Bridging gap between standard and differential polynomial approximation: The case of bin-packing

AbstractThe purpose of this paper is mainly to prove the following theorem: for every polynomial time algorithm running in time T(n) and guaranteeing standard-approximation ratio ϱ for bin-packing, there exists an algorithm running in time O(nT(n)) and achieving differential-approximation ratio 2 − ϱ for BP. This theorem has two main impacts. The first one is “operational”, deriving a polynomial time differential-approximation schema for bin-packing. The second one is structural, establishing a kind of reduction (to our knowledge not existing until now) between standard approximation and differential one

Advanced Ceramic Wafer Seals Demonstrated at 2000 deg. F

Durable, high-temperature sliding seals are required in advanced hypersonic engines and around movable control surfaces on future vehicles. These seals must operate at temperatures of 2000 to 2500 F, limit hot gas flow, remain resilient for multiple cycles, and resist scrubbing damage against rough surfaces. Current seal designs do not meet these demanding requirements, so the NASA Glenn Research Center is developing advanced seals and preload devices to overcome these shortfalls. An advanced ceramic wafer seal design and two silicon nitride compression spring designs were evaluated in a series of compression, scrub, and flow tests

Improved Seals for High Temperature Airframe Applications

Current thermal barrier seals, such as those used on the Space Shuttle, are insufficient to fully meet the demands of future hypersonic vehicles and reentry spacecraft. Previous investigations have demonstrated limited usage temperatures, as evidenced by a decreased ability to maintain sealing effectiveness at high temperatures (i.e., inadequate resiliency). In order to improve resiliency at elevated temperatures, Rene 41 (Allvac) was substituted for Inconel X-750 (Special Metals Corp.) as the spring tube material in the existing seal design. A seal construction incorporating the Rene 41 spring tube was fabricated and tested against the baseline Inconel X-750 spring tube seal. Although resiliency improvements were not as dramatic as in previous tests with the spring tubes alone, seals incorporating the Rene 41 spring tube exhibited an average 20 percent resiliency enhancement up to 1750 F when compared to seals containing the Inconel spring tube. In addition, the seals with the Rene 41 spring tubes showed less reduction in resiliency as temperatures increased above 1200 F. Results also indicated the Saffil (Saffil Ltd.) insulation in the core of the seal contributed more to resiliency than previously thought. Leakage data did not demonstrate an improvement with the seal containing the Rene 41 spring tube. However, based upon resiliency results, one could reasonably expect the Rene 41 version of the seal to track gap openings over a wider range. Therefore it would exhibit lower leakage than the Inconel X-750 version as the seal gap opens during a typical mission

Performance Evaluations of Ceramic Wafer Seals

Future hypersonic vehicles will require high temperature, dynamic seals in advanced ramjet/scramjet engines and on the vehicle airframe to seal the perimeters of movable panels, flaps, and doors. Seal temperatures in these locations can exceed 2000 F, especially when the seals are in contact with hot ceramic matrix composite sealing surfaces. NASA Glenn Research Center is developing advanced ceramic wafer seals to meet the needs of these applications. High temperature scrub tests performed between silicon nitride wafers and carbon-silicon carbide rub surfaces revealed high friction forces and evidence of material transfer from the rub surfaces to the wafer seals. Stickage between adjacent wafers was also observed after testing. Several design changes to the wafer seals were evaluated as possible solutions to these concerns. Wafers with recessed sides were evaluated as a potential means of reducing friction between adjacent wafers. Alternative wafer materials are also being considered as a means of reducing friction between the seals and their sealing surfaces and because the baseline silicon nitride wafer material (AS800) is no longer commercially available

An Evaluation of High Temperature Airframe Seals for Advanced Hypersonic Vehicles

High temperature seals are required for advanced hypersonic airframe applications. In this study, both spring tube thermal barriers and innovative wafer seal systems were evaluated under relevant hypersonic test conditions (temperatures, pressures, etc.) via high temperature compression testing and room temperature flow assessments. Thermal barriers composed of a Rene 41 spring tube filled with Saffil insulation and overbraided with a Nextel 312 sheath showed acceptable performance at 1500 F in both short term and longer term compression testing. Nextel 440 thermal barriers with Rene 41 spring tubes and Saffil insulation demonstrated good compression performance up to 1750 F. A silicon nitride wafer seal/compression spring system displayed excellent load performance at temperatures as high as 2200 F and exhibited room temperature leakage values that were only 1/3 those for the spring tube rope seals. For all seal candidates evaluated, no significant degradation in leakage resistance was noted after high temperature compression testing. In addition to these tests, a superalloy seal suitable for dynamic seal applications was optimized through finite element techniques

Design Study of Wafer Seals for Future Hypersonic Vehicles

Future hypersonic vehicles require high temperature, dynamic seals in advanced hypersonic engines and on the vehicle airframe to seal the perimeters of movable panels, flaps, and doors. Current seals do not meet the demanding requirements of these applications, so NASA Glenn Research Center is developing improved designs to overcome these shortfalls. An advanced ceramic wafer seal design has shown promise in meeting these needs. Results from a design of experiments study performed on this seal revealed that several installation variables played a role in determining the amount of leakage past the seals. Lower leakage rates were achieved by using a tighter groove width around the seals, a higher seal preload, a tighter wafer height tolerance, and a looser groove length. During flow testing, a seal activating pressure acting behind the wafers combined with simulated vibrations to seat the seals more effectively against the sealing surface and produce lower leakage rates. A seal geometry study revealed comparable leakage for full-scale wafers with 0.125 and 0.25 in. thicknesses. For applications in which lower part counts are desired, fewer 0.25-in.-thick wafers may be able to be used in place of 0.125-in.-thick wafers while achieving similar performance. Tests performed on wafers with a rounded edge (0.5 in. radius) in contact with the sealing surface resulted in flow rates twice as high as those for wafers with a flat edge. Half-size wafers had leakage rates approximately three times higher than those for full-size wafers

Further Investigations of High Temperature Knitted Spring Tubes for Advanced Control Surface Seal Applications

Knitted metallic spring tubes are the structural backbones that provide resiliency in control surface seals for use on current and future reusable space launch vehicles. Control surface seals fill the space between movable control surfaces such as body flaps, rudders and elevons, and the static body structures to which they are attached. These seals must remain in continuous contact with opposing surfaces to prevent the ingestion of damaging hot gases encountered during atmospheric re-entry. The Inconel X-750 (Special Metals Corporation) spring tube utilized in the baseline control surface seal shows significant resiliency loss when compressed at temperatures as low as 1200 F. High temperature compression testing and microstructural analysis show that creep is the dominant deformation mechanism leading to permanent set and resiliency loss in tested spring tube samples. Additional evaluation using a structured design of experiments approach shows that spring tube performance, primarily high temperature resiliency, can be enhanced through material substitution of Rene 41 (Allvac) alloy (for the baseline Inconel X-750 material) when coupled with specialized thermal processing

Biorthogonal quantum mechanics

The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called 'biorthogonal quantum mechanics', is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems. © 2014 IOP Publishing Ltd

Oriented coloring: complexity and approximation

International audienceThis paper is devoted to an oriented coloring problem motivated by a task assignment model. A recent result established the NP-completeness of deciding whether a digraph is k-oriented colorable; we extend this result to the classes of bipartite digraphs and circuit-free digraphs. Finally, we investigate the approximation of this problem: both positive and negative results are devised

Advanced Control Surface Seal Development at NASA GRC for Future Space Launch Vehicles

NASA s Glenn Research Center (GRC) is developing advanced control surface seal technologies for future space launch vehicles as part of the Next Generation Launch Technology project (NGLT). New resilient seal designs are currently being fabricated and high temperature seal preloading devices are being developed as a means of improving seal resiliency. GRC has designed several new test rigs to simulate the temperatures, pressures, and scrubbing conditions that seals would have to endure during service. A hot compression test rig and hot scrub test rig have been developed to perform tests at temperatures up to 3000 F. Another new test rig allows simultaneous seal flow and scrub tests at room temperature to evaluate changes in seal performance with scrubbing. These test rigs will be used to evaluate the new seal designs. The group is also performing tests on advanced TPS seal concepts for Boeing using these new test facilities