Index of content:
Volume 104, Issue 3, September 1998
- NONLINEAR ACOUSTICS, MACROSONICS 
104(1998); http://dx.doi.org/10.1121/1.424336View Description Hide Description
In order to evaluate the possible side effects of diagnosticmedicalultrasound, and in particular the effects of nonlinear propagation of sound, it is necessary to characterize the scanners used. To this end, the acoustic field emitted by a phased-array Hitachi EUB-26 ultrasoundscanner operating in a strongly focused mode was measured a small distance from the scanner head, and the velocity field at the surface of the head deduced. A finite difference model was then used to propagate the pressure field beyond the focus, taking into account nonlinear effects, attenuation and diffraction, and the result compared with observations in water, giving reasonable agreement out to the scanplane focus. The extrapolated field was then examined in detail, revealing those regions in which most power is lost to the medium, some of which are off-axis, and so might not be detected by normal calibration procedures.
104(1998); http://dx.doi.org/10.1121/1.424337View Description Hide Description
A chamber cavity, which has a square cross section and pressure-release walls, is used to produce a well-defined, 160-kHz standing ultrasonic field. A suspension of latex microspheres in aqueous metrizamide fills the chamber. The chamber rotates about a horizontal axis producing the centripetal force necessary to contain the buoyant spheres in the axial region. At low particle concentrations, clusters of microspheres form at half-wavelength intervals near the axial positions of acoustic pressure amplitude minima, as expected because of rotational and acoustic radiation forces. At higher concentrations, additional particle distributions are often seen that suggest the presence of flow. When high concentrations of larger particles are used, small clusters also form at axial positions of maxima. Theory for acoustic streaming in a rotating fluid predicts flow speeds that are too small to account for the observed flow. Reasonable agreement with observations is obtained using a theory for flowgenerated by the buoyant gravitational force acting on the clusters.
Nonanalytic nonlinear oscillations: Christiaan Huygens, quadratic Schrödinger equations, and solitary waves104(1998); http://dx.doi.org/10.1121/1.424338View Description Hide Description
An example of an oscillatory system with a time-reversible nonanalytic nonlinearity is shown to be a pendulum with a flexible cord sandwiched between two identical circular disks, in contrast to the analytic case of a pendulum interrupted by a single circular disk. The amplitude-dependent frequencies of both cases are perturbatively calculated, and are compared to numerical simulations over the entire range of amplitudes. The nonanalyticity causes the unusual effect of the frequency to vary linearly with amplitude for small amplitudes, which has also been observed in the resonant frequencies of compressional standing waves in sandstone. A general condition for a nonanalytic nonlinearity to yield this behavior is presented. The amplitude-dependent frequency for the double-interrupted pendulum allows an explanation for Huygens’surprising observation that circular interrupters were as effective as cycloidal interrupters in achieving isochronous motion. A lattice of linearly coupled double-interrupted pendulums is described near the lower and upper cutoff modes by quadratic nonlinear Schrödinger (NLS) equations, in contrast to cubic NLS equations which arise for analytic pendulum lattices as well as typical acoustic and surface waveguides. Solitary breather and kink solutions to the quadratic NLS equations are presented, and are compared to the known soliton solutions of the corresponding cubic NLS equations. Compressional waves in sandstone are shown to be modeled by the inclusion of a nonanalytic quadratic nonlinearity in the stress–strain relationship. Quadratic NLS breathers are predicted to occur in a waveguide of sandstone, and an analysis indicates that such an observation is feasible.