Self-similar parabolic optical solitary waves

We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE.

Stochastically driven instability in rotating shear flows

Origin of hydrodynamic turbulence in rotating shear flows is investigated. The particular emphasis is on flows whose angular velocities decrease but specific angular momenta increase with increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain observed data. Such a mismatch between the linear theory and observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and the corresponding turbulence therein is ruled out. The present work explores the effect of stochastic noise on such hydrodynamic flows. We focus on a small section of such a flow which is essentially a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disk. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities, and hence large energy dissipations, that presumably generate instability. A range of angular velocity profiles (for the steady flow), starting with the constant angular momentum to that of the constant circular velocity are explored. It is shown that the growth and roughness exponents calculated from the contour (envelope) of the perturbed flows are all identical, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand origin of instability and turbulence in the three-dimensional Rayleigh stable rotating shear flows by introducing additive stochastic noise to the underlying linearized governing equations. This has important implications in resolving the turbulence problem in astrophysical hydrodynamic flows such as accretion disks.

Seminar 1 impurity in the tomonaga-luttinger model:a functional integral approach

This chapter explains a functional integral approach about impurity in the Tomonaga–Luttinger model. The Tomonaga–Luttinger model of one-dimensional (1D) strongly correlates electrons gives a striking example of non-Fermi-liquid behavior. For simplicity, the chapter considers only a single-mode Tomonaga–Luttinger model, with one species of right- and left-moving electrons, thus, omitting spin indices and considering eventually the simplest linearized model of a single-valley parabolic electron band. The standard operator bosonization is one of the most elegant methods developed in theoretical physics. The main advantage of the bosonization, either in standard or functional form, is that including the quadric electron–electron interaction does not substantially change the free action. The chapter demonstrates the way to develop the formalism of bosonization based on the functional integral representation of observable quantities within the Keldysh formalism.

Dynamic analysis of submerged microscale plates:the effects of acoustic radiation and viscous dissipation

The aim of this paper is to study the dynamic characteristics of micromechanical rectangular plates used as sensing elements in a viscous compressible fluid. A novel modelling procedure for the plate- fluid interaction problem is developed on the basis of linearized Navier-Stokes equations and noslip conditions. Analytical expression for the fluidloading impedance is obtained using a double Fourier transform approach. This modelling work provides us an analytical means to study the effects of inertial loading, acoustic radiation and viscous dissipation of the fluid acting on the vibration of microplates. The numerical simulation is conducted on microplates with different boundary conditions and fluids with different viscosities. The simulation results reveal that the acoustic radiation dominates the damping mechanism of the submerged microplates. It is also proved that microplates offer better sensitivities (Q-factors) than the conventional beam type microcantilevers beingmass sensing platforms in a viscous fluid environment. The frequency response features of microplates under highly viscous fluid loading are studied using the present model. The dynamics of the microplates with all edges clamped are less influenced by the highly viscous dissipation of the fluid than the microplates with other types of boundary conditions.

Radiation fluxes, soil heat flux, air temperature, soil temperature, soil moisture and vegetation at dwarf shrubs and wet sedges in Kytalyk, NE Siberia

Vegetation changes, such as shrub encroachment and wetland expansion, have been observed in many Arctic tundra regions. These changes feed back to permafrost and climate. Permafrost can be protected by soil shading through vegetation as it reduces the amount of solar energy available for thawing. Regional climate can be affected by a reduction in surface albedo as more energy is available for atmospheric and soil heating. Here, we compared the shortwave radiation budget of two common Arctic tundra vegetation types dominated by dwarf shrubs (Betula nana) and wet sedges (Eriophorum angustifolium) in North-East Siberia. We measured time series of the shortwave and longwave radiation budget above the canopy and transmitted radiation below the canopy. Additionally, we quantified soil temperature and heat flux as well as active layer thickness. The mean growing season albedo of dwarf shrubs was 0.15 ± 0.01, for sedges it was higher (0.17 ± 0.02). Dwarf shrub transmittance was 0.36 ± 0.07 on average, and sedge transmittance was 0.28 ± 0.08. The standing dead leaves contributed strongly to the soil shading of wet sedges. Despite a lower albedo and less soil shading, the soil below dwarf shrubs conducted less heat resulting in a 17 cm shallower active layer as compared to sedges. This result was supported by additional, spatially distributed measurements of both vegetation types. Clouds were a major influencing factor for albedo and transmittance, particularly in sedge vegetation. Cloud cover reduced the albedo by 0.01 in dwarf shrubs and by 0.03 in sedges, while transmittance was increased by 0.08 and 0.10 in dwarf shrubs and sedges, respectively. Our results suggest that the observed deeper active layer below wet sedges is not primarily a result of the summer canopy radiation budget. Soil properties, such as soil albedo, moisture, and thermal conductivity, may be more influential, at least in our comparison between dwarf shrub vegetation on relatively dry patches and sedge vegetation with higher soil moisture.

Stable-isotope ratios and accumulation rates of four firn cores from the Dronning Maud Land, Antarctica

Four firn cores were retrieved in 2007 at two ridges in the area of the Ekström Ice Shelf, Dronning Maud Land, coastal East Antarctica, in order to investigate the recent regional climate variability and the potential for future extraction of an intermediate-depth core. Stable water-isotope analysis, tritium content and electrical conductivity were used to date the cores. For the period 1981-2006 a strong and significant correlation between the stable-isotope composition of firn cores in the hinterland and mean monthly air temperatures at Neumayer station was (r=0.54-0.71). No atmospheric warming or cooling trend is inferred from our stable-isotope data for the period 1962-2006. The stable-isotope record of the ice/firn cores could expand well beyond the meteorological record of the region. No significant temporal variation of accumulation rates was detected. However, decreasing accumulation rates were found from coast to hinterland, as well as from east (Halvfarryggen) to west (Søråsen). The deuterium excess (d) exhibits similar differences (higher d at Søråsen, lower d at Halvfarryggen), with a weak negative temporal trend on Halvfarryggen (0.04 per mil/a), probably implying increasing oceanic input. We conclude that Halvfarryggen acts as a natural barrier for moisture-carrying air masses circulating in the region from east to west.

Alkenones and alkenes in surface waters and sediments of the Southern Ocean

The concentration of C37-C39 long-chain alkenones and alkenes were determined in surface water and surface sediment samples from the subpolar waters of the Southern Ocean. Distributions of these compounds were similar in both sample sets indicating little differential degradation between or within compound classes. The relative amounts of the tri- to tetra-unsaturated C37 alkenones increased with increasing temperature for temperatures below 6°C similar to the di- and tri-unsaturated C37 alkenones. The C37 di-, tri-, and tetra-unsaturated methyl alkenones are used in paleotemperature calculations via the U37K and the U37K ratios. In these datasets, the relative abundances of the C37:2 and the C37.3 alkenones as a proportion of the total C37 alkenones were opposite and strongly related to temperature (the latter with more scatter), but the abundance of the C37:4 alkenone showed no relationship with temperature. The original definition of U37K includes the abundance of 37:4 in both the numerator and denominator, and thus it is perhaps not surprising that there is considerable scatter in the values obtained for U37K at low temperatures. Of the two, we suggest that U37K' is the better parameter for use in paleotemperature estimations, even in cold locations. U37K' values in the sediments fall on virtually the same regression line obtained for the water column samples of Sikes and Volkman (1993, doi:10.1016/0016-7037(93)90120-L), indicating that their calibration is suitable for use in Southern Ocean sediments. The comparison of water column data with sedimentary temperature estimates suggests that the alkenone distributions are dominated by contributions from the summer when the biomass of Emiliania huxleyi and presumably flux to the sediment, is expected to be high.