Third-order statistics and the dynamics of strongly anisotropic turbulent flows

Anisotropy is induced by body forces and/or mean large-scale gradients in turbulent flows. For flows without energy production, the dynamics of second-order velocity or second-order vorticity statistics are essentially governed by triple correlations, which are at the origin of the anisotropy that penetrates towards the inertial range, deeply altering the cascade and the eventual dissipation process, with a series of consequences on the evolution of homogeneous turbulence statistics: in the case of rotating turbulence, the anisotropic spectral transfer slaves the multiscale anisotropic energy distribution; nonlinear dynamics are responsible for the linear growth in terms of Ωt of axial integral length-scales; third-order structure functions, derived from velocity triple correlations, exhibit a significant departure from the 4/5 Kolmogorov law. We describe all these implications in detail, starting from the dynamical equations of velocity statistics in Fourier space, which yield third-order correlations at three points (triads) and allow the explicit removal of pressure fluctuations. We first extend the formalism to anisotropic rotating turbulence with ‘production’, in the presence of mean velocity gradients in the rotating frame. Second, we compare the spectral approach at three points to the two-point approach directly performed in physical space, in which we consider the transport of the scalar second-order structure function ?(δq)²?. This calls into play componental third-order correlations ?(δq)²δu?(r) in axisymmetric turbulence. This permits to discuss inhomogeneous anisotropic effects from spatial decay, shear, or production, as in the central region of a rotating round jet. We show that the above-mentioned important statistical quantities can be estimated from experimental planar particle image velocimetry, and that explicit passage relations systematically exist between one- and two-point statistics in physical and spectral space for second-order tensors, but also sometimes for third-order tensors that are involved in the dynamics.     

A Polynomial Time Approximation Scheme for the Grade of Service Steiner Minimum Tree Problem

In this paper, we present the design of a Polynomial Time Approximation Scheme (PTAS) for the Grade of Service Steiner Minimum Tree (GOSST) problem, which is known to be NP-Complete. Previous research has focused on geometric analyses and different approximation algorithms have been designed. We propose a PTAS that provides a polynomial time, near-optimal solution with performance ratio 1+. The GOSST problem has some important applications. In network design, a fundamental issue for the physical construction of a network structure is the interconnection of many communication sites with the best choice of the connecting lines and the best allocation of the transmission capacities over these lines. Good solutions should provide paths with enough communication capacities between any two sites, with the least network construction costs. Also, the GOSST problem has applications in transportation, for road constructions and some potential uses in CAD in terms of interconnecting the elements on a plane to provide enough flux between any two elements.     

Existence and numerical modelling of vortex rings with elliptic boundaries

We revisit in this paper the theory of axisymmetric vortex rings in an ideal fluid. The boundary separating the vortex ring from the external (potential) flow is assumed of elliptic shape. For a given distribution of vorticity in the vortex core, we theoretically put into evidence the critical parameter for the existence of non-trivial solutions, thus confirming the numerical observation of Durst et al. [ZAMP 32 (1981) 156]. A sharp estimation of the critical threshold is analytically derived. Theoretical predictions are confirmed by numerical simulations using finite elements. A new numerical algorithm is presented and shown to display better performances compared to previous published algorithms using finite differences. The convergence of the iterative algorithm is proved using the theory of elliptic partial differential equations with discontinuous nonlinearities.     

The Quantum Cohomology Ring of Flag Varieties

We describe the small quantum cohomology ring of complete flag varieties by algebro-geometric methods, as presented in our previous work Quantum cohomology of flag varieties (Internat. Math. Res. Notices, no. 6 (1995), 263-277). We also give a geometric proof of the quantum Monk formula.

     

Compatibility study between indomethacin and excipients in their physical mixtures

Thermal analysis is a routine method for analysis of drugs and substances of pharmaceutical interest. Thermogravimetry/derivative thermogravimetry (TG/DTG) and differential scanning calorimetry (DSC) are thermoanalytical methods which offer important information about the physical and chemical properties of drugs (purity, stability, phase transition, polymorphism, compatibility, kinetic analysis, etc.). This work exemplifies a general method of studying the drug-excipient interactions with the aim of predicting rapidly and inexpensively the long thermal stability of their mixtures. The TG/DTG and DSC were used as screening techniques for assessing the compatibility between indomethacin (IND) and its physical associations as binary mixtures with some common excipients. Based on their frequent use in preformulations eleven different excipients: corn starch, microcrystalline cellulose (PH 101; PH 102), colloidal silicon dioxide, lactose (monohydrate and anhydre), polyvinilpyrrolidone K30, magnesium stearate, talc, stearic acid, and manitol were blended with IND. The samples were prepared by mixing the analyte and excipients in a proportion of 1:1 (w:w). In order to investigate the possible interactions between the components, the thermal curves of IND and each selected excipient were compared with those of their 1:1 (w/w) physical mixtures. FT-IR spectroscopy and X-ray powder diffraction were used as complementary techniques to adequately implement and assist in interpretation of thermal results. On the basis of thermal results, confirmed by FT-IR and X-ray analyses, a possible interaction was found between IND with polyvinylpyrrolidone K30, magnesium stearate, and stearic acid.     

Turbulent Energy Scale-Budget Equations for nearly Homogeneous Sheared Turbulence

For moderate Reynolds numbers, the isotropic relation between second-order and third-order moments for velocity increments (Kolmogorov's equation) is not respected, reflecting a non-negligible correlation between the scales responsible for the injection, transfer and dissipation of the turbulent energy. For (shearless) grid turbulence, there is only one dominant large-scale phenomenon, which is the non-stationarity of statistical moments resulting from the decay of energy downstream of the grid. In this case, the extension of Kolmogorov's analysis, as carried out by Danaila, Anselmet, Zhou and Antonia, J. Fluid Mech. 391, 1999 359-369) is quite straightforward. For shear flows, several large-scale phenomena generally coexist with similar amplitudes. This is particularly the case for wall-bounded flows, where turbulent diffusion and shear effects can present comparable amplitudes. The objective of this work is to quantify, in a fully developed turbulent channel flow and far from the wall, the influence of these two effects on the scale-by-scale energy budget equation. A generalized Kolmogorov equation is derived. Relatively good agreement between the new equation and hot-wire measurements is obtained in the outer region (40 < x ⁺ ₃ < 150) of the channel flow, for which the turbulent Reynolds number is R _λ≈ 36.     

Small-scale measurements in a partially stirred reactor

This paper describes an experimental study of a partially stirred reactor (PaSR). The reactor is a cubic box in which air (either pure or mixed with a tracer) is continuously injected through 12 jets situated in two opposite planes and impinging through the center. The flow in the reactor interior is well approximated as stationary, globally homogeneous and isotropic. Global properties of turbulent flow and passive scalar mixing are studied, in terms of length scales, characteristic times, spectra, etc. Particular attention has been paid to a proper determination of the mean value of the passive scalar variance dissipation rate 〈ε _Z 〉, in the central quasi-homogeneous zone of the reactor.     

Experimental and numerical study of mixed convection with flow reversal in coaxial double-duct heat exchangers

Velocity vectors in a vertical coaxial double-duct heat exchanger for parallel ascending flow of water under conditions of laminar mixed convection have been determined experimentally using the particle image velocimetry technique. The measured velocity distributions for large annular flow rates, resulting in an essentially isothermal environment for the stream in the inner tube, are in very good agreement with corresponding numerical predictions. For flow rates of the same order of magnitude in the inner tube and the annulus, and corresponding temperature differences of about 20 °C, experimental observations show that flow reversal occurs simultaneously in both streams over large axial distances for both heating and cooling of the flow in the inner tube.     

Effect of Fish Bone Bioactive Peptides on Oxidative,Inflammatory and Pigmentation Processes Triggered by UVB Irradiation in Skin Cells

In the present study, we evaluated for the first time the photoprotective effect of fish bone bioactive peptides (FBBP) preparation isolated from silver carp (Hypophthalmichthys molitrix) discarded tissue using in vitro experimental models of skin cells exposed to ultraviolet B (UVB) irradiation and stressing agents. FBBP preparation was obtained by papain treatment of minced bones and centrifugal ultrafiltration, and the molecular weight (MW) distribution was characterized by size exclusion and reversed-phase high performance liquid chromatography (RP-HPLC). In vitro assessment of the effect of FBBP pretreatment in UVB-irradiated L929 fibroblasts and HaCaT keratinocytes revealed their cytoprotective activity. Their capacity to efficiently reduce reactive oxygen species (ROS) production and lipid peroxidation varied in a dose-dependent manner, and it was greater in fibroblasts. A decrease of proinflammatory cytokines secretion, in particular of tumor necrosis factor alpha (TNF-α), was found after FBBP pretreatment of THP-1-derived inflamed macrophages. Melanin production and tyrosinase activity investigated in UVB-irradiated Mel-Juso cells were lowered in direct relation to FBBP concentrations. FBBP fractions with high radical scavenging activity were separated by ion exchange chromatography, and two collagenic sequences were identified. All these results offer new scientific data on aquaculture fish bone-derived peptides confirming their ability to control the antioxidant, anti-inflammatory and pigmentation processes developed during UV irradiation of skin cells and recommend their use as valuable natural ingredients of photoprotective cosmeceutical products.