Chaos in non lineal Alfven waves using the DNLS equations

The electro-dynamical tethers emit waves in structured denominated Alfven wings. The Derivative Nonlineal Schrödinger Equation (DNLS) possesses the capacity to describe the propagation of circularly polarized Alfven waves of finite amplitude in cold plasmas. The DNLS equation is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In this article is presented a theoretical and numerical analysis when the growth rate of the unstable wave is next to zero considering two damping models: Landau and resistive. The DNLS equation presents a chaotic dynamics when is consider only three wave truncation. The evolution to chaos possesses three routes: hard transition, period-doubling and intermittence of type I.

Hard transition to chaotic dynamics in Alfven wave fronts

The derivative nonlinear Schrodinger DNLS equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model equal dampings of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase, no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic relaxation oscillations that are absent for zero growth rate. This hard transition in phase-space behavior occurs for left-hand LH polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable, with damping less than about unstable wave frequency 2/4 x ion cyclotron frequency. The structural stability of the transition was explored by going into a fully 3-wave model different dampings of daughter waves,four-dimensional flow; both models differ in significant phase-space features but keep common features essential for the transition.

Reduced three-wave model to study the hard transition to chaotic dynamics in Alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model (equal damping of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase), no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic dynamics that is absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralelling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable.

Fully 3-wave model to study the hard transition to chaotic dynamics in alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. No matter how small the growth rate of the unstable wave, the four-dimensional flow for the three wave amplitudes and a relative phase, with both resistive damping and linear Landau damping, exhibits chaotic relaxation oscillations that are absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable. The parameter domain developing chaos is much broader than the corresponding domain in a reduced 3-wave model that assumes equal dampings of the daughter waves

Damping models in the truncated derivative nonlinear Schrödinger equation

Four-dimensional flow in the phase space of three amplitudes of circularly polarized Alfven waves and one relative phase, resulting from a resonant three-wave truncation of the derivative nonlinear Schrödinger equation, has been analyzed; wave 1 is linearly unstable with growth rate , and waves 2 and 3 are stable with damping 2 and 3, respectively. The dependence of gross dynamical features on the damping model as characterized by the relation between damping and wave-vector ratios, 2 /3, k2 /k3, and the polarization of the waves, is discussed; two damping models, Landau k and resistive k2, are studied in depth. Very complex dynamics, such as multiple blue sky catastrophes and chaotic attractors arising from Feigenbaum sequences, and explosive bifurcations involving Intermittency-I chaos, are shown to be associated with the existence and loss of stability of certain fixed point P of the flow. Independently of the damping model, P may only exist as against flow contraction just requiring.In the case of right-hand RH polarization, point P may exist for all models other than Landau damping; for the resistive model, P may exist for RH polarization only if 2+3/2.

Science with an electrodynamic tether

Ionospheric interaction experiments using a conductive, fully bare tether are discussed. With an optimal design, requiring 1.15 mm diameter and 7.5 km full length for a collected current of 0.87 A at day conditions, the tether radiates 0.33 watts as Fast Magnetosonic waves and 0.16 watts as Alfven waves. Secondary keV electrons are produced over a 6.5 km length, giving raise to noticeable auroral effects in the D-layer, at low geomagnetic latitudes. A preliminary design of the experiment, to be implemented on either a satellite or a Station, has been carried out. An ejector gives an initial velocity to an end mass, a free spool of tether unwinding from that mass during a first stage of deployment; other phases are monitored through the tether velocity, driving a reel with an unwinding device.

A review of electrodynamic tethers for science applications

A bare electrodynamic tether (EDT) is a conductive thin wire or tape tens of kilometres long, which is kept taut in space by gravity gradient or spinning, and is left bare of insulation to collect (and carry) current as a cylindrical Langmuir probe in an ambient magnetized plasma. An EDT is a probe in mesothermal flow at highly positive (or negative) bias, with a large or extremely large 2D sheath, which may show effects from the magnetic self-field of its current and have electrons adiabatically trapped in its ram front. Beyond technical applications ranging from propellantless propulsion to power generation in orbit, EDTs allow broad scientific uses such as generating electron beams and artificial auroras; exciting Alfven waves and whistlers; odifying the radiation belts; and exploring interplanetary space and the Jovian magnetosphere. Asymptotic analysis, numerical simulations, laboratory tests, and planned missions on EDTs are reviewed

Variational Stereo Imaging of Oceanic Waves with Statistical Constraints

An image processing observational technique for the stereoscopic reconstruction of the wave form of oceanic sea states is developed. The technique incorporates the enforcement of any given statistical wave law modeling the quasi Gaussianity of oceanic waves observed in nature. The problem is posed in a variational optimization framework, where the desired wave form is obtained as the minimizer of a cost functional that combines image observations, smoothness priors and a weak statistical constraint. The minimizer is obtained combining gradient descent and multigrid methods on the necessary optimality equations of the cost functional. Robust photometric error criteria and a spatial intensity compensation model are also developed to improve the performance of the presented image matching strategy. The weak statistical constraint is thoroughly evaluated in combination with other elements presented to reconstruct and enforce constraints on experimental stereo data, demonstrating the improvement in the estimation of the observed ocean surface.

Offshore stereo measurements of gravity waves: classical epipolar and novel variational techniques

Stereo video techniques are effective for estimating the space-time wave dynamics over an area of the ocean. Indeed, a stereo camera view allows retrieval of both spatial and temporal data whose statistical content is richer than that of time series data retrieved from point wave probes. Classical epipolar techniques and modern variational methods are reviewed to reconstruct the sea surface from the stereo pairs sequentially in time. Current improvements of the variational methods are presented.

Determination of the average ionization and thermodynamic regimes of xenon plasmas with an application to the characterization of blast waves launched in xenon clusters

Radiative shock waves play a pivotal role in the transport energy into the stellar medium. This fact has led to many efforts to scale the astrophysical phenomena to accessible laboratory conditions and their study has been highlighted as an area requiring further experimental investigations. Low density material with high atomic mass is suitable to achieve radiative regime, and, therefore, low density xenon gas is commonly used for the medium in which the radiative shock propagates. In this work the averageionization and the thermodynamicregimes of xenonplasmas are determined as functions of the matter density and temperature in a wide range of plasma conditions. The results obtained will be applied to characterize blastwaveslaunched in xenonclusters

A Variational Stereo Method for the Three-Dimensional Reconstruction of Ocean Waves

We develop a novel remote sensing technique for the observation of waves on the ocean surface. Our method infers the 3-D waveform and radiance of oceanic sea states via a variational stereo imagery formulation. In this setting, the shape and radiance of the wave surface are given by minimizers of a composite energy functional that combines a photometric matching term along with regularization terms involving the smoothness of the unknowns. The desired ocean surface shape and radiance are the solution of a system of coupled partial differential equations derived from the optimality conditions of the energy functional. The proposed method is naturally extended to study the spatiotemporal dynamics of ocean waves and applied to three sets of stereo video data. Statistical and spectral analysis are carried out. Our results provide evidence that the observed omnidirectional wavenumber spectrum S(k) decays as k-2.5 is in agreement with Zakharov's theory (1999). Furthermore, the 3-D spectrum of the reconstructed wave surface is exploited to estimate wave dispersion and currents.

Spectral-analysis-surface-waves-method in ground characterization

The prediction of train induced vibration levels in structures close to railway tracks before track construction starts is important in order to avoid having to implement costly mitigation measures afterwards. The used models require an accurate characterization of the propagation medium i.e. the soil layers. To this end the spectral analysis of surface waves (SASW) method has been chosen among the active surface waves techniques available. As dynamic source a modal sledge hammer has been used. The generated vibrations have been measured at known offsets by means of several accelerometers. There are many parameters involved in estimating the experimental dispersion curve and, later on, thickness and propagation velocities of the different layers. Tests have been carried out at the Segovia railway station. Its main building covers some of the railway tracks and vibration problems in the building should be avoided. In the paper these tests as well as the influence of several parameters on the estimated soil profile will be detailed.

Synchronization waves in geometric networks

We report synchronization of networked excitable nodes embedded in a metric space, where the connectivity properties are mostly determined by the distance between units. Such a high clustered structure, combined with the lack of long-range connections, prevents full synchronization and yields instead the emergence of synchronization waves. We show that this regime is optimal for information transmission through the system, as it enhances the options of reconstructing the topology from the dynamics. Measurements of topological and functional centralities reveal that the wave-synchronization state allows detection of the most structurally relevant nodes from a single observation of the dynamics, without any a priori information on the model equations ruling the evolution of the ensemble

Influence of Crystal Quality on the Excitation and Propagation of Surface and Bulk Acoustic Waves in Polycrystalline AlN Films

We investigate the excitation and propagation of acoustic waves in polycrystalline aluminum nitride films along the directions parallel and normal to the c-axis. Longitudinal and transverse propagations are assessed through the frequency response of surface acoustic wave and bulk acoustic wave devices fabricated on films of different crystal qualities. The crystalline properties significantly affect the electromechanical coupling factors and acoustic properties of the piezoelectric layers. The presence of misoriented grains produces an overall decrease of the piezoelectric activity, degrading more severely the excitation and propagation of waves traveling transversally to the c-axis. It is suggested that the presence of such crystalline defects in c-axis-oriented films reduces the mechanical coherence between grains and hinders the transverse deformation of the film when the electric field is applied parallel to the surface.

Compression of matter by hypersphsericla shock waves

A novel compression scheme is proposed, in which hollow targets with specifically curved structures initially filled with uniform matter, are driven by converging shock waves. The self-similar dynamics is analyzed for converging and diverging shock waves. The shock-compressed densities and pressures are much higher than those achieved using spherical shocks due to the geometric accumulation. Dynamic behavior is demonstrated using two-dimensional hydrodynamic simulations. The linear stability analysis for the spherical geometry reveals a new dispersion relation with cut-off mode numbers as a function of the specific heat ratio, above which eigenmode perturbations are smeared out in the converging phase.