HelioSwarm: Swarm Establishment and Reconfiguration in Perturbed Eccentric Orbit
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OBJECTIVE: To test whether unloading increases vulnerability to eccentric exercise-induced dysfunction and muscle injury. DESIGN: Before-after trial. SETTING: General community. PATIENTS OR OTHER PARTICIPANTS: Two women and 5 men (73 +/- 3kg [mean +/- SE]) who were active college students but were not trained in lower body resistance exercise volunteered. INTERVENTION: Five weeks of unilateral lower limb suspension (ULLS), which has been shown to decrease strength and size of the unloaded, left, but not load-bearing, right quadriceps femoris muscle group (QF) by 20% and 14%, respectively; performance of 10 sets of ten eccentric actions with each QF immediately after the ULLS strength tests with a load equivalent to 65% of the post-ULLS eccentric 1-repetition maximum. MAIN OUTCOME MEASURE(S): Concentric and eccentric 1-repetition maximum for the left, unloaded and the right, load-bearing QF measured immediately after ULLS and 1,4,7,9, and 11 days later; cross-sectional area and spin-spin relaxation time (T2) of each QF as determined by magnetic resonance imaging and measured the last day of ULLS and 3 days later. RESULTS: The mean load used for eccentric exercise was 23 +/- 2 and 30 +/- 3kg for the left, unloaded and right, load-bearing QF, respectively. The concentric and eccentric 1-repetition maximum for the unloaded and already weakened left QF was further decreased by 18% (p = .000) and 27% (p = .000), respectively, 1 day after eccentric exercise. Strength did not return to post-ULLS levels until 7 days of recovery. The right, load-bearing QF showed a 4% decrease (p = .002) in the eccentric 1-repetition maximum 1 day after eccentric exercise. The left, unloaded QF showed an increase in T2 (p = .002) in 18% of its cross-sectional area 3 days after the eccentric exercise, thus indicating muscle injury. The right, load-bearing QF showed no elevation in T2 (p = .280). CONCLUSION: Unloading increases vulnerability to eccentric exercise-induced dysfunction and muscle injury, even at relatively light loads.
Mark Lewis has extended his them is work by completing a series of N-body simulations of a narrow ring that: is in the location of Saturn's F-ring and is perturbed by a single satellite comparable to Prometheus, but on a circular orbit. We had previously shown how the satellite perturbations can cause a broadly distributed sparse population of ring particles to become concentrated into narrow rings that can be maintained outside of any resonance location. For low optical depths, the collisions between ring particles are highly localized in the peaks of the satellite wakes. The inelastic collisions therefore occur at a particular orbital phase angle so as to damp the azimuthal component of the relative velocities. Since particle positions are not changed by collisions, the semimajor axes of the particles are shifted toward the actual particle positions where the collisions occur. Thus, negative radial diffusion can occur while conserving orbital angular momentum so long as the forced eccentricity is continually re-excited by the satellite. We speculated that the separation between the final ringlets was largely determined by the magnitude of the forced eccentricities induced by the satellite at closest approach. We carried out a series of simulations with a variety of different satellite masses in order to vary the magnitude of the forced eccentricity. We found that indeed the final spacing of the ringlets does increase with the magnitude of the forced eccentricity (Lewis and Stewart 2002). This occurs because neighboring eccentric ringlets drift out of phase with one another due to Keplerian shear and eventually collide with one another, leading to a smaller number of more widely spaced ringlets, The time scale required to form narrow ringlets in these simulations is much shorter than one would expect from standard theories based upon the orbit-averaged torque produced by multiple passes by the satellite. We find that the initial ringlets form in less than two synodic periods and the final state is typically reached in 10 to 20 synodic periods. These studies move us closer to understanding the significantly more complex system of Saturn's F ring, where the perturbation magnitude varies over short temporal and spatial time scales due to the orbital eccentricities of the perturbing satellite. We are currently extending the simulation to allow for an eccentric orbit of the satellite.