Emergence of a non trivial fluctuating phase in the XY model on regular networks

We study an XY-rotor model on regular one dimensional lattices by varying the number of neighbours. The parameter $2\ge\gamma\ge1$ is defined. $\gamma=2$ corresponds to mean field and $\gamma=1$ to nearest neighbours coupling. We find that for $\gamma<1.5$ the system does not exhibit a phase transition, while for $\gamma > 1.5$ the mean field second order transition is recovered. For the critical value $\gamma=\gamma_c=1.5$, the systems can be in a non trivial fluctuating phase for whichthe magnetisation shows important fluctuations in a given temperature range, implying an infinite susceptibility. For all values of $\gamma$ the magnetisation is computed analytically in the low temperatures range and the magnetised versus non-magnetised state which depends on the value of $\gamma$ is recovered, confirming the critical value $\gamma_{c}=1.5$

Unveiling the nature of out-of-equilibrium phase transitions in a system with long-range interactions

Recently, there has been some vigorous interest in the out-of-equilibrium quasistationary states (QSSs), with lifetimes diverging with the number N of degrees of freedom, emerging from numerical simulations of the ferromagnetic XY Hamiltonian Mean Field (HMF) starting from some special initial conditions. Phase transitions have been reported between low-energy magnetized QSSs and large-energy unexpected, antiferromagnetic-like, QSSs with low magnetization. This issue is addressed here in the Vlasov N \rightarrow \infty limit. It is argued that the time-asymptotic states emerging in the Vlasov limit can be related to simple generic time-asymptotic forms for the force field. The proposed picture unveils the nature of the out-of-equilibrium phase transitions reported for the ferromagnetic HMF: this is a bifurcation point connecting an effective integrable Vlasov one-particle time-asymptotic dynamics to a partly ergodic one which means a brutal open-up of the Vlasov one-particle phase space. Illustration is given by investigating the time-asymptotic value of the magnetization at the phase transition, under the assumption of a sufficiently rapid time-asymptotic decay of the transient force field

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.Comment: 18 pages, 15 figure

Chaotic motion of charged particles in toroidal magnetic configurations

We study the motion of a charged particle in a tokamak magnetic field and discuss its chaotic nature. Contrary to most of recent studies, we do not make any assumption on any constant of the motion and solve numerically the cyclotron gyration using Hamiltonian formalism. We take advantage of a symplectic integrator allowing us to make long-time simulations. First considering an idealized magnetic configuration, we add a non generic perturbation corresponding to a magnetic ripple, breaking one of the invariant of the motion. Chaotic motion is then observed and opens questions about the link between chaos of magnetic field lines and chaos of particle trajectories. Second, we return to a axi-symmetric configuration and tune the safety factor (magnetic configuration) in order to recover chaotic motion. In this last setting with two constants of the motion, the presence of chaos implies that no third global constant exists, we highlight this fact by looking at variations of the first order of the magnetic moment in this chaotic setting. We are facing a mixed phase space with both regular and chaotic regions and point out the difficulties in performing a global reduction such as gyrokinetics

Anomalous transport in Charney-Hasegawa-Mima flows

Transport properties of particles evolving in a system governed by the Charney-Hasegawa-Mima equation are investigated. Transport is found to be anomalous with a non linear evolution of the second moments with time. The origin of this anomaly is traced back to the presence of chaotic jets within the flow. All characteristic transport exponents have a similar value around $\mu=1.75$, which is also the one found for simple point vortex flows in the literature, indicating some kind of universality. Moreover the law $\gamma=\mu+1$ linking the trapping time exponent within jets to the transport exponent is confirmed and an accumulation towards zero of the spectrum of finite time Lyapunov exponent is observed. The localization of a jet is performed, and its structure is analyzed. It is clearly shown that despite a regular coarse grained picture of the jet, motion within the jet appears as chaotic but chaos is bounded on successive small scales.Comment: revised versio

Stabilizing the intensity of a wave amplified by a beam of particles

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 re-shaping the macro-particle. This strategy involves the study of the linear stability (using the residue method) of selected periodic orbits of a mean-field model. As parameters of an additional perturbation are varied, bifurcations occur in the system which have drastic effect on the modification of the self-consistent dynamics, and in particular, of the macro-particle. We show how to obtain an appropriate tuning of the parameters which is able to strongly decrease the oscillations of the intensity without reducing its mean-value

Effect of an alkyl substituent and spacer length in benzene-centered tripodal diglycolamides on the sequestration of minor actinides

Three benzene-centered tripodal diglycolamide (Bz-T-DGA) ligands, where diglycolamide (DGA) moieties are tethered to the central benzene ring through a methylene spacer and having either a hydrogen atom (LI) or an isopentyl group (LII) attached to the N-atom, and DGA moieties attached via an ethylene spacer and having an isopentyl group attached to the N-atom (LIII), were studied for their complexation and extraction abilities towards trivalent actinides and lanthanides. The distribution ratio of Am(iii) and Eu(iii) with 1 mmol L-1 ligand in 5% iso-decanol/n-dodecane followed the order: LII &gt; LIII &gt; LI. The substitution of the H atom with the isopentyl group on the N-atom of the DGA moieties resulted in two orders of magnitude enhancement in the extraction ability of the ligand. On the other hand, increase in the spacer length between the benzene ring and the DGA moieties resulted in several fold reduction in the extraction ability of the ligand. Spectroscopic studies with Eu3+ ions in acetonitrile also confirmed the metal/ligand complex formation constant in the order: LII &gt; LIII &gt; LI. Luminescence decay lifetimes of Eu3+/ligand complexes confirmed the absence of water molecules and that all the primary coordination sites of the metal ion are occupied by the ligands.</p

Syphilis with HIV in Florence, 2003-2009: a 7-year epidemiological study.

SUMMARYThe aims of this study were to describe the trend of acquired syphilis in the city of Florence and its province over a 7-year period, to investigate sexual behaviours in the syphilis-infected population and to analyse syphilis/HIV co-infection. A total of 259 patients were classified according to age, sex and HIV infection. We estimated that from 2004 to 2008 cases increased by 248%. Most patients with concurrent HIV infection were male (31–45 years), but 40- to 60-year-old men who had sex with men predominated in both male and HIV-positive patients. Oral sex was identified as the most significant route of transmission, although most patients did not consider it so. Late-presenters with HIV accounted for 33% of HIV-positive patients: they were unaware of their HIV status and showed syphilis lesions only. In these cases, syphilis heralded the presence of HIV infection and allowed earlier diagnosis

Targeted mixing in an array of alternating vortices

Transport and mixing properties of passive particles advected by an array of vortices are investigated. Starting from the integrable case, it is shown that a special class of perturbations allows one to preserve separatrices which act as effective transport barriers, while triggering chaotic advection. In this setting, mixing within the two dynamical barriers is enhanced while long range transport is prevented. A numerical analysis of mixing properties depending on parameter values is performed; regions for which optimal mixing is achieved are proposed. Robustness of the targeted mixing properties regarding errors in the applied perturbation are considered, as well as slip/no-slip boundary conditions for the flow