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Parallel solution of high-order numerical schemes for solving incompressible flows

A new parallel numerical scheme for solving incompressible steady-state flows is presented. The algorithm uses a finite-difference approach to solving the Navier-Stokes equations. The algorithms are scalable and expandable. They may be used with only two processors or with as many processors as are available. The code is general and expandable. Any size grid may be used. Four processors of the NASA LeRC Hypercluster were used to solve for steady-state flow in a driven square cavity. The Hypercluster was configured in a distributed-memory, hypercube-like architecture. By using a 50-by-50 finite-difference solution grid, an efficiency of 74 percent (a speedup of 2.96) was obtained.

Milner, Edward J.

Design of a cooperative problem-solving system for en-route flight planning: An empirical evaluation

Both optimization techniques and expert systems technologies are popular approaches for developing tools to assist in complex problem-solving tasks. Because of the underlying complexity of many such tasks, however, the models of the world implicitly or explicitly embedded in such tools are often incomplete and the problem-solving methods fallible. The result can be 'brittleness' in situations that were not anticipated by the system designers. To deal with this weakness, it has been suggested that 'cooperative' rather than 'automated' problem-solving systems be designed. Such cooperative systems are proposed to explicitly enhance the collaboration of the person (or a group of people) and the computer system. This study evaluates the impact of alternative design concepts on the performance of 30 airline pilots interacting with such a cooperative system designed to support en-route flight planning. The results clearly demonstrate that different system design concepts can strongly influence the cognitive processes and resultant performances of users. Based on think-aloud protocols, cognitive models are proposed to account for how features of the computer system interacted with specific types of scenarios to influence exploration and decision making by the pilots. The results are then used to develop recommendations for guiding the design of cooperative systems.

Layton, Charles

Enroute flight planning: Evaluating design concepts for the development of cooperative problem-solving systems

There are many problem-solving tasks that are too complex to fully automate given the current state of technology. Nevertheless, significant improvements in overall system performance could result from the introduction of well-designed computer aids. We have been studying the development of cognitive tools for one such problem-solving task, enroute flight path planning for commercial airlines. Our goal has been two-fold. First, we have been developing specific system designs to help with this important practical problem. Second, we have been using this context to explore general design concepts to guide in the development of cooperative problem-solving systems. These design concepts are described below, along with illustrations of their application.

Smith, Philip J.

Design of a cooperative problem-solving system for en-route flight planning: An empirical evaluation

Both optimization techniques and expert systems technologies are popular approaches for developing tools to assist in complex problem-solving tasks. Because of the underlying complexity of many such tasks, however, the models of the world implicitly or explicitly embedded in such tools are often incomplete and the problem-solving methods fallible. The result can be 'brittleness' in situations that were not anticipated by the system designers. To deal with this weakness, it has been suggested that 'cooperative' rather than 'automated' problem-solving systems be designed. Such cooperative systems are proposed to explicitly enhance the collaboration of the person (or a group of people) and the computer system. This study evaluates the impact of alternative design concepts on the performance of 30 airline pilots interacting with such a cooperative system designed to support enroute flight planning. The results clearly demonstrate that different system design concepts can strongly influence the cognitive processes and resultant performances of users. Based on think-aloud protocols, cognitive models are proposed to account for how features of the computer system interacted with specific types of scenarios to influence exploration and decision making by the pilots. The results are then used to develop recommendations for guiding the design of cooperative systems.

Layton, Charles

A Numerical Method for Solving the Equations of Compressible Viscous Flow

Although much progress has already been made In solving problems in aerodynamic design, many new developments are still needed before the equations for unsteady compressible viscous flow can be solved routinely. This paper describes one such development. A new method for solving these equations has been devised that 1) is second-order accurate in space and time, 2) is unconditionally stable, 3) preserves conservation form, 4) requires no block or scalar tridiagonal inversions, 5) is simple and straightforward to program (estimated 10% modification for the update of many existing programs), 6) is more efficient than present methods, and 7) should easily adapt to current and future computer architectures. Computational results for laminar and turbulent flows at Reynolds numbers from 3 x 10(exp 5) to 3 x 10(exp 7) and at CFL numbers as high as 10(exp 3) are compared with theory and experiment.

MacCormack, R. W.

A Method to Solve Interior and Exterior Camera Calibration Parameters for Image Resection

An iterative method is presented to solve the internal and external camera calibration parameters, given model target points and their images from one or more camera locations. The direct linear transform formulation was used to obtain a guess for the iterative method, and herein lies one of the strengths of the present method. In all test cases, the method converged to the correct solution. In general, an overdetermined system of nonlinear equations is solved in the least-squares sense. The iterative method presented is based on Newton-Raphson for solving systems of nonlinear algebraic equations. The Jacobian is analytically derived and the pseudo-inverse of the Jacobian is obtained by singular value decomposition.

Samtaney, Ravi

An Assessment of the Ozone Loss During the 1999-2000 SOLVE Arctic Campaign

Ozone observations from ozonesondes, the lidars aboard the DC-8, in situ ozone measurements from the ER-2, and satellite ozone measurements from Polar Ozone and Aerosol Measurement III (POAM) were used to assess ozone loss during the Sage III Ozone Loss and Validation Experiment (SOLVE) 1999-2000 Arctic campaign. Two methods of analysis were used. In the first method a simple regression analysis is performed on the ozonesonde and POAM measurements within the vortex. In the second method, the ozone measurements from all available ozone data were injected into a free running diabatic trajectory model and carried forward in time from December 1 to March 15. Vortex ozone loss was then estimated by comparing the ozone values of those parcels initiated early in the campaign with those parcels injected later in the campaign. Despite the variety of observational techniques used during SOLVE, the measurements provide a fairly consistent picture. Over the whole vortex, the largest ozone loss occurs between 550 and 400 K potential temperatures (approximately 23-16 km) with over 1.5 ppmv lost by March 15, the end of the SOLVE mission period. An ozone loss rate of 0.04-0.05 ppmv/day was computed for March 15. Ozonesondes launched after March 15 suggest that an additional 0.5 ppmv or more ozone was lost between March 15 and April 1. The small disagreement between ozonesonde and POAM analysis of January ozone loss is found to be due to biases in vortex sampling. POAM makes most of its solar occultation measurements at the vortex edge during January 2000 which bias samples toward air parcels that have been exposed to sunlight and likely do experience ozone loss. Ozonesonde measurements and the trajectory technique use observations that are more distributed within the interior of the vortex. Thus the regression analysis of the POAM measurements tends to overestimate mid-winter vortex ozone loss. Finally, our loss calculations are broadly consistent with other loss computations using ER-2 tracer data and MLS satellite data, but we find no evidence for the 1992 high mid-January loss reported using the Match technique.

Schoeberl, Mark R.

Supporting Scientific Analysis within Collaborative Problem Solving Environments

Collaborative problem solving environments for scientists should contain the analysis tools the scientists require in addition to the remote collaboration tools used for general communication. Unfortunately, most scientific analysis tools have been designed for a "stand-alone mode" and cannot be easily modified to work well in a collaborative environment. This paper addresses the questions, "What features are desired in a scientific analysis tool contained within a collaborative environment?", "What are the tool design criteria needed to provide these features?", and "What support is required from the architecture to support these design criteria?." First, the features of scientific analysis tools that are important for effective analysis in collaborative environments are listed. Next, several design criteria for developing analysis tools that will provide these features are presented. Then requirements for the architecture to support these design criteria are listed. Sonic proposed architectures for collaborative problem solving environments are reviewed and their capabilities to support the specified design criteria are discussed. A deficiency in the most popular architecture for remote application sharing, the ITU T. 120 architecture, prevents it from supporting highly interactive, dynamic, high resolution graphics. To illustrate that the specified design criteria can provide a highly effective analysis tool within a collaborative problem solving environment, a scientific analysis tool that contains the specified design criteria has been integrated into a collaborative environment and tested for effectiveness. The tests were conducted in collaborations between remote sites in the US and between remote sites on different continents. The tests showed that the tool (a tool for the visual analysis of computer simulations of physics) was highly effective for both synchronous and asynchronous collaborative analyses. The important features provided by the tool (and made possible by the specified design criteria) are: 1. The tool provides highly interactive, dynamic, high resolution, 3D graphics. 2. All remote scientists can view the same dynamic, high resolution, 3D scenes of the analysis as the analysis is being conducted. 3. The responsiveness of the tool is nearly identical to the responsiveness of the tool in a stand-alone mode. 4. The scientists can transfer control of the analysis between themselves. 5. Any analysis session or segment of an analysis session, whether done individually or collaboratively, can be recorded and posted on the Web for other scientists or students to download and play in either a collaborative or individual mode. 6. The scientist or student who downloaded the session can, individually or collaboratively, modify or extend the session with his/her own "what if" analysis of the data and post his/her version of the analysis back onto the Web. 7. The peak network bandwidth used in the collaborative sessions is only 1K bit/second even though the scientists at all sites are viewing high resolution (1280 x 1024 pixels), dynamic, 3D scenes of the analysis. The links between the specified design criteria and these performance features are presented.

Watson, Velvin R.

Tracer Evolution at High Latitudes in Winter (SOLVE)

Prior to the SOLVE deployment, we modified and ran a chemical transport model (CTM) to set up a stratospheric climatology for 1 September 1999. During and immediately following the SOLVE deployments, we ran the model in near-real-time and used these results in conjunction with SOLVE observations to draw conclusions about stratospheric transport.

Plumb, R. Alan

In Situ Measurements of N2O and CH4 During SOLVE on the ER-2 Using a New Tunable Diode Laser Instrument

This report is the final report for Cooperative Agreement NCC2-1105: 'In Situ Measurements of N2O and CH4 during SOLVE on the ER-2 using a new tunable diode laser instrument.' The tasks outlined in the proposal are listed below with a brief comment. The publications and the conference presentations are listed. Finally the important publications are attached. The Cooperative Agreement made possible a research effort to produce high precision and high accuracy in situ measurements of methane and nitrous oxide on the ER-2 during the SOLVE field campaign and to analyze these measurements. These measurements of CH4 and N2O were of utmost importance to studies of the ozone losses in the Arctic winter and spring. The concentrations measured over a large spatial and temporal range allowed the separation of the dynamical and chemical ozone loss. The most important results of the SOLVE program were contained in two scientific papers. This Cooperative Agreement allowed the participation of the Argus instrument in the program and the analysis of the data.

Jost, Hansjurg

Retrieval of Ozone Column Content from Airborne Sun Photometer Measurements During SOLVE II: Comparison with SAGE III, POAM III,THOMAS and GOME Measurements

During the Second SAGE 111 Ozone Loss and Validation Experiment (SOLVE II), the 14- channel NASA Ames Airborne Trackmg Sunphotometer (AATS-14) was mounted on the NASA DC-8 and successfully measured spectra of total and aerosol optical depth (TOD and AOD) during the sunlit portions of eight science flights. Values of ozone column content above the aircraft have been derived from the AATS-14 data by using a linear least squares method. For each AATS-14 measured TOD spectrum, this method iteratively finds the ozone column content that yields the best match between measured and calculated TOD. The calculations assume the known Chappuis ozone band shape and a three-parameter AOD shape (quadratic in log-log space). Seven of the AATS-14 channels (each employing an interference filter with a nominal full-width at half maximum bandpass of -5 nm) are within the Chappuis band, with center wavelengths between 452.9 nm and 864.5 nm. One channel (604.4 nm) is near the peak, and three channels (499.4, 519.4 and 675.1 nm) have ozone absorption within 30-40% of that at the peak. For the typical DC-8 SOLVE II cruising altitudes of approx. 8-12 km and the background stratospheric aerosol conditions that prevailed during SOLVE 11, absorption of incoming solar radiation by ozone comprised a significant fraction of the aerosol-plus-ozone optical depth measured in the four AATS-14 channels centered between 499.4 and 675.1 nm. Typical AODs above the DC-8 ranged from 0.003-0.008 in these channels. For comparison, an ozone overburden of 0.3 atm-cm (300 DU) translates to ozone optical depths of 0.009,0.014, 0.041, and 0.012, respectively, at these same wavelengths. In this paper, we compare AATS-14 values of ozone column content with temporally and spatially near-coincident values derived from measurements acquired by the Stratospheric Aerosol and Gas Experiment III (SAGE III) and the Polar Ozone and Aerosol Measurement 111 (POAM III) satellite sensors. We also compare AATS-14 ozone retrievals during selected DC-8 latitudinal and longitudinal transects with total column ozone data acquired by the Total Ozone Mapping Spectrometer (TOMS) and the Global Ozone Monitoring Experiment (GOME) satellite sensors. To enable this comparison, the amount of ozone in the column below the aircraft is estimated by combining SAGE and/or POAM data with high resolution, fast response in-situ ozone measurements acquired during the DC-8 ascent at the start of each science flight.

Livingston, J.

Optimal Planning and Problem-Solving

CTAEMS MDP Optimal Planner is a problem-solving software designed to command a single spacecraft/rover, or a team of spacecraft/rovers, to perform the best action possible at all times according to an abstract model of the spacecraft/rover and its environment. It also may be useful in solving logistical problems encountered in commercial applications such as shipping and manufacturing. The planner reasons around uncertainty according to specified probabilities of outcomes using a plan hierarchy to avoid exploring certain kinds of suboptimal actions. Also, planned actions are calculated as the state-action space is expanded, rather than afterward, to reduce by an order of magnitude the processing time and memory used. The software solves planning problems with actions that can execute concurrently, that have uncertain duration and quality, and that have functional dependencies on others that affect quality. These problems are modeled in a hierarchical planning language called C_TAEMS, a derivative of the TAEMS language for specifying domains for the DARPA Coordinators program. In realistic environments, actions often have uncertain outcomes and can have complex relationships with other tasks. The planner approaches problems by considering all possible actions that may be taken from any state reachable from a given, initial state, and from within the constraints of a given task hierarchy that specifies what tasks may be performed by which team member.

Clemet, Bradley

Investment in Open Innovation Service Providers: NASA's Innovative Strategy for Solving Space Exploration Challenges

In an effort to expand routes for open communication and create additional opportunities for public involvement with NASA, Open Innovation Service Provider (OISP) methodologies have been incorporated as a tool in NASA's problem solving strategy. NASA engaged the services of two OISP providers, InnoCentive and Yet2.com, to test this novel approach and its feasibility in solving NASA s space flight challenges. The OISPs were chosen based on multiple factors including: network size and knowledge area span, established process, methodology, experience base, and cost. InnoCentive and Yet2.com each met the desired criteria; however each company s approach to Open Innovation is distinctly different. InnoCentive focuses on posting individual challenges to an established web-based network of approximately 200,000 solvers; viable solutions are sought and granted a financial award if found. Based on a specific technological need, Yet2.com acts as a talent scout providing a broad external network of experts as potential collaborators to NASA. A relationship can be established with these contacts to develop technologies and/or maintained as an established network of future collaborators. The results from the first phase of the pilot study have shown great promise for long term efficacy of utilizing the OISP methodologies. Solution proposals have been received for the challenges posted on InnoCentive and are currently under review for final disposition. In addition, Yet2.com has identified new external partners for NASA and we are in the process of understanding and acting upon these new opportunities. Compared to NASA's traditional routes for external problem solving, the OISP methodologies offered NASA a substantial savings in terms of time and resources invested. In addition, these strategies will help NASA extend beyond its current borders to build an ever expanding network of experts and global solvers.

Fogarty, Jennifer A.

Solving Nonlinear Euler Equations with Arbitrary Accuracy

A computer program that efficiently solves the time-dependent, nonlinear Euler equations in two dimensions to an arbitrarily high order of accuracy has been developed. The program implements a modified form of a prior arbitrary- accuracy simulation algorithm that is a member of the class of algorithms known in the art as modified expansion solution approximation (MESA) schemes. Whereas millions of lines of code were needed to implement the prior MESA algorithm, it is possible to implement the present MESA algorithm by use of one or a few pages of Fortran code, the exact amount depending on the specific application. The ability to solve the Euler equations to arbitrarily high accuracy is especially beneficial in simulations of aeroacoustic effects in settings in which fully nonlinear behavior is expected - for example, at stagnation points of fan blades, where linearizing assumptions break down. At these locations, it is necessary to solve the full nonlinear Euler equations, and inasmuch as the acoustical energy is of the order of 4 to 5 orders of magnitude below that of the mean flow, it is necessary to achieve an overall fractional error of less than 10-6 in order to faithfully simulate entropy, vortical, and acoustical waves.

Dyson, Rodger W.

Improve Problem Solving Skills through Adapting Programming Tools

There are numerous ways for engineers and students to become better problem-solvers. The use of command line and visual programming tools can help to model a problem and formulate a solution through visualization. The analysis of problem attributes and constraints provide insight into the scope and complexity of the problem. The visualization aspect of the problem-solving approach tends to make students and engineers more systematic in their thought process and help them catch errors before proceeding too far in the wrong direction. The problem-solver identifies and defines important terms, variables, rules, and procedures required for solving a problem. Every step required to construct the problem solution can be defined in program commands that produce intermediate output. This paper advocates improved problem solving skills through using a programming tool. MatLab created by MathWorks, is an interactive numerical computing environment and programming language. It is a matrix-based system that easily lends itself to matrix manipulation, and plotting of functions and data. MatLab can be used as an interactive command line or a sequence of commands that can be saved in a file as a script or named functions. Prior programming experience is not required to use MatLab commands. The GNU Octave, part of the GNU project, a free computer program for performing numerical computations, is comparable to MatLab. MatLab visual and command programming are presented here.

Shaykhian, Linda H.

Use of the NLP10x10 Sequential Quadratic Programming Algorithm To Solve Rotorcraft Hub Loads Minimisation Problems

Previous research and experimentation on the use of a non-linear programming constrained optimisation technique to define an optimal control vector for rotorcraft applications indicated that use of this methodology was feasible and desirable in many cases. In particular, use of non-linear programming methods that solve a sequence of related quadratic-programming sub-problems were used successfully to solve these problems. Accordingly, a licence for one of the latest versions of Professor Klaus Schittkowskis very successful Sequential Quadratic Programming NLPQLP software was obtained and used to experiment with and analyse typical optimisation problems of the type encountered in various rotorcraft wind tunnel and flight tests. This research resulted in the development of the general NLPQLP Computation System that could be used to solve problems of the type encountered in various rotorcraft applications where there is a linear dependence of the measurement vector on the control vector, and where equality andor inequality constraints might be imposed. This development was accomplished on a mainframe computer not part of actual wind tunnel andor flight-test experiment, but in a format which was transferable to wind tunnel lap-top computers. Emphasis was directed toward obtaining efficiency, robustness and speed in computation.The System was developed in support of the five-bladed SMART Rotor Active Flap Rotor Hub Loads analytical minimisation research. The design and development of the Computation System was tailored to address the particular requirements of the problem to minimise a performance metric function of measured hub load harmonic angular couple components by optimising the control vector harmonic flap angular couple components subject to constraints on the amplitudes of these control vector harmonic flap angular couple components. In addition, to facilitate real time wind tunnel experimentation, the ability to rapidly selectchange the particular hub load harmonic angular couple components andor the particular control vector harmonic angular couple components to be considered in the optimisation procedure was provided in the System. This capability allows the singling out of particular hub load frequencies andor particular flap angle frequencies to be analysed during testing operations. The System was used very successfully for the SMART Active Flap Rotor Hub minimisation problems considered in the study, the results of which were presented at the American Helicopter Society Fifth Decennial Aeromechanics Specialist Conference in January 2014. Excellent agreement between cases initiated with best guess starting estimates for the control vector elements and cases initiated with zero control vector starting element estimates resulted, indicating the robustness of the NLP10x10 algorithm.

Rotorcraft Hub Loads

What can solve the strong CP problem?

Three possible strategies have been advocated to solve the strong CP problem. The first is the axion, a dynamical mechanism that relaxes any initial value of the CP violating angle $\overline{θ}$ to zero. The second is the imposition of new symmetries that are believed to set $\overline{θ}$ to zero in the UV. The third is the acceptance of the fine tuning of parameters. We argue that the latter two solutions do not solve the strong CP problem. The θ term of QCD is not a parameter — it does not exist in the Hamiltonian. Rather, it is a property of the quantum state that our universe finds itself in, arising from the fact that there are CP violating states of a CP preserving Hamiltonian. It is not eliminated by imposing parity as a symmetry since the underlying theory is already parity symmetric and that does not preclude the existence of CP violating states. Moreover, since the value of θ realized in our universe is a consequence of measurement, it is inherently random and cannot be fine tuned by choice of parameters. Rather any fine tuning would require a tuning between parameters in the theory and the random outcome of measurement. Our results considerably strengthen the case for the existence of the axion and axion dark matter. The confusion around θ arises from the fact that unlike classical mechanics, the Hamiltonian and Lagrangian are not equivalent in quantum mechanics. The Hamiltonian defines the differential time evolution, whereas the Lagrangian is a solution to this evolution. Consequently, initial conditions could in principle appear in the Lagrangian but not in the Hamiltonian. This results in aspects of the initial condition such as θ misleadingly appearing in the Lagrangian as parameters. We comment on the similarity between the θ vacua and the violations of the constraint equations of classical gauge theories in quantum mechanics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

An end-to-end deep learning method for solving nonlocal Allen–Cahn and Cahn–Hilliard phase-field models

Here, we propose an efficient end-to-end deep learning method for solving nonlocal Allen–Cahn (AC) and Cahn–Hilliard (CH) phase-field models. One motivation for this effort emanates from the fact that discretized partial differential equation-based AC or CH phase-field models result in diffuse interfaces between phases, with the only recourse for remediation is to severely refine the spatial grids in the vicinity of the true moving sharp interface whose width is determined by a grid-independent parameter that is substantially larger than the local grid size. In this work, we introduce non-mass conserving nonlocal AC or CH phase-field models with regular, logarithmic, or obstacle double-well potentials. Because of non-locality, some of these models feature totally sharp interfaces separating phases. The discretization of such models can lead to a transition between phases whose width is only a single grid cell wide. Another motivation is to use deep learning approaches to ameliorate the otherwise high cost of solving discretized nonlocal phase-field models. To this end, loss functions of the customized neural networks are defined using the residual of the fully discrete approximations of the AC or CH models, which results from applying a Fourier collocation method and a temporal semi-implicit approximation. To address the long-range interactions in the models, we tailor the architecture of the neural network by incorporating a nonlocal kernel as an input channel to the neural network model. We then provide the results of extensive computational experiments to illustrate the accuracy, predictive capabilities, and cost reductions of the proposed method.

42 ENGINEERING