Crack roughness and avalanche precursors in the random fuse model

We analyze the scaling of the crack roughness and of avalanche precursors in the two dimensional random fuse model by numerical simulations, employing large system sizes and extensive sample averaging. We find that the crack roughness exhibits anomalous scaling, as recently observed in experiments. The roughness exponents ($\zeta$, $\zeta_{loc}$) and the global width distributions are found to be universal with respect to the lattice geometry. Failure is preceded by avalanche precursors whose distribution follows a power law up to a cutoff size. While the characteristic avalanche size scales as $s_0 \sim L^D$, with a universal fractal dimension $D$, the distribution exponent $\tau$ differs slightly for triangular and diamond lattices and, in both cases, it is larger than the mean-field (fiber bundle) value $\tau=5/2$

Ataxia with oculomotor apraxia type 2: a clinical, pathologic, and genetic study

BACKGROUND: Ataxia with oculomotor apraxia type 2 (AOA2) is characterized by onset between age 10 and 22 years, cerebellar atrophy, peripheral neuropathy, oculomotor apraxia (OMA), and elevated serum alpha-fetoprotein (AFP) levels. Recessive mutations in SETX have been described in AOA2 patients. OBJECTIVE: To describe the clinical features of AOA2 and to identify the SETX mutations in 10 patients from four Italian families. METHODS: The patients underwent clinical examination, routine laboratory tests, nerve conduction studies, sural nerve biopsy, and brain MRI. All were screened for SETX mutations. RESULTS: All the patients had cerebellar features, including limb and truncal ataxia, and slurred speech. OMA was observed in two patients, extrapyramidal symptoms in two, and mental impairment in three. High serum AFP levels, motor and sensory axonal neuropathy, and marked cerebellar atrophy on MRI were detected in all the patients who underwent these examinations. Sural nerve biopsy revealed a severe depletion of large myelinated fibers in one patient, and both large and small myelinated fibers in another. Postmortem findings are also reported in one of the patients. Four different homozygous SETX mutations were found (a large-scale deletion, a missense change, a single-base deletion, and a splice-site mutation). CONCLUSIONS: The clinical phenotype of oculomotor apraxia type 2 is fairly homogeneous, showing only subtle intrafamilial variability. OMA is an inconstant finding. The identification of new mutations expands the array of SETX variants, and the finding of a missense change outside the helicase domain suggests the existence of at least one more functional region in the N-terminus of senataxin

Universality in sandpiles

We perform extensive numerical simulations of different versions of the sandpile model. We find that previous claims about universality classes are unfounded, since the method previously employed to analyze the data suffered a systematic bias. We identify the correct scaling behavior and conclude that sandpiles with stochastic and deterministic toppling rules belong to the same universality class.Comment: 4 pages, 4 ps figures; submitted to Phys. Rev.

Gravity model in the Korean highway

We investigate the traffic flows of the Korean highway system, which contains both public and private transportation information. We find that the traffic flow T(ij) between city i and j forms a gravity model, the metaphor of physical gravity as described in Newton's law of gravity, P(i)P(j)/r(ij)^2, where P(i) represents the population of city i and r(ij) the distance between cities i and j. It is also shown that the highway network has a heavy tail even though the road network is a rather uniform and homogeneous one. Compared to the highway network, air and public ground transportation establish inhomogeneous systems and have power-law behaviors.Comment: 13 page

Crossover phenomenon in self-organized critical sandpile models

We consider a stochastic sandpile where the sand-grains of unstable sites are randomly distributed to the nearest neighbors. Increasing the value of the threshold condition the stochastic character of the distribution is lost and a crossover to the scaling behavior of a different sandpile model takes place where the sand-grains are equally transferred to the nearest neighbors. The crossover behavior is numerically analyzed in detail, especially we consider the exponents which determine the scaling behavior.Comment: 6 pages, 9 figures, accepted for publication in Physical Review

From waves to avalanches: two different mechanisms of sandpile dynamics

Time series resulting from wave decomposition show the existence of different correlation patterns for avalanche dynamics. For the d=2 Bak-Tang-Wiesenfeld model, long range correlations determine a modification of the wave size distribution under coarse graining in time, and multifractal scaling for avalanches. In the Manna model, the distribution of avalanches coincides with that of waves, which are uncorrelated and obey finite size scaling, a result expected also for the d=3 Bak et al. model.Comment: 5 pages, 4 figure

Field theory of absorbing phase transitions with a non-diffusive conserved field

We investigate the critical behavior of a reaction-diffusion system exhibiting a continuous absorbing-state phase transition. The reaction-diffusion system strictly conserves the total density of particles, represented as a non-diffusive conserved field, and allows an infinite number of absorbing configurations. Numerical results show that it belongs to a wide universality class that also includes stochastic sandpile models. We derive microscopically the field theory representing this universality class.Comment: 13 pages, 1 eps figure, RevTex styl

Logarithmic corrections of the avalanche distributions of sandpile models at the upper critical dimension

We study numerically the dynamical properties of the BTW model on a square lattice for various dimensions. The aim of this investigation is to determine the value of the upper critical dimension where the avalanche distributions are characterized by the mean-field exponents. Our results are consistent with the assumption that the scaling behavior of the four-dimensional BTW model is characterized by the mean-field exponents with additional logarithmic corrections. We benefit in our analysis from the exact solution of the directed BTW model at the upper critical dimension which allows to derive how logarithmic corrections affect the scaling behavior at the upper critical dimension. Similar logarithmic corrections forms fit the numerical data for the four-dimensional BTW model, strongly suggesting that the value of the upper critical dimension is four.Comment: 8 pages, including 9 figures, accepted for publication in Phys. Rev.

The universality class of absorbing phase transitions with a conserved field

We investigate the critical behavior of systems exhibiting a continuous absorbing phase transition in the presence of a conserved field coupled to the order parameter. The results obtained point out the existence of a new universality class of nonequilibrium phase transitions that characterizes a vast set of systems including conserved threshold transfer processes and stochastic sandpile models.Comment: RevTeX, 4 pages, 3 EPS figure

Universal 1/f Noise from Dissipative SOC Models

We introduce a model able to reproduce the main features of 1/f noise: hyper-universality (the power-law exponents are independent on the dimension of the system; we show here results in d=1,2) and apparent lack of a low-frequency cutoff in the power spectrum. Essential ingredients of this model are an activation-deactivation process and dissipation.Comment: 3 Latex pages, 2 eps Figure