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

Effect of fluid-colloid interactions on the mobility of a thermophoretic microswimmer in non-ideal fluids

Janus colloids propelled by light, e.g., thermophoretic particles, offer promising prospects as artificial microswimmers. However, their swimming behavior and its dependence on fluid properties and fluid-colloid interactions remain poorly understood. Here, we investigate the behavior of a thermophoretic Janus colloid in its own temperature gradient using numerical simulations. The dissipative particle dynamics method with energy conservation is used to investigate the behavior in non-ideal and ideal-gas like fluids for different fluid-colloid interactions, boundary conditions, and temperature-controlling strategies. The fluid-colloid interactions appear to have a strong effect on the colloid behavior, since they directly affect heat exchange between the colloid surface and the fluid. The simulation results show that a reduction of the heat exchange at the fluid-colloid interface leads to an enhancement of colloid's thermophoretic mobility. The colloid behavior is found to be different in non-ideal and ideal fluids, suggesting that fluid compressibility plays a significant role. The flow field around the colloid surface is found to be dominated by a source-dipole, in agreement with the recent theoretical and simulation predictions. Finally, different temperature-control strategies do not appear to have a strong effect on the colloid's swimming velocity

Stability of heterogeneous parallel-bond adhesion clusters under static load

Adhesion interactions mediated by multiple bond types are relevant for many biological and soft matter systems, including the adhesion of biological cells and functionalized colloidal particles to various substrates. To elucidate advantages and disadvantages of multiple bond populations for the stability of heterogeneous adhesion clusters of receptor-ligand pairs, a theoretical model for a homogeneous parallel adhesion bond cluster under constant loading is extended to several bond types. The stability of the entire cluster can be tuned by changing densities of different bond populations as well as their extensional rigidity and binding properties. In particular, bond extensional rigidities determine the distribution of total load to be shared between different sub-populations. Under a gradual increase of the total load, the rupture of a heterogeneous adhesion cluster can be thought of as a multistep discrete process, in which one of the bond sub-populations ruptures first, followed by similar rupture steps of other sub-populations or by immediate detachment of the remaining cluster. This rupture behavior is qualitatively independent of involved bond types, such as slip and catch bonds. Interestingly, an optimal stability is generally achieved when the total cluster load is shared such that loads on distinct bond populations are equal to their individual critical rupture forces. We also show that cluster heterogeneity can drastically affect cluster lifetime.Comment: 11 pages, 8 figure

Higher order relations in Fedosov supermanifolds

Higher order relations existing in normal coordinates between affine extensions of the curvature tensor and basic objects for any Fedosov supermanifolds are derived. Representation of these relations in general coordinates is discussed.Comment: 11 LaTex pages, no figure

Sharp-edged geometric obstacles in microfluidics promote deformability-based sorting of cells

Sorting cells based on their intrinsic properties is a highly desirable objective, since changes in cell deformability are often associated with various stress conditions and diseases. Deterministic lateral displacement (DLD) devices offer high precision for rigid spherical particles, while their success in sorting deformable particles remains limited due to the complexity of cell traversal in DLDs. We employ mesoscopic hydrodynamics simulations and demonstrate prominent advantages of sharp-edged DLD obstacles for probing deformability properties of red blood cells (RBCs). By consecutive sharpening of the pillar shape from circular to diamond to triangular geometry, a pronounced cell bending around an edge is achieved, serving as a deformability sensor. Bending around the edge is the primary mechanism, which governs the traversal of RBCs through such DLD device. This strategy requires an appropriate degree of cell bending by fluid stresses, which can be controlled by the flow rate, and exhibits good sensitivity to moderate changes in cell deformability. We expect that similar mechanisms should be applicable for the development of novel DLD devices that target intrinsic properties of many other cells.Comment: 16 pages, 9 figure