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At least 181 records · Page 10

Dynamic Flow Management Problems in Air Transportation

In 1995, over six hundred thousand licensed pilots flew nearly thirty-five million flights into over eighteen thousand U.S. airports, logging more than 519 billion passenger miles. Since demand for air travel has increased by more than 50% in the last decade while capacity has stagnated, congestion is a problem of undeniable practical significance. In this thesis, we will develop optimization techniques that reduce the impact of congestion on the national airspace. We start by determining the optimal release times for flights into the airspace and the optimal speed adjustment while airborne taking into account the capacitated airspace. This is called the Air Traffic Flow Management Problem (TFMP). We address the complexity, showing that it is NP-hard. We build an integer programming formulation that is quite strong as some of the proposed inequalities are facet defining for the convex hull of solutions. For practical problems, the solutions of the LP relaxation of the TFMP are very often integral. In essence, we reduce the problem to efficiently solving large scale linear programming problems. Thus, the computation times are reasonably small for large scale, practical problems involving thousands of flights. Next, we address the problem of determining how to reroute aircraft in the airspace system when faced with dynamically changing weather conditions. This is called the Air Traffic Flow Management Rerouting Problem (TFMRP) We present an integrated mathematical programming approach for the TFMRP, which utilizes several methodologies, in order to minimize delay costs. In order to address the high dimensionality, we present an aggregate model, in which we formulate the TFMRP as a multicommodity, integer, dynamic network flow problem with certain side constraints. Using Lagrangian relaxation, we generate aggregate flows that are decomposed into a collection of flight paths using a randomized rounding heuristic. This collection of paths is used in a packing integer programming formulation, the solution of which generates feasible and near-optimal routes for individual flights. The algorithm, termed the Lagrangian Generation Algorithm, is used to solve practical problems in the southwestern portion of United States in which the solutions are within 1% of the corresponding lower bounds.

Patterson, Sarah Stock↗

Retrospective studies of operating problems in air transport

An epidemiological model for the study of human errors in aviation is presented. In this approach, retrospective data are used as the basis for formulation of hypotheses as to system factors which may have contributed to such errors. Prospective experimental studies of aviation operations are also required in order to prove or disprove the hypotheses, and to evaluate the effectiveness of intervention techniques designed to solve operational problems in the aviation system.

Billings, C. E.↗

Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport

We analyze the well-posedness of an anisotropic, nonlocal diffusion equation. Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector calculus, we apply our analysis to a class of fractional-order operators and present rigorous estimates for the solution of the corresponding anisotropic anomalous diffusion equation. Furthermore, we extend our analysis to the anisotropic diffusion-advection equation and prove well-posedness for fractional orders s ∊ [0.5, 1). We also present an application of the advection-diffusion equation to anomalous transport of solutes.

97 MATHEMATICS AND COMPUTING↗

Transportation options for solar power satellites

Advantages of solar power satellites compared to ground-based solar power installations are related to an almost continuous exposure to sunlight and to a much smaller collector area. An investigation of the transportation cost problem is conducted. Transportation systems based on presently understood technology are considered for the deployment of solar power satellites at potentially competitive costs. It is found that the cost of placement in a geosynchronous orbit is reducible to the range from $500 to $1000/kW. Approaches for achieving dramatic cost reductions are discussed.

Woodcock, G. R.↗

The new Space Shuttle Transportation System (STS) - Problem, performance, supportability, and programmatic trending program

This paper describes the NASA Space Shuttle Trend Analysis program. The four main areas of the program - problem/reliability, performance, supportability, and programmatic trending - are defined, along with motivation for these areas, the statistical methods used, and illustrative Space Shuttle applications. Also described is the NASA Safety, Reliability, Maintainability and Quality Assurance (SRM&QA) Management Information Center, used to focus management attention on key near-term launch concerns and long-range mission trend issues. Finally, the computer data bases used to support the program and future program enhancements are discussed.

Crawford, J. L.↗

General theory of spherically symmetric boundary-value problems of the linear transport theory.

A general theory of spherically symmetric boundary-value problems of the one-speed neutron transport theory is presented. The formulation is also applicable to the 'gray' problems of radiative transfer. The Green's function for the purely absorbing medium is utilized in obtaining the normal mode expansion of the angular densities for both interior and exterior problems. As the integral equations for unknown coefficients are regular, a general class of reduction operators is introduced to reduce such regular integral equations to singular ones with a Cauchy-type kernel. Such operators then permit one to solve the singular integral equations by the standard techniques due to Muskhelishvili. We discuss several spherically symmetric problems. However, the treatment is kept sufficiently general to deal with problems lacking azimuthal symmetry. In particular the procedure seems to work for regions whose boundary coincides with one of the coordinate surfaces for which the Helmholtz equation is separable.

Kanal, M.↗

Approximation for Horizontal Photon Transport in Cloud Remote Sensing Problems

The effect of horizontal photon transport within real-world clouds can be of consequence to remote sensing problems based on plane-parallel cloud models. An analytic approximation for the root-mean-square horizontal displacement of reflected and transmitted photons relative to the incident cloud-top location is derived from random walk theory. The resulting formula is a function of the average number of photon scatterings, and particle asymmetry parameter and single scattering albedo. In turn, the average number of scatterings can be determined from efficient adding/doubling radiative transfer procedures. The approximation is applied to liquid water clouds for typical remote sensing solar spectral bands, involving both conservative and non-conservative scattering. Results compare well with Monte Carlo calculations. Though the emphasis is on horizontal photon transport in terrestrial clouds, the derived approximation is applicable to any multiple scattering plane-parallel radiative transfer problem. The complete horizontal transport probability distribution can be described with an analytic distribution specified by the root-mean-square and average displacement values. However, it is shown empirically that the average displacement can be reasonably inferred from the root-mean-square value. An estimate for the horizontal transport distribution can then be made from the root-mean-square photon displacement alone.

Plantnick, Steven↗

A pseudo-spectral collocation method applied to the problem of convective diffusive transport in fluids subject to unsteady residual accelerations

The problem of determining the sensitivity of Bridgman-Stockbarger directional solidification experiments to residual accelerations of the type associated with spacecraft in low earth orbit is analyzed numerically using a pseudo-spectral collocation method. The approach employs a novel iterative scheme combining the method of artificial compressibility and a generalized ADI method. The results emphasize the importance of the consideration of residual accelerations and careful selection of the operating conditions in order to take full advantages of the low gravity conditions.

Alexander, J. Iwan↗

Challenges and Opportunities Specific to Microreactors: Compact and Light-Weight Shielding During Operation and Transportation

The problem of designing a shield for a mobile microreactor has been addressed. The principal challenges encountered in this endeavor are the dual goals of increasing radiation protection and decreasing weight. It is recognized that these two goals are contradictory. Increasing shielding naturally increases weight. Conversely, decreasing weight naturally calls for decreasing material inventory, including possibly decreasing shield mass. The operational and regulatory drivers for shielding and transportation constraints are identified and summarized. The main constraints pertain to volume, mass, radiation dose, material feasibility and availability, and decommissioning expectations. The latter are limits on residual contamination and dose rates after the reactor is removed. Progress toward solving the challenge of shielding a transportable microreactor is made by considering a tungsten tetraboride (WB4) shell surrounding the reactor vessel. The shield and a generic microreactor were modeled using the MCNP code. It was determined that the presence of a 16-cm-thick WB4 shield reduces the dose equivalent rate during operations to 3.6 mrem/h just outside of a concrete vault and dome and soil berm surrounding the reactor, which is very near the occupational dose rate limits. Without the WB4 layer, the dose rate at the same location outside the berm would be 120 mrem/h. Most importantly, the presence of the WB4 shield substantially protects the surrounding concrete and soil from activation, thus decreasing the duration of administrative control for the site following removal of the reactor from 16 to 3.4 years. At that point, the site may be decommissioned and returned to unrestricted public access. A limitation on the incorporation of a WB4 shield as an intrinsic component of a microreactor is that it results in a design that is transportable only by using the largest road conveyances and that the load would require special permits for transit through the U.S. highway system. New directions for further improvements and possibly more effective solutions to the shielding problem of a mobile microreactor are discussed in the conclusion section.

Microreactor↗