ALBERT

Description: We propose an equivalence class of nonstationary Gaussian stochastic processes defined in the wavelet domain. These processes are characterized by means of wavelet multipliers and exhibit well-defined time-dependent spectral properties. They allow one to generate realizations of any wavelet spectrum. Based on this framework, we study the estimation of continuous wavelet spectra, i.e., we calculate variance and bias of arbitrary estimated continuous wavelet spectra. Finally, we develop an areawise significance test for continuous wavelet spectra to overcome the difficulties of multiple testing; it uses basic properties of continuous wavelet transform to decide whether a pointwise significant result is a real feature of the process or indistinguishable from typical stochastic fluctuations. This test is compared to the conventional one in terms of sensitivity and specificity. A software package for continuous wavelet spectral analysis and synthesis is presented.

Description: The first detailed quantitative observations of the two-dimensional collapse of a granular column along a horizontal channel are presented for a variety of materials. Together with the complementary study for the axisymmetric situation, we conclude that for granular collapses the generally accepted approaches, that are highly dependent on frictional parameters, do not describe the main flow phenomena. The motion divides in two main flow regimes at a∼1.8, where the aspect ratio a=hi∕di and hi and di are the initial height and width of the column. We describe the details of collapse by emphasizing the sequential occurrence of a main spreading followed by a final avalanching phase. For the low a regime, a〈1.8, we derive descriptions of the final geometry by direct physical arguments. For the large a regime, a〉1.8, we determine that nearly all details of the collapse, including the position of the flow front as a function of time, the emplacement time, the self-similar final profiles, and especially their maximum vertical and horizontal extension, are established during the spreading phase and can be expressed in terms of the initial geometrical parameters but are independent of basal and internal friction parameters.

Description: Modern models for the development and evolution of the geochemical heterogeneity in the Earth's mantle and the genesis of mantle magmas attach much importance to the processes of interaction between deepseated rocks and metasomatic fluids, which are able, when occurring under mantle conditions, to dissolve significant amounts of major and trace elements (see, for example, [1]). Fluorine is one of the major anions of natural fluids and also one of the principal complex-forming ligands of several metals. To evaluate the possible role of fluorine in the processes of mantle magma genesis and to identify the source of this element in natural magmas in various geodynamic environments, it is necessary to know the fluorine concentration in primitive mantle melts. These data are still relatively scarce, particularly for low alkaline magmas [2-4]. The fluorine concentrations in magmas from suprasubduction zones, whose genesis is largely controlled by the interaction between mantle rocks and fluids, remain poorly known and need further refinement. Data presented in this paper are among the first to characterize the concentrations of fluorine in primitive magmas of suprasubduction zones. These data were obtained by secondary ion mass spectrometry of chill glasses from the lava complex of the Troodos ophiolites in Cyprus. Along with information on the concentrations of major and trace elements, H2O, and Cl in the glasses, our results make it possible to utilize the example of the Troodos ophiolites to characterize the main regularities in the geochemistry of fluorine during the origin of magmas above subduction zones and to assay the contributions of various components that participated in the processes of mantle melting. These data are among the first to demonstrate that subduction-related melts became enriched in F relative to LREE.

Description: Results of an experimental study of a Hopf bifurcation with broken translation symmetry that organizes chaotic homoclinic dynamics from a T2 torus in a fluid flow as a direct consequence of physical boundaries are presented. It is shown that the central features of the theory of Hopf bifurcation in O(2)-symmetric systems where the translation symmetry is broken are robust and are appropriate to describe the appearance of modulated waves, homoclinic bifurcation, Takens-Bogdanov point, and chaotic dynamics in a fluid flow experiment.

Description: Experimental evidence for standing waves resulting from a supercritical Hopf bifurcation that appears as the first pattern-forming instability in counterrotating Taylor-Couette flow is presented. Depending on the aspect ratio two different types of standing waves, denoted as SW0 and SWp, could be observed. Both modes have an azimuthal wave number m51 but differ in symmetry. While for SWp , a spatiotemporal glide-reflection symmetry could be found, SW0 is purely spatial reflection symmetric. The transition between the two modes is found to be organized in a cusp bifurcation unfolded by variations of the aspect ratio. The ‘‘classical’’ spiral vortex flow appears in this control parameter regime only as a result of a secondary steady bifurcation from SW0. This transition is found to be either subcritical or supercritical. The experimentally observed bifurcation structure has been predicted by theory of Hopf bifurcation to spiral vortex flow in finite counterrotating Taylor-Couette systems.