432 research outputs found

    Exponential self-similar mixing and loss of regularity for continuity equations

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    We consider the mixing behaviour of the solutions of the continuity equation associated with a divergence-free velocity field. In this announcement we sketch two explicit examples of exponential decay of the mixing scale of the solution, in case of Sobolev velocity fields, thus showing the optimality of known lower bounds. We also describe how to use such examples to construct solutions to the continuity equation with Sobolev but non-Lipschitz velocity field exhibiting instantaneous loss of any fractional Sobolev regularity.Comment: 8 pages, 3 figures, statement of Theorem 11 slightly revise

    Exponential self-similar mixing by incompressible flows

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    We study the problem of the optimal mixing of a passive scalar under the action of an incompressible flow in two space dimensions. The scalar solves the continuity equation with a divergence-free velocity field, which satisfies a bound in the Sobolev space Ws,pW^{s,p}, where s≄0s \geq 0 and 1≀p≀∞1\leq p\leq \infty. The mixing properties are given in terms of a characteristic length scale, called the mixing scale. We consider two notions of mixing scale, one functional, expressed in terms of the homogeneous Sobolev norm H˙−1\dot H^{-1}, the other geometric, related to rearrangements of sets. We study rates of decay in time of both scales under self-similar mixing. For the case s=1s=1 and 1≀p≀∞1 \leq p \leq \infty (including the case of Lipschitz continuous velocities, and the case of physical interest of enstrophy-constrained flows), we present examples of velocity fields and initial configurations for the scalar that saturate the exponential lower bound, established in previous works, on the time decay of both scales. We also present several consequences for the geometry of regular Lagrangian flows associated to Sobolev velocity fields.Comment: To appear in Journal of the American Mathematical Society. Some results were announced in G. Alberti, G. Crippa, A. L. Mazzucato, "Exponential self-similar mixing and loss of regularity for continuity equations", C. R. Math. Acad. Sci. Paris, 352(11):901--906, 2014, arXiv:1407.2631v

    Exponential self-similar mixing and loss of regularity for continuity equations

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    We consider the mixing behavior of the solutions to the continuity equation associated with a divergence-free velocity field. In this note we sketch two explicit examples of exponential decay of the mixing scale of the solution, in case of Sobolev velocity fields, thus showing the optimality of known lower bounds. We also describe how to use such examples to construct solutions to the continuity equation with Sobolev but non-Lipschitz velocity field exhibiting instantaneous loss of any fractional Sobolev regularity

    Exponential self-similar mixing by incompressible flows

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    We study the problem of the optimal mixing of a passive scalar under the action of an incompressible flow in two space dimensions. The scalar solves the continuity equation with a divergence-free velocity field, which satisfies a bound in the Sobolev space Ws,p, where s ≄ 0 and 1 ≀ p ≀ ∞. The mixing properties are given in terms of a characteristic length scale, called the mixing scale. We consider two notions of mixing scale, one functional, expressed in terms of the homogeneous Sobolev norm H−1, the other geometric, related to rearrangements of sets. We study rates of decay in time of both scales under self-similar mixing. For the case s = 1 and 1 ≀ p ≀ ∞ (including the case of Lipschitz continuous velocities, and the case of physical interest of enstrophy-constrained flows), we present examples of velocity fields and initial configurations for the scalar that saturate the exponential lower bound, established in previous works, on the time decay of both scales. We also present several consequences for the geometry of regular Lagrangian flows associated to Sobolev velocity fields

    Nutraceutical characterization of anthocyanin-rich fruits produced by «Sun Black» tomato line

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    Tomato (Solanum lycopersicum L.) is one of the most cultivated vegetable in the world and it represents a large source of bioactive compounds, including carotenoids and polyphenols (phenolic acids and flavonoids). However, the concentration of flavonoids in tomato is considered sub-optimal, particularly because anthocyanins are not generally present. Therefore, this crop has been the object of an intense metabolic engineering in order to obtain anthocyanin-enriched tomatoes by using either breeding or transgenic strategies. Some wild tomato species, such as S. chilense and S. cheesmaniae, biosynthesize anthocyanins in the fruit sub-epidermal tissue, and some alleles from those genotypes have been introgressed into a new developed purple tomato line, called “Sun Black” (SB). It is a tomato line with a purple skin color, both in green and in red fruit stages, due to the biosynthesis of anthocyanins in the peel, and a normal red color pulp, with a taste just like a traditional tomato. SB is the result of a breeding programme and it is not a genetically modified (GM) product. We report the chemical characterization and structure elucidation of the attractive anthocyanins found in the peel of SB tomato, as well as other bioactive compounds (carotenoids, polyphenols, vitamin C) of the whole fruit. Using one- and two-dimensional NMR experiments, the two main anthocyanins were identified to be petunidin 3-O-[6″-O-(4‮-O-E-p-coumaroyl-α-rhamnopyranosyl) -ÎČ-glucopyranoside]-5-O-ÎČ-glucopyranoside (petanin) and malvidin 3-O-[6″-O-(4‮-O-E-p-coumaroyl-α-rhamnopyranosyl)-ÎČ-glucopyranoside]-5-O-ÎČ-glucopyranoside (negretein). The total anthocyanins in the whole ripe fruit was 1.2 mg/g dry weight (DW); 7.1 mg/100 g fresh weight (FW). Chlorogenic acid (the most abundant phenolic acid) was 0.6 mg/g DW; 3.7 mg/100 g FW. The main flavonol, rutin was 0.8 mg/g DW; 5 mg/100 g FW. The total carotenoid content was 211.3 ÎŒg/g DW; 1,268 ÎŒg/100 g FW. The total phenolic content was 8.6 mg/g DW; 52.2 mg/100 g FW. The vitamin C content was 37.3 mg/100 g FW. The antioxidant activities as measured by the TEAC and ORAC assays were 31.6 and 140.3 ÎŒmol TE/g DW, respectively (193 and 855.8 ÎŒmol TE/100 g FW, respectively). The results show the unique features of this new tomato genotype with nutraceutical properties.publishedVersio

    Improved GMP compliant approach to manipulate lipoaspirates, to cryopreserve stromal vascular fraction, and to expand adipose stem cells in xeno-free media

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    Abstract Background The stromal vascular fraction (SVF) derived from adipose tissue contains adipose-derived stromal/stem cells (ASC) and can be used for regenerative applications. Thus, a validated protocol for SVF isolation, freezing, and thawing is required to manage product administration. To comply with Good Manufacturing Practice (GMP), fetal bovine serum (FBS), used to expand ASC in vitro, could be replaced by growth factors from platelet concentrates. Methods Throughout each protocol, GMP-compliant reagents and devices were used. SVF cells were isolated from lipoaspirates by a standardized enzymatic protocol. Cells were cryopreserved in solutions containing different albumin or serum and dimethylsulfoxide (DMSO) concentrations. Before and after cryopreservation, we analyzed: cell viability (by Trypan blue); immunophenotype (by flow cytometry); colony-forming unit-fibroblast (CFU-F) formation; and differentiation potential. ASC, seeded at different densities, were expanded in presence of 10% FBS or 5% supernatant rich in growth factors (SRGF) from platelets. The differentiation potential and cell transformation grade were tested in expanded ASC. Results We demonstrated that SVF can be obtained with a consistent yield (about 185 × 103 cells/ml lipoaspirate) and viability (about 82%). Lipoaspirate manipulation after overnight storage at +4 °C reduced cell viability (−11.6%). The relative abundance of ASC (CD34+CD45−CD31–) and endothelial precursors (CD34+CD45−CD31+) in the SVF product was about 59% and 42%, respectively. A period of 2 months cryostorage in autologous serum with added DMSO minimally affected post-thaw SVF cell viability as well as clonogenic and differentiation potentials. Viability was negatively affected when SVF was frozen at a cell concentration below 1.3 × 106 cells/ml. Cell viability was not significantly affected after a freezing period of 1 year. Independent of seeding density, ASC cultured in 5% SRGF exhibited higher growth rates when compared with 10% FBS. ASC expanded in both media showed unaltered identity (by flow cytometry) and were exempt from genetic lesions. Both 5% SRGF- and 10% FBS-expanded ASC efficiently differentiated to adipocytes, osteocytes, and chondrocytes. Conclusions This paper reports a GMP-compliant approach for freezing SVF cells isolated from adipose tissue by a standardized protocol. Moreover, an ASC expansion method in controlled culture conditions and without involvement of animal-derived additives was reported

    High serum levels of soluble CD40-L in patients with undifferentiated nasopharyngeal carcinoma: pathogenic and clinical relevance

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    BACKGROUND: Engagement of CD40 promotes survival of undifferentiated nasopharyngeal carcinoma (UNPC) cells and similar effects are induced by the EBV oncoprotein LMP-1 that is expressed in a fraction of cases. Considering that CD40 may be activated also by the soluble isoform of CD40L (sCD40L), we investigated the serum levels of sCD40L in a series of 61 UNPC patients from Italy, a non-endemic area for this disease. RESULTS: At diagnosis, serum samples of UNPC patients contained significantly higher levels of sCD40L than age-matched healthy controls (p < 0.001). High levels of sCD40L (i.e., >18 ng/ml) were more frequently found in patients <40 years of age (p = 0.03) and with distant metastases at presentation (p = 0.03). Serum levels of sCD40L were inversely associated with the expression of the EBV oncoprotein LMP-1 (p = 0.03), which mimics a constitutively activated CD40. The amount of sCD40L decreased in a fraction of patients treated with local radiotherapy alone. Moreover, CD40L(+ )lymphoid cells admixed to neoplastic UNPC cells were detected in cases with high serum levels of sCD40L, suggesting that sCD40L is probably produced within the tumor mass. CONCLUSION: sCD40L may contribute to CD40 activation in UNPC cells, particularly of LMP-1-negative cases, further supporting the crucial role of CD40 signalling in the pathogenesis of UNPC. sCD40L levels may be useful to identify UNPC patients with occult distant metastases at presentation

    Search for the standard model Higgs boson in the H to ZZ to 2l 2nu channel in pp collisions at sqrt(s) = 7 TeV

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    A search for the standard model Higgs boson in the H to ZZ to 2l 2nu decay channel, where l = e or mu, in pp collisions at a center-of-mass energy of 7 TeV is presented. The data were collected at the LHC, with the CMS detector, and correspond to an integrated luminosity of 4.6 inverse femtobarns. No significant excess is observed above the background expectation, and upper limits are set on the Higgs boson production cross section. The presence of the standard model Higgs boson with a mass in the 270-440 GeV range is excluded at 95% confidence level.Comment: Submitted to JHE

    X-ray emission from the Sombrero galaxy: discrete sources