Analytical Study of Certain Magnetohydrodynamic-alpha Models

In this paper we present an analytical study of a subgrid scale turbulence model of the three-dimensional magnetohydrodynamic (MHD) equations, inspired by the Navier-Stokes-alpha (also known as the viscous Camassa-Holm equations or the Lagrangian-averaged Navier-Stokes-alpha model). Specifically, we show the global well-posedness and regularity of solutions of a certain MHD-alpha model (which is a particular case of the Lagrangian averaged magnetohydrodynamic-alpha model without enhancing the dissipation for the magnetic field). We also introduce other subgrid scale turbulence models, inspired by the Leray-alpha and the modified Leray-alpha models of turbulence. Finally, we discuss the relation of the MHD-alpha model to the MHD equations by proving a convergence theorem, that is, as the length scale alpha tends to zero, a subsequence of solutions of the MHD-alpha equations converges to a certain solution (a Leray-Hopf solution) of the three-dimensional MHD equations.Comment: 26 pages, no figures, will appear in Journal of Math Physics; corrected typos, updated reference

The existence of an inverse limit of inverse system of measure spaces - a purely measurable case

The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the birth of the modern probability theory. Results from Kolmogorov [10], Bochner [2], Choksi [5], Metivier [14], Bourbaki [3] among others have paved the way of the deep understanding of the problem under consideration. All the above results, however, call for some topological concepts, or at least ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sucient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given

Synthesis and characterisation of pyrene-labelled polydimethylsiloxane networks: towards the in situ detection of strain in silicone elastomers

Pyrene-substituted polyhydromethylsiloxanes (PHMS-Py-x) were synthesised by the hydrosilylation reaction of prop-3-enyloxymethylpyrene with polyhydromethylsiloxane (M-n = 3700). The ratio of pyrene substituent to Si-H unit was varied to afford a range of pyrene-functionalised polysiloxanes. These copolymers were subsequently incorporated into polydimethylsiloxane (PDMS) elastomers by curing via either Pt(0) catalysed hydrosilylation with divinyl-terminated PDMS (M-n = 186) and tetrakis(dimethylsiloxy) silane, or Sn(II) catalysed condensation with alpha,omega-dihydroxyPDMS (M-n = 26 000) and tetraethoxysilane. An alternative method involving the synthesis and integration of [3-(pyren-1-ylmethoxy)propyl]triethoxysilane (Py-TEOS) into PDMS elastomers was also investigated: a mixture of alpha,omega-dihydroxyPDMS (M-n = 26 000), tetraethoxysilane, and Py-TEOS was cured using an Sn( II) catalyst. Certain of the resulting fluorescent pyrene-labelled elastomers were studied by differential scanning calorimetry and dynamic mechanical analysis. No significant changes were observed in the thermal or mechanical properties of the elastomers containing pyrene when compared to otherwise identical samples not containing pyrene. All of the pyrene-containing elastomers were demonstrated to be fluorescent under suitable excitation in a photoluminescent spectrometer. Two of the elastomers were placed in a photoluminescence spectrometer and subjected to cycles of extension and relaxation (strain = 0-16.7%) while changes in the emission spectra were monitored. The resulting spectra of the elastomer containing the PHMS-Py-50 copolymers were variable and inconsistent. However, the emission peaks of elastomers containing Py-TEOS displayed clear and reproducible changes in fluorescence intensity upon stretching and relaxation. The intensity of the monomer and excimer emission peaks was observed to increase with elongation of the sample and decrease upon relaxation. Furthermore, the ratio of the intensities of the excimer : monomer peak decreased with elongation and increased with relaxation. In neither case was there appreciable hysteresis, suggesting that fluorescent labelling of elastomers is a valid approach for the non-invasive in situ monitoring of stress and strain in such materials

Stochastic Reaction-diffusion Equations Driven by Jump Processes

We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative functional. The drift in the equations contains a dissipative nonlinearity of polynomial growth.Comment: See journal reference for teh final published versio

Assessment of Xenoestrogens Using Three Distinct Estrogen Receptors and the Zebrafish Brain Aromatase Gene in a Highly Responsive Glial Cell System

The brain cytochrome P450 aromatase (Aro-B) in zebrafish is expressed in radial glial cells and is strongly stimulated by estrogens (E(2)); thus, it can be used in vivo as a biomarker of xenoestrogen effects on the central nervous system. By quantitative real-time polymerase chain reaction, we first confirmed that the expression of Aro-B gene is robustly stimulated in juvenile zebrafish exposed to several xenoestrogens. To investigate the impact of environmental estrogenic chemicals on distinct estrogen receptor (ER) activity, we developed a glial cell-based assay using Aro-B as the target gene. To this end, the ER-negative glial cell line U251-MG was transfected with the three zebrafish ER subtypes and the Aro-B promoter linked to a luciferase reporter gene. E(2) treatment of U251-MG glial cells cotransfected with zebrafish ER-α and the Aro-B promoter–luciferase reporter resulted in a 60- to 80-fold stimulation of luciferase activity. The detection limit was < 0.05 nM, and the EC(50) (median effective concentration) was 1.4 nM. Interestingly, in this glial cell context, maximal induction achieved with the Aro-B reporter was three times greater than that observed with a classical estrogen-response-element reporter gene (ERE-tk-Luc). Dose–response analyses with ethynylestradiol (EE(2)), estrone (E(1)), α-zeralenol, and genistein showed that estrogenic potency of these agents markedly differed depending on the ER subtype in the assay. Moreover, the combination of these agents showed an additive effect according to the concept of concentration addition. This confirmed that the combined additive effect of the xenoestrogens leads to an enhancement of the estrogenic potency, even when each single agent might be present at low effect concentrations. In conclusion, we demonstrate that our bioassay provides a fast, reliable, sensitive, and efficient test for evaluating estrogenic potency of endocrine disruptors on ER subtypes in a glial context

Multifragment production in Au+Au at 35 MeV/u

Multifragment disintegration has been measured with a high efficiency detection system for the reaction $Au + Au$ at $E/A = 35\ MeV$. From the event shape analysis and the comparison with the predictions of a many-body trajectories calculation the data, for central collisions, are compatible with a fast emission from a unique fragment source.Comment: 9 pages, LaTex file, 4 postscript figures available upon request from [email protected]. - to appear in Phys. Lett.

Genomic modelling of the ESR1 Y537S mutation for evaluating function and new therapeutic approaches for metastatic breast cancer

Drugs that inhibit estrogen receptor-α (ER) activity have been highly successful in treating and reducing breast cancer progression in ER-positive disease. However, resistance to these therapies presents a major clinical problem. Recent genetic studies have shown that mutations in the ER gene are found in >20% of tumours that progress on endocrine therapies. Remarkably, the great majority of these mutations localize to just a few amino acids within or near the critical helix 12 region of the ER hormone binding domain, where they are likely to be single allele mutations. Understanding how these mutations impact on ER function is a prerequisite for identifying methods to treat breast cancer patients featuring such mutations. Towards this end, we used CRISPR-Cas9 genome editing to make a single allele knock-in of the most commonly mutated amino acid residue, tyrosine 537, in the estrogen-responsive MCF7 breast cancer cell line. Genomic analyses using RNA-seq and ER ChIP-seq demonstrated that the Y537S mutation promotes constitutive ER activity globally, resulting in estrogen-independent growth. MCF7-Y537S cells were resistant to the anti-estrogen tamoxifen and fulvestrant. Further, we show that the basal transcription factor TFIIH is constitutively recruited by ER-Y537S, resulting in ligand-independent phosphorylation of Serine 118 (Ser118) by the TFIIH kinase, cyclin-dependent kinase (CDK)7. The CDK7 inhibitor, THZ1 prevented Ser118 phosphorylation and inhibited growth of MCF7-Y537S cells. These studies confirm the functional importance of ER mutations in endocrine resistance, demonstrate the utility of knock-in mutational models for investigating alternative therapeutic approaches and highlight CDK7 inhibition as a potential therapy for endocrine-resistant breast cancer mediated by ER mutations

Reconstitution d'une unité transcriptionnelle à partir du promoteur du gène du récepteur aux oestrogènes de truite arc-en-ciel dans la levure Saccharomyces cerevisiae

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