Energetics, skeletal dynamics and long-term predictions in Kolmogorov-Lorenz systems

We study a particular return map for a class of low dimensional chaotic models called Kolmogorov Lorenz systems, which received an elegant general Hamiltonian description and includes also the famous Lorenz63 case, from the viewpoint of energy and Casimir balance. In particular it is considered in detail a subclass of these models, precisely those obtained from the Lorenz63 by a small perturbation on the standard parameters, which includes for example the forced Lorenz case in Ref.[6]. The paper is divided into two parts. In the first part the extremes of the mentioned state functions are considered, which define an invariant manifold, used to construct an appropriate Poincare surface for our return map. From the experimental observation of the simple orbital motion around the two unstable fixed points, together with the circumstance that these orbits are classified by their energy or Casimir maximum, we construct a conceptually simple skeletal dynamics valid within our sub class, reproducing quite well the Lorenz map for Casimir. This energetic approach sheds some light on the physical mechanism underlying regime transitions. The second part of the paper is devoted to the investigation of a new type of maximum energy based long term predictions, by which the knowledge of a particular maximum energy shell amounts to the knowledge of the future (qualitative) behaviour of the system. It is shown that, in this respect, a local analysis of predictability is not appropriate for a complete characterization of this behaviour. A perspective on the possible extensions of this type of predictability analysis to more realistic cases in (geo)fluid dynamics is discussed at the end of the paper.Comment: 21 pages, 14 figure

Shear-banding in a lyotropic lamellar phase, Part 2: Temporal fluctuations

We analyze the temporal fluctuations of the flow field associated to a shear-induced transition in a lyotropic lamellar phase: the layering transition of the onion texture. In the first part of this work [Salmon et al., submitted to Phys. Rev. E], we have evidenced banded flows at the onset of this shear-induced transition which are well accounted for by the classical picture of shear-banding. In the present paper, we focus on the temporal fluctuations of the flow field recorded in the coexistence domain. These striking dynamics are very slow (100--1000s) and cannot be due to external mechanical noise. Using velocimetry coupled to structural measurements, we show that these fluctuations are due to a motion of the interface separating the two differently sheared bands. Such a motion seems to be governed by the fluctuations of $\sigma^\star$, the local stress at the interface between the two bands. Our results thus provide more evidence for the relevance of the classical mechanical approach of shear-banding even if the mechanism leading to the fluctuations of $\sigma^\star$ remains unclear

Surface compositional mapping by spectral ratioing of ERTS-1 MSS data in the Wind River Basin and Range, Wyoming

The author has identified the following significant results. ERTS data collected in August and October 1972 were processed on digital and special purpose analog recognition computers using ratio enhancement and pattern recognition. Ratios of band-averaged laboratory reflectances of some minerals and rock types known to be in the scene compared favorably with ratios derived from the data by ratio normalization procedures. A single ratio display and density slice of the visible channels of ERTS MSS data, Channel 5/Channel 4 (R5,4), separated the Triassic Chugwater formation (redbeds) from other formations present and may have enhanced iron oxide minerals present at the surface in abundance. Comparison of data sets collected over the same area at two different times of the year by digital processing indicated that spectral variation due to environmental factors was reduced by ratio processing

Slow flows of an relativistic perfect fluid in a static gravitational field

Relativistic hydrodynamics of an isentropic fluid in a gravitational field is considered as the particular example from the family of Lagrangian hydrodynamic-type systems which possess an infinite set of integrals of motion due to the symmetry of Lagrangian with respect to relabeling of fluid particle labels. Flows with fixed topology of the vorticity are investigated in quasi-static regime, when deviations of the space-time metric and the density of fluid from the corresponding equilibrium configuration are negligibly small. On the base of the variational principle for frozen-in vortex lines dynamics, the equation of motion for a thin relativistic vortex filament is derived in the local induction approximation.Comment: 4 pages, revtex, no figur

Velocity profiles in shear-banding wormlike micelles

Using Dynamic Light Scattering in heterodyne mode, we measure velocity profiles in a much studied system of wormlike micelles (CPCl/NaSal) known to exhibit both shear-banding and stress plateau behavior. Our data provide evidence for the simplest shear-banding scenario, according to which the effective viscosity drop in the system is due to the nucleation and growth of a highly sheared band in the gap, whose thickness linearly increases with the imposed shear rate. We discuss various details of the velocity profiles in all the regions of the flow curve and emphasize on the complex, non-Newtonian nature of the flow in the highly sheared band.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

Shear-banding in a lyotropic lamellar phase, Part 1: Time-averaged velocity profiles

Using velocity profile measurements based on dynamic light scattering and coupled to structural and rheological measurements in a Couette cell, we present evidences for a shear-banding scenario in the shear flow of the onion texture of a lyotropic lamellar phase. Time-averaged measurements clearly show the presence of structural shear-banding in the vicinity of a shear-induced transition, associated to the nucleation and growth of a highly sheared band in the flow. Our experiments also reveal the presence of slip at the walls of the Couette cell. Using a simple mechanical approach, we demonstrate that our data confirms the classical assumption of the shear-banding picture, in which the interface between bands lies at a given stress $\sigma^\star$. We also outline the presence of large temporal fluctuations of the flow field, which are the subject of the second part of this paper [Salmon {\it et al.}, submitted to Phys. Rev. E]

Spin-Glass Attractor on Tridimensional Hierarchical Lattices in the Presence of an External Magnetic Field

A nearest-neighbor-interaction Ising spin glass, in the presence of an external magnetic field, is studied on different hierarchical lattices that approach the cubic lattice. The magnetic field is considered as uniform, or random (following either a bimodal or a Gaussian probability distribution). In all cases, a spin-glass attractor is found, in the plane magnetic field versus temperature, associated with a low-temperature phase. The physical consequences of this attractor are discussed, in view of the present scenario of the spin-glass problem.Comment: Accepted for publication in Physical Review

Social presence in the 21st Century: an adjustment to the Community of Inquiry framework

The Community of Inquiry framework, originally proposed by Garrison, Anderson and Archer (2000) identifies teaching, social and cognitive presences as central to a successful online educational experience. This article presents the findings of a study conducted in Uruguay between 2007 and 2010. The research aimed to establish the role of cognitive, social and teaching presences in the professional development of 40 English language teachers on Continuous Professional Development (CPD) programmes delivered in blended learning settings. The findings suggest that teaching presence and cognitive presence have themselves 'become social'. The research points to social presence as a major lever for engagement, sense-making and peer support. Based on the patterns identified in the study, this article puts forward an adjustment to the Community of Inquiry framework, which shows social presence as more prominent within the teaching and cognitive constructs than the original version of the framework suggests