Geometric phases for corotating elliptical vortex patches

We describe a geometric phase that arises when two elliptical vortex patches corotate. Using the Hamiltonian moment model of Melander, Zabusky, and Styczek [J. Fluid Mech. 167, 95–115 (1986)] we consider two corotating uniform elliptical patches evolving according to the second order truncated equations of the model. The phase is computed in the adiabatic setting of a slowly varying Hamiltonian as in the work of Hannay [J. Phys. A 18, 221–230 (1985)] and Berry [Proc. R. Soc. London, Ser. A 392, 45–57 (1984)]. We also discuss the geometry of the symplectic phase space of the model in the context of nonadiabatic phases. The adiabatic phase appears in the orientation angle of each patch—it is similiar in form and is calculated using a multiscale perturbation procedure as in the point vortex configuration of Newton [Physica D 79, 416–423 (1994)] and Shashikanth and Newton [J. Nonlinear Sci. 8, 183–214 (1998)], however, an extra factor due to the internal stucture of the patch is present. The final result depends on the initial orientation of the patches unlike the phases in the works of Hannay and Berry [J. Phys. A 18, 221–230 (1985)]; [Proc. R. Soc. London, Ser. A 392, 45–57 (1984)]. We then show that the adiabatic phase can be interpreted as the holonomy of a connection on the trivial principal fiber bundle pi:T2×S1-->S1, where T2 is identified with the product of the momentum level sets of two Kirchhoff vortex patches and S1 is diffeomorphic to the momentum level set of two point vortex motion. This two point vortex motion is the motion that the patch centroids approach in the adiabatic limit

STEREO SELECTIVE SYNTHESIS OF NOVEL LIGNAN INTERMEDIATES AS ANTIMICROBIAL AGENTS

Objectives: The aim of the present study was to synthesize a series of new lignan intermediates as potential antimicrobial agents.Methods: Substituted benzene and aromatic acids or acid chlorides were converted to benzophenones 1(a-f). The benzophenones 1(a-f) on Stobbe condensation with and diethyl succinate in the presence of potassium t-butoxide yielded 4-(4-aryl)-4-(4-aryl)-3-ethoxycarbonyl-but-3-enoic acids (2a, 2f) and a mixture of E and Z-isomers of 4,4-diaryl-3-ethoxycarbonyl-but-3-enoic acids 2(b-e) and 3(b-e) in relatively good yields. The synthesized compounds were tested for their antimicrobial susceptibility against different fungi and bacteria species.Results: The Stobbe condensation of benzophenones 1(a-f) and diethyl succinate in the presence of potassium t-butoxide yielded 4-(4-aryl)-4-(4-aryl)-3-ethoxycarbonyl-but-3-enoic acids (2a, 2f) and a mixture of E and Z-isomers of 4,4-diaryl-3-ethoxycarbonyl-but-3-enoic acids 2(b-e) and 3(b-e) in good yields. The compounds 1a and 1f yielded only 2a and 2f but not 3a and 3f due to symmetrical substitution in the aromatic rings. The structures of the new lignan intermediates were confirmed by spectral studies and elemental analysis.Conclusions: Results of the antimicrobial activity reveal that some of the compounds particularly 2c, 2d, 3c and 3d act as potential antimicrobial agents different fungal and bacterial organisms.Â

The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation

We consider the motion of a planar rigid body in a potential flow with circulation and subject to a certain nonholonomic constraint. This model is related to the design of underwater vehicles. The equations of motion admit a reduction to a 2-dimensional nonlinear system, which is integrated explicitly. We show that the reduced system comprises both asymptotic and periodic dynamics separated by a critical value of the energy, and give a complete classification of types of the motion. Then we describe the whole variety of the trajectories of the body on the plane.Comment: 25 pages, 7 figures. This article uses some introductory material from arXiv:1109.321

Ethyl 2-Cyano-5-Oxo-5-(thiophen-2-yl)-3-(3,4,5-trimethoxyphenyl) Pentanoate

In the title compound, C21H23NO6S, the dihedral angle between the thio­pene and benzene rings is 88.66 (6)°. In the crystal, mol­ecules are connected by C—H⋯N and C—H⋯O hydrogen bonds, forming a tape along [10-1]. In addition, C—H⋯π and π–π stacking [centroid–centroid distance = 3.879 (2) Å between the thio­phene rings] inter­actions are observed

Ecology and abundance of zooplankton in Karanja reservoir

The present work aims to study the Zooplankton seasonal distribution and diversity in Karanja reservoir, Bidar district for the period of two years from October 2001 to September 2003. We have recorded 36 species of which, 15 species belongs to rotifera, 11 species belongs to cladocera, nine species belongs to copepoda and ostracoda three species. Among zooplankton, particularly rotifera was the dominant group throughout the study period and highest count was recorded in the month of March 2003. Cluster analysis was also revealed by dendrogram and Shannon diversity index is also presented. Zooplankton community is also correlated with physicochemical parameters

Identification of QTLs and candidate genes for high grain Fe and Zn concentration in sorghum [Sorghum bicolor (L.)Moench]

Sorghum is a major food crop in the semi-arid tropics of Africa and Asia. Enhancing the grain iron (Fe) and zinc (Zn) concentration in sorghum using genetic approaches would help alleviate micronutrient malnutrition in millions of poor people consuming sorghum as a staple food. To localize genomic regions associated with grain Fe and Zn, a sorghum F6 recombinant inbred line (RIL) population (342 lines derived from cross 296B PVK 801) was phenotyped in six environments, and genotyped with simple sequence repeat (SSR), DArT (Diversity Array Technology) and DArTSeq (Diversity Array Technology) markers. Highly significant genotype environment interactions were observed for both micronutrients. Grain Fe showed greater variation than Zn. A sorghum genetic map was constructed with 2088 markers (1148 DArTs, 927 DArTSeqs and 13 SSRs) covering 1355.52 cM with an average marker interval of 0.6 cM. Eleven QTLs (individual) and 3 QTLs (across) environments for Fe and Zn were identified. We identified putative candidate genes from the QTL interval of qfe7.1, qzn7.1, and qzn7.2 (across environments) located on SBI-07 involved in Fe and Zn metabolism. These were CYP71B34, and ZFP 8 (ZINC FINGER PROTEIN 8). After validation, the linked markers identified in this study can help in developing high grain Fe and Zn sorghum cultivars in sorghum improvement programs globally

Paneth cell dysfunction in radiation injury and radio-mitigation by human α-defensin 5

IntroductionThe mechanism underlying radiation-induced gut microbiota dysbiosis is undefined. This study examined the effect of radiation on the intestinal Paneth cell α-defensin expression and its impact on microbiota composition and mucosal tissue injury and evaluated the radio-mitigative effect of human α-defensin 5 (HD5).MethodsAdult mice were subjected to total body irradiation, and Paneth cell α-defensin expression was evaluated by measuring α-defensin mRNA by RT-PCR and α-defensin peptide levels by mass spectrometry. Vascular-to-luminal flux of FITC-inulin was measured to evaluate intestinal mucosal permeability and endotoxemia by measuring plasma lipopolysaccharide. HD5 was administered in a liquid diet 24 hours before or after irradiation. Gut microbiota was analyzed by 16S rRNA sequencing. Intestinal epithelial junctions were analyzed by immunofluorescence confocal microscopy and mucosal inflammatory response by cytokine expression. Systemic inflammation was evaluated by measuring plasma cytokine levels.ResultsIonizing radiation reduced the Paneth cell α-defensin expression and depleted α-defensin peptides in the intestinal lumen. α-Defensin down-regulation was associated with the time-dependent alteration of gut microbiota composition, increased gut permeability, and endotoxemia. Administration of human α-defensin 5 (HD5) in the diet 24 hours before irradiation (prophylactic) significantly blocked radiation-induced gut microbiota dysbiosis, disruption of intestinal epithelial tight junction and adherens junction, mucosal barrier dysfunction, and mucosal inflammatory response. HD5, administered 24 hours after irradiation (treatment), reversed radiation-induced microbiota dysbiosis, tight junction and adherens junction disruption, and barrier dysfunction. Furthermore, HD5 treatment also prevents and reverses radiation-induced endotoxemia and systemic inflammation.ConclusionThese data demonstrate that radiation induces Paneth cell dysfunction in the intestine, and HD5 feeding prevents and mitigates radiation-induced intestinal mucosal injury, endotoxemia, and systemic inflammation