Related papers: Scaling in Steiner Random Surfaces

We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{\"a}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that,…

When stretched in one direction, most solids shrink in the transverse directions. In soft silicone gels, however, we observe that small-scale topographical features grow upon stretching. A quantitative analysis of the topography shows that…

A detailed comparison between data from experimental measurements and numerical simulations of Lagrangian velocity structure functions in turbulence is presented. By integrating information from experiments and numerics, a quantitative…

The total elastic stiffness of two contacting bodies with a microscopically rough interface has an interfacial contribution K that is entirely attributable to surface roughness. A quantitative understanding of K is important because it can…

We consider the minimization of an objective function given access to unbiased estimates of its gradient through stochastic gradient descent (SGD) with constant step-size. While the detailed analysis was only performed for quadratic…

Abstract. The purpose of this paper is twofold. We introduce the theory of random tensors, which naturally extends the method of random averaging operators in our earlier work arXiv:1910.08492, to study the propagation of randomness under…

The main purpose of this paper is to investigates structure scalars in the context of $f(\mathcal{G}, T)$ gravity, where $\mathcal{G}$ is the Gauss-Bonnet invariant and $T$ is the trace of stress energy tensor. For this aim, we have…

In the selective withdrawal experiment fluid is withdrawn through a tube with its tip suspended a distance S above a two-fluid interface. At sufficiently low withdrawal rates, Q, the interface forms a steady state hump and only the upper…

Seismogenic plate boundaries are presumed to behave in a similar manner to a densely packed granular medium, where fault and blocks systems rapidly rearrange the distribution of forces within themselves, as particles do in slowly sheared…

We consider a random surface representation of the three-dimensional Ising model.The model exhibit scaling behaviour and a new critical index $\k$ which relates $\g_{string}$ for the bosonic string to the exponent $\a$ of the specific heat…

In previous work, we have performed amplitude expansions of the continuum equations for the Grinfeld instability and carried them to high orders. Nevertheless, the approach turned out to be restricted to relatively small amplitudes. In this…

We study the fluctuations of the two-time dependent global roughness of finite size elastic lines in a quenched random environment. We propose a scaling form for the roughness distribution function that accounts for the two-time,…

We investigate the dynamic evolution of jamming in granular media through fluctuations in the granular drag force. The successive collapse and formation of jammed states give a stick-slip nature to the fluctuations which is independent of…

In this paper, we investigated the statistical differences between active and passive scalars in isotropic compressible turbulence. In the inertial range, the kinetic energy and scalar have the Kolmogorov spectra, and the Kolmogorov and…

We perform a benchmark study of the step scaling procedure for the ratios of renormalization constants extracted from position space correlation functions. We work in the quenched approximation and consider the pseudoscalar, scalar, vector…

Shearing stresses can change the volume of a material via a nonlinear effect known as shear dilatancy. We calculate the elastic dilatancy coefficient of soft sphere packings and random spring networks, two canonical models of marginal…

We study the motion of a particle sliding under the action of an external field on a stochastically fluctuating one-dimensional Edwards-Wilkinson surface. Numerical simulations using the single-step model shows that the mean-square…

Scaling of the Reynolds stresses has been sought by many researchers, since it provides a template of universal dynamical patterns across a range of Reynolds numbers. Various statistical and normalization schemes have been attempted, but…

We argue that fracture surfaces may exhibit anomalous dynamic scaling properties akin to what occurs in some models of kinetic roughening. We determine the complete scaling behavior of the local fluctuations of a brittle fracture in a…

We consider the scaling behaviour of the fluctuation susceptibility associated with the average activation in the Greenberg-Hastings neural network model and its relation to microscopic spontaneous activation. We found that, as the…