arXiv subjects

X. Leoncini

Publications and source records attributed to X. Leoncini.

6 recordsLinked to original sources

arXiv2020

Sticky islands in stochastic webs and anomalous chaotic cross-field particle transport by ExB electron drift instability

The ExB electron drift instability, present in many plasma devices, is an important agent in cross-field particle transport. In presence of a resulting low frequency electrostatic wave, the motion of a charged particle becomes chaotic and generates a stochastic web in phase space. We define a scaling exponent to characterise transport in phase space and we show that the transport is anomalous, of super-diffusive type. Given the values of the model parameters, the trajectories stick to different kinds of islands in phase space, and their different sticking time power-law statistics generate successive regimes of the super-diffusive transport.

physics.plasm-ph↗

arXiv2013

Fractional Fourier detection of Lévy Flights: application to Hamiltonian chaotic trajectories

A signal processing method designed for the detection of linear (coherent) behaviors among random fluctuations is presented. It is dedicated to the study of data recorded from nonlinear physical systems. More precisely the method is suited for signals having chaotic variations and sporadically appearing regular linear patterns, possibly impaired by noise. We use time-frequency techniques and the Fractional Fourier transform in order to make it robust and easily implementable. The method is illustrated with an example of application: the analysis of chaotic trajectories of advected passive particles. The signal has a chaotic behavior and encounter Lévy flights (straight lines). The method is able to detect and quantify these ballistic transport regions, even in noisy situations.

nlin.CD↗

arXiv2008

Stabilizing the intensity for a Hamiltonian model of the FEL

The intensity of an electromagnetic wave interacting self-consistently with a beam of charged particles, as in a Free Electron Laser, displays large oscillations due to an aggregate of particles, called the macro-particle. In this article, we propose a strategy to stabilize the intensity by destabilizing the macro-particle. This strategy involves the study of the linear stability of a specific periodic orbit of a mean-field model. As a control parameter - the amplitude of an external wave - is varied, a bifurcation occur in the system which has drastic effects on the self-consistent dynamics, and in particular, on the macro-particle. We show how to obtain an appropriate tuning of the control parameter which is able to strongly decrease the oscillations of the intensity without reducing its mean-value.

physics.plasm-ph↗

arXiv2006

Chaotic Advection near 3-Vortex Collapse

Dynamical and statistical properties of tracer advection are studied in a family of flows produced by three point-vortices of different signs. A collapse of all three vortices to a single point is then possible. Tracer dynamics is analyzed by numerical construction of Poincaré sections, and is found to be strongly chaotic: advection pattern in the region around the center of vorticity is dominated by a well developed stochastic sea, which grows as the vortex system approaches the collapse; at the same time, the islands of regular motion around vortices, known as vortex cores, shrink. An estimation of the core's radii from the minimum distance of vortex approach to each other is obtained. Tracer transport was found to be anomalous: for all of the three numerically investigated cases, the variance of the tracer distribution grows faster than a linear function of time, corresponding to a super-diffusive regime. The transport exponent varies with time decades, implying the presence of multi-fractal transport features. Yet, its value is never too far from 3/2, indicating some kind of universality. Statistics of Poincaré recurrences is non-Poissonian: distributions have long power-law tails. The anomalous properties of tracer statistics are the result of the complex structure of the advection phase space, in particular, of strong stickiness on the boundaries between the regions of chaotic and regular motion. The role of the different phase space structures involved in this phenomenon is analyzed. Based on this analysis, a kinetic description is constructed, which takes into account different time and space scalings by using a fractional equation.

nlin.CD↗

arXiv2002

Passive Tracer Dynamics in 4 Point-Vortex Flow

The advection of passive tracers in a system of 4 identical point vortices is studied when the motion of the vortices is chaotic. The phenomenon of vortex-pairing has been observed and statistics of the pairing time is computed. The distribution exhibits a power-law tail with exponent $\sim 3.6$ implying finite average pairing time. This exponents is in agreement with its computed analytical estimate of 3.5. Tracer motion is studied for a chosen initial condition of the vortex system. Accessible phase space is investigated. The size of the cores around the vortices is well approximated by the minimum inter-vortex distance and stickiness to these cores is observed. We investigate the origin of stickiness which we link to the phenomenon of vortex pairing and jumps of tracers between cores. Motion within the core is considered and fluctuations are shown to scale with tracer-vortex distance $r$ as $r^{6}$. No outward or inward diffusion of tracers are observed. This investigation allows the separation of the accessible phase space in four distinct regions, each with its own specific properties: the region within the cores, the reunion of the periphery of all cores, the region where vortex motion is restricted and finally the far-field region. We speculate that the stickiness to the cores induced by vortex-pairings influences the long-time behavior of tracers and their anomalous diffusion.

physics.flu-dyn↗

arXiv2000

Motion of Three Vortices near Collapse

A system of three point vortices in an unbounded plane has a special family of self-similarly contracting or expanding solutions: during the motion, vortex triangle remains similar to the original one, while its area decreases (grows) at a constant rate. A contracting configuration brings three vortices to a single point in a finite time; this phenomenon known as vortex collapse is of principal importance for many-vortex systems. Dynamics of close-to-collapse vortex configurations depends on the way the collapse conditions are violated. Using an effective potential representation, a detailed quantitative analysis of all the different types of near-collapse dynamics is performed when two of the vortices are identical. We discuss time and length scales, emerging in the problem, and their behavior as the initial vortex triangle is approaching to an exact collapse configuration. Different types of critical behaviors, such as logarithmic or power-law divergences are exhibited, which emphasizes the importance of the way the collapse is approached. Period asymptotics for all singular cases are presented as functions of the initial vortices configurations. Special features of passive particle mixing by a near-collapse flows are illustrated numerically.

physics.flu-dyn↗