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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

Bifurcation Analysis Using Rigorous Branch and Bound Methods

For the study of nonlinear dynamic systems, it is important to locate the equilibria and bifurcations occurring within a specified computational domain. This paper proposes a new approach for solving these problems and compares it to the numerical continuation method. The new approach is based upon branch and bound and utilizes rigorous enclosure techniques to yield outer bounding sets of both the equilibrium and local bifurcation manifolds. These sets, which comprise the union of hyper-rectangles, can be made to be as tight as desired. Sufficient conditions for the existence of equilibrium and bifurcation points taking the form of algebraic inequality constraints in the state-parameter space are used to calculate their enclosures directly. The enclosures for the bifurcation sets can be computed independently of the equilibrium manifold, and are guaranteed to contain all solutions within the computational domain. A further advantage of this method is the ability to compute a near-maximally sized hyper-rectangle of high dimension centered at a fixed parameter-state point whose elements are guaranteed to exclude all bifurcation points. This hyper-rectangle, which requires a global description of the bifurcation manifold within the computational domain, cannot be obtained otherwise. A test case, based on the dynamics of a UAV subject to uncertain center of gravity location, is used to illustrate the efficacy of the method by comparing it with numerical continuation and to evaluate its computational complexity.

Smith, Andrew P.↗
DOE OSTI2025

Electrochemical Observation and pH Dependence of All Three Expected Redox Couples in an Extremophilic Bifurcating Electron Transfer Flavoprotein with Fused Subunits

Bifurcating enzymes employ energy from a favorable electron transfer to drive unfavorable transfer of a second electron, thereby generating a more reactive product. They are therefore highly desirable in catalytic systems, for example, to drive challenging reactions such as nitrogen fixation. While most bifurcating enzymes contain air-sensitive metal centers, bifurcating electron transfer flavoproteins (bETFs) employ flavins. However, they have not been successfully deployed on electrodes. Herein, we demonstrate immobilization and expected thermodynamic reactivity of a bETF from a hyperthermophilic archaeon, Sulfolobus acidocaldarius (SaETF). SaETF differs from previously biochemically characterized bETFs in being a single protein, representing a concatenation of the two subunits of known ETFs. However, SaETF retains the chemical properties of heterodimeric bETFs, including possession of two FADs: one that undergoes sequential 1-electron (1e) reductions at high E° and forms an anionic semiquinone, and another that is amenable to lower-E° 2e reduction, including by NADH. We found homologous monomeric ETF genes in archaeal and bacterial genomes, accompanied by genes that also commonly flank heterodimeric ETFs, and SaETF’s sequence conservation is 50% higher with bETFs than with canonical ETFs. Thus, SaETF is best described as a bETF. Our direct electrochemical trials capture reversible redox couples for all three thermodynamically expected redox events. We document electrochemical activity over a range of pH values and reveal a conformational change coupled to proton acquisition that affects the electrochemical activity of the higher-E° FAD. Thus, this well-behaved monomeric bETF opens the door to bioinspired bifurcating devices or bifurcation on a chip.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

A new era for electron bifurcation

Electron bifurcation, or the coupling of exergonic and endergonic oxidation-reduction reactions, was discovered by Peter Mitchell and provides an elegant mechanism to rationalize and understand the logic that underpins the Q cycle of the respiratory chain. Thought to be a unique reaction of respiratory complex III for nearly 40 years, about a decade ago Wolfgang Buckel and Rudolf Thauer discovered that flavin-based electron bifurcation is also an important component of anaerobic microbial metabolism. Their discovery spawned a surge of research activity, providing a basis to understand flavin-based bifurcation, forging fundamental parallels with Mitchell's Q cycle and leading to the proposal of metal-based bifurcating enzymes. New insights into the mechanism of electron bifurcation provide a foundation to establish the unifying principles and essential elements of this fascinating biochemical phenomenon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Insight Into the High-Potential Branch of the Alternate Nad+-Dependent NADPH:Ferredoxin Oxidoreductase II (NfnII) from Pyrococcus Furiosus. Evidence for the Gating Step in Electron Bifurcation

We have investigated the rapid-reaction kinetics of the NAD+-dependent NADPH:ferredoxin oxidoreductase II (NfnII) from Pyrococcus furiosus, permitting a comparison with recent work done with the paralog NfnI from the same organism. The half-potentials of the electron-bifurcating L-FAD are highly crossed in both NfnI, meaning the potential for the quinone/semiquinone couple is significantly lower than that for the semiquinone/hydroquinone couple so that the semiquinone oxidation state is thermodynamically unstable. The same appears to be the case with NfnII on the basis of its similar behavior in transient absorption spectroscopy experiments and the absence of any evidence for FAD*- accumulation in the course of reductive titrations (which would be manifested as a transient increase in absorbance at ~380 nm)1. Reductive titrations with both the one-electron donor sodium dithionite and the obligate two-electron donor NADPH demonstrate that, in contrast to NfnI, little FADH* accumulates in the high-potential pathway of NfnII in the course of reduction, as reflected in the absence of a transient increase in absorbance in the 500-600 nm region. This indicates that the half-potentials of the S-FAD are crossed in NfnII by a minimum of 120 mV. Rapid-reaction experiments mixing oxidized NfnII with NADPH also show no evidence of S-FADH* accumulation. Furthermore, the enzyme is only partially reduced at the end of the reaction with NADPH, indicating that there is little electron transfer into the high-potential pathway of NfnII. When the reaction is carried out in the presence of the one-electron carrier ferredoxin, only approximately one equivalent of ferredoxin becomes reduced, in contrast to the maximum of three equivalents seen with NfnI. This is consistent with only a single electron bifurcation event taking place under these conditions with NfnII, with only a single high-potential electron passing into the [2Fe-2S] cluster of the high-potential pathway of NfnII but not progressing further to the S-FAD. This accounts for the observation that NfnII has greatly reduced bifurcating activity compared to NfnI. The lack of electron transfer into the S-FAD of NfnII due to its crossed half-potentials prevents successive bifurcation activity and indicates that electron transfer within the high-potential branch gates bifurcation activity in NfnI.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Comparison of bifurcation dynamics of turbulent transport models for the L-H transition

In more than three decades, a large amount of models and mechanisms have been proposed to describe a very beneficial feature of magnetically confined fusion plasmas: the L-H transition. Bifurcation theory can be used to compare these different models based on their dynamical transition structure. In this paper, we employ bifurcation theory to distinguish two fundamentally different descriptions of the interaction between turbulence levels and sheared flows. The analytic bifurcation analysis characterises the parameter space structure of the transition dynamics. Herewith, in these models three dynamically different types of transitions are characterised, sharp transitions, oscillatory transitions, and smooth transitions. One of the two models has a very robust transition structure and is therefore likely to be more accurate for such a robust phenomenon as the L-H transition. The other model needs more fine-tuning to get non-oscillatory transitions. These conclusions from the analytic bifurcation analysis are confirmed by dedicated numerical simulations, with the newly developed code Bifurcator.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Detection of bifurcations in noisy coupled systems from multiple time series

We generalize a method of detecting an approaching bifurcation in a time series of a noisy system from the special case of one dynamical variable to multiple dynamical variables. For a system described by a stochastic differential equation consisting of an autonomous deterministic part with one dynamical variable and an additive white noise term, small perturbations away from the system's fixed point will decay slower the closer the system is to a bifurcation. This phenomenon is known as critical slowing down and all such systems exhibit this decay-type behaviour. However, when the deterministic part has multiple coupled dynamical variables, the possible dynamics can be much richer, exhibiting oscillatory and chaotic behaviour. In our generalization to the multi-variable case, we find additional indicators to decay rate, such as frequency of oscillation. In the case of approaching a homoclinic bifurcation, there is no change in decay rate but there is a decrease in frequency of oscillations. The expanded method therefore adds extra tools to help detect and classify approaching bifurcations given multiple time series, where the underlying dynamics are not fully known. Our generalisation also allows bifurcation detection to be applied spatially if one treats each spatial location as a new dynamical variable. One may then determine the unstable spatial mode(s). This is also something that has not been possible with the single variable method. The method is applicable to any set of time series regardless of its origin, but may be particularly useful when anticipating abrupt changes in the multi-dimensional climate system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Generative learning for slow manifolds and bifurcation diagrams

In dynamical systems characterized by separation of time scales, the approximation of so called “slow manifolds”, on which the long term dynamics lie, is a useful step for model reduction. Initializing on such slow manifolds is a useful step in modeling, since it circumvents fast transients, and is crucial in multiscale algorithms (like the equation-free approach) alternating between fine scale (fast) and coarser scale (slow) simulations. In a similar spirit, when one studies the infinite time dynamics of systems depending on parameters, the system attractors (e.g., its steady states) lie on bifurcation diagrams (curves for one-parameter continuation, and more generally, on manifolds in state parameter space. Sampling these manifolds gives us representative attractors (here, steady states of ODEs or PDEs) at different parameter values. Algorithms for the systematic construction of these manifolds (slow manifolds, bifurcation diagrams) are required parts of the “traditional” numerical nonlinear dynamics toolkit. In more recent years, as the field of Machine Learning develops, conditional score-based generative models (cSGMs) have been demonstrated to exhibit remarkable capabilities in generating plausible data from target distributions that are conditioned on some given label. It is tempting to exploit such generative models to produce samples of data distributions (points on a slow manifold, steady states on a bifurcation surface) conditioned on (consistent with) some quantity of interest (QoI, observable). In this work, we present a framework for using cSGMs to quickly (a) initialize on a low-dimensional (reduced-order) slow manifold of a multi-time-scale system consistent with desired value(s) of a QoI (a “label”) on the manifold, and (b) approximate steady states in a bifurcation diagram consistent with a (new, out-of-sample) parameter value. This conditional sampling can help uncover the geometry of the reduced slow-manifold and/or approximately “fill in” missing segments of steady states in a bifurcation diagram. Finally, the quantity of interest, which determines how the sampling is conditioned, is either known a priori or identified using manifold learning-based dimensionality reduction techniques applied to the training data.

Dynamical systems↗
DOE OSTI2014

Poster — Thur Eve — 70: Automatic lung bronchial and vessel bifurcations detection algorithm for deformable image registration assessment

Purpose: To investigate an automatic bronchial and vessel bifurcations detection algorithm for deformable image registration (DIR) assessment to improve lung cancer radiation treatment. Methods: 4DCT datasets were acquired and exported to Varian treatment planning system (TPS) EclipseTM for contouring. The lungs TPS contour was used as the prior shape for a segmentation algorithm based on hierarchical surface deformation that identifies the deformed lungs volumes of the 10 breathing phases. Hounsfield unit (HU) threshold filter was applied within the segmented lung volumes to identify blood vessels and airways. Segmented blood vessels and airways were skeletonised using a hierarchical curve-skeleton algorithm based on a generalized potential field approach. A graph representation of the computed skeleton was generated to assign one of three labels to each node: the termination node, the continuation node or the branching node. Results: 320 ± 51 bifurcations were detected in the right lung of a patient for the 10 breathing phases. The bifurcations were visually analyzed. 92 ± 10 bifurcations were found in the upper half of the lung and 228 ± 45 bifurcations were found in the lower half of the lung. Discrepancies between ten vessel trees were mainly ascribed to large deformation and in regions where the HU varies. Conclusions: We established an automatic method for DIR assessment using the morphological information of the patient anatomy. This approach allows a description of the lung's internal structure movement, which is needed to validate the DIR deformation fields for accurate 4D cancer treatment planning.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Shells, orbit bifurcations, and symmetry restorations in Fermi systems

The periodic-orbit theory based on the improved stationary-phase method within the phase-space path integral approach is presented for the semiclassical description of the nuclear shell structure, concerning themain topics of the fruitful activity ofV.G. Soloviev. We apply this theory to study bifurcations and symmetry breaking phenomena in a radial power-law potential which is close to the realistic Woods–Saxon one up to about the Fermi energy. Using the realistic parametrization of nuclear shapes we explain the origin of the double-humped fission barrier and the asymmetry in the fission isomer shapes by the bifurcations of periodic orbits. The semiclassical origin of the oblate–prolate shape asymmetry and tetrahedral shapes is also suggested within the improved periodic-orbit approach. The enhancement of shell structures at some surface diffuseness and deformation parameters of such shapes are explained by existence of the simple local bifurcations and new non-local bridge-orbit bifurcations in integrable and partially integrable Fermi-systems. We obtained good agreement between the semiclassical and quantum shell-structure components of the level density and energy for several surface diffuseness and deformation parameters of the potentials, including their symmetry breaking and bifurcation values.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1987

Multigrid methods for bifurcation problems: The self adjoint case

This paper deals with multigrid methods for computational problems that arise in the theory of bifurcation and is restricted to the self adjoint case. The basic problem is to solve for arcs of solutions, a task that is done successfully with an arc length continuation method. Other important issues are, for example, detecting and locating singular points as part of the continuation process, switching branches at bifurcation points, etc. Multigrid methods have been applied to continuation problems. These methods work well at regular points and at limit points, while they may encounter difficulties in the vicinity of bifurcation points. A new continuation method that is very efficient also near bifurcation points is presented here. The other issues mentioned above are also treated very efficiently with appropriate multigrid algorithms. For example, it is shown that limit points and bifurcation points can be solved for directly by a multigrid algorithm. Moreover, the algorithms presented here solve the corresponding problems in just a few work units (about 10 or less), where a work unit is the work involved in one local relaxation on the finest grid.

Taasan, Shlomo↗
DOE OSTI2018

Hopf bifurcation of a delayed chemostat model with general monotone response functions

In this paper, a chemostat model with general monotone response functions and two discrete time delays is proposed to describe the dynamical behavior about predator–prey system. First, by analyzing the characteristic equation associated with the model, we obtain the conditions of the existence and stability of extinction equilibrium and positive equilibrium. Choosing delays as bifurcation parameters, the existence of Hopf bifurcations is investigated in detail. Second, by virtue of the Poincaré normal form method and center manifold theorem, explicit formulas are derived to determine the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Finally, some numerical simulations are carried out to illustrate the theoretical results and the biological significance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Differential Ligation Alters Electronic State and Coupling Signals of Iron-Sulfur Clusters in Flavin-Based Electron Bifurcation

Flavin-based electron bifurcation (FBEB) is employed by microorganisms for controlling pools of redox equivalents by reversibly splitting electron pairs into high- and low-energy levels from an initial midpoint potential. Our ability to harness this phenomenon is crucial for biocatalytic design which is limited by our understanding of energy coupling in the bifurcation system. In Pyrococcus furiosus, FBEB is carried out by the NADH-dependent ferredoxin:NADP+-oxidoreductase (NfnSL), coupling the uphill reduction of ferredoxin in NfnL to the downhill reduction of NAD+ in NfnS from oxidation of NADPH. Flanking the bifurcating flavin are two site-differentiated iron-sulfur clusters; the nearest is a glutamate-ligated [4Fe-4S] cluster in NfnL. Recent biochemical experiments substituting the native glutamate with cysteine led to loss of coupling between the uphill and downhill pathways, in contrast to the tight thermodynamic coupling in the native system. To understand how this decoupling is biochemically manifested by the cysteine-substituted [4Fe-4S] in NfnL, we employed electron paramagnetic resonance (EPR) spectroscopy to identify changes in electronic architecture and square wave voltammetry (SWV) to probe thermodynamic shifts produced by the substitution. We observed notable g-value shifts in the EPR for the cysteine-substituted iron-sulfur cluster in addition to significant downward shifts in the redox potential, as well as the disappearance of several low-field signals observed in the native NfnSL complex. These results suggest the site-differentiated glutamate residue facilitates higher spin states in the [4Fesingle bond4S] cluster to bridge energetic gaps in electron transfer to the bifurcating flavin in the native complex, preventing unwanted short-circuiting seen in the cysteine-substituted complex.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

A numerical study of crack initiation in a bcc iron system based on dynamic bifurcation theory

Crack initiation under dynamic loading conditions is studied under the framework of dynamic bifurcation theory. An atomistic model for BCC iron is considered to explicitly take into account the detailed molecular interactions. To understand the strain-rate dependence of the crack initiation process, we first obtain the bifurcation diagram from a computational procedure using continuation methods. The stability transition associated with a crack initiation, as well as the connection to the bifurcation diagram, is studied by comparing direct numerical results to the dynamic bifurcation theory [R. Haberman, SIAM J. Appl. Math. 37, 69–106 (1979)].

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Delay-induced stochastic bifurcations in a bistable system under white noise

In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Bifurcation dynamics of the tempered fractional Langevin equation

Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Cryoelectron microscopy structure and mechanism of the membrane-associated electron-bifurcating flavoprotein Fix/EtfABCX

Significance Electron bifurcation is a recently recognized mechanism of biological energy conservation that is widespread in anaerobic microorganisms and provides low-potential, high-energy electrons to drive otherwise nonspontaneous metabolic reactions. Here we describe the structure of a membrane-associated bifurcating enzyme from an aerobic microorganism. Termed Fix/EtfABCX, this enzyme is used by some nitrogen-fixing microbes to drive the low-potential reduction of nitrogen gas to ammonia. Fix/EtfABCX is a superdimer and a catalytic mechanism is proposed involving six flavins, two of which bifurcate, four iron-sulfur clusters, and two menaquinones. Fix/EtfABCX shares structural similarity with mammalian quinone oxidoreductase involved in mitochondrial fatty acid oxidation, suggesting an unexpected evolutionary link between bifurcating and nonbifurcating systems.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

An uncharacteristically low-potential flavin governs the energy landscape of electron bifurcation

Significance Nature has long been an inspiration for materials design, as it exemplifies exquisite control of both matter and energy. Electron bifurcation, a mechanism employed in biological systems to drive thermodynamically unfavorable and energetically challenging chemical reactions, is one such example. A key feature of bifurcating enzymes is the ability of a single redox cofactor to distribute a pair of electrons across two spatially separated electron transfer pathways. Here, we report on the empirical determination of both the one-electron potential and two-electron potential of the bifurcating flavin cofactor in the NADH-dependent ferredoxin-NADP + oxidoreductase I (NfnSL) enzyme. Insights arising from the defined energy landscape of this bifurcation site may underlie the design of synthetic catalysts capable of generating high-energy intermediates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Bifurcation physics of magnetic islands and stochasticity explored by heat pulse propagation studies in toroidal plasmas

Bifurcation physics of the magnetic island was investigated using the heat pulse propagation technique produced by the modulation of electron cyclotron heating. There are two types of bifurcation phenomena observed in LHD and DIII-D. One is a bifurcation of the magnetic topology between nested and stochastic fields. The nested state is characterized by the bi-directional (inward and outward) propagation of the heat pulse with slow propagation speed. The stochastic state is characterized by the fast propagation of the heat pulse with electron temperature flattening. The other bifurcation is between magnetic island with larger thermal diffusivity and that with smaller thermal diffusivity. The damping of toroidal flow is observed at the O-point of the magnetic island both in helical plasmas and in tokamak plasmas during a mode locking phase with strong flow shears at the boundary of the magnetic island. Associated with the stochastization of the magnetic field, the abrupt damping of toroidal flow is observed in LHD. The toroidal flow shear shows a linear decay, while the ion temperature gradient shows an exponential decay. Lastly, this observation suggests that this flow damping is due to the change in the non-diffusive term of momentum transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗