arXiv subjects

A. Gabrielli

Publications and source records attributed to A. Gabrielli.

78 records · Page 5Linked to original sources

arXiv1998

Dynamics of Fractures in Quenched Disordered Media

We introduce a model for fractures in quenched disordered media. This model has a deterministic extremal dynamics, driven by the energy function of a network of springs (Born Hamiltonian). The breakdown is the result of the cooperation between the external field and the quenched disorder. This model can be considered as describing the low temperature limit for crack propagation in solids. To describe the memory effects in this dynamics, and then to study the resistance properties of the system we realized some numerical simulations of the model. The model exhibits interesting geometric and dynamical properties, with a strong reduction of the fractal dimension of the clusters and of their backbone, with respect to the case in which thermal fluctuations dominate. This result can be explained by a recently introduced theoretical tool as a screening enhancement due to memory effects induced by the quenched disorder.

cond-mat.stat-mech↗

arXiv1997

A Hierarchical Model of Slow Constrained Dynamics

We introduce a new simple hierarchically constrained model of slow relaxation. The configurational energy has a simple form as there is no coupling among the spins defining the system; the associated stationary distribution is an equilibrium, Gibbsian one. However, due to the presence of hierarchical constraints in the dynamics the system is found to relax to its equilibrium distribution in an extremely slow fashion when suddenly cooled from an initial temperature, $T_0$, to a final one $T_f$. The relaxation curve in that case can be fit by an stretched exponential curve. On the other hand the relaxation function is found to be exponential when $T_f >T_0$, with characteristic times depending on both $T_f$ and $T_0$, with characteristic times obeying an Arrhenius law. Numerical results as well as some analytical studies are presented. In particular we introduce a simple equation that captures the essence of the slow relaxation.

cond-mat↗

arXiv1997

Galaxy number counts and Fractal correlations

We report the correlation analysis of various redshift surveys which shows that the available data are consistent with each other and manifest fractal correlations (with dimension $D \simeq 2$) up to the present observational limits ($\approx 150 \hmp$) without any tendency towards homogenization. This result points to a new interpretation of the number counts that represents the main subject of this letter. We show that an analysis of the small scale fluctuations allows us to reconcile the correlation analysis and the number counts in a new perspective which has a number of important implications.

astro-ph↗

arXiv1997

Laplacian Fractal Growth in Media with Quenched Disorder

We analyze the combined effect of a Laplacian field and quenched disorder for the generation of fractal structures with a study, both numerical and theoretical, of the quenched dielectric breakdown model (QDBM). The growth dynamics is shown to evolve from the avalanches of invasion percolation (IP) to the smooth growth of Laplacian fractals, i. e. diffusion limited aggregation (DLA) and the dielectric breakdown model (DBM). The fractal dimension is strongly reduced with respect to both DBM and IP, due to the combined effect of memory and field screening. This implies a specific relation between the fractal dimension of the breakdown structures (dielectric or mechanical) and the microscopic properties of disordered materials.

cond-mat.dis-nn↗

arXiv1997

Theory of Self-organized Criticality for Problems with Extremal Dynamics

We introduce a general theoretical scheme for a class of phenomena characterized by an extremal dynamics and quenched disorder. The approach is based on a transformation of the quenched dynamics into a stochastic one with cognitive memory and on other concepts which permit a mathematical characterization of the self-organized nature of the avalanche type dynamics. In addition it is possible to compute the relevant critical exponents directly from the microscopic model. A specific application to Invasion Percolation is presented but the approach can be easily extended to various other problems.

cond-mat.dis-nn↗

arXiv1996

Finite size effects on the galaxy number counts: evidence for fractal behavior up to the deepest scale

We introduce and study two new concepts which are essential for the quantitative analysis of the statistical quality of the available galaxy samples. These are the dilution effect and the small scale fluctuations. We show that the various data that are considered as pointing to a homogenous distribution are all affected by these spurious effects and their interpretation should be completely changed. In particular, we show that finite size effects strongly affect the determination of the galaxy number counts, namely the number versus magnitude relation ($N(<m)$) as computed from the origin. When one computes $N(<m)$ averaged over all the points of a redshift survey one observes an exponent $α= D/5 \approx 0.4$ compatible with the fractal dimension $D \approx 2$ derived from the full correlation analysis. Instead the observation of an exponent $α\approx 0.6$ at relatively small scales, where the distribution is certainly not homogeneous, is shown to be related to finite size effects. We conclude therefore that the observed counts correspond to a fractal distribution with dimension $D \approx 2$ in the entire range $12 \ltapprox m \ltapprox 28$, that is to say the largest scales ever probed for luminous matter. In addition our results permit to clarify various problems of the angular catalogs, and to show their compatibility with the fractal behavior. We consider also the distribution of Radio-galaxies, Quasars and $γ$ ray burst, and we show their compatibility with a fractal structure with $D \approx 1.6 ÷1.8$. Finally we have established a quantitative criterion that allows us to define and {\em predict} the statistical validity of a galaxy catalog (angular or three dimensional).

astro-ph↗