Related papers: Multifractality and intermittency in the limit evo…
This study makes the first attempt to use the 2/3-order fractional Laplacian modeling of enhanced diffusing movements of random turbulent particle resulting from nonlinear inertial interactions. A combined effect of the inertial…
The fractional Fourier transform (FrFT), which is a generalization of the Fourier transform, has become the focus of many research papers in recent years because of its applications in electrical engineering and optics. In this paper, we…
We examine integrable turbulence (IT) in the framework of the defocusing cubic one-dimensional nonlinear Schr\"{o}dinger equation. This is done theoretically and experimentally, by realizing an optical fiber experiment in which the…
We develop the theory of multiresolutions in the context of Hausdorff measure of fractional dimension between 0 and 1. While our fractal wavelet theory has points of similarity that it shares with the standard case of Lebesgue measure on…
For generic systems exhibiting power law behaviors, and hence multiscale dependencies, we propose a new, and yet simple, tool to analyze multifractality and intermittency, after noticing that these concepts are directly related to the…
We used the Density Functional formalism, in particular the Scaled Particle Theory, applied to a length-polydisperse hard-rectangular fluid to study its phase behavior as a function of the mean particle aspect ratio ($\kappa_0$) and…
The appearance of vortex filaments, the power-law dependence of velocity and vorticity correlators and their multiscaling behavior are derived from the Navier-Stokes equation. This is possible due to interpretation of the Navier-Stokes…
In this article, we construct two families of nonsymmetrical multifractal fields. One of these families is used for the modelization of the velocity field of turbulent flows.
We find that multifractal scaling is a robust property of a large class of continuous stochastic processes, constructed as exponentials of long-memory processes. The long memory is characterized by a power law kernel with tail exponent…
Small-scale intermittency is a defining feature of fully developed fluid turbulence, marked by rare and extreme fluctuations of velocity increments and gradients that defy mean-field descriptions. Existing multifractal descriptions of…
We present a collection of eight data sets, from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range $R_\lambda…
We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…
The creativity and emergence of biological and psychological behavior are nonlinear. However, that does not necessarily mean only that the measurements of the behaviors are curvilinear. Furthermore, the linear model might fail to reduce…
In this paper, we consider the evolution of the Vortex Filament equation (VFE): \begin{equation*} \mathbf X_t = \mathbf Xs \wedge \mathbf Xss, \end{equation*} taking $M$-sided regular polygons with nonzero torsion as initial data. Using…
This paper develops a simple model of the inertial range of turbulent flow, based on a cascade of vortical filaments. A binary branching structure is proposed, involving the splitting of filaments at each step into pairs of daughter…
Pipe flow often traverses a regime where laminar and turbulent flow co-exist. Prandtl and Tietjens explained this intermittency as a feedback between the fluctuations of the internal flow resistance and the constant pressure drop driving…
We present a systematic study of a mobile impurity immersed in a three-dimensional Fermi sea of fermions at finite temperature, by using the standard non-self-consistent many-body $T$-matrix theory that is equivalent to a finite-temperature…
Elastic turbulence is the chaotic fluid motion resulting from elastic instabilities due to the addition of polymers in small concentrations at very small Reynolds ($\mbox{Re}$) numbers. Our direct numerical simulations show that elastic…
The system of a closed vortex filament is an integrable Hamiltonian one, namely, a Hamiltonian system with an infinite sequense of constants of motion in involution. An algebraic framework is given for the aim of describing differential…
In this paper, the spectrum and the decomposability of a multivariate rational function are studied by means of the effective Noether's irreducibility theorem given by Ruppert. With this approach, some new effective results are obtained. In…