Biomedical subjects

L Pietronero

Publications and source records attributed to L Pietronero.

At least 19 recordsLinked to original sources

PubMed2002

Local rigidity in sandpile models.

We address the problem of the role of the concept of local rigidity in the family of sandpile systems. We define rigidity as the ratio between the critical energy and the amplitude of the external perturbation and we show, in the framework of the dynamically driven renormalization group, that any finite value of the rigidity in a generalized sandpile model renormalizes to an infinite value at the fixed point, i.e., on a large scale. The fixed-point value of the rigidity allows then for a nonambiguous distinction between sandpilelike systems and diffusive systems. Numerical simulations support our analytical results.

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PubMed2002

Probabilistic approach to the Bak-Sneppen model.

We study here the Bak-Sneppen model, a prototype model for the study of self-organized criticality. In this model several species interact and undergo extinction with a power-law distribution of activity bursts. Species are defined through their "fitness" whose distribution in the system is uniform above a certain threshold. Run time statistics is introduced for the analysis of the dynamics in order to explain the peculiar properties of the model. This approach based on conditional probability theory, takes into account the correlations due to memory effects. In this way, we may compute analytically the value of the fitness threshold with the desired precision. This represents a substantial improvement with respect to the traditional mean field approach.

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PubMed2002

High T(c) superconductivity in MgB2 by nonadiabatic pairing.

The evidence for the key role of the sigma bands in the electronic properties of MgB2 points to the possibility of nonadiabatic effects in the superconductivity of these materials. These are governed by the small value of the Fermi energy due to the vicinity of the hole doping level to the top of the sigma bands. We show that the nonadiabatic theory leads to a coherent interpretation of T(c) = 39 K and the boron isotope coefficient alphaB = 0.30 without invoking very large couplings and it naturally explains the role of the disorder on T(c). It also leads to various specific predictions for the properties of MgB2 and for the material optimization of these types of compounds.

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PubMed2001

Growing dynamics of Internet providers.

In this paper we present a model for the growth and evolution of Internet providers. The model reproduces the data observed for the Internet connection as probed by tracing routes from different computers. This problem represents a paramount case of study for growth processes in general, but can also help in the understanding the properties of the Internet. Our main result is that this network can be reproduced by a self-organized interaction between users and providers that can rearrange in time. This model can then be considered as a prototype model for the class of phenomena of aggregation processes in social networks.

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PubMed2001

Perturbative approach to the Bak-Sneppen model.

We study the Bak-Sneppen model in the probabilistic framework of the run time statistics (RTS). This model has attracted a large interest for its simplicity being a prototype for the whole class of models showing self-organized criticality. The dynamics is characterized by a self-organization of almost all the species fitnesses above a nontrivial threshold value, and by a lack of spatial and temporal characteristic scales. This results in avalanches of activity power law distributed. In this Letter we use the RTS approach to compute the value of x(c), the value of the avalanche exponent tau, and the asymptotic distribution of minimal fitnesses.

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PubMed2000

Discretized diffusion processes

We study the properties of the "rigid Laplacian" operator; that is we consider solutions of the Laplacian equation in the presence of fixed truncation errors. The dynamics of convergence to the correct analytical solution displays the presence of a metastable set of numerical solutions, whose presence can be related to granularity. We provide some scaling analysis in order to determine the value of the exponents characterizing the process. We believe that this prototype model is also suitable to provide an explanation of the widespread presence of power law in a social and economic system where information and decision diffuse, with errors and delay from agent to agent.

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PubMed2000

Nonadiabatic channels in the superconducting pairing of fullerides

We show the intrinsic inconsistency of the conventional phonon mediated theory of superconductivity in relation to the observed properties of Rb3C60. The recent, highly accurate measurement of the carbon isotope coefficient alpha(C) = 0.21, together with the high value of T(c) (30 K) and the very small Fermi energy E(F) (0.25 eV), unavoidably implies the opening of nonadiabatic channels in the superconducting pairing. We estimate these effects and show that they are actually the key elements for the high value of T(c) in these materials compared to the very low values of graphite intercalation compounds.

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PubMed2000

Invasion percolation with temperature and the nature of self-organized criticality in real systems

In this paper we present a theoretical approach that allows us to describe the transition between critical and noncritical behavior when stocastic noise is introduced in extremal models with disorder. Namely, we show that the introduction of thermal noise in invasion percolation (IP) brings the system outside the critical point. This result suggests a possible definition of self-organized criticality systems as ordinary critical systems where the critical point corresponds to set to 0 one of the parameters. We recover both the IP and Eden models for T-->0 and T-->infinity, respectively. For small T we find a dynamical second-order transition with correlation length diverging when T-->0.

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PubMed1999

Scale invariant dynamics of surface growth.

We describe in detail and extend a recently introduced nonperturbative renormalization group (RG) method for surface growth. The scale invariant dynamics which is the key ingredient of the calculation is obtained as the fixed point of a RG transformation relating the representation of the microscopic process at two different coarse-grained scales. We review the RG calculation for systems in the Kardar-Parisi-Zhang (KPZ) universality class and compute the roughness exponent for the strong coupling phase in dimensions from 1 to 9. Discussions of the approximations involved and possible improvements are also presented. Moreover, very strong evidence of the absence of a finite upper critical dimension for KPZ growth is presented. Finally, we apply the method to the linear Edwards-Wilkinson dynamics where we reproduce the known exact results, proving the ability of the method to capture qualitatively different behaviors.

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PubMed1999

Renormalization-group study of one-dimensional systems with roughening transitions.

A recently introduced real-space renormalization-group technique, developed for the analysis of processes in the Kardar-Parisi-Zhang universality class, is generalized and tested by applying it to a different family of surface-growth processes. In particular, we consider a growth model exhibiting a rich phenomenology even in one dimension. It has four different phases and a directed percolation-related roughening transition. The renormalization method reproduces extremely well all of the phase diagram, the roughness exponents in all the phases, and the separatrix among them. This proves the versatility of the method and elucidates interesting physical mechanisms.

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PubMed1996