| Applied and bio mathematics Mathematics is a key element of virtually all research carried out in the T&AM field. TAM faculty and students develop and explore mathematical models of biological systems such as: the small-world phenomenon in social networks (popularly known as "six degrees of separation"); the collective behavior of biological oscillators; the geometry and mechanics of supercoiled DNA; and the neurobiology of lampreys' pattern generation for swimming.
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| Biorobotics and biomechanics brings insights from mechanics to the understanding of biological phenomena. Some recent topics include: the fluid mechanics of insect flight; the mechanics of terrestrial locomotion, including walking and ape swinging; models for the red-blood-cell and lipid vesicles.
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| Computational mechanics is increasingly a critical element of both practical engineering design and of scientific studies. Active areas of research include: the development of highly efficient methods for stress analysis of multiply cracked solids, the mesh less boundary node method (BNM); efficient method for coupled fluid-solid systems; optimization of coordination; limit cycle analysis.
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| Dynamics and nonlinear systems concerns the study of things which change over time. This includes, for example, the study of chaos and bifurcations using analytical, numerical and experimental methods. Applications include nonlinear vibrations (MEMS, lasers), celestial mechanics (including planetary rings and rotations of celestial bodies), biodynamics (including interaction of populations of fireflies, flight of insects, and human walking) and control (including satellite dynamics and manufacturing processes).
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| Fluid mechanics and granular flows research topics include aerodynamics of insect flight, granular flow, multi-phase flow, stokes flow, vortex dynamics, and turbulence. Classical mathematical methods, computer simulations, and experiments are used to tackle these wide ranges of problems.
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| Microelectromechanical systems or MEMS, are small machines built at on micron-size scales using techniques developed for the manufacture of integrated circuits. Such machines hold promise for sensors, actuators, and other applications. We have recently studied the nonlinear dynamics of systems with very low damping, fracture of nanostructures and the dynamics of carbon nanotubes.
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| Solid mechanics and materials is concerned with the mechanical response of structures and materials. Using a synthesis of mathematical analysis, computation, and experiments, we study structures ranging in size from molecules to thin films only a few hundred atoms thick to micron-sized actuators to aircraft and geological structures. Materials studied include DNA, cell membranes, polymers, metals, polymer-matrix composites, ceramic-matrix composites, and semiconductors. Applications include development of bio-inspired adhesives, improved body armor, high altitude airships and novel composite materials.
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