Experimental Studies and Dynamics Modeling Analysis of the Swimming and Diving of Whirligig Beetles (Coleoptera: Gyrinidae)

Whirligig beetles (Coleoptera, Gyrinidae) can fly through the air, swiftly swim on the surface of water, and quickly dive across the air-water interface. The propulsive efficiency of the species is believed to be one of the highest measured for a thrust generating apparatus within the animal kingdom. The goals of this research were to understand the distinctive biological mechanisms that allow the beetles to swim and dive, while searching for potential bio-inspired robotics applications. Through static and dynamic measurements obtained using a combination of microscopy and high-speed imaging, parameters associated with the morphology and beating kinematics of the whirligig beetle\u27s legs in swimming and diving were obtained. Using data obtained from these experiments, dynamics models of both swimming and diving were developed. Through analysis of simulations conducted using these models it was possible to determine several key principles associated with the swimming and diving processes. First, we determined that curved swimming trajectories were more energy efficient than linear trajectories, which explains why they are more often observed in nature. Second, we concluded that the hind legs were able to propel the beetle farther than the middle legs, and also that the hind legs were able to generate a larger angular velocity than the middle legs. However, analysis of circular swimming trajectories showed that the middle legs were important in maintaining stable trajectories, and thus were necessary for steering. Finally, we discovered that in order for the beetle to transition from swimming to diving, the legs must change the plane in which they beat, which provides the force required to alter the tilt angle of the body necessary to break the surface tension of water. We have further examined how the principles learned from this study may be applied to the design of bio-inspired swimming/diving robots. DOI: 10.1371/journal.pcbi.100279

Observation and analysis of diving beetle movements while swimming

The fast swimming speed, flexible cornering, and high propulsion efficiency of diving beetles are primarily achieved by their two powerful hind legs. Unlike other aquatic organisms, such as turtle, jellyfish, fish and frog et al., the diving beetle could complete retreating motion without turning around, and the turning radius is small for this kind of propulsion mode. However, most bionic vehicles have not contained these advantages, the study about this propulsion method is useful for the design of bionic robots. In this paper, the swimming videos of the diving beetle, including forwarding, turning and retreating, were captured by two synchronized high-speed cameras, and were analyzed via SIMI Motion. The analysis results revealed that the swimming speed initially increased quickly to a maximum at 60% of the power stroke, and then decreased. During the power stroke, the diving beetle stretched its tibias and tarsi, the bristles on both sides of which were shaped like paddles, to maximize the cross-sectional areas against the water to achieve the maximum thrust. During the recovery stroke, the diving beetle rotated its tarsi and folded the bristles to minimize the cross-sectional areas to reduce the drag force. For one turning motion (turn right about 90 degrees), it takes only one motion cycle for the diving beetle to complete it. During the retreating motion, the average acceleration was close to 9.8 m/s2 in the first 25 ms. Finally, based on the diving beetle's hind-leg movement pattern, a kinematic model was constructed, and according to this model and the motion data of the joint angles, the motion trajectories of the hind legs were obtained by using MATLAB. Since the advantages of this propulsion method, it may become a new bionic propulsion method, and the motion data and kinematic model of the hind legs will be helpful in the design of bionic underwater unmanned vehicles

Whirligig beetles as corralled active Brownian particles

We study the collective dynamics of groups of whirligig beetles Dineutus discolor (Coleoptera: Gyrinidae) swimming freely on the surface of water. We extract individual trajectories for each beetle, including positions and orientations, and use this to discover (i) a density-dependent speed scaling like v ∼ ρ−ν with ν ≈ 0.4 over two orders of magnitude in density (ii) an inertial delay for velocity alignment of approximately 13 ms and (iii) coexisting high and low-density phases, consistent with motility-induced phase separation (MIPS). We modify a standard active Brownian particle (ABP) model to a corralled ABP (CABP) model that functions in open space by incorporating a density-dependent reorientation of the beetles, towards the cluster. We use our new model to test our hypothesis that an motility-induced phase separation (MIPS) (or a MIPS like effect) can explain the co-occurrence of high- and low-density phases we see in our data. The fitted model then successfully recovers a MIPS-like condensed phase for N = 200 and the absence of such a phase for smaller group sizes N = 50, 100

Dynamics and hydrodynamic efficiency of diving beetle while swimming

Diving beetle, an excellent biological prototype for bionic underwater vehicles, can achieve forward swimming, backward swimming, and flexible cornering by swinging its two powerful hind legs. An in-depth study of the propulsion performance of them will contribute to the micro underwater vehicles. In this paper, the kinematic and dynamic parameters, and the hydrodynamic efficiency of the diving beetle are studied by analysis of swimming videos using Motion Capture Technology, combined with CFD simulations. The results show that the hind legs of diving beetle can achieve high propulsion force and low return resistance during one propulsion cycle at both forward and backward swimming modes. The propulsion efficiencies of forward and backward swimming are 0.47 and 0.30, respectively. Although the efficiency of backward swimming is lower, the diving beetle can reach a higher speed in a short time at this mode, which can help it avoid natural enemies. At backward swimming mode, there is a long period of passive swing of hind legs, larger drag exists at higher speed during the recovery stroke, which reduces the propulsion efficiency to a certain extent. Reasonable planning of the swing speed of the hind legs during the power stroke and the recovery stroke can obtain the highest propulsion efficiency of this propulsion method. This work will be useful for the development of a bionic propulsion system of micro underwater vehicle

Top-down and bottom-up models of collective motion

Active matter is an expanding field of physics covering a diverse range of complex and beautiful phenomena. From examples we see in our everyday lives, such as the flight of birds and organisation of insects, to more esoteric bacteria and other micro-scale biological systems. What we can learn about the physical rules that pin these diverse systems together is important not just for our understanding of physics but our ability to utilise the natural world around us. The core of our understanding of Active matter spans between out-of-equilibrium analogues of wellknown thermodynamics to the realm of complex intelligent decision-making. From a top-down view point, we observe phenomena such as aggregation, ordered motion, dynamic pattern formation, leader-follower relationships, long range interactions, collisions avoidance, and coordinated motion to name a few, and model these directly within a mathematical formalism. From a bottom-up perspective we attempt to explain the generation of these phenomena from intrinsic process driving individual agents. In this thesis we consider a data-driven analysis of collective motion in an insect system, a top-down approach, as well as developing a model of individual decision making based upon future path entropy, a bottom-up approach. The latter results in the spontaneous emergence of some basic features of collective motion seen in real world examples, lending explanatory power

Control and Morphology Optimization of Passive Asymmetric Structures for Robotic Swimming

Aquatic creatures exhibit remarkable adaptations of their body to efficiently interact with the surrounding fluid. The tight coupling between their morphology, motion, and the environment are highly complex but serves as a valuable example when creating biomimetic structures in soft robotic swimmers. We focus on the use of asymmetry in structures to aid thrust generation and maneuverability. Designs of structures with asymmetric profiles are explored so that we can use morphology to `shape' the thrust generation. We propose combining simple simulation with automatic data-driven methods to explore their interactions with the fluid. The asymmetric structure with its co-optimized morphology and controller is able to produce 2.5 times the useful thrust compared to a baseline symmetric structure. Furthermore these asymmetric feather-like arms are validated on a robotic system capable of forward swimming motion while the same robot fitted with a plain feather is not able to move forward

Surface Driven Flows : Liquid Bridges, Drops and Marangoni Propulsion

Molecules sitting at a free liquid surface against vacuum or gas have weaker binding than molecules in the bulk. The missing (negative) binding energy can therefore be viewed as a positive energy added to the surface itself. Since a larger area of the surface contains larger surface energy, external forces must perform positive work against internal surface forces to increase the total area of the surface. Mathematically, the internal surface forces are represented by surface tension, defined as the normal force per unit of length. One common manifestation of surface tension is the difference in pressure it causes across a curved surface. This is the main principle behind capillary breakup extensional rheometry (CaBER). The other manifestation is the Marangoni flow which drives the interface towards the direction of the increasing surface tension gradient. The surface tension gradient can be caused by concentration gradient or by a temperature gradient (surface tension is a function of temperature). Both of these phenomenon will be investigated through various experimental techniques. Predicting and controlling the rheology of polymeric fluids as a function of molecular chemistry has been of great interest in both academia and industry. While extensional rheology measurements of polymer melts have been performed in the past, those experiments were performed under nitrogen and at temperatures chosen to avoid polymer degradation and reaction. In this work we will explore the effect that oxygen at high temperatures can have on both the shear and extensional rheology of a series of polymer melts. We will demonstrate the high temperature evolution of extensional viscosity of three selected commercially available polycarbonates – one linear, one branched and one hyper-branched. The measurements were performed using a custom built high temperature capillary extensional break up rheometer (CABER). The experiments were performed in the temperature range of T= 250C and 370C both in air and nitrogen. We will present a stark difference in the extensional behavior of the three grades of polycarbonate and demonstrate an obvious differentiation between random chain scission which is the first phase of polymer degradation and repolymerization or crosslinking which takes place at higher temperatures. In a number of recent studies, the large extensional viscosity of dilute polymer solutions has been shown to dramatically delay the breakup of jets into drops. For the low shear viscosity solutions, the jet breakup is initially governed by a balance of inertial and capillary stresses before transitioning to a balance of viscoelastic and capillary stresses at later times. This transition occurs at a critical time when the radius decay dynamics shift from a 2/3 power law to an exponential decay as the increasing deformation rate imposed on the fluid filament results in large molecular deformations and rapid crossover into the elastocapillary regime. By experimental fits of the elasto-capillary thinning diameter data, relaxation time as low as 40 microseconds have been successfully measured. In this work, we will show that with better understand of the transition from the inertia-capillary to the elasto-capillary breakup regimes that relaxation times close to a single microsecond can be measured with the relaxation time resolution limited only by the frame rate and spatial resolution of the high speed camera. In this work, the dynamics of drop formation and pinch-off will be presented using Dripping onto Substrate Extensional Rheometry (DoS) for a series of dilute solutions Polyethylene Oxide in water and in a water and glycerin mixture. Four different molecular weights between 100k and 1M g/mol will be shown with varying solvent viscosities between 1mPa-s and 22mPa-s and at concentrations between 0.004 and 0.5c*. We will show the dependence of the relaxation time and extensional viscosity on these varying parameters while searching for the lower limit in solution elasticity that can be detected. We will also show that this approach is a powerful technique for characterizing a notoriously difficult material, namely low-viscosity printing inks. In this last project we have investigated the flow dynamics around a cylindrical disk propelled by Marangoni propulsion. Self-propulsion was achieved by coating one quarter of the disk with either soap or isopropyl alcohol in order to generate and then maintain a surface tension gradient across the surfer. As the propulsion strength and the resulting disk velocity were increased, a transition from a straight-line translational motion to a rotational motion was observed. Although spinning has been observed before for asymmetric objects, these are the first observations of spinning of a symmetric Marangoni surfer. Particle tracking and Particle Image Velocimetry (PIV) measurements were used to interrogate the resulting flow field and understand the origin of the rotational motion of the disk. These measurements showed that as the Reynolds number was increased, interfacial vortices attached to sides of the disk were formed and intensified. Beyond a critical Reynolds number of Re \u3e 120, a single vortex was observed to shed resulting in an unbalanced torque on the disk that caused it to rotate. The interaction between the disk and the confining wall of the Petri dish was also studied. Upon approaching the bounding wall, a transition from straight-line motion to rotational motion was observed at significantly lower Reynolds numbers than on an unconfined interface. Interfacial curvature was found to either enhance or eliminate rotation motion depending on whether the curvature was repulsive (concave) or attractive (convex). Along with investigations done for the case of a disk shaped Marangoni surfer, we have also look at the effect of shape and orientation of motion on the on the stability of these surfers. We have looked at spherical shaped Marangoni surfers and also at elliptical disks. The stability of the elliptical disks were found to be strongly linked to their aspect ratio and their orientation. While looking at shape effects on Marangoni propulsion we have also investigated the effect of reverse flow underneath the surfer and its effect on the motion. We were experimentally able to observe the phenomenon of reverse Marangoni propulsion of surfers which was found to be a function of water depth underneath the surfer. We performed a parametric study on the effect of depth of water on the mode of motion of a cylindrical disk shaped and a spherical shaped surfer. Along with critical depth, it was found that the Reynolds number also played a critical role in flow reversal. At higher Reynolds number, no reverse phenomenon was observed as inertia dominated the motion of the disk whereas at low Reynolds numbers and at the critical Depth, flow reversal was observed

The dynamics and kinematics of bio-in swimming systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013.Cataloged from PDF version of thesis. Page 168 blank.Includes bibliographical references (p. 155-167).The motion of biological systems in fluids is inherently complex, even for the simplest organisms. In this thesis, we develop methods of analyzing locomotion of both mechanical and biological systems with the aim of rationalizing biology and informing robotic design. We begin by building on existing visualization framework by studying an idealized swimmer: Purcell's three-link swimmer, at low Reynolds number. This framework allows us to illustrate the complete dynamics of the system, design gaits for motion planning and identify optimal gaits in terms of efficiency and speed. We extend the three-link swimmer case to include effects such as the interaction between the links. By studying several systems, we broaden the applicability of our framework. These systems include a two-link swimmer at low Reynolds number with offset centers of buoyancy and mass and a swimmer with a continuously deformable shape, the serpenoid swimmer. Drawing on the principles behind the serpenoid swimmer, we develop the kinematic decomposition, a method using a singular value decomposition (SVD) that describes the motion of complex systems in a low order manner. We show that with only two degrees of freedom, one can adequately describe an animal's motion. We apply this method to species in both high and low Reynolds number environments to elucidate different phenomena, including chemotaxing and species comparison in spermatozoa, gait changes in eels (steady versus accelerating), kinematic responses to viscosity and viscoelasticity in C. elegans (nematodes), and the Kirmin gait in trout. Combined with our visualization framework, we successfully illustrate the generalized utility of the kinematic decomposition method to explore and understand fundamental kinematics of a wide range of both natural and man-made systems.by Lisa Janelle Burton.Ph.D

Mathematical Biology

Mathematical biology is a fast growing field of research, which on one hand side faces challenges resulting from the enormous amount of data provided by experimentalists in the recent years, on the other hand new mathematical methods may have to be developed to meet the demand for explanation and prediction on how specific biological systems function