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NASA NTRS2022

Structural and chemical complexity of minerals: An update

The complexities of chemical composition and crystal structure are fundamental characteristics of minerals that have high relevance to the understanding of their stability, occurrence and evolution. This review summarises recent developments in the field of mineral complexity and outlines possible directions for its future elaboration. The database of structural and chemical complexity parameters of minerals is updated by H-correction of structures with unknown H positions and the inclusion of new data. The revised average complexity values (arithmetic means) for all minerals are 3.54(2) bits/atom and 345(10) bits/cell (based upon 4443 structure reports). The distributions of atomic information amounts, chemIG and strIG, versus the number of mineral species fit the normal modes, whereas the distributions of total complexities, chemIG,total and strIG,total, along with numbers of atoms per formula and per unit cell are log normal. The three most complex mineral species known today are ewingite, morrisonite and ilmajokite, all either discovered or structurally characterised within the last five years. The most important complexity-generating mechanisms in minerals are: (1) the presence of isolated large clusters; (2) the presence of large clusters linked together to form three-dimensional frameworks; (3) formation of complex three-dimensional modular frameworks; (4) formation of complex modular layers; (5) high hydration state in salts with complex heteropolyhedral units; and (6) formation of ordered superstructures of relatively simple structure types. The relations between symmetry and complexity are considered. The analysis of temporal dynamics of mineralogical discoveries since 1875 with the step of 25 years show the increasing chemical and structural complexities of human knowledge of the mineral kingdom in the history of mineralogy. In the Earth’s history, both diversity and complexity of minerals experience dramatic increases associated with the formation of Earth’s continental crust, initiation of plate tectonics and the Great Oxidation event.

complexity↗

NASA NTRS2019

Appreciative Methods Applied to the Assessment of Complex Systems

Complex systems have characteristics that challenge traditional systems engineering processes and methods. These characteristics have been defined in various ways. INCOSE has previously identified characteristics of complex systems and potential methods to deal with complexity in system development. The purpose of this paper is to provide definitions and describe distinguishing characteristics of complexity using example systems to illustrate approaches to assessing the extent of complexity. The paper applies Appreciative Inquiry to identify and assess complex system characteristics. The characteristics are used to examine several different examples of systems to illuminate areas of complexity. These examples range from seemingly simple systems to complicated systems to complex systems. Different tiers of complexity are identified as a result of the assessment. The paper also identified and introduces topics on managing complexity and the integrating system perspective that represent new directions for the engineering of complex systems. The Appreciative Inquiry approach provides a method for systems engineering practitioners to more readily identify complexity when they encounter it, and to deal more effectively with this complexity once it has been identified.

Watson, Michael↗

NASA NTRS1999

Environmental Conditions and Threatened and Endangered Species Populations near the Titain, Atlas, and Delta Launch Complexes, Cape Canaveral Air Station

Launches of Delta, Atlas, and Titan rockets from Cape Canaveral Air Station (CCAS) have potential environmental effects. These could occur from direct impacts of launches or indirectly from habitat alterations. This report summarizes a three-year study (1995-1998) characterizing the environment, with particular attention to threatened and endangered species, near Delta, Atlas, and Titan launch facilities. Cape Canaveral has been modified by Air Force development and by 50 years of fire suppression. The dominant vegetation type around the Delta and Atlas launch complexes is coastal oak hammock forest. Oak scrub is the predominant upland vegetation type near the Titan launch complexes. Compositionally, these are coastal scrub communities that has been unburned for greater than 40 years and have developed into closed canopy, low-stature forests. Herbaceous vegetation around active and inactive facilities, coastal strand and dune vegetation near the Atlantic Ocean, and exotic vegetation in disturbed areas are common. Marsh and estuarine vegetation is most common west of the Titan complexes. Launch effects to vegetation include scorch, acid, and particulate deposition. Discernable, cumulative effects are limited to small areas near the launch complexes. Water quality samples were collected at the Titan, Atlas, and Delta launch complexes in September 1995 (wet season) and January 1996 (dry season). Samples were analyzed for heavy metals, chloride, total organic carbon, calcium, iron, magnesium, sodium, total alkalinity, pH, and conductivity. Differences between fresh, brackish, and saline surface waters were evident. The natural buffering capacity of the environment surrounding the CCAS launch complexes is adequate for neutralizing acid deposition in rainfall and launch deposition. Populations of the Florida Scrub-Jay (Aphelocoma coerulescens), a Federally- listed, threatened species, reside near the launch complexes. Thirty-seven to forty-one scrub-jay territories were located at Titan, Atlas, and Delta launch complexes between 1995 and 1997. No direct impacts to scrub-jays were observed as a result of normal launches. The explosion of the Delta rocket in January 1997 caused direct impacts to the habitat of several scrub-jays families, from fire and debris; however, no scrub-jay mortality was observed. Mortality exceeded reproductive output at all areas over the course of the study. Populations of the southeastern beach mouse (Peromyscus polionotus niveiventris) populations, a Federally listed, threatened species, reside near all the launch complexes. Hurricane Erin and several other tropical storms impacted several areas at the inception of the study in 1995 causing coastal habitat alterations as a result of salt-water intrusion. Both the habitat and the beach mice populations recovered during the course of the study. No direct impacts to southeastern beach mice were observed as a result of normal launch operations. Direct impacts were observed to the habitat as a result of the explosion of the Delta rocket in January 1997. This alteration of the habitant resulted in a shift in use with the mice moving on to the newly burned part of the site. Waterbirds use wetlands and aquatic systems near the launch complexes. Species include the Federally-listed, endangered Wood Stork (Mycteria americana) and several state-listed species of special concern including the Snowy Egret (Egretta thula thula), Reddish Egret (Egretta rufescens rufescens), White Ibis (Eudocimus albus), Roseate Spoonbill (Ajaia ajaja), Tricolored Heron (Egretta tricolor ruficolis), and Little Blue Heron (Egretta caerulea). No impacts to these populations resulting from any launch operations were observed. Gopher tortoises (Gopherus polyphemus) also occur around the launch complexes. Most of those observed appeared to be in good condition; however, upper respiratory tract disease is known to occur in the population. Cape Canaveral Air Station, including areas near active launch complexes, remains important habitat for a variety of native plants and animals including threatened and endangered species. Direct negative effects of current launch systems appear limited. Additional monitoring of these populations and habitats is required to determine if subtle, long-term changes are occurring, to determine if new launch systems and facilities cause other effects, and to determine the effects of habitat restoration and management.

Oddy, Donna M.↗

NASA NTRS1999

Environmental Conditions and Threatened and Endangered Species Populations near the Titan, Atlas, and Delta Launch Complexes, Cape Canaveral Air Station

Launches of Delta, Atlas, and Titan rockets from Cape Canaveral Air Station (CCAS) have potential environmental effects. These could occur from direct impacts of launches or indirectly from habitat alterations. This report summarizes a three-year study (1 995-1 998) characterizing the environment, with particular attention to threatened and endangered species, near Delta, Atlas, and Titan launch facilities. Cape Canaveral has been modified by Air Force development and by 50 years of fire suppression. The dominant vegetation type around the Delta and Atlas launch complexes is coastal oak hammock forest. Oak scrub is the predominant upland vegetation type near the Titan launch complexes. Compositionally, these are coastal scrub communities that has been unburned for > 40 years and have developed into closed canopy, low-stature forests. Herbaceous vegetation around active and inactive facilities, coastal strand and dune vegetation near the Atlantic Ocean, and exotic vegetation in disturbed areas are common. Marsh and estuarine vegetation is most common west of the Titan complexes. Launch effects to vegetation include scorch, acid, and particulate deposition. Discernable, cumulative effects are limited to small areas near the launch complexes. Water quality samples were collected at the Titan, Atlas, and Delta launch complexes in September 1995 (wet season) and January 1996 (dry season). Samples were analyzed for heavy metals, chloride, total organic carbon, calcium, iron, magnesium, sodium, total alkalinity, pH, and conductivity. Differences between fresh, brackish, and saline surface waters were evident. The natural buffering capacity of the environment surrounding the CCAS launch complexes is adequate for neutralizing acid deposition in rainfall and launch deposition. Populations of the Florida Scrub-Jay (Aphelocoma coerulescens), a Federally-listed, threatened species, reside near the launch complexes. Thirty-seven to forty-one scrub-jay territories were located at Titan, Atlas, and Delta launch complexes between 1995 and 1997. No direct impacts to scrub-jays were observed as a result of normal launches. The explosion of the Delta rocket in January 1997 caused direct impacts to the habitat of several scrub-jays families, from fire and debris; however, no scrub-jay mortality was observed. Mortality exceeded reproductive output at all areas over the course of the study. Populations of the southeastern beach mouse (Peromyscus polionotus niveiventris) populations, a Federally listed, threatened species, reside near all the launch complexes. Hurricane Erin and several other tropical storms impacted several areas at the inception of the study in 1995 causing coastal habitat alterations as a result of salt-water intrusion. Both the habitat and the beach mice populations recovered during the course of the study. No direct impacts to southeastern beach mice were observed as a result of normal launch operations. Direct impacts were observed to the habitat as a result of the explosion of the Delta rocket in January 1997. This alteration of the habitat resulted in a shift in use with the mice moving on to the newly burned part of the site. Waterbirds use wetlands and aquatic systems near the launch complexes. Species include the Federally-listed, endangered Wood Stork (Mycferia americana) and several state-listed species of special concern including the Snowy Egret (Egretfa thula fhula), Reddish Egret (Egreffa rufescens rufescens), White Ibis (Eudocimus albus), Roseate Spoonbill (Ajaia ajaja), Tricolored Heron (Egreffa tricolor ruficolis), and Little Blue Heron (Egreffa caerulea). No impacts to these populations resulting from any launch operations were observed. Gopher tortoises (Gopherus polyphemus) also occur around the launch complexes. Most of those observed appeared to be in good condition; however, upper respiratory tract disease is known to occur in the population. Cape Canaveral Air Station, including areas near active launch colexes, remains important habitat for a variety of native plants and animals including threatened and endangered species. Direct negative effects of current launch systems appear limited. Additional monitoring of these populations and habitats is required to determine if subtle, long-term changes are occurring, to determine if new launch systems and facilities cause other effects, and to determine the effects of habitat restoration and management.

Oddy, Donna M.↗

NASA NTRSDate not supplied

MAGE: Alleviating Uncertainty in Real-Time Decision-Making as a Function of Problem Complexity

In this paper, we discuss a critical aspect of uncertainty in the operation of complex systems, such as the future air traffic: the ability of agents in the system to arrive at satisfactory decisions and the attendant actions as a function of problem complexity. Intuitively, when the problem complexity is manageable, given an appropriate decision problem formulation and solution tools, an agent (computational or human) has no trouble arriving at a solution that yields good outcomes for the agent and the system. Growing problem complexity results in progressively larger computational problems that may yield suboptimal solutions or even be intractable within required time limits or at all. We propose a measurable representation of complexity in terms of problem tractability and quality of solutions. We also propose a computational scheme, MAGE (Monitor, Anticipate, Guide, Evolve), for detecting approaching transitions from efficient decision-making states to inefficient to unsafe ones, so that operations based on decision-making can be reconfigured to forestall unfavorable transitions, returning to efficient modes when complexity diminishes. Maintaining tractable complexity reduces the uncertainty in the outcomes of decision-making. We describe the general scheme, an outline of MAGE applied to managing airspace complexity, and initial examples of investigating the tractability of problem-solving schemes.

complexity management↗

NASA NTRS2019

Scenario Complexity for Unmanned Aircraft System Traffic

This work introduces an approach to estimate the complexity of a low-altitude air traffic scenario involving multiple UASs using mathematical programming. Given a set of multi-point UAS flight trajectories, vehicle dynamics, and a conflict resolution algorithm, an abstract model is developed such that it can be solved quickly using a mathematical programming optimization software without running high-fidelity simulations that can be computationally expensive and may not suit real-time apA quick and accurate assessment of complexity for a given traffic scenario can help plan and schedule flights to alleviate traffic bottleneck and mitigate operation risks, especially for unmanned aerial system traffic management where high traffic density or complexity is expected. This work introduces a traffic scenario complexity metric that was constructed based on the number of potential conflicts weighted by the conflict resolution cost associated. The cost associated with a conflict is calculated based on the corresponding conflict resolution maneuvers. To obtain the conflict resolution maneuvers, a MILP-based optimization was formulated with the vehicle model and conflict management parameters incorporated. To evaluate the complexity metrics, an approach of using measurements from high-fidelity simulations was proposed. The scenario complexity measurements for 920 random-generated scenarios were obtained through high-fidelity simulations and treated as the ground truth. Two statistics methods: Pearson and Alternative Conditional Expectations were applied for analysis. The results showed that the number of flights has low correlation with the scenario complexity according to the correlation coefficients calculated by both methods. The Alternative Conditional Expectations method shows that the proposed scenario complexity metric has better correlation with the ground truth than the number of potential conflicts.plications. In the abstract model, each vehicle is represented by a time-varied vector associated with position, speed, and heading information. The total extra distance that aircraft need to divert from their original routes to avoid collisions is computed and used to setup a quadratic programming formula. The metrics including the number of conflicts and extra distances travelled by all vehicles are then utilized to estimate the complexity of a given UAS flight scenario. Results and verification against high-fidelity simulations will be provided in the final draft.

traffic complexity↗

NASA NTRS2011

Initiating Molecular Growth in the Interstellar Medium via Dimeric Complexes of Observed Ions and Molecules

A feasible initiation step for particle growth in the interstellar medium (ISM) is simulated by means of ab quantum chemistry methods. The systems studied are dimer ions formed by pairing nitrogen containing small molecules known to exist in the ISM with ions of unsaturated hydrocarbons or vice versa. Complexation energies, structures of ensuing complexes and electronic excitation spectra of the encounter complexes are estimated using various quantum chemistry methods. Moller-Plesset perturbation theory (MP2, Z-averaged perturbation theory (ZAP2), coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)), and density functional theory (DFT) methods (B3LYP) were employed along with the correlation consistent cc-pVTZ and aug-cc-pVTZ basis sets. Two types of complexes are predicted. One type of complex has electrostatic binding with moderate (7-20 kcal per mol) binding energies, that are nonetheless significantly stronger than typical van der Waals interactions between molecules of this size. The other type of complex develops strong covalent bonds between the fragments. Cyclic isomers of the nitrogen containing complexes are produced very easily by ion-molecule reactions. Some of these complexes show intense ultraviolet visible spectra for electronic transitions with large oscillator strengths at the B3LYP, omegaB97, and equations of motion coupled cluster (EOM-CCSD) levels. The open shell nitrogen containing carbonaceous complexes especially exhibit a large oscillator strength electronic transition in the visible region of the electromagnetic spectrum.

Bera, Partha P.↗

NASA NTRS1986

Two contrasting metamorphosed ultramafic-mafic complexes from greenstone belts, the northern Kaapvaal Craton and their significance in Archaen tectonics

The character of Archaean ultramafic-mafic complexes can, given their prominance in greenstone belts, provide critical clues to help deduce the tectonic setting of these belts. Here are described two contrasting, metamorphosed, ultramafic-mafic complexes, the first a partially serpentinized dunitic body with associated chromite from Lemoenfontein, one of several peridotitic bodies occurring as discrete lenses and pods in granulite facies gneisses of the northern Kaapvaal craton. The second, the Rooiwater complex is a major layered igneous body, now metamorphosed in the amphibolite facies, but without pervasive deformation, which crops out in the northern Murchison greenstone belt. The Lemoenfontein chromites and associated ultramafic rocks are lithologically and chemically similar to their Phanerozoic equivalents of ophiolitic origin, interpreted as obducted oceanic crust. The Lemoenfontein complex is a remnant of Archaean oceanic material. In contrast, the Rooiwater complex is, despite the lack of exposed intrusive contacts, similar to layered igneous complexes such as Ushushwana or Bushveld. These complexes are intrusive in continental environments. It is concluded that contrasting ultramafic-mafic complexes represent a heterogeneity in greenstone belts with either oceanic or continental environments involved.

Smit, C. A.↗

NASA NTRS1986

The largest molecular cloud complexes in the first galactic quadrant

The Columbia CO survey of the first Galactic quadrant was used to determine the locations and physical properties of the largest molecular complexes in the inner Galaxy. Within the range of the survey (l = 12-60 deg), 26 complexes were detected with masses greater than 5 x 10 to the 5th solar masses, and roughly several hundred such complexes are deduced to exist throughout the Galaxy within the solar circle. These complexes are the parent objects of much of the Population I in the Galaxy. Distances to most of the complexes were determined kinematically, the distance ambiguity being resolved with the aid of associated H II regions, OB associations, masers, and other early Population I objects. The largest complexes are good tracers of spiral structure, the Sagittarius arm in particular being delineated with unprecedented clarity. A total of 17 large complexes are distributed rather uniformly along a 15 kpc stretch of the arm with a spacing comparable to that of the strings of regularly spaced H Ii regions observed in external galaxies. Power-law relations exist between the line widths and sizes of the complexes and between their densities and sizes. The forms of these relations are in good agreement with those found previously and are extended by roughly an order of magnitude in cloud mass.

Dame, T. M.↗

NASA NTRS1996

Recrystallized Impact Glasses of the Onaping Formation and the Sudbury Igneous Complex, Sudbury Structure, Ontario, Canada

The origin of the Sudbury Structure and of the associated heterolithic breccias of the Onaping Formation and the Sudbury Igneous Complex have been controversial. While an impact origin of the structure has gained wide acceptance over the last 15 years, the origin of the recrystallized Onaping Formation glasses and of the igneous complex is still being debated. Recently the interpretation of the breccias of the Onaping Formation as suevitic fall-back impact breccias has been challenged. The igneous complex is interpreted either as a differentiated impact melt sheet or as a combination of an upper impact melt represented by the granophyre, and a lower, impact-triggered magmatic body consisting of the norite-sublayer formations. The Onaping Formation contains glasses as fluidal and nonfluidal fragments of various shapes and sizes. They are recrystallized, and our research indicates that they are petrographically heterogeneous and span a wide range of chemical compositions. These characteristics are not known from glasses of volcanic deposits. This suggests an origin by shock vitrification, an interpretation consistent with their association with numerous and varied country rock clasts that exhibit microscopic shock metamorphic features. The recrystallized glass fragments represent individual solid-state and liquid-state vitrified rocks or relatively small melt pods. The basal member lies beneath the Gray and Black members of the Onaping Formation and, where not metamorphic, has an igneous matrix. Igneous-textured melt bodies occur in the upper two members and above the Basal Member. A comparison of the chemical compositions of recrystallized glasses and of the matrices of the Basal Member and the melt bodies with the components and the bulk composition of the igneous complex is inconclusive as to the origin of the igneous complex. Basal Member matrix and Melt Bodies, on average, are chemically similar to the granophyre of the Sudbury Igneous Complex, suggesting that they are genetically related. Our chemical results allow interpretation of the entire igneous complex as a differentiated impact melt. However, they are also consistent with the granophyre alone being the impact melt and the nofite and quartz gabbro beneath it representing an impact-triggered magmatic body. This interpretation is preferred, as it is consistent with a number of field observations. A re-evaluation and extension of structural field studies and of geochemical data, as well as a systematic study of the contact relationships of the various igneous phases of the igneous complex, are needed to establish a Sudbury impact model consistent with all data and observations

Dressler, B. O.↗

NASA NTRS2010

Complexity Analysis of Traffic in Corridors-in-the-Sky

The corridors-in-the-sky concept imitates the highway system in ground transportation. The benefit expected from a corridor relies on its capability of handling high density traffic with negligible controller workload, the acceptance of extra fuel or distance, and the complexity reduction in underlying sectors. This work evaluates a selected corridor from these perspectives through simulations. To examine traffic inside the corridor, a corridor traffic simulation tool that can resolve conflicts is developed using C language. Prescribed conflict resolution maneuvers mimic corridor users behaviors and conflict resolution counts measure complexity. Different lane options and operational policies are proposed to examine their impacts on complexity. Fuel consumption is calculated and compared for corridor traffic. On the other hand, to investigate the complexity of non-corridor traffic in underlying sectors, the existing Airspace Concept Evaluation System tool is utilized along with the Automated Airspace Concept tool. The number of conflict resolutions is examined and treated as the complexity measurement. The results show heavy traffic can be managed with low complexity for a historical traffic schedule simulated with appropriate operational policies and lane options. For instance, with 608 flights and peak aircraft count of 100, only 84 actions need to be taken in a 24-hour period to resolve the conflicts for an 8-lane corridor. Compared with the fuel consumptions with great circle trajectories, the simulation of corridor traffic shows that the total extra fuel for corridor flights is 26,373 gallons, or 2.76%, which is 0.38% less than flying filed flight plans. Without taking climb and descent portions of corridor traffic, the complexity of underlying sectors is reduced by 17.71%. However the climb and descent portions will eliminate the reduction and the overall complexity of sectors is actually increased by 9.14%.

Xue, Min↗

NASA NTRS2014

Humic Acid Complexation of Th, Hf and Zr in Ligand Competition Experiments: Metal Loading and Ph Effects

The mobility of metals in soils and subsurface aquifers is strongly affected by sorption and complexation with dissolved organic matter, oxyhydroxides, clay minerals, and inorganic ligands. Humic substances (HS) are organic macromolecules with functional groups that have a strong affinity for binding metals, such as actinides. Thorium, often studied as an analog for tetravalent actinides, has also been shown to strongly associate with dissolved and colloidal HS in natural waters. The effects of HS on the mobilization dynamics of actinides are of particular interest in risk assessment of nuclear waste repositories. Here, we present conditional equilibrium binding constants (Kc, MHA) of thorium, hafnium, and zirconium-humic acid complexes from ligand competition experiments using capillary electrophoresis coupled with ICP-MS (CE- ICP-MS). Equilibrium dialysis ligand exchange (EDLE) experiments using size exclusion via a 1000 Damembrane were also performed to validate the CE-ICP-MS analysis. Experiments were performed at pH 3.5-7 with solutions containing one tetravalent metal (Th, Hf, or Zr), Elliot soil humic acid (EHA) or Pahokee peat humic acid (PHA), and EDTA. CE-ICP-MS and EDLE experiments yielded nearly identical binding constants for the metal- humic acid complexes, indicating that both methods are appropriate for examining metal speciation at conditions lower than neutral pH. We find that tetravalent metals form strong complexes with humic acids, with Kc, MHA several orders of magnitude above REE-humic complexes. Experiments were conducted at a range of dissolved HA concentrations to examine the effect of [HA]/[Th] molar ratio on Kc, MHA. At low metal loading conditions (i.e. elevated [HA]/[Th] ratios) the ThHA binding constant reached values that were not affected by the relative abundance of humic acid and thorium. The importance of [HA]/[Th] molar ratios on constraining the equilibrium of MHA complexation is apparent when our estimated Kc, MHA values attained at very low metal loading conditions are compared to existing literature data. Overall, experimental data suggest that the tetravalent transition metal/-actinide-humic acid complexation is important over a wide range of pH values, including mildly acidic conditions, and thus, these complexes should be included in speciation models.

humic acid↗

NASA NTRSDate not supplied

Applying the System Complexity Metric (SCM)

A fundamental cause of difficulty in larger engineering projects is their inherent complexity. An impression of complexity occurs if a system is simply difficult to understand, so that there is no obvious mental model that correctly predicts its behavior. Higher complexity is usually associated with higher cost and higher failure rate. Complexity is indicated by a system having more and diverse components, multiple interactions and feedback loops, transients and dynamic behavior, and often the emergence of unanticipated failure modes. Identifying and removing these signs of complexity should reduce complexity and improve performance. Here we limit complexity measurement to the number of components and their interactions. A System Complexity Metric (SCM) is defined as equal to the sum of the number of parts in a system, N, plus the sum of the one-way interconnections between them, I. SCM = N + I. The SCM is easily determined by direct inspection of system block diagrams. Previous work found that life support system cost was directly proportional to SCM and that failure rate increased faster than SCM squared. SCM can be used to compare systems or to guide their redesign to reduce cost and failure rate. Carbon dioxide removal systems will be analyzed using SCM, cost, and failure rate.

Harry W Jones↗

NASA NTRS2021

Vegetation structural complexity and biodiversity in the Great Smoky Mountains

Vegetation structural complexity and biodiversity tend to be positively correlated, but understanding of this relationship is limited in part by structural metrics tending to quantify only horizontal or vertical variation, and that do not reflect internal structure. We developed new metrics for quantifying internal vegetation structural complexity using terrestrial LiDAR scanning and applied them to 12 NEON forest plots across an elevational gradient in Great Smoky Mountains National Park, USA. We asked (1) How do our newly developed structure metrics compare to traditional metrics? (2) How does forest structure vary with elevation in a high-biodiversity, high topographic complexity region? (3) How do forest structural metrics vary in the strength of their relationships with vascular plant biodiversity? Our new measures of canopy density (Depth) and structural complexity (σDepth), and their canopy height-normalized counterparts, were sensitive to structural variations and effectively summarized horizontal and vertical dimensions of structural complexity. Forest structure varied widely across plots spanning the elevational range of GRSM, with taller, more structurally complex forests at lower elevation. Vascular plant biodiversity was negatively correlated with elevation and more strongly positively correlated with vegetation structure variables. The strong correlations we observed between canopy structural complexity and biodiversity suggest that structural complexity metrics could be used to assay plant biodiversity over large areas in concert with airborne and spaceborne platforms.

Jonathan A. Walter↗

NASA NTRSDate not supplied

An Impedance-Based Complexity Metric for Unmanned Aircraft System Traffic Scenario Classification

This paper introduces an impedance-based metric to capture the complexity of a given unmanned aircraft system traffic scenario. The metric accounts for both the number of aircraft and the traffic flow pattern. The work presented here extends an earlier approach that introduced another scenario complexity metric based on the number of potential conflicts weighted by the conflict resolution cost associated. Complexity measurements for randomly-generated scenarios were produced through high-fidelity fast-time simulations and treated as baseline. Then the impedance based metric was evaluated, for the same scenarios, without the need for an actual flight simulation and a conflict resolution method. The results show that the impedance-based metric has a strong correlation to the baseline data and performs marginally better than the weighted conflict-based complexity metric introduced in the earlier work. The metric computation generates impedance maps which are useful for identifying high complexity regions in a scenario, where flight plan changes might be necessitated. This metric can therefore be used, in conjunction with other complexity metrics, to inform adequate traffic management strategies and classify a traffic scenario as acceptable, unacceptable or acceptable with changes made to flight plans that pass through the high complexity regions. The metric can also be used as a guidance metric for strategic conflict management methods.

Complexity↗

NASA NTRS1986

A system of three-dimensional complex variables

Some results of a new theory of multidimensional complex variables are reported, including analytic functions of a three-dimensional (3-D) complex variable. Three-dimensional complex numbers are defined, including vector properties and rules of multiplication. The necessary conditions for a function of a 3-D variable to be analytic are given and shown to be analogous to the 2-D Cauchy-Riemann equations. A simple example also demonstrates the analogy between the newly defined 3-D complex velocity and 3-D complex potential and the corresponding ordinary complex velocity and complex potential in two dimensions.

Martin, E. Dale↗

NASA NTRS1989

Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices

We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Freund, Roland↗

NASA NTRS1998

Lanthanide Complexes as a Test for Evidence of Life

The objective of this research is to advance the understanding of the interaction of lanthanide metals with biological organic molecules and to develop a technique to detect these compounds in the solid state and in situ in Mars and other planetary bodies. The detection of these complexes should provide evidence of life past or present. In addition, detection of the metals alone will provide important information about the geological history of a planetary body. Lanthanides were chosen as our focus of interest because they form very stable complexes with organic molecules in solution and they produce intense luminescence in the ultraviolet and visible spectra. The rare earth complexes available are mostly synthetic for diverse applications in medicine. There is not much work done on the complexes that form in nature. Lanthanides have many applications and they are mined aR over the world, however, since the interest has been only in the elements, the analytical techniques employed destroy any organic ligands that may be present. In order to determine if and which lanthanide complexes form in nature and their concentration, soil samples have been collected from areas rich in soluble lanthanide compounds like phosphates and also rich in vegetation. The soil samples will be analyzed and the lanthanide complexes if present will be isolated and characterized. A spectrometer to detect the lanthanide complexes in situ and in the solid state will be designed. In this workshop, the research approach and its implications will be discussed.

Benavides, Jeannette↗