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All sources NASA NTRS DOE OSTI

DOE OSTI2023

Effective description of sub-maximal chaos: stringy effects for SYK scrambling

It has been proposed that the exponential decay and subsequent power law saturation of out-of-time-order correlation functions can be universally described by collective ‘scramblon’ modes. We develop this idea from a path integral perspective in several examples, thereby establishing a general formalism. After reformulating previous work on the Schwarzian theory and identity conformal blocks in two-dimensional CFTs relevant for systems in the infinite coupling limit with maximal quantum Lyapunov exponent, we focus on theories with sub-maximal chaos: we study the large-q limit of the SYK quantum dot and chain, both of which are amenable to analytical treatment at finite coupling. In both cases we identify the relevant scramblon modes, derive their effective action, and find bilocal vertex functions, thus constructing an effective description of chaos. The final results can be matched in detail to stringy corrections to the gravitational eikonal S-matrix in holographic CFTs, including a stringy Regge trajectory, bulk to boundary propagators, and multi-string effects that are unexplored holographically.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Combining DPG in space with DPG time-marching scheme for the transient advection–reaction equation

In this article, we present a general methodology to combine the Discontinuous Petrov–Galerkin (DPG) method in space and time in the context of methods of lines for transient advection–reaction problems. We first introduce a semidiscretization in space with a DPG method redefining the ideas of optimal testing and practicality of the method in this context. Then, we apply the recently developed DPG-based time-marching scheme, which is of exponential-type, to the resulting system of Ordinary Differential Equations (ODEs). Further, we also discuss how to efficiently compute the action of the exponential of the matrix coming from the space semidiscretization without assembling the full matrix. Finally, we verify the proposed method for 1D+time advection–reaction problems showing optimal convergence rates for smooth solutions and more stable results for linear conservation laws comparing to the classical exponential integrators.

42 ENGINEERING↗

DOE OSTI2024

A multiscale model to understand the interface chemistry, contacts, and dynamics during lithium stripping

A reversible Li-metal electrode, paired with a solid electrolyte, is critical for attaining higher energy density and safer batteries beyond the current lithium-ion cells. A stable stripping process may be even harder to attain as the stripping process will remove Li-atoms from the surface, and naturally reduce surface contact area, if not self-corrected by other mechanisms, such as diffusion and plastic deformation under an applied external stack pressure. Here, we capture these mechanisms occurring at multiple length- and time- scales, i.e., interface interactions, vacancy hopping, and plastic deformation, by integrating density functional theory (DFT) simulations, kinetic Monte Carlo (KMC), and continuum finite element method (FEM). By assuming the self-affine nature of multiscale contacts, we predict the steady-state contact area as a function of stripping current density, interface wettability, and stack pressure. We further estimate the exponential increase of overpotential due to contact area loss to maintain the same stripping current density. We demonstrate that a lithiophilic interface requires less stack pressure to reach the same steady-state contact area fraction than a lithiophobic interface. A “tolerable steady-state” contact area loss for maintaining stable stripping is estimated at 20 %, corresponding to a 10 % increase in overpotential. To constrain contact loss within the tolerance, the required stack pressure is 0.1, 0.5, and 2 times the yield strength of lithium metal for three distinct interfaces, lithiophilic Li/lithium oxide(Li2O), Li/lithium lanthanum zirconium oxide(LLZO), and lithiophoblic Li/lithium fluoride(LiF), respectively. The modeling results agree with experiments on the impact of the stack pressure quantitatively, while the discrepancy in stripping rate sensitivity is attributed to the simplifying interface interaction in our simulations. Overall, this multiscale simulation framework demonstrates the importance of electrochemical-mechanical coupling in understanding the dynamics of the Li/SE interface during stripping.

Feng, Min↗

DOE OSTI2019

Reaction Dynamics of Cyanohydrins with Hydrosulfide in Water

We studied the reaction dynamics of a proposed prebiotic reaction theoretically. The chemical process involves acetone cyanohydrin or formalcyanohydrin reacting with hydrosulfide in an aqueous environment. Rate constants and populations of reactant and product bimolecular geometric orientations for the reactions were obtained by using density functional theory for the energies, transition-state theory for the rates, and matrix exponentiation as well as the hybrid tau-leaping algorithm for the population dynamics. The role of including the solvent explicitly versus implicitly was also investigated. We found that adding explicit water or hydrogen sulfide molecules lowers the activation energy barrier and leads to a more efficient reaction pathway. In particular, hydrogen sulfide was a better proton donor. Lastly, we studied the role of including more than one reactant and product bimolecular orientation geometry in the dynamics. Including all initial pathways, reactant to reactant, product to product, reactant to product, and product to reactant led to a larger reaction rate constant compared to the single minimum energy pathway approach. Overall, we found that most reactions which involve formalcyanohydrin occur more rapidly or at the same speed as reactions which involve acetone cyanohydrin at room temperature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

The effect of electron-electron interaction induced dephasing on electronic transport in graphene nanoribbons

The effect of dephasing induced by electron-electron interaction on electronic transport in graphene nanoribbons is theoretically investigated. In the presence of disorder in graphene nanoribbons, wavefunction of electrons can set up standing waves along the channel and the conductance exponentially decreases with the ribbon's length. Employing the non-equilibrium Green's function formalism along with an accurate model for describing the dephasing induced by electron-electron interaction, we show that this kind of interaction prevents localization and transport of electrons remains in the diffusive regime where the conductance is inversely proportional to the ribbon's length.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2016

Stochastic modelling of intermittent fluctuations in the scrape-off layer: Correlations, distributions, level crossings, and moment estimation

A stochastic model is presented for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas. The fluctuations in the plasma density are modeled by a super-position of uncorrelated pulses with fixed shape and duration, describing radial motion of blob-like structures. In the case of an exponential pulse shape and exponentially distributed pulse amplitudes, predictions are given for the lowest order moments, probability density function, auto-correlation function, level crossings, and average times for periods spent above and below a given threshold level. Also, the mean squared errors on estimators of sample mean and variance for realizations of the process by finite time series are obtained. These results are discussed in the context of single-point measurements of fluctuations in the scrape-off layer, broad density profiles, and implications for plasma–wall interactions due to the transient transport events in fusion grade plasmas. The results may also have wide applications for modelling fluctuations in other magnetized plasmas such as basic laboratory experiments and ionospheric irregularities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Continuous and discrete phasor analysis of binned or time-gated periodic decays

The time-resolved analysis of periodically excited luminescence decays by the phasor method in the presence of time-gating or binning is revisited. Analytical expressions for discrete configurations of square gates are derived, and the locus of the phasors of such modified periodic single-exponential decays is compared to the canonical universal semicircle. The effects of instrument response function offset, decay truncation, and gate shape are also discussed. Finally, modified expressions for the phase and modulus lifetimes are provided for some simple cases. A discussion of a modified phasor calibration approach is presented, and an illustration of the new concepts with examples from the literature concludes this work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

Approximation of Müntz-Szász type in weighted spaces

The paper looks at whether a system of exponentials exp(-λ{sub n}t), Reλ{sub n}>0, is complete in various function spaces on the half-line R{sub +}. Wide classes of Banach spaces E and F of functions on R{sub +} are described such that this system is complete in E and F simultaneously. A test is established to determine when this system is complete in the weighted spaces C{sub 0} and L{sup p} with weight (1+t){sup α} on R{sub +}, for α<0 and α<-1, respectively. Bibliography: 18 titles.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

On the time growth of the error of the DG method for advective problems

Abstract In this paper we derive a priori $L^{\infty }(L^{2})$ and L2(L2) error estimates for a linear advection–reaction equation with inlet and outlet boundary conditions. The goal is to derive error estimates for the discontinuous Galerkin method that do not blow up exponentially with respect to time, unlike the usual case when Gronwall’s inequality is used. While this is possible in special cases, such as divergence-free advection fields, we take a more general approach using exponential scaling of the exact and discrete solutions. Here we use a special scaling function, which corresponds to time taken along individual pathlines of the flow. For advection fields, where the time that massless particles carried by the flow spend inside the spatial domain is uniformly bounded from above by some $\widehat{T}$, we derive $\mathcal{O}$(hp+1/2) error estimates where the constant factor depends only on $\widehat{T}$, but not on the final time T. This can be interpreted as applying Gronwall’s inequality in the error analysis along individual pathlines (Lagrangian setting), instead of physical time (Eulerian setting).

Mathematics↗

DOE OSTI2018

Shear banding leads to accelerated aging dynamics in a metallic glass

Traditionally, strain localization in metallic glasses is related to the thickness of the shear defect, which is confined to the nanometer scale. In this study, using site-specific x-ray photon correlation spectroscopy (XPCS), we reveal significantly accelerated relaxation dynamics around a shear band in a metallic glass at a length scale that is orders of magnitude larger than the defect itself. The relaxation time in the shear-band vicinity is up to ten-times smaller compared to the as-cast matrix, and the relaxation dynamics occurs in a characteristic three-stage aging response that manifests itself in the temperature-dependent shape parameter known from classical stretched exponential relaxation dynamics of disordered materials. We demonstrate that the time-dependent correlation functions describing the aging at different temperatures can be captured and collapsed using simple scaling functions. Finally, these insights highlight how an ubiquitous nano-scale strain-localization mechanism in metallic glasses leads to a fundamental change of the relaxation dynamics at the mesoscale.

36 MATERIALS SCIENCE↗

DOE OSTI2011

Investigation of advanced UQ for CRUD prediction with VIPRE.

This document summarizes the results from a level 3 milestone study within the CASL VUQ effort. It demonstrates the application of 'advanced UQ,' in particular dimension-adaptive p-refinement for polynomial chaos and stochastic collocation. The study calculates statistics for several quantities of interest that are indicators for the formation of CRUD (Chalk River unidentified deposit), which can lead to CIPS (CRUD induced power shift). Stochastic expansion methods are attractive methods for uncertainty quantification due to their fast convergence properties. For smooth functions (i.e., analytic, infinitely-differentiable) in L{sup 2} (i.e., possessing finite variance), exponential convergence rates can be obtained under order refinement for integrated statistical quantities of interest such as mean, variance, and probability. Two stochastic expansion methods are of interest: nonintrusive polynomial chaos expansion (PCE), which computes coefficients for a known basis of multivariate orthogonal polynomials, and stochastic collocation (SC), which forms multivariate interpolation polynomials for known coefficients. Within the DAKOTA project, recent research in stochastic expansion methods has focused on automated polynomial order refinement ('p-refinement') of expansions to support scalability to higher dimensional random input spaces [4, 3]. By preferentially refining only in the most important dimensions of the input space, the applicability of these methods can be extended from O(10{sup 0})-O(10{sup 1}) random variables to O(10{sup 2}) and beyond, depending on the degree of anisotropy (i.e., the extent to which randominput variables have differing degrees of influence on the statistical quantities of interest (QOIs)). Thus, the purpose of this study is to investigate the application of these adaptive stochastic expansion methods to the analysis of CRUD using the VIPRE simulation tools for two different plant models of differing random dimension, anisotropy, and smoothness.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2022

Combining DPG in space with DPG time-marching scheme for the transient advection-reaction equation

In this article, we present a general methodology to combine the Discontinuous PetrovGalerkin (DPG) method in space and time in the context of methods of lines for transient advection-reaction problems. We first introduce a semidiscretization in space with a DPG method redefining the ideas of optimal testing and practicality of the method in this context. Then, we apply the recently developed DPG-based time-marching scheme, which is of exponential-type, to the resulting system of Ordinary Differential Equations (ODEs). We also discuss how to efficiently compute the action of the exponential of the matrix coming from the space semidiscretization without assembling the full matrix. Finally, we verify the proposed method for 1D+time advection-reaction problems showing optimal convergence rates for smooth solutions and more stable results for linear conservation laws comparing to the classical exponential integrators.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Hamiltonian variational ansatz without barren plateaus

Variational quantum algorithms, which combine highly expressive parameterized quantum circuits (PQCs) and optimization techniques in machine learning, are one of the most promising applications of a near-term quantum computer. Despite their huge potential, the utility of variational quantum algorithms beyond tens of qubits is still questioned. One of the central problems is the trainability of PQCs. The cost function landscape of a randomly initialized PQC is often too flat, asking for an exponential amount of quantum resources to find a solution. This problem, dubbed barren plateaus , has gained lots of attention recently, but a general solution is still not available. In this paper, we solve this problem for the Hamiltonian variational ansatz (HVA), which is widely studied for solving quantum many-body problems. After showing that a circuit described by a time-evolution operator generated by a local Hamiltonian does not have exponentially small gradients, we derive parameter conditions for which the HVA is well approximated by such an operator. Based on this result, we propose an initialization scheme for the variational quantum algorithms and a parameter-constrained ansatz free from barren plateaus.

Physics↗

DOE OSTI2017

Quantum algorithms for Gibbs sampling and hitting-time estimation

In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. For a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2 ), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Characteristics of vertical air motion in isolated convective clouds

The vertical velocity and air mass flux in isolated convective clouds are statistically analyzed using aircraft in situ data collected from three field campaigns: High-Plains Cumulus (HiCu) conducted over the midlatitude High Plains, COnvective Precipitation Experiment (COPE) conducted in a midlatitude coastal area, and Ice in Clouds Experiment-Tropical (ICE-T) conducted over a tropical ocean. The results show that small-scale updrafts and downdrafts (< 500 m in diameter) are frequently observed in the three field campaigns, and they make important contributions to the total air mass flux. The probability density functions (PDFs) and profiles of the observed vertical velocity are provided. The PDFs are exponentially distributed. The updrafts generally strengthen with height. Relatively strong updrafts (> 20 m s −1 ) were sampled in COPE and ICE-T. The observed downdrafts are stronger in HiCu and COPE than in ICE-T. The PDFs of the air mass flux are exponentially distributed as well. The observed maximum air mass flux in updrafts is of the order 10 4 kg m −1 s −1 . The observed air mass flux in the downdrafts is typically a few times smaller in magnitude than that in the updrafts. Since this study only deals with isolated convective clouds, and there are many limitations and sampling issues in aircraft in situ measurements, more observations are needed to better explore the vertical air motion in convective clouds.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2014

Retrospective Analysis of NIST Standard Reference Material 1450, Fibrous Glass Board, for Thermal Insulation Measurements

Thermal conductivity data acquired previously for the establishment of Standard Reference Material (SRM) 1450, Fibrous Glass Board, as well as subsequent renewals 1450a, 1450b, 1450c, and 1450d, are re-analyzed collectively and as individual data sets. Additional data sets for proto-1450 material lots are also included in the analysis. The data cover 36 years of activity by the National Institute of Standards and Technology (NIST) in developing and providing thermal insulation SRMs, specifically high-density molded fibrous-glass board, to the public. Collectively, the data sets cover two nominal thicknesses of 13 mm and 25 mm, bulk densities from 60 kg∙m -3 to 180 kg∙m -3 , and mean temperatures from 100 K to 340 K. The analysis repetitively fits six models to the individual data sets. The most general form of the nested set of multilinear models used is given in the following equation: λ(ρ, T) = α 0 + α 1 ρ +α 2 T + α 3 T 3 +α 4 e - ($\frac{T-a_{5}}{a_{6}}$) 2 = where λ(ρ,T) is the predicted thermal conductivity (W∙m -1 ∙K -1 ), ρ is the bulk density (kg∙m -3 ), T is the mean temperature (K) and $a_i$ (for i = 1, 2, … 6) are the regression coefficients. The least squares fit results for each model across all data sets are analyzed using both graphical and analytic techniques. The prevailing generic model for the majority of data sets is the bilinear model in ρ and T. λ(ρ, T) = α 0 + α 1 ρ +α 2 T One data set supports the inclusion of a cubic temperature term and two data sets with low-temperature data support the inclusion of an exponential term in T to improve the model predictions. Physical interpretations of the model function terms are described. Recommendations for future renewals of SRM 1450 are provided. An Addendum provides historical background on the origin of this SRM and the influence of the SRM on external measurement programs.

regression analysis↗

NASA NTRS1981

Observations of the ionization states of energetic particles accelerated in solar flares

The ionization states and spectra of 0.3 to 2.4 MeV/nuc He, C, O and Fe are measured in a survey of ten solar flare particle events. He(plus) is found to be present in all events, which indicates the common presence of energetic He(plus) in the source material from which solar particles are accelerated. The distribution functions of He(plus), He(plus plus) and heavier elements are represented by simple exponentials of the particle speed times its rigidity to a power n, where n is between 0 and 1, and equal e-folding values. Results are consistent with a model where ions are accelerated in the corona by multi-dimensional shocks out of a population taken from both hot and cold coronal regions.

Gloeckler, G.↗

NASA NTRS1991

Shot model parameters for Cygnus X-1 through phase portrait fitting

Shot models for systems having about 1/f power density spectrum are developed by utilizing a distribution of shot durations. Parameters of the distribution are determined by fitting the power spectrum either with analytic forms for the spectrum of a shot model with a given shot profile, or with the spectrum derived from numerical realizations of trial shot models. The shot fraction is specified by fitting the phase portrait, which is a plot of intensity at a given time versus intensity at a delayed time and in principle is sensitive to different shot profiles. These techniques have been extensively applied to the X-ray variability of Cygnus X-1, using HEAO 1 A-2 and an Exosat ME observation. The power spectra suggest models having characteristic shot durations lasting from milliseconds to a few seconds, while the phase portrait fits give shot fractions of about 50 percent. Best fits to the portraits are obtained if the amplitude of the shot is a power-law function of the duration of the shot. These fits prefer shots having a symmetric exponential rise and decay. Results are interpreted in terms of a distribution of magnetic flares in the accretion disk.

Lochner, James C.↗