Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Group Theory and Generalizations”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Interacting fractons in 2+1-dimensional quantum field theory

We analyze, in perturbation theory, a theory of weakly interacting fractons and non-relativistic fermions in a 2+1 dimensional Quantum Field Theory. In particular we compute the 1-loop corrections to the self energies and interaction vertex, and calculate the associated 1-loop Renormalization Group flows of the coupling constants. Surprisingly, we find that the fracton-fermion coupling does not flow due to an emergent coordinate-dependent symmetry of the effective Lagrangian, making this model a well-defined quantum field theory. We provide additional discussions on the regularization and renormalization of interacting fractonic theories, as well as both qualitative and quantitative remarks regarding the theory at finite temperature and finite chemical potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Modification to the Hawking temperature of a dynamical black hole by a flow-induced supertranslation

One interesting proposal to solve the black hole information loss paradox without modifying either general relativity or quantum field theory, is the soft hair, a diffeomorphism charge that records the anisotropic radiation in the asymptotic region. This proposal, however, has been challenged, given that away from the source the soft hair behaves as a coordinate transformation that forms an Abelian group, thus unable to store any information. To maintain the spirit of the soft hair but circumvent these obstacles, we consider Hawking radiation as a probe sensitive to the entire history of the black hole evaporation, where the soft hairs on the horizon are induced by the absorption of a null anisotropic flow, generalizing the shock wave considered in [1, 2]. To do so we introduce two different time-dependent extensions of the diffeomorphism associated with the soft hair, where one is the backreaction of the anisotropic null flow, and the other is a coordinate transformation that produces the Unruh effect and a Doppler shift to the Hawking spectrum. Together, they form an exact BMS charge generator on the entire manifold that allows the nonperturbative analysis of the black hole horizon, whose surface gravity, i.e. the Hawking temperature, is found to be modified. The modification depends on an exponential average of the anisotropy of the null flow with a decay rate of 4M, suggesting the emergence of a new 2-D degree of freedom on the horizon, which could be a way out of the information loss paradox.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Systematic improvement of x -dependent unpolarized nucleon generalized parton distributions in lattice-QCD calculation

We present a first study of the effects of renormalization-group resummation (RGR) and leading-renormalon resummation (LRR) on the systematic errors of the unpolarized isovector nucleon generalized parton distribution in the framework of large-momentum effective theory. This work is done using lattice gauge ensembles generated by the MILC Collaboration, consisting of 2 + 1 + 1 flavors of highly improved staggered quarks with a physical pion mass at lattice spacing a ≈ 0.09 fm and a box width L ≈ 5.76 fm . We present results for the nucleon H and E generalized parton distributions (GPDs) with average boost momentum P z ≈ 2 GeV at momentum transfers Q 2 = [ 0 , 0.97 ] GeV 2 at skewness ξ = 0 as well as Q 2 ∈ 0.23 GeV 2 at ξ = 0.1 , renormalized in the modified minimal subtraction ( MS ¯ ) scheme at scale μ = 2.0 GeV , with two- and one-loop matching, respectively. We demonstrate that the simultaneous application of RGR and LRR significantly reduces the systematic errors in renormalized matrix elements and distributions for both the zero and nonzero skewness GPDs, and that it is necessary to include both RGR and LRR at higher orders in the matching and renormalization processes. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2021

The anomaly that was not meant IIB

Type IIB supergravity enjoys a discrete non-Abelian duality group, which has potential quantum anomalies. In this paper we explicitly compute these, and present the bordism group that controls them, modulo some physically motivated assumptions. Quite surprisingly, we find that they do not vanish, which naively would signal an inconsistency of F-theory. Remarkably, a subtle modification of the standard 10d Chern-Simons term cancels these anomalies, a fact which relies on the specific field content of type IIB supergravity. We also discover other ways to cancel this anomaly, via a topological analog of the Green-Schwarz mechanism. These alternative type IIB theories have the same low energy supergravity limit as ordinary type IIB, but a different spectrum of extended objects. They could either be part of the Swampland, or connect to the standard theory via domain walls.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Water-enhanced bifunctional metal-acid catalyst for C=C bond hydrogenation

Water-assisted proton shuttling can promote hydrogenation of polar functional groups, and it is generally believed that such an effect can be hardly applied to hydrogenation of C═C bonds due to the latter's weak interaction with water. Here, we report density functional theory calculations and metadynamics simulations, through which we show a dynamic bifunctional metal–acid site that can be transformed, when interacting with water, into an active configuration for unexpected water-enhanced proton shuttling to C═C bonds. In particular, we investigated B(OH)3 anchored to a Ni catalyst for hydrogenation of cyclohexene in an organic solvent, which showed in experiments an increased rate by 100 times when adding a small amount of water. Metadynamics simulations suggest that a B(OH)3–H2O cluster can form on Ni(111), which promotes the proton transfer in the first hydrogenation step, while the second hydrogenation is still driven by metal-mediated direct H-transfer. The recovery process of B(OH)3–H2O also involves a proton shuttling step. We find that the boric species on the surface serves as an electron reservoir and carries the negative charge to balance the positive charge in the proton transfer steps. This work thus provides fundamental insights into this dynamic transformation process of the metal–acid interface, which can in principle be applied to many other bifunctional systems for hydrogenating non-polar unsaturated groups by engineering the interfacial charge separation.

Sun, Shoutian↗
DOE OSTI2022

A note on the analytic structure of celestial amplitudes

Celestial amplitudes, obtained by applying Mellin transform and analytic continuation on “ordinary” amplitudes, have interesting properties which may provide useful insights on the underlying theory. Their analytic structures are thus of great interest and need to be better understood. In this paper, we critically examine the analytic structure of celestial amplitudes in a massless low-energy effective field theory. We find that, fixed-order loop contributions, which generate multipoles on the negative β-plane, in general do not provide an accurate description of the analytic structure of celestial amplitudes. By resumming over the leading logarithmic contributions using renormalization group equations (RGEs), we observe much richer analytic structures, which generally contain branch cuts. It is also possible to generate multipoles or shifted single poles if the RGEs satisfy certain relations. Including sub-leading logarithmic contributions is expected to introduce additional corrections to the picture. However, without a new approach, it is difficult to make a general statement since the analytic form of the Mellin transform is challenging to obtain.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Many-body localization transition with correlated disorder

We address the critical properties of the many-body localization (MBL) phase transition in one-dimensional systems subject to spatially correlated disorder. Rather than starting from a microscopic model, we analyze the transition within a strong-randomness renormalization group (RG) framework. We argue that anticorrelations in the disorder are generally irrelevant at the MBL transition. Furthermore, assuming the MBL transition is described by the recently developed renormalization-group scheme, we argue that even positively correlated disorder leaves the critical theory unchanged, although it modifies certain properties of the many-body localized phase.

1-dimensional systems↗
DOE OSTI2022

Reduced-order modeling of neutron transport separated in energy by Minimax Proper Generalized Decomposition

In this article, we demonstrate a Petrov-Galerkin Proper Generalized Decomposition (PGD) known as Minimax PGD for modeling neutron transport separated in energy. To compare the Minimax with the classical Galerkin PGD, we assess both on a model problem of UO{sub 2} or Mixed Oxide (MOX) fuel pins in an infinite lattice with 3 industry-standard energy meshes. We find the Minimax PGD achieves a superior decomposition to Galerkin PGD, both with and without update of the energy modes. This suggests Minimax PGD may be more computationally efficient, provided this reduction in modes (to achieve a given accuracy) outweighs the cost of solving the necessary adjoint problems. In either case, we note that PGD offers an a priori Reduced-Order Model (ROM) which may be dramatically cheaper to solve than the full-order model, especially in problems with fine to ultrafine energy meshes. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Long-Range Interaction between Molecules with Electronic Degeneracy: Beyond the Born–Oppenheimer Approximation

Long-range intermolecular interaction plays an essential role in (ultra)cold collisions. For monomers with degenerate electronic states, an accurate description of the long-range interaction can be challenging due to the potential breakdown of the Born–Oppenheimer approximation. In this work, we developed a general method to construct long-range interaction potential energy surfaces (IPESs) between arbitrary molecules using the degenerate perturbation theory of Schrödinger. To further simplify the application of this method, a group-theoretical method is introduced to identify nonzero components of electrostatic properties of monomers, especially for the nonlinear molecules. To demonstrate this approach, we report the long-range IPESs of the O( 3 P)–OH( 2 Π) and OH( 2 Π)–OH( 2 Π) systems. The excellent agreement with ab initio calculations in large separations, even near electronic degeneracies, confirms the accuracy of our approach. The method is expected to lay the groundwork for the accurate investigation of (ultra)cold collisional dynamics involving open-shell species.

ab initio calculations↗
DOE OSTI2020

Many-Body Effects in FeN4 Center Embedded in Graphene

We introduce a computational approach to study porphyrin-like transition metal complexes, bridging density functional theory and exact many-body techniques, such as the density matrix renormalization group (DMRG). We first derive a multi-orbital Anderson impurity Hamiltonian starting from first principles considerations that qualitatively reproduce generalized gradient approximation (GGA)+U results when ignoring inter-orbital Coulomb repulsion U ′ and Hund exchange J. An exact canonical transformation is used to reduce the dimensionality of the problem and make it amenable to DMRG calculations, including all many-body terms (both intra- and inter-orbital), which are treated in a numerically exact way. We apply this technique to FeN 4 centers in graphene and show that the inclusion of these terms has dramatic effects: as the iron orbitals become single occupied due to the Coulomb repulsion, the inter-orbital interaction further reduces the occupation, yielding a non-monotonic behavior of the magnetic moment as a function of the interactions, with maximum polarization only in a small window at intermediate values of the parameters. Furthermore, U ′ changes the relative position of the peaks in the density of states, particularly on the iron d z 2 orbital, which is expected to affect the binding of ligands greatly.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Holographic entanglement from the UV to the IR

In AdS/CFT, observables on the boundary are invariant under renormalization group (RG) flow in the bulk. In this paper, we study holographic entanglement entropy under bulk RG flow and find that it is indeed invariant. We focus on tree-level RG flow, where massive fields in a UV theory are integrated out to give the IR theory. We explicitly show that in several simple examples, holographic entanglement entropy calculated in the UV theory agrees with that calculated in the IR theory. Moreover, we give an argument for this agreement to hold for general tree-level RG flow. Along the way, we generalize the replica method of calculating holographic entanglement entropy to bulk theories that include matter fields with nonzero spin.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A topological way of finding solutions to the Yang–Mills equation

We propose a systematic way of finding solutions to the classical Yang–Mills equation with nontrivial topology. This approach is based on one of the Wightman axioms for quantum field theory, which is referred to as the form invariance condition in this paper. For a given gauge group and a spacetime with certain isometries, thanks to this axiom that imposes strong constraints on the general ansatz, a systematic way of solving the Yang–Mills equation can be obtained in both flat and curved spacetimes. In order to demonstrate this method, we recover various known solutions as special cases, as well as producing new solutions not previously reported in the literature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Group structure selection with random forests

Choosing an appropriate group structure for multigroup transport is far from an exact science. For some applications, one blindly uses a group structure developed years ago by forgotten methods. Furthermore, one sometimes uses the same group structure for a variety of problems, even if the group structure was originally developed with a certain application in mind. In this work, we create optimized group structures with simulated annealing for critical assembly test problems and apply a random forest regressor with bagging to choose the best group structure based on parameters of the different test problems. The optimized group structures were generated using a simulated annealing optimizer for several simple, spherical, and unreflected problems. The optimization was performed to minimize a cost function that included fission rate, absorption rate, leakage, and k{sub eff}. A random forest regressor was then trained on a set of International Criticality Safety Benchmark Evaluation Project inputs and used to select one of these six group structures. The trained machine learning model chose the best group structure 65% of the time, and one of the three best 89% of the time. Furthermore, it decreased the L2 error over all test problems by a factor of 25 when compared to the standard Los Alamos 70-group structure. In other words, the model chose group structure that were far more appropriate for the test problems than the traditional LANL group structure. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

U(1) fields from qubits: An approach via D-theory algebra

A new quantum link microstructure was proposed for the lattice quantum chromodynamics (QCD) Hamiltonian, replacing the Wilson gauge links with a bilinear of fermionic qubits, later generalized to D-theory. This formalism provides a general framework for building lattice field theory algorithms for quantum computing. We focus mostly on the simplest case of a quantum rotor for a single compact U(1) field. We also make some progress for non-Abelian setups, making it clear that the ideas developed in the U(1) case extend to other groups. These in turn are building blocks for 1 + 0 -dimensional ( 1 + 0 -D) matrix models, 1 + 1 -D sigma models and non-Abelian gauge theories in 2 + 1 and 3 + 1 dimensions. By introducing multiple flavors for the U(1) field, where the flavor symmetry is gauged, we can efficiently approach the infinite-dimensional Hilbert space of the quantum O(2) rotor with increasing flavors. The emphasis of the method is on preserving the symplectic algebra exchanging fermionic qubits by sigma matrices (or hard bosons) and developing a formal strategy capable of generalization to a SU ( 3 ) field for lattice QCD and other non-Abelian 1 + 1 -D sigma models or 3 + 1 -D gauge theories. For U(1), we discuss briefly the qubit algorithms for the study of the discrete 1 + 1 -D sine-Gordon equation. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2022

Diabatic Valence-Hole States in the C 2 Molecule: “Putting Humpty Dumpty Together Again”

Despite the long history of spectroscopic studies of the C$_2$ molecule, fundamental questions about its chemical bonding are still being hotly debated. The complex electronic structure of C$_2$ is a consequence of its dense manifold of near-degenerate, low-lying electronic states. A global multi-state diabatic model is proposed here to disentangle the numerous configuration interactions within four symmetry manifolds of C$_2$ ($^{1}\Pi_g$, $^{3}\Pi_g$, $^{1}\Sigma_u^+$, and $^{3}\Sigma_u^+$). The key concept of our model is the existence of two "valence-hole" configurations, $2\sigma_g^22\sigma_u^11\pi_{u}^33\sigma_g^2$ for $^{1,3}\Pi_g$ states and $2\sigma_g^22\sigma_u^11\pi_{u}^43\sigma_g^1$ for $^{1,3}\Sigma_u^+$ states that derive from $3\sigma_g\leftarrow2\sigma_u$ electron promotion. The lowest-energy state from each of the four C$_2$ symmetry species is dominated by this type of valence-hole configuration at its equilibrium internuclear separation. Finally, as a result of their large binding energy (nominal bond order of 3) and correlation with the 2s$^2$2p$^2$+2s2p$^3$ separated-atom configurations, the presence of these valence-hole configurations has a profound impact on the $global$ electronic structure and unimolecular dynamics of C$_2$.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Minimization of Disorder as a Key Design Principle for Natural Sizes of Light Harvesting 2 Complexes

The light harvesting 2 (LH2) complex of purple bacteria has excellent energy conversion efficiency. Clarifying the design principle behind such efficiency at the atomistic level is crucial for understanding its structure–function relationship and can be utilized for the design of artificial light harvesting systems. To this end, we conducted comprehensive computational investigation of the dynamical and statistical nature of electronic excited states of pigment molecules in a natural LH2 complex with 9-fold symmetry and its two non-natural in silico analogues with 6- and 12-fold symmetries. To ensure reliable and efficient all-atomistic molecular dynamics simulations, we combined a well established interpolation approach for the construction of the potential energy surface with a neural network machine learning approach. Outcomes of these calculations clarify that non-natural forms of LH2-type complexes have significantly larger quasistatic disorder than those for the natural one. In addition, non-natural systems have more disruptions of the hydrogen bonding, underscoring its crucial role for reducing the disorder. On the other hand, local environmental dynamics are relatively insensitive to the structural changes although there is moderate enhancement in the anharmonic or interatomic components for the synthetic ones. These findings based on all-atomistic simulations provide direct computational evidence that the structure and sizes of natural LH2 complexes are designed to minimize the energetic disorder. We analyze quantitative implications of these for the energy transferring capability of the LH2 complex.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Chiral algebra, localization, modularity, surface defects, and all that

We study the 2D vertex operator algebra (VOA) construction in 4D N = 2 superconformal field theories on S 3 × S 1 , focusing on both old puzzles and new observations. The VOA lives on a two-torus T 2 ⊂ S 3 × S 1 , it is 1 2 Z -graded, and this torus is equipped with the natural choice of spin structure (1,0) for the Z + 1 2 -graded operators, corresponding to the NS sector vacuum character. By analyzing the possible refinements of the Schur index that preserves the VOA, we find that it admits discrete deformations, which allows access to the remaining spin structures (1,1), (0,1), and (0,0), of which the latter two involve the inclusion of a particular surface defect. For Lagrangian theories, we perform the detailed analysis: we describe the natural supersymmetric background, perform localization, and derive the gauged symplectic boson action on a torus in any spin structure. In the absence of flavor fugacities, the 2D and 4D path integrals precisely match, including the Casimir factors. We further analyze the 2D theory: we identify its integration cycle and the two-point functions and interpret flavor holonomies as screening charges in the VOA. Next, we make some observations about modularity; the T-transformation acts on our four partition functions and lifts to a large diffeomorphism on S 3 × S 1 . More interestingly, we generalize the four partition functions on the torus to an infinite family labeled by both the spin structure and the integration cycle inside the complexified maximal torus of the gauge group. Members of this family transform into one another under the full modular group, and we confirm the recent observation that the S-transform of the Schur index in Lagrangian theories exhibits logarithmic behavior. Finally, we comment on how locally our background reproduces the Ω-background.

97 MATHEMATICS AND COMPUTING↗