Related papers: Scaling Exponents for Driven Two-Dimensional Growt…
The main technical and conceptual features of the lattice $1/N$ expansion in the scaling region are discussed in the context of a two-parameter two-dimensional spin model interpolating between $CP^{N-1}$ and $O(2N)$ $\sigma$ models, with…
An isotropic passive scalar field $T$ advected by a rapidly-varying velocity field is studied. The tail of the probability distribution $P(\theta,r)$ for the difference $\theta$ in $T$ across an inertial-range distance $r$ is found to be…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
In this work I present a numerical study of the Finite Size Scaling (FSS) of a correlation length in the framework of the $CP ^{N-1}$ model by means of the 1/N expansion. This study has been thought as propedeutical to the application of…
I show that the evolution of a two dimensional surface in a Laplacian field can be described by Hamiltonian dynamics. First the growing region is mapped conformally to the interior of the unit circle, creating in the process a set of…
We study the two-dimensional (2D) shear flow of amorphous solids within variants of an elastoplastic model, paying particular attention to spatial correlations and time fluctuations of, e.g., local stresses. The model is based on the local…
We study numerically the phase-ordering kinetics of the two-dimensional site-diluted Ising model. The data can be interpreted in a framework motivated by renormalization-group concepts. Apart from the usual fixed point of the non-diluted…
We show that the correction-to-scaling exponents in two-dimensional percolation are bounded by Omega <= 72/91, omega = D Omega <= 3/2, and Delta_1 = nu omega <= 2, based upon Cardy's result for the critical crossing probability on an…
We introduce a set of statistical measures that can be used to quantify non-equilibrium surface growth. They are used to deduce new information about spatiotemporal dynamics of model systems for spinodal decomposition and surface…
Scalar-tensor theories have taken on a key role in attempts to confront the growing open questions in standard cosmology. It is important to understand entirely their dynamics at perturbative level including any possible spatial dependence…
A competitive growth model (CGM) describes aggregation of a single type of particle under two distinct growth rules with occurrence probabilities $p$ and $1-p$. We explain the origin of scaling behaviors of the resulting surface roughness…
We introduce a model in which cells belonging to two species proliferate with volume exclusion on an expanding surface. If the surface expands uniformly, we show that the domains formed by the two species present a critical behavior. We…
We study numerically spatio-temporal fluctuations during the out-of-equilibrium relaxation of the three-dimensional Edwards-Anderson model. We focus on two issues. (1) The evolution of a growing dynamical length scale in the glassy phase of…
We apply the recently introduced distribution of sign-times (DST) to non-equilibrium interface growth dynamics. We are able to treat within a unified picture the persistence properties of a large class of relaxational and noisy linear…
Analysis of self-similarity in scale-free $N$-body simulations reveals the spatial and temporal scales for which statistics measured in cosmological simulations are converged to the physical continuum limit. We examine how the range of…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
In this paper, we investigate the dynamics of surface growth resulting from sedimentation of spherical granular particles in a fluid environment, using experiments and simulations. In the experimental part, spherical polystyrene particles…
We present an empirical study in the geometric task of learning interatomic potentials, which shows equivariance matters even more at larger scales; we show a clear power-law scaling behaviour with respect to data, parameters and compute…
The pinning-depinning phase transitions of interfaces for two classes of discrete elastic-string models are investigated numerically. In the (1+1)-dimensions, we revisit these two elastic-string models with slight modification to growth…
Local expansion exponents for nonequilibrium dynamical systems, described by partial differential equations, are introduced. These exponents show whether the system phase volume expands, contracts, or is conserved in time. The ways of…