Flow Phase Diagram for the Helium Superfluids

The flow phase diagram for He II and $^3$He-B is established and discussed based on available experimental data and the theory of Volovik [JETP Letters {\bf{78}} (2003) 553]. The effective temperature - dependent but scale - independent Reynolds number $Re_{eff}=1/q=(1+\alpha')/\alpha$, where $\alpha$ and $\alpha'$ are the mutual friction parameters and the superfluid Reynolds number characterizing the circulation of the superfluid component in units of the circulation quantum are used as the dynamic parameters. In particular, the flow diagram allows identification of experimentally observed turbulent states I and II in counterflowing He II with the turbulent regimes suggested by Volovik.Comment: 2 figure

Where Nanophotonics and Microfluidics Meet

A new generation of photonic devices has recently emerged that relies on using geometries of sub-wavelength microstructures within a high refractive index contrast materials system. These geometries are used to confine and manipulate light within very small volumes. High optical field densities can be obtained within such structures, and these in turn can amplify optical nonlinearities. Moreover, many of these structures, as for example photonic crystals and slotted waveguides, can be engineered for the efficient localization of light within the low-index regions of high index contrast microstructures. When such structures are back-filled nonlinear polymers or liquids, devices can be tuned and novel phenomena can be observed. In particular, such devices are very interesting when constructed from silicon on insulator (SOI) material in which the optical waveguide also serves as a transparent electrical contact. Here we show examples of the design, fabrication and testing of optical microstructures in which the electro-optic (χ2) and photorefractive (χ3) nonlinearities are used for electro-optic tuning, frequency mixing, optical rectification, and high-speed switching of light

Soliton equations and the zero curvature condition in noncommutative geometry

Familiar nonlinear and in particular soliton equations arise as zero curvature conditions for GL(1,R) connections with noncommutative differential calculi. The Burgers equation is formulated in this way and the Cole-Hopf transformation for it attains the interpretation of a transformation of the connection to a pure gauge in this mathematical framework. The KdV, modified KdV equation and the Miura transformation are obtained jointly in a similar setting and a rather straightforward generalization leads to the KP and a modified KP equation. Furthermore, a differential calculus associated with the Boussinesq equation is derived from the KP calculus.Comment: Latex, 10 page

The present and future system for measuring the Atlantic meridional overturning circulation and heat transport

of the global combined atmosphere-ocean heat flux and so is important for the mean climate of the Atlantic sector of the Northern Hemisphere. This meridional heat flux is accomplished by both the Atlantic Meridional Overturning Circulation (AMOC) and by basin-wide horizontal gyre circulations. In the North Atlantic subtropical latitudes the AMOC dominates the meridional heat flux, while in subpolar latitudes and in the subtropical South Atlantic the gyre circulations are also important. Climate models suggest the AMOC will slow over the coming decades as the earth warms, causing widespread cooling in the Northern hemisphere and additional sea-level rise. Monitoring systems for selected components of the AMOC have been in place in some areas for decades, nevertheless the present observational network provides only a partial view of the AMOC, and does not unambiguously resolve the full variability of the circulation. Additional observations, building on existing measurements, are required to more completely quantify the Atlantic meridional heat transport. A basin-wide monitoring array along 26.5°N has been continuously measuring the strength and vertical structure of the AMOC and meridional heat transport since March 31, 2004. The array has demonstrated its ability to observe the AMOC variability at that latitude and also a variety of surprising variability that will require substantially longer time series to understand fully. Here we propose monitoring the Atlantic meridional heat transport throughout the Atlantic at selected critical latitudes that have already been identified as regions of interest for the study of deep water formation and the strength of the subpolar gyre, transport variability of the Deep Western Boundary Current (DWBC) as well as the upper limb of the AMOC, and inter-ocean and intrabasin exchanges with the ultimate goal of determining regional and global controls for the AMOC in the North and South Atlantic Oceans. These new arrays will continuously measure the full depth, basin-wide or choke-point circulation and heat transport at a number of latitudes, to establish the dynamics and variability at each latitude and then their meridional connectivity. Modeling studies indicate that adaptations of the 26.5°N type of array may provide successful AMOC monitoring at other latitudes. However, further analysis and the development of new technologies will be needed to optimize cost effective systems for providing long term monitoring and data recovery at climate time scales. These arrays will provide benchmark observations of the AMOC that are fundamental for assimilation, initialization, and the verification of coupled hindcast/forecast climate models

'Surely the most natural scenario in the world’: Representations of ‘Family’ in BBC Pre-school Television

Historically, the majority of work on British children’s television has adopted either an institutional or an audience focus, with the texts themselves often overlooked. This neglect has meant that questions of representation in British children’s television – including issues such as family, gender, class or ethnicity - have been infrequently analysed in the UK context. In this article, we adopt a primarily qualitative methodology and analyse the various textual manifestations of ‘family’, group, or community as represented in a selected number of BBC pre-school programmes. In doing so, we question the (limited amount of) international work that has examined representations of the family in children’s television, and argue that nuclear family structures do not predominate in this sphere

Noncommutative Geometry of Finite Groups

A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding framework has been developed by Woronowicz, more generally for Hopf algebras including quantum groups. A differential calculus is regarded as the most basic structure needed for the introduction of further geometric notions like linear connections and, moreover, for the formulation of field theories and dynamics on finite sets. Associated with each bicovariant first order differential calculus on a finite group is a braid operator which plays an important role for the construction of distinguished geometric structures. For a covariant calculus, there are notions of invariance for linear connections and tensors. All these concepts are explored for finite groups and illustrated with examples. Some results are formulated more generally for arbitrary associative (Hopf) algebras. In particular, the problem of extension of a connection on a bimodule (over an associative algebra) to tensor products is investigated, leading to the class of `extensible connections'. It is shown that invariance properties of an extensible connection on a bimodule over a Hopf algebra are carried over to the extension. Furthermore, an invariance property of a connection is also shared by a `dual connection' which exists on the dual bimodule (as defined in this work).Comment: 34 pages, Late

Proliferative reactive gliosis is compatible with glial metabolic support and neuronal function

<p>Abstract</p> <p>Background</p> <p>The response of mammalian glial cells to chronic degeneration and trauma is hypothesized to be incompatible with support of neuronal function in the central nervous system (CNS) and retina. To test this hypothesis, we developed an inducible model of proliferative reactive gliosis in the absence of degenerative stimuli by genetically inactivating the cyclin-dependent kinase inhibitor <it>p27^Kip1</it>(<it>p27 </it>or <it>Cdkn1b</it>) in the adult mouse and determined the outcome on retinal structure and function.</p> <p>Results</p> <p>p27-deficient Müller glia reentered the cell cycle, underwent aberrant migration, and enhanced their expression of intermediate filament proteins, all of which are characteristics of Müller glia in a reactive state. Surprisingly, neuroglial interactions, retinal electrophysiology, and visual acuity were normal.</p> <p>Conclusion</p> <p>The benign outcome of proliferative reactive Müller gliosis suggests that reactive glia display context-dependent, graded and dynamic phenotypes and that reactivity in itself is not necessarily detrimental to neuronal function.</p

Non-commutative Geometry and Kinetic Theory of Open Systems

The basic mathematical assumptions for autonomous linear kinetic equations for a classical system are formulated, leading to the conclusion that if they are differential equations on its phase space $M$, they are at most of the 2nd order. For open systems interacting with a bath at canonical equilibrium they have a particular form of an equation of a generalized Fokker-Planck type. We show that it is possible to obtain them as Liouville equations of Hamiltonian dynamics on $M$ with a particular non-commutative differential structure, provided certain geometric in character, conditions are fulfilled. To this end, symplectic geometry on $M$ is developped in this context, and an outline of the required tensor analysis and differential geometry is given. Certain questions for the possible mathematical interpretation of this structure are also discussed.Comment: 22 pages, LaTe