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DOE OSTI2023

What controls the interannual variation of Hadley cell extent in the Northern Hemisphere: physical mechanism and empirical model for edge variation

Abstract The Hadley circulation is the most prominent atmospheric meridional circulation, reducing the radiatively driven equator-to-pole temperature gradient. While the Hadley cell extent varies by several degrees from year to year, the detailed dynamical mechanisms behind such variations have not been well elucidated. During the expanded phase of the Hadley cell, many regions on the periphery of the subtropics experience unfavorable climatic conditions. In this study, using ERA5 reanalysis data, we examine the physical chain of events responsible for the interannual variation of the Hadley cell edge (HCE) latitude in the Northern Hemisphere. This variation is mainly caused by changing eddy activity and wave breaking from both stationary and transient waves. In particular, we show that transient waves cause the HCE to shift poleward by increasing the eddy momentum flux divergence (EMFD) and reducing the baroclinicity over 20°–40°N, shifting the region of peak baroclinicity poleward. El Niño/La Niña and the Arctic Oscillation (AO) account for a significant portion (60%) of the interannual fluctuation of the HCE latitude. Through the poleward displacement of eddy activity, La Niña and a positive AO state are associated with the poleward shift of the HCE. The analysis of 28 CMIP5 models reveals statistical relationships between EMFD, vertical shear, and HCE latitude similar to those observed.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Generalized hydrodynamic analysis of transport through a finite open nanopore for two-component single-file systems

Single-file diffusion (SFD) in finite open nanopores is characterized by nonzero spatially varying tracer diffusion coefficients within a generalized hydrodynamic description. This contrasts with infinite SFD systems where tracer diffusivity vanishes. In standard tracer counterpermeation (TCP) analysis, two reservoirs, each containing a different species, are connected to opposite ends of a finite pore. Here, we implement an extended TCP analysis to allow the two reservoirs to contain slightly different mixtures of the two species. Then, determination of diffusion fluxes through the pore allows extraction of diffusion coefficients for near-constant partial concentrations of the two species. This analysis is applied for a lattice-gas model describing two-component SFD through a finite linear pore represented by a one-dimensional array of cells. Two types of particles, A and B, can hop only to adjacent empty cells with generally different rates, $h_A$ and $h_B$. Particles are noninteracting other than exclusion of multiple cell occupancy. Results reveal generalized hydrodynamic tracer diffusion coefficients which adopt small values inversely proportional to pore length in the pore center, but which are strongly enhanced near pore openings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Modeling iterative reconstruction and displacement field in the large scale structure

The next generation of galaxy surveys like the Dark Energy Spectroscopic Instrument and Euclid will provide datasets orders of magnitude larger than anything available to date. Our ability to model nonlinear effects in late time matter perturbations will be a key to unlock the full potential of these datasets, and the area of initial condition reconstruction is attracting growing attention. Iterative reconstruction developed by Marcel Schmittfull et al. is a technique designed to reconstruct the displacement field from the observed galaxy distribution. The nonlinear displacement field and initial linear density field are highly correlated. Therefore, reconstructing the nonlinear displacement field enables us to extract the primordial cosmological information better than from the late time density field at the level of the two-point statistics. This paper will test to what extent the iterative reconstruction can recover the true displacement field and construct a perturbation theory model for the postreconstructed field. We model the iterative reconstruction process with Lagrangian perturbation theory (LPT) up to third order for dark matter in real space and compare it with N-body simulations. Here we find that the simulated iterative reconstruction does not converge to the nonlinear displacement field, and the discrepancy mainly appears in the shift term, i.e., the term correlated directly with the linear density field. On the contrary, our 3LPT model predicts that the iterative reconstruction should converge to the nonlinear displacement field. We discuss the sources of discrepancy, including numerical noise/artifacts on small scales, and present an ad hoc phenomenological model that improves the agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Surface deformation coupled with self-organized pattern on a liquid anode of 1 atm DC glow discharge

Intricate, self-organized plasma structures observed above the surface of a liquid anode of atmospheric DC glow discharge were found to give rise to coherent, organized surface deformation and mechanical wave formation at the plasma–liquid interface. This new phenomenon indicates that the liquid is closely coupled to the plasma by the anode sheath’s electrohydrodynamic (EHD) force. A scientific question then arises: Do surface perturbations, coupled with the nonuniform surface charge distribution, enhance the electric field and induce self-organization? Using the reflective background-oriented schlieren technique, the liquid surface profile under the plasma pattern was measured for the first time. The results show that surface distortions are driven by the repulsive Coulomb force of nonuniform net-negative surface charge acted by the anode sheath field. The impacts of various operating parameters on the patterns and surface waves were examined, revealing the significance of gas heating and liquid charge relaxation time in the pattern formation mechanism. Time-resolved dynamics of a pulsed DC discharge indicated that the surface deformation only appeared after the establishment of plasma patterns. Statistically, the surface wave under the plasma has high wave numbers (8000–16000 m −1 ) and small amplitudes ($<$ 10 µm), generally found in the capillary wave regime. Yet the motion of surface deformations is in tandem with the plasma pattern and exhibits a nondispersive nature of constant phase velocity (0.1–0.4 m s −1 ), suggesting the dominant role of EHD force over the surface tension in the observed surface wave. These results indicate that the deformed liquid surface is driven by the EHD force of the plasma sheath. Although they share a similar geometry, the deformation and wave dynamics of the liquid surface do not stimulate a plasma pattern. Importantly, the complex EHD coupling in the plasma–liquid system raises awareness and new challenges for plasma control engineering, and the quantitative characteristics of the nondispersive surface wave are informative for advancing relevant theory and modeling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Ensemble approximate control variate estimators: Applications to multi-fidelity importance sampling.

The recent growth in multifidelity uncertainty quantification has given rise to a large set of variance reduction techniques that leverage information from model ensembles to provide variance reduction for estimates of the statistics of a high-fidelity model. In this paper we provide two contributions: (1) we utilize an ensemble estimator to account for uncertainties in the optimal weights of approximate control variate (ACV) approaches and derive lower bounds on the number of samples required to guarantee variance reduction; and (2) we extend an existing multifidelity importance sampling (MFIS) scheme to leverage control variates. Our approach directly addresses a limitation of many multifidelity sampling strategies that require the usage of pilot samples to estimate covariances. As such we make significant progress towards both increasing the practicality of approximate control variates—for instance, by accounting for the effect of pilot samples—and using multifidelity approaches more effectively for estimating low-probability events. The numerical results indicate our hybrid MFIS-ACV estimator achieves up to 50% improvement in variance reduction over the existing state-of-the-art MFIS estimator, which had already shown an outstanding convergence rate compared to the Monte Carlo method, on several problems of computational mechanics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Approximating the linear response of physical chaos

Abstract Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence of chaos, the rigorous computation of these quantities is certainly possible, but mathematically complicated and computationally expensive. Based on Ruelle’s formalism, this paper shows that the sophisticated linear response algorithm can be dramatically simplified in higher-dimensional systems featuring statistical homogeneity in the physical space. We argue that the contribution of the SRB (Sinai–Ruelle–Bowen) measure gradient, which is an integral yet the most cumbersome part of the full algorithm, is negligible if the objective function is appropriately aligned with unstable manifolds. This abstract condition could potentially be satisfied by a vast family of real-world chaotic systems, regardless of the physical meaning and mathematical form of the objective function and perturbed parameter. We demonstrate several numerical examples that support these conclusions and that present the use and performance of a simplified linear response algorithm. In the numerical experiments, we consider physical models described by differential equations, including Lorenz 96 and Kuramoto–Sivashinsky.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

State-to-State Molecular Reactions in the Ultracold Regime (Final Scientific Report)

We have achieved the proposed goal to experimentally probe the AB + CD and AB + C types of reactions with state-to-state resolution, which we also compared to advanced theoretical calculations to help elucidate the role of quantum mechanics in the processes of bond breakage and formation. Our approach uses reactants that are prepared at ultracold temperatures (< 1µK) such that the quantum effects of translational motion are an important factor. Specific example reactions, including the potassium-rubidium metathesis reaction KRb + KRb → K 2 + Rb 2 as well as the atom exchange reaction Rb + KRb → Rb2 + K, are chosen because the technology of quantum internal and motional state control of these types of molecules is particularly advanced. The results for the entire funding period are fruitful. For the majority of this grant, we have constructed a one-of-the-kind quantum degenerate gas apparatus that integrates ion detection and velocity map imaging capabilities, allowing us to explore the KRb + KRb → K 2 + Rb 2 bimolecular reaction in detail. Specifically, we first verified such a reaction indeed proceed at ultracold temperatures by direct detection of reaction products. We then mapped out the complete product state distribution, which was compared to a state-counting model based on statistical theory. Our results show an overall agreement with the statistical state counting model, but also reveal several deviating state-pairs. An exact quantum calculation for molecule-molecule collisions, that is needed to understand these deviations, is however beyond the current state-of-the-art. Beside scrutinizing the reaction products, we also directly observe the reaction intermediate complex, which was quite a surprise to us. The intermediate complexes are long-lived and can interact with the inferred light that we use to trap the ultracold gas. After molecule-molecule collisions, we then explored the more theoretically tractable Rb + KRb reaction, which is endothermic. Surprisingly, we observed an exceedingly long-lived KRb$^*_2$ collisional complexes, with our experimentally measured complex lifetime deviating from conventional theoretical calculations by five orders of magnitude. This discrepancy has motivated many explorations of possible underlying causes, though no model yet captures this phenomenon completely. In the final year and the work that continues today, we extend upon these atom-molecule collision experiments to explore the origin of the long-lived KRb$^*_2$ complex lifetime and develop means to control the outcome of the reaction complex. The 5-year funded work advanced our understanding of chemical reactions at the lowest possible temperatures and at the same time opened up many new questions that are beyond our initial imaginations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Long-Term Stochasticity Combines With Short-Term Variability in Assembly Processes to Underlie Rice Paddy Sustainability

Revealing temporal patterns of community assembly processes is important for understanding how microorganisms underlie the sustainability of agroecosystem. The ancient terraced rice paddies at Longji provide an ideal platform to study temporal dynamics of agroecosystem sustainability due to their chronosequential records of soil physicochemistry and well-archived microbial information along 630-year rice cultivation. We used statistical null models to evaluate microbial assembly processes along the soil chronosequences of Longji rice paddies through time. Stochastic and deterministic assembly processes jointly governed microbial community composition within successional eras (less than 250 years), and within-era determinism was mainly driven by soil fertility and redox conditions alone or in combination. Conversely, across successional eras (i.e., over 300 years), stochasticity linearly increased with increasing duration between eras and was eventually predominant for the whole 630 years. We suggest that the impact of stochasticity vs. determinism on assembly is timescale-dependent, and we propose that the importance of stochastic assembly of microbial community at longer timescales is due to the gradual changes in soil properties under long-term rice cultivation, which in turn contribute to the sustainability of paddy ecosystem by maintaining a diverse community of microorganisms with multi-functional traits. In total, our results indicate that knowledge on the timescales at which assembly processes govern microbial community composition is key to understanding the ecological mechanisms generating agroecosystem sustainability.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Impact of Porcine Arterivirus, Influenza B, and Their Coinfection on Antiviral Response in the Porcine Lung

Interferon (IFN) cytokines induce an autonomous antiviral state in cells of the infected site to restrict virus spreading and critically regulate overall antiviral response. The antiviral state leads to host protection through expression of hundreds of IFN-stimulated genes that restrict viral infection through multiple mechanisms, for example, directly in viral genome degradation and indirectly through cellular metabolic inhibition. Young pigs were split into four treatment groups: control, porcine reproductive and respiratory syndrome virus (PRRSV, also known as porcine arterivirus) infected, influenza B virus (IBV) infected, and IBV/PRRSV coinfection. Lung tissue was collected at 3, 5, and 7 days post infection (dpi) for control, PRRSV and IBV/PRRSV coinfection, and at 3 and 5 dpi for IBV. Transcriptomic analysis, using usegalaxy.org tools, was performed against the S.scrofa 11.1 reference genome. Differentially expressed gene (DEG) analysis was carried out using DeSeq2 based on the model treatment + dpi + treatment:dpi + E. Downstream analysis examined the interaction of DEG at each dpi for over-enriched gene ontology (G.O.) terms and pathways. Comparisons of the infected groups vs. the controls yielded a total of (n = 1412) DEGs for the PRRSV group and (n = 1578) for the IBV/PRRSV group across all timepoints. The IBV group had (n = 64) total DEGs across 3 and 5 dpi. Expression data were considered statistically significant based on false discovery rate (FDR) ⫹ 0.1. Venn diagram comparisons of the DEGs across dpi showed that groups shared only 16 DEGs at 3 dpi, no DEGs were shared at 5 dpi, and for 7 dpi, only the PRRSV and IBV/PRRSV groups were compared and shared a total of 43 DEGs. Across the comparisons, differential expression was observed in antiviral genes such as IRF1, MX1, and OAS2. The IBV and IBV/PRRSV groups showed higher expression of antiviral genes at earlier dpi than the PRRSV group. Additionally, downregulated genes from the comparisons clustered around Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways effecting lung development and cellular integrity. Early expression of host IFN and antiviral genes may lead to viral RNA degradation, and assembly and transcription inhibition in the IBV infections. In comparison, expression of antiviral genes in the PRRSV group decreased across time. The decrease may explain why PRRSV infections persist, while IBV clears. Moreover, all infected groups showed prolonged upregulation in neutrophil degranulation pathway activity, possibly exacerbating symptomatic lung lesion pathology seen in these respiratory infections.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

A MeerKAT-meets-LOFAR study of Abell 1413: a moderately disturbed non-cool-core cluster hosting a ~500 kpc ‘mini’-halo

Many relaxed cool-core clusters host diffuse radio emission on scales of hundreds of kiloparsecs: mini-haloes. However, the mechanism responsible for generating them, as well as their connection with central active galactic nuclei, is elusive and many questions related to their physical properties and origins remain unanswered. This paper presents new radio observations of the galaxy cluster Abell 1413 performed with MeerKAT (L-band; 872 to 1712 MHz) and LOFAR HBA (120 to 168 MHz) as part of a statistical and homogeneous census of mini-haloes. Abell 1413 is unique among mini-halo clusters as it is a moderately disturbed non-cool-core cluster. Our study reveals an asymmetric mini-halo up to 584 kpc in size at 1283 MHz, twice as large as first reported at similar frequencies. The spectral index is flatter than previously reported, with an integrated value of α = −1.01 ± 0.06, shows significant spatial variation, and a tentative radial steepening. We studied the point-to-point X-ray/radio surface brightness correlation to investigate the thermal/non-thermal connection: our results show a strong connection between these components, with a superlinear slope of $b = 1.63^{+0.10}_{-0.10}$ at 1283 MHz and $b = 1.20^{+0.13}_{-0.11}$ at 145 MHz. We also explore the X-ray surface brightness/radio spectral index correlation, finding a slope of $b = 0.59^{+0.11}_{-0.11}$. Both investigations support the evidence of spectral steepening. Finally, in the context of understanding the particle acceleration mechanism, we present a simple theoretical model which demonstrates that hybrid scenarios – secondary electrons (re-)accelerated by turbulence – reproduce a superlinear correlation slope.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1989

A Bayesian approach to reliability and confidence

The historical evolution of NASA's interest in quantitative measures of reliability assessment is outlined. The introduction of some quantitative methodologies into the Vehicle Reliability Branch of the Safety, Reliability and Quality Assurance (SR and QA) Division at Johnson Space Center (JSC) was noted along with the development of the Extended Orbiter Duration--Weakest Link study which will utilize quantitative tools for a Bayesian statistical analysis. Extending the earlier work of NASA sponsor, Richard Heydorn, researchers were able to produce a consistent Bayesian estimate for the reliability of a component and hence by a simple extension for a system of components in some cases where the rate of failure is not constant but varies over time. Mechanical systems in general have this property since the reliability usually decreases markedly as the parts degrade over time. While they have been able to reduce the Bayesian estimator to a simple closed form for a large class of such systems, the form for the most general case needs to be attacked by the computer. Once a table is generated for this form, researchers will have a numerical form for the general solution. With this, the corresponding probability statements about the reliability of a system can be made in the most general setting. Note that the utilization of uniform Bayesian priors represents a worst case scenario in the sense that as researchers incorporate more expert opinion into the model, they will be able to improve the strength of the probability calculations.

Barnes, Ron↗

NASA NTRS1992

The 1991 AVIRIS/POLDER experiment in Camargue, France

Airborne campaigns during the eighties provided high spectral resolution data, collected with imaging instruments such as AIS, AVIRIS, FLI, CAESI, and ISM, in order to investigate the relationship with canopy biophysical characteristics. The statistical approaches used to analyze these data do not allow investigation of the causality and the applicability of the observed correlations. Further, statistical studies demonstrated the high degree of redundancy of the spectral information amongst many others. And for retrieving vegetation biophysical characteristics, few results demonstrate the real information gain attributable to the high spectral resolution capability as compared to the use of a few wide wavelength bands. With several new imaging spectrophotometers scheduled for launch during the next 10 years (MERIS, MODIS, HIRIS), progress in the description and understanding of the mechanisms that drive the spectral variation of canopy reflectance is required. Most of these new sensor systems will also have the capability to observe the target under differing view directions. The problem of the combination and the use of the synergy between both the spectral and the directional sources of canopy reflectance variations has to be addressed. Apart from the atmospheric effects, the spectral variation of the light reflected by canopies originates from the leaves, the soil or the other vegetation elements such as branches and fruits. At leaf level, both diffuse reflectance and transmittance may be simulated by simple models, although no accurate information exists on the absorption features of the biochemicals (except water) in the 900-2500nm wavelength range. Many models mimic the directional variability of canopy reflectance at a given wavelength. Combining a leaf spectral model with a canopy directional model provides a powerful tool to analyze this problem. Some of us have initiated such a study, but our approach and theory remain to be tested using canopy data with their complexity, associated experimental error, and atmospheric effects. The main objective of the 1990 POLDER/AVIRIS experiment in Camargue was to provide a consistent data set over various canopies in order to test the applicability of the theory. The experiment, part of the 1991 MAC Europe experiment, involved simultaneous data collection using two sensors: AVIRIS and POLDER which measures the bidirectional and polarization properties of the targets at 670 and 880nm wavebands.

Baret, F.↗

DOE OSTI2023

Spectral statistics of a minimal quantum glass model

Glasses have the interesting feature of being neither integrable nor fully chaotic. They thermalize quickly within a subspace but thermalize much more slowly across the full space due to high free energy barriers which partition the configuration space into sectors. Past works have examined the Rosenzweig-Porter (RP) model as a minimal quantum model which transitions from localized to chaotic behavior. In this work we generalize the RP model in such a way that it becomes a minimal model which transitions from glassy to chaotic behavior, which we term the “Block Rosenzweig-Porter” (BRP) model. We calculate the spectral form factors of both models at all timescales larger than the inverse spectral width. Whereas the RP model exhibits a crossover from localized to ergodic behavior at the Thouless timescale, the new BRP model instead crosses over from glassy to fully chaotic behavior, as seen by a change in the steepness of the ramp of the spectral form factor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Generation of Fragment Angular Momentum in Fission

A recent analysis of experimental data [J. Wilson et al., Nature (London) 590, 566 (2021)] found that the angular momenta of nuclear fission fragments are uncorrelated. Based on this finding, the authors concluded that the spins are therefore determined only after scission has occurred. We show here that the nucleon-exchange mechanism, as implemented in the well-established event-by-event fission model freya, while agitating collective rotational modes in which the two spins are highly correlated, nevertheless leads to fragment spins that are largely uncorrelated. We find that this counterexample invalidates the conclusion in [J. Wilson et al.] that uncorrelated spins must necessarily have been generated after scission (a potentious conclusion that would rule out all models that generate the fragment spins prior to scission). Furthermore, it was reported [J. Wilson et al.] that the mass dependence of the average fragment spin has a sawtooth structure. We demonstrate that such a behavior naturally emerges when shell and deformation effects are included in the moments of inertia of the fragments at scission.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

A Gaussian process autoregressive model capturing microstructure evolution paths in a Ni–Mo–Nb alloy

Additive manufacturing is increasingly being employed to produce components of complex geometries in structural alloys because of the expected energy savings associated with the near-net-shape capability and the ability to build in novel internal features that are not possible with many conventional manufacturing approaches. However, because of the extreme thermal conditions encountered, the non-equilibrium microstructures produced during powder bed-based additive manufacturing processes must be subjected to custom post-heat treatment processes to recover the target mechanical properties. Phase-field models and simulation techniques have matured to a state where the microstructure evolution paths, and the morphologies of the resulting precipitate phases can be predicted reasonably accurately, considering alloy-specific thermodynamic and kinetic aspects of the nucleation and growth processes. However, phase-field simulations are computationally intensive, which precludes the ability to apply the simulations directly to the length scale of the entire component. Therefore, it is highly desirable to develop low-computational-cost surrogate models that effectively capture the physics at the microstructural length scale, while facilitating the design of optimized processing conditions resulting in location-specific targeted microstructures at the component scale. The work presented here demonstrates the application of the materials knowledge system framework to develop a surrogate model that effectively captures the microstructural path during annealing of a Ni–Mo–Nb alloy containing different Mo and Nb compositions known to segregate during solidification under additive manufacturing conditions. Specifically, the surrogate model built in this work is based on a Gaussian process autoregressive model informed by statistical representation of simulated microstructures using two-point correlations and dimensionality reduction through principal component analysis. In conclusion, this surrogate model is shown to capture the bifurcation of the microstructural path during precipitation, which yields a microstructure dominated by the $\gamma^{\prime\prime}$ phase at high Nb concentrations and the $\delta$ phase at low Nb concentrations.

36 MATERIALS SCIENCE↗

NASA NTRS2010

Hidden Statistics Approach to Quantum Simulations

Recent advances in quantum information theory have inspired an explosion of interest in new quantum algorithms for solving hard computational (quantum and non-quantum) problems. The basic principle of quantum computation is that the quantum properties can be used to represent structure data, and that quantum mechanisms can be devised and built to perform operations with this data. Three basic non-classical properties of quantum mechanics superposition, entanglement, and direct-product decomposability were main reasons for optimism about capabilities of quantum computers that promised simultaneous processing of large massifs of highly correlated data. Unfortunately, these advantages of quantum mechanics came with a high price. One major problem is keeping the components of the computer in a coherent state, as the slightest interaction with the external world would cause the system to decohere. That is why the hardware implementation of a quantum computer is still unsolved. The basic idea of this work is to create a new kind of dynamical system that would preserve the main three properties of quantum physics superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. In other words, such a system would reinforce the advantages and minimize limitations of both quantum and classical aspects. Based upon a concept of hidden statistics, a new kind of dynamical system for simulation of Schroedinger equation is proposed. The system represents a modified Madelung version of Schroedinger equation. It preserves superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. Such an optimal combination of characteristics is a perfect match for simulating quantum systems. The model includes a transitional component of quantum potential (that has been overlooked in previous treatment of the Madelung equation). The role of the transitional potential is to provide a jump from a deterministic state to a random state with prescribed probability density. This jump is triggered by blowup instability due to violation of Lipschitz condition generated by the quantum potential. As a result, the dynamics attains quantum properties on a classical scale. The model can be implemented physically as an analog VLSI-based (very-large-scale integration-based) computer, or numerically on a digital computer. This work opens a way of developing fundamentally new algorithms for quantum simulations of exponentially complex problems that expand NASA capabilities in conducting space activities. It has been illustrated that the complexity of simulations of particle interaction can be reduced from an exponential one to a polynomial one.

Zak, Michail↗

DOE OSTI2021

Power spectrum and form factor in random diagonal matrices and integrable billiards

Triggered by a controversy surrounding a universal behavior of the power spectrum in quantum systems exhibiting regular classical dynamics, we focus on a model of random diagonal matrices (RDM), often associated with the Poisson spectral universality class, and examine how the power spectrum and the form factor get affected by two-sided truncations of RDM spectra. Having developed a nonperturbative description of both statistics, we perform their detailed asymptotic analysis to demonstrate explicitly how a traditional assumption (lying at the heart of the controversy) – that the power spectrum is merely determined by the spectral form factor – breaks down for truncated spectra. This observation has important consequences as we further argue that bounded quantum systems with integrable classical dynamics are described by heavily truncated rather than complete RDM spectra. High-precision numerical simulations of semicircular and irrational rectangular billiards lend independent support to these conclusions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

First-principles calculation of the configurational energy density of states for a solid-state ion conductor with a variant of the Wang and Landau algorithm

In this work, a variant of the Wang and Landau algorithm for calculation of the configurational energy density of states is proposed. The algorithm was developed for the purpose of using first-principles simulations, such as density functional theory, to calculate the partition function of disordered sublattices in crystal materials. The expensive calculations of first-principles methods make a parallel algorithm necessary for a practical computation of the configurational energy density of states within a supercell approximation of a solid-state material. The algorithm developed in this work is tested with the two-dimensional (2d) Ising model to bench mark the algorithm and to help provide insight for implementation to a materials science application. Tests with the 2d Ising model revealed that the algorithm has good performance compared to the original Wang and Landau algorithm and the 1/$\textit{t}$ algorithm, in particular the short iteration performance. Further, a proof of convergence is presented within an adiabatic assumption, and the analysis is able to correctly predict the time dependence of the modification factor to the density of states. The algorithm was then applied to the lithium and lanthanum sublattice of the solid-state lithium ion conductor Li 0.5 La 0.5 TiO 3 . This was done to help understand the disordered nature of the lithium and lanthanum. The results find, overall, that the algorithm performs very well for the 2d Ising model and that the results for Li 0.5 La 0.5 TiO 3 are consistent with experiment while providing additional insight into the lithium and lanthanum ordering in the material. The primary result is that the lithium and lanthanum become more mixed between layers along the c axis for increasing temperature. In part, the simulation of the disordered Li 0.5 La 0.5 TiO 3 system serves as a benchmark for what size systems are currently and in the near future practical to calculate with density functional theory methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗