Search NASA⌕ Search

SEARCH · Search NASA

Results for “EIGENVECTOR”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

31 records · Page 2
All sourcesNASA NTRSDOE OSTI
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 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 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 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↗
DOE OSTI2025

Atomic dynamics in 𝑀⁢Cr⁢𝑋 2 (𝑀=Ag, Cu; 𝑋 = S, Se) across magnetic and superionic transitions

Here, a systematic study of atomic dynamics and thermal properties of the family of layered chalcogenide compounds 𝑀⁢Cr⁢𝑋 2 (𝑀= Ag, Cu; 𝑋 = S, Se) was performed, including neutron and x-ray scattering, thermal characterization, and first-principles simulations. In all compounds, we observe a breakdown of specific phonon modes across the superionic phase transition, for phonons whose eigenvectors exhibit large contributions of mobile ions. In particular, the nondispersive portions of transverse acoustic (TA) branches at short-wavelengths and the low-energy optical phonons with large contributions from Ag + or Cu + become severely damped in the superionic phase. However, well-defined quasiparticles persist in the superionic state for long-wavelength TA phonons. In the case of AgCrS 2 , the coupling of lattice dynamics with its antiferromagnetic transition was also investigated. The magnetic ordering couples with the monoclinic–rhombohedral structural transition, and the Cr 3+ spin arrangement strongly affects the phonon dispersions. We qualitatively reproduce the magnetic and nuclear components of the INS measurement for antiferromagnetic AgCrS 2 by combining models of spin-waves and spin-polarized first-principles phonon simulations. Quasielastic magnetic fluctuations persist in the paramagnetic phase up to high temperature, but are clearly distinguished from the nuclear component through their momentum dependence. Finally, we report measurements of the thermal properties of the selenide compounds and find good agreement with our DFT simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Lindblad many-body scars

Quantum many-body scars have received much recent attention for being both intriguing nonergodic states in otherwise quantum chaotic systems and promising candidates to encode quantum information efficiently. So far, these studies have mostly been restricted to Hermitian systems. Here, we study many-body scars in many-body quantum chaotic systems coupled to a Markovian bath, which we term Lindblad many-body scars. They are defined as simultaneous eigenvectors of the Hamiltonian and dissipative parts of the vectorized Liouvillian. Importantly, because their eigenvalues are purely real, they are not related to revivals. The number and nature of the scars depend on both the symmetry of the Hamiltonian and the choice of jump operators. For a dissipative four-body Sachdev-Ye-Kitaev (SYK) model with 𝑁 fermions, either Majorana or complex, we construct analytically some of these Lindblad scars while others could only be obtained numerically. As an example of the former, we identify 𝑁/2+1 scars for complex fermions due to the 𝑈⁡(1) symmetry of the model and two scars for Majorana fermions as a consequence of the parity symmetry. Similar results are obtained for a dissipative XXZ spin chain. We also characterize the physical properties of Lindblad scars. First, the operator size is independent of the disorder realization and has a vanishing variance. By contrast, the operator size for nonscarred states, believed to be quantum chaotic, is well described by a distribution centered around a specific size and a finite variance, which could be relevant for a precise definition of the eigenstate thermalization hypothesis in dissipative quantum chaos. Moreover, the entanglement entropy of these scars has distinct features such as a strong dependence on the partition choice and, in certain cases, a large entanglement.

Eigenstate thermalization↗
DOE OSTI2024

Analysis and Mitigation of Cascading Failures Using a Stochastic Interaction Graph with Eigen-analysis

In studies on complex network systems using graph theory, eigen-analysis is typically performed on an undirected graph model of the network. However, when analyzing cascading failures in a power system, the interactions among failures suggest the need for a directed graph beyond the topology of the power system to model directions of failure propagation. To accurately quantify failure interactions for effective mitigation strategies, this paper proposes a stochastic interaction graph model and associated eigen-analysis. Different types of modes on failure propagations are defined and characterized by the eigenvalues of a stochastic interaction matrix, whose absolute values are unity, zero, or in between. Finding and interpreting these modes helps identify the probable patterns of failure propagation, either local or widespread, and the participating components based on eigenvectors. Then, by lowering the failure probabilities of critical components highly participating in a mode of widespread failures, cascading can be mitigated. Here, the validity of the proposed stochastic interaction graph model, eigen-analysis and the resulting mitigation strategies is demonstrated using simulated cascading failure data on an NPCC 140-bus system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Parallel-in-Time Solution of Hyperbolic PDE Systems via Characteristic-Variable Block Preconditioning

We consider the parallel-in-time solution of both linear and nonlinear hyperbolic partial differential equation (PDE) systems in one spatial dimension. In the nonlinear setting, the discretized equations are solved with a preconditioned residual iteration based on a global linearization. The linear(ized) equation systems are approximately solved parallel-in-time using a block preconditioner applied in the characteristic variables of the underlying linear(ized) hyperbolic PDE. This change of variables is motivated by the observation that intervariable coupling between characteristic variables is weak, at least locally where spatio-temporal variations in the eigenvectors of the associated flux Jacobian are sufficiently small, while that between the original variables is not. For an ℓ-dimensional system of PDEs, applying the preconditioner consists of solving a sequence of ℓ scalar linear(ized)-advection-like problems, each associated with a different characteristic wave-speed in the underlying linear(ized) PDE. Furthermore, we approximately solve these linear advection problems using multigrid reduction-in-time (MGRIT); however, any other suitable parallel-in-time method could be used. Numerical examples are shown for the (linear) acoustics equations in heterogeneous media and for the (nonlinear) shallow water equations and Euler equations of gas dynamics with shocks and rarefactions. For many test problems, the solver converges in just a handful of iterations and with mesh-independent convergence rates.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

An experimental and computational investigation of the structure and spectroscopic signatures of α -UO 3

α-UO 3 is a common intermediate compound found in the nuclear fuel cycle, yet the exact crystal structure of this material has long been debated. Inconsistent computational and experimental data in previous works has led to varying conclusions between authors. Furthermore, to ensure the validity of our results in this work, the structural and spectroscopic signatures of pure phase α-UO 3 are investigated using powder X-ray diffraction and optical vibrational spectroscopy (infrared and Raman). Rietveld refinement of powder X-ray diffraction data on pure phase α-UO 3 collected in this work allows us to propose an alteration to the currently accepted C2mm structure (a = 3.9705 Å, b = 6.8553 Å, c = 4.15955 Å, α = β = γ = 90°) for α-UO 3 with no uranyl [UO 2 2+ ] bonds. Raman spectra collected using two excitation wavelengths (two instruments using 532 nm and one 785 nm) are presented, and differences with recently published results are discussed. Infrared spectra from two instruments used here agree well with recently published results, but the spectral range encompassed in our data extends past what has been reported with modern techniques. Additionally, we provide tentative vibrational mode assignments based on density functional perturbation theory calculations and resulting phonon eigenvector visualizations. Unexpected features in the optical vibrational spectra of α-UO 3 are explained by unique features in the structure we present.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2025

Application of automated iterative target detection for standoff hyperspectral imaging

The utility of hyperspectral imaging (HSI) has been well established for a wide array of applications but has generated a need for automated screening of high volumes of large HSI cubes. We report two important automated algorithms for more efficient standoff processing: atmospheric correction and target detection. The atmospheric correction method is based on a fast asymmetric least squares approach that is applied on a pixel-by-pixel basis. Here, the correction can be applied to entire images without manually identifying regions of interest and utilizes only in-scene information, no ancillary modeling of the atmosphere is required. An iterative target detection approach is also introduced which demonstrates faster speeds relative to moving window approaches. The target detection algorithm classifies each pixel as true target detections, near target detections, clutter, and no-calls. The algorithms were tested on forty images of twenty-two solid mineral targets placed at a 14-meter standoff distance allowing general observations on expected detection performance for a variety of minerals. In addition to identifying anomalous pixels, the inclusion of “no-calls” reduced the number of false detections significantly.

47 OTHER INSTRUMENTATION↗