We 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.

VL - 39 UR - https://doi.org/10.1140/epje/i2016-16072-y ER - TY - JOUR T1 - Motility of a model bristle-bot: A theoretical analysis JF - International Journal of Non-Linear Mechanics Y1 - 2015 A1 - Giancarlo Cicconofri A1 - Antonio DeSimone KW - Bristle-robots KW - Crawling motility KW - Frictional interactions AB -Bristle-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.

VL - 76 UR - http://www.sciencedirect.com/science/article/pii/S0020746215000025 ER - TY - JOUR T1 - Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations JF - ESAIM: Mathematical Modelling and Numerical Analysis Y1 - 2013 A1 - Cacace, S. A1 - Antonin Chambolle A1 - Antonio DeSimone A1 - Livio Fedeli PB - EDP Sciences VL - 47 ER - TY - Generic T1 - Mathematical and numerical modeling of liquid crystal elastomer phase transition and deformation T2 - Materials Research Society Symposium Proceedings. Volume 1403, 2012, Pages 125-130 Y1 - 2012 A1 - Mariarita De Luca A1 - Antonio DeSimone KW - Artificial muscle AB - 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. JF - Materials Research Society Symposium Proceedings. Volume 1403, 2012, Pages 125-130 PB - Cambridge University Press SN - 9781605113807 UR - http://hdl.handle.net/1963/7020 U1 - 7011 U2 - Physics U4 - 1 ER - TY - JOUR T1 - Metastable equilibria of capillary drops on solid surfaces: a phase field approach JF - Continuum Mechanics and Thermodynamics Y1 - 2011 A1 - Livio Fedeli A1 - Turco, Alessandro A1 - Antonio DeSimone AB -We 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 Cassieâ€“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.

VL - 23 UR - https://doi.org/10.1007/s00161-011-0189-6 ER -