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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Explicit simulation of the Brownian rotation of arbitrary shaped aerosol particles using quaternions

The shape of an aerosol particle strongly influences its mass and momentum transfer cross-sections, charging properties, and other physical properties. Here, we present an explicit time-stepping procedure to simulate the rotational Brownian motion of arbitrary shaped aerosol particles by solving Euler’s equation of rotation. A Langevin formulation of the rotation equations is used, wherein Brownian motion due to thermal collisions between a particle and background gas molecules is represented using a stochastic fluctuating torque and fluid resistance is included as a drag torque. To avoid singularities associated with describing the orientation of a shape with Euler angles, we employ a quaternion formulation that leads to first-order stochastic differential equations to describe the evolution of the angular position and angular velocity of a rigid body. We perform all the rotational dynamics calculations in the body-fixed frame of reference attached to the rotating shape whose basis vectors are the normalized eigenvectors of the inertia tensor of the particle. Numerical solutions to rotation under torque-free conditions, damped rotation without Brownian motion, and stochastic rotation for arbitrary shapes are presented and discussed. The presented method enables time-resolved simulation of Brownian rotation for direct comparison with experimentally measured trajectories or statistical measures. The second order accuracy of the used time-stepping procedure places a severe restriction on the timestep that can be used for obtaining accurate results. Animations of presented simulations are included for visualizing rotational motion at various gas pressures. To aid implementation, MATLAB ® codes are also provided. Extension to include translation Brownian motion is straightforward.

Roy, Mrittika↗
DOE OSTI2024

Superconductor to exciton condensate transition in a model copper-oxide material

Abstract Superconductivity and exciton condensation are fundamental phenomena in condensed matter physics, associated with the condensation of electron–electron and electron–hole pairs, respectively, into coherent quantum states. In this study, we present evidence of a superconductor to exciton condensate transition within the context of the three-band Hubbard model of copper-oxide-like materials. As the electron–electron repulsion increases, the superconducting phase is superseded by exciton condensation. In support of theoretical predictions—not yet realized experimentally—we observe the coexistence of the two condensates in the vicinity of the transition where the quantum states become a superposition of electron–electron and electron–hole condensates. Coexistence is rigorously computed from large eigenvalues and their eigenvectors in both the two-electron reduced density matrix (2-RDM) and the particle-hole RDM, which we obtain from a direct variational ground-state energy minimization with respect to the 2-RDM by semidefinite programming. We further discern that adjacent d orbitals and intervening p orbitals facilitate electron–electron pairing between copper orbitals, thereby supporting the superexchange mechanism for superconductivity. These observations suggest the feasibility of witnessing a superconductor to exciton condensate transition in copper-oxide analogs, bearing significant implications for identifying materials conducive to efficient transport processes.

Schouten, Anna O. (ORCID:0000000264255219)↗
DOE OSTI2024

Computation of the expectation value of the spin operator S^ 2 for the spin-flip Bethe–Salpeter equation

Spin-flip (SF) methods applied to excited-state approaches like the Bethe–Salpeter equation allow access to the excitation energies of open-shell systems, such as molecules and defects in solids. The eigenstates of these solutions, however, are generally not eigenstates of the spin operator S^ 2 . Even for simple cases where the excitation vector is expected to be, for example, a triplet state, the value of S^ 2 may be found to differ from 2.00; this difference is called 'spin contamination'. The expectation values S^ 2 must be computed for each excitation vector, to assist with the characterization of the particular excitation and to determine the amount of spin contamination of the state. Here, our aim is to provide for the first time in the SF methods literature a comprehensive resource on the derivation of the formulas for S^ 2 as well as its computational implementation. After a brief discussion of the theory of the SF Bethe–Salpeter equation (BSE) and some examples further illustrating the need for calculating S^ 2 , we present the derivation for the general equation for computing S^ 2 with the eigenvectors from an SF-BSE calculation, how it is implemented in a Python script, and timing information on how this calculation scales with the size of the SF-BSE Hamiltonian.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Exploring the energy landscape of RBMs: reciprocal space insights into bosons, hierarchical learning and symmetry breaking

Deep generative models have become ubiquitous due to their ability to learn and sample from complex distributions. Despite the proliferation of various frameworks, the relationships among these models remain largely unexplored, a gap that hinders the development of a unified theory of AI learning. In this work, we address two central challenges: clarifying the connections between different deep generative models and deepening our understanding of their learning mechanisms. We focus on Restricted Boltzmann Machines (RBMs), a class of generative models known for their universal approximation capabilities for discrete distributions. By introducing a reciprocal space formulation for RBMs, we reveal a connection between these models, diffusion processes, and systems of coupled bosons. Our analysis shows that at initialization, the RBM operates at a saddle point, where the local curvature is determined by the singular values of the weight matrix, whose distribution follows the Marc̆enko-Pastur law and exhibits rotational symmetry. During training, this rotational symmetry is broken due to hierarchical learning, where different degrees of freedom progressively capture features at multiple levels of abstraction. This leads to a symmetry breaking in the energy landscape, reminiscent of Landau’s theory. This symmetry breaking in the energy landscape is characterized by the singular values and the weight matrix eigenvector matrix. We derive the corresponding free energy in a mean-field approximation. We show that in the limit of infinite size RBM, the reciprocal variables are Gaussian distributed. Our findings indicate that in this regime, there will be some modes for which the diffusion process will not converge to the Boltzmann distribution. To illustrate our results, we trained replicas of RBMs with different hidden layer sizes using the MNIST dataset. Our findings not only bridge the gap between disparate generative frameworks but also shed light on the fundamental processes underpinning learning in deep generative models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

The stellar mass Fundamental Plane: the virial relation and a very thin plane for slow rotators

ABSTRACT Early-type galaxies – slow and fast rotating ellipticals (E-SRs and E-FRs) and S0s/lenticulars – define a Fundamental Plane (FP) in the space of half-light radius Re, enclosed surface brightness Ie, and velocity dispersion σe. Since Ie and σe are distance-independent measurements, the thickness of the FP is often expressed in terms of the accuracy with which Ie and σe can be used to estimate sizes Re. We show that: (1) The thickness of the FP depends strongly on morphology. If the sample only includes E-SRs, then the observed scatter in Re is $\sim 16{{\ \rm per\ cent}}$, of which only $\sim 9{{\ \rm per\ cent}}$ is intrinsic. Removing galaxies with M* < 1011 M⊙ further reduces the observed scatter to $\sim 13{{\ \rm per\ cent}}$ ($\sim 4{{\ \rm per\ cent}}$ intrinsic). The observed scatter increases to $\sim 25{{\ \rm per\ cent}}$ usually quoted in the literature if E-FRs and S0s are added. If the FP is defined using the eigenvectors of the covariance matrix of the observables, then the E-SRs again define an exceptionally thin FP, with intrinsic scatter of only 5 per cent orthogonal to the plane. (2) The structure within the FP is most easily understood as arising from the fact that Ie and σe are nearly independent, whereas the Re−Ie and Re−σe correlations are nearly equal and opposite. (3) If the coefficients of the FP differ from those associated with the virial theorem the plane is said to be ‘tilted’. If we multiply Ie by the global stellar mass-to-light ratio M*/L and we account for non-homology across the population by using Sérsic photometry, then the resulting stellar mass FP is less tilted. Accounting self-consistently for M*/L gradients will change the tilt. The tilt we currently see suggests that the efficiency of turning baryons into stars increases and/or the dark matter fraction decreases as stellar surface brightness increases.

Bernardi, M.↗
DOE OSTI2022

The parameter-level performance of covariance matrix conditioning in cosmic microwave background data analyses

Empirical estimates of the band power covariance matrix are commonly used in cosmic microwave background (CMB) power spectrum analyses. While this approach easily captures correlations in the data, noise in the resulting covariance estimate can systematically bias the parameter fitting. Conditioning the estimated covariance matrix, by applying prior information on the shape of the eigenvectors, can reduce these biases and ensure the recovery of robust parameter constraints. In this work, we use simulations to benchmark the performance of four different conditioning schemes, motivated by contemporary CMB analyses. The simulated surveys measure the TT, TE, and EE power spectra over the angular multipole range 300 ≤ ℓ ≤ 3500 in Δℓ = 50 wide bins, for temperature map-noise levels of 10, 6.4, and $2\, \mu$K arcmin. We divide the survey data into N real = 30, 50, or 100 uniform subsets. We show the results of different conditioning schemes on the errors in the covariance estimate, and how these uncertainties on the covariance matrix propagate to the best-fitting parameters and parameter uncertainties. The most significant effect we find is an additional scatter in the best-fitting point, beyond what is expected from the data likelihood. For a minimal conditioning strategy, N real = 30, and a temperature map-noise level of 10$\, \mu$K arcmin, we find the uncertainty on the recovered best-fitting parameter to be ×1.3 larger than the apparent posterior width from the likelihood (×1.2 larger than the uncertainty when the true covariance is used). Stronger priors on the covariance matrix reduce the misestimation of parameter uncertainties to $\lt 1{{\ \rm per\ cent}}$. As expected, empirical estimates perform better with higher N real , ameliorating the adverse effects on parameter constraints.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Wave topology in Hall magnetohydrodynamics

Hall magnetohydrodynamics (HMHD) extends ideal MHD by incorporating the Hall effect via the induction equation, making it more accurate for describing plasma behavior at length scales below the ion skin depth. Despite its importance, a comprehensive description of the eigenmodes in HMHD has been lacking. In this work, we derive the complete spectrum and eigenvectors of HMHD waves and identify their underlying topological structure. We prove that the HMHD wave spectrum is homotopic to that of ideal MHD, consisting of three distinct branches: the slow magnetosonic-Hall waves, the shear Alfvén-Hall waves, and the fast magnetosonic-Hall waves, which continuously reduce to their ideal MHD counterparts in the limit of vanishing Hall parameter. Contrary to a recent claim [Mahajan, Sharma, and Lingam, Phys. Plasmas 31, 090701 (2024)], we find that HMHD does not admit any additional wave branches beyond those in ideal MHD. In conclusion, the key qualitative difference lies in the topological nature of the HMHD wave structure: it exhibits nontrivial topology characterized by a Weyl point—an isolated eigenmode degeneracy point—and associated nonzero Chern numbers of the eigenmode bundles over a 2-sphere in 𝐤-space surrounding the Weyl point.

Alfvén waves↗
DOE OSTI2025

Phonon spectrum in the spin-Peierls phase of CuGeO 3

CuGeO 3 has long been studied as a prototypical example of the spin-Peierls transition in a 𝑆 = 1/2 Heisenberg chain. Despite intensive investigation of this quasi-one-dimensional material, systematic measurements and calculations of the phonon excitations in the dimerized phase have not to date been possible, leaving certain aspects of the spin-Peierls phenomenon unresolved. We perform state-of-the-art density functional theory (DFT) calculations to compute the electronic structure and phonon dynamics in the low-temperature dimerized phase. We also perform high-resolution neutron spectroscopy to measure the full phonon spectrum over multiple Brillouin zones. We find excellent agreement between our numerical and experimental results that extend to all measurement temperatures. Notable features of our phonon spectra include a number of steeply dispersive modes, nonmonotonic dispersion features, and specific phonon anticrossings, which we relate to the mode eigenvectors. By calculating the magnetic interactions within DFT and studying the effects of different phonon modes on the superexchange paths, we discuss the possibility of observing spin-phonon hybridization effects in experiments performed both in and out of equilibrium.

density functional theory↗
DOE OSTI2021

Generalized measure of quantum Fisher information

Here, we present a lower bound on the quantum Fisher information (QFI) which is efficiently computable on near-term quantum devices. This bound itself is of interest, as we show that it satisfies the canonical criteria of a QFI measure. Specifically, it is essentially a QFI measure for subnormalized states, and hence it generalizes the standard QFI in this sense. Our bound employs the generalized fidelity applied to a truncated state, which is constructed via the m largest eigenvalues and their corresponding eigenvectors of the probe quantum state ρ θ . Focusing on unitary families of exact states, we analyze the properties of our proposed lower bound, and demonstrate its utility for efficiently estimating the QFI.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Analysis of diagonal G and subspace W approximations within fully self-consistent GW calculations for bulk semiconducting systems

Fully self-consistent GW (sc-GW) methods are now available to evaluate quasiparticle and spectral properties of various molecular and bulk systems. However, such techniques based on the full matrix of G and W are computationally demanding. Additionally, the routinely used single-shot GW approximation (G 0 W 0 ) has an undesirable dependency on the choice of initial exchange-correlation functional. In the literature, many so-called self-consistent GW methods are based on diagonal approximation of G and low-ranking approximation of W. It is thus worth checking how good such approximations are in comparison with the full matrix method. In this work, we consider AlAs, AlP, GaP, and ZnS as the prototype systems to perform sc-GW calculations by expressing the full G matrix using a plane-wave basis set. We compared our sc-GW results with the diagonal G and subspace W approximated sc-GW results (sc-GW-diagG and sc-GW-subW methods). In the sc-GW-diagG method, interacting G is expanded in the eigenvectors of noninteracting G such that only diagonal elements are retained, whereas the number of eigenmodes is truncated in sc-GW-subW calculations. A systematic analysis of the results obtained from the above techniques is presented. The differences in the quasiparticle band gap between the approximated and the full matrix sc-GW approaches are mostly less than 1.7%, which validates such widely adopted approximations, and also shows how such low-ranking approximation can be used to include higher-order terms such as the vertex correction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Rigorous constraints on three-nucleon forces in chiral effective field theory from fast and accurate calculations of few-body observables

We explore the constraints on the three-nucleon force (3NF) of chiral effective field theory (χ EFT) that are provided by bound-state observables in the A = 3 and A = 4 sectors. Our statistically rigorous analysis incorporates experimental error, computational method uncertainty, and the uncertainty due to truncation of the χ EFT expansion at next-to-next-to-leading order. A consistent solution for the 3 H binding energy, the 4 He binding energy and radius, and the 3 H β-decay rate can only be obtained if χ EFT truncation errors are included in the analysis. Here, the β-decay rate is the only one of these that yields a nondegenerate constraint on the 3NF low-energy constants, which makes it crucial for the parameter estimation. We use eigenvector continuation for fast and accurate emulation of no-core shell model calculations of the few-nucleon observables. This facilitates sampling of the posterior probability distribution, allowing us to also determine the distributions of the parameters that quantify the truncation error. We find a χ EFT expansion parameter of Q = 0.33 ± 0.06 for these observables.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Fast emulation of quantum three-body scattering

Here, we develop a class of emulators for solving quantum three-body scattering problems. They are based on combining the variational method for scattering observables and the recently proposed eigenvector continuation concept. The emulators are first trained by the exact scattering solutions of the governing Hamiltonian at a small number of points in its parameter space, and then employed to make interpolations and extrapolations in that space. Through a schematic nuclear-physics model with finite-range two and three-body interactions, we demonstrate the emulators to be extremely accurate and efficient. The computing time for emulation is on the scale of milliseconds (on a laptop), with relative errors ranging from 10 –13 to 10 –4 depending on the case. The emulators also require little memory. We argue that these emulators can be generalized to even more challenging scattering problems. Furthermore, this general strategy may be applicable for building the same type of emulators in other fields, wherever variational methods can be developed for evaluating physical models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Training and projecting: A reduced basis method emulator for many-body physics

Here, we present the reduced basis method as a tool for developing emulators for equations with tun able parameters within the context of the nuclear many-body problem. The method uses a basis expansion informed by a set of solutions for a few values of the model parameters and then projects the equations over a well-chosen low-dimensional subspace. We connect some of the results in the eigenvector continuation literature to the formalism of reduced basis methods and show how these methods can be applied to a broad set of problems. As we illustrate, the possible success of the formalism on such problems can be diagnosed beforehand by a principal component analysis. We apply the reduced basis method to the one-dimensional Gross-Pitaevskii equation with a harmonic trap ping potential and to nuclear density functional theory for 48 Ca, achieving speed-ups of more than x150 and x250, respectively, when compared to traditional solvers. The outstanding performance of the approach, together with its straightforward implementation, show promise for its application to the emulation of computationally demanding calculations, including uncertainty quantification.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Toward scalable bound-to-resonance extrapolations for few- and many-body systems

In open quantum many-body systems, the theoretical description of resonant states of many particles strongly coupled to the continuum can be challenging. Such states are commonplace in, for example, exotic nuclei and hadrons, and can reveal important information about the underlying forces at play in these systems. In this work, we demonstrate that the complex-augmented eigenvector continuation (CA-EC) method, originally formulated for the two-body problem with uniform complex scaling, can reliably perform bound-to-resonance extrapolations for genuine three-body resonances having no bound subsystems. Here, we first establish that three-body bound-to-resonance extrapolations are possible by benchmarking different few-body approaches, and we provide arguments to explain how the extrapolation works in the many-body case. We furthermore pave the way towards scalable resonance extrapolations in many-body systems by showing that the CA-EC method also works in the Berggren basis, studying a realistic application using the Gamow shell model.

Ab initio calculations↗
DOE OSTI2024

Gravitational form factors and mechanical properties of quarks in protons: A basis light-front quantization approach

We compute the gravitational form factors (GFFs) and study their applications for the description of the mechanical properties such as the pressure, shear force distributions, and the mechanical radius of the proton from its light-front wave functions (LFWFs) based on basis light-front quantization (BLFQ). The LFWFs of the proton are given by the lowest eigenvector of a light-front effective Hamiltonian that incorporates a three-dimensional confining potential and a one-gluon exchange interaction with fixed coupling between the constituent quarks solved in the valence Fock sector. We find acceptable agreement between our BLFQ computations and the lattice QCD for the GFFs. Our D -term form factor also agrees well with the extracted data from the deeply virtual Compton scattering experiments at Jefferson Lab, and the results of different phenomenological models. The distributions of pressures and shear forces are similar to those from different models. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2021

Distinct critical behaviors from the same state in quantum spin and population dynamics perspectives

There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations—within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wave-function amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: Phase transitions that are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions that are continuous become governed by new critical exponents. We introduce a more general class of models that encompasses both cases and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Nonlinear deformation and elasticity of BCC refractory metals and alloys

Application of isotropic pressure or uniaxial strain alters the elastic properties of materials; sufficiently large strains can drive structural transformations. Linear elasticity describes stability against infinitesimal strains, while nonlinear elasticity describes the response to finite deformations. Here, it was previously shown that uniaxial strain along [100] drives refractory metals and alloys towards mechanical instabilities. These include an extensional instability, and a symmetry-breaking orthorhombic distortion caused by a Jahn-Teller-Peierls instability that splays the cubic lattice vectors. Here we analyze these transitions in depth. Eigenvalues and eigenvectors of the Wallace tensor identify and classify linear instabilities in the presence of strain. We show that both instabilities are discontinuous, leading to discrete jumps in the lattice parameters. We provide physical intuition for the instabilities by analyzing the changes in first-principles energy, stress, bond lengths, and angles upon application of strain. Electronic band structure calculations show differential occupation of bonding and antibonding orbitals, driven by the changing bond lengths and leading to the structural transformations. Strain thresholds for these instabilities depend on the valence electron count.

36 MATERIALS SCIENCE↗
DOE OSTI2024

First-principles investigation of elastic, vibrational, and thermodynamic properties of kagome metals CsM 3 Te 5 (M = Ti, Zr, Hf)

Kagome metals are a unique class of quantum materials characterized by their distinct atomic lattice arrangement, featuring interlocking triangles and expansive hexagonal voids. These lattice structures impart exotic properties, including superconductivity, interaction-driven topological many-body phenomena, and magnetism, among others. The kagome metal CsM 3 ⁢Te 5 (where M = Ti, Zr, or Hf) exhibits both superconductivity and nontrivial topological electronic properties, offering a promising platform for exploring topological superconductivity. This study employs first-principles density functional theory calculations to systematically analyze the elastic, mechanical, vibrational, thermodynamic, and electronic properties of CsM 3 ⁢Te 5 (M = Ti, Zr, Hf). Our calculations reveal that the studied compounds—CsTi 3 ⁢Te 5 , CsZr 3 ⁢Te 5 , and CsHf 3 ⁢Te 5 —are ductile metals with elastic properties akin to the hexagonal Bi and Sb, with average elastic constants, including a bulk modulus of 27 GPa, a shear modulus of 11 GPa, and Young's modulus of 29 GPa. We observe peculiar dispersionless, flat, phonon branches in the vibrational spectra of these metals. Additionally, we thoroughly analyze the symmetries of the zone-center phonon eigenvectors and predict vibrational fingerprints of the Raman- and infrared-active phonon modes. The analysis of thermodynamic properties reveals the Einstein temperature for CsTi 3 ⁢Te 5 , CsZr 3 ⁢Te 5 , and CsHf 3 ⁢Te 5 to be 66, 54, and 53 K, respectively. Our orbital-decomposed electronic structure calculations reveal significant in-plane steric interactions and multiple Dirac band crossings near the Fermi level. We further investigate the role of spin-orbit coupling effect on the studied properties. Furthermore, this theoretical investigation sheds light on the intriguing quantum behavior of kagome metals.

36 MATERIALS SCIENCE↗