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Input shaping is a method for reducing residual vibrations in computer-controlled machines. Vibration is eliminated by convolving an input shaper, which is a sequence of impulses, with a desired system command to produce a shaped input. The shaped input then becomes the command to the system. Requiring the vibration reduction to be robust to modeling errors and system nonlinearities is critical to the success of the shaping process on any real system, Input shapers can be made very insensitive to parameter uncertainty; however, increasing robustness usually increases system delays. A design process is presented that generates input shapers with insensitivity-to-time-delay ratios that are much larger than traditionally designed input shapers. The advantages of the new shapers are demonstrated with computer simulations and their performance is verified with experimental results from the MIT Middeck Active Control Experiment, which was performed on board the Space Shuttle Endeavor.

Context. Sun-grazing comets almost never re-emerge, but their sublimative destruction near the sun has only recently been observed directly, while chromospheric impacts have not yet been seen, nor impact theory developed. Aims. We seek simple analytic models of comet destruction processes near the sun, to enable estimation of observable signature dependence on original incident mass M o and perihelion distance q. Methods. Simple analytic solutions are found for M(r) versus q and distance r for insolation sublimation and, for the first time, for impact ablation and explosion. Results. Sun-grazers are found to fall into three (M o , q) regimes: sublimation-, ablation-, and explosion-dominated. Most sun-grazers have M o too small (<10 11 g) or q too large (>1.01 R ) to reach atmospheric densities (n > 2.5 × 10 11 /cm 3 ) where ablation exceeds sublimation. Our analytic results for sublimation are similar to numerical models. For q < 1.01 R , M o > 10 11 g, ablation initially dominates but results are sensitive to nucleus strength P c = 10 6 P 6 dyne/cm 2 and entry angle φ to the vertical. Nuclei with M o 10 10 (P 6 sec φ) 3 g are fully ablated before exploding, though the hot wake itself explodes. For most sun-impactors sec φ 1 (since q ∼ r * ), so for q very close to r * the ablation regime applies to moderate M o ∼ 10 13−16 P 3 6 g impactors unless P 6 0.1. For higher masses, or smaller q, nuclei reach densities n > 2.5 × 10 14 P 6 /cm 3 where ram pressure causes catastrophic explosion. Conclusions. Analytic descriptions define (M o , q) regimes where sublimation, ablation and explosion dominate sun-grazer/-impactor destruction. For q ≺ 1.01 R , M o 10 11 g nuclei are destroyed by ablation or explosion (depending on M o cos 3 φ/P c ) in the chromosphere, producing flare-like events with cometary abundance spectra. For all plausible M o , q and physical parameters, nuclei are destroyed above the photosphere.

Thermodynamic properties of silicon (diamond cubic phase) are calculated using an empirical many-body potential developed by Tersoff [Phys. Rev. Lett. 56, 632 (1986)] based on the concept of bond order. It is shown that this model gives predictions in good agreement with experiment for those properties governed by energetics (free energy, entropy, and heat capacity). The thermal expansion coefficient is less well described, which is traced to the fact that the model potential, in its present version, is overly stiff and therefore unable to account properly for the volume dependence of the transverse acoustic modes. Furthermore, sensitivity of the potential to whether each atom remains bonded to only four neighbors indicates that the short-range nature of the potential may necessitate model improvement before it is suitable for studies of thermomechanical properties at elevated temperatures or large deformations.

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