Related papers: Level Crossing Analysis of Growing surfaces
We studied scaling in kinetic roughening and phase ordering during growth of binary systems using 1+1 dimensional single-step solid-on-solid model with two components interacting via Ising-like interaction with the strength K. We found that…
We consider level crossing in a matrix family $H=H_0+\lambda V$ where $H_0$ is a fixed $N\times N$ matrix and $V$ belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing…
Let $X_1$, $X_2$, $...$ be a sequence of independently and identically distributed random variables with $\mathsf{E}X_1=0$, and let $S_0=0$ and $S_t=S_{t-1}+X_t$, $t=1,2,...$, be a random walk. Denote $\tau={cases}\inf\{t>1: S_t\leq0\},…
The level crossing and inverse statistics analysis of DAX and oil price time series are given. We determine the average frequency of positive-slope crossings, $\nu_{\alpha}^+$, where $T_{\alpha} =1/\nu_{\alpha}^+ $ is the average waiting…
The Kardar-Parisi-Zhang (KPZ) equation is accepted as a generic description of interfacial growth. In several recent studies, however, values of the roughness exponent alpha have been reported that are significantly less than that…
The scaling behavior of cyclical growth (e.g. cycles of alternating deposition and desorption primary processes) is investigated theoretically and probed experimentally. The scaling approach to kinetic roughening is generalized to cyclical…
We develop a phenomenological mapping between submonolayer polynuclear growth (PNG) and the interface dynamics at and below the depinning transition in the Kardar-Parisi-Zhang equation for a negative non-linearity \lambda. This is possible…
The effect of etching time on the statistical properties of the hydrophilic surface of SiO_2/TiO_2/Glass nano bi-layer has been studied using Atomic Force Microscopy (AFM) and stochastic approach based on the level crossing analysis. We…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…
We investigate analytically the large dimensional behavior of the Kardar-Parisi-Zhang (KPZ) dynamics of surface growth using a recently proposed non-perturbative renormalization for self-affine surface dynamics. Within this framework, we…
For a random polynomial with standard normal coefficients, two cases of the K-level crossings have been considered by Farahmand. When the coefficients are independent, Farahmand was able to derive an asymptotic value for the expected number…
In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the Fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that…
We study crossing numbers for systoles of congruence surfaces. Taken as a family of curves on a family of surfaces, we show that the growth rate of their intersection is optimally small among all sets of curves of the same cardinality lying…
We study the short-time behavior of the probability distribution $\mathcal{P}(H,t)$ of the surface height $h(x=0,t)=H$ in the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimension. The process starts from a stationary interface: $h(x,t=0)$…
We consider the particle current in the asymmetric avalanche process on a ring. It is known to exhibit a transition from the intermittent to continuous flow at the critical density of particles. The exact expressions for the first two…
Using renormalized field theory, we examine the dynamics of a growing surface, driven by an obliquely incident particle beam. Its projection on the reference (substrate) plane selects a ``parallel'' direction, so that the evolution equation…
We consider a piecewise-deterministic Markov process governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the conditional distribution of jump sizes. We study…
In this communication we introduce a pair of coupled continuum equations to model overlayer growth with evaporation-accretion due to thermal or mechanical agitations of the substrate. We gain insight into the dynamics of growth via one-loop…
Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…
A growth model which describes the deposition of particles (or the growth of a rigid crystal) on a disordered substrate is investigated. The dynamic renormalization group is applied to the stochastic growth equation using the Martin, Sigga,…