Related papers: Multifractality and polygonal vortex filaments
Soliton gas or soliton turbulence is a subject of intense studies due to its great importance to optics, hydrodynamics, electricity, chemistry, biology and plasma physics. Usually, this term is used for integrable models where solitons…
The dynamics of many natural systems is dominated by non-linear waves propagating through the medium. We show that the dynamics of non-linear wave fronts with positive surface tension can be formulated as a gradient system. The variational…
The title of the paper coincides with the title of a paragraph in the famous book by U. Frisch (1995)on classical turbulence. In this paragraph the author discussed the role of statistical dynamics of vortex filaments in the theory of…
Riemann's non-differentiable function is a celebrated example of a continuous but almost nowhere differentiable function. There is strong numeric evidence that one of its complex versions represents a geometric trajectory in experiments…
We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs to, we obtain deterministic upper…
The probability density functions measured by Lewis and Swinney for turbulent Couette-Taylor flow, observed by Bodenschatz and co-workers in the Lagrangian measurement of particle accelerations and those obtained in the DNS by Gotoh et al.…
Wave propagation is studied in a sufficiently anisotropic random medium that backscattering along one direction can be neglected. A Fokker-Planck equation is derived the solution to which would provide a complete statistical description of…
We undertake a general study of multifractal phenomena for functions. We show that the existence of several kinds of multifractal functions can be easily deduced from an abstract statement, leading to new results. This general approach does…
We present a hydrodynamic model of spreading epithelial monolayers as polar viscous fluids, with active contractility and traction on the substrate. The combination of both active forces generate an instability that leads to nonlinear…
Empirical time series of inter-event or waiting times are investigated using a modified Multifractal Detrended Fluctuation Analysis operating on fluctuations of mean detrended dynamics. The core of the extended multifractal analysis is the…
This paper concerns the study of some special ordered structures in turbulent flows. In particular, a systematic and relevant methodology is proposed to construct non trivial and non radial rotating vortices with non necessarily uniform…
In this paper, we study nonlinear desingularization of steady vortex rings of three-dimensional incompressible Euler flows. We construct a family of steady vortex rings (with and without swirl) which constitutes a desingularization of the…
We study the statistical properties of coherent, small-scales, filamentary-like structures in Turbulence. In order to follow in time such complex spatial structures, we integrate Lagrangian and Eulerian measurements by seeding the flow with…
Using a two-dimensional fluid description, we investigate the nonlinear radial-longitudinal dynamics of intense beams in storage rings and cyclotrons. With a multiscale analysis separating the time scale associated with the betatron motion…
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…
In the spirit of Prandtl's conjecture of 1926, for turbulence at high Reynolds number we present an analogy with the kinetic theory of gases, with dipoles made of quasi-rigid and 'dressed' vortex tubes as frictionless, incompressible but…
We consider the multifractal formalism for the dynamics of semigroups of rational maps on the Riemann sphere and random complex dynamical systems. We elaborate a multifractal analysis of level sets given by quotients of Birkhoff sums with…
In this thesis, we consider the dynamics of vortices in the easy plane insulating ferromagnet in two dimensions. In addition to the quasiparticle excitations, here spin waves or magnons, this magnetic system admits a family of vortex…
In this paper, by making use of Duan's topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit points and…
We experimentally study the properties of mean and most probable velocity fields in a turbulent von K\'arm\'an flow. These fields are found to be described by two families of functions, as predicted by a recent statistical mechanics study…