Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “GROUP THEORY”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Non-invertible symmetries in finite-group gauge theory

We investigate the invertible and non-invertible symmetries of topological finite-group gauge theories in general spacetime dimensions, where the gauge group can be abelian or non-abelian. We focus in particular on the 0-form symmetry. The gapped domain walls that generate these symmetries are specified by boundary conditions for the gauge fields on either side of the wall. We investigate the fusion rules of these symmetries and their action on other topological defects including the Wilson lines, magnetic fluxes, and gapped boundaries. We illustrate these constructions with various novel examples, including non-invertible electric-magnetic duality symmetry in 3+1d \mathbb{Z}_2 ℤ 2 gauge theory, and non-invertible analogs of electric-magnetic duality symmetry in non-abelian finite-group gauge theories. In particular, we discover topological domain walls that obey Fibonacci fusion rules in 2+1d gauge theory with dihedral gauge group of order 8. We also generalize the Cheshire string defect to analogous defects of general codimensions and gauge groups and show that they form a closed fusion algebra.

Córdova, Clay↗
DOE OSTI2012

Uncertainty quantification of few group diffusion theory constants generated by the B1 theory-augmented Monte Carlo method

The purpose of this paper is to quantify uncertainties of fuel pin cell or fuel assembly (FA) homogenized few group diffusion theory constants generated from the B1 theory-augmented Monte Carlo (MC) method. A mathematical formulation of the first kind is presented to quantify uncertainties of the few group constants in terms of the two major sources of the MC method; statistical and nuclear cross section and nuclide number density input data uncertainties. The formulation is incorporated into the Seoul National Univ. MC code McCARD. It is then used to compute the uncertainties of the burnup-dependent homogenized two group constants of a low-enriched UO{sub 2} fuel pin cell and a PWR FA on the condition that nuclear cross section input data of U-235 and U-238 from JENDL 3.3 library and nuclide number densities from the solution to fuel depletion equations have uncertainties. The contribution of the MC input data uncertainties to the uncertainties of the two group constants of the two fuel systems is separated from that of the statistical uncertainties. The utilities of uncertainty quantifications are then discussed from the standpoints of safety analysis of existing power reactors, development of new fuel or reactor system design, and improvement of covariance files of the evaluated nuclear data libraries. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1989

Group-kinetic theory and modeling of atmospheric turbulence

A group kinetic method is developed for analyzing eddy transport properties and relaxation to equilibrium. The purpose is to derive the spectral structure of turbulence in incompressible and compressible media. Of particular interest are: direct and inverse cascade, boundary layer turbulence, Rossby wave turbulence, two phase turbulence; compressible turbulence, and soliton turbulence. Soliton turbulence can be found in large scale turbulence, turbulence connected with surface gravity waves and nonlinear propagation of acoustical and optical waves. By letting the pressure gradient represent the elementary interaction among fluid elements and by raising the Navier-Stokes equation to higher dimensionality, the master equation was obtained for the description of the microdynamical state of turbulence.

Tchen, C. M.↗
DOE OSTI2011

SIMILARITY PROPERTIES AND SCALING LAWS OF RADIATION HYDRODYNAMIC FLOWS IN LABORATORY ASTROPHYSICS

The spectacular recent development of modern high-energy density laboratory facilities which concentrate more and more energy in millimetric volumes allows the astrophysical community to reproduce and to explore, in millimeter-scale targets and during very short times, astrophysical phenomena where radiation and matter are strongly coupled. The astrophysical relevance of these experiments can be checked from the similarity properties and especially scaling law establishment, which constitutes the keystone of laboratory astrophysics. From the radiating optically thin regime to the so-called optically thick radiative pressure regime, we present in this paper, for the first time, a complete analysis of the main radiating regimes that we encountered in laboratory astrophysics with the same formalism based on Lie group theory. The use of the Lie group method appears to be a systematic method which allows us to construct easily and systematically the scaling laws of a given problem. This powerful tool permits us to unify the recent major advances on scaling laws and to identify new similarity concepts that we discuss in this paper, and suggests important applications for present and future laboratory astrophysics experiments. All these results enable us to demonstrate theoretically that astrophysical phenomena in such radiating regimes can be explored experimentally thanks to powerful facilities. Consequently, the results presented here are a fundamental tool for the high-energy density laboratory astrophysics community in order to quantify the astrophysics relevance and justify laser experiments. Moreover, relying on Lie group theory, this paper constitutes the starting point of any analysis of the self-similar dynamics of radiating fluids.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

The zipper groups of the amyloid state of proteins

A formal derivation is provided of the 15 symmetry groups (zipper groups) available to the amyloid homosteric zipper. Fibrous proteins in the amyloid state are found both associated with numerous diseases and in the normal functions of cells. Amyloid fibers contain a repetitive spine, commonly built from a pair of β-sheets whose β-strands run perpendicular to the fiber direction and whose side chains interdigitate, much like the teeth of a zipper. In fiber spines known as homosteric zippers, identical protein segments sharing identical packing environments make the two β-sheets. In previous work based on atomic resolution crystal structures of homosteric zippers derived from a dozen proteins, the symmetries of homosteric zippers were categorized into eight classes. Here, it is shown through a formal derivation that each homosteric zipper class corresponds to a unique set of symmetry groups termed ‘zipper groups’. Furthermore, the eight previously identified classes do not account for all of the 15 possible zipper groups, which may be categorized into the complete set of ten classes. Because of their foundations in group theory, the 15 zipper groups provide a mathematically rigorous classification for homosteric zippers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Enhanced Second and Third Harmonic Generations in Metasurfaces Enabled through Point Group Design and Accidental Bound States in the Continuum

Here, we investigate enhanced second‑ and third‑harmonic generation (SHG and THG) in GaAs metasurfaces by combining electromagnetic point‑group designs with accidental bound states in the continuum (BICs). Using group theory, we predict the existence, suppression, and polarization selection rules of SHG and THG for metasurfaces belonging to the D 2h and C 2v point groups. In D 2h metasurfaces, inversion symmetry suppresses SHG while enabling polarization‑selective THG, which is strongly enhanced near accidental BICs with ultrahigh Q‑factors approaching 107. By breaking inversion symmetry to form C 2v metasurfaces through the introduction of nanogaps, SHG is now allowed and is dramatically enhanced near accidental BICs. Importantly, accidental BICs preserve polarization selection rules while providing a robust parameter range for high‑Q resonances, in contrast to quasi‑BICs induced by symmetry breaking. Our results demonstrate that the combination of point‑group theory and accidental‑BIC engineering offers a predictive and robust route toward highly efficient nonlinear metasurfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

A Theoretical Investigation of the Structure and Reactivity of the Molecular Constituents of Oil Sand and Oil Shale

We used a variety of small organic models of asphaltenes to investigate the molecular mechanism for the high temperature decomposition that would take place as part of the oil refinery process. We determined that the decomposition is initiated via four different types of hydrogen migration reactions. According to the energetics of the reactions, the dominant 1,2-H shift mechanism involves two competitive product channels, namely, C 2 H 2 + CH 2 CS and CS + CH 3 CCH. The minor channels include the formation of CS + CH 2 CCH 2 , H 2 S + C 4 H 2 , HCS + CH 2 CCH, CS + CH 2 CHCH, H + C 4 H 3 S, and HS + C 4 H 3 . We also investigated the alkyl substitution effect by exploring the decomposition pathways of models with alkyl arms. The energetics of such systems were very similar to that for unsubstituted model compounds, which suggests that asphaltene alkylation may not play a significant role in the decomposition of asphaltene compounds. This work was published in the Journal of Physical Chemistry A 2011, 115, 2882-2891. A MECHANISTIC STUDY OF THE 2-THIENYLMETHYL + HO2 RADICAL RECOMBINATION REACTION Radicals are molecules which contain single electrons. They are very reactive. Radical recombination reactions are important in the combustion of fuel oils. Shale oil contains radicals. We used quantum mechanics to explore the reactivity of shale oil model radical compounds. Seventeen product channels corresponding to either addition/elimination or direct hydrogen abstraction were characterized. Direct hydrogen abstraction proceeds via a weakly bonded complex, which leads to 2-methylthiophene, 2-methylene-2,3-dihydrothiophene or 2-methylene-2,5-dihydrothiophene depending upon the 2-thienylmethyl radical reaction site. The addition pathway for the two radical reactants is barrierless with the formation of three adducts, as distinguished by HO 2 reaction at three different sites on the 2-thienylmethyl radical. The addition is exothermic by 37 ~ 55 kcal mol-1 relative to the entrance channel. These excess energies are available to promote further decomposition or rearrangement of the adducts that lead to nascent products such as H, OH, H 2 O and CH 2 O. The reaction surfaces are characterized by relatively low barriers (most are lower than 10 kcal mol-1). Based upon a careful analysis of the overall barrier heights and reaction exothermicities, the formation of O2, OH and H2O is likely to be an important pathway in the radical recombination reactions of 2-thienylmethyl + HO 2 . This work was published in the Journal of Physical Chemistry A, 2011, 115, 14546-14557. REACTION OF THIOPHENE AND METHYLTHIOPHENE WITH SINGLET AND TRIPLET MOLECULAR OXYGEN Mechanisms for the reaction of thiophene and 2-methylthiophene with molecular oxygen on both the triplet and singlet potential energy surfaces (PESs) were investigated using ab initio methods. Thiophene and 2-methylthiophene where shown to react with O 2 via two types of mechanisms; namely, direct hydrogen abstraction and addition/elimination. The barriers for reaction with triplet oxygen are all significantly large (i.e., > 30 kcal mol-1), which indicates that the direct oxidation of thiophene by ground state oxygen might be important only in high temperature processes. Reaction of thiophene with singlet oxygen via a 2+4 cycloaddition leading to endoperoxides is the most favorable channel. Moreover, it was found that alkylation of the thiophene ring (i.e., methyl-substituted thiophene) is capable of lowering the barrier height for the addition pathway. The implication of the current theoretical results may shed new light on the initiation mechanisms for combustion of asphaltenes. This work was published in the Journal of Physical Chemistry A, 2012 116, 4934-4946. JAHN-TELLER STABILIZATION IN POSS CATIONS We have a long standing interest in polyoligomeric silsesquioxane (POSS) molecules. 1-2 These molecules have recently been used as advanced surface coatings for photovoltaic devices and have potential as molecular-based energy storage devices as well as magnetically controllable liquid marbles. 3-5 We have been investigating the small molecule encapsulation properties of POSS and discovered some interesting symmetry breaking processes that need to be better understood in order to use POSS in advanced materials. We have investigated this symmetry breaking mechanism in POSS monocations Si8O12(C(CH3)3)8+ and Si8O12Cl8+, using density functional theory (DFT) and group theory. Under Oh symmetry, these ions possess 2T2g and 2Eg electronic states, respectively, and undergo different symmetry breaking mechanisms. The ground states of Si 8 O 12 (C(CH 3 ) 3 ) 8 + and Si 8 O 12 Cl 8 + belong to the C 3v and D 4h point groups and are characterized by Jahn-Teller stabilization energies of 3959 and 1328 cm-1, respectively, at the B3LYP/def2-SVP level of theory. The symmetry distortion mechanism in Si 8 O 12 Cl 8 + is Jahn-Teller type, whereas in Si 8 O 12 (C(CH 3 ) 3 ) 8 + the distortion is a combination of both Jahn-Teller and pseudo-Jahn-Teller effects. The distortion force acting in Si 8 O 12 (C(CH 3 ) 3 ) 8 + is mainly localized on one Si-(tert-butyl) group while in Si 8 O 12 Cl 8 + it is distributed over the oxygen atoms. The main distortion forces acting on the Si8O12 core arise from the coupling between the electronic state and the vibrational modes; identified as 9t 2g +1e g +3a 2u for the Si 8 O 12 (C(CH 3 ) 3 ) 8 + and 1e g +2e g for Si 8 O 12 Cl 8 + . This work was published in the Journal of Physical Chemistry A, 2015, 119, 4237-4243.

04 OIL SHALES AND TAR SANDS↗
DOE OSTI2021

Revisiting group contribution theory for estimating fractional free volume of microporous polymer membranes

Fractional free volume (FFV) is a commonly used metric for the development of structure–property relationships for polymer membranes. The most common method to calculate FFV uses Bondi's group contribution method, first introduced in 1964. While updated in 1997, there has not been a significant compilation of new structural motifs since the advent of linear microporous polymers. Here, in this study, we critically examined the assumptions in Bondi's original method and provide four recommendations to streamline and improve the accuracy of calculating van der Waals volume (V W ) for any group. Using these recommendations, we created an updated list of (V W ) values for structural groups commonly present in microporous polymers. The (V W ) and FFV values were then calculated for a database of 123 microporous and high free volume polymers from the literature, showing an average 7% decrease in (V W ) and corresponding increase in FFV by a factor of 24% when compared to prior group contribution correlations in the literature. The significant apparent increase in estimated FFV provides a new perspective to understand and interpret the role of free volume on the separation performance of linear microporous polymers. Additionally, standardization of the group contribution method allows for the direct comparison of FFV values across studies.

42 ENGINEERING↗
DOE OSTI2010

Size-Dependent Infrared Phonon Modes and Ferroelectric Phase Transition in BiFe03 Nanoparticles

One emergent property of ferroelectric nanoparticles is the sized-induced structural distortion to a high-symmetry paraelectric phase at small particle sizes. Finite length scale effects can thus be advantageously employed to elucidate ferroelectric transition mechanisms. In this work, we combine infrared spectroscopy with group theory and lattice dynamics calculations to reveal the displacive nature of the ferroelectric transition in BiFeO{sub 3}, a room temperature multiferroic. Systematic intensity and frequency trends in selected vibrational modes show that the paraelectric phase is Pm{sub 3}m and the lowest frequency A{sub 1} feature is the soft mode that drives the first order transition. Finite length scale effects are also evident in the electronic structure with a red-shifted band gap in nanoscale BiFeO{sub 3} compared with that of the rhombohedral film, a result that can impact the development of ferroelectric photovoltaics and oxide-based electronics. Taken together, these findings demonstrate the foundational importance of size effects for enhancing the rich functionality and broad utility of transition metal oxides.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1972

System theory on group manifolds and coset spaces.

The purpose of this paper is to study questions regarding controllability, observability, and realization theory for a particular class of systems for which the state space is a differentiable manifold which is simultaneously a group or, more generally, a coset space. We show that it is possible to give rather explicit expressions for the reachable set and the set of indistinguishable states in the case of autonomous systems. We also establish a type of state space isomorphism theorem. Our objective is to reduce all questions about the system to questions about Lie algebras generated from the coefficient matrices entering in the description of the system and in that way arrive at conditions which are easily visualized and tested.

Brockett, R. W.↗
DOE OSTI2023

Benchmarks and results of the two-band Hubbard model from the Gutzwiller conjugate gradient minimization theory

Ground-state properties, such as energies and double occupancies, of a one-dimensional two-band Hubbard model are calculated using a first-principles Gutzwiller conjugate gradient minimization theory. The favorable agreement with the results from the density matrix renormalization group theory demonstrates the accuracy of our method. A rotationally invariant approach is further incorporated into the method to greatly reduce the computational complexity with a speedup of approximately 50 times. Moreover, we investigate the Mott transition between a metal and a Mott insulator by evaluating the charge gap. In conclusion, with greatly reduced computational effort, our method reproduces the phase diagram in reasonable agreement with the density matrix renormalization group theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Symmetry-driven persistent spin texture for the two-dimensional nonsymmorphic CdTe and ZnTe crystal structures

In this paper, two nonsymmorphic two-dimensional structures of CdTe and ZnTe are modeled, and using state-of-the-art density functional theory with the group theory of solids, their symmetry-enforced electronic properties are studied. The in-plane ferroelectricity coupled with strong spin-orbit coupling induces a unidirectional out-of-plane Rashba spin-orbit field that can host a momentum-independent uniform spin configuration known as persistent spin texture (PST) at the Brillouin zone center. PST in these structures is found to be robust against external perturbations such as strain, structural distortion, and independent of layer thickness. These unprecedented intrinsic spin transport properties hold utmost importance in spintronics, as the experimental stringent condition of equal Rashba and Dresselhaus constants [Phys. Rev. Lett. 90, 146801 (2003)] is eliminated. The calculated persistent spin helix wavelength of <~5 nm paves the way for developing next-generation nanosized nonballistic spin field-effect transistors compared with micrometer-sized GaAs/AlGaAs quantum wells. Further, these materials exhibit finite spin Hall conductivity at the band edges and hence can be used in ferromagnet-free spin Hall transistors. Although CdTe and ZnTe systems have been widely studied for photocatalysis and solar cell applications over the past few decades, their potential application in spintronic devices has not been explored. Mono/few layers of CdTe and ZnTe synthesized from (110) facets of bulk zinc-blende crystals [Nat. Commun. 3, 1057 (2012)] satisfy all symmetry operations of the nonsymmorphic space group and hence can be considered ideal materials to verify our theoretical results experimentally.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Divisible Rigid Groups. Algebraic Closedness and Elementary Theory

A group G is said to be rigid if it contains a normal series G = G{sub 1} > G{sub 2} > … > Gm > G{sub m+1} = 1, whose quotients G{sub i}/G{sub i+1} are Abelian and, treated as right ℤ[G/G{sub i}]-modules, are torsion-free. A rigid group G is divisible if elements of the quotient G{sub i}/G{sub i+1} are divisible by nonzero elements of the ring ℤ[G/G{sub i}]. Every rigid group is embedded in a divisible one. We prove two theorems. Theorem 1 says that the following three conditions for a group G are equivalent: G is algebraically closed in the class Σ{sub m} of all m-rigid groups; G is existentially closed in the class Σ{sub m}; G is a divisible m-rigid group. Theorem 2 states that the elementary theory of a class of divisible m-rigid groups is complete.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Bianisotropic metamaterial

The topology of the elements of a metamaterial can be engineered from its desired electromagnetic constitutive tensor using an inverse group theory method. Therefore, given a desired electromagnetic response and a generic metamaterial elemental design, group theory is applied to predict the various ways that the element can be arranged in three dimensions to produce the desired functionality. An optimizer can then be applied to an electromagnetic modeling tool to fine tune the values of the electromagnetic properties of the resulting metamaterial topology.

36 MATERIALS SCIENCE↗
DOE OSTI2011

Laser-induced breathing modes in metallic nanoparticles: A symmetric molecular dynamics study

A highly efficient simulation method based on molecular dynamics and group theory is adopted to investigate the laser-induced breathing oscillation of gold and silver nanospheres. Nanoparticles with size ranging from 5.8 to 46.2 nm are discussed. The effect due to laser-induced heating is modeled by a symmetric sudden expansion of the nanospheres by increasing the interatomic distances. A long-range empirical potential model which is capable of describing the phonon dispersion curves of noble metals in the full frequency range is established. Group theory is fully exploited to increase the computation efficiency, and the oscillation behavior of nanospheres of over 3 x 10{sup 6} atoms can be simulated efficiently. Oscillation frequencies of nanospheres are obtained by calculating the Fourier transform of the velocity autocorrelation function. The breathing modes of nanospheres are identified as the excitation of A{sub 1g} modes with in-phase radial displacement of atoms in the nanospheres. The resulting oscillation spectra are in very good agreement with experimental data.

36 MATERIALS SCIENCE↗