Symmetric equilibria of a thin elastic rod with self-contacts

Vibrations and spatial patterns in biomimetic surfaces: using the shark-skin effect to control blood clotting

We study the effect of small-amplitude fast vibrations and small-amplitude spatial patterns on various systems involving wetting and liquid flow, such as superhydrophobic surfaces, membranes and flow pipes. First, we introduce a mathematical method of averaging the effect of small spatial and temporal patterns and substituting them with an effective force. Such an effective force can change the equilibrium state of a system as well as a phase state, leading to surface texture-induced and vibration-induced phase control. Vibration and patterns can effectively jam holes in vessels with liquid, separate multi-phase flow, change membrane properties, result in propulsion and locomotion and lead to many other multi-scale, nonlinear effects including the shark-skin effect. We discuss the application of such effects to blood flow for novel biomedical 'haemophobic' applications which can prevent blood clotting and thrombosis by controlling the surface pattern at a wall of a vessel (e.g. a catheter or stent).This article is part of the themed issue 'Bioinspired hierarchically structured surfaces for green science'.

Vibrations and Spatial Patterns Change Effective Wetting Properties of Superhydrophobic and Regular Membranes

Small-amplitude fast vibrations and small surface micropatterns affect properties of various systems involving wetting, such as superhydrophobic surfaces and membranes. We review a mathematical method of averaging the effect of small spatial and temporal patterns. For small fast vibrations, this method is known as the method of separation of motions. The vibrations are substituted by effective force or energy terms, leading to vibration-induced phase control. A similar averaging method can be applied to surface micropatterns leading surface texture-induced phase control. We argue that the method provides a framework that allows studying such effects typical to biomimetic surfaces, such as superhydrophobicity, membrane penetration and others. Patterns and vibration can effectively jam holes and pores in vessels with liquid, separate multi-phase flow, change membrane properties, result in propulsion, and lead to many other multiscale, non-linear effects. Here, we discuss the potential application of these effects to novel superhydrophobic membranes.

An introduction to the mechanics of DNA

This article gives an overview of recent research on the mechanical properties and spatial deformations of the DNA molecule. Globally the molecule behaves like a uniform elastic rod, and its twisting and writhing govern its compaction and packaging within a cell. Meanwhile high mechanical stresses can induce structural transitions of DNA giving, for example, a phase diagram in the space of the applied tension and torque. Locally, the mechanical properties vary according to the local sequence organization. These variations play a vital role in the biological functioning of the molecule.