SCIENTIFIC PROGRAMS AND ACTIVITIES

2009-10 Schedule

Jane Wang, Cornell University
Computing Insect Flight and Falling Paper

Our interest in computing the Navier-Stokes equations coupled to moving boundaries is directed toward understanding the unsteady aerodynamics of insect flight and fluttering and tumbling objects. While many interesting fluid phenomena originate near a moving sharp interface, computational schemes typically encounter great difficulty in resolving them. We have been designing efficient computational codes that are aimed at resolving the moving sharp interfaces in flows at Reynolds number relevant to insect flight. The first set of codes are Navier-Stokes solvers for simulating a 2D rigid flapping wing, which are based on high-order schemes in vorticity-stream function formulation. In these solvers we take advantage of coordinate transformations and 2D conformal mapping to resolve the sharp wing tips so as to avoid grid-regeneration. These methods were used to elucidate the unsteady aerodynamics of forward and hovering flight. They were also used to examine the aerodynamics of the fluttering and tumbling of plates falling through fluids.

To go beyond 2D simulations of rigid objects, we recently developed a more general- purpose code for simulating 3D flexible wing flight, based on immersed interface method. The main improvement is to obtain the 2nd order accuracy along the sharp moving surface. To avoid introducing ad-hoc boundary conditions at the moving interface, we employ a systematic method to derive from the 3D Navier-Stokes equation the jump conditions on the fluid variables caused by the singular force. In addition, the temporal jump conditions must be included in order to have a correct scheme. To handle the spatial and temporal jump conditions in the finite difference scheme, we derive generalized Taylor expansions for functions with discontinuities of arbitrary order. The code has been applied to simulate 3D flows around a dragonfly wing.

Jane Wang, Cornell University
How Insects Fly and Turn.

Insects' aerial acrobatics result from the concerted efforts of their brains, flight muscles, and flapping wings. To understand insect flight, we started from the outer scale, analyzing the unsteady aerodynamics of flapping flight, and are gradually working toward the inner scale, deducing control algorithms. In this approach, the physics of flight informs us about the internal control scheme for a specific behavior.

I will first describe the aerodynamic tricks that dragonflies employ to hover and fly efficiently. I will then describe how fruit flies recover from aerial stumbles, and how they make subtle wing movements to induce sharp turns in tens of wing beats, or 40-80ms.

Previous Seminars

Coupled oscillators arise in contexts as diverse as the brain, synchronized flashing of fireflies, coupled Josephson junctions, or unstable modes of the Millennium bridge in London. Generally, such systems are only analysed for a small number of oscillators or in the infinite oscillator, mean-field limit. The dynamics of a large but finite network of coupled oscillators are largely unknown. Here, I will show how concepts from the kinetic theory of gases and plasmas can be applied to a system of coupled oscillators to infer the large scale collective behavior from the small scale dynamics. Calculations are facilitated by perturbative methods developed for quantum field theory.

Thursday
December 3
4:10pm
Location
MP 102

Carson Chow, National Institutes of Health
The physics of obesity

The past few decades have seen a surge in the incidence of obesity in the developed world. Changes in body weight that can lead to obesity are known to result from imbalances between the energy derived from food
and the energy expended to maintain life and perform physical work. However, measuring and quantifying this relationship has proved to be difficult. Here, I will show how simple ideas from thermodynamics and nonlinear dynamics can be used to provide a general theoretical description of how body weight will change over time. The theory can then be used to answer open questions (and dispel some myths) regarding weight loss and gain.