On role of symmetries in Kelvin wave turbulence

E.V. Kozik and B.V. Svistunov (KS) paper "Symmetries and Interaction Coefficients of Kelvin waves", arXiv:1006.1789v1, [cond-mat.other] 9 Jun 2010, contains a comment on paper "Symmetries and Interaction coefficients of Kelvin waves", V. V. Lebedev and V. S. L'vov, arXiv:1005.4575, 25 May 2010. It relies mainly on the KS text "Geometric Symmetries in Superfluid Vortex Dynamics}", arXiv:1006.0506v1 [cond-mat.other] 2 Jun 2010. The main claim of KS is that a symmetry argument prevents linear in wavenumber infrared asymptotics of the interaction vertex and thereby implies locality of the Kelvin wave spectrum previously obtained by these authors. In the present note we reply to their arguments. We conclude that there is neither proof of locality nor any refutation of the possibility of linear asymptotic behavior of interaction vertices in the texts of KS

Scanning Superfluid-Turbulence Cascade by Its Low-Temperature Cutoff

On the basis of recently proposed scenario of the transformation of the Kolmogorov cascade into the Kelvin-wave cascade, we develop a theory of low-temperature cutoff. The theory predicts a specific behavior of the quantized vortex line density, $L$, controlled by the frictional coefficient, $\alpha(T) \ll 1$, responsible for the cutoff. The curve $\ln L(\ln \alpha)$ is found to directly reflect the structure of the cascade, revealing four qualitatively distinct wavenumber regions. Excellent agreement with recent experiment by Walmsley {\it et al.} [arXiv:0710.1033]--in which $L(T)$ has been measured down to $T \sim 0.08$K--implies that the scenario of low-temperature superfluid turbulence is now experimentally validated, and allows to quantify the Kelvin-wave cascade spectrum.Comment: 4 pages, 2 figures, v2: extended introduction, the controversy with the scenario by L'vov et al. [13] is discussed in conclusio

Geometric Symmetries in Superfluid Vortex Dynamics

Dynamics of quantized vortex lines in a superfluid feature symmetries associated with the geometric character of the complex-valued field, $w(z)=x(z)+iy(z)$, describing the instant shape of the line. Along with a natural set of Noether's constants of motion, which---apart from their rather specific expressions in terms of $w(z)$---are nothing but components of the total linear and angular momenta of the fluid, the geometric symmetry brings about crucial consequences for kinetics of distortion waves on the vortex lines---the Kelvin waves. It is the geometric symmetry that renders Kelvin-wave cascade local in the wavenumber space. Similar considerations apply to other systems with purely geometric degrees of freedom.Comment: 4 REVTeX pages, minor stylistic changes, references to recent related preprints adde

Symmetries and Interaction coefficients of Kelvin waves

We considered symmetry restriction on the interaction coefficients of Kelvin waves and demonstrated that linear in small wave vector asymptotic is not forbidden, as one can expect by naive reasoning.Comment: 4 pages, submitted to J. of Low Temp. Phy

The composition and structure of iron(III) complex compounds with salicylic acid in ethanol solution and in the solid thin film state

Owing to their properties iron(III) salicylate complexes are interest of for application in biomedicine and environmental monitoring. Recently this complex compounds also are investigated as a potential candidate for preparing Fe2O3 films by sol-gel method from ethanol film-forming solution. Relevance of the work was caused by necessity to determine the structure and composition of iron(III) salicylate complexes in ethanol solution and in the solid film state, which influence on film properties. Nowadays this information is absence in the literature. UV spectroscopy, NMR measurement, methods of isomolar series and thermal analysis were used to analyze the composition of complex in ethanol solution and in the solid state. It was found, that salicylic acid interacts with iron(III) chloride in ethanol solution promotes the formation of [FeC6H4OCOO]+ complex, where salicylate ligand behaves as bidentate ligand. After removal of the solvent from solution iron(III) chloride salicylate crystal hydrate complex of 1:1 stoichiometry was formed in solid state. Thermal decomposition of this compound led to formation α–Fe2O3

Photocatalytic activity of titania nanopowders prepared by a sol–gel process at various pHs

A strategy has been proposed to prepare photocatalytically active titania nanopowders through a sol-gel route using high-degree molecular separation upon the dilution of reagents, high water/alkoxide ratios, high reagent mixing rates, and pH effects. This strategy has been successfully used to isolate, from sols, anatase powders with high surface areas (100–310 m2/g) dependent on the pH value during the synthesis. The photocatalytic activity of titania nanopowders prepared by the sol-gel process at various pHs has been tested in photodestruction of organic dyes (Rodamine B, Methylene Blue, and Anthraquinone AcidBlue) in acid solutions. UV-radiation-induced dye destruction rates are found to depend on the surface properties (including surface area and ζ potential) and hydration specifics of the titania

TiO2-NiO and TiO2-Co3O4 spheres: synthesis and characterization

TiO2-based composites doped with d-metal oxides are prospective catalysts. In this paper we obtained spherical particles of TiO2–NiO and TiO2–Co3O4 composites by a template method accompanied with sol-gel one. Ion exchange resin of TOKEM-100 and TOKEM-250 was used as an organic polymer matrix. Complex studies were carried out to identify the formation process, compositions and morphology of obtained particles by thermal analysis, X-ray diffractometey, scanning electron microscopy and micro-X-ray spectral analyses The formation of TiO2–Co3O4 and TiO2–NiO composite particles ends at 600 and 500°C, respectively at using TOKEM-100 and TOKEM-250 resins. The size of final spherical particles found to be in a range from 300 to 700 μm, and their morphology depends on its compositio

Modeling Kelvin wave cascades in superfluid helium

We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the later and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in k-space via using a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and closeness of numerics for the higher-order DAM to the analytical predictions for the lower-order DAM

Diagrammatic Monte Carlo for Correlated Fermions

We show that Monte Carlo sampling of the Feynman diagrammatic series (DiagMC) can be used for tackling hard fermionic quantum many-body problems in the thermodynamic limit by presenting accurate results for the repulsive Hubbard model in the correlated Fermi liquid regime. Sampling Feynman's diagrammatic series for the single-particle self-energy we can study moderate values of the on-site repulsion ($U/t \sim 4$) and temperatures down to $T/t=1/40$. We compare our results with high temperature series expansion and with single-site and cluster dynamical mean-field theory.Comment: 4 pages, 5 figures, stylistic change