Diving parameters obtained from high-speed video analysis.

<p>Diving parameters obtained from high-speed video analysis.</p

DataSheet1_Wave Equation Numerical Simulation and RTM With Mixed Staggered-Grid Finite-Difference Schemes.docx

For the conventional staggered-grid finite-difference scheme (C-SFD), although the spatial finite-difference (FD) operator can reach 2Mth-order accuracy, the FD discrete wave equation is the only second-order accuracy, leading to low modeling accuracy and poor stability. We proposed a new mixed staggered-grid finite-difference scheme (M-SFD) by constructing the spatial FD operator using axial and off-axial grid points jointly to approximate the first-order spatial partial derivative. This scheme is suitable for modeling the stress–velocity acoustic and elastic wave equation. Then, based on the time–space domain dispersion relation and the Taylor series expansion, we derived the analytical expression of the FD coefficients. Theoretically, the FD discrete acoustic wave equation and P- or S-wave in the FD discrete elastic wave equation given by M-SFD can reach the arbitrary even-order accuracy. For acoustic wave modeling, with almost identical computational costs, M-SFD can achieve higher modeling accuracy than C-SFD. Moreover, with a larger time step used in M-SFD than that used in C-SFD, M-SFD can achieve higher computational efficiency and reach higher modeling accuracy. For elastic wave simulation, compared to C-SFD, M-SFD can obtain higher modeling accuracy with almost the same computational efficiency when the FD coefficients are calculated based on the S-wave time–space domain dispersion relation. Solving the split elastic wave equation with M-SFD can further improve the modeling accuracy but will decrease the efficiency and increase the memory usage as well. Stability analysis shows that M-SFD has better stability than C-SFD for both acoustic and elastic wave simulations. Applying M-SFD to reverse time migration (RTM), the imaging artifacts caused by the numerical dispersion are effectively eliminated, which improves the imaging accuracy and resolution of deep formation.</p

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

<div><p>Whirligig beetles (<i>Coleoptera</i>, <i>Gyrinidae</i>) 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's 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.</p></div

The sequence of one hind leg stroke.

<p>In frames 1–5, only the hind leg is visible, with the middle leg emerging in frame 6. In frames 6–10 it is possible to observe the beating of both legs. During the course of one leg stroke, the effective area of the legs decreases in the horizontal plane, indicating that the effective area for forward propelling increases.</p

Swimming parameters obtained from high-speed video analysis.

<p>Swimming parameters obtained from high-speed video analysis.</p

Parameters obtained from micrographs.

<p>Parameters obtained from micrographs.</p

The SEM micrographs of the legs of <i>Gyrinus</i>.

<p>(A) SEM micrograph of the middle leg showing the folded swimming laminae. On the middle leg, the laminae are predominately on the outer surface. (B) SEM micrograph of the hind leg demonstrating the presence of laminae on both the inner and outer surface of the rowing blade. (C) SEM micrograph showing the significantly altered morphology of the foreleg. (D) Image of the point of attachment of a leg. The inset demonstrates the location of the micrograph relative to the beetle's body, with the area analyzed highlighted by the red box. SEM micrographs were used to measure the length (<i>L_laminae</i>) and width (<i>W_laminae</i>) of the laminae for calculation of the effective are of the hind (<i>S_h+</i>) and middle legs (<i>S_m+</i>) with laminae extended. In all micrographs, the scale bar = 100 µm.</p

Net forward trajectories from swimming simulations.

<p>As indicated above each frame, the beating patterns that generated a true linear path were those where the right and left middle legs (<i>m_r</i>+<i>m_l</i>), hind legs (<i>h_r</i>+<i>h_l</i>), and hind followed by middle legs (<i>h_r</i>+<i>h_l</i>, <i>m_r</i>+<i>m_l</i>) beat simultaneously. In these three cases, the total distance traveled was equal to Δy. For the other three cases where the middle right and left legs (<i>m_r</i>, <i>m_l</i>) and the hind right and left legs (<i>h_r</i>, <i>h_l</i>) beat alternately, and the simultaneous beating of the hind legs followed by the beating of a middle leg (<i>h_r</i>+<i>h_l</i>, <i>m_r</i>, <i>h_r</i>+<i>h_l</i>, <i>m_l</i>) the net forward distance traveled was calculated from a line between the start and end point. Numerical analysis of these trajectories is shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002792#pcbi-1002792-t004" target="_blank"><b>Table 4</b></a>.</p

Time-lapse images of the diving process.

<p>This image shows the complete diving process, from the 83 ms pre-diving to the 89 ms diving process. To illustrate the diving motion, images captured every 17 ms are overlaid onto each other to show the complete diving motion.</p

Diagram demonstrating how each parameter was calculated.

<p>(A) Top-down view of the body showing key parameters for swimming. (B&C) Side view of the body on the surface of water (indicated by blue line) showing both the maximum and minimum position of the legs during a leg beat when diving. In all of the above diagrams, the hind legs are indicated by the subscript <i>h</i>, while the middle legs are indicated by the subscript <i>m</i>. Using this notation, the length of the hind legs is <i>L_h</i>, etc. The direction of motion of the beetle is indicated by an arrow showing the forward velocity (<i>U_y</i>). The dashed line in B&C indicates the submerged portion of the beetle. All other parameters designations are listed in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002792#pcbi-1002792-t001" target="_blank"><b>Tables 1</b></a><b>–</b><a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002792#pcbi-1002792-t002" target="_blank"></a><a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002792#pcbi-1002792-t003" target="_blank"><b>3</b></a>.</p