated by the models where X is ballistic deposition and where X is RD with surface relaxation. Another claim is that in the limit $p \to 0^+$, for any lattice size $L$, the time evolution of $w(t)$ generally obeys the scaling $w(p,t) \propto (L^{\alpha}/p^{\delta}) F(p^{2\delta}t/L^z)$, where $F$ is Family-Vicsek universal scaling function. We show that these claims are incorrect.Comment: 2 pages, 3 figures, accepted for publication in Physical Review E in Aug. 200

Quantum Dot and Hole Formation in Sputter Erosion

Recently it was experimentally demonstrated that sputtering under normal incidence leads to the formation of spatially ordered uniform nanoscale islands or holes. Here we show that these nanostructures have inherently nonlinear origin, first appearing when the nonlinear terms start to dominate the surface dynamics. Depending on the sign of the nonlinear terms, determined by the shape of the collision cascade, the surface can develop regular islands or holes with identical dynamical features, and while the size of these nanostructures is independent of flux and temperature, it can be modified by tuning the ion energy

Quantum Dot and Hole Formation in Sputter Erosion

Recently it was experimentally demonstrated that sputtering under normal incidence leads to the formation of spatially ordered uniform nanoscale islands or holes. Here we show that these nanostructures have inherently nonlinear origin, first appearing when the nonlinear terms start to dominate the surface dynamics. Depending on the sign of the nonlinear terms, determined by the shape of the collision cascade, the surface can develop regular islands or holes with identical dynamical features, and while the size of these nanostructures is independent of flux and temperature, it can be modified by tuning the ion energy

Nanowire formation on sputter eroded surfaces

Rotated ripple structures (RRS) on sputter eroded surfaces are potential candidates for nanoscale wire fabrication. We show that the necessary condition for RRS formation is that the width of the collision cascade in the longitudinal direction has to be larger than that in the transverse direction, which can be achieved by using high energy ion beams. By calculating the structure factor for the RRS we find that they are more regular and their amplitude is more enhanced compared to the much studied ripple structure forming in the linear regime of sputter erosion.Comment: 3 pages, 5 figures, 2 column revtex format, submitted to Appl. Phys. Let

An exact solution for the KPZ equation with flat initial conditions

We provide the first exact calculation of the height distribution at arbitrary time $t$ of the continuum KPZ growth equation in one dimension with flat initial conditions. We use the mapping onto a directed polymer (DP) with one end fixed, one free, and the Bethe Ansatz for the replicated attractive boson model. We obtain the generating function of the moments of the DP partition sum as a Fredholm Pfaffian. Our formula, valid for all times, exhibits convergence of the free energy (i.e. KPZ height) distribution to the GOE Tracy Widom distribution at large time.Comment: 4 pages, no figur

Analysis of the Web Graph Aggregated by Host and Pay-Level Domain

In this paper the web is analyzed as a graph aggregated by host and pay-level domain (PLD). The web graph datasets, publicly available, have been released by the Common Crawl Foundation and are based on a web crawl performed during the period May-June-July 2017. The host graph has $\sim$1.3 billion nodes and $\sim$5.3 billion arcs. The PLD graph has $\sim$91 million nodes and $\sim$1.1 billion arcs. We study the distributions of degree and sizes of strongly/weakly connected components (SCC/WCC) focusing on power laws detection using statistical methods. The statistical plausibility of the power law model is compared with that of several alternative distributions. While there is no evidence of power law tails on host level, they emerge on PLD aggregation for indegree, SCC and WCC size distributions. Finally, we analyze distance-related features by studying the cumulative distributions of the shortest path lengths, and give an estimation of the diameters of the graphs

Stochastic Model in the Kardar-Parisi-Zhang Universality With Minimal Finite Size Effects

We introduce a solid on solid lattice model for growth with conditional evaporation. A measure of finite size effects is obtained by observing the time invariance of distribution of local height fluctuations. The model parameters are chosen so that the change in the distribution in time is minimum. On a one dimensional substrate the results obtained from the model for the roughness exponent $\alpha$ from three different methods are same as predicted for the Kardar-Parisi-Zhang (KPZ) equation. One of the unique feature of the model is that the $\alpha$ as obtained from the structure factor $S(k,t)$ for the one dimensional substrate growth exactly matches with the predicted value of 0.5 within statistical errors. The model can be defined in any dimensions. We have obtained results for this model on a 2 and 3 dimensional substrates.Comment: 8 pages, 7 figures, accepted in Phys. Rev.

Roughening of ion-eroded surfaces

Recent experimental studies focusing on the morphological properties of surfaces eroded by ion-bombardment report the observation of self-affine fractal surfaces, while others provide evidence about the development of a periodic ripple structure. To explain these discrepancies we derive a stochastic growth equation that describes the evolution of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be calculated explicitly in terms of the physical parameters characterizing the sputtering process. Exploring the connection between the ion-sputtering problem and the Kardar-Parisi-Zhang and Kuramoto-Sivashinsky equations, we find that morphological transitions may take place when experimental parameters, such as the angle of incidence of the incoming ions or their average penetration depth, are varied. Furthermore, the discussed methods allow us to calculate analytically the ion-induced surface diffusion coefficient, that can be compared with experiments. Finally, we use numerical simulations of a one dimensional sputtering model to investigate certain aspects of the ripple formation and roughening.Comment: 20 pages, LaTeX, 5 ps figures, contribution to the 4th CTP Workshop on Statistical Physics "Dynamics of Fluctuating Interfaces and Related Phenomena", Seoul National University, Seoul, Korea, January 27-31, 199