Related papers: Behavior of the scaling correlation functions unde…
This article presents a theoretical study of the scaling properties of the kinetic energy spectrum in compressible turbulence. From the fundamental symmetries and linear transformations of the microscopic action, we derive exact relations…
The scaling of the shear modulus near the gelation/vulcanization transition is explored heuristically and analytically. It is found that in a dense melt the effective chains of the infinite cluster have sizes that scale sub-linearly with…
We consider long strips of finite width $L \leq 13$ sites of ferromagnetic Ising spins with random couplings distributed according to the binary distribution: $P(J_{ij})= {1 \over 2} ( \delta (J_{ij} -J_0) + \delta (J_{ij} -rJ_0) ) ,\ 0 < r…
Covariances and variances of linear statistics of a point process can be written as integrals over the truncated two-point correlation function. When the point process consists of the eigenvalues of a random matrix ensemble, there are often…
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…
This paper addresses the stability analysis of infinite-dimensional sampled-data systems under unbounded perturbations. We present two classes of unbounded perturbations preserving the exponential stability of sampled-data systems. To this…
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…
We study universal traits which emerge both in real-world complex datasets, as well as in artificially generated ones. Our approach is to analogize data to a physical system and employ tools from statistical physics and Random Matrix Theory…
We analyze numerically three different models exhibiting an absorbing phase transition. We focus on the finite-size scaling as well as the dynamical scaling behavior. An accurate determination of several critical exponents allows to…
Driven suspensions, where energy is input at a particle scale, are a framework for understanding general principles of out-of-equilibrium organization. A large number of simple interacting units can give rise to non-trivial structure and…
Spectroscopy infers the internal structure of physical systems by measuring their response to perturbations. We apply this principle to neural networks: perturbing the data distribution by upweighting a token $y$ in context $x$, we measure…
We develop the hypothesis that the dynamics of a given system may lead to the activity being constricted to a subset of space, characterized by a fractal dimension smaller than the space dimension. We also address how the response function…
The aim of this review article is to give a comprehensive description of the scaling properties detected for the distribution of cosmic structures. Due to the great variety of statistical methods to describe the large-scale structure of the…
We develop an analytic framework to understand fragmentation in turbulent, self-gravitating media. Previously, we showed some properties of turbulence can be predicted with the excursion-set formalism. Here, we generalize to fully…
We consider the large-sparse symmetric linear systems of equations that arise in the solution of weak constraint four-dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can…
Irreversible adsorption of spheres on flat collectors having dimension $d<2$ is studied. Molecules are adsorbed on Sierpinski's Triangle and Carpet like fractals ($1<d<2$), and on General Cantor Set ($d<1$). Adsorption process is modeled…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
We analyze the robustness of the exponential stability of infinite-dimensional sampled-data systems with unbounded control operators. The unbounded perturbations we consider are the so-called Desch-Schappacher perturbations, which arise,…
Reset systems can overcome fundamental limitations of linear time-invariant control. The recently introduced notion of scaled (relative) graphs provides a promising framework for developing graphical analysis and design tools for reset…
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…