Reynolds-number effects and anisotropy in transverse-jet mixing

Experiments are described which measured concentration fields in liquid-phase strong transverse jets over the Reynolds-number range 1.0×10^3 ≤ Rej ≤ 20×10^3. Laser-induced-fluorescence measurements were made of the jet-fluid-concentration fields at a jet-to-freestream velocity ratio of Vr =10. The concentration-field data for far-field (x/dj =50) slices of the jet show that turbulent mixing in the transverse jet is Reynolds number dependent over the range investigated, with a scalar-field PDF that evolves with Reynolds number. A growing peak in the PDF, indicating enhanced spatial homogenization of the jet-fluid concentration field, is found with increasing Reynolds number. Comparisons between transverse jets and jets discharging into quiescent reservoirs show that the transverse jet is an efficient mixer in that it entrains more fluid than the ordinary jet, yet is able to effectively mix and homogenize the additional entrained fluid. Analysis of the structure of the scalar field using distributions of scalar increments shows evidence for well-mixed plateaux separated by sharp cliffs in the jet-fluid concentration field, as previously shown in other flows. Furthermore, the scalar field is found to be anisotropic, even at small length scales. Evidence for local anisotropy is seen in the scalar power spectra, scalar microscales, and PDFs of scalar increments in different directions. The scalar-field anisotropy is shown to be correlated to the vortex-induced large-scale strain field of the transverse jet. These experiments add to the existing evidence that the large and small scales of high-Schmidt-number turbulent mixing flows can be linked, with attendant consequences for the universality of small scales of the scalar field for Reynolds numbers up to at least Re=20×10^4

Categorification of quantum symmetric pairs I

We categorify a coideal subalgebra of the quantum group of $\mathfrak{sl}_{2r+1}$ by introducing a $2$-category \`a la Khovanov-Lauda-Rouquier, and show that self-dual indecomposable $1$-morphisms categorify the canonical basis of this algebra. This allows us to define a categorical action of this coideal algebra on the categories of modules over cohomology rings of partial flag varieties and on the BGG category $\mathcal{O}$ of type B/C.Comment: final version, to appear in Quantum Topolog

Detection of sequential polyubiquitylation on a millisecond timescale

The pathway by which ubiquitin chains are generated on substrate through a cascade of enzymes consisting of an E1, E2 and E3 remains unclear. Multiple distinct models involving chain assembly on E2 or substrate have been proposed. However, the speed and complexity of the reaction have precluded direct experimental tests to distinguish between potential pathways. Here we introduce new theoretical and experimental methodologies to address both limitations. A quantitative framework based on product distribution predicts that the really interesting new gene (RING) E3 enzymes SCF^(Cdc4) and SCF^(β-TrCP) work with the E2 Cdc34 to build polyubiquitin chains on substrates by sequential transfers of single ubiquitins. Measurements with millisecond time resolution directly demonstrate that substrate polyubiquitylation proceeds sequentially. Our results present an unprecedented glimpse into the mechanism of RING ubiquitin ligases and illuminate the quantitative parameters that underlie the rate and pattern of ubiquitin chain assembly

An alternative simplified model of tensile membrane action of slabs in fire

This paper presents an initial re-examination of the mechanisms of tensile membrane action of thin concrete floor slabs. The study is based on a large-deflection plastic analysis, which can apply to either isolated or continuous slabs at ambient or high temperatures. The basic calculation method considers plain flat slabs, but is in no way limited to these, or to isotropic reinforcement.  The new method is compared against the generic Bailey-BRE method, indicating for some typical examples that the actual enhancement of yield-line capacity due to TMA can be over-estimated by the latter

THE MECHANICS OF TENSILE MEMBRANE ACTION IN COMPOSITE SLABS AT HIGH TEMPERATURES

The mechanics of tensile membrane action of thinlightly-reinforced concrete slabs has been re-examined during the last two years.The re-examination is based on large-deflection plastic yield-line analysis, applied to flat slabs. As deflection increases beyond the optimum yield-line pattern, tensile membrane action is mobilized and further load carrying capacity is provided. This paper represents an extension of this re-examination to include composite slabs at high temperatures. As temperature increases, the unprotected downstand steel beams significantly lose capacity, allowing for further deflection until the overall capacity degrades to the applied load. Tensile membrane action then allows further increase of steel temperature until a maximum is reached

Quantized Quasi-Two Dimensional Bose-Einstein Condensates with Spatially Modulated Nonlinearity

We investigate the localized nonlinear matter waves of the quasi-two dimensional Bose-Einstein condensates with spatially modulated nonlinearity in harmonic potential. It is shown that the whole Bose-Einstein condensates, similar to the linear harmonic oscillator, can have an arbitrary number of localized nonlinear matter waves with discrete energies, which are mathematically exact orthogonal solutions of the Gross-Pitaevskii equation. Their novel properties are determined by the principle quantum number n and secondary quantum number l: the parity of the matter wave functions and the corresponding energy levels depend only on n, and the numbers of density packets for each quantum state depend on both n and l which describe the topological properties of the atom packets. We also give an experimental protocol to observe these novel phenomena in future experiments.Comment: 5 pages, 5 figure