Bioengineering Program, Georgia Institute of Technology, Atlanta, GA 30332-0250, USA.
J R Soc Interface. 2011 Sep 7;8(62):1332-45. doi: 10.1098/rsif.2010.0678. Epub 2011 Mar 4.
We integrate biological experiment, empirical theory, numerical simulation and a physical model to reveal principles of undulatory locomotion in granular media. High-speed X-ray imaging of the sandfish lizard, Scincus scincus, in 3 mm glass particles shows that it swims within the medium without using its limbs by propagating a single-period travelling sinusoidal wave down its body, resulting in a wave efficiency, η, the ratio of its average forward speed to the wave speed, of approximately 0.5. A resistive force theory (RFT) that balances granular thrust and drag forces along the body predicts η close to the observed value. We test this prediction against two other more detailed modelling approaches: a numerical model of the sandfish coupled to a discrete particle simulation of the granular medium, and an undulatory robot that swims within granular media. Using these models and analytical solutions of the RFT, we vary the ratio of undulation amplitude to wavelength (A/λ) and demonstrate an optimal condition for sand-swimming, which for a given A results from the competition between η and λ. The RFT, in agreement with the simulated and physical models, predicts that for a single-period sinusoidal wave, maximal speed occurs for A/λ ≈ 0.2, the same kinematics used by the sandfish.
我们整合了生物学实验、经验理论、数值模拟和物理模型，以揭示在颗粒介质中波动运动的原理。对沙虎蜥（Scincus scincus）在 3 毫米玻璃颗粒中的高速 X 光成像显示，它在不使用肢体的情况下在介质中游泳，而是通过在身体上传播单个周期的正弦行波，从而产生波效率 η，即其平均前进速度与波速的比值，约为 0.5。平衡颗粒推力和阻力的阻力理论（RFT）预测 η 接近观察到的值。我们通过两种更详细的建模方法对该预测进行了测试：与离散颗粒模拟颗粒介质耦合的沙虎蜥数值模型，以及在颗粒介质中游泳的波动机器人。使用这些模型和 RFT 的解析解，我们改变了波动幅度与波长的比值（A/λ），并展示了沙中游泳的最佳条件，对于给定的 A，这是由 η 和 λ 之间的竞争产生的。RFT 与模拟和物理模型一致，预测对于单个周期的正弦波，最大速度出现在 A/λ≈0.2 时，这与沙虎蜥的运动学相同。
