The effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin’s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.

10aCircumnutations10aFlutter instability10aGravitropism10aHopf bifurcation1 aAgostinelli, Daniele1 aLucantonio, Alessandro1 aNoselli, Giovanni1 aDeSimone, Antonio uhttp://www.sciencedirect.com/science/article/pii/S002250961930610601765nas a2200217 4500008004100000022001400041245005300055210005300108300001400161490000700175520110000182653002201282653002501304653002801329653003001357653002701387100002201414700001801436700002201454856007101476 2015 eng d a0022-509600aLiquid crystal elastomer strips as soft crawlers0 aLiquid crystal elastomer strips as soft crawlers a254 - 2720 v843 aIn this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, ‘breathing-like’ deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

10aCrawling motility10aDirectional surfaces10aFrictional interactions10aLiquid crystal elastomers10aSoft biomimetic robots1 aDeSimone, Antonio1 aGidoni, Paolo1 aNoselli, Giovanni uhttp://www.sciencedirect.com/science/article/pii/S002250961530043001733nas a2200217 4500008004100000022001400041245003700055210003700092300001200129490000700141520111900148653002901267653001901296653002201315653002501337653002001362100001801382700002201400700002201422856007101444 2014 eng d a0020-746200aCrawling on directional surfaces0 aCrawling on directional surfaces a65 - 730 v613 aIn this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding ‘along the grain’, and high resistance when sliding ‘against the grain’. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.

10aBio-mimetic micro-robots10aCell migration10aCrawling motility10aDirectional surfaces10aSelf-propulsion1 aGidoni, Paolo1 aNoselli, Giovanni1 aDeSimone, Antonio uhttp://www.sciencedirect.com/science/article/pii/S002074621400021301213nas a2200145 4500008004100000245011200041210006900153260001300222520069800235653001900933100002200952700002000974700002200994856005101016 2014 en d00aDiscrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost0 aDiscrete onedimensional crawlers on viscous substrates achievabl bElsevier3 aWe study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility.10aCell migration1 aNoselli, Giovanni1 aTatone, Amabile1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3444901083nas a2200121 4500008004100000245012700041210006900168260002900237520052100266100002200787700002200809856013000831 2014 en d00aA robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model0 arobotic crawler exploiting directional frictional interactions e bRoyal Society Publishing3 aWe present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. ‘breathing-like’ deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations.1 aNoselli, Giovanni1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/robotic-crawler-exploiting-directional-frictional-interactions-experiments-numerics-and01071nas a2200145 4500008004100000245006700041210006600108260001300174520054900187100002200736700002400758700002200782700002000804856010100824 2013 en d00aCrawlers in viscous environments: linear vs nonlinear rheology0 aCrawlers in viscous environments linear vs nonlinear rheology bElsevier3 aWe study model self-propelled crawlers which derive their propulsive capabilities from the tangential resistance to motion offered by the environment. Two types of relationships between tangential forces and slip velocities are considered: a linear, Newtonian one and a nonlinear one of Bingham-type. Different behaviors result from the two different rheologies. These differences and their implications in terms of motility performance are discussed. Our aim is to develop new tools and insight for future studies of cell motility by crawling.1 aDeSimone, Antonio1 aGuarnieri, Federica1 aNoselli, Giovanni1 aTatone, Amabile uhttps://www.math.sissa.it/publication/crawlers-viscous-environments-linear-vs-nonlinear-rheology