Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Perturbative methods”

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.

At least 289 records · Page 16

Full-waveform tomography reveals iron spin crossover in Earth’s lower mantle

Abstract Three-dimensional models of Earth’s seismic structure can be used to identify temperature-dependent phenomena, including mineralogical phase and spin transformations, that are obscured in 1-D spherical averages. Full-waveform tomography maps seismic wave-speeds inside the Earth in three dimensions, at a higher resolution than classical methods. By providing absolute wave speeds (rather than perturbations) and simultaneously constraining bulk and shear wave speeds over the same frequency range, it becomes feasible to distinguish variations in temperature from changes in composition or spin state. We present a quantitative joint interpretation of bulk and shear wave speeds in the lower mantle, using a recently published full-waveform tomography model. At all depths the diversity of wave speeds cannot be explained by an isochemical mantle. Between 1000 and 2500 km depth, hypothetical mantle models containing an electronic spin crossover in ferropericlase provide a significantly better fit to the wave-speed distributions, as well as more realistic temperatures and silica contents, than models without a spin crossover. Below 2500 km, wave speed distributions are explained by an enrichment in silica towards the core-mantle boundary. This silica enrichment may represent the fractionated remains of an ancient basal magma ocean.

58 GEOSCIENCES↗

Spin-polarization anisotropy controlled by bending in tungsten diselenide nanoribbons and tunable excitonic states

A WSe 2 monolayer shows many interesting properties due to its spin-orbit coupling induced spin splitting in bands around the Fermi level and the spin-valley configuration. The orientation of the spin polarization in the relevant bands is crucial for the nature of exciton states and the optical valley selectivity. In this work, we studied the WSe 2 nanoribbons under different mechanical bending curvatures and electron/hole doping with density functional theory and their optical absorption and excitonic states with many-body perturbation GW and BSE (Bethe-Salpeter equation) methods. We found that the WSe 2 nanoribbons can exhibit an enhanced SOC effect and a spatially varying spin polarization in bands around the Fermi level under bending. The spin-polarization can show an anisotropy (or asymmetry) in those nearly degenerate bands, leading to a controllable magnetism via bending and electron/hole doping to the nanoribbons, suggesting a potential application in compact and controllable magnetic nanodevices and spintronics. The optical absorption spectrum of the nanoribbon presents a large tunability with bending within the near infrared region of about 0.4 to 1.5 eV, showing an enhanced absorption at a large bending condition. Finally, the exciton states generally show mixed or various spin configuration in the electron and hole pairs that are controlled by bending, potentially useful for applications in spin-based quantum information processes.

36 MATERIALS SCIENCE↗

Reconstruction of magnetic island electron temperature in mixed second and third harmonic electron cyclotron emission conditions

Here we develop a method to use the mixed third and second harmonic electron cyclotron emission (ECE) signal in the DIII-D tokamak to reconstruct the electron temperature profile of a rotating magnetic island. The third harmonic ECE is removed by extracting the rotating-island-associated fluctuations in the mixed signal, and the extracted fluctuation is combined with the equilibrium temperature obtained from other diagnostics after correcting for the third harmonic reabsorption. The accuracy of the reconstruction is studied by considering a DIII-D shot where an unmixed signal from an island is available on the low field side of the plasma and a mixed signal from the same island is available from the high field side. It is found that the reconstruction method successfully reproduces the island shape and temperature perturbation magnitude without the distortion caused by third harmonic ECE mixing. However, the radial location of the reconstructed island is somewhat displaced relative to the location of the q = 2 surface in the axisymmetric equilibrium reconstruction, resulting in a corresponding inaccuracy in the absolute temperature of the island. It is conjectured that this may arise from an inaccuracy of the reconstructed axisymmetric equilibrium in this region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Low-temperature breakdown of many-body perturbation theory for thermodynamics

It is shown analytically and numerically that the finite-temperature many-body perturbation theory in the grand canonical ensemble has zero radius of convergence at zero temperature when the energy ordering or degree of degeneracy for the ground state changes with the perturbation strength. When the degeneracy of the reference state is partially or fully lifted at the first-order Hirschfelder-Certain degenerate perturbation theory, the grand potential and internal energy diverge as T → 0. Contrary to earlier suggestions of renormalizability by the chemical potential μ, this nonconvergence, first suspected by W. Kohn and J. M. Luttinger, is caused by the nonanalytic nature of the Boltzmann factor e –E/k e T at T = 0, also plaguing the canonical ensemble, which does not involve chemical potential. The finding reveals a fundamental flaw in perturbation theory, which is deeply rooted in the mathematical limitation of power-series expansions and is unlikely to be removed within its framework.

74 ATOMIC AND MOLECULAR PHYSICS↗

International Workshop on Electronic Structure 2024 (ES 24)

The 36th annual Workshop on Recent Developments in Electronic Structure Theory commenced on June 2-5, 2024 at Boston University with 136 in-person and 75 virtual attendees. The organizing committee was composed of five faculty at Boston University with seven local area faculty comprising the greater Boston area advisory committee. On the first day, two hands-on workshops, NEXMD and ComDMFT were held on June 2, two full days of presentations were held on June 3-4 and one half day on June 5. There were 19 invited speakers who spoke about the state-of-the-art in electronic structure methods, including density functional theory, many-body perturbation theory, and the incorporation of machine learning into electronic structure calculations. In addition, 45 young scientists presented posters on June 4. Housing at a reduced rate was provided at the Boston University dormitories. This conference provided a valuable opportunity for scientists, students, postdocs, and senior researchers alike, to disseminate their latest research results, discuss their ideas and best practices, learn from each other, and form new collaborations.

42 ENGINEERING↗

Excited States of Crystalline Point Defects with Multireference Density Matrix Embedding Theory

Accurate and affordable methods to characterize the electronic structure of solids are important for targeted materials design. Embedding-based methods provide an appealing balance in the trade-off between cost and accuracy-particularly when studying localized phenomena. Here, we use the density matrix embedding theory (DMET) algorithm to study the electronic excitations in solid-state defects with a restricted open-shell Hartree-Fock (ROHF) bath and multireference impurity solvers, specifically, complete active space self-consistent field (CASSCF) and n-electron valence state second-order perturbation theory (NEVPT2). In this work, we apply the method to investigate the electronic excitations in an oxygen vacancy (OV) on a MgO(100) surface and find absolute deviations within 0.05 eV between DMET using the CASSCF/NEVPT2 solver, denoted as CAS-DMET/NEVPT2-DMET, and the nonembedded CASSCF/NEVPT2 approach. Next, we establish the practicality of DMET by extending it to larger supercells for the OV defect and a neutral silicon vacancy in diamond where the use of nonembedded CASSCF/NEVPT2 is extremely expensive.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Computing the QRPA level density with the finite amplitude method

Here, we describe a new algorithm to calculate the vibrational nuclear level density of an atomic nucleus. Fictitious perturbation operators that probe the response of the system are generated by drawing their matrix elements from some probability distribution function. We use the Finite Amplitude Method to explicitly compute the response for each such sample. With the help of the Kernel Polynomial Method, we build an estimator of the vibrational level density and provide the upper bound of the relative error in the limit of infinitely many random samples. The new algorithm can give accurate estimates of the vibrational level density. Since it is based on drawing multiple samples of perturbation operators, its computational implementation is naturally parallel and scales like the number of available processing units.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Community detection robustness of graph neural networks

Graph neural networks (GNNs) are increasingly widely used for community detection in attributed networks. They combine structural topology with node attributes through message passing and pooling. However, their robustness or lack thereof with respect to different perturbations and targeted attacks in conjunction with community detection tasks is not well understood. To shed light on latent mechanisms behind GNN sensitivity on community detection tasks, we conduct a systematic computational evaluation of six widely adopted GNN architectures graph convolutional network, graph attention network, graph sample and aggregate (GraphSAGE), differentiable pooling (DiffPool), minimum cut pooling (MinCUT), and deep modularity networks (DMoN). The analysis covers three perturbation categories: node attribute manipulations, edge topology distortions, and adversarial attacks. We use element-centric similarity as the evaluation metric on synthetic benchmarks and real-world citation networks. Our findings indicate that supervised GNNs tend to achieve higher baseline accuracy, while unsupervised methods, particularly DMoN, maintain stronger resilience under targeted and adversarial perturbations. Furthermore, robustness appears to be strongly influenced by community strength, with well-defined communities reducing performance loss. Across all models, node attribute perturbations associated with targeted edge deletions and shifts in attribute distributions tend to cause the largest degradation in community recovery. These findings highlight important trade-offs between accuracy and robustness in GNN-based community detection and offer insights into selecting architectures resilient to noise and adversarial attacks.

Goel, Jaidev [Virginia Polytechnic Inst. and State↗

Stochastic equation of motion approach to fermionic dissipative dynamics. I. Formalism

In this work, we establish formally exact stochastic equation of motion (SEOM) theory to describe the dissipative dynamics of fermionic open systems. The construction of the SEOM is based on a stochastic decoupling of the dissipative interaction between the system and fermionic environment, and the influence of environmental fluctuations on the reduced system dynamics is characterized by stochastic Grassmann fields. Meanwhile, numerical realization of the time-dependent Grassmann fields has remained a long-standing challenge. To solve this problem, we propose a minimal auxiliary space (MAS) mapping scheme with which the stochastic Grassmann fields are represented by conventional c-number fields along with a set of pseudo-levels. This eventually leads to a numerically feasible MAS-SEOM method. The important properties of the MAS-SEOM are analyzed by making connection to the well-established time-dependent perturbation theory and the hierarchical equations of motion theory. The MAS-SEOM method provides a potentially promising approach for the accurate and efficient simulation of fermionic open systems at ultra-low temperatures.

Han, Lu (ORCID:0000000339002225)↗

Self-consistency in GWΓ formalism leading to quasiparticle-quasiparticle couplings

Within many-body perturbation theory, Hedin's formalism offers a systematic way to iteratively compute the self-energy Σ of any dynamically correlated interacting system, provided one can evaluate the interaction vertex Γ exactly. This is, however, impossible, in general, for it involves the functional derivative of Σ with respect to the Green's function. Here, we analyze the structure of this derivative, splitting it into four contributions and outlining the type of quasiparticle interactions that each of them generate. Moreover, we show how, in the implementation of self-consistency, the action of these contributions can be classified into two: A quantitative renormalization of previously included interaction terms and the inclusion of qualitatively distinct interaction terms through successive functional derivatives of Γ itself. Implementing this latter type of self-consistency can extend the validity of perturbative approximations based on Hedin's equations toward the high interaction limit, as we show in the example of the Hubbard dimer. Furthermore, our analysis also provides a unifying perspective on the perturbation theory landscape, showing how the T-matrix approach is completely contained in Hedin's formalism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Real-time equation-of-motion CC cumulant and CC Green’s function simulations of photoemission spectra of water and water dimer

Newly developed coupled-cluster (CC) methods enable simulations of ionization potentials and spectral functions of molecular systems in a wide range of energy scales ranging from core-binding to valence. This paper discusses the results obtained with the real-time equation-of-motion CC cumulant (RT-EOM-CC) approach and CC Green’s function (CCGF) approaches in applications to the water and water dimer molecules. Here, we compare the ionization potentials obtained with these methods for the valence region with the results obtained with the coupled-cluster with singles, doubles, and perturbative triples formulation as a difference of energies for N and N – 1 electron systems. All methods show good agreement with each other. They also agree well with the experiment with errors usually below 0.1 eV for the ionization potentials. We also analyze unique features of the spectral functions, associated with the position of satellite peaks, obtained with the RT-EOM-CC and CCGF methods employing single and double excitations, as a function of the monomer OH bond length and the proton transfer coordinate in the dimer. Finally, we analyze the impact of the basis set effects on the quality of calculated ionization potentials and find that the basis set effects are less pronounced for the augmented-type sets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Predicting transcription factor activity using prior biological information

Dysregulation of normal transcription factor activity is a common driver of disease. Therefore, the detection of aberrant transcription factor activity is important to understand disease pathogenesis. We have developed Priori, a method to predict transcription factor activity from RNA sequencing data. Priori has two key advantages over existing methods. First, Priori utilizes literature-supported regulatory information to identify transcription factor-target gene relationships. It then applies linear models to determine the impact of transcription factor regulation on the expression of its target genes. Second, results from a third-party benchmarking pipeline reveals that Priori detects aberrant activity from 124 single-gene perturbation experiments with higher sensitivity and specificity than 11 other methods. We applied Priori and other top-performing methods to predict transcription factor activity from two large primary patient datasets. Our work demonstrates that Priori uniquely discovered significant determinants of survival in breast cancer and identified mediators of drug response in leukemia.

59 BASIC BIOLOGICAL SCIENCES↗

Diagonalizing the Born–Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom

This article describes a method for calculating higher order or nonadiabatic corrections in Born–Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner–Weyl correspondence to map nuclear operators into functions on the classical phase space and the Moyal star product to represent operator multiplication on those functions. These are explained in the body of the paper. The result is a power series in κ 2 , where κ = (m/M)1/4 is the usual Born–Oppenheimer parameter. The lowest order term is the usual Born–Oppenheimer approximation, while higher order terms are nonadiabatic corrections. These are needed in calculations of electronic currents, momenta, and densities. The separation of nuclear and electronic degrees of freedom takes place in the context of the exact symmetries (for an isolated molecule) of translations and rotations, and these, especially translations, are explicitly incorporated into our discussion. This article presents an independent derivation of the Moyal expansion in molecular Born–Oppenheimer theory. Here, we show how electronic currents and momenta can be calculated within the framework of Moyal perturbation theory; we derive the transformation laws of the electronic Hamiltonian, the electronic eigenstates, and the derivative couplings under translations; we discuss in detail the rectilinear motion of the molecular center of mass in the Born–Oppenheimer representation; and we show how the elimination of the translational components of the derivative couplings leads to a unitary transformation that has the effect of exactly separating the translational degrees of freedom.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Proposal and application of ROM-Lasso method for sensitivity coefficient evaluation

We propose a novel method for evaluating sensitivity coefficients of neutronics parameters to cross sections, so-called the reduced-order modeling technique ROM-Lasso. In this method, cross sections of interest are randomly sampled, and corresponding perturbed core analyses are performed. Then, the sensitivity coefficient vector of the higher-level model is expanded via the active subspace bases obtained with the lower-level model whose dimensional complexity is smaller than that of the higher-level model, and the expansion coefficients are estimated by the Lasso regression. A unique feature of the ROM-Lasso method allows the use of different bases optimized for each neutronics parameter. We conducted a verification calculation for an accelerator-driven system and demonstrated that the ROM-Lasso method can reproduce the sensitivity coefficients with a much smaller number of forward calculations than the direct method. The proposed method can be used to practically evaluate sensitivity coefficients. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Cosmological angular trispectra and non-Gaussian covariance

Angular cosmological correlators are infamously difficult to compute due to the highly oscillatory nature of the projection integrals. Motivated by recent development on analytic approaches to cosmological perturbation theory, in this paper we present an efficient method for computing cosmological four-point correlations in angular space, generalizing previous works on lower-point functions. This builds on the FFTLog algorithm that approximates the matter power spectrum as a sum over power-law functions, which makes certain momentum integrals analytically solvable. The computational complexity is drastically reduced for correlators in a "separable" form—we define a suitable notion of separability for cosmological trispectra, and derive formulas for angular correlators of different separability classes. As an application of our formalism, we compute the angular galaxy trispectrum at tree level, with and without primordial non-Gaussianity. This includes effects of redshift space distortion and bias parameters up to cubic order. We also compute the non-Gaussian covariance of the angular matter power spectrum due to the connected four-point function, beyond the Limber approximation. Finally, we demonstrate that, in contrast to the standard lore, the Limber approximation can fail for the non-Gaussian covariance computation even for large multipoles.

79 ASTRONOMY AND ASTROPHYSICS↗

Localizing resonant magnetic perturbations for edge localized mode control in KSTAR

An external 3D magnetic perturbation typically drives a resonant response at the rational surfaces from the core to the edge of tokamak plasmas, due to strong mode coupling and amplification. In this paper, we present a method to isolate the edge from core resonant fields using the ideal perturbed equilibrium code and to design an edge-localized resonant magnetic perturbation (RMP) for effective edge localized mode (ELM) control. A robust feature of the edge-localized RMP is the curtailed response to the field at the low-field-side (LFS) midplane, as opposed to typical RMPs which strongly resonate with the LFS fields. This emphasizes the importance of off-midplane coils to improve ELM control without provoking a large core response that could lead to devastating instabilities. The conceptual design of new ELM control coils based on the edge-localized RMP in KSTAR shows how this new insight can be utilized to enhance the efficiency of our ELM suppression capabilities. Simple window-pane coils matching the edge-localized resonant mode structure substantially expand in the ELM suppression window beyond the existing coil. Further optimization using the flexible optimized coils using space-curves code leads to additional enhancement in the edge-localized control.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Instability and turbulent relaxation in a stochastic magnetic field

An analysis of instability dynamics in a stochastic magnetic field is presented for the tractable case of the resistive interchange. Externally prescribed static magnetic perturbations convert the eigenmode problem to a stochastic differential equation, which is solved by the method of averaging. The dynamics are rendered multi-scale, due to the size disparity between the test mode and magnetic perturbations. Maintaining quasi-neutrality at all orders requires that small-scale convective cell turbulence be driven by disparate scale interaction. Here, the cells in turn produce turbulent mixing of vorticity and pressure, which is calculated by fluctuation-dissipation type analyses, and are relevant to pump-out phenomena. The development of correlation between the ambient magnetic perturbations and the cells is demonstrated, showing that turbulence will 'lock on' to ambient stochasticity. Magnetic perturbations are shown to produce a magnetic braking effect on vorticity generation at large scale. Detailed testable predictions are presented. The relations of these findings to the results of available simulations and recent experiments are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗