It has been shown recently that a specific class of path-dependent stochastic processes, which reduce their sample space as they unfold, lead to exact scaling laws in frequency and rank distributions. Such sample space reducing processes offer an alternative newmechanism to understand the emergence of scaling in countless processes. The corresponding power law exponents were shown to be related...

The form of the relationship between the basal metabolic rate (BMR) and body mass (M) of mammals has been at issue for almost seven decades, with debate focusing on the value of the scaling exponent (b, where BMR is proportional to M(b)) and the relative merits of b= 0.67 (geometric scaling) and b= 0.75 (quarter-power scaling). However, most analyses are not phylogenetically informed (PI) and t...

Using multi-fractal detrended fluctuation analysis (MF-DFA), the scaling features of wind speed time series (WSTS) could be explored. In this paper, we discuss the influence of sub-daily variation, which is a natural feature of wind, in MF-DFA of WSTS. First, the choice of the lower bound of the segment length, a significant parameter of MF-DFA, was studied. The results of expanding the lower b...

The stiffness exponents in the glass phase for lattice spin glasses in dimensions d = 3, . . . , 6 are determined. To this end, we consider bond-diluted lattices near the T = 0 glass transition point p∗. This transition for discrete bond distributions occurs just above the bond percolation point pc in each dimension. Numerics suggests that both points, pc and p ∗, seem to share the same 1/d-exp...

We study temperature structure functions of second, fourth, and sixth orders at heights of up to 2 m above the ground in moderately heated atmosphere. Most of the data come from measurements over salt flats of the Utah desert, with well-defined wind direction and uniform temperature boundary conditions. As in high-Rayleigh-number convection in a closed container, a thermal boundary layer develo...

Capacitance-Voltage (CV) measurements along with the Mott-Schottky (MS) analysis are widely used for characterization of material and device parameters. Using a simple analytical model, supported by detailed numerical simulations, here we predict that the capacitance of thin film devices scale as V (V is the applied potential), instead of the often used V dependence of MS analysis – with signif...

We analyze the long time behavior of an initial value problem that models a chemical reaction{di usion process A+B ! C: The problem has previously been studied by G al and R acz [1], who predicted the critical indices associated with the reaction by using a scaling ansatz motivated by numerical simulations. In this paper we point out some di culties which appear in problems of this type due to ...

The scaling function of a one-dimensional Markov map is defined and studied. We prove that the scaling function of a non-critical geometrically finite one-dimensional map is Hölder continuous, while the scaling function of a critical geometrically finite one-dimensional map is discontinuous. We prove that scaling functions determine Lipschitz conjugacy classes, and moreover, that the scaling fu...