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DOE OSTI2018

Biparametric investigation of the general standard map: multistability and global bifurcations

We investigate multistability and global bifurcations in the general standard map, a biparametric two-dimensional map. Departing from the conservative case of the map, we describe the evolution of periodic solutions and their basins of attraction as dissipation builds up, paying special attention on how the biparametric variation affects multistability. We examine general and specific phenomena and behavior for three distinct dynamical regimes, namely small, moderate, and large damping and different forcing amplitudes. Also, we report numerically the mechanism of global bifurcations associated to small chaotic attractors in the multistable system. Several global bifurcations are investigated as dissipation increases. Specifically, through the characterization of an interior, a merging and a boundary crisis, we study the crucial role played by fundamental hyperbolic invariant structures, such as unstable periodic orbits and their stable and unstable invariant manifolds, in the mechanisms by which the phase space is globally transformed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Energy transduction by reversible electron bifurcation

Electron bifurcation is a biological energy conversion process that oxidizes a two-electron donor at medium potential, coupled to the reduction of a high- and a low-potential acceptor species. This process is often fully reversible (can occur close to ΔG ≈ 0), allowing the creation of strong reductants with minimal free energy cost, using compounds with higher reduction potentials. For many years, the internal workings of electron bifurcating enzymes were poorly understood, especially regarding how short-circuit reactions are prevented. Recently, a conserved energy landscape was proposed to naturally insulate against short-circuit reactions, enabling efficient and reversible electron bifurcation (the reversible EB scheme). Here, we review the physical principles that underpin the EB scheme, describe how the reversible EB scheme is distinct from previous views, and outline questions that remain open.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Uncertainty estimation of bifurcated solutions in the Rayleigh–Bénard problem for advanced nuclear reactors applications

Multiphysics models of nuclear reactors frequently comprise nonlinear systems of equations. The nonlinear nature of these models could lead to solution bifurcations, where a small change in a certain parameter, e.g., the thermophysical properties of the coolant, can lead to a sudden change in the system’s behavior. At the point in parameter space where this happens, called a critical point, the Jacobian matrix of the model’s nonlinear operator becomes singular potentially permitting multiple solutions to coexist. In this paper, we perform uncertainty estimation (UE) in a parameter range that includes bifurcated solutions within the context of Rayleigh–Bénard problem. We perform this analysis assuming uncertain temperature difference, and tilt angle for the iterative solution algorithm with a unit Prandtl number (Pr = 1). Also, we perform this analysis under uncertain thermophysical properties for both FLiBe molten salt and liquid sodium as working fluid. We deploy two approaches to compute statistical moments for the resulting distributions of selected flow-field variables. The first approach is the blind computation of the mean and the standard deviation without any consideration of solution bifurcation, while the second approach utilizes k-means clustering to cluster each branch’s solutions together and compute separate statistical moments for each branch. The statistical distributions are obtained by perturbing the selected parameters about nominal values that correspond to a solution on one of the valid branches, and that solution is used as initial guess for the iterative solution algorithm. We found that perturbation of any parameter when its nominal value is close to its critical point always leads to branch jumping, i.e., the iterations converge to a solution on a branch different from the branch of the initial guess. This produces a statistical ensemble comprised of fundamentally different solutions leading to wrong mean values and uncertainty estimates, whereas clustering provides an efficient way to deal with this type of computation. This work is important for developing Gen IV nuclear systems because many of these systems rely on natural convection for cooling especially in accident conditions.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Photoinduced Electron Transfer Informs on Pathway Coupling in Flavin-Based Electron Bifurcation

Flavin-based electron bifurcation (FBEB) is an enzymatic mechanism that generates extremely high-energy electrons to drive unfavorable chemical reactions. It is utilized by the NADHdependent ferredoxin:NADP + -oxidoreductase (Nfn) enzyme in hyperthermophile Pyrococcus furiosus to bifurcate electrons from NADPH into the coupled low-potential (endergonic) and highpotential (exergonic) pathways. This process enables P. furiosus to live in harsh and uninviting environments. Despite its biological importance, the mechanisms used by Nfn to facilitate exceptional directional control over short-lived, high-energy electrons and to prevent undesired transfer, particularly along the low-potential pathway, are still not well understood. To elucidate how the protein environment contributes to electronic control in the lowpotential pathway, new techniques must be utilized to probe these unstable intermediates. In this study, we have adapted lowtemperature photoexcitation combined with electron paramagnetic resonance (EPR) to accumulate the short-lived intermediate and place it in the context of the other cofactors involved in the low-potential pathway of Nfn. We observed coincident growth of both the radical intermediate and its nearby [4Fe-4S] cluster over 4.5 h of illumination with NADPH at cryogenic temperatures. The photogenerated paramagnetic species were stable in LN 2 storage indefinitely and recombined when warmed to higher temperatures. The results provide insights into the electron transfer steps and cofactor interactions along the low potential pathway, facilitating a more robust mechanistic understanding of the high-energy events of electron bifurcation. Furthermore, through comparison of cryogenic and room temperature experiments, a potential gating step involving the movement of key residues important for the reversibility of electron flow along this pathway is suggested.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Electron bifurcation: progress and grand challenges

Electron bifurcation moves electrons from a two-electron donor to reduce two spatially separated one-electron acceptors. If one of the electrons reduces a high-potential (lower energy) acceptor, then the other electron may proceed “uphill” to reduce a low-potential (higher energy) acceptor. This mechanism is now considered the third mode of energy transduction in biology, and offers promise for the development of novel bioinspired energy conversion strategies. Nature uses electron bifurcation to realize highly sought-after reactions: reversible CO 2 reduction, nitrogen fixation, and hydrogen production. In this review, we summarize the current understanding of electron bifurcation, including both recent progress and outstanding questions in understanding and developing artificial EB systems.

09 BIOMASS FUELS↗

DOE OSTI2026

Mechanistic implications of excited high-spin states, spin–spin coupling, and differential [2Fe–2S] + cluster temperature relaxations in the electron-bifurcating NfnABC from Thermococcus sibiricus

Electron bifurcation (EB) is a mechanism of biological energy transduction in which multiple oxidation–reduction (redox) reactions are thermodynamically coupled within a single enzyme, enabling the enzyme to harness the excess free energy from an exergonic process to drive an endergonic process. Because of this unprecedented chemistry, there is interest to translate EB principles to artificial and bioengineered systems, but a hurdle is that knowledge pertaining to the fundamental design principles of EB enzymes remains scarce. Here, we investigated the fundamental physical and electronic properties of electron transfer sites in a spectroscopically uncharacterized member of the BfuABC family of EB enzymes, the NADH-dependent reduced-ferredoxin:NADP + oxidoreductase from Thermococcus sibiricus (Tsi NfnABC). Cryo-EM structures of Tsi NfnABC previously demonstrated that it contains twelve redox cofactors: two flavins (one FAD and one FMN), eight [4Fe–4S] clusters, and two [2Fe–2S] clusters. The FMN, one [4Fe–4S] cluster, and one [2Fe–2S] cluster comprise the bifurcating active site termed the electron-bifurcating flavobicluster (BF-FBC), which is found in all BfuABC family members. By using electron paramagnetic resonance spectroscopy, we identified spectral signatures originating from interactions between the FMN radical and [4Fe–4S] + cluster in the BF-FBC and observed temperature dependent behavior of the BF-FBC's [2Fe–2S] + cluster indicative of moderately slow spin–lattice relaxation. Additionally, we uncovered numerous spectral features corresponding to half-integer, S > ½ spin states of [4Fe–4S] + clusters, including one attributable to the consequences of lysine-ligation of a [4Fe–4S] cluster unique to NfnABC. We contextualize these findings to electron transfer theory and NfnABC's structure. Our insights further the understanding of how enzymes are designed to exert control over electron transfer to conduct thermodynamically challenging reactions.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2014

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Transitions and bifurcations of transient natural convection in a horizontal annulus with radiatively participating medium are numerically investigated using the coupled lattice Boltzmann and direct collocation meshless (LB-DCM) method. As a hybrid approach based on a common multi-scale Boltzmann-type model, the LB-DCM scheme is easy to implement and has an excellent flexibility in dealing with the irregular geometries. Separate particle distribution functions in the LBM are used to calculate the density field, the velocity field and the thermal field. In the radiatively participating medium, the contribution of thermal radiation to natural convection must be taken into account, and it is considered as a radiative term in the energy equation that is solved by the meshless method with moving least-squares (MLS) approximation. The occurrence of various instabilities and bifurcative phenomena is analyzed for different Rayleigh number Ra and Prandtl number Pr with and without radiation. Then, bifurcation diagrams and dual solutions are presented for relevant radiative parameters, such as convection-radiation parameter Rc and optical thickness τ. Numerical results show that the presence of volumetric radiation changes the static temperature gradient of the fluid, and generally results in an increase in the flow critical value. Besides, the existence and development of dual solutions of transient convection in the presence of radiation are greatly affected by radiative parameters. Finally, the advantage of LB-DCM combination is discussed, and the potential benefits of applying the LB-DCM method to multi-field coupling problems are demonstrated.

42 ENGINEERING↗

DOE OSTI2014

On noise induced Poincaré–Andronov–Hopf bifurcation

It has been numerically seen that noise introduces stable well-defined oscillatory state in a system with unstable limit cycles resulting from subcritical Poincaré–Andronov–Hopf (or simply Hopf) bifurcation. This phenomenon is analogous to the well known stochastic resonance in the sense that it effectively converts noise into useful energy. Herein, we clearly explain how noise induced imperfection in the bifurcation is a generic reason for such a phenomenon to occur and provide explicit analytical calculations in order to explain the typical square-root dependence of the oscillations' amplitude on the noise level below a certain threshold value. Also, we argue that the noise can bring forth oscillations in average sense even in the absence of a limit cycle. Thus, we bring forward the inherent general mechanism of the noise induced Hopf bifurcation naturally realisable across disciplines.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Bifurcation of resistive wall mode dynamics predicted by magnetohydrodynamic-kinetic hybrid theory

The magnetohydrodynamic-kinetic hybrid theory has been extensively and successfully applied for interpreting experimental observations of macroscopic, low frequency instabilities, such as the resistive wall mode, in fusion plasmas. In this work, it is discovered that an analytic version of the hybrid formulation predicts a bifurcation of the mode dynamics while varying certain physical parameters of the plasma, such as the thermal particle collisionality or the ratio of the thermal ion to electron temperatures. This bifurcation can robustly occur under reasonably large parameter spaces as well as with different assumptions, for instance, on the particle collision model. Qualitatively similar bifurcation features are also observed in full toroidal computations presented in this work, based on a non-perturbative hybrid formulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Bifurcations and chaos of a vibration isolation system with magneto-rheological damper

Magneto-rheological (MR) damper possesses inherent hysteretic characteristics. We investigate the resulting nonlinear behaviors of a two degree-of-freedom (2-DoF) MR vibration isolation system under harmonic external excitation. A MR damper is identified by employing the modified Bouc-wen hysteresis model. By numerical simulation, we characterize the nonlinear dynamic evolution of period-doubling, saddle node bifurcating and inverse period-doubling using bifurcation diagrams of variations in frequency with a fixed amplitude of the harmonic excitation. The strength of chaos is determined by the Lyapunov exponent (LE) spectrum. Semi-physical experiment on the 2-DoF MR vibration isolation system is proposed. We trace the time history and phase trajectory under certain values of frequency of the harmonic excitation to verify the nonlinear dynamical evolution of period-doubling bifurcations to chaos. The largest LEs computed with the experimental data are also presented, confirming the chaotic motion in the experiment. We validate the chaotic motion caused by the hysteresis of the MR damper, and show the transitions between distinct regimes of stable motion and chaotic motion of the 2-DoF MR vibration isolation system for variations in frequency of external excitation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Bifurcation, chaos, and scan instability in dynamic atomic force microscopy

The dynamical motion at any point on the cantilever of an atomic force microscope can be expressed quite generally as a superposition of simple harmonic oscillators corresponding to the vibrational modes allowed by the cantilever shape. Central to the dynamical equations is the representation of the cantilever-sample interaction force as a polynomial expansion with coefficients that account for the interaction force “stiffness,” the cantilever-to-sample energy transfer, and the displacement amplitude of cantilever oscillation. Renormalization of the cantilever beam model shows that for a given cantilever drive frequency cantilever dynamics can be accurately represented by a single nonlinear mass-spring model with frequency-dependent stiffness and damping coefficients [S. A. Cantrell and J. H. Cantrell, J. Appl. Phys. 110, 094314 (2011)]. Application of the Melnikov method to the renormalized dynamical equation is shown to predict a cascade of period doubling bifurcations with increasing cantilever drive force that terminates in chaos. The threshold value of the drive force necessary to initiate bifurcation is shown to depend strongly on the cantilever setpoint and drive frequency, effective damping coefficient, nonlinearity of the cantilever-sample interaction force, and the displacement amplitude of cantilever oscillation. The model predicts the experimentally observed interruptions of the bifurcation cascade for cantilevers of sufficiently large stiffness. Operational factors leading to the loss of image quality in dynamic atomic force microscopy are addressed, and guidelines for optimizing scan stability are proposed using a quantitative analysis based on system dynamical parameters and choice of feedback loop parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Quasi-adiabatic dynamics of ions in a bifurcated current sheet

The study is devoted to ion dynamics in bifurcated current sheets with a two-peak current-density distribution observed in the Earth's magnetotail and solar wind. The ion motion is described by a Hamiltonian system with two degrees of freedom. The presence of a small parameter {kappa} characterizing the ratio between the amplitudes of the normal and tangential magnetic field components allows one to separate variables into fast and slow ones and introduce the quasi-adiabatic invariant of motion I{sub z}. Conservation of this invariant makes it possible to analytically describe the dynamics of charged particles. Deviations of the particle dynamics from the quasi-adiabatic one, which are caused by the nonconservation of the quasi-adiabatic invariant, are investigated. The jump of the invariant {Delta}I{sub z} is shown to depend on the small parameter according to the power-law {Delta}I{sub z} {approx} {kappa}{sup h}, where the exponent h varies between unity and 3/4, depending on the level of current sheet bifurcation. The obtained dependence of {Delta}I{sub z} on {kappa} coincides with analytic expressions in the limiting cases of nonbifurcated and completely bifurcated current sheets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

The Role of Mass Spectrometry in Structural Studies of Flavin-Based Electron Bifurcating Enzymes

For decades, biologists and biochemists have taken advantage of atomic resolution structural models of proteins from X-ray crystallography, nuclear magnetic resonance spectroscopy, and more recently cryo-electron microscopy. However, not all proteins relent to structural analyses using these approaches, and as the depth of knowledge increases, additional data elucidating a mechanistic understanding of protein function is desired. Flavin-based electron bifurcating enzymes, which are responsible for producing high energy compounds through the simultaneous endergonic and exergonic reduction of two intercellular electron carriers (i.e., NAD + and ferredoxin) are one class of proteins that have challenged structural biologists and in which there is great interest to understand the mechanism behind electron gating. A limited number of X-ray crystallography projects have been successful; however, it is clear that to understand how these enzymes function, techniques that can reveal detailed in solution information about protein structure, dynamics, and interactions involved in the bifurcating reaction are needed. In this review, we cover a general set of mass spectrometry-based techniques that, combined with protein modeling, are capable of providing information on both protein structure and dynamics. Techniques discussed include surface labeling, covalent cross-linking, native mass spectrometry, and hydrogen/deuterium exchange. We cover how biophysical data can be used to validate computationally generated protein models and develop mechanistic explanations for regulation and performance of enzymes and protein complexes. Our focus will be on flavin-based electron bifurcating enzymes, but the broad applicability of the techniques will be showcased.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Site-Differentiated Iron–Sulfur Cluster Ligation Affects Flavin-Based Electron Bifurcation Activity

Electron bifurcation is an elegant mechanism of biological energy conversion that effectively couples three different physiologically relevant substrates. As such, enzymes that perform this function often play critical roles in modulating cellular redox metabolism. One such enzyme is NADH-dependent reduced-ferredoxin: NADP+ oxidoreductase (NfnSL), which couples the thermodynamically favorable reduction of NAD+ to drive the unfavorable reduction of ferredoxin from NADPH. The interaction of NfnSL with its substrates is constrained to strict stoichiometric conditions, which ensures minimal energy losses from non-productive intramolecular electron transfer reactions. However, the determinants for this are not well understood. One curious feature of NfnSL is that both initial acceptors of bifurcated electrons are unique iron–sulfur (FeS) clusters containing one non-cysteinyl ligand each. The biochemical impact and mechanistic roles of site-differentiated FeS ligands are enigmatic, despite their incidence in many redox active enzymes. Herein, we describe the biochemical study of wild-type NfnSL and a variant in which one of the site-differentiated ligands has been replaced with a cysteine. Results of dye-based steady-state kinetics experiments, substrate-binding measurements, biochemical activity assays, and assessments of electron distribution across the enzyme indicate that this site-differentiated ligand in NfnSL plays a role in maintaining fidelity of the coordinated reactions performed by the two electron transfer pathways. Given the commonality of these cofactors, our findings have broad implications beyond electron bifurcation and mechanistic biochemistry and may inform on means of modulating the redox balance of the cell for targeted metabolic engineering approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRSDate not supplied

AMOC Stability in GISS-E2-1-G: A Case of Stochastic Bifurcation

A 10-member ensemble simulation using the NASA GISS-E2-1-G climate model shows a clear bifurcation in the Atlantic Meridional Overturning Circulation (AMOC) strength under the SSP2-4.5 future scenario, leading to 8 stable AMOC-on and 2 stable AMOC-off climate states after 400 years of integration, despite identical forcing of each ensemble member. Ocean models have previously shown a tipping point where sufficient forcing (e.g. by freshwater inputs) can shut down the AMOC. A variety of fully coupled models have demonstrated this, either through hosing experiments or increased precipitation and warming at high latitudes due to increased concentrations of greenhouse gases. In the GISS simulations, there are no external freshwater perturbations. The bifurcation arises freely in the coupled system and is the result of stochastic variability associated with sea-ice transport and melting in the Irminger Sea following a slowing of the GHG concentration increase at the end of the twenty-first century. We believe this is the first time that a CMIP-class model has shown such a bifurcation across an initial condition ensemble.

GISS ModelE2.1↗

NASA NTRSDate not supplied

Bypass Duct Acoustic Liner Design With and Without Bifurcation Effects

The growth in air traffic and the commitment to sustainable aviation continue to provide new challenges to reducing aircraft noise levels. Acoustic liner design methodologies must therefore provide the capability to efficiently predict the acoustic benefits of novel liner configurations within complex aircraft nacelle geometries. With these observations in mind, a broadband acoustic liner optimization process has been developed and assessed through a series of design and experimental studies at increasing technology readiness levels. This work applies the design process to the aft-fan noise component and explores the effects of bypass duct bifurcations (e.g., the pylon and lower bifurcation). In addition to this new application, the design study is expanded to include the use of a commercially available duct propagation code. Despite the different general workflow for the two propagation codes, consistent optimized impedance spectra and in-duct attenuation predictions were obtained for several acoustic treatment options. The preliminary results are promising, and this work increases confidence in the enhanced broadband liner design methodology and lays the groundwork for complimentary use of the codes in future studies. The potential benefits of acoustic treatment on the upper and lower bifurcations are also demonstrated. The knowledge gained through this preliminary stage of the liner design process will be used to guide the identification of candidate liner designs for a proposed static engine test within the next year.

Acoustic Liner Design↗

NASA NTRSDate not supplied

Bypass Duct Acoustic Liner Design with and without Bifurcation Effects

Acoustic Liner Design↗

DOE OSTI2017

A “Train-Track” Technique in Anatomic Reconstruction of SVC Bifurcation Complicated by Cardiac Tamponade: An Introspection

This report describes a stenting technique used to anatomically reconstruct superior vena cava (SVC) bifurcation in a patient with benign SVC syndrome. After recanalizing the SVC bifurcation, we exchanged two 0.035-in. wires for two 0.018-in. wires, deployed the SVC stent over these two wires (“train-track” technique), and stented each innominate vein over one wire. However, our decisions to recanalize both innominate veins, use the “buddy-wire” technique for SVC dilation, and dilate the SVC to 16 mm before stent deployment likely contributed to SVC tear, which was managed by resuscitation, SVC stent placement, and pericardial drainage. Here, we describe the steps of the train-track technique, which can be adopted to reconstruct other bifurcations; we also discuss the controversial aspects of this case.

62 RADIOLOGY AND NUCLEAR MEDICINE↗