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

Sintering characteristics of red mud compact

It is beyond doubt that activity of primary industries often yields substantial amounts of byproducts. The disposal in the original industrial site is favoured by economic reasons though traditional storage in nearby dumps can be impractical owing to the considerable masses involved and environmental restrictions. The local exploitation of these by-products is therefore a growing technological aspect of basic industries and one tenable option is their re-use as starting materials for other productions.This huge amount of industrial yproducts/wastes which is becoming a client for increasing environmental pollution & generation of a huge amount of unutilized resources. With a view to the above, this research is aimed at finding out utilization of such things/material/industrial byproducts for value added applications & also helps to solve the environmental problems. The present piece of my research work aims at, to provide a valued input/utilization to industrial byproduct/waste. An emblematic case is the ‘red mud’ discharged by industry producing alumina from bauxite: alkaline digestion of 2.5 t of bauxite affords alumina and ≈1.5 t of red mud ,so that an average Al2O3 productivity of 5×105 t year−1 involves a mass of by-products of ≈7.5×105 t year−1 discharged as slurry retaining variable water contents. This amount is composed of Fe and Ti oxides, behaving as chemically inert matter, with variable percentages of nominal SiO2,Al2O3 and Na2O. The material is available as a watery mixture which settles slowly and may easily be conveyed from station to station by continuous fluid-carrying machinery.The recycling of the mud, after curing or high temperature annealing — up to 1200°C — for large-rate daily mass consumption industries such as bricks and tile kilns has been put forward in a number of papers[2,3,4,5,6,7,8,9]Most of the above reports appear fragmentary and, to some extent surprising, characterization work is limited to the elemental analysis of the raw material and the identification of the crystalline phases in dried samples. However, the definition of thermal behaviour in a wide working range of temperatures appears mandatory for a feasible exploitation of the mud in high temperature applications. Indeed, the reactivity of red mud components on heating may promote ceramization and shrinkage and, apart from other qualities, may affect the mechanical features of clay-based items fabricated with bauxite-waste addition.Accordingly, we focus here on the thermal behaviour of the mud, the solid-state transformations and solid–liquid phase transitions. The use of thermal analysis coupled with of X-ray diffraction methods seemed well suitable for the problem at hand. The present study is a part of a long-term project on the exploitation of red mud as a clay additive for the ceramic industry or as a compound for self-binding mortars in the fabrication of stoneware

Sintering Behavior of Red Mud Compact

It is beyond doubt that activity of primary industries often yields substantial amounts of byproducts. The disposal in the original industrial site is favoured by economic reasons though traditional storage in nearby dumps can be impractical owing to the considerable masses involved and environmental restrictions. The local exploitation of these by-products is therefore a growing technological aspect of basic industries and one tenable option is their re-use as starting materials for other productions. This huge amount of industrial byproducts/wastes which is becoming a client for increasing environmental pollution & generation of a huge amount of unutilized resources. With a view to the above, this research is aimed at finding out utilization of such things/materials/industrial byproducts for value added applications & also helps to solve the environmental problems. The present piece of my research work aims at, to provide a valued input/utilization to industrial byproduct/waste

The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with N point vortices

This paper studies the dynamical fluid plus rigid-body system consisting of a two-dimensional rigid cylinder of general cross-sectional shape interacting with N point vortices. We derive the equations of motion for this system and show that, in particular, if the vortex strengths sum to zero and the rigid-body has a circular shape, the equations are Hamiltonian with respect to a Poisson bracket structure that is the sum of the rigid body Lie–Poisson bracket on Se(2)*, the dual of the Lie algebra of the Euclidean group on the plane, and the canonical Poisson bracket for the dynamics of N point vortices in an unbounded plane. We then use this Hamiltonian structure to study the linear and nonlinear stability of the moving Föppl equilibrium solutions using the energy-Casimir method

Non-invasive determination of external forces in vortex-pair-cylinder interactions

Expressions for the conserved linear and angular momenta of a dynamically coupled fluid + solid system are derived. Based on the knowledge of the flow velocity field, these expressions allow the determination of the external forces exerted on a body moving in the fluid such as, e.g., swimming fish. The verification of the derived conserved quantities is done numerically. The interaction of a vortex pair with a circular cylinder in various configurations of motions representing a generic test case for a dynamically coupled fluid + solid system is investigated in a weakly compressible Navier-Stokes setting using a Cartesian cut-cell method, i.e., the moving circular cylinder is represented by cut cells on a moving mesh. The objectives of this study are twofold. The first objective is to show the robustness of the derived expressions for the conserved linear and angular momenta with respect to bounded and discrete data sets. The second objective is to study the coupled dynamics of the vortex pair and a neutrally buoyant cylinder free to move in response to the fluid stresses exerted on its surface. A comparison of the vortex-body interaction with the case of a fixed circular cylinder evidences significant differences in the vortex dynamics. When the cylinder is fixed strong secondary vorticity is generated resulting in a repeating process between the primary vortex pair and the cylinder. In the neutrally buoyant cylinder case, a stable structure consisting of the primary vortex pair and secondary vorticity shear layers stays attached to the moving cylinder. In addition to these fundamental cases, the vortex-pair-cylinder interaction is studied for locomotion at constant speed and locomotion at constant thrust. It is shown that a similar vortex structure like in the neutrally buoyant cylinder case is obtained when the cylinder moves away from the approaching vortex pair at a constant speed smaller than the vortex pair translational velocity. Finally, the idealized symmetric settings are complemented by an asymmetric interaction of a vortex pair and a cylinder. This case is discussed for a fixed and a neutrally buoyant cylinder to show the validity of the derived relations for multi-dimensional body dynamics

Regulation of cadherin adhesion at intercellular junctions

Adhesion proteins maintain cell-cell interactions, which are critical for tissue formation and the hierarchical organization of all multicellular organisms, and among them, cadherins are the major transmembrane cell-cell adhesion proteins in all vertebrate tissues. Regulation of cadherin mediated adhesion at cell-cell junctions is crucial to our understanding of development and disease. This thesis focuses on the regulation of cadherin adhesion, which can be influenced by its extracellular domain interactions, ligand or antibody binding, post translational modifications, or inside out signaling from cytoplasmic binding proteins. In this thesis, micropipette-based adhesion frequency measurements of cadherin-mediated, cell-cell binding kinetics identified a unique kinetic signature that appears to reflect both adhesive (trans) bonds between cadherins on opposing cells and lateral (cis) interactions between cadherins on the same cell. These kinetic measurements were used to assess the impact of confinement within narrow adhesion zones on the assembly of intercellular adhesions. Specifically, a unique kinetic signature suggested the formation of lateral interactions that were not detected in solution binding assays. Mutations postulated to disrupt lateral cadherin association altered the kinetic signature, but did not affect cadherin binding affinity. Perturbed kinetics further correlated with altered cadherin clustering at cell-cell junctions, wound healing dynamics, and paracellular permeability. Adhesion frequency measurements were used to demonstrate the allosteric regulation of cadherin adhesive function. In this thesis, measured kinetics of cadherin-mediated intercellular adhesion demonstrated quantitatively that activating anti-E-cadherin monoclonal antibodies or the dephosphorylation of a cytoplasmic binding partner, p120 catenin, increased the homophilic binding affinity of E-cadherin on Colo 205 cells. Further studies of Colo 205 cells demonstrated that four treatments, which similarly altered p120 catenin phosphorylation resulted in quantitatively similar enhancement in E-cadherin affinity. Using this approach, I further investigated the effect of N-linked and O-linked glycosylation on E-cadherin activity and function. Results revealed that, contrary to the influence of glycosylation on N-cadherin function, N-glycosylation of E-cadherin in the EC4 and EC5 domains negatively regulated cadherin adhesion, by altering binding kinetics and clustering at cell-cell junctions. This suggests the influence of N-glycosylation depends on its position in the cadherin ectodomain. In conclusion, this dissertation describes studies which elucidated different mechanisms regulating cadherin adhesive function. Results showed that cadherin binding is regulated by its ectodomain interactions at cell-cell junctions, by glycosylation, and by allosteric inside-out signaling. These findings were enabled by the adhesion frequency measurements, which enabled quantitative assessment of cadherin binding function, in the native context of the cell membrane and cytosolic binding partners