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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The Kalai-Smorodinsky solution for many-objective Bayesian optimization

An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the R package GPGame available on CRAN at https://cran.r-project.org/package=GPGame.

Game theory↗
NASA NTRS1985

Shape Preserving Spline Interpolation

A rational spline solution to the problem of shape preserving interpolation is discussed. The rational spline is represented in terms of first derivative values at the knots and provides an alternative to the spline-under-tension. The idea of making the shape control parameters dependent on the first derivative unknowns is then explored. The monotonic or convex shape of the interpolation data can then be preserved automatically through the solution of the resulting non-linear consistency equations of the spline.

Gregory, J. A.↗
DOE OSTI2023

An Incremental Gradient Method for Optimization Problems With Variational Inequality Constraints

We consider minimizing a sum of agent-specific nondifferentiable merely convex functions over the solution set of a variational inequality (VI) problem in that each agent is associated with a local monotone mapping. This problem finds an application in computation of the best equilibrium in nonlinear complementarity problems arising in transportation networks. We develop an iteratively regularized incremental gradient method where at each iteration, agents communicate over a directed cycle graph to update their solution iterates using their local information about the objective and the mapping. The proposed method is single-timescale in the sense that it does not involve any excessive hard-to-project computation per iteration. We derive nonasymptotic agent-wise convergence rates for the suboptimality of the global objective function and infeasibility of the VI constraints measured by a suitably defined dual gap function. Finally, the proposed method appears to be the first fully iterative scheme equipped with iteration complexity that can address distributed optimization problems with VI constraints over cycle graphs.

convergence↗
NASA NTRS2005

Analysis of Slope Limiters on Irregular Grids

This paper examines the behavior of flux and slope limiters on non-uniform grids in multiple dimensions. Many slope limiters in standard use do not preserve linear solutions on irregular grids impacting both accuracy and convergence. We rewrite some well-known limiters to highlight their underlying symmetry, and use this form to examine the proper - ties of both traditional and novel limiter formulations on non-uniform meshes. A consistent method of handling stretched meshes is developed which is both linearity preserving for arbitrary mesh stretchings and reduces to common limiters on uniform meshes. In multiple dimensions we analyze the monotonicity region of the gradient vector and show that the multidimensional limiting problem may be cast as the solution of a linear programming problem. For some special cases we present a new directional limiting formulation that preserves linear solutions in multiple dimensions on irregular grids. Computational results using model problems and complex three-dimensional examples are presented, demonstrating accuracy, monotonicity and robustness.

Berger, Marsha↗
NASA NTRS1994

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

Slack, David C.↗
DOE OSTI2022

Complex pH-Dependent Interactions between Weak Polyelectrolyte Block Copolymer Micelles and Molecular Fluorophores

Amphiphilic block copolymers with weak polyelectrolyte blocks can assemble stimulus-responsive nanostructures and interfaces. Applications of these materials in drug delivery, biomimetics, and sensing largely rely on the well-understood swelling of polyelectrolyte chains upon deprotonation, often induced by changes in pH or ionic strength. This deprotonation can also tune interfacial interactions between the polyelectrolyte blocks and surrounding solution, an effect which is less studied than morphological swelling of polyelectrolytes but can be just as critical for intended function. Here, we investigate whether the pH-driven morphological response of polyelectrolyte-bearing nanostructures also affects the interactions of these nanostructures with molecules in solution, using micelles of a short-chain polybutadiene-block-poly(acrylic acid) (pBd–pAA) as a model system. Here we introduce a Förster resonance energy transfer (FRET) approach to probe interactions between micelles and fluorescent molecular solutes as a function of solution pH. As expected, the pAA corona of these pBd–pAA micelles increases in thickness monotonically as a function of pH. However, FRET efficiency, which provides a metric of the spatial proximity of fluorescently labeled micelles and freely diffusing fluorophores, exhibits complex nonmonotonic behavior as a function of pH, indicating that the average separation of micelles and acceptor fluorophores is not strictly correlated with micelle swelling. Dialysis experiments quantify the affinity of fluorophores for micelles as a function of pH, confirming that changes in FRET are driven almost entirely by the pH-dependent affinity of the pAA block for the investigated molecular fluorophores, not simply by a shape change of the pAA corona. This study provides key insights into the interfacial interactions between weak-polyelectrolyte-bearing nanostructures and molecular solutes, of importance for the development of their stimulus-responsive applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2022

Stability of the Dual-Frequency Radar Equations and a New Method Applied to the GPM’s Dual-Frequency Precipitation Radar (DPR) Data

A new algorithm is proposed that estimates two parameters of the particle size distribution (PSD) at each range bin from the Global Precipitation Measurement’s (GPM’s) Dual-frequency Precipitation Radar data. The equation that expresses the relationship of the PSD parameters between adjacent range bins is derived. By including the attenuation effect within the bin in the discretized equation, the new algorithm alleviates the double-solution problem when attenuation within the bin is sufficiently large. The stability of the solutions to the equation depends on the value of the mean diameter D(sub m) and its gradient with respect to range in the case of liquid precipitation. If the critical diameter above which the dual-frequency ratio (DFR) of radar reflectivity factors becomes a monotonically increasing function of D(sub m), the backward processing of the equation provides a stable or moderately diverging solution, unlike the forward processing that often gives unstable solutions. To provide a set of initial conditions without using the surface reference technique (SRT) in the backward processing, an initialization method using the Hitschfeld-Bordan attenuation correction method is proposed and tested. The proposed algorithm may provide a tool for investigating the assumptions used in various algorithms.

GPM↗
NASA NTRS1993

A solution scheme for the Euler equations based on a multi-dimensional wave model

A scheme for the solution of scalar advection on an unstructured mesh has been developed, tested, and extended to the Euler equations. The scheme preserves a linear function exactly, and yields nearly monotone results. The flux function associated with the Euler scheme is based on a discrete 'wave model' for the system of equations. The wave model decomposes the solution gradient at a location into shear waves, entropy waves and acoustic waves and calculates the speeds, strengths and directions associated with the waves. The approach differs from typical flux-difference splitting schemes in that the waves are not assumed to propagate normal to the faces of the control volumes; directions of propagation of the waves are instead computed from solution-gradient information. Results are shown for three test cases, and two different wave models. The results are compared to those from other approaches, including MUSCL and Galerkin least squares schemes.

Powell, Kenneth G.↗
DOE OSTI2021

Temperature-Dependent Configurational Entropy Calculations for Refractory High-Entropy Alloys

The cluster expansion formalism for alloys is used to construct surrogate models for three refractory high-entropy alloys (NbTiVZr, HfNbTaTiZr, and AlHfNbTaTiZr). These cluster expansion models are then used along with Monte Carlo methods and thermodynamic integration to calculate the configurational entropy of these refractory high-entropy alloys as a function of temperature. Many solid solution alloy design guidelines are based on the ideal entropy of mixing, which increases monotonically with N , the number of elements in the alloy. However, our results show that at low temperatures, the configurational entropy of these materials is largely independent of N , and the assumption described above only holds in the high-temperature limit. This suggests that alloy design guidelines based on the ideal entropy of mixing require further examination.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Computational thermomechanics for crystalline rock. Part II: Chemo-damage-plasticity and healing in strongly anisotropic polycrystals

We present a thermal–mechanical–chemical-phase field model that captures the multi-physical coupling effects of precipitation creeping, crystal plasticity, anisotropic fracture, and crack healing in polycrystalline rock at various temperature and strain-rate regimes. This model is solved via a fast Fourier transfer solver with an operator-split algorithm to update displacement, temperature and phase field, and chemical concentration incrementally. In nuclear waste disposal in salt formation, brine inside the crystal salt may migrate along the grain boundary and cracks due to the gradient of interfacial energy and pressure. This migration has a significant implication on the permeability evolution, creep deformation, and crack healing within rock salt but is difficult to incorporate implicitly via effective medium theories compared with computational homogenization. As such, we introduce a thermodynamic framework and a corresponding computational implementation that explicitly captures the brine diffusion along the grain boundary and crack at the grain scale. Meanwhile, the anisotropic fracture and healing are captured via a high-order phase field that represents the regularized crack region in which a newly derived non-monotonic driving force is used to capture the fracture and healing due to the solution–precipitation. Numerical examples are presented to demonstrate the capacity of the thermodynamic framework to capture the multiphysics material behaviors of rock salt.

42 ENGINEERING↗
NASA NTRS1985

Momentum-dependent diffusive particle acceleration in modified shock fronts

In the presently derived analytic solutions of the steady transport equation for diffusive particle acceleration in a modified, planar shock front having free escape boundaries, the fluid velocity profile through the shock transition decreases monotonically between the upstream and downstream boundaries. The spatial diffusion coefficient's spatial dependence is linked to that of the fluid velocity profile. Attention is given to the solution corresponding to monoenergetic particle injection at the shock front, with free particle escape at finite distances both upstream and downstream of the shock. The accelerated particle spectrum is dominated at high energies by an exponential cutoff, due to the competition between acceleration by the first-order Fermi mechanism and particle loss through the free escape boundaries.

Webb, G. M.↗
NASA NTRS1994

Numerical investigation of separated nozzle flows

A numerical study of axisymmetric overexpanded nozzle is presented. The flow structure of the startup and throttle-down processes are examined. During the impulsive startup process, observed flow features include the Mach disk, separation shock, Mach stem, vortex core, contact surface, slip stream, initial shock front, and shocklet. Also the movement of the Mach disk is not monotonical in the downstream direction. For a range of pressure ratios, hysteresis phenomenon occurs; different solutions were obtained depending on different processes. Three types of flow structures were observed. The location of separation point and the lower end turning point of hysteresis are closely predicted. A high peak of pressure is associated with the nozzle flow reattachment. The reversed vortical structure and affects engine performance.

Chen, C. L.↗
NASA NTRS1996

Excess chemical potential of small solutes across water--membrane and water--hexane interfaces

The excess chemical potentials of five small, structurally related solutes, CH4, CH3F, CH2F2, CHF3, and CF4, across the water-glycerol 1-monooleate bilayer and water-hexane interfaces were calculated at 300, 310, and 340 K using the particle insertion method. The excess chemical potentials of nonpolar molecules (CH4 and CF4) decrease monotonically or nearly monotonically from water to a nonpolar phase. In contrast, for molecules that possess permanent dipole moments (CH3F, CH2F, and CHF3), the excess chemical potentials exhibit an interfacial minimum that arises from superposition of two monotonically and oppositely changing contributions: electrostatic and nonelectrostatic. The nonelectrostatic term, dominated by the reversible work of creating a cavity that accommodates the solute, decreases, whereas the electrostatic term increases across the interface from water to the membrane interior. In water, the dependence of this term on the dipole moment is accurately described by second order perturbation theory. To achieve the same accuracy at the interface, third order terms must also be included. In the interfacial region, the molecular structure of the solvent influences both the excess chemical potential and solute orientations. The excess chemical potential across the interface increases with temperature, but this effect is rather small. Our analysis indicates that a broad range of small, moderately polar molecules should be surface active at the water-membrane and water-oil interfaces. The biological and medical significance of this result, especially in relation to the mechanism of anesthetic action, is discussed.

NASA Center ARC↗
DOE OSTI2022

Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian

Abstract Ising spin Hamiltonians are often used to encode a computational problem in their ground states. Quantum Annealing (QA) computing searches for such a state by implementing a slow time-dependent evolution from an easy-to-prepare initial state to a low energy state of a target Ising Hamiltonian of quantum spins, H I . Here, we point to the existence of an analytical solution for such a problem for an arbitrary H I beyond the adiabatic limit for QA. This solution provides insights into the accuracy of nonadiabatic computations. Our QA protocol in the pseudo-adiabatic regime leads to a monotonic power-law suppression of nonadiabatic excitations with time T of QA, without any signature of a transition to a glass phase, which is usually characterized by a logarithmic energy relaxation. This behavior suggests that the energy relaxation can differ in classical and quantum spin glasses strongly, when it is assisted by external time-dependent fields. In specific cases of H I , the solution also shows a considerable quantum speedup in computations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Characterizing the Impacts of Multi-Scale Heterogeneity on Solute Transport in Fracture Networks

We model flow and transport in fracture networks with varying degrees of fracture-to-fracture aperture heterogeneity and network intensity to show how changes in these properties can cause the emergence of anomalous flow and transport behavior. If fracture-to-fracture aperture heterogeneity is increased in sparse networks, velocity fluctuations inhibit high flow rates and solute transport can be delayed. Surprisingly, transport can be slowed even in cases where hydraulic aperture is monotonically increased. As the intensity of the networks is increased, more connected pathways allow for particles to bypass these effects. There exists transition behavior where with relatively few connected pathways in a network, first arrival times of particles are not heavily affected by fracture-to-fracture aperture heterogeneity, but the scaling behavior of the tails is strongly influenced. These results reinforce the importance of considering multi-scale effects in fractured systems and can inform flow and transport processes in both natural and engineered fractured systems.

58 GEOSCIENCES↗
DOE OSTI2026

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

On the design of stable, consistent, and conservative high-order methods for multi-material hydrodynamics

Obtaining stable and high-order numerical solutions for multi-material hydrodynamics is an open challenge. Although slope limiters are widely used to maintain monotonicity near discontinuities, typical limiting procedures violate closure laws at the discrete level when applied to multi-material hydrodynamics equations. Due to this, the high-order expansions of quantities related by the closure laws are no longer consistent. The commonly observed symptom of this consistency-violation is that the numerical method fails to maintain constant pressure and velocity across material interfaces. This leads to sub-optimal convergence rates for smooth multi-material problems as well. Specialized limiting procedures that satisfy consistency while maintaining conservation need to be developed for such equations. A novel procedure that re-instates consistency into slope-limited high-order discretizations applied to the multi-material hydrodynamics equations is presented here. Using simple examples, it is demonstrated that the presented method satisfies closure laws at the discrete level, while maintaining conservative properties of the high-order method. Furthermore, this procedure involves a projection step which relies on the compact basis of the underlying spatial discretization, i.e. for discontinuous schemes (viz. DG and FV) the projection is local, and does not involve global matrix solves. Comparisons with conventional approaches emphasizes the necessity of the consistent closure-law preserving limiting approach, in order to maintain design order of accuracy for smooth multi-material problems.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Electrochemistry at Back-Gated, Ultrathin ZnO Electrodes: Field-Effect Modulation of Heterogeneous Electron Transfer Rate Constants by 30× with Enhanced Gate Capacitance

We report steady-state voltammetry of outer-sphere redox species at back-gated ultrathin ZnO working electrodes in order to determine electron transfer rate constants k ET as a function of independently-controlled gate bias, V G . We demonstrate that k ET can be modulated as much as 30-fold by application of V G ≤ 8 V. Key to this demonstration was integrating the ultrathin (5 nm) ZnO on a high dielectric constant (k) insulator, HfO 2 (30 nm), which was grown on a Pd metal gate. The high-k HfO 2 dramatically decreased the required V G values and increased the gate-induced charge in ZnO compared to previous studies. Importantly, the enhanced gating power of the Pd/HfO 2 /ZnO stack meant it was possible to observe a non-monotonic dependence of k ET on V G , which reflects the inherent density of redox acceptor states in solution. Furthermore, this work adds to the growing body of literature demonstrating that electrochemical kinetics (i.e., rate constants and overpotentials) at ultrathin working electrodes can be tuned by V G , independent of the conventional electrochemical working electrode potential.

36 MATERIALS SCIENCE↗