Related papers: Singularity spectrum of self-organized criticality
For a large class of self-similar sets F in R^d analogues of the higher order mean curvatures of differentiable submanifolds are introduced, in particular, the fractal Gauss-type curvature. They are shown to be the densities of associated…
The primordial bispectrum has been considered in the past decade as a powerful probe of the physical processes taking place in the early Universe. Within the inflationary paradigm, the properties of the bispectrum are one of the keys that…
A prototypical model of symmetry-broken active matter -- biased quorum-sensing active particles (bQSAPs) -- is used to extend notions of dynamic critical phenomena to the paradigmatic setting of driven transport, where characteristic…
We review some recent extensions of the Ginzburg-Landau model able to describe several properties of non-conventional superconductors. In the first extension, s-wave superconductors endowed with two different critical temperatures are…
Monte Carlo study of the deconfined critical action phase diagram reveals a region where spinon deconfinement occurs through a weak first-order phase transition, in agreement with Ginzburg-Landau theory. Wilson renormalization argument in…
Based on general and minimal properties of the {\it discrete} circuit complexity, we define the complexity in {\it continuous} systems in a geometrical way. We first show that the Finsler metric naturally emerges in the geometry of the…
We consider Prandtl's equations for the impulsively started disk and follow the process of the formation of the singularity in the complex plane using the singularity tracking method. We classify Van Dommelen and Shen's singularity as a…
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long…
We use the generalized squeezed state description in the framework of the Ginzburg-Landau theory. Multiplicity distributions of the squeezed states are studied at second-order phase transition at different squeeze factors. It is shown that…
The singular subspaces perturbation theory is of fundamental importance in probability and statistics. It has various applications across different fields. We consider two arbitrary matrices where one is a leave-one-column-out submatrix of…
Some peculiarities of the exploitation of the entropy inequality in case of weakly nonlocal continuum theories are investigated and refined. As an example it is shown that the proper application of the Liu procedure leads to the…
In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible…
Conformable derivatives have attracted increasing interest for bridging classical and fractional calculus while retaining analytical tractability. However, their physical foundations remain underexplored. In this work, we provide a…
By analogy with the Landau-Ginzburg theory of ordinary zero-form symmetries, we introduce and develop a Landau-Ginzburg theory of one-form global symmetries, which we call mean string field theory. The basic dynamical variable is a string…
We consider the inhomogeneous Landau equation with $\gamma \in (\sqrt{3},2]$ and construct smooth, strictly positive initial data that develop a finite time singularity. The $C^{\alpha}$-norm of the distribution function blows up for every…
New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point…
This is a review of the properties of spectral fluctations in disordered metals, their relation with Random Matrix Theory and semiclassical picture. We also review the physics of persistent currents in mesoscopic isolated rings, the…
An abstract mathematical concept of fractal organization of certain complex objects received significant attention in astrophysics during last decades. The concept evolved into a broad field including multi-fractality and intermittency,…
In a variety of contexts, we prove that singular continuous spectrum is generic in the sense that for certain natural complete metric spaces of operators, those with singular spectrum are a dense $G_\delta$.
The generalized recurrence plot is a modern tool for quantification of complex spatial patterns. Its application spans the analysis of trabecular bone structures, Turing patterns, turbulent spatial plankton patterns, and fractals.…