Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting in Muonium

We calculate three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with the first order electron and muon polarization loop insertions in graphs with two exchanged photons. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm squared contribution was obtained a long time ago. Here we calculate the single-logarithmic and nonlogarithmic contributions. We previously calculated the three-loop radiative-recoil corrections generated by two-loop polarization insertions in the exchanged photons. The current paper therefore concludes calculation of all three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by diagrams with closed fermion loop insertions in the exchanged photons. The new results obtained here improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from experimental data on the muonium hyperfine splitting.Comment: 27 pages, 6 figures, 7 table

Directional wave measurements from the ASIS (Air-Sea Interaction Spar) buoy

During the spring of 1997 the Air Sea Interaction Spar (ASIS) buoy was deployed in the northeastern Gulf of Mexico to study meteorological forcing and ocean wave dynamics. This buoy is specially designed to produce little surface disturbance, and to be a partial wave follower at low frequencies. The relative location of the interface is measured by an array of 8 capacitance wave staffs, while the motion of the buoy is monitored using linear accelerometers and rate gyros. This combination permits high resolution measurement of wave directional properties from 10 cm to 600 m. We compare directional frequency spectra measured from the ASIS buoy with those obtained from a 3-meter discus buoy located roughly 1 km away

Swimming gaits, passive drag and buoyancy of diving sperm whales <em>Physeter macrocephalus</em>.

Drag and buoyancy are two primary external forces acting on diving marine mammals. The strength of these forces modulates the energetic cost of movement and may influence swimming style (gait). Here we use a high-resolution digital tag to record depth, 3-D orientation, and sounds heard and produced by 23 deep-diving sperm whales in the Ligurian Sea and Gulf of Mexico. Periods of active thrusting versus gliding were identified through analysis of oscillations measured by a 3-axis accelerometer. Accelerations during 382 ascent glides of five whales (which made two or more steep ascents and for which we obtained a measurement of length) were strongly affected by depth and speed at Reynold's numbers of 1.4-2.8x10(7). The accelerations fit a model of drag, air buoyancy and tissue buoyancy forces with an r(2) of 99.1-99.8% for each whale. The model provided estimates (mean +/- S.D.) of the drag coefficient (0.00306+/-0.00015), air carried from the surface (26.4+/-3.9 l kg(-3) mass), and tissue density (1030+/-0.8 kg m(-3)) of these five animals. The model predicts strong positive buoyancy forces in the top 100 in of the water column, decreasing to near neutral buoyancy at 250-850 m. Mean descent speeds (1.45+/-0.19 m s(-1)) were slower than ascent speeds (1.63+/-0.22 m s(-1)), even though sperm whales stroked steadily (glides 5.3+/-6.3%) throughout descents and employed predominantly stroke-and-glide swimming (glides 37.7+/-16.4%) during ascents. Whales glided more during portions of dives when buoyancy aided their movement, and whales that glided more during ascent glided less during descent (and vice versa), supporting the hypothesis that buoyancy influences behavioural swimming decisions. One whale rested at similar to10 m depth for more than 10 min without fluking, regulating its buoyancy by releasing air bubbles.</p