Showing papers by "Albert-László Barabási published in 1991"
TL;DR: The concept of multifractality is extended to self-affine fractals in order to provide a more complete description of fractal surfaces and it is demonstrated on the example of random walks along a chain that for stochastic lattice models leading toSelf-affinity fractals exhibits phase-transition-like behavior.
Abstract: The concept of multifractality is extended to self-affine fractals in order to provide a more complete description of fractal surfaces. We show that for a class of iteratively constructed self-affine functions there exists an infinite hierarchy of exponents ${\mathit{H}}_{\mathit{q}}$ describing the scaling of the qth order height-height correlation function ${\mathit{c}}_{\mathit{q}}$(x)\ensuremath{\sim}${\mathit{x}}_{\mathit{q}}^{\mathit{q}\mathit{H}}$. Possible applications to random walks and turbulent flows are discussed. It is demonstrated on the example of random walks along a chain that for stochastic lattice models leading to self-affine fractals ${\mathit{H}}_{\mathit{q}}$ exhibits phase-transition-like behavior.
334 citations
TL;DR: In this paper, self-affine functions with multiscaling height correlations are described in terms of the standard multifractal formalism with a modified assumption for the partition, and the corresponding quantities and expressions are shown to exhibit some characteristic differences from the standard ones.
Abstract: Self-affine functions F(x) with multiscaling height correlations cq(x) ∼xqHq are described in terms of the standard multifractal formalism with a modified assumption for the partition. The corresponding quantities and expressions are shown to exhibit some characteristic differences from the standard ones. According to our calculations the f(α) type spectra are not uniquely determined by the Hq spectrum, but depend on the particular choice which is made for the dependence of N on x, where N is the number of points over which the average is taken. Our results are expected to be relevant in the analysis of signal type data obtained in experiments on systems with an underlying multiplicative process.
82 citations