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We show how to construct, for a Lagrangian of arbitrary order, a Lepage equivalent satisfying the closure property: that the Lepage equivalent vanishes precisely when the Lagrangian is null. The construction uses a homotopy operator for the horizontal differential of the variational bicomplex. A choice of symmetric linear connection on the manifold of independent variables, and a global homotopy operator constructed using that connection, may then be used to extend any global Lepage equivalent to one satisfying the closure property. In the second part of the paper we investigate the r\^ole of vertical endomorphisms in constructing such Lepage equivalents. These endomorphisms may be used directly to construct local homotopy operators. Together with a symmetric linear connection they may also be used to construct global vertical tensors, and these define infinitesimal nonholonomic projections which in turn may be used to construct Lepage equivalents. We conjecture that these global vertical tensors may also be used to define global homotopy operators.

While solar-like oscillations in red giants have been observed at massive scale by the Kepler mission, few features of these oscillation mode frequencies, other than their global properties, have been exploited for stellar characterization. The signatures of acoustic glitches in mode frequencies have been used for studying main-sequence stars, but the validity of applying such techniques to evolved red giants, particularly pertaining to the inclusion of nonradial modes, has been less well-examined. Making use of new theoretical developments, we characterize glitches using the $\pi$ modes associated with red giant stellar models, and use our procedure to examine for the first time how properties of the He II acoustic glitch -- specifically its amplitude and associated acoustic depth -- vary over the course of evolution up the red giant branch, and with respect to other fundamental stellar properties. We find that the acoustic depths of these glitches, in conjunction with other spectroscopic information, discriminates between red giants in the first-ascent and core-helium-burning phases. We critically reexamine previous attempts to constrain acoustic glitches from nonradial (in particular dipole) modes in red giants. Finally, we apply our fitting procedure to Kepler data, to evaluate its robustness to noise and other observational systematics., Comment: 15 pages, 12 figures; accepted to ApJ

We investigate the problem of finding upper and lower bounds for a Choquet risk measure of a nonlinear function of two risk factors, when the marginal distributions of the risk factors are ambiguous and represented by nonadditive measures on the marginal spaces and the joint nonadditive distribution on the product space is unknown. We treat this problem as a generalization of the optimal transport problem to the setting of nonadditive measures. We provide explicit characterizations of the optimal solutions for finite marginal spaces, and we investigate some of their properties. We further discuss the connections with linear programming, showing that the optimal transport problems for capacities are linear programs, and we also characterize their duals explicitly. Finally, we investigate a series of numerical examples, including a comparison with the classical optimal transport problem, and applications to counterparty credit risk., Comment: 30 pages, 3 figures, 4 tables

Consider the inverse first-passage problem: Given a diffusion process $\{\frak{X}_{t}\}_{t\geqslant 0}$ on a probability space $(\Omega,\mathcal{F},\mathbb{P})$ and a survival probability function $p$ on $[0,\infty)$, find a boundary, $x=b(t)$, such that $p$ is the survival probability that $\frak{X}$ does not fall below $b$, i.e., for each $t\geqslant 0$, $p(t)= \mathbb{P}(\{\omega\in\Omega\;|\; {\frak{X}}_s(\omega) \geqslant b(s),\ \forall\, s\in(0,t)\})$. In earlier work, we analyzed viscosity solutions of a related variational inequality, and showed that they provided the only upper semi-continuous (usc) solutions of the inverse problem. We furthermore proved weak regularity (continuity) of the boundary $b$ under additional assumptions on $p$. The purpose of this paper is to study higher-order regularity properties of the solution of the inverse first-passage problem. In particular, we show that when $p$ is smooth and has negative slope, the viscosity solution, and therefore also the unique usc solution of the inverse problem, is smooth. Consequently, the viscosity solution furnishes a unique classical solution to the free boundary problem associated with the inverse first-passage problem., Comment: 24 pages

This paper aims to extend downside protection to a hedge fund investment portfolio based on shared loss fee structures that have become increasing popular in the market. In particular, we consider a second tranche and suggest the purchase of an upfront reinsurance contract for any losses on the fund beyond the threshold covered by the first tranche, i.e. gaining full portfolio protection. We identify a fund's underlying liquidity as a key parameter and study the pricing of this additional reinsurance using two approaches: First, an analytic closed-form solution based on the Black-Scholes framework and second, a numerical simulation using a Markov-switching model. In addition, a simplified backtesting method is implemented to evaluate the practical application of the concept.

We consider the problem of determining an upper bound for the value of a spectral risk measure of a loss that is a general nonlinear function of two factors whose marginal distributions are known, but whose joint distribution is unknown. The factors may take values in complete separable metric spaces. We introduce the notion of Maximum Spectral Measure (MSP), as a worst-case spectral risk measure of the loss with respect to the dependence between the factors. The MSP admits a formulation as a solution to an optimization problem that has the same constraint set as the optimal transport problem, but with a more general objective function. We present results analogous to the Kantorovich duality, and we investigate the continuity properties of the optimal value function and optimal solution set with respect to perturbation of the marginal distributions. Additionally, we provide an asymptotic result characterizing the limiting distribution of the optimal value function when the factor distributions are simulated from finite sample spaces. The special case of Expected Shortfall and the resulting Maximum Expected Shortfall is also examined.

Consider the set of probability measures with given marginal distributions on the product of two complete, separable metric spaces, seen as a correspondence when the marginal distributions vary. In problems of optimal transport, continuity of this correspondence from marginal to joint distributions is often desired, in light of Berge's Maximum Theorem, to establish continuity of the value function in the marginal distributions, as well as stability of the set of optimal transport plans. Bergin (1999) established the continuity of this correspondence, and in this note, we present a novel and considerably shorter proof of this important result. We then examine an application to an assignment game (transferable utility matching problem) with unknown type distributions.

If a Lagrangian defining a variational problem has order $k$ then its Euler-Lagrange equations generically have order $2k$. This paper considers the case where the Euler-Lagrange equations have order strictly less than $2k$, and shows that in such a case the Lagrangian must be a polynomial in the highest-order derivative variables, with a specific upper bound on the degree of the polynomial. The paper also provides an explicit formulation, derived from a geometrical construction, of a family of such $k$-th order Lagrangians, and it is conjectured that all such Lagrangians arise in this way.

In this paper we consider three types of embedded options in pension benefit design. The first is the Florida second election (FSE) option, offered to public employees in the state of Florida in 2002. Employees were given the option to convert from a defined contribution (DC) plan to a defined benefit (DB) plan at a time of their choosing. The cost of the switch was assessed in terms of the ABO (Accrued Benefit Obligation), which is the expected present value of the accrued DB pension at the time of the switch. If the ABO was greater than the DC account, the employee was required to fund the difference. The second is the DB Underpin option, also known as a floor offset, under which the employee participates in a DC plan, but with a guaranteed minimum benefit based on a traditional DB formula. The third option can be considered a variation on each of the first two. We remove the requirement from the FSE option for employees to fund any shortfall at the switching date. The resulting option is very similar to the DB underpin, but with the possibility of early exercise. Since we assume that exercise is only permitted at discrete, annual intervals, this option is a Bermudan variation on the DB Underpin. We adopt an arbitrage-free pricing methodology to value the option. We analyse and value the optimal switching strategy for the employee by constructing an exercise frontier, and illustrate numerically the difference between the FSE, DB Underpin and Bermudan DB Underpin options.

Numerical challenges inherent in algorithms for computing worst Value-at-Risk in homogeneous portfolios are identified and solutions as well as words of warning concerning their implementation are provided. Furthermore, both conceptual and computational improvements to the Rearrangement Algorithm for approximating worst Value-at-Risk for portfolios with arbitrary marginal loss distributions are given. In particular, a novel Adaptive Rearrangement Algorithm is introduced and investigated. These algorithms are implemented using the R package qrmtools.

We study the problem of finding the worst-case joint distribution of a set of risk factors given prescribed multivariate marginals and a nonlinear loss function. We show that when the risk measure is CVaR, and the distributions are discretized, the problem can be conveniently solved using linear programming technique. The method has applications to any situation where marginals are provided, and bounds need to be determined on total portfolio risk. This arises in many financial contexts, including pricing and risk management of exotic options, analysis of structured finance instruments, and aggregation of portfolio risk across risk types. Applications to counterparty credit risk are emphasized, and they include assessing wrong-way risk in the credit valuation adjustment, and counterparty credit risk measurement. Lastly a detailed application of the algorithm for counterparty risk measurement to a real portfolio case is also presented in this paper.

This paper presents a novel Coprime Blurred Pair (CBP) model for visual data-hiding for security in camera surveillance. While most previous approaches have focused on completely encrypting the video stream, we introduce a spatial encryption scheme by blurring the image/video contents to create a CBP. Our goal is to obscure detail in public video streams by blurring while allowing behavior to be recognized and to quickly deblur the stream so that details are available if behavior is recognized as suspicious. We create a CBP by blurring the same latent image with two unknown kernels. The two kernels are coprime when mapped to bivariate polynomials in the z domain. To deblur the CBP we first use the coprime constraint to approximate the kernels and sample the bivariate CBP polynomials in one dimension on the unit circle. At each sample point, we factor the 1D polynomial pair and compose the results into a 2D kernel matrix. Finally, we compute the inverse Fast Fourier Transform (FFT) of the kernel matrices to recover the coprime kernels and then the latent video stream. It is therefore only possible to deblur the video stream if a user has access to both streams. To improve the practicability of our algorithm, we implement our algorithm using a graphics processing unit (GPU) to decrypt the blurred video streams in real-time, and extensive experimental results demonstrate that our new scheme can effectively protect sensitive identity information in surveillance videos and faithfully reconstruct the unblurred video stream when two blurred sequences are available.

We study the inverse boundary crossing problem for diffusions. Given a diffusion process $X_t$, and a survival distribution $p$ on $[0,\infty)$, we demonstrate that there exists a boundary $b(t)$ such that $p(t)=\mathbb{P}[\tau >t]$, where $\tau$ is the first hitting time of $X_t$ to the boundary $b(t)$. The approach taken is analytic, based on solving a parabolic variational inequality to find $b$. Existence and uniqueness of the solution to this variational inequality were proven in earlier work. In this paper, we demonstrate that the resulting boundary $b$ does indeed have $p$ as its boundary crossing distribution. Since little is known regarding the regularity of $b$ arising from the variational inequality, this requires a detailed study of the problem of computing the boundary crossing distribution of $X_t$ to a rough boundary. Results regarding the formulation of this problem in terms of weak solutions to the corresponding Kolmogorov forward equation are presented., Comment: Published in at http://dx.doi.org/10.1214/10-AAP714 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

The Mars Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight) spacecraft, which successfully touched down on the planet surface on November 26, 2018, was proposed as a near build-to-print copy of the Mars Phoenix vehicle to reduce the overall cost and risk of the mission. Since the lander payload and the atmospheric entry trajectory were similar enough to those of the Phoenix mission, it was expected that the Phoenix thermal protection material thickness would be sufficient to withstand the entry heat load. However, allowances were made for increasing the heatshield thickness because the planned spacecraft arrival date coincided with the Mars dust storm season. The aftbody Thermal Protection System (TPS) components were not expected to change. In a first for a US Mars mission, the aerothermal environments for InSight included estimates of radiative heat flux to the aftbody from the wake. The combined convective and radiative heat fluxes were used to determine if the as-flown Phoenix thermal protection system (TPS) design would be sufficient for InSight. Although the radiative heat fluxes on the aftbody were predicted to be comparable to, or even higher than the local convective heat fluxes, all analyses of the aftbody TPS showed that the design would still be adequate. Aerothermal environments were computed for the vehicle from post-flight reconstruction of the atmosphere and trajectory and compared.

The Mars Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight) spacecraft, which successfully touched down on the planet surface on November 26, 2018, was proposed as a near build-to-print copy of the Mars Phoenix vehicle to reduce the overall cost and risk of the mission. Since the lander payload and the atmospheric entry trajectory were similar enough to those of the Phoenix mission, it was expected that the Phoenix thermal protection material thickness would be sufficient to withstand the entry heat load. However, allowances were made for increasing the heatshield thickness because the planned spacecraft arrival date coincided with the Mars dust storm season. The aftbody Thermal Protection System (TPS) components were not expected to change. In a first for a US Mars mission, the aerothermal environments for InSight included estimates of radiative heat flux to the aftbody from the wake. The combined convective and radiative heat fluxes were used to determine if the as-flown Phoenix thermal protection system (TPS) design would be sufficient for InSight. Although the radiative heat fluxes on the aftbody were predicted to be comparable to, or even higher than the local convective heat fluxes, all analyses of the aftbody TPS showed that the design would still be adequate. Aerothermal environments were computed for the vehicle from post-flight reconstruction of the atmosphere and trajectory and compared with the design environments. These comparisons showed that the predicted as-flown conditions were less severe than the design conditions.

The status of Australian law and policy concerning college faculty's intellectual property rights is examined briefly. A number of recent occurrences, some reflecting trends and some discrete events, are used to illustrate the legal and cultural circumstances that frame the discussion about intellectual property and academics. (MSE)

The simulation tools and processes used to generate aerothermodynamic environment definitions for the Mars 2020 entry capsule are presented. The Mars 2020 capsule leverages the heritage Mars Science Laboratory design, but the entry will follow a different trajectory, landing at a different location and altitude on Mars. The general strategy for creating the Mars 2020 mission-specific environments follows from the Mars Science Laboratory experience. The primary difference is that now the effects of shock-layer radiation are modeled, with particular concern for the backshell.

Dragonfly is a proposed spacecraft and mission that would send a mobile robotic rotorcraft lander to Titan, the largest moon of Saturn, in order to study prebiotic chemistry and extraterrestrial habitability at various locations. Titan is unique in having an abundant, complex, and diverse carbon-rich chemistry on the surface of a water-ice-dominated world with an interior water ocean, making it a high priority target for astrobiology and origin of life studies. The mission was initially proposed in April 2017 to NASA's New Frontiers program by the Johns Hopkins Applied Physics Laboratory. In December 2017, it was selected as one of two finalists (out of twelve proposals) to further refine the mission's concept. NASA Ames Research Center and NASA Langley Research Center are partnering as the leads for the Dragonfly's entry system to provide the completed EDL Assembly. The aerothermal analysis for Dragonfly utilizes four simulation tools from NASA Ames Research Center. Traj for calculating the trajectory, DPLR 4.04.0 for calculating the flowfield around the vehicle and convective heating, NEQAIR V15.0 for calculating the radiative heating, and FIAT for calculating the material response and thermal protection system (TPS) sizing for the heatshield. The entry conditions are relatively benign and can readily be accommodated with a tiled PICA heatshield similar to MSL and a number of flight proven materials for the backshell. This work will demonstrate that the aerothermal entry environments can be readily solved using heritage materials and techniques.

A software utility employed for post-processing computational fluid dynamics solutions about atmospheric entry vehicles is described as a supplement to the documentation within the source code. This BLAYER application and its ancillary utilities are in the public domain at https://sourceforge.net/projects/cfdutilities/. BLAYER was developed at NASA Ames Research Center in support of the DPLR (Data Parallel Line Relaxation) flow solver. Its underlying algorithm has since been incorporated by others into the LAURA and US3D flow solvers at NASA Langley Research Center and the University of Minnesota respectively. The essence of the algorithm is to locate the boundary layer edge by seeking the peak curvature in a total enthalpy profile. Turning that insight into a practical tool suited to a wide range of possible profiles has led to a hybrid two-stage method. The traditional method-location of (say) 99.5% of free-stream total enthalpy-remains an option, though it may be less robust. Details are provided and multiple examples are presented.

The specific heat, enthalpy and free energy of nitrogen and oxygen are calculated for pressures between 1 and 100 bars and temperatures between 10,000 and 100,000 degrees Kelvin. The data are presented in a form suitable for input into computational fluid dynamics computer codes. This range of temperature and pressure are typical of the conditions expected in the bow shock layer of a meteor or small asteroid entering Earth's atmosphere. The extent of double and triple ionization of nitrogen and oxygen atoms under these conditions will be estimated.

Program used to simulate atmospheric flight trajectories of entry capsules [1] Includes models of atmospheres of different planetary destinations - Earth, Mars, Venus, Jupiter, Saturn, Uranus, Titan, ... Solves 3-­‐degrees of freedom (3DoF) equations for a single body treated as a point mass. Also supports 6-DoF trajectory simula4on and Monte Carlo analyses. Uses Fehlberg-­‐Runge-­‐Kuna (4th-5th order) time integraion with automaic step size control. Includes rotating spheroidal planet with gravitational field having a J2 harmonic. Includes a variety of engineering aerodynamic and heat flux models. Capable of specifying events - heatshield jettison, parachute deployment, etc. - at predefined altitudes or Mach number. Has material thermal response models of typical aerospace materials integrated.

A new research effort at NASA Ames Research Center has been initiated in Planetary Defense, which integrates the disciplines of planetary science, atmospheric entry physics, and physics-based risk assessment. This paper describes work within the new program and is focused on meteor entry and breakup. Over the last six decades significant effort was expended in the US and in Europe to understand meteor entry including ablation, fragmentation and airburst (if any) for various types of meteors ranging from stony to iron spectral types. These efforts have produced primarily empirical mathematical models based on observations. Weaknesses of these models, apart from their empiricism, are reliance on idealized shapes (spheres, cylinders, etc.) and simplified models for thermal response of meteoritic materials to aerodynamic and radiative heating. Furthermore, the fragmentation and energy release of meteors (airburst) is poorly understood. On the other hand, flight of human-made atmospheric entry capsules is well understood. The capsules and their requisite heatshields are designed and margined to survive entry. However, the highest speed Earth entry for capsules is less than 13 km/s (Stardust). Furthermore, Earth entry capsules have never exceeded diameters of 5 m, nor have their peak aerothermal environments exceeded 0.3 atm and 1 kW/cm2. The aims of the current work are: (i) to define the aerothermal environments for objects with entry velocities from 13 to greater than 20 km/s; (ii) to explore various hypotheses of fragmentation and airburst of stony meteors in the near term; (iii) to explore the possibility of performing relevant ground-based tests to verify candidate hypotheses; and (iv) to quantify the energy released in airbursts. The results of the new simulations will be used to anchor said risk assessment analyses. With these aims in mind, state-of-the-art entry capsule design tools are being extended for meteor entries. We describe: (i) applications of current simulation tools to spherical geometries of diameters ranging from 1 to 100 m for an entry velocity of 20 km/s and stagnation pressures ranging from 1 to 100 atm; (ii) the influence of shape and departure of heating environment predictions from those for a simple spherical geometry; (iii) assessment of thermal response models for silica subject to intense radiation; and (iv) results for porosity-driven gross fragmentation of meteors, idealized as a collection of smaller objects. Lessons learned from these simulations will be used to help understand the Chelyabinsk meteor entry up to its first point of fragmentation.

The 70deg sphere-cone - the standard geometry for all US Mars entry missions - is thoroughly examined via flow field simulations at a select few peak heating points along candidate flight trajectories. Emphasis is placed on turbulent heating based on the Baldwin- Lomax turbulence model. It is shown that increased leeward turbulent heating for a 70 sphere-cone flying at angle of attack is primarily due to the discontinuity in curvature between the spherical nose cap and the conical frustum - the attachment of the sonic line at this sphere-cone junction leads to a supersonic edge Mach number over the leeward acreage. In an attempt to mitigate this problem of elevated turbulent heating, alternate geometries, without any curvature discontinuities in the acreage, are developed. Two approaches, one based on nonlinear optimization with constraints, and one based on the use of non-uniform rational B-splines, are considered. All configurations examined remain axisymmetric. The aerothermal performance of alternate geometries is shown to be superior to that of the 70 sphere-cone.

Predicted shock-layer emission signatures of the Japanese Hayabusa capsule during its reentry are presented for comparison with flight measurements made during an airborne observation mission using NASA s DC-8 Airborne Laboratory. For each altitude, lines of sight were extracted from flow field solutions computed using an inhouse high-fidelity CFD code, DPLR, at 11 points along the flight trajectory of the capsule. These lines of sight were used as inputs for the line-by-line radiation code NEQAIR, and emission spectra of the air plasma were computed in the wavelength range from 300 nm to 1600 nm, a range which covers all of the different experiments onboard the DC-8. In addition, the computed flow field solutions were post-processed with the material thermal response code FIAT, and the resulting surface temperatures of the heat shield were used to generate thermal emission spectra based on Planck radiation. Both spectra were summed and integrated over the flow field. The resulting emission at each trajectory point was propagated to the DC-8 position and transformed into incident irradiance. Comparisons with experimental data are shown.

On June 13, 2010 the Japanese Hayabusa capsule performed its reentry into the Earths atmosphere over Australia after a seven year journey to the asteroid Itokawa. The reentry was studied by numerous imaging and spectroscopic instruments onboard NASA's DC-8 Airborne Laboratory and from three sites on the ground, in order to measure surface and plasma radiation generated by the Hayabusa Sample Return Capsule (SRC). Post flight, the flow solutions were recomputed to include the whole flow field around the capsule at 11 points along the reentry trajectory using updated trajectory information. Again, material response was taken into account to obtain most reliable surface temperature information. These data will be used to compute thermal radiation of the glowing heat shield and plasma radiation by the shock/post-shock layer system to support analysis of the experimental observation data. For this purpose, lines of sight data are being extracted from the flow field volume grids and plasma radiation will be computed using NEQAIR [4] which is a line-by-line spectroscopic code with one-dimensional transport of radiation intensity. The procedures being used were already successfully applied to the analysis of the observation of the Stardust reentry [5].

Reynolds-number criteria are developed for acceptable variations in Space Shuttle Orbiter entry trajectories for use in computational aeroheating analyses. The criteria determine if an existing computational fluid dynamics solution for a particular trajectory can be extrapolated to a different trajectory. The criteria development considers twelve types of computational aeroheating data, such as boundary layer thickness. For each type of datum, the allowable uncertainty contribution due to trajectory variation has been set by the Entry Aeroheating Subsystem team. Then Reynolds-number relations between trajectory variation and output uncertainty are determined. From these relations the criteria are established for the maximum allowable trajectory variations. The most restrictive criterion allows a 25% variation in Reynolds number at constant Mach number between trajectories.

An advanced charger has been proposed for a battery that comprises several lithium-ion cells in series. The proposal is directed toward charging the cells in as nearly an optimum manner as possible despite unit-to-unit differences among the nominally identical cells. The particular aspect of the charging problem that motivated the proposal can be summarized as follows: During bulk charging (charging all the cells in series at the same current), the voltages of individual cells increase at different rates. Once one of the cells reaches full charge, bulk charging must be stopped, leaving other cells less than fully charged. To make it possible to bring all cells up to full charge once bulk charging has been completed, the proposed charger would include a number of top-off chargers one for each cell. The top-off chargers would all be powered from the same DC source, but their outputs would be DC-isolated from each other and AC-coupled to their respective cells by means of transformers, as described below. Each top-off charger would include a flyback transformer, an electronic switch, and an output diode. For suppression of undesired electromagnetic emissions, each top-off charger would also include (1) a resistor and capacitor configured to act as a snubber and (2) an inductor and capacitor configured as a filter. The magnetic characteristics of the flyback transformer and the duration of its output pulses determine the energy delivered to the lithium-ion cell. It would be necessary to equip the cell with a precise voltage monitor to determine when the cell reaches full charge. In response to a full-charge reading by this voltage monitor, the electronic switch would be held in the off state. Other cells would continue to be charged similarly by their top-off chargers until their voltage monitors read full charge.

Trajectory optimization program Traj_opt was developed at Ames Research Center to help assess the potential benefits of ultrahigh temperature ceramic materials applied to reusable space vehicles with sharp noses and wing leading edges. Traj_opt loosely couples the Ames three-degrees-of-freedom trajectory package Traj (see NASA-TM-2004-212847) with the SNOPT optimization package (Stanford University Technical Report SOL 98-1). Traj_opt version January 22, 2003 is covered by this user guide. The program has been applied extensively to entry and ascent abort trajectory calculations for sharp and blunt crew transfer vehicles. The main optimization variables are control points for the angle of attack and bank angle time histories. No propulsion options are provided, but numerous objective functions may be specified and the nonlinear constraints implemented include a distributed surface heating constraint capability. Aero-capture calculations are also treated with an option to minimize orbital eccentricity at apoapsis. Traj_opt runs efficiently on a single processor, using forward or central differences for the gradient calculations. Results may be displayed conveniently with Gnuplot scripts. Control files recommended for five standard reentry and ascent abort trajectories are included along with detailed descriptions of the inputs and outputs.

This viewgraph presentation reviews the efforts of Ames Research Center to develop Slender Hypersonic Aerothermodynamic Research Probes (SHARP) technologies as applied to the new Crew Transfer Vehicle (CTV). Amongst these technologies are ultra high temperature ceramics (UHTC). The results of Computational Fluid Dynamic simulations on prospective designs of the CTV are shown as well as wind tunnel test results.

The computational results of the optimized complete configurations, including nacelles and diverters, are presented in terms of drag count improvement compared with the TCA baseline configuration at Mach 2.4, C(sub L)=0.1. The three candidate designs are designated by the organization from which they were derived. ARC represents the Ames Research Center 1-03 design, BCAG represents the Boeing Commercial Aircraft Group's design from Seattle, and BLB represents the design from Boeing Long Beach. All CFD methods are in unanimous agreement that the Ames 1-03 configuration has the largest performance improvement, followed closely by the BCAG configuration, with a much smaller improvement attained by Boeing Long Beach. The Ames design was obtained using the single-block wing/body code SYN87-SB with its "pseudo" nacelle option-an elaborate technique for incorporating nacelle/diverter effects into the design optimization process. This technique uses AIRPLANE surface pressure coefficient data with and without the nacelles/diverters. Further details of this method are described. It is reasonable to expect that further improvements could be achieved by including the "real" nacelles directly into the optimization process by use of the newly-developed multiblock optimization code, SYN107-MB, which can handle full configurations.

This report provides user information for program PROFILE, an aerodynamics design utility for plotting, tabulating, and manipulating airfoil profiles. A dozen main functions are available. The theory and implementation details for two of the more complex options are also presented. These are the REFINE option, for smoothing curvature in selected regions while retaining or seeking some specified thickness ratio, and the OPTIMIZE option, which seeks a specified curvature distribution. Use of programs QPLOT and BPLOT is also described, since all of the plots provided by PROFILE (airfoil coordinates, curvature distributions, pressure distributions)) are achieved via the general-purpose QPLOT utility. BPLOT illustrates (again, via QPLOT) the shape functions used by two of PROFILE's options. These three utilities should be distributed as one package. They were designed and implemented for the Applied Aerodynamics Branch at NASA Ames Research Center, Moffett Field, California. They are all written in FORTRAN 77 and run on DEC and SGI systems under OpenVMS and IRIX.

An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat complete configuration designs subject to multiple design points and geometric constraints. Examples are presented for both transonic and supersonic configurations ranging from wing alone designs to complex configuration designs involving wing, fuselage, nacelles and pylons.

This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods (13, 12, 43, 38). In our earlier studies (19, 20, 22, 23, 39, 25, 40, 41, 42) it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations (39, 25). In our most recent works (40, 42) the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet.