22,801 research outputs found
How to discriminate easily between Directed-percolation and Manna scaling
Here we compare critical properties of systems in the directed-percolation
(DP) universality class with those of absorbing-state phase transitions
occurring in the presence of a non-diffusive conserved field, i.e. transitions
in the so-called Manna or C-DP class. Even if it is clearly established that
these constitute two different universality classes, most of their universal
features (exponents, moment ratios, scaling functions,...) are very similar,
making it difficult to discriminate numerically between them. Nevertheless, as
illustrated here, the two classes behave in a rather different way upon
introducing a physical boundary or wall. Taking advantage of this, we propose a
simple and fast method to discriminate between these two universality classes.
This is particularly helpful in solving some existing discrepancies in
self-organized critical systems as sandpiles.Comment: 7 Pages, 4 Figure
On the real linear polarization constant problem
The present paper deals with lower bounds for the norm of products of linear forms. It has been proved by J. Arias-de-Reyna [2], that the so-called n(th) linear polarization constant c(n)(C-n) is n(n/2), for arbitrary n is an element of N. The same value for c(n) (R-n) is only conjectured. In a recent work A. Pappas and S. Revesz prove that c(n) (R-n) = n(n/2) for n <= 5. Moreover, they show that if the linear forms are given as f(j)(x) = [x, a(j)),for some unit vectors a(j) (1 <= j <= n), then the product of the f(j)'s attains at least the value n(-n/2) at the normalized signed sum of the vectors having maximal length. Thus they asked whether this phenomenon remains true for arbitrary n is an element of N. We show that for vector systems {a(j)}(j=1)(n) close to an orthonormal system, the Pappas-Revesz estimate does hold true. Furthermore, among these vector systems the only system giving n(-n/2) as the norm of the product is the orthonormal system. On the other hand, for arbitrary vector systems we answer the question of A. Pappas and S. Revesz in the negative when n is an element of N is large enough. We also discuss various further examples and counterexamples that may be instructive for further research towards the determination of c(n)(R-n)
Improved spectral algorithm for the detection of network communities
We review and improve a recently introduced method for the detection of
communities in complex networks. This method combines spectral properties of
some matrices encoding the network topology, with well known hierarchical
clustering techniques, and the use of the modularity parameter to quantify the
goodness of any possible community subdivision. This provides one of the best
available methods for the detection of community structures in complex systems.Comment: 4 pages, 1 fugure; to appear in the Proceedings of the 8th Granada
Seminar - Computational and Statistical Physic
Digital filter synthesis computer program
Digital filter synthesis computer program expresses any continuous function of a complex variable in approximate form as a computational algorithm or difference equation. Once the difference equation has been developed, digital filtering can be performed by the program on any input data list
Critical behavior of a bounded Kardar-Parisi-Zhang equation
A host of spatially extended systems, both in physics and in other
disciplines, are well described at a coarse-grained scale by a Langevin
equation with multiplicative-noise. Such systems may exhibit non-equilibrium
phase transitions, which can be classified into universality classes. Here we
study in detail one of such classes that can be mapped into a
Kardar-Parisi-Zhang (KPZ) interface equation with a positive (negative)
non-linearity in the presence of a bounding lower (upper) wall. The wall limits
the possible values taken by the height variable, introducing a lower (upper)
cut-off, and induce a phase transition between a pinned (active) and a depinned
(absorbing) phase. This transition is studied here using mean field and field
theoretical arguments, as well as from a numerical point of view. Its main
properties and critical features, as well as some challenging theoretical
difficulties, are reported. The differences with other multiplicative noise and
bounded-KPZ universality classes are stressed, and the effects caused by the
introduction of ``attractive'' walls, relevant in some physical contexts, are
also analyzed.Comment: Invited paper to a special issue of the Brazilian J. of Physics. 5
eps Figures. 9 pagres. Revtex
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