Bessel beam expansion of linear focused ultrasound.

Previous work on scattering by Bessel beams shows that expansion of incident sound fields in term of these beams has application to scattering [P. L. Marston, J. Acoust. Soc. Am. 122, 247-252 (2007)]. In this work, an expression for the expansion coefficients of propagating, axisymmetric, sound fields are derived. In this paper, this expression is applied to a linear focused axisymmetric sound field and is expanded in terms of Bessel beam components. This is done for focused beams radiated from a spherical cap source. A physical optics model is applied to sound propagation close to the source to facilitate the calculation of the Bessel beam expansion coefficients. This type of model is useful for focused scattering [P. L. Marston and D. S. Langley, J. Acoust. Soc. Am. 73, 1464-1475 (1983)]. Once the expansion coefficients are found, the sound field can be evaluated by superposition. The model agrees approximately with Chen, Schwarz, and Parker [J. Acoust. Soc. Am. 94, 2979-2991 (1993)] and O'Neil [J. Acoust. Soc. Am. 21, 516-526 (1949)] on axis and with direct integration of a Kirchhoff integral both on and off axis. This type of expansion will have applications to scattering problems.

Leveraging single protein polymers to measure flexural rigidity.

The micrometer-scale length of some protein polymers allows them to be mechanically manipulated in single-molecule experiments. This provides a direct way to measure persistence length. We have used a double optical trap to elastically deform single microtubules and actin filaments. Axial extensional force was exerted on beads attached laterally to the filaments. Because the attachments are off the line of force, pulling the beads apart couples to local bending of the filament. We present a simple mechanical model for the resulting highly nonlinear elastic response of the dumbbell construct. The flexural rigidities of the microfilaments that were found by fitting the model to the experimentally observed force-distance curves are (7.1 +/- 0.8) x 10(4) pN nm2 (persistence length L(p) = 17.2 microm) for F-actin and (6.1 +/- 1.3) x 10(6) pN nm2 (L(p) = 1.4 mm) for microtubules.