Related papers: On generalized scaling laws with continuously vary…
We formulate multifractal models for velocity differences and gradients which describe the full range of length scales in turbulent flow, namely: laminar, dissipation, inertial, and stirring ranges. The models subsume existing models of…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…
A generalized logarithmic law for high-order moments of passive scalars is proposed for turbulent boundary layers. This law is analogous to the generalized log law that has been proposed for high-order moments of the turbulent longitudinal…
We present a method to determine the equilibrium geometry of large atomistic systems with linear scaling. It is based on a separate treatment of long and short wavelength components of the forces. While the rapidly varying part is handled…
Martensites subjected to quasistatic deformation are known to exhibit power law distributed acoustic emission in a broad range of scales, however, the origin of the observed scaling behavior and the mechanism of self-organization towards…
Individual resource intake rates are known to depend on both individual body size and resource availability. Here, we have developed a model to integrate these two drivers, accounting explicitly for the scaling of perceived resource…
Universal properties of turbulence have been associated traditionally with very high Reynolds numbers, but recent work has shown that the onset of the power-laws in derivative statistics occurs at modest microscale Reynolds numbers of the…
We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness…
Power law generalized covariance functions provide a simple model for describing the local behavior of an isotropic random field. This work seeks to extend this class of covariance functions to spatial-temporal processes for which the…
Disclosure of scaling relationship between observable quantities gives direct information about dynamics of natural phenomenon. This is the main reason why scaling plays a key role in the methodology of natural sciences. In this talk, Part…
We present a simple, unified approach to determining the growth law for the characteristic length scale, $L(t)$, in the phase ordering kinetics of a system quenched from a disordered phase to within an ordered phase. This approach, based on…
The self-similarity in space and time (hereafter self-similarity), either deterministic or statistical, is characterized by similarity exponents and a function of scaled variable, called the scaling function. In the present paper, we…
We cosider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. We proove the existence of an exponentially attractive invariant measure and the strong law of…
Universal scaling laws form one of the central issues in physics. A non-standard scaling law or a breakdown of a standard scaling law, on the other hand, can often lead to the finding of a new universality class in physical systems.…
When traversing a symmetry breaking second order phase transition at a finite rate, topological defects form whose number dependence on the quench rate is given by simple power laws. We propose a general approach for the derivation of such…
We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming problems and obtain, for each of these…
Experimental and empirical data are often analyzed on log-log plots in order to find some scaling argument for the observed/examined phenomenon at hands, in particular for rank-size rule research, but also in critical phenomena in…
We present a self-contained formalism for analyzing scale invariant differential equations. We first cast the scale invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background…
The scaling of the spatio-temporal response of coarsening systems is studied through simulations of the 2D and 3D Ising model with Glauber dynamics. The scaling functions agree with the prediction of local scale invariance, extending…
We study a few dynamical systems composed of many components whose sizes evolve according to multiplicative stochastic rules. We compare them with respect to the emergence of power laws in the size distribution of their components. We show…