Local and Global relations between the number of contacts and density in monodisperse sphere packs

The topological structure resulting from the network of contacts between grains (\emph{contact network}) is studied for large samples of monosized spheres with densities (fraction of volume occupied by the spheres) ranging from 0.59 to 0.64. We retrieve the coordinates of each bead in the pack and we calculate the average coordination number by using three different methods. We show that, in the range of density investigated, the coordination number is larger than 4 and it increases with the packing fraction. At local level we also observe a positive correlation between local packing fraction and number of neighbors. We discover a dependence between the local densities of configurations with few neighbors in contact and the global sample-denities. This might indicate that local configurations with small number of neighbors are able to deform plastically when the sample is compactifying. PACS: 45.70.-n, Granular Systems; 45.70.Cc, Static sandpiles; Granular Compaction.Comment: 10 pages, 6 figure

Surface instabilities in granular matter and ion-sputtered surfaces

We apply a theoretical approach, originally introduced to describe aeolian ripples formation in sandy deserts, to the study of surface instability in ion sputtered surfaces. The two phenomena are distinct by several orders of magnitudes and by several physical mechanisms, but they obey to similar geometrical constraints and therefore they can be described by means of the same approach. This opens a novel conceptual framework for the study of the dynamical surface roughening and ripple formation on crystal and amorphous surfaces during ion sputtering.Comment: 14 pages, 3 figure

Volume fluctuations and geometrical constraints in granular packs

Structural organization and correlations are studied in very large packings of equally sized acrylic spheres, reconstructed in three-dimensions by means of X-ray computed tomography. A novel technique, devised to analyze correlations among more than two spheres, shows that the structural organization can be conveniently studied in terms of a space-filling packing of irregular tetrahedra. The study of the volume distribution of such tetrahedra reveals an exponential decay in the region of large volumes; a behavior that is in very good quantitative agreement with theoretical prediction. I argue that the system's structure can be described as constituted of two phases: 1) an `unconstrained' phase which freely shares the volume; 2) a `constrained' phase which assumes configurations accordingly with the geometrical constraints imposed by the condition of non-overlapping between spheres and mechanical stability. The granular system exploits heterogeneity maximizing freedom and entropy while constraining mechanical stability.Comment: 5 pages, 4 figure

The Geometrical Structure of Disordered Sphere Packings

The three dimensional structure of large packings of monosized spheres with volume fractions ranging between 0.58 and 0.64 has been studied with X-ray Computed Tomography. We search for signatures of organization, we classify local arrangements and we explore the effects of local geometrical constrains on the global packing. This study is the largest and the most accurate empirical analysis of disordered packings at the grain-scale to date with over 140,000 sphere coordinates mapped. We discuss topological and geometrical ways to characterize and classify these systems, and discuss implications that local geometry can have on the mechanisms of formation of these amorphous structures.Comment: 15 pages; 16 figure

Exchanges in complex networks: income and wealth distributions

We investigate the wealth evolution in a system of agents that exchange wealth through a disordered network in presence of an additive stochastic Gaussian noise. We show that the resulting wealth distribution is shaped by the degree distribution of the underlying network and in particular we verify that scale free networks generate distributions with power-law tails in the high-income region. Numerical simulations of wealth exchanges performed on two different kind of networks show the inner relation between the wealth distribution and the network properties and confirm the agreement with a self-consistent solution. We show that empirical data for the income distribution in Australia are qualitatively well described by our theoretical predictions.Comment: 8 pages, 11 figure

Causal construction of the massless vertex diagram

The massless one-loop vertex diagram is constructed by exploiting the causal structure of the diagram in configuration space, which can be translated directly into dispersive relations in momentum space.Comment: 14 pages, LATEX with style file, corresponds to published versio

Long term memories of developed and emerging markets: using the scaling analysis to characterize their stage of development

The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of daily Foreign Exchange rates, Stock Market indices and fixed income instruments by using the generalized Hurst approach. We show that the scaling exponents are associated with characteristics of the specific markets and can be used to differentiate markets in their stage of development. The robustness of the results is tested by both Monte-Carlo studies and a computation of the scaling in the frequency-domain.Comment: 46 pages, 7 figures, accepted for publication in Journal of Banking & Financ