Tractrices, Bicycle Tire Tracks, Hatchet Planimeters, and a 100-year-old Conjecture

Geometry of the tracks left by a bicycle is closely related with the so-called Prytz planimeter and with linear fractional transformations of the complex plane. We describe these relations, along with the history of the problem, and give a proof of a conjecture made by Menzin in 1906.Comment: 20 pages, 18 figure

A Possible Case of Spatial Isolation in Brine Flies of the Genus \u3ci\u3eEphydra\u3c/i\u3e (Diptera: Ephydridae)

(excerpt) During the summer of 1975, adults and larvae of Ephydra riparia Fallen and E. cinerea Jones were encountered in the many brine pools occurring on the property of the Morton Salt Company at Rittman, Wayne County, Ohio (Scheiring and Foote, 1973). Larvae of both species have been reported to be salt tolerant (Bayly, 1972). E. ripariu larvae can survive in salinities up to 80°/oo (Sutcliffe, 1960), and the larvae of cinerea have been encountered by Nemenz (1960) in the Great Salt Lake of Utah at a salinity of 300°/oo

\u3ci\u3eAnaphes\u3c/i\u3e (Hymenoptera: Mymaridae) Reared from the Eggs of a Shore Fly (Diptera: Ephydridae)

Members of the family Mymaridae are obligate parasitoids of insect eggs, and some species attack the eggs of aquatic insects. Only one account of egg parasitism by the mymarid genus Anaphes on Diptera has been disclosed in the literature. Bakkendorf (1971) bred Anaphes autumnalis Foerster from an egg of Tipula autumnalis Loew

Review of Non-destructive Testing (NDT) Techniques and their applicability to thick walled composites

A tier 1 automotive supplier has developed a novel and unique kinetic energy recovery storage system for both retro-fitting and OEM application for public transport systems where periodic stop start behaviour is paramount. A major component of the system is a composite flywheel spinning at up to 36,000 rpm (600 Hz). Material soundness is an essential requirement of the flywheel to ensure failure does not occur. The component is particularly thick for a composite being up to 30 mm cross section in some places. The geometry, scale and material make-up pose some challenges for conventional NDT systems. Damage can arise in composite materials during material processing, fabrication of the component or in-service activities among which delamination, cracks and porosity are the most common defects. A number of non-destructive testing (NDT) techniques are effective in testing components for defects without damaging the component. NDT techniques like Ultrasonic Testing, X-Ray, Radiography, Thermography, Eddy current and Acoustic Emission are current techniques for various testing applications. Each of these techniques uses different principles to look into the material for defects. However, the geometry, physical and material properties of the component being tested are important factors in the applicability of a technique. This paper reviews these NDT techniques and compares them in terms of characteristics and applicability to composite parts

SIMS chemical analysis of extended impacts on the leading and trailing edges of LDEF experiment AO187-2

Numerous 'extended impacts' found in both leading and trailing edge capture cells were successfully analyzed for the chemical composition of projectile residues by secondary ion mass spectrometry (SIMS). Most data were obtained from the trailing edge cells where 45 of 58 impacts were classified as 'probably natural' and the remainder as 'possibly man-made debris.' This is in striking contrast to leading edge cells where 9 of 11 impacts so far measured are definitely classified as orbital debris. Although all the leading edge cells had lost their plastic entrance foils during flight, the rate of foil failure was similar to that of the trailing edge cells, 10 percent of which were recovered intact. Ultraviolet embrittlement is suspected as the major cause of failure on both leading and trailing edges. The major impediment to the accurate determination of projectile chemistry is the fractionation of volatile and refractory elements in the hypervelocity impact and redeposition processes. This effect had been noted in a simulation experiment but is more pronounced in the LDEF capture cells, probably due to the higher average velocities of the space impacts. Surface contamination of the pure Ge surfaces with a substance rich in Si, but also containing Mg and Al, provides an additional problem for the accurate determination of impactor chemistry. The effect is variable, being much larger on surfaces that were exposed to space than in those cells that remained intact. Future work will concentrate on the analyses of more leading edge impacts and the development of new SIMS techniques for the measurement of elemental abundances in extended impacts

Depth-dependent target strengths of gadoids by the boundary-element method

Author Posting. © Acoustical Society of America, 2003. This article is posted here by permission of Acoustical Society of America for personal use, not for redistribution. The definitive version was published in Journal of the Acoustical Society of America 114 (2003): 3136-3146, doi:10.1121/1.1619982.The depth dependence of fish target strength has mostly eluded experimental investigation because of the need to distinguish it from depth-dependent behavioral effects, which may change the orientation distribution. The boundary-element method (BEM) offers an avenue of approach. Based on detailed morphometric data on 15 gadoid swimbladders, the BEM has been exercised to determine how the orientation dependence of target strength changes with pressure under the assumption that the fish swimbladder remains constant in shape and volume. The backscattering cross section has been computed at a nominal frequency of 38 kHz as a function of orientation for each of three pressures: 1, 11, and 51 atm. Increased variability in target strength and more abundant and stronger resonances are both observed with increasing depth. The respective backscattering cross sections have been averaged with respect to each of four normal distributions of tilt angle, and the corresponding target strengths have been regressed on the logarithm of fish length. The tilt-angle-averaged backscattering cross sections at the highest pressure have also been averaged with respect to frequency over a 2-kHz band for representative conditions of insonification. For all averaging methods, the mean target strength changes only slightly with depth.This work began with sponsorship by the European Commission through its RTD-program, Contract No. MAS3-CT95-0031 (BASS), and was completed with support by the Office of Naval Research, Contract No. N000140310368

Utility and lower limits of frequency detection in surface electrode stimulation for somatosensory brain-computer interface in humans

Objective: Stimulation of the primary somatosensory cortex (S1) has been successful in evoking artificial somatosensation in both humans and animals, but much is unknown about the optimal stimulation parameters needed to generate robust percepts of somatosensation. In this study, the authors investigated frequency as an adjustable stimulation parameter for artificial somatosensation in a closed-loop brain-computer interface (BCI) system. Methods: Three epilepsy patients with subdural mini-electrocorticography grids over the hand area of S1 were asked to compare the percepts elicited with different stimulation frequencies. Amplitude, pulse width, and duration were held constant across all trials. In each trial, subjects experienced 2 stimuli and reported which they thought was given at a higher stimulation frequency. Two paradigms were used: first, 50 versus 100 Hz to establish the utility of comparing frequencies, and then 2, 5, 10, 20, 50, or 100 Hz were pseudorandomly compared. Results: As the magnitude of the stimulation frequency was increased, subjects described percepts that were “more intense” or “faster.” Cumulatively, the participants achieved 98.0% accuracy when comparing stimulation at 50 and 100 Hz. In the second paradigm, the corresponding overall accuracy was 73.3%. If both tested frequencies were less than or equal to 10 Hz, accuracy was 41.7% and increased to 79.4% when one frequency was greater than 10 Hz (p = 0.01). When both stimulation frequencies were 20 Hz or less, accuracy was 40.7% compared with 91.7% when one frequency was greater than 20 Hz (p < 0.001). Accuracy was 85% in trials in which 50 Hz was the higher stimulation frequency. Therefore, the lower limit of detection occurred at 20 Hz, and accuracy decreased significantly when lower frequencies were tested. In trials testing 10 Hz versus 20 Hz, accuracy was 16.7% compared with 85.7% in trials testing 20 Hz versus 50 Hz (p < 0.05). Accuracy was greater than chance at frequency differences greater than or equal to 30 Hz. Conclusions: Frequencies greater than 20 Hz may be used as an adjustable parameter to elicit distinguishable percepts. These findings may be useful in informing the settings and the degrees of freedom achievable in future BCI systems