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Article overview
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Statistics of zero crossings in rough interfaces with fractional elasticity | Arturo L. Zamorategui
; Vivien Lecomte
; Alejandro B. Kolton
; | Date: |
20 Oct 2017 | Abstract: | We study numerically the distribution of zero crossings in one-dimensional
elastic interfaces described by an overdamped Langevin dynamics with periodic
boundary conditions. We model the %restoring elastic forces with a Riesz-Feller
fractional Laplacian of order $z = 1 + 2zeta$, such that the interfaces
spontaneously relax, with a dynamical exponent $z$, to a self-affine geometry
with roughness exponent $zeta$. By continuously increasing from $zeta=-1/2$
(macroscopically flat interface described by independent Ornstein--Uhlenbeck
processes) to $zeta=3/2$ (super-rough Mullins--Herring interface), three
different regimes are identified: (I) $-1/2<zeta<0$, (II) $0<zeta<1$, and
(III) $1<zeta<3/2$. Starting from a flat initial condition, the mean number of
zeros of the discretized interface (I) decays exponentially in time and reaches
an extensive value in the system size, or decays as a power-law towards (II) a
sub-extensive or (III) an intensive value. In the steady-state, the
distribution of intervals between zeros changes from an exponential decay in
(I) to a power-law decay $P(ell) sim ell^{-gamma}$ in (II) and (III). While
in (II) $gamma=1- heta$ with $ heta=1-zeta$ the steady-state persistence
exponent, in (III) we obtain $gamma = 3-2zeta$, different from the exponent
$gamma=1$ expected from the prediction $ heta=0$ for infinite super-rough
interfaces with $zeta>1$. The effect on $P(ell)$ of short-scale smoothening
is also analyzed numerically and analytically. A tight relation between the
mean interval, the mean width of the interface and the density of zeros is also
reported. The results drawn from our analysis of rough interfaces subject to
particular boundary conditions or constraints, along with discretization
effects, are relevant for the practical analysis of zeros in interface imaging
experiments or in numerical analysis. | Source: | arXiv, 1710.7671 | Services: | Forum | Review | PDF | Favorites |
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