Showing papers by "Luciano Pietronero published in 2003"

Universal scaling relations in food webs

Abstract: The structure of ecological communities is usually represented by food webs. In these webs, we describe species by means of vertices connected by links representing the predations. We can therefore study different webs by considering the shape (topology) of these networks. Comparing food webs by searching for regularities is of fundamental importance, because universal patterns would reveal common principles underlying the organization of different ecosystems. However, features observed in small food webs are different from those found in large ones. Furthermore, food webs (except in isolated cases) do not share general features with other types of network (including the Internet, the World Wide Web and biological webs). These features are a small-world character and a scale-free (power-law) distribution of the degree (the number of links per vertex). Here we propose to describe food webs as transportation networks by extending to them the concept of allometric scaling (how branching properties change with network size). We then decompose food webs in spanning trees and loop-forming links. We show that, whereas the number of loops varies significantly across real webs, spanning trees are characterized by universal scaling relations.

Generation of primordial cosmological perturbations from statistical mechanical models

Abstract: The initial conditions describing seed fluctuations for the formation of structure in standard cosmological models, i.e. the Harrison-Zeldovich distribution, have very characteristic ‘‘super-homogeneous’’ properties: they are statistically translation invariant and isotropic, and the variance of the mass fluctuations in a region of volume V grows more slowly than V. We discuss the geometrical construction of distributions of points in R 3 with similar properties encountered in tiling and in statistical physics, e.g. the Gibbs distribution of a onecomponent system of charged particles in a uniform background @one-component plasma ~OCP!#. Modifications of the OCP can produce equilibrium correlations of the kind assumed in the cosmological context. We then describe how such systems can be used for the generation of initial conditions in gravitational N-body simulations.

Electron-phonon renormalization in small Fermi energy systems

Abstract: The puzzling features of recent photoemission data in cuprates have been the object of several analyses in order to identity the nature of the underlying electron-boson interaction. In this paper we point out that many basic assumptions of the conventional analysis are expected to fail in small Fermi energy systems, when, as in the cuprates, the Fermi energy ${E}_{F}$ is comparable with the boson energy scale. We discuss in detail the features appearing in the self-energy of small Fermi energy systems and the possible implications for the angle-resolved photoemission spectroscopy data in cuprates.

Band-filling effects on electron-phonon properties of normal and superconducting states

Abstract: We address the effect of band filling on the effective electron mass m* and the superconducting critical temperature Tc in a electron-phonon system We compare the vertex corrected theory with the noncrossing approximationof the Holstein model within a local approximation. We identify two regions of the electron density where m* and T c are enhanced or decreased by the inclusion of the vertex diagrams. We show that the crossover between the enhancement at low density and the decrease towards half filling is almost independent of the microscopic electron-phonon parameters. These different behaviors are explained in terms of the net sign of the vertex diagrams which is positive at low densities and negative close to half filling. Predictions of the present theory for doped MgB 2 , which is argued to he in the low density regime, are discussed.

Poor screening and nonadiabatic superconductivity in correlated systems

Abstract: In this paper we investigate the role of the electronic correlation on the hole doping dependence of electron-phonon and superconducting properties of cuprates. We introduce a simple analytical expression for the one-particle Green's function in the presence of electronic correlation and we evaluate the reduction of the screening properties as the electronic correlation increases by approaching half filling. The poor screening properties play an important role within the context of the nonadiabatic theory of superconductivity. We show that a consistent inclusion of the reduced screening properties in the nonadiabatic theory can account in a natural way for the ${T}_{c}\ensuremath{-}\ensuremath{\delta}$ phase diagram of cuprates. Experimental evidences are also discussed.

Generalized Network Growth: from Microscopic Strategies to the Real Internet Properties

Abstract: In this paper we present a generalized model for network growth that links the microscopical agent strategies with the large scale behavior This model is intended to reproduce the largest number of features of the Internet network at the Autonomous System (AS) level Our model of network grows by adding both new vertices and new edges between old vertices In the latter case a ``rewarding attachment'' takes place mimicking the disassortative mixing between small routers to larger ones We find a good agreement between experimental data and the model for the degree distribution, the betweenness distribution, the clustering coefficient and the correlation functions for the degrees

The origin of phonon anharmonicity in MgB2 and related compounds

Abstract: The recent discovery of a superconducting transition at 39 K in MgB2?made of alternating Mg and graphene-like B planes?has raised great interest, for both its technological and theoretical implications It was clear since the very beginning that the properties of this material are related to an anomalous coupling between the charge carriers in the ? bands?due to in-plane bonds between Boron atoms?and the phonon mode (E2g) which involves in-plane vibrations of the B ions Theoretical studies have thus been focused on the search for possible anomalies in the e?ph coupling: one of the first results was the discovery that the E2g phonon is highly anharmonic, but the connection between anharmonicity and Tc in this material is still a controversial point We first present a detailed first-principles study of the E2g phonon anharmonicity in MgB2 and analogous compounds which are not superconducting, AlB2 and graphite, and in a hypothetical hole-doped graphite (C2+2); we then introduce an analytical model which allows us to relate the onset of anharmonicity with the small Fermi energy of the carriers in ? bands Our study suggests a possible relation between anharmonicity and non-adiabaticity; non-adiabatic effects, which can lead to a sensible increase of Tc with respect to values predicted by conventional theory, become in fact relevant when phonon frequencies are comparable to electronic energy scales

Food Web Structure and the Evolution of Complex Networks

Abstract: In addition to traditional properties such as the degree distribution P(k), in this work we propose two other useful quantities that can help in characterizing the topology of food webs quantitatively, namely the allometric scaling relations C(A) and the branch size distribution P(A) which are defined on the spanning tree of the webs. These quantities, whose use has proved relevant in characterizing other different networks appearing in nature (such as river basins, Internet, and vascular systems), are related (in the context of food webs) to the efficiency in the resource transfer and to the stability against species removal. We present the analysis of the data for both real food webs and numerical simulations of a growing network model. Our results allow us to conclude that real food webs display a high degree of both efficiency and stability due to the evolving character of their topology.

Scaling in cosmic structures

Abstract: The study of the properties of cosmic structures in the universe is one of the most fascinating subject of the modern cosmology research. Far from being predicted, the large scale structure of the matter distribution is a very recent discovery, which continuosly exhibits new features and issues. We have faced such topic along two directions; from one side we have studied the correlation properties of the cosmic structures, that we have found substantially different from the commonly accepted ones. From the other side, we have studied the statistical properties of the very simplified system, in the attempt to capture the essential ingredients of the formation of the observed strucures.

A cellular automaton model of gravitational clustering

Abstract: Gravitational clustering of a random distribution of point masses is dominated by the effective short-range interactions due to large-scale isotropy. We introduce a one-dimensional cellular automaton to reproduce this effect in the most schematic way: at each time particles move towards their nearest neighbours with whom they coalesce on collision. This model shows an extremely rich phenomenology with features of scale-invariant dynamics leading to a tree-like structure in space–time whose topological self-similarity are characterised with universal exponents. Our model suggests a simple interpretation of the non-analytic hierarchical clustering and can reproduce some of the self-similar features of gravitational N-body simulations.

NONADIABATIC EFFECTS AND THE ROLE OF SMALL FERMI ENERGY IN MgB 2

Abstract: There is nowadays a general agreement on a key role of the σ bands in the superconducting properties of MgB2. We show that peculiar characteristics of the σ bands give rise to nonadiabatic and anharmonic effects which break the conventional Migdal-Eliashberg framework. Both these features are governed by the small value of the Fermi energy due to the vicinity of the hole doping level to the top of the σ bands. In this context we discuss how the nonadiabatic theory leads to a coherent interpretation of the superconducting properties of MgB2 without invoking very large couplings and it naturally explains the role of the disorder on Tc. It also leads to various specific predictions for the properties of MgB2 and for the material optimization of these type of compounds. Anharmonicity is also investigated by means of LDA calculations. We find that the anharmonic character of the E2g phonon is essentially driven by the small Fermi energy of the σ holes. We present a simple analytic model which allows us to understand in microscopic terms the role of the small Fermi energy and of the electronic structure. The relation between anharmonicity and nonadiabaticity is pointed out and discussed in relation to various materials.

N-body simulations for structure formation from random initial conditions

Abstract: We present the results of an extensive series of high-performance simulations of the evolution of self-gravitating systems with periodic boundary conditions. The main aim of the project is to investigate the role of gravitation and of initial conditions and boundary conditions into the following evolution toward a metastable equilibrium, in a way such to distinguish the role of the various ingredients in the overall dynamics. In particular, we compare the evolution of spatially infinite self-gravitating systems embedded in an expanding universe with that of systems in a static frame. We discuss the differences and the similarities in several statistical quantities, as the density profiles of clusters and the two point autocorrelation function.