We perform numerical simulations of odd microswimmers consisting three spheres and two springs. To describe the hydrodynamic interaction, both Oseen-type Rotne–Prager–Yamakawa (RPY)-type mobilities are used. For mobility, simulation results quantitatively reproduce asymptotic expression average velocity. RPY-type on other hand, velocity is smaller than that mobility deviation more pronounced fo...

The Drosophila pair-rule gene odd-skipped (odd) and two related genes, sister of odd (sob) and bowel (bowl), encode zinc finger containing proteins, two of which play important roles in embryonic development probably functioning as transcription factors. Here we report the cloning and expression analysis of a mouse gene related to odd, odd-skipped related 1 (Osr1). During early embryogenesis Os...

We consider odd Laplace operators arising in odd symplectic geometry. Approach based on semidensities (densities of weight 1/2) is developed. The role of semidensities in the Batalin–Vilkovisky formalism is explained. In particular, we study the relations between semidensities on an odd symplectic supermanifold and differential forms on a purely even Lagrangian submanifold. We establish a crite...

When time reversal is broken the viscosity tensor can have a non vanishing odd part. In two dimensions, and only then, such odd viscosity is compatible with isotropy. Allowing for odd viscosity leads to a generalization of the wave and Navier-Stokes equations. Elementary features of odd viscosity are examined by considering solutions of these equations for hypothetical fluids where the stress i...