The statistical topography of two-dimensional interfaces in the presence of quenched disorder is studied utilizing combinatorial optimization algorithms. Finite-size scaling is used to measure geometrical exponents associated with contour loops and fully packed loops. We find that contour-loop exponents depend on the type of disorder (periodic vs nonperiodic) and that they satisfy scaling relat...

Extensive kinetic Monte Carlo simulations are presented for ballistic deposition (BD) in (1+1) dimensions. Asymptotic scaling is found only for lattice sizes L≳2¹². Such a large system size for the onset of scaling explains the widespread discrepancies of previous reports for exponents of BD in one and likely higher dimensions. The exponents obtained from our simulations, α=0.499±0.004 and β=0....

In this article we investigate the behaviour of the scaling exponentsof KPZ equation through changing three parameters of the equation. Inother words we would like to know how the growth exponent β and theroughness exponent α will change if the surface tension ν , the averagevelocity λ and the noise strength γchange. Using the discrete form of theequation , first we come to the results α = 0.5 ...

The West, Brown, and Enquist (WBE) theory for the origin of allometric scaling laws is centered on the idea that the geometry of the vascular network governs how a suite of organismal traits covary with each other and, ultimately, how they scale with organism size. This core assumption has been combined with other secondary assumptions based on physiological constraints, such as minimizing the ...

The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently, a stationary stochastic process (time series) can yield anomalous time variation in the scaling exponents, suggestive of nonstationarity. The variance in the estimates of scaling exponents compu...

The scaling properties of correlation functions of non-scalar fields (constructed from velocity derivatives) in isotropic hydrodynamic turbulence are characterized by a set of universal exponents. It is explained that these exponents also characterize the rate of decay of the effects of anisotropic forcing in developed turbulence. This set has never been measured in either numerical or laborato...

Cascading failures may lead to dramatic collapse in interdependent networks, where the breakdown takes place as a discontinuity of the order parameter. However, this is a hybrid transition, meaning that, besides this first order character, the transition shows scaling too. Recently we showed that there are two sets of exponents describing respectively the order parameter and the cascade statist...

Scaling laws characterize diverse complex systems in a broad range of fields, including physics, biology, finance, and social science. The human language is another example of a complex system of words organization. Studies on written texts have shown that scaling laws characterize the occurrence frequency of words, words rank, and the growth of distinct words with increasing text length. Howev...

The problem of anisotropy and its effects on the statistical theory of high Reynoldsnumber (Re) turbulence (and turbulent transport) is intimately related and intermingled with the problem of the universality of the (anomalous) scaling exponents of structure functions. Both problems had seen tremendous progress in the last five years. In this review we present a detailed description of the new ...

Scale-free fluctuations are ubiquitous in behavioral performance and neuronal activity. In time scales from seconds to hundreds of seconds, psychophysical dynamics and the amplitude fluctuations of neuronal oscillations are governed by power-law-form long-range temporal correlations (LRTCs). In millisecond time scales, neuronal activity comprises cascade-like neuronal avalanches that exhibit po...