Related papers: Universal scaling relation for growth phenomena
We analyse the scaling properties of the energy spectra in fully developed incompressible turbulence in forced, rotating fluids in three dimensions (3D), which are believed to be characterised by universal scaling exponents in the inertial…
Interfacial roughening denotes the nonequilibrium process by which an initially flat interface reaches its equilibrium state, characterized by the presence of thermally excited capillary waves. Roughening of fluid interfaces has been first…
We provide a detailed Dynamic Renormalization Group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We consider explicitly both the morphologically stable case, and…
We investigated two-dimensional brittle fragmentation with a flat impact experimentally, focusing on the low impact energy region near the fragmentation-critical point. We found that the universality class of fragmentation transition…
A nonperturbative weak noise scheme is applied to the Kardar-Parisi-Zhang equation for a growing interface in all dimensions. It is shown that the growth morphology can be interpreted in terms of a dynamically evolving texture of localized…
The universal scaling function of the square lattice Ising model in a magnetic field is obtained numerically via Baxter's variational corner transfer matrix approach. The high precision numerical data is in perfect agreement with the…
Universality, where microscopic details become irrelevant, takes place in thermodynamic phase transitions. The universality is captured by a singular scaling function of the thermodynamic variables, where the scaling exponents are…
It is shown that an alternative approach for the characterization of growing branched patterns consists of the statistical analysis of frozen structures, which cannot be modified by further growth, that arise due to competitive processes…
Many stochastic complex systems are characterized by the fact that their configuration space doesn't grow exponentially as a function of the degrees of freedom. The use of scaling expansions is a natural way to measure the asymptotic growth…
We consider a model of a quenched disordered geometry in which a random metric is defined on ${\mathbb R}^2$, which is flat on average and presents short-range correlations. We focus on the statistical properties of balls and geodesics,…
The notions of self-organised criticality (SOC) and turbulence are traditionally considered to be applicable to disjoint classes of phenomena. Nevertheless, scale-free burst statistics is a feature shared by turbulent as well as…
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…
We employ a functional renormalization group to study interfaces in the presence of a pinning potential in $d=4-\epsilon$ dimensions. In contrast to a previous approach [D.S. Fisher, Phys. Rev. Lett. {\bf 56}, 1964 (1986)] we use a…
For the fully anisotropic simple-cubic Ising lattice, the critical finite-size scaling amplitudes of both the spin-spin and energy-energy inverse correlation lengths and the singular part of the reduced free-energy density are calculated by…
The critical behavior of driven lattice gas models has been studied for decades as a paradigm to explore nonequilibrium phase transitions and critical phenomena. However, there exists a long-standing controversy in the universality classes…
Urban scaling laws relate socio-economic, behavioral, and physical variables to the population size of cities and allow for a new paradigm of city planning, and an understanding of urban resilience and economies. Independently of culture…
We study the phase turbulence of the one-dimensional complex Ginzburg-Landau equation, in which the defect-free chaotic dynamics of the order parameter maps to a phase equation well approximated by the Kuramoto-Sivashinsky model. In this…
A model is presented for the origin of the large scale structure of the universe and their Mass-Radius scaling law; a fractal power law, $M \propto R^D$, with dimension $D=2$, most significantly. The physics is conventional, orthodox, but…
In this work a symmetry of universal finite-size scaling functions under a certain anisotropic scale transformation is postulated. This transformation connects the properties of a finite two-dimensional system at criticality with…
Dynamical properties of lattice systems with long-range pair interactions, decaying like 1/r^{\alpha} with the distance r, are investigated, in particular the time scales governing the relaxation to equilibrium. Upon varying the interaction…