arXiv subjects

Attilio L. Stella

Publications and source records attributed to Attilio L. Stella.

40 records · Page 3Linked to original sources

arXiv1998

Boundary effects in a random neighbor model of earthquakes

We introduce spatial inhomogeneities (boundaries) in a random neighbor version of the Olami, Feder and Christensen model [Phys. Rev. Lett. 68, 1244 (1992)] and study the distributions of avalanches starting both from the bulk and from the boundaries of the system. Because of their clear geophysical interpretation, two different boundary conditions have been considered (named free and open, respectively). In both cases the bulk distribution is described by the exponent $τ\simeq {3/2}$. Boundary distributions are instead characterized by two different exponents $τ' \simeq {3/2}$ and $τ' \simeq {7/4}$, for free and open boundary conditions, respectively. These exponents indicate that the mean-field behavior of this model is correctly described by a recently proposed inhomogeneous form of critical branching process.

cond-mat.stat-mech↗

arXiv1997

Branching Transition of a Directed Polymer in Random Medium

A directed polymer is allowed to branch, with configurations determined by global energy optimization and disorder. A finite size scaling analysis in 2D shows that, if disorder makes branching more and more favorable, a critical transition occurs from the linear scaling regime first studied by Huse and Henley [Phys. Rev. Lett. 54, 2708 (1985)] to a fully branched, compact one. At criticality clear evidence is obtained that the polymer branches at all scales with dimension ${\bar d}_c$ and roughness exponent $ζ_c$ satisfying $({\bar d}_c-1)/ζ_c = 0.13\pm 0.01$, and energy fluctuation exponent $ω_c=0.26 \pm0.02$, in terms of longitudinal distance

cond-mat.stat-mech↗

arXiv1995

Branching Interfaces with Infinitely Strong Couplings

A hierarchical froth model of the interface of a random $q$-state Potts ferromagnet in $2D$ is studied by recursive methods. A fraction $p$ of the nearest neighbour bonds is made inaccessible to domain walls by infinitely strong ferromagnetic couplings. Energetic and geometric scaling properties of the interface are controlled by zero temperature fixed distributions. For $p<p_c$, the directed percolation threshold, the interface behaves as for $p=0$, and scaling supports random Ising ($q=2$) critical behavior for all $q$'s. At $ p=p_c$ three regimes are obtained for different ratios of ferro vs. antiferromagnetic couplings. With rates above a threshold value the interface is linear ( fractal dimension $d_f=1$) and its energy fluctuations, $ΔE$ scale with length as $ΔE\propto L^ω$, with $ω\simeq 0.48$. When the threshold is reached the interface branches at all scales and is fractal ($d_f\simeq 1.046$) with $ω_c \simeq 0.51$. Thus, at $p_c$, dilution modifies both low temperature interfacial properties and critical scaling. Below threshold the interface becomes a probe of the backbone geometry ($\df\simeq{\bar d}\simeq 1.305$; $\bar d$ = backbone fractal dimension ), which even controls energy fluctuations ($ω\simeq d_f\simeq\bar d$). Numerical determinations of directed percolation exponents on diamond hierarchical lattice are also presented.

cond-mat↗

arXiv1994

The Unusual Universality of Branching Interfaces in Random Media

We study the criticality of a Potts interface by introducing a {\it froth} model which, unlike its SOS Ising counterpart, incorporates bubbles of different phases. The interface is fractal at the phase transition of a pure system. However, a position space approximation suggests that the probability of loop formation vanishes marginally at a transition dominated by {\it strong random bond disorder}. This implies a linear critical interface, and provides a mechanism for the conjectured equivalence of critical random Potts and Ising models.

cond-mat↗