Mathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research.

%B Mathematics in Engineering %V 2 %P 230 %G eng %U http://dx.doi.org/10.3934/mine.2020011 %9 Perspective %R 10.3934/mine.2020011 %0 Journal Article %J The European Physical Journal E %D 2016 %T Motion planning and motility maps for flagellar microswimmers %A Giancarlo Cicconofri %A Antonio DeSimone %XWe study two microswimmers consisting of a spherical rigid head and a passive elastic tail. In the first one the tail is clamped to the head, and the system oscillates under the action of an external torque. In the second one, head and tail are connected by a joint allowing the angle between them to vary periodically, as a result of an oscillating internal torque. Previous studies on these models were restricted to sinusoidal actuations, showing that the swimmers can propel while moving on average along a straight line, in the direction given by the symmetry axis around which beating takes place. We extend these results to motions produced by generic (non-sinusoidal) periodic actuations within the regime of small compliance of the tail. We find that modulation in the velocity of actuation can provide a mechanism to select different directions of motion. With velocity-modulated inputs, the externally actuated swimmer can translate laterally with respect to the symmetry axis of beating, while the internally actuated one is able to move along curved trajectories. The governing equations are analysed with an asymptotic perturbation scheme, providing explicit formulas, whose results are expressed through motility maps. Asymptotic approximations are further validated by numerical simulations.

%B The European Physical Journal E %V 39 %P 72 %8 Jul %G eng %U https://doi.org/10.1140/epje/i2016-16072-y %R 10.1140/epje/i2016-16072-y %0 Journal Article %J International Journal of Non-Linear Mechanics %D 2015 %T Motility of a model bristle-bot: A theoretical analysis %A Giancarlo Cicconofri %A Antonio DeSimone %K Bristle-robots %K Crawling motility %K Frictional interactions %XBristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.

%B International Journal of Non-Linear Mechanics %V 76 %P 233 - 239 %G eng %U http://www.sciencedirect.com/science/article/pii/S0020746215000025 %R https://doi.org/10.1016/j.ijnonlinmec.2014.12.010 %0 Journal Article %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %T Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations %A Cacace, S. %A Antonin Chambolle %A Antonio DeSimone %A Livio Fedeli %B ESAIM: Mathematical Modelling and Numerical Analysis %I EDP Sciences %V 47 %P 837–858 %G eng %R 10.1051/m2an/2012048 %0 Conference Proceedings %B Materials Research Society Symposium Proceedings. Volume 1403, 2012, Pages 125-130 %D 2012 %T Mathematical and numerical modeling of liquid crystal elastomer phase transition and deformation %A Mariarita De Luca %A Antonio DeSimone %K Artificial muscle %X Liquid crystal (in particular, nematic) elastomers consist of cross-linked flexible polymer chains with embedded stiff rod molecules that allow them to behave as a rubber and a liquid crystal. Nematic elastomers are characterized by a phase transition from isotropic to nematic past a temperature threshold. They behave as rubber at high temperature and show nematic behavior below the temperature threshold. Such transition is reversible. While in the nematic phase, the rod molecules are aligned along the direction of the "nematic director". This molecular rearrangement induces a stretch in the polymer chains and hence macroscopic spontaneous deformations. The coupling between nematic order parameter and deformation gives rise to interesting phenomena with a potential for new interesting applications. In the biological field, the ability to considerably change their length makes them very promising as artificial muscles actuators. Their tunable optical properties make them suitable, for example, as lenses for new imaging systems. We present a mathematical model able to describe the behavior of nematic elastomers and numerical simulations reproducing such peculiar behavior. We use a geometrically linear version of the Warner and Terentjev model [1] and consider cooling experiments and stretching experiments in the direction perpendicular to the one of the director at cross-linking. %B Materials Research Society Symposium Proceedings. Volume 1403, 2012, Pages 125-130 %I Cambridge University Press %@ 9781605113807 %G en %U http://hdl.handle.net/1963/7020 %1 7011 %2 Physics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-12T10:02:18Z No. of bitstreams: 0 %R 10.1557/opl.2012.249 %0 Journal Article %J Continuum Mechanics and Thermodynamics %D 2011 %T Metastable equilibria of capillary drops on solid surfaces: a phase field approach %A Livio Fedeli %A Turco, Alessandro %A Antonio DeSimone %XWe discuss a phase field model for the numerical simulation of metastable equilibria of capillary drops resting on rough solid surfaces and for the description of contact angle hysteresis phenomena in wetting. The model is able to reproduce observed transitions of drops on micropillars from Cassie–Baxter to Wenzel states. When supplemented with a dissipation potential which describes energy losses due to frictional forces resisting the motion of the contact line, the model can describe metastable states such as drops in equilibrium on vertical glass plates. The reliability of the model is assessed by a detailed comparison of its predictions with experimental data on the maximal size of water drops that can stick on vertical glass plates which have undergone different surface treatments.

%B Continuum Mechanics and Thermodynamics %V 23 %P 453–471 %8 Sep %G eng %U https://doi.org/10.1007/s00161-011-0189-6 %R 10.1007/s00161-011-0189-6