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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Quantum complexity of time evolution with chaotic Hamiltonians

We study the quantum complexity of time evolution in large-N chaotic systems, with the SYK model as our main example. This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value, and is related to the length of minimal geodesics on the manifold of unitary operators that act on Hilbert space. Using the Euler-Arnold formalism, we demonstrate that there is always a geodesic between the identity and the time evolution operator e -iHt whose length grows linearly with time. This geodesic is minimal until there is an obstruction to its minimality, after which it can fail to be a minimum either locally or globally. We identify a criterion — the Eigenstate Complexity Hypothesis (ECH) — which bounds the overlap between offdiagonal energy eigenstate projectors and the k-local operators of the theory, and use it to argue that the linear geodesic will at least be a local minimum for exponential time. We show numerically that the large-N SYK model (which is chaotic) satisfies ECH and thus has no local obstructions to linear growth of complexity for exponential time, as expected from holographic duality. In contrast, we also study the case with N = 2 fermions (which is integrable) and find short-time linear complexity growth followed by oscillations. Our analysis relates complexity to familiar properties of physical theories like their spectra and the structure of energy eigenstates and has implications for the hypothesized computational complexity class separations PSPACE * BQP/poly and PSPACE * BQSUBEXP/subexp, and the “fast-forwarding” of quantum Hamiltonians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Review on crystal structures and magnetic properties of RTX 3 materials

The structural and compositional diversity of the RTX 3 family of materials offers various magnetic and thermodynamic properties such as complex magnetic structure, vibronic bound states, heavy-fermions, valence fluctuations, metamagnetism, spin glass behavior, quantum criticality, and unconventional superconductivity. In this study we present an overview of the crystal structures, crystal growth and magnetic properties of RTX 3 compounds as well as a discussion of the relevant physics. The magnetic properties of several compounds of the RTX 3 family still remain unexplored. The compounds with a complex magnetic structure could potentially host exotic topological phases. This review article may help explore exotic magnetic properties such as the vibron state and topological spin textures.

quantum materials↗
DOE OSTI2023

Molecular Cage Reports on Its Contents: Spectroscopic Signatures of Cryo-Cooled K + - and Ba 2+ -Benzocryptand Complexes

UV photofragment spectroscopy and IR–UV double resonance methods are used to determine the structure and spectroscopic responses of a three-dimensional [2.2.2]-benzocryptand cage to the incorporation of a single K + or Ba 2+ imbedded inside it (labeled as K + -BzCrypt, Ba 2+ -BzCrypt). We studied the isolated ion-cryptand complex under cryo-cooled conditions, brought into the gas phase by nano-electrospray ionization. Incorporation of a phenyl ring in place of the central ethyl group in one of the three N-CH 2 -CH 2 -O-CH 2 -CH 2 -O-CH 2 -CH 2 -N chains provides a UV chromophore whose S 0 –S 1 transition we probe. K + -BzCrypt and Ba 2+ -BzCrypt have their S 0 –S 1 origin transitions at 35,925 and 36,446 cm –1 , respectively, blue-shifted by 174 and 695 cm –1 from that of 1,2-dimethoxybenzene. These origins are used to excite a single conformation of each complex selectively and record their IR spectra using IR–UV dip spectroscopy. The alkyl CH stretch region (2800–3000 cm –1 ) is surprisingly sensitive to the presence and nature of the encapsulated ion. We carried out an exhaustive conformational search of cage conformations for K + -BzCrypt and Ba 2+ -BzCrypt, identifying two conformations (A and B) that lie below all others in energy. Here, we extend our local mode anharmonic model of the CH stretch region to these strongly bound ion-cage complexes to predict conformation-specific alkyl CH stretch spectra, obtaining quantitative agreement with experiment for conformer A, the gas-phase global minimum. The large electrostatic effect of the charge on the O- and N-lone pairs affects the local mode frequencies of the CH 2 groups adjacent to these atoms. The localized CH 2 scissors modes are pushed up in frequency by the adjacent O/N-atoms so that their overtones have little effect on the alkyl CH stretch region. However, the localized CH 2 wags are nearly degenerate and strongly coupled to one another, producing an array of delocalized wag normal modes, whose highest frequency members reach up above 1400 cm –1 . As such, their overtones mix significantly with the CH stretch modes, most notably involving the CH 2 symmetric stretch fundamentals of the central ethyl groups in the all-alkyl chains and the CH stretches adjacent to the N-atoms and antiperiplanar to the nitrogen lone pair.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Multi-parametric analysis for mixed integer linear programming: An application to transmission upgrade and congestion management

Upgrading the capacity of existing transmission lines is essential for meeting the growing energy demands, facilitating the integration of renewable energy, and ensuring the security of the transmission system. This study focuses on the selection of lines whose capacities and by how much should be expanded from the perspective of the Independent System Operators (ISOs) to minimize the total system cost. We employ advanced multi-parametric programming and an enhanced branch-and-bound algorithm to address complex mixed-integer linear programming (MILP) problems, considering multi-period time constraints and physical limitations of generators and transmission lines. To characterize the various decisions in transmission expansion, we model the increased capacity of existing lines as parameters within a specified range. This study first relaxes the binary variables to continuous variables and applies the Lagrange method and Karush-Kuhn-Tucker (KKT) conditions to obtain optimal solutions and identify critical regions associated with active and inactive constraints. Moreover, we extend the traditional branch-and-bound (B&B) method by determining the problem’s upper and lower bounds at each node of the B&B decision tree, helping to manage computational challenges in large-scale MILP problems. Here, we compare the difference between the upper and lower bounds to obtain an approximate optimal solution within the decision-makers’ tolerable error range. In addition, the first derivative of the objective function on the parameters of each line is used to inform the selection of lines for easing congestion and maximizing social welfare. Finally, the capacity upgrades are selected by weighing the reductions in system costs against the expense of upgrading line capacities. The findings are supported by numerical simulations and provide transmission-line planners with decision-making guidance.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Effect of Adsorbed Carboxylates on the Dissolution of Boehmite Nanoplates in Highly Alkaline Solutions

Understanding the dissolution of boehmite in highly alkaline solutions is important to the processing of the complex nuclear wastes stored at the Hanford (WA) and Savannah River (SC) sites. Here, we report the adsorption of model carboxylate anions on boehmite nanoplates in alkaline solutions and their effects on subsequent boehmite dissolution in 3 M NaOH at 80 °C. Although expectedly lower than at circumneutral pH, adsorption of oxalate at pH 13 at room temperature was significant and remained so through a linear decrease to 3 M NaOH conditions with no evidence for the appearance of new phases. Modeling of the adsorption data and rate were consistent with the formation of outer-sphere surface complexes. By using these conditions to preload the boehmite nanoplates with oxalate, and separately acetate, we measured and compared their dissolution behavior at 80 °C and observed a clear suppression of the dissolution rate for the case of adsorbed oxalate by 23% and for adsorbed acetate by 10% compared to pure solids. Ex situ scanning electron microscopy (SEM) and transmission electron microscopy (TEM) characterization revealed no detectable difference in the morphologic evolution of the dissolving boehmite materials. In conclusion, we nonetheless conclude that pre-adsorbed carboxylate anions, even as nominally weakly bound outer-sphere complexes, can persist on the surface through highly alkaline conditions, decreasing the density of dissolution-active sites and thereby adding an extrinsic control on the dissolution rate.

Adsorption kinetics↗
DOE OSTI2022

Structures and function of a tailoring oxidase in complex with a nonribosomal peptide synthetase module

Nonribosomal peptide synthetases (NRPSs) are large modular enzymes that synthesize secondary metabolites and natural product therapeutics. Most NRPS biosynthetic pathways include an NRPS and additional proteins that introduce chemical modifications before, during or after assembly-line synthesis. The bacillamide biosynthetic pathway is a common, three-protein system, with a decarboxylase that prepares an NRPS substrate, an NRPS, and an oxidase. Here, the pathway is reconstituted in vitro. The oxidase is shown to perform dehydrogenation of the thiazoline in the peptide intermediate while it is covalently attached to the NRPS, as the penultimate step in bacillamide D synthesis. Structural analysis of the oxidase reveals a dimeric, two-lobed architecture with a remnant RiPP recognition element and a dramatic wrapping loop. The oxidase forms a stable complex with the NRPS and dimerizes it. We visualized co-complexes of the oxidase bound to the elongation module of the NRPS using X-ray crystallography and cryo-EM. The three active sites (for adenylation, condensation/cyclization, and oxidation) form an elegant arc to facilitate substrate delivery. The structures enabled a proof-of-principle bioengineering experiment in which the BmdC oxidase domain is embedded into the NRPS.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Inverse Trans Influence and Uranium-Arene σ-Bonding Drive Molecular Geometry: Ligand Modification from Hard to Soft Flips the Oxide from Axial to Equatorial

A rare example of an equatorially bound terminal uranium(V) oxo complex in a chelating sulfur-based ligand environment, namely [(mes( Me,Ad ArS) 3 )U V (O eq )(THF)] (2), is presented. Octahedrally coordinated 2 is obtained by reaction of the mesitylene-anchored tris-thiophenolate-coordinated uranium(III) complex [U III ((SAr Ad,Me ) 3 mes)] (1) with the oxygen-atom transfer reagent N 2 O. The observed, equatorially bound oxo ligand in 2 is in stark contrast to its known tris-aryloxide analog, [(mes( Me,Ad ArO) 3 )U V (O ax )(THF)] (A), where the oxo ligand occupies the typically observed axial coordination site. Complexes 1 and 2 are characterized by single-crystal X-ray diffraction analyses and spectroscopic and magnetochemical methods, including 1 H NMR, UV/vis/NIR electronic absorption, as well as EPR spectroscopy and SQUID magnetometry, thus confirming the C S symmetry and the pentavalent oxidation state of 2. Encompassing quantum chemical calculations (DFT and CASPT2) on 2 and its tris-phenolate analog A, support and rationalize the structural and electronic differences. The molecular orbital pictures show that a stabilizing σ-bonding interaction arising from the U–O eq inverse trans influence (ITI) is present in 2 but missing in A. In 2, the sulfur 3p orbitals are closer in energy to the uranium 5f manifold than the arene π-system, leading to an ITI, while U–arene σ- or δ-bonding is not observed. Although the arene orbitals remain separated from the uranium 5f orbitals in A, the absence of an ITI allows the arene a 2u orbital to engage in a σ-type interaction with the metal. Thus, incorporating a tris-thiophenolate to an arene anchor introduces a new design concept in molecular f-element chemistry. This approach stabilizes an equatorially bound U(V) oxo center, contrasting with its tris-phenolate counterpart, where oxo coordination is axial. The observed geometric divergence, driven by competing ITI and U–arene interactions, not only tunes electronic structure but also leads to differentiated reactivity: only the phenolate analogs activate H 2 O, while the thiolates do not.

Hydrocarbons↗
DOE OSTI2025

EPR and 31 P ENDOR Characterization of Pseudo-Jahn–Teller Dynamics and N 2 Activation in Functional Nitrogenase Models, P 3 E M(N 2 ) (M = Fe, Co; E = Si, B, C)

Here, the nominally trigonal, pseudo-Jahn-Teller (PJT)-active, S = ½ N 2 -bound transition-metal complexes, P 3 E M(N 2 ), M = Fe, Co, with three in-plane phosphine-ligands and axial donors, E = Si, B, C, include functional nitrogenase models that catalyze reduction of N 2 to NH 3 . We applied EPR, 31 P ENDOR spectroscopy and DFT computations to characterize the PJT-induced distortions of four selected P 3 E M(N 2 ), revealing how the metal-ion and axial ligand E together tune both PJT dynamics and N 2 activation for reduction. Comparisons reveal an unrecognized correlation between PJT distortion, M-E bond elasticity, and N 2 activation, providing guidelines for designing bioinspired N 2 -reduction catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Catalytic Ambient Temperature Dinitrogen Conversion to a Bis(silyl)amine by Mononuclear Group 4 Aryloxide Complexes

The homogeneous conversion of ambient dinitrogen to amine products via the N2 reduction reaction (N2RR) remains a prized yet challenging feat for d-block complexes and is scarcely reported for f-block complexes. New, mononuclear TiIV and ZrIV aryloxide complexes Ti(DP)2 (1Ti), Zr(DP)2 (1Zr), and DP = [2-(OC6H2-2-tBu,4-Me)2CHPh] produce up to 51 eq. and up to 7.0 eq. of HN(SiMe3)2 per Ti/Zr, from N2, K0, weak acid, and chlorotrimethylsilane. Complex 1Ti exhibits more than double the activity toward N2-silylation of any previously reported Ti N2RR catalyst and can also catalyze the formation of up to 19 eq. of NH3, a new feature in early metal N2RR chemistry. The mononuclear 1Zr is the most active Zr catalyst for N2-silylation to date. [KSm(DP)2(THF)3] (1Sm), the mononuclear analogue of our previously reported dinuclear A-Sm complex, displays only stoichiometric N2-silylation due to its vulnerability to deleterious side reactions. DFT calculations confirm the catalysis can proceed via a monomeric Ti complex with a terminally bound, activated N2, agreeing with experimental 1H DOSY NMR measurements; the N-H bond is formed first, directing the catalyst selectivity. The isolable reduction product [K3(THF)Ti(DP)(DP-)(N2)] is also an active catalyst, and an intermediate in the calculated cycle.

Hernandez, Matthew↗
DOE OSTI2025

Cation-π Bonding in Actinides: UO x + (Benzene) ( x = 0, 1, 2) Complexes Studied with Threshold Photodissociation Spectroscopy and Theory

Cation-π complexes of the form UO x + (benzene) (x = 0, 1, 2) are produced by laser vaporization and cooled in a supersonic molecular beam. These ions are mass selected and studied with UV–visible laser photodissociation spectroscopy. Each of these complexes photodissociates by elimination of the benzene ligand. Above an energetic threshold, the absorption and photodissociation are continuous, indicating a high density of strongly coupled electronic states. The thresholds for the dissociation of each of these three complexes are measured and assigned as their respective bond dissociation energies. The bond energies determined [U + –(benzene): 42.5 ± 0.3 kcal/mol; UO + –(benzene): 41.0 ± 0.3 kcal/mol; UO 2 + –(benzene): 39.7 ± 0.3 kcal/mol] are comparable to those of transition metal ion-benzene complexes. Computational studies at the DFT/B3LYP level complement the experiments, predicting dissociation energies in reasonably good agreement with the experiments. Experiments and theory agree that the U+(benzene) complex is more strongly bound than its corresponding oxide ions. This new thermochemistry on actinide cation-π bonding should stimulate higher-level computational studies on these systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

H 2 Evolution from a Thiolate-Bound Ni(III) Hydride

A thiolate-bound Ni(III) hydride complex, related to the intermediates proposed in Ni-based hydrogenase enzymes, was synthesized and characterized. This paramagnetic complex was demonstrated to be competent for H 2 release upon warming, and the H-H bond forming step was mechanistically probed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Multi-variate model of T cell clonotype competition and homeostasis

Abstract Diversity of the naive T cell repertoire is maintained by competition for stimuli provided by self-peptides bound to major histocompatibility complexes (self-pMHCs). We extend an existing bi-variate competition model to a multi-variate model of the dynamics of multiple T cell clonotypes which share stimuli. In order to understand the late-time behaviour of the system, we analyse: (i) the dynamics until the extinction of the first clonotype, (ii) the time to the first extinction event, (iii) the probability of extinction of each clonotype, and (iv) the size of the surviving clonotypes when the first extinction event takes place. We also find the probability distribution of the number of cell divisions per clonotype before its extinction. The mean size of a new clonotype at quasi-steady state is an increasing function of the stimulus available to it, and a decreasing function of the fraction of stimuli it shares with other clonotypes. Thus, the probability of, and time to, extinction of a new clonotype entering the pool of T cell clonotypes is determined by the extent of competition for stimuli it experiences and by its initial number of cells.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Hidden features in the OH-stretching spectra of amino acid decorated air–water interfaces

Chemical reactivity at the air–water interface is governed by the interfacial solvation of reactive species. For instance, during aqueous amino acid-based CO 2 absorption, water reorganizes around the reactive sites and couples dynamically with reaction pathways, facilitating the reaction. In this context, surface-sensitive vibrational sum-frequency generation (vSFG) spectroscopy can probe the OH stretch vibrations of interfacial water and determine the solvation structures around reactants and products, thereby furthering our understanding of the role of interfacial solvation. However, vSFG spectra of the air–water interface in the presence of charged species can be remarkably complex; key species-bound local water structures with distinct orientations may be hidden beneath prominent vSFG peaks arising from water–water hydrogen bonds and remain difficult to resolve. Here, we measure and compute vSFG spectra of the water OH stretch at air–water interfaces decorated with amino acids in their zwitterionic and anionic forms, as well as equimolar mixtures of these forms with bicarbonate. The latter represents post-CO 2 -absorption conditions. We find that computing depth- and frequency-dependent spectral densities—decomposed into contributions from water molecules hydrogen-bonded exclusively to other water molecules, exclusively to amines, exclusively to carboxylates, or shared between these polar/charged groups—is indispensable for accurate interpretation of the vSFG spectra. Key findings include orientational flip-flop in water sub-layers, strong carboxylate-water H-bonding, and water orientational ordering extending into the bulk aqueous phase induced by anionic amino acids. Here, this study provides a computational spectroscopic platform for improved understanding of interfacial solvation relevant to interfacial reactivity.

Air-water interface↗
DOE OSTI2020

The cryoelectron microscopy structure of the human CDK-activating kinase

The human CDK-activating kinase (CAK), a complex composed of cyclin-dependent kinase (CDK) 7, cyclin H, and MAT1, is a critical regulator of transcription initiation and the cell cycle. It acts by phosphorylating the C-terminal heptapeptide repeat domain of the RNA polymerase II (Pol II) subunit RPB1, which is an important regulatory event in transcription initiation by Pol II, and it phosphorylates the regulatory T-loop of CDKs that control cell cycle progression. Here, we have determined the three-dimensional (3D) structure of the catalytic module of human CAK, revealing the structural basis of its assembly and providing insight into CDK7 activation in this context. The unique third component of the complex, MAT1, substantially extends the interaction interface between CDK7 and cyclin H, explaining its role as a CAK assembly factor, and it forms interactions with the CDK7 T-loop, which may contribute to enhancing CAK activity. We have also determined the structure of the CAK in complex with the covalently bound inhibitor THZ1 in order to provide insight into the binding of inhibitors at the CDK7 active site and to aid in the rational design of therapeutic compounds.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Pre–T cell receptors topologically sample self-ligands during thymocyte β-selection

Self-discrimination, a critical but ill-defined molecular process programmed during thymocyte development, requires myriad pre–T cell receptors (preTCRs) and αβTCRs. Using x-ray crystallography, we show how a preTCR applies the concave β-sheet surface of its single variable domain (Vβ) to “horizontally” grab the protruding MHC α2-helix. By contrast, αβTCRs purpose all six complementarity-determining region (CDR) loops of their paired VαVβ module to recognize peptides bound to major histocompatibility complex molecules (pMHCs) in “vertical” head-to-head binding. Additionally, the preTCR topological fit ensures that CDR3β reaches the peptide’s featured C-terminal segment for pMHC sampling, establishing the subsequent αβTCR canonical docking mode. “Horizontal” docking precludes germline CDR1β- and CDR2β-MHC binding to broaden β-chain repertoire diversification before αβTCR-mediated selection refinement. Thus, one subunit successively attunes the recognition logic of related multicomponent receptors.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

An Abundant and Diverse New Family of Electron Bifurcating Enzymes With a Non-canonical Catalytic Mechanism

Microorganisms utilize electron bifurcating enzymes in metabolic pathways to carry out thermodynamically unfavorable reactions. Bifurcating FeFe-hydrogenases (HydABC) reversibly oxidize NADH (E′∼−280 mV, under physiological conditions) and reduce protons to H 2 gas (E°′−414 mV) by coupling this endergonic reaction to the exergonic reduction of protons by reduced ferredoxin (Fd) (E′∼−500 mV). We show here that HydABC homologs are surprisingly ubiquitous in the microbial world and are represented by 57 phylogenetically distinct clades but only about half are FeFe-hydrogenases. The others have replaced the hydrogenase domain with another oxidoreductase domain or they contain additional subunits, both of which enable various third reactions to be reversibly coupled to NAD + and Fd reduction. We hypothesize that all of these enzymes carry out electron bifurcation and that their third substrates can include hydrogen peroxide, pyruvate, carbon monoxide, aldehydes, aryl-CoA thioesters, NADP + , cofactor F 420 , formate, and quinones, as well as many yet to be discovered. Some of the enzymes are proposed to be integral membrane-bound proton-translocating complexes. These different functionalities are associated with phylogenetically distinct clades and in many cases with specific microbial phyla. We propose that this new and abundant class of electron bifurcating enzyme be referred to as the Bfu family whose defining feature is a conserved bifurcating BfuBC core. This core contains FMN and six iron sulfur clusters and it interacts directly with ferredoxin (Fd) and NAD(H). Electrons to or from the third substrate are fed into the BfuBC core via BfuA. The other three known families of electron bifurcating enzyme (abbreviated as Nfn, EtfAB, and HdrA) contain a special FAD that bifurcates electrons to high and low potential pathways. The Bfu family are proposed to use a different electron bifurcation mechanism that involves a combination of FMN and three adjacent iron sulfur clusters, including a novel [2Fe-2S] cluster with pentacoordinate and partial non-Cys coordination. The absolute conservation of the redox cofactors of BfuBC in all members of the Bfu enzyme family indicate they have the same non-canonical mechanism to bifurcate electrons. A hypothetical catalytic mechanism is proposed as a basis for future spectroscopic analyses of Bfu family members.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Elucidation of Agonist and Antagonist Dynamic Binding Patterns in ER-α by Integration of Molecular Docking, Molecular Dynamics Simulations and Quantum Mechanical Calculations

Estrogen receptor alpha (ERα) is a ligand-dependent transcriptional factor in the nuclear receptor superfamily. Many structures of ERα bound with agonists and antagonists have been determined. However, the dynamic binding patterns of agonists and antagonists in the binding site of ERα remains unclear. Therefore, we performed molecular docking, molecular dynamics (MD) simulations, and quantum mechanical calculations to elucidate agonist and antagonist dynamic binding patterns in ERα. 17β-estradiol (E2) and 4-hydroxytamoxifen (OHT) were docked in the ligand binding pockets of the agonist and antagonist bound ERα. The best complex conformations from molecular docking were subjected to 100 nanosecond MD simulations. Hierarchical clustering was conducted to group the structures in the trajectory from MD simulations. The representative structure from each cluster was selected to calculate the binding interaction energy value for elucidation of the dynamic binding patterns of agonists and antagonists in the binding site of ERα. The binding interaction energy analysis revealed that OHT binds ERα more tightly in the antagonist conformer, while E2 prefers the agonist conformer. The results may help identify ERα antagonists as drug candidates and facilitate risk assessment of chemicals through ER-mediated responses.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1976

The eigenvalue spectrum of the Orr-Sommerfeld problem

A numerical investigation of the temporal eigenvalue spectrum of the ORR-Sommerfeld equation is presented. Two flow profiles are studied, the plane Poiseuille flow profile and the Blasius boundary layer (parallel): flow profile. In both cases a portion of the complex c-plane bounded by 0 less than or equal to CR sub r 1 and -1 less than or equal to ci sub i 0 is searched and the eigenvalues within it are identified. The spectra for the plane Poiseuille flow at alpha = 1.0 and R = 100, 1000, 6000, and 10000 are determined and compared with existing results where possible. The spectrum for the Blasius boundary layer flow at alpha = 0.308 and R = 998 was found to be infinite and discrete. Other spectra for the Blasius boundary layer at various Reynolds numbers seem to confirm this result. The eigenmodes belonging to these spectra were located and discussed.

Antar, B. N.↗