Showing papers by "Luciano Pietronero published in 1991"
TL;DR: In this paper, a continuous-energy model is analyzed using a self-consistent effective medium method and it is shown that energy is homogeneously and isotropically distributed in space.
Abstract: We study various aspects of the self-organized critical phenomena. A continuous-energy model is analyzed using a self-consistent effective medium method. We find that energy is homogeneously and isotropically distributed in space. We have calculated analytically the critical energy, which is very close to that of numerical simulations. We found that the critical energy is quite universal whereas the energy distribution per site depends on particular models. Using scaling arguments we have estimated the various exponents. We have also performed a detailed study of the noise spectrum. The result shows a 1/f2 behavior in the frequency region that we have probed.
37 citations
TL;DR: In two dimensions the clusters of sites involved in a relaxation process turn out to be compact (D=2) because of the absence of effective screening, so they are more similar to Eden-type clusters than to those of the usual fractal growth models.
Abstract: We use the fixed scale transformation method, developed for fractal growth, to investigate analytically the nature of clusters in self-organized criticality (SOC). In two dimensions the clusters of sites involved in a relaxation process turn out to be compact (D=2) because of the absence of effective screening. Therefore they are more similar to Eden-type clusters (possibly with a rough surface) than to those of the usual fractal growth models. This result is in good agreement with the computer simulations and one can conjecture that it should hold for any dimensions. The critical state corresponding to SOC dynamics is therefore of much simpler nature with respect to those of the usual fractal growth models.
12 citations
TL;DR: In this article, a coarse-grained model of a charge density wave pinned by random impurities gives rise to a dynamical critical behavior of new type with properties analogous to those of glassy systems.
Abstract: The depinning transition of a charge density wave pinned by random impurities gives rise to a dynamical critical behaviour of new type with properties analogous to those of glassy systems. In order to discuss these properties, it is convenient to introduce a coarse-grained model that should belong to the same class of universality of the usual models. This allows to derive analytical results for the critical exponents and for the stretched exponential relaxation below threshold. These results are in excellent agreement with computer simulations and elucidate the nature of this dynamical phase transition and of the glassy-type relaxation in the pinned region.
12 citations
TL;DR: In this article, the critical behavior at the depinning transition and the stretched exponential relaxation in the pinned region of a charge density wave (CDW) under the influence of an applied field are analyzed.
Abstract: We study analytically and numerically the critical behavior at the depinning transition and the stretched exponential relaxation in the pinned region of a charge density wave (CDW) under the influence of an applied field. The original model of an elastic string pinned by random sinusoidal impurity potentials is transformed, by a coarse graining operation, into a simpler model for which analytical expressions for the exponents corresponding to the critical behavior and to the stretched exponential relaxation can be derived in any dimension. In particular we can identify different correlation lenghts (static and dynamic) that diverge at the depinning transition with different exponents. Computer simulations on the coarse grained model and on the original CDW model turn out to be in very good agreement with our analytical expressions. These results clarify the nature of the critical behavior of the depinning transition and of the glassy-type relaxation in the pinned region. In addition our theoretical analysis may provide a new point of view for the description of other disordered and glassy systems.
9 citations
TL;DR: In this paper, the fixed scale transformation (FST) was applied to fractal growth in three dimensions and applied to diffusion limited aggregation and to the dielectric breakdown model for different values of the parameter η.
Abstract: We extend the method of the fixed scale transformation (FST) to the case of fractal growth in three dimensions and apply it to diffusion limited aggregation and to the dielectric breakdown model for different values of the parameter η. The scheme is formally similar to the two-dimensional case with the following technical complications: (i) The basis configurations for the fine graining process are five (instead of two) and consist of 2 × 2 cells. (ii) The treatment of the fluctuations of boundary conditions is far more complex and requires new schemes of approximations. In order to test the convergency of the theoretical results we consider three different schemes of increasing complexity. For DBM in three dimensions the computed values of the fractal dimension for η = 1, 2 and 3 result to be in very good agreement with corresponding values obtained by computer simulations. These results provide an important test for the FST method as a new theoretical tool to study irreversible fractal growth.
6 citations
TL;DR: In this paper, the authors studied the growth probability for diffusion limited aggregation and the dielectric breakdown model in the steady state regime of the cylinder geometry and showed a rather unambiguous picture with the following properties: growth probability along the growth direction is exponential, contrary to the Gaussian behavior of the radial case.
Abstract: We study the properties of the growth probabilities for diffusion limited aggregation and the dielectric breakdown model in the steady state regime of the cylinder geometry. The results show a rather unambiguous picture with the following properties: The projection of the growth probability along the growth direction is exponential , contrary to the Gaussian behavior of the radial case. One can distinguish two regions, one with simple multifractal properties corresponding to the growing zone and a second one which accounts for the exponential decay of the growth probability. This situation can be explained in terms of a first order transition in the multifractal spectrum at q = 1. This corresponds to a different picture with respect to those that have been proposed in the literature. The properties of the growing interface could be universal while the small probability part is non-universal and it depends on the particular geometry. However, we can show that this part is irrelevant with respect to the growth process, even though it is determined by it.
6 citations
TL;DR: In this article, the distribution of points corresponding to the angular projection of a fractal is shown to become homogeneous for relatively large angels, and the corresponding correlation function w(θ) depends strongly on the angular half-width of the considered sample.
Abstract: The distribution of points corresponding to the angular projection of a fractal is shown to become homogeneous for relatively large angels. In addition the corresponding correlation function w(θ) depends strongly on the angular half-width of the considered sample. These results show that, contrary to the usual interpretation, the observed angular correlations of galaxies can actually be compatible with a fractal structure in space.
5 citations
TL;DR: In this paper, the universality of growth rules in fractal-growth models has been studied and a theoretical scheme that allows us to address this question has been proposed, showing that growth defined per site and rules that include diagonal processes renormalize asymptotically into effective growth rules of simple bond type.
Abstract: We consider the problem of the universality of growth rules in fractal-growth models and introduce a theoretical scheme that allows us to address this question. In particular we show that growth defined per site and rules that include diagonal processes renormalize asymptotically into effective growth rules of simple bond type. Therefore, we identify the general nature of the asymptotic, scale-invariant growth dynamics for coarse-grained variables.
5 citations
TL;DR: In this article, the authors presented analytical calculations for the regular part of the multifractal spectrum of the dielectric breakdown model with different values of the parameter ν, and showed that for small η values, and in order to recover the Eden limit, it is necessary to go to higher order and possibly to include self-affine properties explicitly.
Abstract: The separation of the properties of the growth probability distribution in two different contributions, as discussed in the previous paper, corresponds naturally to the approximation scheme of the fixed scale transformation (FST) method. The growth probabilities used to compute the FST matrix elements represent the essential elements of the multiplicative process that gives rise to the regular part (the only one relevant to the growth process) of the multifractal spectrum. The FST uses these probabilities directly without the need of introducing a multifractal spectrum explicitly. This, however, can be obtained as a by-product of the FST method. We present here analytical calculations for the regular part of the multifractal spectrum of the dielectric breakdown model with different values of the parameter ν. The results are good for η ⩾ 1 and less accurate for η < 1. In fact for small η values, and in order to recover the Eden limit, it is necessary to go to higher order and possibly to include self-affine properties explicitly.
2 citations
01 Dec 1991
TL;DR: In this article, the conditions of stability of the solid state with respect to quantum fluctuations are analyzed in order to define their implications on the fundamental constants and on the masses of particles, and the result is that the requirement of a stable solid state implies the condition that the electron should be much lighter than the proton, regardless of the values of h ande (electron charge).
Abstract: The theory of the Standard Model, or any quantum theory of this nature, cannot give information on the value of the coupling constants and the masses of the particles. On the other hand, according to Landau and Lifshitz and further developments, we must require the existence of classical objects (the detectors) for a satisfactory formulation of the measurement process. We conjecture that these statements imply the existence of a «solid state» of matter, in order to give operational meaning to our theory. In fact stable matter is necessary to establish a unit of length and to measure the coordinates of an event. From this perspective we analyze the conditions of stability of the solid state with respect to quantum fluctuations in order to define their implications on the fundamental constants and on the masses of particles. The result is that the requirement of a stable solid state implies the condition that the electron should be much lighter than the proton, regardless of the values ofh ande (electron charge). This condition results from any attempt to give an experimental significance to the Standard Model.
1 citations