A tight lower bound for an online hypercube packing problem and bounds for prices of anarchy of a related game

We prove a tight lower bound on the asymptotic performance ratio $\rho$ of the bounded space online $d$-hypercube bin packing problem, solving an open question raised in 2005. In the classic $d$-hypercube bin packing problem, we are given a sequence of $d$-dimensional hypercubes and we have an unlimited number of bins, each of which is a $d$-dimensional unit hypercube. The goal is to pack (orthogonally) the given hypercubes into the minimum possible number of bins, in such a way that no two hypercubes in the same bin overlap. The bounded space online $d$-hypercube bin packing problem is a variant of the $d$-hypercube bin packing problem, in which the hypercubes arrive online and each one must be packed in an open bin without the knowledge of the next hypercubes. Moreover, at each moment, only a constant number of open bins are allowed (whenever a new bin is used, it is considered open, and it remains so until it is considered closed, in which case, it is not allowed to accept new hypercubes). Epstein and van Stee [SIAM J. Comput. 35 (2005), no. 2, 431-448] showed that $\rho$ is $\Omega(\log d)$ and $O(d/\log d)$, and conjectured that it is $\Theta(\log d)$. We show that $\rho$ is in fact $\Theta(d/\log d)$. To obtain this result, we elaborate on some ideas presented by those authors, and go one step further showing how to obtain better (offline) packings of certain special instances for which one knows how many bins any bounded space algorithm has to use. Our main contribution establishes the existence of such packings, for large enough $d$, using probabilistic arguments. Such packings also lead to lower bounds for the prices of anarchy of the selfish $d$-hypercube bin packing game. We present a lower bound of $\Omega(d/\log d)$ for the pure price of anarchy of this game, and we also give a lower bound of $\Omega(\log d)$ for its strong price of anarchy

Low-thrust chemical propulsion system propellant expulsion and thermal conditioning study. Executive summary

Preferred techniques for providing abort pressurization and engine feed system net positive suction pressure (NPSP) for low thrust chemical propulsion systems (LTPS) were determined. A representative LTPS vehicle configuration is presented. Analysis tasks include: propellant heating analysis; pressurant requirements for abort propellant dump; and comparative analysis of pressurization techniques and thermal subcoolers

Low-thrust chemical propulsion system propellant expulsion and thermal conditioning study

Thermal conditioning systems for satisfying engine net positive suction pressure (NPSP) requirements, and propellant expulsion systems for achieving propellant dump during a return-to-launch site (RTLS) abort were studied for LH2/LO2 and LCH4/LO2 upper stage propellant combinations. A state-of-the-art thermal conditioning system employing helium injection beneath the liquid surface shows the lowest weight penalty for LO2 and LCH4. A technology system incorporating a thermal subcooler (heat exchanger) for engine NPSP results in the lowest weight penalty for the LH2 tank. A preliminary design of two state-of-the-art and two new technology systems indicates a weight penalty difference too small to warrant development of a LH2 thermal subcooler. Analysis results showed that the LH2/LO2 propellant expulsion system is optimized for maximum dump line diameters, whereas the LCH4/LO2 system is optimized for minimum dump line diameter (LCH4) and maximum dump line diameter (LO2). The primary uncertainty is the accurate determination of two-phase flow rates through the dump system; experimentation is not recommended because this uncertainty is not considered significant

Numerical study of the lattice vacancy effects on the single-channel electron transport of graphite ribbons

Lattice vacancy effects on electrical conductance of nanographite ribbon are investigated by means of the Landauer approach using a tight binding model. In the low-energy regime ribbons with zigzag boundary provide a single conducting channel whose origin is connected with the presence of edge states. It is found that the chemical potential dependence of conductance strongly depends on the difference ($\Delta$) of the number of removed A and B sublattice sites. The large lattice vacancy with $\Delta\neq 0$ shows $2\Delta$ zero-conductance dips in the single-channel region, however, the large lattice vacancy with $\Delta=0$ has no dip structure in this region. The connection between this conductance rule and the Longuet-Higgins conjecture is also discussed

Uniform current in graphene strip with zigzag edges

Graphene exhibits zero-gap massless-Dirac fermion and zero density of states at E = 0. These particles form localized states called edge states on finite width strip with zigzag edges at E = 0. Naively thinking, one may expect that current is also concentrated at the edge, but Zarbo and Nikolic numerically obtained a result that the current density shows maximum at the center of the strip. We derive a rigorous relation for the current density, and clarify the reason why the current density of edge state has a maximum at the center.Comment: 5 pages, 3 figures; added references and corrected typos, to be published in J. Phys. Soc. Jpn. Vol.78 No.

Nonuniversal Shot Noise in Disordered Quantum Wires with Channel-Number Imbalance

The number of conducting channels for one propagating direction is equal to that for the other direction in ordinary quantum wires. However, they can be imbalanced in graphene nanoribbons with zigzag edges. Employing the model system in which a degree of channel-number imbalance can be controlled, we calculate the shot-noise power at zero frequency by using the Boltzmann-Langevin approach. The shot-noise power in an ordinary diffusive conductor is one-third of the Poisson value. We show that with increasing the degree of channel-number imbalance, the universal one-third suppression breaks down and a highly nonuniversal behavior of shot noise appears.Comment: 10 pages, 3 figure

A C-band backscatter model for lake ice in Alaska

ERS-1 SAR imagery of lake ice growing on shallow tundra lakes in northern Alaska shows interesting radar backscatter variations. Based on the analysis of ice cores from these lakes, a multi-layer backscatter model comprised of the following elements has been developed: (1) specular air-ice; ice-water and ice-frozen soil boundaries; (2) an ice layer of variable thickness; (3) ice sub-layers with air inclusions of variable density, size and shape including spheres, prolate spheroids, and cylinders of finite length. Preliminary model results confirm that backscatter is a sensitive function of greater reflectivity than from an ice-frozen soil interface. The model has also been tested using bubble data derived from ice cores in April 1992. The modelled backscatter is compared with backscatter derived from ERS-1 SAR images obtained at the same time as the fieldwork

ERS-1 SAR backscatter changes associated with ice growing on shallow lakes in Arctic Alaska

Spatial and temporal backscatter intensity (sigma(sup o)) variations from ice growing on shallow lakes during winter 1991-92 near Barrow, NW Alaska, have been quantified for the first time using ERS-I C-band SAR data acquired at the Alaska SAR Facility. A field and laboratory validation program, including measurements of the thickness and structure-stratigraphy of the ice, indicates that sigma(sup o) values are strongly dependent on whether the ice freezes to the lake bottom, or remains afloat. Backscatter intensity decreases significantly when the ice grounds on the bottom. Strong backscatter from floating ice is attributed to a specular ice-water interface and vertically oriented tubular bubbles. During the spring thaw, backscatter undergoes a reversal; sigma(sup o) values from ice that was grounded increase, while sigma(sup o) values from ice that was afloat decrease. This phenomenon has not previously been reported