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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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NASA NTRS1996

Effective Numerical Methods for Solving Elliptical Problems in Strengthened Sobolev Spaces

Fourth-order elliptic boundary value problems in the plane can be reduced to operator equations in Hilbert spaces G that are certain subspaces of the Sobolev space W(sub 2)(exp 2)(Omega) is identical with G(sup (2)). Appearance of asymptotically optimal algorithms for Stokes type problems made it natural to focus on an approach that considers rot w is identical with (D(sub 2)w - D(sub 1)w) is identical with vector of u as a new unknown vector-function, which automatically satisfies the condition div vector of u = 0. In this work, we show that this approach can also be developed for an important class of problems from the theory of plates and shells with stiffeners. The main mathematical problem was to show that the well-known inf-sup condition (normal solvability of the divergence operator) holds for special Hilbert spaces. This result is also essential for certain hydrodynamics problems.

D'yakonov, Eugene G.↗

NASA NTRS1991

An exact algebraic solution of the infimum in H-infinity optimization with output feedback

This paper presents a simple and noniterative procedure for the computation of the exact value of the infimum in the standard H-infinity-optimal control with output feedback. The problem formulation is general and does not place any restrictions on the direct feedthrough terms between the control input and the controlled output variables, and between the disturbance input and the measurement output variables. The method is applicable to systems that satisfy (1) the transfer function from the control input to the controlled output is right-invertible and has no invariant zeros on the j(w) axis and, (2) the transfer function from the disturbance to the measurement output is left-invertible and has no invariant zeros on the j(w) axis. A set of necessary and sufficient conditions for the solvability of H-infinity-almost disturbance decoupling problem via measurement feedback with internal stability is also given.

Chen, Ben M.↗

DOE OSTI2020

Integrable multistate Landau–Zener models with parallel energy levels

In this paper, we discuss solvable multistate Landau–Zener (MLZ) models whose Hamiltonians have commuting partner operators with ~1/τ-time-dependent parameters. Many already known solvable MLZ models belong precisely to this class. We derive the integrability conditions on the parameters of such commuting operators, and demonstrate how to use such conditions in order to derive new solvable cases. We show that MLZ models from this class must contain bands of parallel diabatic energy levels. The structure of the scattering matrix and other properties are found to be the same as in the previously discussed completely solvable MLZ Hamiltonians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1975

Estimation and Analysis of Nonlinear Stochastic Systems

The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were discussed. Two classes of estimation problems involving bilinear systems were considered. It was proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. The theory of harmonic analysis was used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.

Marcus, S. I.↗

NASA NTRS1991

Shape selection criterion for cellular array during constrained growth of binary alloys - Need for low gravity experiment

Development of steady-state periodic cellular array is one of the critical problems in the study of nonlinear pattern formation during directional solidification of binary alloys. The criterion which establishes the values of cell tip radius and spacing under given growth condition is not known. Theoretical models, such as marginal stability and microscopic solvability, have been developed for purely diffusive regime. However, the experimental conditions where cellular structures are stable are precisely the ones where the convection effects are predominant. Thus, the critical data for meaningful evaluation of cellular array growth models can only be obtained by partial directional solidification and quenching experiments carried out in the low gravity environment of space.

Tewari, Surendra N.↗

DOE OSTI2022

MIDAS-DC-AC Tool: Fully Automating the Acquisition of AC Power Flow Solution (MIDAS-DC2AC)

MIDAS DC2AC is an automated tool for achieving a converged AC power flow solution from any dispatch, e.g., determined using DC power flow model based optimal power flow. The entire process is free of human interference. It is usually encountered in practice that, even with a DC power flow solution, acquiring the solved AC power flow solution, if exists, sometimes could be a challenging task, especially during the planning stage. It is also difficult to distinguish the unsolvable cases from diverging iterations. Manual adjustments to approach the desired power flow condition has been largely relied on in the past using lots of engineering heuristics. This tool provides a systematic way to first achieve a solvable AC power flow case by modifying the power flow condition, and then try to track the AC power flow solution while gradually removing the adopted changes. If all adopted changes can be completely removed, then the original AC power flow solution is obtained. Otherwise, insights for actionable controls are derived to help operation and planning. Currently, this tool has been implemented in Python using SIEMENS PTI PSS/E as power flow solver, where only adjusting generator terminal voltage set point is considered as an available means to try to turn an unsolved power flow to a solved one. In future, more means should be considered, including the operation of tap-changing transformers, switched shunts and redispatch of active power.

Tan, Jin↗

DOE OSTI2022

DC-AC Tool: Fully Automating the Acquisition of AC Power Flow Solution

DC2AC is an automated tool for achieving a converged AC power flow solution from any dispatch, e.g., determined using DC power flow model based optimal power flow. The entire process is free of human interference. It is usually encountered in practice that, even with a DC power flow solution, acquiring the solved AC power flow solution, if exists, sometimes could be a challenging task, especially during the planning stage. It is also difficult to distinguish the unsolvable cases from diverging iterations. Manual adjustments to approach the desired power flow condition has been largely relied on in the past using lots of engineering heuristics. This tool provides a systematic way to first achieve a solvable AC power flow case by modifying the power flow condition, and then try to track the AC power flow solution while gradually removing the adopted changes. If all adopted changes can be completely removed, then the original AC power flow solution is obtained. Otherwise, insights for actionable controls are derived to help operation and planning. Currently, this tool has been implemented in Python using SIEMENS PTI PSS/E as power flow solver, where only adjusting generator terminal voltage set point is considered as an available means to try to turn an unsolved power flow to a solved one. In future, more means should be considered, including the operation of tap-changing transformers, switched shunts and redispatch of active power.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1992

Tidal disruption of viscous bodies

Tidal disruptions are investigated in viscous-fluid planetesimals whose radius is small relative to the distance of closest (parabolic-orbit) approach to a planet. The planetesimal surface is in these conditions always ellipsoidal, facilitating treatment by coupled ODEs which are solvable with high accuracy. While the disrupted planetesimals evolve into needlelike ellipsoids, their density does not decrease. The validity of viscous fluid treatment holds for solid (ice or rock) planetesimals in cases where tidal stresses are greater than material strength, but integrity is maintained by self-gravity.

Sridhar, S.↗

NASA NTRS1992

Simultaneous H2/H-infinity optimal control - The state feedback case

A simultaneous H2/H-infinity control problem is considered. This problem seeks to minimize the H2 norm of a closed-loop transfer matrix while simultaneously satisfying a prescribed H-infinity norm bound on some other closed-loop transfer matrix by utilizing dynamic state feedback controllers. Such a problem was formulated earlier by Rotea and Khargonekar (1991) who considered only so called regular problems. Here, for a class of singular problems, necessary and sufficient conditions are established so that the posed simultaneous H2/H-infinity problem is solvable by using state feedback controllers. The class of singular problems considered have a left invertible transfer function matrix from the control input to the controlled output which is used for the H2 norm performance measure. This class of problems subsumes the class of regular problems.

Saberi, Ali↗

DOE OSTI2021

Modeling the Strategic Behavior of an Active Distribution Network in the ISO Markets

With increasing integration of distributed energy resources (DERs), active distribution networks (ADNs) can actively participate in the electricity markets by dispatching their DERs, which can change the existing electricity market paradigm. It is essential to investigate the strategic behaviors of ADNs and their DER dispatch when they participate in the wholesale market as price-makers. This paper proposes a bi-level optimization model to study the strategic behavior of an ADN in both energy and reserve markets. The optimal scheduling of DERs in the ADN is modeled as the upper level problem and the joint energy and reserve market-clearing of the ISO is modeled as the lower-level problem. The two-level optimization models exchange bidding information and energy/reserve prices with each other. The proposed bi-Ievel optimization problem is converted to a mathematical programming with equilibrium constraints (MPEC) by using Karush-Kuhn Tucker (KKT) conditions and strong duality theory. Further, the MPEC problem is reformulated as a computationally-solvable mixed integer second order cone programming (MISOCP) model. The simulation results on an illustrative case demonstrate the impact of the strategic bidding of the ADN on the day-ahead energy and reserve market prices.

active distribution network↗

NASA NTRS2013

Demonstration of Detection and Ranging Using Solvable Chaos

Acoustic experiments demonstrate a novel approach to ranging and detection that exploits the properties of a solvable chaotic oscillator. This nonlinear oscillator includes an ordinary differential equation and a discrete switching condition. The chaotic waveform generated by this hybrid system is used as the transmitted waveform. The oscillator admits an exact analytic solution that can be written as the linear convolution of binary symbols and a single basis function. This linear representation enables coherent reception using a simple analog matched filter and without need for digital sampling or signal processing. An audio frequency implementation of the transmitter and receiver is described. Successful acoustic ranging measurements are presented to demonstrate the viability of the approach.

Corron, Ned J.↗

DOE OSTI2021

Modeling the Strategic Behavior of an Active Distribution Network in the ISO Markets

Xue, Yaosuo↗

DOE OSTI2024

Ecosystem Water‐Saving Timescale Varies Spatially With Typical Drydown Length

Abstract Stomatal optimization theory is a commonly used framework for modeling how plants regulate transpiration in response to the environment. Most stomatal optimization models assume that plants instantaneously optimize a reward function such as carbon gain. However, plants are expected to optimize over longer timescales given the rapid environmental variability they encounter. There are currently no observational constraints on these timescales. Here, a new stomatal model is developed and is used to analyze the timescales over which stomatal closure is optimized. The proposed model assumes plants maximize carbon gain subject to the constraint that they cannot draw down soil moisture below a critical value. The reward is integrated over time, after being weighted by a discount factor that represents the timescale ( τ ) that a plant considers when optimizing stomatal conductance to save water. The model is simple enough to be analytically solvable, which allows the value of τ to be inferred from observations of stomatal behavior under known environmental conditions. The model is fitted to eddy covariance data in a range of ecosystems, finding the value of τ that best predicts the dynamics of evapotranspiration at each site. Across 82 sites, the climate metrics with the strongest correlation to τ are measures of the average number of dry days between rainfall events. Values of τ are similar in magnitude to the longest such dry period encountered in an average year. The results here shed light on which climate characteristics shape spatial variations in ecosystem‐level water use strategy.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Stochastic Strategic Participation of Active Distribution Networks With High-Penetration DERs in Wholesale Electricity Markets

With the increasing penetration of distributed energy resources (DERs), traditional distribution networks as load-serving entities in wholesale electricity markets, now evolve towards active distribution networks (ADNs) which can proactively participate in wholesale markets by optimally controlling the DERs in their networks. A stochastic bilevel optimization model is proposed in this paper for the strategic participation of ADNs and DERs to provide energy and grid services in wholesale electricity markets. The bilevel optimization model can capture the interactions between the ADN and the wholesale energy and ancillary service markets, considering the uncertainties of DERs in the ADN. In the upper-level model, the ADN makes optimal decisions on energy and reserve bidding considering the availability, uncertainties, and flexibility of DERs. The joint energy and reserve market-clearing of the independent system operator (ISO) is modeled as the lower-level problem. Using strong duality theory and Karush-Kuhn Tucker (KKT) conditions, the proposed bilevel optimization problem is reformulated as mathematical programming with equilibrium constraints (MPEC) problem and further converted into a computationally-solvable mixed-integer second-order-cone programming (MISOCP) model. The simulation results demonstrate the effectiveness of the model and the interactions between an ADN and wholesale electricity markets.

active distribution network↗

DOE OSTI2021

An explicitly solvable energy-conserving algorithm for pitch-angle scattering in magnetized plasmas

In this work, we develop an Explicitly Solvable Energy-Conserving (ESEC) algorithm for the Stochastic Differential Equation (SDE) describing the pitch-angle scattering process in magnetized plasmas. The Cayley transform is used to calculate both the deterministic gyromotion and stochastic scattering, affording the algorithm to be explicitly solvable and exactly energy conserving. An unusual property of the SDE for pitch-angle scattering is that its coefficients diverge at the zero velocity and do not satisfy the global Lipschitz condition. Consequently, when standard numerical methods, such as the Euler-Maruyama (EM), are applied, numerical convergence is difficult to establish. For the proposed ESEC algorithm, its energy-preserving property enables us to overcome this obstacle. We rigorously prove that the ESEC algorithm is order 1/2 strongly convergent. This result is confirmed by detailed numerical studies. For the case of pitch-angle scattering in a magnetized plasma with a constant magnetic field, the numerical solution is benchmarked against the analytical solution, and excellent agreements are found.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1988

Consistent boundary conditions for reduced Navier-Stokes (RNS) scheme applied to three-dimensional internal viscous flows

Three-dimensional internal viscous flow problems are presently addressed by a consistent and efficient set of boundary conditions for the multisweep space-marching, pressure-elliptic Reduced Navier-Stokes scheme. Since continuity is by this means directly satisfied at all points in the flow domain, the first-order momentum equations are directly solvable for pressure without the requirement for a Poisson pressure-correction equation. Incompressible flow solutions are obtained for straight and curved ducts of square cross section, in order to validate the procedure. Usefulness is demonstrated for internal flows with strong interactions, as would be found in turbomachine geometries.

Reddy, D. R.↗

DOE OSTI2025

Solving k –SAT problems with generalized quantum measurement

We generalize the projection–based quantum measurement–driven k –SAT algorithm of Benjamin, Zhao, and Fitzsimons to arbitrary strength quantum measurements, including the limit of continuous monitoring. In doing so, we clarify that this algorithm is a particular case of the measurement–driven quantum control strategy elsewhere referred to as “Zeno dragging”. We argue that the algorithm is most efficient with finite time and measurement resources in the continuum limit, where measurements have an infinitesimal strength and duration. Moreover, for solvable k -SAT problems, the dynamics generated by the algorithm converge deterministically towards target dynamics in the long–time (Zeno) limit, implying that the algorithm can successfully operate autonomously via Lindblad dissipation, without detection. We subsequently study both the conditional and unconditional dynamics of the algorithm implemented via generalized measurements, quantifying the advantages of detection for heralding errors. These strategies are investigated first in a computationally–trivial 2-qubit 2-SAT problem to build intuition, and then we consider the scaling of the algorithm on 3-SAT problems encoded with 4–10 qubits. We numerically investigate the scaling of 3-SAT with respect to algorithmic runtime and find that the optimized time to solution scales with qubit number n as λ n , where λ is slightly larger than $\sqrt{2}$ for unconditional dynamics and less than $\sqrt{2}$ for conditional dynamics. We assess the implications for using this analog measurement–driven approach to quantum computing in practice.

quantum information↗

NASA NTRS1983

On the stabilizability of multivariable systems by minimum order compensation

In this paper, a derivation is provided of the necessary condition, mp equal to or greater than n, for stabilizability by constant gain feedback of the generic degree n, p x m system. This follows from another of the main results, which asserts that generic stabilizability is equivalent to generic solvability of a deadbeat control problem, provided mp equal to or less than n. Taken together, these conclusions make it possible to make some sharp statements concerning minimum order stabilization. The techniques are primarily drawn from decision algebra and classical algebraic geometry and have additional consequences for problems of stabilizability and pole-assignability. Among these are the decidability (by a Sturm test) of the equivalence of generic pole-assignability and generic stabilizability, the semi-algebraic nature of the minimum order, q, of a stabilizing compensator, and the nonexistence of formulae involving rational operations and extraction of square roots for pole-assigning gains when they exist, answering in the negative a question raised by Anderson, Bose, and Jury (1975).

Byrnes, C. I.↗