Anisotropic fluctuations in turbulent sheared flows

An experimental analysis of small-scales anisotropic turbulent fluctuations has been performed in two different flows. We analyzed anisotropic properties of an homogeneous shear flows and of a turbulent boundary layer by means of two cross-wire probes to obtain multi-point multi-component measurements. Data are analyzed at changing inter-probe separation without the use of Taylor hypothesis. The results are consistent with the ``exponent-only'' scenario for universality, i.e. all experimental data can be fit by fixing the same set of anisotropic scaling exponents at changing only prefactors, for different shear intensities and boundary conditions.Comment: 11 pages, 8 figure

Tensor Rank: Some Lower and Upper Bounds

The results of Strassen and Raz show that good enough tensor rank lower bounds have implications for algebraic circuit/formula lower bounds. We explore tensor rank lower and upper bounds, focusing on explicit tensors. For odd d, we construct field-independent explicit 0/1 tensors T:[n]^d->F with rank at least 2n^(floor(d/2))+n-Theta(d log n). This matches (over F_2) or improves (all other fields) known lower bounds for d=3 and improves (over any field) for odd d>3. We also explore a generalization of permutation matrices, which we denote permutation tensors. We show, by counting, that there exists an order-3 permutation tensor with super-linear rank. We also explore a natural class of permutation tensors, which we call group tensors. For any group G, we define the group tensor T_G^d:G^d->F, by T_G^d(g_1,...,g_d)=1 iff g_1 x ... x g_d=1_G. We give two upper bounds for the rank of these tensors. The first uses representation theory and works over large fields F, showing (among other things) that rank_F(T_G^d)<= |G|^(d/2). We also show that if this upper bound is tight, then super-linear tensor rank lower bounds would follow. The second upper bound uses interpolation and only works for abelian G, showing that over any field F that rank_F(T_G^d)<= O(|G|^(1+log d)log^(d-1)|G|). In either case, this shows that many permutation tensors have far from maximal rank, which is very different from the matrix case and thus eliminates many natural candidates for high tensor rank. We also explore monotone tensor rank. We give explicit 0/1 tensors T:[n]^d->F that have tensor rank at most dn but have monotone tensor rank exactly n^(d-1). This is a nearly optimal separation.Comment: 27 page

Inertial particles in homogeneous shear turbulence: Experiments and direct numerical simulation

The properties of the transport of heavy inertial particles in a uniformly sheared turbulent flow have been investigated by combining experimental and numerical data at particle Stokes number St ≈ 0.3 ÷ 0.5 respectively. As in isotropic turbulence, particles are observed to avoid zones of intense enstrophy and to cluster in strain-dominated regions, resulting in highly intermittent spatial distributions. Moreover, the anisotropy of the mean flow is found to imprint a clear preferential orientation of the particle clusters in the direction of the maximum mean strain. These features are observed both in the numerics and in the experiments, and have been consistently quantified by a number of complementary statistical tools, such as the Voronoï tessellations and the pair correlation function. The latter quantity has been generalized in the form of the Angular Distribution Function and has allowed to evaluate the anisotropy content of the particle field at each scale. The behavior of this observable exhibits the same trend in the two datasets and suggests that, owing to increased inertia, the particle distribution starts to recover isotropy at scales smaller than the carrier velocity field. A proper rescaling of the two datasets in terms of their respective values of the shear scale allows to account for differences in the Reynolds number of experiments and numerics in the range of scales dominated by the mean shear. © 2013 Springer Science+Business Media Dordrecht

Alternative promoter usage of the membrane glycoprotein CD36

BACKGROUND: CD36 is a membrane glycoprotein involved in a variety of cellular processes such as lipid transport, immune regulation, hemostasis, adhesion, angiogenesis and atherosclerosis. It is expressed in many tissues and cell types, with a tissue specific expression pattern that is a result of a complex regulation for which the molecular mechanisms are not yet fully understood. There are several alternative mRNA isoforms described for the gene. We have investigated the expression patterns of five alternative first exons of the CD36 gene in several human tissues and cell types, to better understand the molecular details behind its regulation. RESULTS: We have identified one novel alternative first exon of the CD36 gene, and confirmed the expression of four previously known alternative first exons of the gene. The alternative transcripts are all expressed in more than one human tissue and their expression patterns vary highly in skeletal muscle, heart, liver, adipose tissue, placenta, spinal cord, cerebrum and monocytes. All alternative first exons are upregulated in THP-1 macrophages in response to oxidized low density lipoproteins. The alternative promoters lack TATA-boxes and CpG islands. The upstream region of exon 1b contains several features common for house keeping gene and monocyte specific gene promoters. CONCLUSION: Tissue-specific expression patterns of the alternative first exons of CD36 suggest that the alternative first exons of the gene are regulated individually and tissue specifically. At the same time, the fact that all first exons are upregulated in THP-1 macrophages in response to oxidized low density lipoproteins may suggest that the alternative first exons are coregulated in this cell type and environmental condition. The molecular mechanisms regulating CD36 thus appear to be unusually complex, which might reflect the multifunctional role of the gene in different tissues and cellular conditions

Scaling of mixed structure functions in turbulent boundary layers

We address the issue of the scaling of the anisotropic components of the hierarchy of correlation tensors in the logarithmic region of a turbulent boundary layer over a flat plate, at Re?15000. We isolate the anisotropic observables by means of decomposition tools based on the SO(3) symmetry group of rotations. By employing a dataset made of velocity signals detected by two X probes, we demonstrate that the behavior of the anisotropic fluctuations throughout the boundary layer may be understood in terms of the superposition of two distinct regimes. The transition is controlled by the magnitude of the mean shear and occurs in correspondence with the shear scale. Below the shear scale, an isotropy-recovering behavior occurs, which is characterized by a set of universal exponents which roughly match dimensional predictions based on Lumley's argument [J. L. Lumley, Phys. Fluids 8, 1056 (1965)]. Above the shear scale, the competition between energy production and transfer mechanisms gives rise to a completely different scenario with strong alterations of the observed scaling laws. This aspect has significant implications for the correct parametrization of the anisotropy behavior in the near wall region since, approaching the wall, an increasingly larger fraction of the scaling interval tends to conform to the shear-dominated power laws