Related papers: On generalized scaling laws with continuously vary…
Allometric scaling can reflect underlying mechanisms, dynamics and structures in complex systems; examples include typical scaling laws in biology, ecology and urban development. In this work, we study allometric scaling in scientific…
Wall turbulence has a sublayer where one-point statistics, e.g., the mean velocity and the variances of some velocity fluctuations, vary logarithmically with the distance from the wall. This logarithmic scaling is found here for two-point…
We consider a class of real numbers, a subset of irrational numbers and certain mathematical constants, for which the elements in the simple continued fraction appears to be random. As an illustrative example, one can consider $\pi = \{x_0,…
Multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical-mechanical systems. Here, a Lee-Yang zero approach is used to systematically analyse the exponents of such…
We describe an approach to logarithmic conformal field theories as limits of sequences of ordinary conformal field theories with varying central charge c. Logarithmic behaviour arises from degeneracies in the spectrum of scaling dimensions…
The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is…
To describe the small-scale intermittency of turbulence, a self-similarity is assumed for the probability density function of a logarithm of the rate of energy dissipation smoothed over a length scale among those in the inertial range. The…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
Scaling laws in ecology, intended both as functional relationships among ecologically-relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and…
We study the dynamic scaling hypothesis in invariant surface growth. We show that the existence of power-law scaling of the correlation functions (scale invariance) does not determine a unique dynamic scaling form of the correlation…
In this paper, we address the logarithmic corrections to the leading power laws that govern thermodynamic quantities as a second-order phase transition point is approached. For phase transitions of spin systems on d-dimensional lattices,…
In a setting, where only "exit measures" are given, as they are associated with an arbitrary right continuous strong Markov process on a separable metric space, we provide simple criteria for the validity of Harnack inequalities for…
A logarithmic scaling for structure functions, in the form $S_p \sim [\ln (r/\eta)]^{\zeta_p}$, where $\eta$ is the Kolmogorov dissipation scale and $\zeta_p$ are the scaling exponents, is suggested for the statistical description of the…
In this study, we show that the energy eigenvalues and the eigenfunctions of the Schrodinger equation for the power-law and the logarithmic potential can be easily obtained by using variation technique for special type wave functions. The…
Based on the effective field theory philosophy, a universal form of the scaling laws could be easily derived with the scaling anomalies naturally clarified as the decoupling effects of underlying physics. In the novel framework, the…
Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized…
The work is based on two premises: local availability of mathematics to an observer at any space time location, and the observation that number systems, as structures satisfying axioms for the number type being considered, can be scaled by…
Local availability of mathematics and number scaling provide an approach to a coherent theory of physics and mathematics. Local availability of mathematics assigns separate mathematical universes, U_{x}, to each space time point, x. The…
We analyze the stochastic scaling laws arising in the invicid limit of the decaying solutions of the Burgers equation. The linear scaling of the velocity structure functions is shown to reflect the domination by shocks of the long-time…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…