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123 results
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ItemWalking and running on yielding and fluidizing ground(Georgia Institute of Technology, 2012-07) Qian, Feifei ; Zhang, Tingnan ; Li, Chen ; Masarati, Pierangelo ; Birkmeyer, Paul ; Pullin, Andrew ; Hoover, Aaron ; Fearing, Ronald S. ; Golman, Daniel I.We study the detailed locomotor mechanics of a small, lightweight robot (DynaRoACH, 10 cm, 25 g) which can move on a granular substrate of closely packed 3 mm diameter glass particles at speeds up to 50 cm/s (5 body length/s), approaching the performance of small, high-performing, desert-dwelling lizards. To reveal how the robot achieves this high performance, we use high speed imaging to capture kinematics, and develop a numerical multi-body simulation of the robot coupled to an experimentally validated discrete element method (DEM) simulation of the granular media. Average forward speeds measured in both experiment and simulation agreed well, and increased non-linearly with stride frequency, reflecting a change in the mode of propulsion. At low frequencies, the robot used a quasi-static “rotary walking” mode, in which the granular material yielded as the legs penetrated and then solidified once vertical force balance was achieved. At high frequencies, duty factor decreased below 0.5 and aerial phases occurred. The propulsion mechanism was qualitatively different: the robot ran rapidly by utilizing the speed-dependent fluid-like inertial response of the material. We also used our simulation tool to vary substrate parameters that were inconvenient to vary in experiment (e.g., granular particle friction) to test performance and reveal limits of stability of the robot. Using small robots as physical models, our study reveals a mechanism by which small animals can achieve high performance on granular substrates, which in return advances the design and control of small robots in deformable terrains.
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ItemMulti-functional foot use during running in the zebra-tailed lizard (Callisaurus draconoides)(Georgia Institute of Technology, 2012-05) Li, Chen ; Hsieh, S. Tonia ; Goldman, Daniel I.A diversity of animals that run on solid, level, flat, non-slip surfaces appear to bounce on their legs; elastic elements in the limbs can store and return energy during each step. The mechanics and energetics of running in natural terrain, particularly on surfaces that can yield and flow under stress, is less understood. The zebra-tailed lizard (Callisaurus draconoides), a small desert generalist with a large, elongate, tendinous hind foot, runs rapidly across a variety of natural substrates. We use high-speed video to obtain detailed three-dimensional running kinematics on solid and granular surfaces to reveal how leg, foot and substrate mechanics contribute to its high locomotor performance. Running at ~10bodylengthss–1 (~1ms–1), the center of mass oscillates like a spring-mass system on both substrates, with only 15% reduction in stride length on the granular surface. On the solid surface, a strut-spring model of the hind limb reveals that the hind foot saves ~40% of the mechanical work needed per step, significant for the lizardʼs small size. On the granular surface, a penetration force model and hypothesized subsurface foot rotation indicates that the hind foot paddles through fluidized granular medium, and that the energy lost per step during irreversible deformation of the substrate does not differ from the reduction in the mechanical energy of the center of mass. The upper hind leg muscles must perform three times as much mechanical work on the granular surface as on the solid surface to compensate for the greater energy lost within the foot and to the substrate.
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ItemComparative studies reveal principles of movement on and within granular media(Georgia Institute of Technology, 2010-06) Ding, Yang ; Gravish, Nick ; Li, Chen ; Maladen, Ryan D. ; Mazouchova, Nicole ; Sharpe, Sarah S. ; Umbanhowar, Paul B. ; Goldman, Daniel I.Terrestrial locomotion can take place on complex substrates such as leaf litter, debris, and soil that flow or solidify in response to stress. While principles of movement in air and water are revealed through study of the hydrodynamic equations of fluid motion, discovery of principles of movement in complex terrestrial environments is less advanced in part because describing the physics of limb and body interaction with such environments remains challenging. We report progress our group has made in discovering principles of movement of organisms and models of organisms (robots) on and within granular materials (GM) like sand. We review current understanding of localized intrusion in GM relevant to foot and body interactions. We discuss the limb-ground interactions of a desert lizard, a hatchling sea turtle, and various robots and reveal that control of granular solidification can generate effective movement. We describe the sensitivity of movement on GM to gait parameters and discuss how changes in material state can strongly affect locomotor performance. We examine subsurface movement, common in desert animals like the sandfish lizard. High speed x-ray imaging resolves subsurface kinematics, while electromyography (EMG) allows muscle activation patterns to be studied. Our resistive force theory, numerical, and robotic models of sand-swimming reveal that subsurface swimming occurs in a “frictional fluid” whose properties differ from Newtonian fluids.
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ItemAsymptotic Almost Periodicity of Scalar Parabolic Equations with Almost Periodic Time Dependence(Georgia Institute of Technology, 2009-12-07) Shen, Wenxian ; Yi, Yingfei
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ItemDynamics of Almost Periodic Scalar Parabolic Equations(Georgia Institute of Technology, 2009-12-07) Shen, Wenxian ; Yi, Yingfei
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ItemRandom Restarts in Global Optimization(Georgia Institute of Technology, 2009-12-07) Hu, X. ; Shonkwiler, Ronald W. ; Spruill, Marcus C.In this article we study stochastic multistart methods for global optimization, which combine local search with random initialization, and their parallel implementations. It is shown that in a minimax sense the optimal restart distribution is uniform. We further establish the rate of decrease of the ensemble probability that the global minimum has not been found by the nth iteration. Turning to parallelization issues, we show that under independent identical processing (iip), exponential speedup in the time to hit the goal bin normally results. Our numerical studies are in close agreement with these finndings.
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ItemA Curious Binomial Identity(Georgia Institute of Technology, 2009-12-07) Calkin, Neil J.In this note we shall prove the following curious identity of sums of powers of the partial sum of binomial coefficients.
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ItemConverse Poincaré Type Inequalities for Convex Functions(Georgia Institute of Technology, 2009-12-07) Bobkov, S. G. ; Houdré, ChristianConverse Poincaré type inequalities are obtained within the class of smooth convex functions. This is, in particular, applied to the double exponential distribution.
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ItemHierarchical Reconstruction with up to Second Degree Remainder for Solving Nonlinear Conservation Laws(Georgia Institute of Technology, 2009-07-31) Liu, Yingjie ; Shu, Chi-Wang ; Xu, ZhiliangThe hierarchical reconstruction (HR) [Liu, Shu, Tadmor and Zhang, SINUM ’07] can effectively reduce spurious oscillations without local characteristic decomposition for numerical capturing of discontinuous solutions. However, there are still small re- maining overshoots/undershoots in the vicinity of discontinuities. HR with partial neighboring cells [Xu, Liu and Shu, JCP ’09] essentially overcomes this drawback for the third order case, and in the mean time further improves the resolution of the numer- ical solution. Extending the technique to higher order cases we observe the returning of overshoots/undershoots. In this paper, we introduce a new technique to work with HR on partial neighboring cells, which lowers the order of the remainder while maintaining the theoretical order of accuracy, essentially eliminates overshoots/undershoots for the fourth and fifth order cases (in one dimensional numerical examples) and reduces the numerical cost.
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ItemWKB and Turning Point Theory for Second Order Difference Equations: External Fields and Strong Asymptotics for Orthogonal Polynomials(Georgia Institute of Technology, 2009-05) Geronimo, Jeffrey S.A LG-WKB and Turning point theory is developed for three term recurrence formulas associated with monotonic recurrence coefficients. This is used to find strong asymptotics for certain classical orthogonal polynomials including Wilson polynomials.