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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Galvanostatic Intermittent Titration Technique Reinvented: Part I. A Critical Review

The galvanostatic intermittent titration technique (GITT), introduced in 1977 by Weppner and Huggins, provided a readily accessible means to measuring the chemical diffusion coefficient of electrochemical electrode materials. The method continues to be widely used today, but the reported diffusivity values are highly inconsistent, ranging as much as four orders of magnitude for some Li layered oxide compositions. Even qualitative trends of diffusivity are inconsistent, suggesting significant flaws in the implementation of the method. Other variants of the GITT method also suffer from similar inconsistency problems. Here we identify numerous sources of significant error including composition-dependent reaction overpotentials, mathematical flaws in the relaxation analysis methods, finite-size and non-planar geometry effects, inter-particle inhomogeneity issues, early transient effects, and surface area uncertainties. We propose a simple relaxation analysis scheme using the time variable t relax + τ - t relax , where t relax is relaxation time and τ is the galvanostatic pulse duration. We also propose to use dense diffusion-limited samples to isolate the bulk-diffusion process in the time domain. Chemical diffusivity can be extracted much more reliably with this improved implementation of the GITT method.

25 ENERGY STORAGE↗
DOE OSTI2015

A Relaxation Approach to Vector-Valued Allen–Cahn MPEC Problems

In this paper we consider a vector-valued Allen–Cahn MPEC problem. To derive optimality conditions we exploit a regularization–relaxation technique. The optimality system of the regularized–relaxed subproblems are investigated by applying the classical result of Zowe and Kurcyusz. Finally we show that the stationary points of the regularized–relaxed subproblems converge to weak stationary points of the limit problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation

A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Lastly, dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Learning Optimal Multigrid Smoothers via Neural Networks

Multigrid methods are one of the most efficient techniques for solving large sparse linear systems arising from partial differential equations (PDEs) and graph Laplacians from machine learning applications. One of the key components of multigrid is smoothing, which aims at reducing high-frequency errors on each grid level. However, finding optimal smoothing algorithms is problem-dependent and can impose challenges for many problems. In this paper, we propose an efficient adaptive framework for learning optimized smoothers from operator stencils in the form of convolutional neural networks (CNNs). Here, the CNNs are trained on small-scale problems from a given type of PDEs based on a supervised loss function derived from multigrid convergence theories and can be applied to large-scale problems of the same class of PDEs. Numerical results on anisotropic rotated Laplacian problems and variable coefficient diffusion problems demonstrate improved convergence rates and solution time compared with classical hand-crafted relaxation methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Transient viscoelasticity study of tobacco mosaic virus/Ba2+ superlattice

Recently, we reported a new method to synthesize the rod-like tobacco mosaic virus (TMV) superlattice. To explore its potentials in nanolattice templating and tissue scaffolding, this work focused the viscoelasticity of the superlattice with a novel transient method via atomic force microscopy (AFM). For measuring viscoelasticity, in contrast to previous methods that assessed the oscillating response, the method proposed in this work enabled us to determine the transient response (creep or relaxation) of micro/nanobiomaterials. The mathematical model and numerical process were elaborated to extract the viscoelastic properties from the indentation data. The adhesion between the AFM tip and the sample was included in the indentation model. Through the functional equation method, the elastic solution for the indentation model was extended to the viscoelastic solution so that the time dependent force vs. displacement relation could be attained. To simplify the solving of the differential equation, a standard solid model was modified to obtain the elastic and viscoelastic components of the sample. The viscoelastic responses with different mechanical stimuli and the dynamic properties were also investigated.

36 MATERIALS SCIENCE↗
DOE OSTI2021

The impacts of convex piecewise linear cost formulations on AC optimal power flow

Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration of this is the treatment of power generation cost functions, where nonlinear network optimization has largely used polynomial representations and market optimization has adopted piecewise linear encodings. This work combines state-of-the-art results from both lines of research to understand the best mathematical formulations of the nonlinear AC optimal power flow problem with piecewise linear generation cost functions. An extensive numerical analysis of non-convex models, linear approximations, and convex relaxations across fifty-four realistic test cases illustrates that nonlinear optimization methods are surprisingly sensitive to the mathematical formulation of piecewise linear functions. The results indicate that a poor formulation choice can slow down algorithm performance by a factor of ten, increasing the runtime from seconds to minutes. Furthermore, these results provide valuable insights into the best formulations of nonlinear optimal power flow problems with piecewise linear cost functions, an important step towards building a new generation of energy markets that incorporate the nonlinear AC power flow model.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2015

Dynamic heterogeneity in crossover spin facilitated model of supercooled liquid and fractional Stokes-Einstein relation

Kinetically constrained models have gained much interest as models that assign the origins of interesting dynamic properties of supercooled liquids to dynamical facilitation mechanisms that have been revealed in many experiments and numerical simulations. In this work, we investigate the dynamic heterogeneity in the fragile-to-strong liquid via Monte Carlo method using the model that linearly interpolates between the strong liquid-like behavior and the fragile liquid-like behavior by an asymmetry parameter b. When the asymmetry parameter is sufficiently small, smooth fragile-to-strong transition is observed both in the relaxation time and the diffusion constant. Using these physical quantities, we investigate fractional Stokes-Einstein relations observed in this model. When b is fixed, the system shows constant power law exponent under the temperature change, and the exponent has the value between that of the Frederickson-Andersen model and the East model. Furthermore, we investigate the dynamic length scale of our systems and also find the crossover relation between the relaxation time. We ascribe the competition between energetically favored symmetric relaxation mechanism and entropically favored asymmetric relaxation mechanism to the fragile-to-strong crossover behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2011

A Block-Asynchronous Relaxation Method for Graphics Processing Units

In this paper, we analyze the potential of asynchronous relaxation methods on Graphics Processing Units (GPUs). For this purpose, we developed a set of asynchronous iteration algorithms in CUDA and compared them with a parallel implementation of synchronous relaxation methods on CPU-based systems. For a set of test matrices taken from the University of Florida Matrix Collection we monitor the convergence behavior, the average iteration time and the total time-to-solution time. Analyzing the results, we observe that even for our most basic asynchronous relaxation scheme, despite its lower convergence rate compared to the Gauss-Seidel relaxation (that we expected), the asynchronous iteration running on GPUs is still able to provide solution approximations of certain accuracy in considerably shorter time then Gauss- Seidel running on CPUs. Hence, it overcompensates for the slower convergence by exploiting the scalability and the good fit of the asynchronous schemes for the highly parallel GPU architectures. Further, enhancing the most basic asynchronous approach with hybrid schemes – using multiple iterations within the ”subdomain” handled by a GPU thread block and Jacobi-like asynchronous updates across the ”boundaries”, subject to tuning various parameters – we manage to not only recover the loss of global convergence but often accelerate convergence of up to two times (compared to the effective but difficult to parallelize Gauss-Seidel type of schemes), while keeping the execution time of a global iteration practically the same. This shows the high potential of the asynchronous methods not only as a stand alone numerical solver for linear systems of equations fulfilling certain convergence conditions but more importantly as a smoother in multigrid methods. Due to the explosion of parallelism in todays architecture designs, the significance and the need for asynchronous methods, as the ones described in this work, is expected to grow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

The linear and nonlinear response of infinite periodic systems to static and/or dynamic electric fields. Implementation in CRYSTAL code

An implementation of the vector potential approach (VPA) for treating the response of infinite periodic systems to static and dynamic electric fields has been initiated within the CRYSTAL code. The VPA method is based on the solution of a time-dependent Hartree-Fock or Kohn-Sham equation for the crystal orbitals wherein the usual scalar potential, that describes interaction with the field, is replaced by the vector potential. This equation may be solved either by perturbation theory or by finite field methods. With some modification all the computational procedures of molecular ab initio quantum chemistry can be adapted for periodic systems. Accessible properties include the linear and nonlinear responses of both the nuclei and the electrons. The programming of static field pure electronic (hyper)polarizabilities has been successfully tested. Dynamic electronic (hyper)polarizabilities, as well as infrared and Raman intensities, are in progress while the addition of finite fields for calculation of vibrational (hyper)polarizabilities, through nuclear relaxation procedures, will begin shortly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

A quantum energy transport model for semiconductor device simulation

This paper describes numerical methods for a quantum energy transport (QET) model in semiconductors, which is derived by using a diffusion scaling in the quantum hydrodynamic (QHD) model. We newly drive a four-moments QET model similar with a classical ET model. Space discretization is performed by a new set of unknown variables. Numerical stability and convergence are obtained by developing numerical schemes and an iterative solution method with a relaxation method. Numerical simulations of electron transport in a scaled MOSFET device are discussed. The QET model allows simulations of quantum confinement transport, and nonlocal and hot-carrier effects in scaled MOSFETs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Algorithms for Mathematical Programming with Emphasis on Bi-level Models (Final Scientific/Technical Report)

The research supported by this grant was focused primarily on first-order methods for solving large scale and structured convex optimization problems and convex relaxations of nonconvex problems. These include optimal gradient methods, operator and variable splitting methods, alternating direction augmented Lagrangian methods, and block coordinate descent methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

When do we need attractive-repulsive intermolecular potentials?

The role of attractive-repulsive interactions in direct simulation Monte Carlo (DSMC) simulations is studied by comparing with traditional purely repulsive interactions. The larger collision cross section of the long-range LJ potential is shown to result in a higher collision frequency and hence a lower mean free path, by at least a factor of two, for given conditions. This results in a faster relaxation to equilibrium as is shown by comparing the fourth and sixth moments of the molecular velocity distribution obtained using 0-D DSMC simulations. A 1-D Fourier-Couette flow with a large temperature and velocity difference between the walls is used to show that matching transport properties will result in identical solutions using both LJPA and VSS models in the near-continuum regime. However, flows in the transitional regime with Knudsen number, Kn ∼ 0.5 show a dependence on the intermolecular potential in spite of matching the viscosity coefficient due to differences in the collision frequency. Attractive-repulsive potentials should be used when both transport coefficients and collision frequencies should be matched.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Compact finite difference relaxation method for chaotic and hyperchaotic initial value systems

In this paper, we present a new application of higher order compact finite differences to solve nonlinear initial value problems exhibiting chaotic behaviour. The method involves dividing the domain of the problem into multiple sub-domains, with each sub-domain integrated using higher order compact finite difference schemes. The nonlinearity is dealt using a Gauss–Seidel-like relaxation. The method is, therefore, referred to as the multi-domain compact finite difference relaxation method (MD-CFDRM). In this new application, the MD-CFDRM is used to solve famous chaotic systems and hyperchaotic systems. The main advantage of the new approach is that it offers better accuracy on coarser grids which significantly improves the computational speed of the method. The results are compared with spectral-based multi-domain method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

THE FORCE-FREE MAGNETOSPHERE OF A ROTATING BLACK HOLE

We revisit the Blandford-Znajek process and solve the fundamental equation that governs the structure of the steady-state force-free magnetosphere around a Kerr black hole. The solution depends on the distributions of the magnetic field angular velocity {omega} and the poloidal electric current I. These are not arbitrary. They are determined self-consistently by requiring that magnetic field lines cross smoothly the two singular surfaces of the problem: the inner ''light surface'' located inside the ergosphere and the outer ''light surface'' which is the generalization of the pulsar light cylinder. We find the solution for the simplest possible magnetic field configuration, the split monopole, through a numerical iterative relaxation method analogous to the one that yields the structure of the steady-state axisymmetric force-free pulsar magnetosphere. We obtain the rate of electromagnetic extraction of energy and confirm the results of Blandford and Znajek and of previous time-dependent simulations. Furthermore, we discuss the physical applicability of magnetic field configurations that do not cross both ''light surfaces''.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Non-equilibrium reaction and relaxation dynamics in a strongly interacting explicit solvent: F + CD{sub 3}CN treated with a parallel multi-state EVB model

We describe a parallelized linear-scaling computational framework developed to implement arbitrarily large multi-state empirical valence bond (MS-EVB) calculations within CHARMM and TINKER. Forces are obtained using the Hellmann-Feynman relationship, giving continuous gradients, and good energy conservation. Utilizing multi-dimensional Gaussian coupling elements fit to explicitly correlated coupled cluster theory, we built a 64-state MS-EVB model designed to study the F + CD{sub 3}CN → DF + CD{sub 2}CN reaction in CD{sub 3}CN solvent (recently reported in Dunning et al. [Science 347(6221), 530 (2015)]). This approach allows us to build a reactive potential energy surface whose balanced accuracy and efficiency considerably surpass what we could achieve otherwise. We ran molecular dynamics simulations to examine a range of observables which follow in the wake of the reactive event: energy deposition in the nascent reaction products, vibrational relaxation rates of excited DF in CD{sub 3}CN solvent, equilibrium power spectra of DF in CD{sub 3}CN, and time dependent spectral shifts associated with relaxation of the nascent DF. Many of our results are in good agreement with time-resolved experimental observations, providing evidence for the accuracy of our MS-EVB framework in treating both the solute and solute/solvent interactions. The simulations provide additional insight into the dynamics at sub-picosecond time scales that are difficult to resolve experimentally. In particular, the simulations show that (immediately following deuterium abstraction) the nascent DF finds itself in a non-equilibrium regime in two different respects: (1) it is highly vibrationally excited, with ∼23 kcal mol{sup −1} localized in the stretch and (2) its post-reaction solvation environment, in which it is not yet hydrogen-bonded to CD{sub 3}CN solvent molecules, is intermediate between the non-interacting gas-phase limit and the solution-phase equilibrium limit. Vibrational relaxation of the nascent DF results in a spectral blue shift, while relaxation of the post-reaction solvation environment results in a red shift. These two competing effects mean that the post-reaction relaxation profile is distinct from what is observed when Franck-Condon vibrational excitation of DF occurs within a microsolvation environment initially at equilibrium. Our conclusions, along with the theoretical and parallel software framework presented in this paper, should be more broadly applicable to a range of complex reactive systems.

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

Lifetime Extension Report: Progress on the SAVY-4000 Lifetime Extension Program

The 3-year accelerated aging study of the SAVY-4000 O-ring shows very little evidence of significant degradation to samples subjected to aggressive elevated temperature and radiation conditions. Whole container thermal aging studies followed by helium leakage testing and compression set measurements were used to establish an estimate for a failure criterion for O-ring compression set of ≥65 %. The whole container aging studies further show that the air flow and efficiency functions of the filter do not degrade significantly after thermal aging. However, the degradation of the water-resistant function leads to water penetration failure after four months at 210°C, but does not cause failure after 10 months at 120°C (130°C is the maximum operating temperature for the PTFE membrane). The thermal aging data for O-ring compression set do not meet the assumptions of standard time-temperature superposition analysis for accelerated aging studies. Instead, the data suggest that multiple degradation mechanisms are operative, with a reversible mechanism operative at low aging temperatures and an irreversible mechanism dominating at high aging temperatures. To distinguish between these mechanisms, we have measured compression set after allowing the sample to physically relax, thereby minimizing the effect of the reversible mechanism. The resulting data were analyzed using two distinct mathematical methods to obtain a lifetime estimate based on chemical degradation alone. Both methods support a lifetime estimate of greater than 150 years at 80°C. Although the role of the reversible mechanism is not fully understood, it is clear that the contribution to the total compression set is small in comparison to that due to the chemical degradation mechanism. To better understand the chemical degradation mechanism, thermally aged O-ring samples have been characterized by Fourier Transform Infrared (FTIR), Electron Paramagnetic Resonance (EPR), Gel Permeation Chromatography (GPC), and Differential Scanning Calorimetry (DSC). These experiments detect no significant O-ring degradation below 80°C. Furthermore, durometer measurements indicate that there is no significant change in O-ring hardness at all aging conditions examined. Therefore, our current conservative lifetime estimate for the O-ring and the filter is 10 years at 80°C. In FY17, we will continue to probe the chemical degradation mechanism using oxygen consumption measurements under accelerated aging conditions to reveal temperatures at which oxidation occurs, along with any differences in oxidation rate at the low vs. high aging temperatures. We will also refine the failure criteria and finalize the radiation/thermal synergistic studies to determine a final design lifetime.

42 ENGINEERING↗
DOE OSTI2020

Scalable Asynchronous Domain Decomposition Solvers

We discuss how parallel implementations of linear iterative solvers generally alternate between phases of data exchange and phases of local computation. Increasingly large problem sizes and more heterogeneous compute architectures make load balancing and the design of low latency network interconnects that are able to satisfy the communication requirements of linear solvers very challenging tasks. In particular, global communication patterns such as inner products become increasingly limiting at scale. We explore the use of asynchronous communication based on one-sided Message Passing Interface primitives in the context of domain decomposition solvers. In particular, a scalable asynchronous two-level Schwarz method is presented. We discuss practical issues encountered in the development of a scalable solver and show experimental results obtained on a state-of-the-art supercomputer system that illustrate the benefits of asynchronous solvers in load balanced as well as load imbalanced scenarios. Using the novel method, we can observe speedups of up to four times over its classical synchronous equivalent.

97 MATHEMATICS AND COMPUTING↗