Collective and relative variables for a classical Klein-Gordon field

In this paper a set of canonical collective variables is defined for a classical Klein-Gordon field and the problem of the definition of a set of canonical relative variables is discussed. This last point is approached by means of a harmonic analysis is momentum space. This analysis shows that the relative variables can be defined if certain conditions are fulfilled by the field configurations. These conditions are expressed by the vanishing of a set of conserved quantities, referred to as supertranslations since as canonical observables they generate a set of canonical transformations whose algebra is the same as that which arises in the study of the asymptotic behaviour of the metric of an isolated system in General Relativity.Comment: 47 pages, no figur

Time Scaling of Chaotic Systems: Application to Secure Communications

The paper deals with time-scaling transformations of dynamical systems. Such scaling functions operate a change of coordinates on the time axis of the system trajectories preserving its phase portrait. Exploiting this property, a chaos encryption technique to transmit a binary signal through an analog channel is proposed. The scheme is based on a suitable time-scaling function which plays the role of a private key. The encoded transmitted signal is proved to resist known decryption attacks offering a secure and reliable communication.Comment: 15 pages, 7 figure

Metriplectic framework for dissipative magneto-hydrodynamics

International audienceThe metriplectic framework, which allows for the formulation of an algebraic structure for dissipative systems, is applied to visco-resistive Magneto-Hydrodynamics (MHD), adapting what had already been done for non-ideal Hydrodynamics (HD). The result is obtained by extending the HD symmetric bracket and free energy to include magnetic field dynamics and resistive dissipation. The correct equations of motion are obtained once one of the Casimirs of the Poisson bracket for ideal MHD is identified with the total thermodynamic entropy of the plasma. The metriplectic framework of MHD is shown to be invariant under the Galileo Group. The metriplectic structure also permits us to obtain the asymptotic equilibria toward which the dynamics of the system evolves. This scheme is finally adapted to the two-dimensional incompressible resistive MHD, that is of major use in many applications

Determining the verse of magnetic turbulent cascades in the Earth's magnetospheric cusp via transfer entropy analysis: preliminary results

International audienceThe inter-scale coupling in the dynamics of the magnetic field in the Earth's magnetospheric cusp is studied with the technique of transfer entropy. This is a non-linear data analysis technique conceived to determine which is the process that plays the role of the "dynamical driver" between two processes interacting. The time series of the magnetic field components measured along the trajectory of a spacecraft through the cusp are decomposed via continuous wavelets, so a time series of the square modulus of the wavelet coefficients may be associated to each scale ? considered. The coupling between to two nearby scales is studied, with the purpose of singling out turbulent cascade directions from large to small scales and viceversa. Preliminary physical conclusions are proposed

Imaging of the equatorial ionosphere

The equatorial anomaly is the dominant structure in free electron concentration in the tropical ionosphere. Due to its edges (crests) which are characterised by steep latitudinal gradients in TEC and are temporally and spatially variable, it is one of the ionospheric regions most difficult to image with inversion methods. In this paper we reconstruct an International Reference Ionosphere model of the equatorial ionosphere by employing a grid of virtual ground GPS receivers and actual GPS satellite positions. The MIDAS algorithm, an inversion method for reconstructing the ionosphere as a linear composition of given empirical orthogonal functions, is used. Comparing the true model ionosphere with the resulting images a fine tuning of the basis functions (vertical profile contraints) in the inversion is realised

On Geometrical Invariants of the Magnetic Field Gradient Tensor in Turbulent Space Plasmas: Scale Variability in the Inertial Range

In a recent paper, Consolini et al. investigated the statistics of geometrical invariants of the coarse-grained gradient tensor of plasma velocity for a case study of space plasma turbulence. They showed how, at spatial scales near the proton inertial length, there is evidence for the occurrence of dissipation structures along the Vieillefosse's tail. Here, we extend the previous analysis to the statistics of the geometrical invariants of the magnetic field coarse-grained gradient tensor, computed using magnetic field measurements by the ESA-Cluster mission in the solar wind region. In detail, we investigate the evolution of the joint probability distribution functions of the magnetic geometrical invariants at different scales in the inertial range of turbulent solar wind. The results show a clear dependence of the joint statistics of geometrical invariants on the distance from the proton inertial length scale in the inertial range, which seems to be compatible with a variation of the dimensionality of the fluctuation field from two dimensions to three dimensions at the smallest scales. Evidence of an increasing role of the ingoing spiral saddle and current-associated dissipation structures is found at the smallest investigated scales, where dissipation can occur