This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size scaling ansatz for the timedependent order parameter distribution function is proposed, and tested with extensive Monte-Carlo simulations of domain growth in the 2-D spin-flip kinetic Ising model. The scaling properties of the distribution function...

This review is intended to give a pedagogical and unified view on the subject of the statistics and scaling of physical quantities in disordered electron systems at very low temperatures. Quantum coherence at low temperatures and randomness of microscopic details can cause large fluctuations of physical quantities. In such mesoscopic systems a localization-delocalization transition can occur wh...

Entropy weighting used in some soft subspace clustering algorithms is sensitive to the scaling parameter. In this paper, we propose a novel soft subspace clustering algorithm by using log-transformed distances in the objective function. The proposed algorithm allows users to choose a value of the scaling parameter easily because the entropy weighting in the proposed algorithm is less sensitive ...

The accumulation point of the period-tripling bifurcation cascade in complex quadratic map was discovered by Golberg, Sinai, and Khanin (Russ.Math.Surv. 38:1, 1983, 187), and independently by Cvitanović and Myrheim (Phys.Lett. A94:8, 1983, 329). As we argue, in the extended parameter space of smooth maps, not necessary satisfying the Cauchy – Riemann equations, the scaling properties associated...

The idea of universal finite-size-scaling functions of the Ising model is tested by Monte Carlo simulations for various lattices. Not only regular lattices such as the square lattice but quasiperiodic lattices such as the Penrose lattice are treated. We show that the finite-size-scaling functions of the order parameter for various lattices are collapsed on a single curve by choosing two nonuniv...

It is shown that there is a second properly normalized KNO scaling function, nPn(n/n̄) = φ(z), which has certain advantages in the analysis of KNO scaling. First, the nPn are not influenced by the statistical and systematic uncertainties of n̄ hence φ(z) provides more selective power than the original KNO scaling function n̄Pn(n/n̄) = ψ(z). Second, the new scaling function generates scale parameter...

We investigate the connection between two classical models for the study of phase transition phenomena, the Becker–Döring equations, and the Lifshitz–Slyozov system. More precisely, we introduce a scaling parameter and show that the solution to the Becker–Döring equations converges to that of the Lifshitz–Slyozov system as the scaling parameter goes to 0.