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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Perturbative unorientable JT gravity and matrix models

We consider an orthogonal polynomial formulation of the double scaling limit of multicritical matrix models in the β = 1 Dyson-Wigner class. They capture the physics of 2D quantum gravity coupled to minimal matter on unorientable surfaces, otherwise called unoriented minimal strings. We derive a formula for the density of states valid to all orders in perturbation theory. We show how to define an interpolation between the multicritical models and that a certain interpolation among an infinite number of them provides an alternative definition of unoriented JT gravity. We discuss the strengths and weaknesses of our formulation.

1/N Expansion↗
DOE OSTI2020

Spectral fluctuations in the Sachdev-Ye-Kitaev model

We present a detailed quantitative analysis of spectral correlations in the Sachdev-Ye-Kitaev (SYK) model. We find that the deviations from universal Random Matrix Theory (RMT) behavior are due to a small number of long-wavelength fluctuations (of the order of the number of Majorana fermions N ) from one realization of the ensemble to the next one. These modes can be parameterized effectively in terms of Q-Hermite orthogonal polynomials, the main contribution being due to scale fluctuations for which we give a simple analytical estimate. Our numerical results for N = 32 show that only the lowest eight polynomials are needed to eliminate the nonuniversal part of the spectral fluctuations. The covariance matrix of the coefficients of this expansion can be obtained analytically from low-order double-trace moments. We evaluate the covariance matrix of the first six moments and find that it agrees with the numerics. We also analyze the spectral correlations in terms of a nonlinear σ-model, which is derived through a Fierz transformation, and evaluate the one and two-point spectral correlation functions to two-loop order. The wide correlator is given by the sum of the universal RMT result and corrections whose lowest-order term corresponds to scale fluctuations. However, the loop expansion of the σ-model results in an ill-behaved expansion of the resolvent, and it gives universal RMT fluctuations not only for q= 4 or higher even q-body interactions, but also for the q= 2 SYK model albeit with a much smaller Thouless energy while the correct result in this case should have been Poisson statistics. In our numerical studies we analyze the number variance and spectral form factor for N = 32 and q = 4. We show that the quadratic deviation of the number variance for large energies appears as a peak for small times in the spectral form factor. After eliminating the long-wavelength fluctuations, we find quantitative agreement with RMT up to an exponentially large number of level spacings for the number variance or exponentially short times in the case of the spectral form factor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Data-Driven Constitutive Model for the Inelastic Response of Metals: Application to 316H Steel

Here, predictions of the mechanical response of structural elements are conditioned by the accuracy of constitutive models used at the engineering length-scale. In this regard, a prospect of mechanistic crystal-plasticity-based constitutive models is that they could be used for extrapolation beyond regimes in which they are calibrated. However, their use for assessing the performance of a component is computationally onerous. To address this limitation, a new approach is proposed whereby a surrogate constitutive model (SM) of the inelastic response of 316H steel is derived from a mechanistic crystal plasticity-based polycrystal model tracking the evolution of dislocation densities on all slip systems. The latter is used to generate a database of the expected plastic response and dislocation content evolution associated with several instances of creep loading. From the database, a SM is developed. It relies on the use of orthogonal polynomial regression to describe the evolution of the dislocation content. The SM is then validated against predictions of the dead load creep response given by the polycrystal model across a range of temperatures and stresses. When the SM is used to predict the response of 316H during complex non monotonic loading, extrapolating to new loading conditions, it is found that predictions compare particularly well against those from the physics-based polycrystal model.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Spatially-resolved lithiation dynamics from operando X-ray diffraction and electrochemical modeling of lithium-ion cells

In this study, energy dispersive X-ray diffraction is used to profile the time evolution of ordered Li x C 6 phases in solid electrodes of lithium-ion cells charged at rates between 0.2 and 4.7C (where 1C corresponds to full discharge in 1 h). The methods for quantifying lithium concentration in these phases from the acquired diffraction patterns are described. Compact expressions for time-dependent concentration gradients in the solid electrodes using orthogonal polynomial expansions are presented. Experimentally, these gradients persisted in lithiated graphite electrodes even after the cells rested at open-circuit for over 9 h. A multiphase electrochemical model of graphite intercalation captured many of the observed behaviors, including the progression of phase transitions and the persistent gradients at zero current. However, the magnitude of concentration gradients in both the oxide cathode and graphite anode is underestimated by the model, even at moderate currents.

25 ENERGY STORAGE↗
DOE OSTI2023

Machine-learning-based spectral methods for partial differential equations

Spectral methods are an important part of scientific computing’s arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the solution of a PDE. The last decade has seen the emergence of deep learning as a strong contender in providing efficient representations of complex functions. In the current work, we present an approach for combining deep neural networks with spectral methods to solve PDEs. In particular, we use a deep learning technique known as the Deep Operator Network (DeepONet) to identify candidate functions on which to expand the solution of PDEs. We have devised an approach that uses the candidate functions provided by the DeepONet as a starting point to construct a set of functions that have the following properties: (1) they constitute a basis, (2) they are orthonormal, and (3) they are hierarchical, i.e., akin to Fourier series or orthogonal polynomials. We have exploited the favorable properties of our custom-made basis functions to both study their approximation capability and use them to expand the solution of linear and nonlinear time-dependent PDEs. The proposed approach advances the state of the art and versatility of spectral methods and, more generally, promotes the synergy between traditional scientific computing and machine learning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Influence of non-adiabatic effects on linear absorption spectra in the condensed phase: Methylene blue

Modeling linear absorption spectra of solvated chromophores is highly challenging as contributions are present both from coupling of the electronic states to nuclear vibrations and from solute–solvent interactions. In systems where excited states intersect in the Condon region, significant non-adiabatic contributions to absorption line shapes can also be observed. Here, we introduce a robust approach to model linear absorption spectra accounting for both environmental and non-adiabatic effects from first principles. This model parameterizes a linear vibronic coupling (LVC) Hamiltonian directly from energy gap fluctuations calculated along molecular dynamics (MD) trajectories of the chromophore in solution, accounting for both anharmonicity in the potential and direct solute–solvent interactions. The resulting system dynamics described by the LVC Hamiltonian are solved exactly using the thermalized time-evolving density operator with orthogonal polynomials algorithm (T-TEDOPA). The approach is applied to the linear absorption spectrum of methylene blue in water. We show that the strong shoulder in the experimental spectrum is caused by vibrationally driven population transfer between the bright S1 and the dark S2 states. The treatment of the solvent environment is one of many factors that strongly influence the population transfer and line shape; accurate modeling can only be achieved through the use of explicit quantum mechanical solvation. The efficiency of T-TEDOPA, combined with LVC Hamiltonian parameterizations from MD, leads to an attractive method for describing a large variety of systems in complex environments from first principles.

Dunnett, Angus J. (ORCID:0000000285797826)↗
DOE OSTI2021

Efficient numerical method for evaluating normal and anomalous time-domain equilibrium Green's functions in inhomogeneous systems

In this work we develop EPOCH (equilibrium propagator by orthogonal polynomial chain), a computationally efficient method to calculate the time-dependent equilibrium Green's functions, including the anomalous Green's functions of superconductors, to capture the time evolution in large inhomogeneous systems. The EPOCH method generalizes the Chebyshev wave-packet propagation method from quantum chemistry and efficiently incorporates the Fermi-Dirac statistics that is needed for equilibrium quantum condensed matter systems. The computational cost of EPOCH scales only linearly in the system degrees of freedom, generating an extremely efficient algorithm also for very large systems. We demonstrate the power of the EPOCH method by calculating the time evolution of an excitation near a superconductor–normal metal interface in two and three dimensions, capturing transmission as well as normal and Andreev reflections.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Random matrix model of the Virasoro minimal string

The model of two dimensional quantum gravity defining the Virasoro minimal string, presented recently by Collier, Eberhardt, Mühlmann, and Rodriguez, was also shown to be perturbatively (in topology) equivalent to a random matrix model. An alternative definition is presented here, in terms of double-scaled orthogonal polynomials, thereby allowing direct access to nonperturbative physics. Already at leading order, the defining string equation’s properties yield valuable information about the nonperturbative fate of the model, confirming that the case ( c = 25 , c ^ = 1 ) (central charges of spacelike and timelike Liouville sectors) is special, by virtue of sharing certain key features of the N = 1 supersymmetric JT gravity string equation. Solutions of the full string equation are constructed using a special limit, and the (Cardy) spectral density is completed to all genus and beyond. The distributions of the underlying discrete spectra are readily accessible too, as is the spectral form factor. Some examples of these are exhibited. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2024

Supersymmetric Virasoro minimal strings

A random matrix model definition of a family of N = 1 supersymmetric extensions of the Virasoro minimal string of Collier, Eberhardt, Mühlmann, and Rodriguez is presented. An analysis of the defining string equations shows that the models all naturally have unambiguous nonperturbative completions, which are explicitly supplied by the double-scaled orthogonal polynomial techniques employed. Perturbatively, the multiloop correlation functions of the model define a special supersymmetric class of “quantum volumes,” generalizing the prototype case, some of which are computed. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2025

Inference of response functions with the help of machine-learning algorithms

Response functions are a key quantity to describe the near-equilibrium dynamics of strongly interacting many-body systems. Recent techniques that attempt to overcome the challenges of calculating these ab initio have employed expansions in terms of orthogonal polynomials. We employ a neural network prediction algorithm to reconstruct a response function 𝑆⁡(𝜔) defined over a range in frequencies 𝜔. Here, we represent the calculated response function as a truncated Chebyshev series whose coefficients can be optimized to reduce the representation error. We compare the quality of response functions obtained using coefficients calculated using a neural network (NN) algorithm with those computed using the Gaussian integral transform (GIT) method. In the regime where only a small number of terms in the Chebyshev series are retained, we find that the NN scheme outperforms the GIT method.

Kurkcuoglu, Doga Murat [Fermi National Accelerator↗
DOE OSTI2021

Time-Resolved X-ray Operando Observations of Lithiation Gradients across the Cathode Matrix and Individual Oxide Particles during Fast Cycling of a Li-Ion Cell

Lithiated transition metal oxides serve as active materials in the positive electrode (cathode) of lithium-ion cells. During electrochemical cycling, lithium ions intercalate and deintercalate into these oxide particles. This behavior causes two types of lithiation gradients to emerge: (i) a bulk gradient across the depth of the cathode matrix (averaged over individual oxide particles) and (ii) a microscopic gradient across the particles themselves, which also depends on their location in the electrode. Here we show how both gradients can be studied using operando X-ray diffraction during 4C charge and 4C discharge. The oxide (de)lithiation is estimated from the unit cell parameters by indexing the X-ray diffraction spectra. By fitting the lithiation profiles with orthogonal polynomials, the bulk gradients across the electrode thickness are quantified. These gradients develop as the current flows through the cell and dissipate during open-circuit and potentiostatic-hold periods. Further details of lithiation dynamics can be obtained through shape analysis of the Bragg peaks. In particular, from electrochemical model simulations, we show that the width and skewness of the (003) peak track (de)lithiation fronts moving across the individual oxide particles.

(003) peak↗
DOE OSTI2021

RISE: robust iterative surface extension for sub-nanometer X-ray mirror fabrication

Precision optics have been widely required in many advanced technological applications. X-ray mirrors, as an example, serve as the key optical components at synchrotron radiation and free electron laser facilities. They are rectangular silicon or glass substrates where a rectangular Clear Aperture (CA) needs to be polished to sub-nanometer Root Mean Squared (RMS) to keep the imaging capability of the incoming X-ray wavefront at the diffraction limit. The convolutional polishing model requires a CA to be extended with extra data, from which the dwell time is calculated via deconvolution. However, since deconvolution is very sensitive to boundary errors and noise, the existing surface extension methods can hardly fulfill the sub-nanometer requirement. On one hand, the figure errors in a CA were improperly modeled during the extension, leading to continuity issues along the boundary. On the other hand, uncorrectable high-frequency errors and noise were also extended. In this study, we propose a novel Robust Iterative Surface Extension (RISE) method that resolves these problems with a data fitting strategy. RISE models the figure errors in a CA with orthogonal polynomials and ensures that only correctable errors are fit and extended. Combined with boundary conditions, an iterative refinement of dwell time is then proposed to compensate the errors brought by the extension and deconvolution, which drastically reduces the estimated figure error residuals in a CA while the increase of total dwell time is negligible. To our best knowledge, RISE is the first data fitting-based surface extension method and is the first to optimize dwell time based on iterative extension. An experimental verification of RISE is given by fabricating two elliptic cylinders (10 mm × 80 mm CAs) starting from a sphere with a radius of curvature around 173 m using ion beam figuring. The figure errors in the two CAs greatly improved from 204.96 nm RMS and 190.28 nm RMS to 0.62 nm RMS and 0.71 nm RMS, respectively, which proves that RISE is an effective method for sub-nanometer level X-ray mirror fabrication.

36 MATERIALS SCIENCE↗
NASA NTRS1975

Programs for computing abscissas and weights for classical and nonclassical Gaussian quadrature formulas

Computer programs for computing Gaussian quadrature abscissas and weights are described. For the classical case the programs use Laguerre iteration to compute abscissas as zeros of orthogonal polynomials. The polynomials are evaluated from known recursion coefficients. The nonclassical case is handled similarly except that the recursion coefficients are computed by numerical integration. A sample problem, with input and output, is presented to illustrate the use of the programs. It computes the quadrature abscissas and weights associated with the weight function over the interval (0,1) for quadrature orders from 16 to 96 in increments of 8.

Desmarais, R. N.↗
NASA NTRS1979

Integrating matrices for arbitrarily spaced grid points

Integrating matrices are derived for arbitrarily spaced grid points using either interpolating or least squares fit orthogonal polynomials. Several features of the equally spaced grid case are also discussed.

Lakin, W. D.↗
NASA NTRS1982

A numerical method for integrating the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes

An extension of the method of moments is developed for the numerical integration of the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes. The number density function n sub k (x,t) in each separate droplet packet between droplet mass grid points (x sub k, x sub k+1) is represented by an expansion in orthogonal polynomials with a given weighting function. In this way droplet number concentrations, liquid water contents and other moments in each droplet packet are conserved and the problem of solving the kinetic equations is replaced by one of solving a set of coupled differential equations for the number density function moments. The method is tested against analytic solutions of the corresponding kinetic equations. Numerical results are obtained for different coalescence/breakup and condensation/evaporation kernels and for different initial droplet spectra. Also droplet mass grid intervals, weighting functions, and time steps are varied.

Emukashvily, I. M.↗
NASA NTRS1986

Plates and shells containing a surface crack under general loading conditions

The severity of the underlying assumptions of the line-spring model (LSM) are such that verification with three-dimensional solutions is necessary. Such comparisons show that the model is quite accurate, and therefore, its use in extensive parameter studies is justified. Investigations into the endpoint behavior of the line-spring model have led to important conclusions about the ability of the model to predict stresses in front of the crack tip. An important application of the LSM was to solve the contact plate bending problem. Here the flexibility of the model to allow for any crack shape is exploited. The use of displacement quantities as unknowns in the formulation of the problem leads to strongly singular integral equations, rather than singular integral equations which result from using displacement derivatives. The collocation method of solving the integral equations was found to be better and more convenient than the quadrature technique. Orthogonal polynomials should be used as fitting functions when using the LSM as opposed to simpler functions such as power series.

Joseph, Paul F.↗
NASA NTRS1990

Unitary-matrix models as exactly solvable string theories

Exact differential equations are presently found for the scaling functions of models of unitary matrices which are solved in a double-scaling limit, using orthogonal polynomials on a circle. For the case of the simplest, k = 1 model, the Painleve II equation with constant 0 is obtained; possible nonperturbative phase transitions exist for these models. Equations are presented for k = 2 and 3, and discussed with a view to asymptotic behavior.

Periwal, Vipul↗