ALBERT

Description: Nonlinear elastic response in rock is established as a robust and representative characteristic rock rather than a curiosity. We show measurements of this behaviour from a variety of experiments on rock taken over many orders of magnitude in strain and frequency. The evidence leads to a pattern of unifying behaviour in rock: (1) Nonlinear response in rock is ubiquitous. (2) The response takes place over a large frequency interval (dc to 105 kHz at least). (3) The response not only occurs, as is commonly appreciated, large strains but also at small strains where this behaviour and the manifestations of this behaviour are commonly disregarded.

Description: In this paper, we present evidence that intermittency of Eulerian and Lagrangian turbulence of ocean temperature and plankton fields is multifractal and furthermore can be analysed with the help of universal multifractals. We analyse time series of temperature and in vivo fluorescence taken from a drifter in the mixed coastal waters of the eastern English Channel. Two analysis techniques are used to compute the fundamental universal multifiractal parameters, which describe all the statistics of the turbulent fluctuations: the analysis of the scale invariant structure function exponent ζ(q) and the Double Trace Moment technique. At small scales, we do not detect any significant difference between the universal multifiractal behavior of temperature and fluorescence in an Eulerian framework. This supports the hypothesis that the latter is passively advected with the flow as the former. On the one hand, we show that large scale measurements are Lagrangian and indeed we obtain for temperature fluctuations a ω2 power spectrum corresponding to the theoretical scaling of a Lagrangian passive scalar. Furthermore, we show that Lagrangian temperature fluctuations are multiscaling and intermittent. On the other hand, the flatter slope at large scales of the fluorescence power spectrum points out that the plankton is at these scales a "biologically active" scalar.

Description: We study theoretically the physical origin of the proposed discrete scale invariance of earthquake processes, at the origin of the universal log-periodic corrections to scaling, recently discovered in regional seismic activity (Sornette and Sammis (1995)). The discrete scaling symmetries which may be present at smaller scales are shown to be robust on a global scale with respect to disorder. Furthermore, a single complex exponent is sufficient in practice to capture the essential properties of the leading correction to scaling, whose real part may be renormalized by disorder, and thus be specific to the system. We then propose a new mechanism for discrete scale invariance, based on the interplay between dynamics and disorder. The existence of non-linear corrections to the renormalization group flow implies that an earthquake is not an isolated "critical point", but is accompanied by an embedded set of "critical points", its foreshocks and any subsequent shocks for which it may be a foreshock.

Description: The ESA/NASA Cluster mission has four identical satellites and is due for launch at the end of 1995. It will provide a unique opportunity to study medium scale processes in the region from inside the magnetopause to the solar wind. The polar orbit will allow measurements in the cusp and along auroral field lines, both regions where turbulence is to be expected. Five of the eleven instruments on each payload form the Wave Experiment Consortium (WEC); EFW, STAFF, VMISPER, WBD and DWP. The WEC is capable of a wide variety of wave and turbulence measurements. This paper outlines these capabilities and describes the form of the data which will be collected. The paper gives a discussion of how the WEC data may be analysed so as to give an insight into the non-linear processes which occur in these regions of the space plasmas. There are many ways in which a plasma may be considered to behave in a non-linear manner. We concentrate on how the spatio-temporal turbulence in the plasma may be investigated so as to yield the energy spectrum with respect to both the frequency and wave number.

Description: We examine the time series of cosmic ray (CR) intensity recorded by two neutron monitors (NMs) at medium latitudes for scaling properties on time scales shorter than the diurnal variation. Scaling of the data with 10 sec as well as I min resolution is shown to be complicated, indicating that there is probably not a unique process governing the CR fluctuations in the whole interval studied. For T 〈 20 min the general characteristics are similar to those of white noise. Above 40-60 min the scaling characteristics are dependent on the level of interplanetary disturbance. This is consistent with the concept of scattering CRs by inhomogeneities of the interplanetary magnetic field (IMF). With increasing interplanetary turbulence the dimensionality of the CR time series decreases. The region of stable scaling is, however, narrow, only up to 6 hours. Multifractality signatures in the region 1-6 hours are similar to those in the IMF, however the deviations from monofractality are relatively small.

Description: The recent availability of complete three dimensional samples of galaxies and clusters permits a direct study of their spatial properties. We present a brief review of galaxy correlations based on the methods modern statistical Physics. These methods which able to identify self-similar and non-analytical prop ties, allow us to test the usual homogeneity assumption of luminous matter distribution. We conclude that both the three dimensional prop ties, and the angular log N - log S relation, point out the fact that the distribution of galaxies and clusters fractal with D ≈ 2 up to the deepest scale probed luminous matter (≈≥ 1000h-1 Mpc). This result has important implications for the theoretical framework that should be adopted.

Description: Statistical properties of collisionless plasmas in the vicinity of the Earth's bow shock are investigated with the aim to characterize the intermittent behaviour of non- magnetohydrodynamic turbulence. The structure functions of the fluctuating magnetic field reveal an increasing departure from Gaussianity at small scales, which is similar to that observed in solar wind turbulence and is surprisingly little affected by the abrupt shock transition. While these results may be the signature of a multifractal process, a deeper inspection reveals caveats in such an interpretation. Several effects, including the anisotropy of the wavefield, the violation of the Taylor hypothesis and the occasional occurrence of coherent wave packets, strongly affect the higher order statistical properties. Most of the small differences observed between the up- and downstream sides of the shock can be ascribed to the occurrence of discrete whistler wavetrains, while the wavefield itself is much less intermittent. It is also shown how the finite length of the records prohibits a reliable estimation of structure functions beyond the fourth order. These results preclude an unambiguous identification of underlying models for intermittency.

Description: Synthetic Aperture Radar (SAR) images of the ocean yield a lot of information on the sea-state surface providing that the mapping process between the surface and the image is clearly defined. However it is well known that SAR images exhibit non-gaussian statistics and that the motion of the scatterers on the surface, while the image is being formed, may yield to nonlinearities. The detection and quantification of these nonlinearities are made possible by using Higher Order Spectra (HOS) methods and more specifically, bispectrum estimation. The development of the latter method allowed us to find phase relations between different parts of the image and to recognise their level of coupling, i.e. if and how waves of different wavelengths interacted nonlinearly. This information is quite important as the usual models assume strong nonlinearities when the waves are propagating in the azimuthal direction (i.e. along the satellite track) and almost no nonlinearities when propagating in the range direction. In this paper, the mapping of the ocean surface to the SAR image is reinterpreted and a specific model (i.e. a Second Order Volterra Model) is introduced. The nonlinearities are thus explained as either produced by a nonlinear system or due to waves propagating into selected directions (azimuth or range) and interacting during image formation. It is shown that quadratic nonlinearities occur for waves propagating near the range direction while for those travelling in the azimuthal direction the nonlinearities, when present, are mostly due to wave interactions but are almost completely removed by the filtering effect coming from the surface motion itself (azimuth cut-off). An inherent quadratic interaction filtering (azimuth high pass filter) is also present. But some other effects, apparently nonlinear, are not detected with the methods described here, meaning that either the usual relation developed for the Ocean-to-SAR transform is somewhat incomplete, although the mechanisms leading to its formulation seem to be correct, or that these nonlinearities cannot be detected in the classical bispectrum theory.

Description: Using a recently proposed technique for statistical analysis of non-gridded satellite altimeter data, regime of long equatorially-trapped baroclinic Rossby waves is studied. One-dimensional spatial and spatiotemporal autocorrelation functions of sea surface height (SSH) variations yield a broad spectrum of baroclinic Rossby waves and permit determination of their propagation speed. The 1-d wavenumber spectrum of zonal variations is given by a power-law k-2 on scales from about 103 km to 104 km. We demonstrate that the observed wave regime exhibits features of soliton turbulence developing in the long baroclinic Rossby waves. However, being limited to second statistical moments, the present analysis does not allow us to rule out a possibility of weak wave turbulence.

Description: The centre manifold approach is used to derive an approximate equation for nonlinear waves propagating in a sheared, stably stratified fluid layer. The evolution equation matches limiting forms derived by other methods, including the inviscid, long wave approximation leading to the Korteweg- deVries equation. The model given here allows large modulations of the height of the waveguide. This permits the crude modelling of shear layer instabilities at the upper material surface of the waveguide which excite solitary internal waves in the waveguide. An energy argument is used to support the existence of these waves.