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Interstellar Dust Models

A viable interstellar dust model - characterized by the composition, morphology, and size distribution of the dust grains and by the abundance of the different elements locked up in the dust - should fit all observational constraints arising primarily from the interactions of the dust with incident radiation or the ambient gas. As a minimum, these should include the average interstellar extinction, the infrared emission from the diffuse interstellar medium (ISM), and the observed interstellar abundances of the various refractory elements. The last constraint has been largely ignored, resulting in dust models that require more elements to be in the dust phase than available in the ISM. In this talk I will describe the most recent advances towards the construction of a comprehensive dust model made by Zubko, Dwek, and Arendt, who, for the first time, included the interstellar abundances as explicit constraints in the construction of interstellar dust models. The results showed the existence of many distinct models that satisfy the basic set of observational constraints, including bare spherical silicate and graphite particles, PAHs, as well as spherical composite particles containing silicate, organic refractories, water ice, and voids. Recently, a new interstellar dust constituent has emerged, consisting of metallic needles. These needles constitute a very small fraction of the interstellar dust abundance, and their existence is primarily manifested in the 4 to 8 micron wavelength region, where they dominate the interstellar extinction. Preliminary studies show that these models may be distinguished by their X-ray halos, which are produced primarily by small angle scattering off large dust particles along the line of sight to bright X-ray sources, and probe dust properties largely inaccessible at other wavelengths.

Dwek, Eli

Radar-anomalous, high-altitude features on Venus

Over nearly all of the surface of Venus the reflectivity and emissivity at centimeter wavelengths are about 0.15 and 0.85 respectively. These values are consistent with moderately dense soils and rock populations, but the mean reflectivity is about a factor of 2 greater than that for the Moon and other terrestrial planets. Pettingill and Ford, using Pioneer Venus reflectivities and emissivities, found a number of anomalous features on Venus that showed much higher reflectivities and much lower emissivities with both values approaching 0.5. These include Maxwell Montes, a number of high regions in Aphrodite Terra and Beta Regio, and several isolated mountain peaks. Most of the features are at altitudes above the mean radius by 2 to 3 km or more. However, such features have been found in the Magellan data at low altitudes and the anomalies do not exist on all high structures, Maat Mons being the most outstanding example. A number of papers have been written that attempt to explain the phenomena in terms of the geochemistry balance of weathering effects on likely surface minerals. The geochemists have shown that the fundamentally basaltic surface would be stable at the temperatures and pressures of the mean radius in the form of magnetite, but would evolve to pyrite and/or pyrrhotite in the presence of sulfur-bearing compounds such as SO2. Pyrite will be stable at altitudes above 4 or 5 km on Venus. Although the geochemical arguments are rather compelling, it is vitally important to rationally look at other explanations for radar and radio emission measurements such as that presented by Tryka and Muhleman. The radar reflectivity values are retrieved from the raw Magellan backscatter measurements by fitting the Hagfors' radar scattering model in which a surface roughness parameters and a normal incidence electrical reflectivity are estimated. The assumptions of the theory behind the model must be considered carefully before the results can be believed. These include that the surface roughness exists only at horizontal scales large compared to the wavelength, the vertical deviations are gaussianly distributed, there is no shadowing, and that the reflection occurs at the interface of two homogeneous dielectric half-spaces. Probably all these conditions are violated at the anomalous features under discussion. The most important of these is the homogeneity of the near surface of Venus, particularly in highlands. Under the assumptions of the theory, all of the radio energy is reflected by the impedance jump at the very boundary. However, in heterogeneous soil some fraction of the illuminating energy is propagated into the soil and then scattered back out by impedance discontinuities such as rock, voids, and cracks. In light soils, the latter effect can overwhelm the scattering effects of the true surface and greatly enhance the backscatter power, suggesting a much higher value of an effective dielectric constant that would be estimated from Hagfors' model.

Muhleman, Duane O.

Micromechanics-based Modeling of Laminated SiC/SiC Ceramic Matrix Composites

The behavior and response of ceramic matrix composites (CMCs), in particular silicon carbide fiber reinforced silicon carbide matrix (SiC/SiC), is affected by many factors such as variation of fiber volume fraction, residual stresses resulting from processing of the composites at high temperature, random microstructures, and the presence of matrix flaws (e.g., voids, pores, cracks etc.) as well as general material nonlinearity and heterogeneity that occurs randomly in a composite. Residual stresses arising from the phase change of constituents are evaluated in this paper and it is shown that they do influence composite strength and need to be properly accounted for. Additionally, the microstructures (location of fiber centers, coating thickness etc.) of advanced CMCs are usually disordered (or random) and fiber diameter and strength typically have a distribution. They rarely resemble the ordered fiber packing (square, rectangular, or hexagonal) that is generally assumed in micromechanics-based models with periodic boundary conditions for computational expediency. These issues raise the question of how should one model such systems effectively? Can an ordered hexagonal packed repeating unit cell (RUC) accurately represent the random microstructure behavior? How many fibers need to be included to enable accurate representation? Clearly, the number of fibers within an RUC must be limited to insure a balance between accuracy and efficiency. NASA’s in-house micromechanics-based code MAC/GMC provides a framework to analyze such RUCs for the overall composite behavior and the FEAMAC computer code provides linkage of MAC/GMC to the commercial FEA code, ABAQUS. The appropriate level of discretization of the RUC as well as the analysis method employed, i.e., Generalized Method of Cells (GMC) or High Fidelity Generalized Method of Cells (HFGMC), is investigated in this paper in the context of a unidirectional as well as a cross-ply laminated CMC. Results including effective composite properties, proportional limit stress (an important design parameter) and fatigue are shown utilizing both GMC as well as HFGMC. Finally, a few multiscale analyses are performed on smooth bar test coupons as well as test coupons with features such as open-hole and double notches using FEAMAC. Best practices and guidance are provided to take these phenomena into account and keep a proper balance between fidelity (accuracy) and efficiency. Following these guidelines can account for important physics of the problem and provide significant advantages when performing large multiscale composite structural analyses.

Ceramic Matrix Composites

Investigation of the plastic fracture of high-strength aluminum alloys

In a study of plastic fracture in five high-strength aluminum alloys (2014, 2024, 2124, 7075, and 7079), it has been shown that fracture toughness is affected primarily by the size and volume fraction of the larger (2 to 10 microms) second-phase particles. Certain of these particles crack at small plastic strains, nucleating voids which, with further plastic strain, coalesce to cause fracture. Not all second-phase particles crack at small plastic strains, and qualitative analysis of those which are primarily responsible for void nucleation shows that they contain iron or silicon or both. This result suggests that a reduction in the iron and silicon impurity content of the alloys should improve fracture toughness without loss of strength.

Van Stone, R. H.

Tomography Analysis of Orion Artemis 1 Heatshield Sample

The Orion spacecraft, under NASA's Artemis program, is an integral step in humanity's ambitions of deep space exploration, including our return to the Moon and subsequent mission to Mars. The performance of Orion's heatshield is central to ensuring the safety and success of such missions. This presentation offers a comprehensive overview of the process used in and findings derived from tomography scans of an Artemis 1 heatshield sample executed at the Lawrence Berkeley National Laboratory's Advanced Light Source. These tomography scans captured high-resolution X-Ray images of the heatshield's microstructure, allowing advanced imaging to be employed for 3D image segmentation and visualization of the sample. The Porous Media Analysis (PuMA) software stands central to our analysis, offering robust computational algorithms and methodologies to digitally compute properties of the heatshield material. The presentation discusses the following derived metrics: - Volume fractions, representing the spatial distribution and amounts of various components throughout the heatshield’s depth. - Porosity and crack distributions, offering insights into the void space within the material, critical for understanding the heatshield's structural integrity. - Fiber orientation, detailing the alignment and arrangement of fibers, significant for material orthotropy. - Permeability estimates, quantifying the passage of gas through the material, relevant for re-entry conditions and pyrolysis gasses. One distinctive feature of this study is the comparative evaluation against data obtained from tomography scans of the Exploration Flight Test-1 (EFT-1) heatshield. Such a comparison offers multiple insights, including evaluation of the consistency and repeatability of manufacturing processes as well as understanding of any evolutionary changes in heatshield design or material properties.

Micro-tomography

Characterizing multiscale variability of zero intermittency in spatial rainfall

In this paper the authors study how zero intermittency in spatial rainfall, as described by the fraction of area covered by rainfall, changes with spatial scale of rainfall measurement or representation. A statistical measure of intermittency that describes the size distribution of 'voids' (nonrainy areas imbedded inside rainy areas) as a function of scale is also introduced. Morphological algorithms are proposed for reconstructing rainfall intermittency at fine scales given the intermittency at coarser scales. These algorithms are envisioned to be useful in hydroclimatological studies where the rainfall spatial variability at the subgrid scale needs to be reconstructed from the results of synoptic- or mesoscale meteorological numerical models. The developed methodologies are demsonstrated and tested using data from a severe springtime midlatitude squall line and a mild midlatitude winter storm monitored by a meteorological radar in Norman, Oklahoma.

Kumar, Praveen

How Very Massive Metal-Free Stars Start Cosmological Reionization

The initial conditions and relevant physics for the formation of the earliest galaxies are well specified in the concordance cosmology. Using ab initio cosmological Eulerian adaptive mesh refinement radiation hydrodynamical calculations, we discuss how very massive stars start the process of cosmological reionization. The models include nonequilibrium primordial gas chemistry and cooling processes and accurate radiation transport in the case B approximation using adaptively ray-traced photon packages, retaining the time derivative in the transport equation. Supernova feedback is modeled by thermal explosions triggered at parsec scales. All calculations resolve the local Jeans length by at least 16 grid cells at all times and as such cover a spatial dynamic range of approx.10(exp 6). These first sources of reionization are highly intermittent and anisotropic and first photoionize the small-scale voids surrounding the halos they form in, rather than the dense filaments they are embedded in. As the merging objects form larger, dwarf-sized galaxies, the escape fraction of UV radiation decreases and the H II regions only break out on some sides of the galaxies, making them even more anisotropic. In three cases, SN blast waves induce star formation in overdense regions that were formed earlier from ionization front instabilities. These stars form tens of parsecs away from the center of their parent DM halo. Approximately five ionizing photons are needed per sustained ionization when star formation in 10(exp 6) stellar Mass halos is dominant in the calculation. As the halos become larger than approx.10(exp 7) Stellar Mass, the ionizing photon escape fraction decreases, which in turn increases the number of photons per ionization to 15-50, in calculations with stellar feedback only. Radiative feedback decreases clumping factors by 25% when compared to simulations without star formation and increases the average temperature of ionized gas to values between 3000 and 10,000 K.

Wise, John H.

Advancement of Entry System Modeling to Support Exploration of Giant Planets

This paper describes NASA’s efforts to advance entry system modeling and simulation capabilities to support future exploration of Giant planets. The Giant planets are key destinations of interest to the planetary science community for their potential to provide insight into the formation and evolution of our Solar System, as well as extrasolar planetary systems. To date, the Galileo atmospheric probe is the only purpose-built entry probe to a Giant planet. Post-flight analysis of Galileo’s performance showed that there was significant recession of the thermal protection system (TPS), well beyond what was anticipated on the flank, and this was due in part to insufficiently accurate capability for estimating the flight environment and TPS response. While Galileo ultimately survived its flight, the example serves to highlight the great challenge of designing successful missions for environments that are poorly understood or where models have not yet been validated. An important means to reduce mission risks is the incorporation of physics-based modeling with well-quantified uncertainties. The emphasis on physics-based modeling – in contrast to empirically-driven models – is motivated by the fact that it is impossible to completely replicate entry environments through ground tests and, therefore, extrapolation to the flight environment is required. Basing analysis in fundamental physics removes the bias of ground test limitations, though one must then be careful to properly characterize model inputs, simplifying assumptions, and the limits wherein the model is valid. NASA’s Entry Systems Modeling (ESM) Project is tasked with investigating such considerations for planetary science missions across the Solar System, and in recent years has begun to do so for Giant planets. The most distinctive features of the Giant planets, from an entry system perspective, are the atmospheres composed primarily of hydrogen and helium. The entry velocities of proposed missions are generally very large and can therefore be expected to result in significant convective and radiative heating generated by the vehicle’s shock layer. Yet thermochemical behavior of the hydrogen-helium system is not well understood under such conditions. The ESM project is leading efforts to develop accurate thermochemical databases based on state-of-the-art measurements in the Electric Arc Shock Tube and detailed computational chemistry. The large heat fluxes anticipated by missions has driven interest in new TPS materials, in particular woven materials, which may be enabling but have never been flown before. Consequently, multiscale models are in development to describe properties and performance of the materials from micro- to system-scale. The goal is to not only provide accurate thermal response but also to inform thermostructural reliability predictions for extreme entries. Additionally, new computational models have been developed to evaluate performance of non-destructive evaluation techniques which are vital to establishing acceptance of systems to be free of manufacturing faults like material cracking, voids, and debonding. Finally, in the area of guidance and control, aerocapture has been shown conceptually to provide a number of mission benefits, including reducing transit time and increasing payload fraction. The ESM project is building a launch-to-landing trajectory simulation capability to enable detailed studies of aerocapture maneuvers in the context of Giant planets missions. The final presentation and paper will describe each of these topics in detail, including discussion of specific gaps and the technical approach to solving them. In addition, the final paper will briefly discuss ongoing coordination between ESM project work and an ESA-funded technology development activity comprised of validation testing in the Oxford T6, IRS PWK and IST ESTHER tunnels, as well as state-to-state modeling of the shock layer to better represent non-Boltzmann energy distributions leading to non-equilibrium radiation.

Entry systems

Foliage plants for indoor removal of the primary combustion gases carbon monoxide and nitrogen dioxide

Foliage plants were evaluated for their ability to sorb carbon monoxide and nitrogen dioxide, the two primary gases produced during the combustion of fossil fuels and tobacco. The spider plant (Chlorophytum elatum var. vittatum) could sorb 2.86 micrograms CO/sq cm leaf surface in a 6 h photoperiod. The golden pothos (Scindapsus aureus) sorbed 0.98 micrograms CO/sq cm leaf surface in the same time period. In a system with the spider plant, greater than or equal to 99 percent of an initial concentration of 47 ppm NO2 could be removed in 6 h from a void volume of approximately 0.35 cu m. One spider plant potted in a 3.8 liter container can sorb 3300 micrograms CO and effect the removal of 8500 micrograms NO2/hour, recognizing the fact that a significant fraction of NO2 at high concentrations will be lost by surface sorption, dissolving in moisture, etc.

Wolverton, B. C.

Phase relationship in three-phase composites which include a void phase

The paper shows the relationship among polymer, particles, and voids in a three-phase composite and how some of the properties of a composite may be changed by changing the proportions of the phases. The three-phase composite is an aggregate of microspheres bonded together with a small amount of polymer which may not form a continuous matrix. The void space (third phase) is obtained by limiting the amount of polymer which is mixed with the microspheres. A ternary phase diagram is used to show the proportional relationship among the three phases, with each apex representing a volume fraction of unity for a constituent while the side opposite the apex represents a volume fraction of zero for that constituent. The vertical dimension represents some composite property such as density or strength. The effect of composition on composite properties is shown by plotting them on a binary phase diagram which represents a perpendicular plane coincident with the 0.60 volume fraction microsphere line.

Price, H. L.

Fabricating Composite-Material Structures Containing SMA Ribbons

An improved method of designing and fabricating laminated composite-material (matrix/fiber) structures containing embedded shape-memory-alloy (SMA) actuators has been devised. Structures made by this method have repeatable, predictable properties, and fabrication processes can readily be automated. Such structures, denoted as shape-memory-alloy hybrid composite (SMAHC) structures, have been investigated for their potential to satisfy requirements to control the shapes or thermoelastic responses of themselves or of other structures into which they might be incorporated, or to control noise and vibrations. Much of the prior work on SMAHC structures has involved the use SMA wires embedded within matrices or within sleeves through parent structures. The disadvantages of using SMA wires as the embedded actuators include (1) complexity of fabrication procedures because of the relatively large numbers of actuators usually needed; (2) sensitivity to actuator/ matrix interface flaws because voids can be of significant size, relative to wires; (3) relatively high rates of breakage of actuators during curing of matrix materials because of sensitivity to stress concentrations at mechanical restraints; and (4) difficulty of achieving desirable overall volume fractions of SMA wires when trying to optimize the integration of the wires by placing them in selected layers only.

Turner, Travis L.

Further spectroscopic studies of the Bootes region - Two more galaxies in the void

Redshifts are reported for 40 galaxies in the direction of the Bootes void identified in the Case Low-Dispersion Northern Sky Survey, List IV. Two new emission-line galaxies have been discovered in the void. The density of bright emission-line galaxies in the void is estimated to be a factor of 3 + or - 2 lower than the density of similar galaxies in the field. The galaxies are distributed uniformly with distance from the void center. A previously reported correlation between Case IV redshift estimates and measured redshifts is confirmed. Data for previously observed IRAS galaxies are combined with the present results to compared the luminosity distribution of IRAS galaxies to that for emission-line galaxies. The IRAS luminosity distribution contains a greater fraction of intrinsically bright galaxies than the emission-line galaxy distribution.

Weistrop, Donna

The formation of giant low surface brightness galaxies

It is demonstrated that the initial structure of galaxies can be strongly affected by their large-scale environments. In particular, rare (about 3 sigma) massive galaxies in voids will have normal bulges, but unevolved, extended disks; it is proposed that the low surface brightness objects Malin I and Malin II are prototypes of this class of object. The model predicts that searches for more examples of 'crouching giants' should be fruitful, but that such galaxies do not provide a substantial fraction of mass in the universe. The identification of dwarf galaxies is relatively unaffected by their environment.

Hoffman, Yehuda

Cosmic string wakes and large-scale structure

The formation of structure from infinite cosmic string wakes is modeled for a universe dominated by cold dark matter (CDM). Cross-sectional slices through the wake distribution tend to outline empty regions with diameters which are not inconsistent with the range of sizes of the voids in the CfA slice of the universe. The topology of the wake distribution is found to be spongy rather than cell-like. Correlations between CDM wakes do not extend much beyond a horizon length, so it is unlikely that CDM wakes are responsible for the correlations between clusters of galaxies. An estimate of the fraction of matter to accrete onto CDM wakes indicates that wakes could be more important in galaxy formation than previously anticipated.

Charlton, Jane C.

Geology of Biblis Patera, Ulysses Patera, and Jovis Tholus, Mars

There are a variety of constructional volcanic features in Tharsis. These features range from Olympus Mons and the Tharsis Montes shields, to the small low shields and fissure eruptions that characterize much of the volcanic plains, to the smaller volcanic constructs in the northeast and western parts of Tharsis. I describe the geology of the western group, which includes Biblis Patera, Ulysses Patera, and Jovis Tholus. Each of these volcanoes has had a unique, and complex geologic history. Biblis Patera is located at 2.3 deg. N, 123.8 deg. The volcano is elongate in a northwesterly direction and has a large, faulted caldera complex. The flanks of the volcano and adjacent plains are characterized by lava flows, northwest-trending graben and troughs, and caldera-concentric graben and troughs. Biblis Patera is approximately 66 x 127 km with an oval 51 x 56 km caldera; the summit elevation is approximately 2 km above the surrounding plains. The constrcut has an estimated volume of 8-22 x 10(exp 3) cu km. Ulysses Patera is located at 2.7 deg. N, 121.3 deg. W and stands approx. 2-3 km above the surrounding plain; flank slopes are approximately 7 deg. to 12 deg. The caldera floor is quite deep, lying 1.8 to 2.2 km below the caldera rim. The caldera has a void volume of approximately 5000 cu km, the total solid mass volume of the volcano is 7-16 x 10(exp 3) cu km. Jovis Tholus is centered at 18.3 deg N; 117.5 deg W; it is a low relief, volcano with gentle flank slopes of between 3 and 8 deg. The construct is dominated by a series of inset calderas which make up the largest fraction of the area. The caldera complex is offset to the southwest side. Total shield dimensions are approximately 77 km (e-wt) by 62 km (n-s); the caldera complex is approximately 44 x 34 km. The shield is embayed on all sides by younger Amazonian age volcanics. Total relief, relative to the surrounding plains, is probably approximately 2 km. The total volume of Jovis Tholus is estimated to be approximately 2-5 x 10(exp 3) cu km.

Plescia, J. B.

Intergalactic Hydrogen Clouds at Low Redshift: Connections to Voids and Dwarf Galaxies

We provide new post-COSTAR data on one sightline (Mrk 421) and updated data from another (I Zw 1) from our Hubble Space Telescope (HST) survey of intergalactic Ly(alpha) clouds located along sightlines to four bright quasars passing through well-mapped galaxy voids (16000 km/s pathlength) and superclusters (18000 km/s). We report two more definite detections of low-redshift Ly(alpha) clouds in voids: one at 3047 km/s (heliocentric) toward Mrk 421 and a second just beyond the Local Supercluster at 2861 km/s toward I Zw 1, confirming our earlier discovery of Ly(alpha) absorption clouds in voids (Stocke et al., ApJ, 451, 24). We have now identified ten definite and one probable low-redshift neutral hydrogen absorption clouds toward four targets, a frequency of approximately one absorber every 3400 km/s above 10(exp 12.7/sq cm column density. Of these ten absorption systems, three lie within voids; the probable absorber also lies in a void. Thus, the tendency of Ly(alpha) absorbers to 'avoid the voids' is not as clear as we found previously. If the Ly(alpha) clouds are approximated as homogeneous spheres of 100 kpc radius, their masses are approximately 10(exp 9)solar mass (about 0.01 times that of bright L* galaxies) and they are 40 times more numerous, comparable to the density of dwarf galaxies and of low-mass halos in numerical CDM simulations. The Ly(alpha) clouds contribute a fraction Omega(sub cl)approximately equals 0.003/h(sub 75) to the closure density of the universe, comparable to that of luminous matter. These clouds probably require a substantial amount of nonbaryonic dark matter for gravitational binding. They may represent extended haloes of low-mass protogalaxies which have not experienced significant star formation or low-mass dwarf galaxies whose star formation ceased long ago, but blew out significant gaseous material.

Shull, J. Michael

Understanding the effect of friction stir processing on electrical steel: Microstructural changes and mechanical transformations

Raising Si beyond 3.5 wt% reduces core loss but embrittles electrical steels, constraining processing and application. Here we assess friction stir processing (FSP) as a solid‑state route to enable Fe–4.0 wt% Si with improved mechanical performance. Temperature‑controlled FSP with a PcBN tool produced a defect‑free processed zone. SEM/EBSD revealed dynamic recrystallization and grain refinement from an average 110 μm in the base material to ∼20 μm in the processed region, with ∼ 80% of grains < 40 μm and a reduction in high‑angle boundary fraction to ∼65% (vs >85% in the base). Comparative mechanical property analysis shows a moderate increase in yield strength in FSP samples relative to the base material, with a significant improvement in ductility (∼35–50%). Post‑fracture EBSD identified 60° twin boundaries in the base while sub-grain formation with elevated KAM in the FSP sample. Fractography revealed a shift from quasi‑cleavage in the Base-faceted planes with river patterns, steps, and occasional secondary cracks—to ductile micro void coalescence after FSP. Following FSP, the material retains soft‑magnetic behavior, with modest shifts in saturation magnetization consistent with grain refinement and stored strain, accompanied by a clear gain in formability. These results indicate that FSP provides a viable route to deploy higher‑Si electrical steels with concurrent gains in strength and ductility.

Electrical steel

Development of GENOA Progressive Failure Parallel Processing Software Systems

A capability consisting of software development and experimental techniques has been developed and is described. The capability is integrated into GENOA-PFA to model polymer matrix composite (PMC) structures. The capability considers the physics and mechanics of composite materials and structure by integration of a hierarchical multilevel macro-scale (lamina, laminate, and structure) and micro scale (fiber, matrix, and interface) simulation analyses. The modeling involves (1) ply layering methodology utilizing FEM elements with through-the-thickness representation, (2) simulation of effects of material defects and conditions (e.g., voids, fiber waviness, and residual stress) on global static and cyclic fatigue strengths, (3) including material nonlinearities (by updating properties periodically) and geometrical nonlinearities (by Lagrangian updating), (4) simulating crack initiation. and growth to failure under static, cyclic, creep, and impact loads. (5) progressive fracture analysis to determine durability and damage tolerance. (6) identifying the percent contribution of various possible composite failure modes involved in critical damage events. and (7) determining sensitivities of failure modes to design parameters (e.g., fiber volume fraction, ply thickness, fiber orientation. and adhesive-bond thickness). GENOA-PFA progressive failure analysis is now ready for use to investigate the effects on structural responses to PMC material degradation from damage induced by static, cyclic (fatigue). creep, and impact loading in 2D/3D PMC structures subjected to hygrothermal environments. Its use will significantly facilitate targeting design parameter changes that will be most effective in reducing the probability of a given failure mode occurring.

Abdi, Frank