Papers Published

  1. Howle, L., Schaeffer, D.G., Shearer, M., and Zhong, P, Lithotripsy: The treatment of kidney stones with shock waves, SIAM Review, vol. 40 no. 2 (1998), pp. 356-371 .
    (last updated on 2011/07/05)

    This paper discusses mathematical models for the response of a small air bubble in water to an ultrasound pulse, a context that arises in the modern treatment for kidney stones. The paper reviews Rayleigh's 1917 theory for bubble response, applies asymptotics to describe large-amplitude solutions of Rayleigh's equations, and briefly discusses effects neglected in the simple model. The style is expository, intended both to introduce this application to mathematicians and to illustrate the use of asymptotic methods to nonmathematicians.