Related papers: Generic Dynamic Scaling in Kinetic Roughening
We study a model of fully developed turbulence of a compressible fluid, based on the stochastic Navier-Stokes equation, by means of the field theoretic renormalization group. In this approach, scaling properties are related to the fixed…
We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial…
We show that generic kinetic growth processes with surface relaxations can exhibit a new crumpled phase with short-range orientational order at dimensions $d<4$. A sufficiently strong spatially non-local part of the chemical potential…
We propose an exact analytical formula for the anomalous scaling exponents of inertial range structure functions in incompressible fluid turbulence. The formula is a gravitational Knizhnik-Polyakov-Zamolodchikov (KPZ)-type relation, and is…
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 time-dependent order parameter distribution function is proposed,…
Dynamical scaling and ageing in disordered systems far from equilibrium is reviewed. Particular attention is devoted to the question to what extent a recently introduced generalization of dynamical scaling to local scale-invariance can…
The scaling properties of the maximal height of a growing self-affine surface with a lateral extent $L$ are considered. In the late-time regime its value measured relative to the evolving average height scales like the roughness: $h^{*}_{L}…
A static variational model for shape formation in heteroepitaxial crystal growth is considered. The energy functional takes into account surface energy, elastic misfit-energy and nucleation energy of dislocations. A scaling law for the…
It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach…
We investigate the complex spatio-temporal dynamics in avalanche driven surface growth by means of scaling theory. We study local activity statistics, avalanche kinetics, and temporal correlations in the global interface velocity, obtaining…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
Scaling laws in deep learning -- empirical power-law relationships linking model performance to resource growth -- have emerged as simple yet striking regularities across architectures, datasets, and tasks. These laws are particularly…
We study a random walk problem on the hierarchical network which is a scale-free network grown deterministically. The random walk problem is mapped onto a dynamical Ising spin chain system in one dimension with a nonlocal spin update rule,…
Continuum and soft robots can leverage complex actuator shapes to take on useful shapes while actuating only a few of their many degrees of freedom. Continuum robots that also grow increase the range of potential shapes that can be actuated…
It has been suggested that the modified Steiner action functional has desirable properties for a random surface action. In this paper we investigate the scaling of the string tension and massgap in a variant of this action on dynamically…
Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations…
Unveiling universal non-equilibrium scaling laws has been a central theme in modern statistical physics, with recent attention increasingly directed toward non-equilibrium phases that exhibit rich dynamical phenomena. A striking example…
Dynamical scaling in ageing systems, notably in phase-ordering kinetics, is well-established. New evidence in favour of Galilei-invariance in phase-ordering kinetics is reviewed.
We investigate Kardar-Parisi-Zhang (KPZ) surface growth in the presence of long-term correlated noise. By means of extensive numerical simulations of models in the KPZ universality class we find that, as the noise correlator range…
Recently, the concept of geometric renormalization group provides a good approach for studying the structural symmetry and functional invariance of complex networks. Along this line, we systematically investigate the finite-size scaling of…