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

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

Resummation of mass terms in perturbative massless quantum field theory

The neutral massless scalar quantum field $\Phi$ in four-dimensional space-time is considered, which is subject to a simple bilinear self-interaction. Is is well-known from renormalization theory that adding a term of the form $-\frac{m^2}{2} \Phi^2$ to the Lagrangean has the formal effect of shifting the particle mass from the original zero value to m after resummation of all two-leg insertions in the Feynman graphs appearing in the perturbative expansion of the S-matrix. However, this resummation is accompanied by some subtleties if done in a proper mathematical manner. Although the model seems to be almost trivial, is shows many interesting features which are useful for the understanding of the convergence behavior of perturbation theory in general. Some important facts in connection with the basic principles of quantum field theory and distribution theory are highlighted, and a remark is made on possible generalizations of the distribution spaces used in local quantum field theory. A short discussion how one can view the spontaneous breakdown of gauge symmetry in massive gauge theories within a massless framework is presented.Comment: 15 pages, LaTeX (style files included), one section adde

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

Perturbative quantum gauge invariance: Where the ghosts come from

A condensed introduction to quantum gauge theories is given in the perturbative S-matrix framework; path integral methods are used nowhere. This approach emphasizes the fact that it is not necessary to start from classical gauge theories which are then subject to quantization, but it is also possible to recover the classical group structure and coupling properties from purely quantum mechanical principles. As a main tool we use a free field version of the Becchi-Rouet-Stora-Tyutin gauge transformation, which contains no interaction terms related to a coupling constant. This free gauge transformation can be formulated in an analogous way for quantum electrodynamics, Yang-Mills theories with massless or massive gauge bosons and quantum gravity.Comment: 28 pages, LATEX. Some typos corrected, version to be publishe

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

Investigating the Geometrical Structure of Disordered Sphere Packings

Bead packs of up to 150,000 mono-sized spheres with packing densities ranging from 0.58 to 0.64 have been studied by means of X-ray Computed Tomography. These studies represent the largest and the most accurate description of the structure of disordered packings at the grain-scale ever attempted. We investigate the geometrical structure of such packings looking for signatures of disorder. We discuss ways to characterize and classify these systems and the implications that local geometry can have on densification dynamics.Comment: 3 figures, 9 page

The topological structure of 2D disordered cellular systems

We analyze the structure of two dimensional disordered cellular systems generated by extensive computer simulations. These cellular structures are studied as topological trees rooted on a central cell or as closed shells arranged concentrically around a germ cell. We single out the most significant parameters that characterize statistically the organization of these patterns. Universality and specificity in disordered cellular structures are discussed.Comment: 18 Pages LaTeX, 16 Postscript figure

On Gauge Invariance and Spontaneous Symmetry Breaking

We show how the widely used concept of spontaneous symmetry breaking can be explained in causal perturbation theory by introducing a perturbative version of quantum gauge invariance. Perturbative gauge invariance, formulated exclusively by means of asymptotic fields, is discussed for the simple example of Abelian U(1) gauge theory (Abelian Higgs model). Our findings are relevant for the electroweak theory, as pointed out elsewhere.Comment: 13 pages, latex, no figure