1,575 research outputs found
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
. The claim is made that at saturation the surface width obeys a
power-law scaling , where is only either
or , 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 , for any lattice size , the time evolution
of generally obeys the scaling , where 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 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
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 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 as obtained from the structure factor 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
Kauffman Boolean model in undirected scale free networks
We investigate analytically and numerically the critical line in undirected
random Boolean networks with arbitrary degree distributions, including
scale-free topology of connections . We show that in
infinite scale-free networks the transition between frozen and chaotic phase
occurs for . The observation is interesting for two reasons.
First, since most of critical phenomena in scale-free networks reveal their
non-trivial character for , the position of the critical line in
Kauffman model seems to be an important exception from the rule. Second, since
gene regulatory networks are characterized by scale-free topology with
, the observation that in finite-size networks the mentioned
transition moves towards smaller is an argument for Kauffman model as
a good starting point to model real systems. We also explain that the
unattainability of the critical line in numerical simulations of classical
random graphs is due to percolation phenomena
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