We show how to combine Kesten’s scaling relations, the determination of critical exponents associated to the stochastic Loewner evolution process by Lawler, Schramm, and Werner, and Smirnov’s proof of Cardy’s formula, in order to determine the existence and value of critical exponents associated to percolation on the triangular lattice.

Inspired by a model first studied by W. Li in [7], scaling properties of the correlation function for expansion-modification systems are developed. The existence of several characteristic exponents is proved and the relationship of this fact with long-range correlations in DNA is established. Comparison between theoretical exponents and those obtained from numerical experiments and real biologi...

We study the dynamics of an intriguing crossover from a chaotic to a power-law state as a function of strain rate within the context of a recently introduced model that reproduces the crossover. While the chaotic regime has a small set of positive Lyapunov exponents, interestingly, the scaling regime has a power-law distribution of null exponents which also exhibits a power law. The slow-manifo...

We study the time evolution of classical spin systems with purely relaxational dynamics, quenched from T ≫ T c to the critical point, in the semi-infinite geometry. Shortly after the quench, like in the bulk, a nonequilibrium regime governed by universal power laws is also found near the surface. We show for 'ordinary' and 'special' transitions that the corresponding critical exponents differ f...

We establish an hitherto hidden connection between zero modes and instantons in the context of the Kraichnan model for passive scalar turbulent advection, that relies on the hypothesis that the production of strong gradients of the scalar is associated with Bose-like condensation of Lagrangian particles. It opens the way to the computation of scaling exponents of the N -th order structure funct...

The scaling exponents alpha, beta, and 1/z in thin films of the organic molecule diindenoperylene deposited on SiO2 under UHV conditions are determined. Atomic-force microscopy, x-ray reflectivity, and diffuse x-ray scattering were employed. The surface width displays power law scaling over more than 2 orders of magnitude in film thickness. We obtained alpha = 0.684+/-0.06, beta = 0.748+/-0.05,...

BACKGROUND "A Body Shape Index" (ABSI) is a recently proposed index that standardizes waist circumference for body mass index (BMI) and height. This study aims to: (a) examine if the ABSI scaling exponents for standardizing waist circumference for BMI and height are valid in middle-aged and older Indonesian population, and (b) compare the association between incident hypertension and ABSI and o...