These notes are preliminary and informal. My aim is to provide an introduction to some of the basic ideas that have emerged in recent decades in the fluids literature that have a fundamentally topological character. That is, rather than focusing on details such as velocity profile or pressure field, this material deals with persistent invariant properties of a flow field, features which often h...

We show that a microswimmer trapped thermodynamically at fluid-fluid interfaces experiences torque arising from the hydrodynamic boundary condition interface. This turns force dipoles corresponding to pullers perpendicular and pushers parallel demonstrate in general case, when there is viscosity contrast across interface, steady state orientation given by interplay between torques self-propulsi...

We formalize the concept of fluid particle that it is heuristically introduced in textbooks of fluid mechanics. Fluid particles are regarded as portions of fluid that move along the flow field and they have an extension. A natural way of assigning an extension to a set of points is through a tessellation. With a minimum of physical input information a well-defined discrete fluid particle model ...

Nowadays, atomic-force microscopy plays a significant role in nanoscience and nanotechnology, and is widely used for direct measurement at atomic scale and scanning the sample surfaces. In tapping mode, the microcantilever of atomic-force microscope is excited at resonance frequency. Therefore, it is important to study its resonance. Moreover, atomic-force microscopes can be operated in fluid e...

A central feature that scientists are interested in is the dynamics of fluid interfaces or the so called material boundaries in multi-fluid simulation . Visualization techniques for capturing fluid interface are based on one of about three basic algorithms. In this paper, we give a survey of the existing interface tracking algorithms, including backgrounds, terms, procedures as well as pointers...