Helicoidal Wave Research Articles

A method for calculating eigenfrequencies of arbitrarily shaped convex targets: eigenfrequencies of conducting spheroids and their relation to helicoidal surface wave paths

In a previous study by the authors (1986) the phase matching of surface waves on prolate, perfectly conducting spheroids generated, for example, by the scattering of an incident plane electromagnetic wave was investigated. Now, the considerably more complex spheroidal case with an obliquely incident primary wave, whose scattering will give rise to helicoidally (i.e. quasihelically) propagating surface waves is treated. The conditions under which phase matching of such types of surface waves, which propagate along helicoidal geodesics, can occur are investigated. It is found that only a discrete set of the required closed propagation paths exists, corresponding to a discrete set of allowed angled of incidence. These angles can be associated with different azimuthal quantum numbers m of the azimuthal propagation component around the symmetry axis, where m >

Swimming behaviour of the unicellular biflagellate Oxyrrhis marina: in vivo and in vitro movement of the two flagella.

The movement of the 2 flagella of Oxyrrhis marina was examined with respect to their individual waveforms and the swimming behavior of the organism. The longitudinal flagella propagated helicoidal waves whose amplitude decreased toward the tip of th flagellum. Their beat frequencies were 50-60 Hz. The transverse flagella beat helicoidally within a furrow. Sudden changes in the direction of the cell trajectories were generated by transient arrests of the longitudinal flagellum beat, which were accompanied by a switch from the backward orientation to a forward one. This sweeping motion generated the rotation of the cell body. Ca2+ ions highly stimulated the frequencies of this arrest response, which compared to the "walking-stick" behavior of sea urchin spermatozoa. Isolated flagella were ATA-reactivated after detergent treatment. They exhibited 2 types of motion within the same experimental conditions. A progressive helicoidal motion was generated upon longitudinal flagellum reactivation, whereas a rolling motion with little progression characterized transverse flagellum reactivation. The differences in motile behavior reflect regulations of flagellar movement which were not destroyed by the isolation procedure and may be indicative of regulation by accessory structures.

Resonance frequencies and the phase matching of helicoidal surface waves on impenetrable spheroids

The existence of the (complex) resonance frequencies of acoustic scatterers is explained by the generation of surface waves that match phases after repeated circumnavigations of the objects. The resonance frequencies can be predicted [B. L. Merchant et al., J. Acoust. Soc. Am. 80, 1754 (1986)] for prolate spheroidal objects, in the special case of axial incidence. Here sound‐soft, prolate‐spheroidal targets subject to obliquely incident signals are considered. The generated surface waves propagate along geodesics of helicoidal type, for which we obtain the condition for closing, and the set of discrete “pitch angles” at which closing takes place. An integral condition is formulated for the phase matching of helicoidal surface waves, using local wavelengths of Franz's surface waves. It is solved numerically for the complex resonance frequencies, found to agree closely with the m > 0 (i.e., containing azimuthal components) resonance frequencies obtained from an independent T‐matrix calculation. This agreement confirms the validity of the principle of phase matching for the general case, and the accuracy of the T‐matrix results. [Work supported in part by the Office of Naval Research.]

Live and reactivated motility in the 9+0 flagellum of Anguilla sperm.

The sperm flagella of the eel, Anguilla anguilla, are capable of vigorous motion in spite of having an axoneme with reduced structure that lacks the outer dynein arms, radial spokes and spoke heads, the two central tubules and the central tubule projections that are all part of the standard "9+2" axoneme. These sperm progress forward rapidly as a result of the propagation of helicoidal waves distally along the flagellum. Their flagellar beat frequencies are high, 93 Hz at 21 degrees C, and they roll at a frequency of about 19 Hz. Eel sperm could be demembranated with Nonidet P-40 and reactivated with MgATP2- in 0.22 M K acetate at pH 8.1. The reactivated motility closely resembles that of the live sperm, with a beat frequency of 69 Hz, but the demembranated flagella are unusually fragile, and commonly disintegrate by a combination of splitting, coiling, and sliding within a few minutes. Little reactivation is obtained if acetate is replaced by Cl- in the reactivating medium. The Michaelis constant for beat frequency (0.2 mM) is similar to that obtained for several "9+2" flagella. These sperm, however, appear to lack the mechanism by which Ca2+ regulates waveform. Our results indicate that eel sperm flagella, which at rest are straight, are induced to bend helicoidally by ATP, as the result of sliding between tubules that is blocked at both the base and tip of the organelle. The flagellar waveform consists of a series of planar bends separated by short regions of right-handed twist, which give it an overall left-handed helicoidal form.

Analysis of the Lamp-Dip Structure with Linear and Helicoidal Polarizations

A simple differential analysis of the Lamb-dip structure using a stationary helicoidal wave is described. This technique enables us to separate the anisotropic contribution from the isotropic one and shows that the observed Lamb dip on the 3.39-\ensuremath{\mu}m line of ${\mathrm{Ne}}^{20}$ is partially anisotropic.