1,721,187 research outputs found
Scale-free behavior of the Internet global performance RID A-8794-2009
No full textMeasurements and data analysis have proved very effective in the
study of the Internet's physical fabric and have shown heterogeneities
and statistical fluctuations extending over several orders of magnitude.
Here we focus on the relationship between
the Round-Trip-Time (RTT) and the geographical distance.
We define dimensionless variables that contain information on
the quality of Internet connections finding
that their probability distributions are characterized by
a slow power-law decay signalling the presence of scale-free features.
These results point out the extreme heterogeneity of Internet
delay since the transmission speed between different points of the network
exhibits very large fluctuations.
The associated scaling exponents appear to have fairly stable
values in different data sets and thus define an
invariant characteristic of the Internet that might be used in the future
as a benchmark of the overall state of “health” of the Internet
The Fixed Scale Transformation Approach to Fractal Growth
No full textIrreversible fractal-growth models like diffusion-limited aggregation (DLA) and the dielectric breakdown model (DBM) have confronted us with theoretical problems of a new type for which standard concepts like field theory and renormalization group do not seem to be suitable. The fixed-scale transformation (FST) is a theoretical scheme of a novel type that can deal with such problems in a reasonably systematic way. The main idea is to focus on the irreversible dynamics at a given scale and to compute accurately the nearest-neighbor correlations at this scale by suitable lattice path integrals. The next basic step is to identify the scale-invariant dynamics that refers to coarse-grained variables of arbitrary scale. The use of scale-invariant growth rules allows us to generalize these correlations to coarse-grained cells of any size and therefore to compute the fractal dimension. The basic point is to split the long-time limit (t-->infinity) for the dynamical process at a given scale that produces the asymptotically frozen structure, from the large-scale limit (r-->infinity) which defines the scale-invariant dynamics. In addition, by working at a fixed scale with respect to dynamical evolution, it is possible to include the fluctuations of boundary conditions and to reach;a remarkable level of accuracy for a real-space method. This new framework is able to explain the self-organized critical nature and the origin of fractal structures in irreversible-fractal-growth models, it also provides a rather systematic procedure for the analytical calculation of the fractal dimension and other critical exponents. The FST method can be naturally extended to a variety of equilibrium and nonequilibrium models that generate fractal structures
Fractal and topological properties of directed fractures
No full textWe use the Born model for the energy of elastic networks to simulate ''directed'' fracture growth. We define directed fractures as crack patterns showing a preferential evolution direction imposed by the type of stress and boundary conditions applied. This type of fracture allows a more realistic description of some kinds of experimental cracks and presents several advantages in order to distinguish between the various growth regimes. By choosing this growth geometry it is also possible to use without ambiguity the box-counting method to obtain the fractal dimension for different subsets of the patterns and for a wide range of the internal parameters of the model. We find a continuous dependence of the fractal dimension of the whole patterns and of their backbones on the ratio between the central- and noncentral-force contributions. For the chemical distance we find a one-dimensional behavior independent of the relevant parameters, which seems to be a common feature for fractal growth processes. © 1994 The American Physical Society
Structure of cycles and local ordering in complex networks
No full textWe study the properties of quantities aimed at the characterization of grid-like ordering in complex networks. These quantities are based on the global and local behavior of cycles of order four, which are the minimal structures able to identify rectangular clustering. The analysis of data from real networks reveals the ubiquitous presence of a statistically high level of grid-like ordering that is non-trivially correlated with the local degree properties. These observations provide new insights on the hierarchical structure of complex networks
Fixed scale transformation for fracture growth processes governed by vectorial fields
No full textWe use the Fixed Scale Transformation (FST) approach to study the problem of fractal growth in fracture patterns generated by using the Born Model. The application of the method to this model is very complex because of the vectorial nature of the system considered. In particular, the implementation of this scheme requires a careful choice of the fracture path and the identification of the appropriate way to take into account screening effects. The good agreements of our results with computer simulations shows the validity and flexibility of the FST method which represents a general theoretical approach for the study of fractal patterns evolution. © 1995
Fixed scale transformation approach for born model of fractures
No full textWe use the Fixed Scale Transformation theoretical approach to study the problem of fractal growth in fractures generated by using the Born Model. In this case the application of the method is more complex because of the vectorial nature of the model considered. In particular, one needs a careful choice of the lattice path integral for the fracture evolution and the identification of the appropriate way to take effectively into account screening effects. The good agreement of our results with computer simulations shows the validity and flexibility of the FST method in the study of fractal patterns evolution
Large scale Structure and Dynamics of Complex Webs
No full textThis book is the culmination of three years of research effort on a multidisciplinary project in which physicists, mathematicians, computer scientists and social scientists worked together to arrive at a unifying picture of complex networks. The contributed chapters form a reference for the various problems in data analysis visualization and modeling of complex networks
- …
