On Colorful Bin Packing Games

We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of $m\geq 2$ colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions: the egalitarian cost function which equally shares the cost of a bin among the items it contains, and the proportional cost function which shares the cost of a bin among the items it contains proportionally to their sizes. Although, under both cost functions, colorful bin packing games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we design an algorithm for computing a Nash equilibrium whose running time is polynomial under the egalitarian cost function and pseudo-polynomial for a constant number of colors under the proportional one. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when $m\geq 3$ while they are equal to 3 for black and white games, where $m=2$. We finally focus on games with uniform sizes (i.e., all items have the same size) for which the two cost functions coincide. We show again a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance

An analytically solvable model of probabilistic network dynamics

We present a simple model of network dynamics that can be solved analytically for uniform networks. We obtain the dynamics of response of the system to perturbations. The analytical solution is an excellent approximation for random networks. A comparison with the scale-free network, though qualitatively similar, shows the effect of distinct topology.Comment: 4 pages, 1 figur

Factors Affecting the Corporate Decision-Making Process of Air Transport Manufacturers

Fuel economy is a pivotal question influencing the future sale and utilization of commercial aircraft. The NASA Aircraft Energy Efficiency (ACEE) Program Office has a program intended to accelerate the readiness of advanced technologies for energy efficient aircraft. Because the decision to develop a new airframe or engine is a major financial hazard for manufacturers, it is important to know what factors influence the decision making process. A method is described for identifying and ranking individuals and organizations involved at each stage of commercial air transport development, and the barriers that must be overcome in adopting new technologies

Polarization and readout of coupled single spins in diamond

We study the coupling of a single nitrogen-vacancy center in diamond to a nearby single nitrogen defect at room temperature. The magnetic dipolar coupling leads to a splitting in the electron spin resonance frequency of the nitrogen-vacancy center, allowing readout of the state of a single nitrogen electron spin. At magnetic fields where the spin splitting of the two centers is the same we observe a strong polarization of the nitrogen electron spin. The amount of polarization can be controlled by the optical excitation power. We combine the polarization and the readout in time-resolved pump-probe measurements to determine the spin relaxation time of a single nitrogen electron spin. Finally, we discuss indications for hyperfine-induced polarization of the nitrogen nuclear spin

Causal perturbation theory in terms of retarded products, and a proof of the Action Ward Identity

In the framework of perturbative algebraic quantum field theory a local construction of interacting fields in terms of retarded products is performed, based on earlier work of Steinmann. In our formalism the entries of the retarded products are local functionals of the off shell classical fields, and we prove that the interacting fields depend only on the action and not on terms in the Lagrangian which are total derivatives, thus providing a proof of Stora's 'Action Ward Identity'. The theory depends on free parameters which flow under the renormalization group. This flow can be derived in our local framework independently of the infrared behavior, as was first established by Hollands and Wald. We explicitly compute non-trivial examples for the renormalization of the interaction and the field.Comment: 76 pages, to appear in Rev. Math. Phy

Instability and spatiotemporal rheochaos in a shear-thickening fluid model

We model a shear-thickening fluid that combines a tendency to form inhomogeneous, shear-banded flows with a slow relaxational dynamics for fluid microstructure. The interplay between these factors gives rich dynamics, with periodic regimes (oscillating bands, travelling bands, and more complex oscillations) and spatiotemporal rheochaos. These phenomena, arising from constitutive nonlinearity not inertia, can occur even when the steady-state flow curve is monotonic. Our model also shows rheochaos in a low-dimensional truncation where sharply defined shear bands cannot form

Solar Carboreduction of Alumina under Vacuum

AbstractMain requirements for successful production of aluminum via carboreduction of alumina using solar vacuum reactors are sufficiently high reaction temperature, suitable low partial pressure of the product gases, fast heating and quenching at temperature low enough to prevent backward reaction. Based on these requests a batch solar reactor was modeled, designed, built and tested. Experimental results of the solar tests under different vacuum levels and temperature conditions will be presented. It will be shown that for reaction temperature, which is above the minimal temperature required for full conversion as predicted by thermodynamic calculations for appropriate pressure, the alumina to aluminum conversion is above 90%. Not reaching the full conversion can be explained by the byproducts formation during the initial preheating. At lower reaction temperatures and higher CO partial pressure by products can also be formed when reaching steady state condition both in the forward and backward reactions. This formation in the forward reaction is confirmed by the discovery of larger amounts of Al4C3, Al4CO4 solids as the residual byproducts in the reactants holder and higher alumina content in the deposits on the cold parts of the reactor that originated from the volatile Al2O produced in the forward reaction which during the deposition converts to alumina and aluminum. Decreasing the reaction temperature is accompanied by decreasing the temperature in the hot zone that causes the increasing of the deposit mass there with higher amount of Al4C3 and Al4CO4 produced in the backward reaction. Nano crystalline and amorphous morphology of the deposits in the cold zone caused by fast cooling will also be discussed

Effect of prolonged space flight on cardiac function and dimensions

Echocardiographic studies were performed preflight 5 days before launch and on recovery day and 1, 2, 4, 11, 31 and 68 days postflight. From these echocardiograms measurements were made. From these primary measurements, left ventricular end-diastolic volume, end-systolic volume, stroke volume, and mass were derived using the accepted assumptions. Findings in the Scientist Pilot and Pilot resemble those seen in trained distance runners. Wall thickness measurements were normal in all three crewmembers preflight. Postflight basal studies were unchanged in the Commander on recovery day through 68 days postflight in both the Scientist Pilot and Pilot, however, the left ventricular end-diastolic volume, stroke volume, and mass were decreased slightly. Left ventricular function curves were constructed for the Commander and Pilot by plotting stroke volume versus end-diastolic volume. In both astronauts, preflight and postflight data fell on the same straight line demonstrating that no deterioration in cardiac function had occurred. These data indicate that the cardiovascular system adapts well to prolonged weightlessness and suggest that alterations in cardiac dimensions and function are unlikely to limit man's future in space