Algorithms for 3D rigidity analysis and a first order percolation transition

A fast computer algorithm, the pebble game, has been used successfully to study rigidity percolation on 2D elastic networks, as well as on a special class of 3D networks, the bond-bending networks. Application of the pebble game approach to general 3D networks has been hindered by the fact that the underlying mathematical theory is, strictly speaking, invalid in this case. We construct an approximate pebble game algorithm for general 3D networks, as well as a slower but exact algorithm, the relaxation algorithm, that we use for testing the new pebble game. Based on the results of these tests and additional considerations, we argue that in the particular case of randomly diluted central-force networks on BCC and FCC lattices, the pebble game is essentially exact. Using the pebble game, we observe an extremely sharp jump in the largest rigid cluster size in bond-diluted central-force networks in 3D, with the percolating cluster appearing and taking up most of the network after a single bond addition. This strongly suggests a first order rigidity percolation transition, which is in contrast to the second order transitions found previously for the 2D central-force and 3D bond-bending networks. While a first order rigidity transition has been observed for Bethe lattices and networks with ``chemical order'', this is the first time it has been seen for a regular randomly diluted network. In the case of site dilution, the transition is also first order for BCC, but results for FCC suggest a second order transition. Even in bond-diluted lattices, while the transition appears massively first order in the order parameter (the percolating cluster size), it is continuous in the elastic moduli. This, and the apparent non-universality, make this phase transition highly unusual.Comment: 28 pages, 19 figure

Terminal velocity and drag reduction measurements on superhydrophobic spheres

Super water-repellent surfaces occur naturally on plants and aquatic insects and are created in the laboratory by combining micro- or nanoscale surface topographic features with hydrophobic surface chemistry. When such types of water-repellent surfaces are submerged they can retain a film of air (a plastron). In this work, we report measurements of the terminal velocity of solid acrylic spheres with various surface treatments settling under the action of gravity in water. We observed increases in terminal velocity corresponding to drag reduction of between 5% and 15% for superhydrophobic surfaces that carry plastrons

Self-organization with equilibration: a model for the intermediate phase in rigidity percolation

Recent experimental results for covalent glasses suggest the existence of an intermediate phase attributed to the self-organization of the glass network resulting from the tendency to minimize its internal stress. However, the exact nature of this experimentally measured phase remains unclear. We modify a previously proposed model of self-organization by generating a uniform sampling of stress-free networks. In our model, studied on a diluted triangular lattice, an unusual intermediate phase appears, in which both rigid and floppy networks have a chance to occur, a result also observed in a related model on a Bethe lattice by Barre et al. [Phys. Rev. Lett. 94, 208701 (2005)]. Our results for the bond-configurational entropy of self-organized networks, which turns out to be only about 2% lower than that of random networks, suggest that a self-organized intermediate phase could be common in systems near the rigidity percolation threshold.Comment: 9 pages, 6 figure

Science aspects of a 1980 flyby of Comet Encke with a Pioneer spacecraft

Results are presented of an investigation of the feasibility of a 1980 flyby of Comet Encke using a Pioneer class spacecraft. Specific areas studied include: science objectives and rationale; science observables; effects of encounter velocity; science encounter and targeting requirements; selection and description of science instruments; definition of a candidate science payload; engineering characteristics of suggested payload; value of a separable probe; science instruments for a separable probe; science payload integration problems; and science operations profile

Time Domain Simulations of Arm Locking in LISA

Arm locking is a technique that has been proposed for reducing laser frequency fluctuations in the Laser Interferometer Space Antenna (LISA), a gravitational-wave observatory sensitive in the milliHertz frequency band. Arm locking takes advantage of the geometric stability of the triangular constellation of three spacecraft that comprise LISA to provide a frequency reference with a stability in the LISA measurement band that exceeds that available from a standard reference such as an optical cavity or molecular absorption line. We have implemented a time-domain simulation of arm locking including the expected limiting noise sources (shot noise, clock noise, spacecraft jitter noise, and residual laser frequency noise). The effect of imperfect a priori knowledge of the LISA heterodyne frequencies and the associated 'pulling' of an arm locked laser is included. We find that our implementation meets requirements both on the noise and dynamic range of the laser frequency.Comment: Revised to address reviewer comments. Accepted by Phys. Rev.

Science aspects of 1980 ballistic missions to comet Encke, using Mariner and Pioneer spacecraft

Science aspects of a 1980 spacecraft reconnaissance of Comet Encke are considered. The mission discussed is a ballistic flyby (more exactly, a fly-through) of P/Encke, using either a spin stabilized spacecraft, without despin of instruments, or a 3-axis stabilized spacecraft

Plastron properties of a superhydrophobic surface

Most insects and spiders drown when submerged during flooding or tidal inundation, but some are able to survive and others can remain submerged indefinitely without harm. Many achieve this by natural adaptations to their surface morphology to trap films of air, creating plastrons which fix the water-vapor interface and provide an incompressible oxygen-carbon dioxide exchange surface. Here the authors demonstrate how the surface of an extremely water-repellent foam mimics this mechanism of underwater respiration and allows direct extraction of oxygen from aerated water. The biomimetic principle demonstrated can be applied to a wide variety of man-made superhydrophobic materials

Scientific possibilities of a solar electric powered rendezvous with comet Encke

The minimum scientific spacecraft instrumentation is considered that is likely to result in as complete an understanding of the composition, structure, and activity of a cometary nucleus as is possible without landing on it. The payload will also give useful results on secondary goals of a better understanding of physical processes in the inner and outer coma. Studies of composition, by means of an actual landing on the surface, details of the internal structure of the nucleus, and sample return were considered beyond the scope of this mission

Mesoscopic description of the annealed Ising model and Multiplicative noise

A new type of Langevin equation exhibiting a non trivial phase transition associated with the presence of multiplicative noise is introduced. The equation is derived as a mesoscopic representation of the microscopic annealed Ising model (AIM) proposed by Thorpe and Beeman, and reproduces perfectly its basic phenomenology. The AIM exhibits a non-trivial behavior as the temperature is increased, in particular it presents a disorder-to-order phase transition at low temperatures, and a order-to-disorder transition at higher temperatures. This behavior resembles that of some Langevin equations with multiplicative noise, which exhibit also two analogous phase transitions as the noise-amplitude is increased. By comparing the standard models for noise-induced transitions with our new Langevin equation we elucidate that the mechanisms controlling the disorder-to-order transitions in both of them are essentially different, even though for both of them the presence of multiplicative noise is a key ingredient.Comment: Submitted to Phys. Rev.