The twin concepts of Scaling and Universality have played an important role in the description of statistical systems. Hydrodynamics contains many applications of scaling including descriptions of the behavior of boundary layers (Prandtl, Blasius) and of the fluctuating velocity in turbulent flow (Kolmogorov, Heisenberg, Onsager). Phenomenological theories of behavior near critical points of ph...

We show that contrary to anticipation suggested by the dictionary between rational maps and Kleinian groups and by the " hairiness phenomenon " , there exist many Feigenbaum Julia sets J(f) whose Hausdorff dimension is strictly smaller than two. We also prove that for any Feigen-baum Julia set, the Poincaré critical exponent δcr is equal to the hyperbolic dimension HD hyp (J(f)). Moreover, if a...

We previously developed a reliable method for multiparametric scaling of Fermi contacts to achieve fast and accurate prediction of proton-proton spin-spin coupling constants (SSCC) in (1)H NMR. We now report that utilization of NBO hybridization coefficients for carbon atoms in the involved C-H bonds allows for a significant simplification of this parametric scheme, requiring only four general ...

A new type of scaling applicable to a variety of physical parameters in the universe is proposed here. This utilizes a relation linking the fundamental masses and fundamental constants in nature and an axiomatic approach is developed for the relations between microscopic and macroscopic found by Eddington and Dirac. In this approach, the fundamental constants are changing with time and the vari...

The ordinary Fourier coefficients are difficult to use as input to categorizers because they contain factors dependent upon size and rotation as well as an arbitrary phase angle. From these Fourier coefficients, however, other more useful features are derived. By using these derived property constants, a distinction is made between genuine shape constants and constants representing size, locati...

Trotting, bipedal running, and especially hopping have long been considered the principal bouncing gaits of legged animals. We use the radial-leg spring constant [Formula: see text] to quantify the stiffness of the physical leg during bouncing gaits. The radial-leg is modeled as an extensible strut between the hip and the ground and [Formula: see text] is determined from the force and deflectio...

We build a Markov partition of the Feigenbaum dynamical plane, and a system of “external rays”, which are invariant under rescaling. Applications to geometry of the Feigenbaum map are given.

We propose a general procedure for extracting the running coupling constants of underlying field theory given classical statistical model on two-dimensional lattice, combining tensor network renormalization (TNR) and finite-size scaling conformal theory. By tracking at each scale, we are able to visualize group flow demonstrate it with Ising three-state Potts models. Furthermore, utilizing this...

The spectroscopic hyperfine constants for all the alkali atoms are reported. For from lithium to cesium, only long lived atomic isotopes examined. francium, measured data nuclear ground states of available listed. All results obtained since beginning laser investigations presented, while previous works Arimondo et al. [Rev. Mod. Phys. 49, 31 (1977)] recalled. Global analyses based on scaling la...

We investigate the isochronous bifurcations of the straight-line librating orbit in the Hénon-Heiles and related potentials. With increasing scaled energy e, they form a cascade of pitchfork bifurcations that cumulate at the critical saddlepoint energy e = 1. The stable and unstable orbits created at these bifurcations appear in two sequences whose self-similar properties possess an analytical ...