BRST quantization of quasi-symplectic manifolds and beyond

We consider a class of \textit{factorizable} Poisson brackets which includes almost all reasonable Poisson structures. A particular case of the factorizable brackets are those associated with symplectic Lie algebroids. The BRST theory is applied to describe the geometry underlying these brackets as well as to develop a deformation quantization procedure in this particular case. This can be viewed as an extension of the Fedosov deformation quantization to a wide class of \textit{irregular} Poisson structures. In a more general case, the factorizable Poisson brackets are shown to be closely connected with the notion of $n$-algebroid. A simple description is suggested for the geometry underlying the factorizable Poisson brackets basing on construction of an odd Poisson algebra bundle equipped with an abelian connection. It is shown that the zero-curvature condition for this connection generates all the structure relations for the $n$-algebroid as well as a generalization of the Yang-Baxter equation for the symplectic structure.Comment: Journal version, references and comments added, style improve

Behaviour of the von Willebrand Factor in Blood Flow

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.The von Willebrand factor (vWF), a large multimeric protein, is essential in hemostasis. Under normal conditions, vWF is present in blood as a globular polymer. However, in case of an injury, vWF is able to unwrap and bind to the vessel wall and to flowing platelets. Thus, platelets are significantly slowed down and can adhere to the wall and close the lesion. Nevertheless, it is still not clear how the unwrapping of the vWF is triggered. To better understand these complex processes, we employ a particle-based hydrodynamic simulation method to study the behaviour of vWF in blood flow. The vWF is modelled as a chain of beads (monomers) connected by springs. In addition, the monomers are subject to attractive interactions in order to represent characteristic properties of the vWF. The behaviour of vWF is investigated under different conditions including a freely-suspended polymer in shear flow and a polymer attached to a wall. We also examine the migration of vWF to a wall (margination) depending on shear rate and volume fraction of red blood cells (RBCs). Furthermore, the stretching of the vWF in flow direction depending on its radial position in a capillary is monitored. Our results show that attractive interactions between monomer beads increase margination efficiency and significantly affect the extension of vWF at different radial positions in blood vessels

Blood Flow in silico: From Single Cells to Blood Rheology

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.Mesoscale hydrodynamics simulations of red blood cells under flow have provided much new insight into their shapes and dynamics in microchannel flow. The presented results range from the behavior of single cells in confinement and the shape changes in sedimentation, to the clustering and arrangement of many cells in microchannels and the viscosity of red blood cell suspensions under shear flow. The interaction of red blood cells with other particles and cells, such as white blood cells, platelets, and drug carriers, shows an essential role of red blood cells in the margination of other blood components

Red blood cells (RBCs) visualisation in bifurcations and bends

Bifurcating networks are commonly found in nature. One example is the microvascular system, composed of blood vessels consecutively branching into daughter vessels, driving the blood into the capillaries, where the red blood cells (RBCs) are responsible for delivering O 2 and up taking cell waste and CO 2 . In this preliminary study, we explore a microfluidic bifurcating geometry inspired by such biological models, for investigating RBC partitioning as well as RBC-plasma separation favored by the consecutive bifurcating channels. A biomimetic design rule [1] based on Murray’s law [2] was used to set the channels’ dimensions along the network, which consists of consecutive bifurcating channels of reducing diameter. The ability to apply differential flow resistances by controlling the flow rates at the end of the network allowed us to monitor the formation of a cell-free layer (CFL) for different flow conditions at haematocrits of 1% and 5%. We have also compared the values of CFL thickness determined directly by the measurement on the projection image created from a stack of images or indirectly by analyzing the intensity profile in the same projection. The results obtained from this study confirm the potential to study RBC partitioning along bifurcating networks, which could be of particular interest for the separation of RBCs from plasma in point-of-care devices.JF would like to thank Professor Graça Minas and her coworkers for providing the laboratory facilities and technical help during the experiments.info:eu-repo/semantics/publishedVersio

Multiscale Modeling of Red Blood Cell Mechanics and Blood Flow in Malaria

Red blood cells (RBCs) infected by a Plasmodium parasite in malaria may lose their membrane deformability with a relative membrane stiffening more than ten-fold in comparison with healthy RBCs leading to potential capillary occlusions. Moreover, infected RBCs are able to adhere to other healthy and parasitized cells and to the vascular endothelium resulting in a substantial disruption of normal blood circulation. In the present work, we simulate infected RBCs in malaria using a multiscale RBC model based on the dissipative particle dynamics method, coupling scales at the sub-cellular level with scales at the vessel size. Our objective is to conduct a full validation of the RBC model with a diverse set of experimental data, including temperature dependence, and to identify the limitations of this purely mechanistic model. The simulated elastic deformations of parasitized RBCs match those obtained in optical-tweezers experiments for different stages of intra-erythrocytic parasite development. The rheological properties of RBCs in malaria are compared with those obtained by optical magnetic twisting cytometry and by monitoring membrane fluctuations at room, physiological, and febrile temperatures. We also study the dynamics of infected RBCs in Poiseuille flow in comparison with healthy cells and present validated bulk viscosity predictions of malaria-infected blood for a wide range of parasitemia levels (percentage of infected RBCs with respect to the total number of cells in a unit volume).United States. National Institutes of Health (Grant R01HL094270)National Science Foundation (U.S.). (Grant CBET-0852948)Singapore-MIT Alliance for Research and Technology Cente

The Weyl bundle as a differentiable manifold

Construction of an infinite dimensional differentiable manifold ${\mathbb R}^{\infty}$ not modelled on any Banach space is proposed. Definition, metric and differential structures of a Weyl algebra and a Weyl algebra bundle are presented. Continuity of the $\circ$-product in the Tichonov topology is proved. Construction of the $*$-product of the Fedosov type in terms of theory of connection in a fibre bundle is explained.Comment: 31 pages; revised version - some typoes have been eliminated, notation has been simplifie

Formal Deformations of Dirac Structures

In this paper we set-up a general framework for a formal deformation theory of Dirac structures. We give a parameterization of formal deformations in terms of two-forms obeying a cubic equation. The notion of equivalence is discussed in detail. We show that the obstruction for the construction of deformations order by order lies in the third Lie algebroid cohomology of the Dirac structure. However, the classification of inequivalent first order deformations is not given by the second Lie algebroid cohomology but turns out to be more complicated.Comment: LaTeX 2e, 26 pages, no figures. Minor changes and improvement

Groupoids and an index theorem for conical pseudo-manifolds

We define an analytical index map and a topological index map for conical pseudomanifolds. These constructions generalize the analogous constructions used by Atiyah and Singer in the proof of their topological index theorem for a smooth, compact manifold $M$. A main ingredient is a non-commutative algebra that plays in our setting the role of $C_0(T^*M)$. We prove a Thom isomorphism between non-commutative algebras which gives a new example of wrong way functoriality in $K$-theory. We then give a new proof of the Atiyah-Singer index theorem using deformation groupoids and show how it generalizes to conical pseudomanifolds. We thus prove a topological index theorem for conical pseudomanifolds

The geometry of a bi-Lagrangian manifold

This is a survey on bi-Lagrangian manifolds, which are symplectic manifolds endowed with two transversal Lagrangian foliations. We also study the non-integrable case (i.e., a symplectic manifold endowed with two transversal Lagrangian distributions). We show that many different geometric structures can be attached to these manifolds and we carefully analyse the associated connections. Moreover, we introduce the problem of the intersection of two leaves, one of each foliation, through a point and show a lot of significative examples.Comment: 30 page