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An approximation to the Maxwell-Semiconductor Bloch equations is solved for the transverse modes of vertical-cavity surface-emitting lasers. A finite-difference algorithm will be used to calculate the detailed time evolution of the transverse mode profiles of VCSELs. Effects of pumping current and refractive index profiles will be investigated.
Data from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument that flies in polar orbit on the Terra platform, are used to derive the aerosol optical thickness and properties over land and ocean. The relationships between visible reflectance (at blue, rho(sub blue), and red, rho(sub red)) and mid-infrared (at 2.1 microns, rho(sub 2.1)) are used in the MODIS aerosol retrieval algorithm to derive global distribution of aerosols over the land. These relations have been established from a series of measurements indicating that rho(sub blue) is approximately 0.5 rho(sub red) is approximately 0.25 rho(sub 2.1). Here we use a model to describe the transfer of radiation through a vegetation canopy composed of randomly oriented leaves to assess the theoretical foundations for these relationships. Calculations for a wide range of leaf area indices and vegetation fractions show that rho(sub blue) is consistently about 1/4 of rho(sub 2.1) as used by MODIS for the whole range of analyzed cases, except for very dark soils, such as those found in burn scars. For its part, the ratio rho(sub red)/rho(sub 2.1) varies from less than the empirically derived value of 1/2 for dense and dark vegetation, to more than 1/2 for bright mixture of soil and vegetation. This is in agreement with measurements over uniform dense vegetation, but not with measurements over mixed dark scenes. In the later case the discrepancy is probably mitigated by shadows due to uneven canopy and terrain on a large scale. It is concluded that the value of this ratio should ideally be made dependent on the land cover type in the operational processing of MODIS data, especially over dense forests.
An algorithm has been developed that solves the semiconductor Maxwell-Bloch equations, without making the standard slowly-varying envelope (SVEA) and rotating-wave (RWA) approximations. It is applied to study the propagation of ultrashort pulses in semiconductor materials. The results include many-body effects due to the Coulomb interaction among the charge carriers as well as the nonlinear effects resulting from spectral hole-burning.
The state-of-the-art in vehicle design decouples flight feasible trajectory generation from the optimization process of an entry spacecraft shape. The disadvantage to this decoupled process is seen when a particular aeroshell does not meet in-flight requirements when integrated into Guidance, Navigation, and Control simulations. It is postulated that the integration of a guidance algorithm into the design process will provide a real-time, rapid trajectory generation technique to enhance the robustness of vehicle design solutions. The potential benefit of this integration is a reduction in design cycles (possible cost savings) and increased accuracy in the aerothermal environment (possible mass savings). This work examines two aspects: 1) the performance of a reference tracking guidance algorithm for five different geometries with the same reference trajectory and 2) the potential of mass savings from improved aerothermal predictions. An Apollo Derived Guidance (ADG) algorithm is used in this study. The baseline geometry and five test case geometries were flown using the same baseline trajectory. The guided trajectory results are compared to separate trajectories determined in a vehicle optimization study conducted for NASA's Mars Entry, Descent, and Landing System Analysis. This study revealed several aspects regarding the potential gains and required developments for integrating a guidance algorithm into the vehicle optimization environment. First, the generation of flight feasible trajectories is only as good as the robustness of the guidance algorithm. The set of dispersed geometries modelled aerodynamic dispersions that ranged from +/-1% to +/-17% and a single extreme case was modelled where the aerodynamics were approximately 80% less than the baseline geometry. The ADG, as expected, was able to guide the vehicle into the aeroshell separation box at the target location for dispersions up to 17%, but failed for the 80% dispersion cases. Finally, the results revealed that including flight feasible trajectories for a set of dispersed geometries has the potential to save mass up to 430 kg.
NASA's Meteoroid Environment Office (MEO) recently established a two‐station system to calculate daily automated meteor fluxes in the millimeter‐size‐range for both single‐station and double‐station meteors. The cameras each consist of a 17 mm focal length Schneider lens (f/0.95) on a Watec 902H2 Ultimate CCD video camera, producing a 21.7x15.5 degree field of view. This configuration sees meteors down to a magnitude of +6. This paper outlines the concepts of the system, the hardware and software, and results of 3,000+ orbits from the first 18 months of operations. Video from the cameras are run through ASGARD (All Sky and Guided Automatic Real‐time Detection), which performs the meteor detection/photometry, and invokes MILIG and MORB (Borovicka 1990) codes to determine the trajectory, speed, and orbit of the meteor. A subroutine in ASGARD allows for approximate shower identification in single‐station detections. The ASGARD output is used in routines to calculate the flux. Before a flux can be calculated, a weather algorithm indicates if sky conditions are clear enough to calculate fluxes, at which point a limiting magnitude algorithm is employed. The limiting stellar magnitude is found using astrometry.net (Lang et al. 2012) to identify stars and translated to the corresponding shower and sporadic limiting meteor magnitude. It is found every 10 minutes and is able to react to quickly changing sky conditions. The extensive testing of these results on the Geminids and Eta Aquariids is shown. The flux involves dividing the number of meteors by the collecting area of the system, over the time interval for which that collecting area is valid. The flux algorithm employed here differs from others currently in use in that it does not make the gross oversimplication of choosing a single height to calculate the collection area of the system. In the MEO system, the volume is broken up into a set of height intervals, with the collecting areas determined by the position of the active shower or sporadic source radiant. The flux per height interval is calculated and summed to obtain the total meteor flux. Both single station and double station fluxes are currently found daily. Geminid fluxes on the peak night in 2012 (12‐14‐2012) were 0.058 meteors/km2/hr as found with double‐station meteors and 0.057 meteors/ km2/hr as found with single‐station meteors, to a limiting magnitude of +6.5. Both of those numbers are in agreement with the well‐calibrated fluxes from the Canadian Meteor Orbit Radar. Along with flux algorithms and initial flux results, presented will be results from the first 18 months of operation, covering 3,000+ meteoroid orbits.
A new equilibrium thermodynamics analysis tool was built based on the CEA method using the OpenMDAO framework. The new tool provides forward and adjoint analytic derivatives for use with gradient based optimization algorithms. The new tool was validated against the original CEA code to ensure an accurate analysis and the analytic derivatives were validated against finite-difference approximations. Performance comparisons between analytic and finite difference methods showed a significant speed advantage for the analytic methods. To further test the new analysis tool, a sample optimization was performed to find the optimal air-fuel equivalence ratio, , maximizing combustion temperature for a range of different pressures. Collectively, the results demonstrate the viability of the new tool to serve as the thermodynamic backbone for future work on a full propulsion modeling tool.
Gold mining has played a significant role in Ghana's economy for centuries. Regulation of this industry has varied over time and while industrial mining is prevalent in the country, the expansion of artisanal mining, or Galamsey has escalated in recent years. Many of these artisanal mines are not only harmful to human health due to the use of Mercury (Hg) in the amalgamation process, but also leave a significant footprint on terrestrial ecosystems, degrading and destroying forested ecosystems in the region. In this study, the Landsat image archive available through Google Earth Engine was used to quantify the total footprint of vegetation loss due to artisanal goldmines in Ghana from 2005 to 2019 and understand how conversion of forested regions to mining has changed over a decadal period from 2007 to 2017. A combination of machine learning and change detection algorithms were used to calculate different land cover conversions and the timing of conversion annually. Within the study area of southwestern Ghana, our results indicate that approximately 47,000 ha (⨦2218 ha) of vegetation were converted to mining at an average rate of ~2600 ha yr−1. The results indicate that a high percentage(~50%) of this mining occurred between 2014 and 2017. Around 700 ha of this mining occurred within protected areas as mapped by the World Database of Protected Areas. In addition to deforestation, increased artisanal mining activity in recent years has the potential to affect human health, access to drinking water resources and food security. This work expands upon limited research into the spatial footprint of Galamseyin Ghana, complements mapping efforts by local geographers, and will support efforts by the government of Ghana to monitor deforestation caused by artisanal mining.
In this paper, we present an optimal open-loop slew trajectory algorithm developed at GSFC for the so-called "Yardstick design" of the James Webb Space Telescope (JWST). JWST is an orbiting infrared observatory featuring a lightweight, segmented primary mirror approximately 6 meters in diameter and a sunshield approximately the size of a tennis court. This large, flexible structure will have significant number of lightly damped, dominant flexible modes. With very stringent requirements on pointing accuracy and image quality, it is important that slewing be done within the required time constraint and with minimal induced vibration in order to maximize observing efficiency. With reaction wheels as control actuators, initial wheel speeds as well as individual wheel torque and momentum limits become dominant constraints in slew performance. These constraints must be taken into account when performing slews to ensure that unexpected reaction wheel saturation does not occur, since such saturation leads to control failure in accurately tracking commanded motion and produces high frequency torque components capable of exciting structural modes. A minimum-time constraint is also included and coupled with reaction wheel limit constraints in the optimization to minimize both the effect of the control torque on the flexible body motion and the maneuver time. The optimization is on slew command parameters, such as maximum slew velocity and acceleration, for a given redundant reaction wheel configuration and is based on the dynamic interaction between the spacecraft and reaction wheel motion. Analytical development of the slew algorithm to generate desired slew position, rate, and acceleration profiles to command a feedback/feed forward control system is described. High-fidelity simulation and experimental results are presented to show that the developed slew law achieves the objectives.
A new development of on-board data processing platform has been in progress at NASA Langley Research Center since April, 2012, and the overall review of such work is presented in this paper. The project is called High-Speed On-Board Data Processing for Science Instruments (HOPS) and focuses on a high-speed scalable data processing platform for three particular National Research Council's Decadal Survey missions such as Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS), Aerosol-Cloud-Ecosystems (ACE), and Doppler Aerosol Wind Lidar (DAWN) 3-D Winds. HOPS utilizes advanced general purpose computing with Field Programmable Gate Array (FPGA) based algorithm implementation techniques. The significance of HOPS is to enable high speed on-board data processing for current and future science missions with its reconfigurable and scalable data processing platform. A single HOPS processing board is expected to provide approximately 66 times faster data processing speed for ASCENDS, more than 70% reduction in both power and weight, and about two orders of cost reduction compared to the state-of-the-art (SOA) on-board data processing system. Such benchmark predictions are based on the data when HOPS was originally proposed in August, 2011. The details of these improvement measures are also presented. The two facets of HOPS development are identifying the most computationally intensive algorithm segments of each mission and implementing them in a FPGA-based data processing board. A general introduction of such facets is also the purpose of this paper.
A document discusses a multi-objective, genetic algorithm designed to optimize Lyapunov feedback control law (Q-law) parameters in order to efficiently find Pareto-optimal solutions for low-thrust trajectories for electronic propulsion systems. These would be propellant-optimal solutions for a given flight time, or flight time optimal solutions for a given propellant requirement. The approximate solutions are used as good initial solutions for high-fidelity optimization tools. When the good initial solutions are used, the high-fidelity optimization tools quickly converge to a locally optimal solution near the initial solution. Q-law control parameters are represented as real-valued genes in the genetic algorithm. The performances of the Q-law control parameters are evaluated in the multi-objective space (flight time vs. propellant mass) and sorted by the non-dominated sorting method that assigns a better fitness value to the solutions that are dominated by a fewer number of other solutions. With the ranking result, the genetic algorithm encourages the solutions with higher fitness values to participate in the reproduction process, improving the solutions in the evolution process. The population of solutions converges to the Pareto front that is permitted within the Q-law control parameter space.
Research aimed at faster, more cost effective parallel machines and algorithms for improving designer productivity with finite element computations is discussed. A set of 8 boards, containing 4 nearest neighbor connected arrays of commercially available floating point chips and substantial memory, are inserted into a commercially available machine. One-tenth Mflop (64 bit operation) processors provide an 89% efficiency when solving the equations arising in a finite element problem for a single variable regular grid of size 40 by 40 by 40. This is approximately 15 to 20 times faster than a much more expensive machine such as a VAX 11/780 used in double precision. The efficiency falls off as faster or more processors are envisaged because communication times become dominant. A novel successive overrelaxation algorithm which uses cyclic reduction in order to permit data transfer and computation to overlap in time is proposed.
Presented here is a new algorithm to determine attitude using only magnetometer data under the following conditions: (1) internal torques are known and (2) external torques are negligible. Torque-free rotation of a spacecraft in thruster firing acquisition phase and its magnetic despin in the B-dot mode give typical examples of such situations. A simple analytical formula has been derived in the limiting case of a spacecraft rotating with constant angular velocity. The formula has been tested using low-frequency telemetry data for the Earth Radiation Budget Satellite (ERBS) under normal conditions. Observed small oscillation of body-fixed components of the angular velocity vector near their mean values result in relatively minor errors of approximately 5 degrees. More significant errors come from processing digital magnetometer data. Higher resolution of digitized magnetometer measurements would significantly improve the accuracy of this deterministic scheme. Tests of the general version of the developed algorithm for a free-rotating spacecraft and for the B-dot mode are in progress.
The use of the R sub 0 criterion for modulation system design is investigated for channels with non-white Gaussian noise. A signal space representation of the waveform channel is developed, and the cut-off rate R sub 0 for vector channels with additive nonwhite Gaussian noise and unquantized demodulation is derived. When the signal unput to the channel is a continuous random vector, maximization of R sub 0 with constrained average signal energy leads to a water-filling interpretation of optimal energy distribution in signal space. The necessary condition for a finite signal set to maximize R sub 0 with constrained energy and an equally likely probability assignment of signal vectors is presented, and an algorithm is outlined for numerically computing the optimum signal set. A necessary condition on a constrained energy, finite signal set is found which maximizes a Taylor series approximation of R sub 0. This signal set is compared with the finite signal set which has the water-filling average energy distribution.
Element-by-element approximate factorization procedures are proposed for solving the large finite element equation systems which arise in nonlinear structural mechanics. Architectural and data base advantages of the present algorithms over traditional direct elimination schemes are noted. Results of calculations suggest considerable potential for the methods described.
A dual approximation for the solution to an optimal control problem is analyzed. The differential equation is handled with a Lagrange multiplier while other constraints are treated explicitly. An algorithm for solving the dual problem is presented.
Downstream marching iterative schemes for the solution of the Parabolized or Thin Layer (PNS or TL) Navier-Stokes equations are described. Modifications of the primitive equation global relaxation sweep procedure result in efficient second-order marching schemes. These schemes take full account of the reduced order of the approximate equations as they behave like the SLOR for a single elliptic equation. The improved smoothing properties permit the introduction of Multi-Grid acceleration. The proposed algorithm is essentially Reynolds number independent and therefore can be applied to the solution of the subsonic Euler equations. The convergence rates are similar to those obtained by the Multi-Grid solution of a single elliptic equation; the storage is also comparable as only the pressure has to be stored on all levels. Extensions to three-dimensional and compressible subsonic flows are discussed. Numerical results are presented.
A series of numerical examples is reported and several algorithms compared for estimation of coefficients in differential equation models. Unconstrained, constrained and Tikhonov regularization methods are tested for their behavior with regard to both convergence (of approximation methods for the states and parameters) and stability (continuity of the estimates with respect to perturbations in the data or observed states).
Downstream marching iterative schemes for the solution of the Parabolized or Thin Layer (PNS or TL) Navier-Stokes equations are described. Modifications of the primitive equation global relaxation sweep procedure result in efficient second-order marching schemes. These schemes take full account of the reduced order of the approximate equations as they behave like the SLOR for a single elliptic equation. The improved smoothing properties permit the introduction of Multi-Grid acceleration. The proposed algorithm is essentially Reynolds number independent and therefore can be applied to the solution of the subsonic Euler equations. The convergence rates are similar to those obtained by the Multi-Grid solution of a single elliptic equation; the storage is also comparable as only the pressure has to be stored on all levels. Extensions to three-dimensional and compressible subsonic flows are discussed. Numerical results are presented.