Level crossing analysis of growing surfaces

Abstract

We investigate the average frequency of positive slope ν + α , crossing the height α = h −h in the surface growing processes. The exact level crossing analysis of the random deposition model and the Kardar-Parisi-Zhang equation in the strong coupling limit before creation of singularities are given. PACS: 52.75.Rx, 68.35.Ct.

Controlling surface statistical properties using bias voltage: Atomic force microscopy and stochastic analysis

“…We have utilized the level crossing analysis in the context of surface growth processes, according to 19,20 . In the level crossing analysis, we are interested in determining the average frequency (in spatial dimension) of observing of the definite value for height function h = α in the thin films grown at different bias voltages, ν + α (λ).…”

Investigation of privatization by level crossing approach

“…It has been demonstrated how the frequency parameter ν + α is deduced from the underlying probability distributions for r(t) −r [30]. In the time interval ∆t each level can cross r(t) −r = α with a positive difference, only if it has the property that, r(t) −r < α at the beginning of the time interval.…”

“…In the time interval ∆t each level can cross r(t) −r = α with a positive difference, only if it has the property that, r(t) −r < α at the beginning of the time interval. Furthermore, there is a minimum difference at time t, if the level r(t) −r = α is to be crossed in the interval ∆t, depending on the value of r(t) −r at time t. So, there will be a positive crossing of r(t) −r = α in the next time interval ∆t if, at time t [30],…”

Investigating aluminum thin films properties by stochastic analysis

“…holds for any value of x 2 in the interval x 1 < x 2 < x 3 [15]. One should check the validity of the C-K equation for any x 1 by comparing the directly evaluated conditional probability distributions P(x 3 , h 3 |x 1 , h 1 ) with the ones calculated according to the right side of Eqn (1).…”

“…[1−3] , we can characterize many natural phenomena and processes by a degree of stochasticity. Seismic recordings, analysis of human interbeat, [4−6] turbulent flows, [7−9] cosmic background radiation, [10,11] stock market, [12,13] earthquakes, [14] and the surface roughness during growing of many materials [15] are examples of such phenomena and processes. In the last decades, exploring the morphology of rough surfaces during growth process has been one of the interesting fields of study, because surface roughness has an enormous influence on many important physical phenomena.…”