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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Derivation of the chemical-equilibrium rate coefficient using scattering theory

Scattering theory is applied to derive the equilibrium rate coefficient for a general homogeneous chemical reaction involving ideal gases. The reaction rate is expressed in terms of the product of a number of normalized momentum distribution functions, the product of the number of molecules with a given internal energy state, and the spin-averaged T-matrix elements. An expression for momentum distribution at equilibrium for an arbitrary molecule is presented, and the number of molecules with a given internal-energy state is represented by an expression which includes the partition function.

Mickens, R. E.↗
DOE OSTI2023

Spectral-partitioned Kohn-Sham density functional theory

Here we introduce a general, variational scheme for systematic approximation of a given Kohn-Sham free-energy functional by partitioning the density matrix into distinct spectral domains, each of which may be spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact (unpartitioned) Kohn-Sham free energy, attaining this limit as the representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multiprojector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1990

Collision-induced gas phase dissociation rates

The Landau-Zener theory of reactive cross sections was applied to diatomic molecules dissociating from a ladder of vibrational states. The result predicts a dissociation rate that is quite well duplicated by an Arrhenius function having a preexponential temperature dependence of about T(sub -1/2), at least for inert collision partners. This relation fits experimental data reasonably well. The theory is then used to calculate the effect of vibrational nonequilibrium on dissociation rate. For Morse oscillators, the results are about the same as given by Hammerling, Kivel, and Teare in their analytic approximation for harmonic oscillators, though at very high temperature a correction for the partition function limit is included. The empirical correction for vibration nonequilibrium proposed by Park, which is a convenient algorithm for CFD calculations, is modified to prevent a drastic underestimation of dissociation rates that occurs with this method when vibrational temperature is much smaller than the kinetic temperature of the gas.

Hansen, C. Frederick↗
DOE OSTI2020

Beurling-Selberg extremization and modular bootstrap at high energies

We consider previously derived upper and lower bounds on the number of operators in a window of scaling dimensions [\Delta - \delta,\Delta + \delta] [ Δ − δ , Δ + δ ] at asymptotically large \Delta Δ in 2d unitary modular invariant CFTs. These bounds depend on a choice of functions that majorize and minorize the characteristic function of the interval [\Delta - \delta,\Delta + \delta] [ Δ − δ , Δ + δ ] and have Fourier transforms of finite support. The optimization of the bounds over this choice turns out to be exactly the Beurling-Selberg extremization problem, widely known in analytic number theory. We review solutions of this problem and present the corresponding bounds on the number of operators for any \delta \geq 0 δ ≥ 0 . When 2\delta \in \mathbb Z_{\geq 0} 2 δ ∈ ℤ ≥ 0 the bounds are saturated by known partition functions with integer-spaced spectra. Similar results apply to operators of fixed spin and Virasoro primaries in c>1 c > 1 theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Systematic study on the phase transition of confined fluid mixture up to the critical region

Systematic experimental study on the phase transition of confined fluids up to the critical region has been performed, in which many new insights have been obtained. For confined pure fluids, compared to the bulk phase, the critical point shifts to lower pressure and temperature, but the relative shift of critical pressure is much larger than that of critical temperature. The behavior of the shift, i.e., the shift as a function of pore size, is dependent on the pore type. For confined fluid mixtures, compared to the bulk phase, the critical point also shifts to lower pressure and temperature, and the relative shift of critical pressure is also much larger than that of critical temperature. Confined fluid mixture behaves similarly to confined pure fluid, i.e., it exhibits hysteresis at lower temperature range and does not exhibit phase coexistence or phase envelope. An equation of state for confined pure fluids, based on the Generalized van der Waals partition function, has also been developed and demonstrated to accurately predict the capillary condensation of simple molecules in MCM-41. The parameters of the equation of state are derived from experimental critical point.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2023

Building materials genome from ground‐state configuration to engineering advance

Individual phases are commonly considered as the building blocks of materials. However, the accurate theoretical prediction of properties of individual phases remains elusive. The top-down approach by decoding genomic building blocks of individual phases from experimental observations is nonunique. The density functional theory (DFT), as a state-of-the-art solution of quantum mechanics, prescribes the existence of a ground-state configuration at 0 K for a given system. It is self-evident that the ground-state configuration alone is insufficient to describe a phase at finite temperatures as symmetry-breaking non-ground-state configurations are excited statistically at temperatures above 0 K. Our multiscale entropy approach (recently terms as Zentropy theory) postulates that the entropy of a phase is composed of the sum of the entropy of each configuration weighted by its probability plus the configurational entropy among all configurations. Consequently, the partition function of each configuration in statistical mechanics needs to be evaluated by its free energy rather than total energy. The combination of the ground-state and symmetry-breaking non-ground-state configurations represents the building blocks of materials and can be used to quantitatively predict free energy of individual phases with the free energy of each configuration predicted from DFT as well as all properties derived from free energy of individual phases.

CALPHAD↗
NASA NTRS1976

Electronic energy states

One-electron wave functions are reviewed and approximate solutions of two-electron systems are given in terms of these one-electron functions. The symmetry effects associated with electron spin are reviewed and the effects of electron exchange on energy levels of the two-electron system are given. The coupling of electronic orbital and spin angular momentum is considered next and the Lande interval rule for Russell-Saunders or LS coupling is derived. The configurations possible for various multi-electron LS couplings are enumerated (examples from the first two rows of the periodic table are given), and the meaning of the spectroscopic nomenclature is discussed, particularly with respect to the degeneracies of the electron states involved. Next the nomenclature, symmetries, and degeneracies for electron states of diatomic molecules are discussed, and some examples for N2, O2, and NO are presented. The electronic partition functions and derivative thermodynamic properties are expressed in terms of these energies and degeneracies, and examples are given for some of the simple gas species encountered in the earth's atmosphere.

Source record↗
DOE OSTI2025

Low-lying states and total internal partition sums of CH

The electronic structure and spin-orbit states of the CH radical have been systematically investigated using multi-reference configuration interaction (MRCI) and single-reference coupled-cluster (CC) methods. These calculations were performed in conjunction with large correlation-consistent basis sets of quadruple-, quintuple-, and sextuple-ζ quality. To achieve high accuracy, electronic energies for all states were extrapolated to the complete basis set (CBS) limit, enabling the detailed construction of potential energy curves and determination of reliable spectroscopic constants. Spin-orbit coupling effects were explicitly incorporated, and vibrational energy levels were computed via Numerov analysis. Furthermore, the resulting values exhibit good to excellent agreement with available experimental data. Dipole moment and transition dipole moment curves were evaluated to assess the opacity characteristics of CH, revealing that transitions such as Χ 2 Π (u′′ = 0) → Α 2 Δ (u′ = 0), Χ 2 Π (u′′ = 0) → Β 2 Σ − (u′ = 0), Χ 2 Π (u′′ = 0) → C 2 Σ + (u′ = 0), and Χ 2 Π (u′′ = 0) → D 2 Σ + (u′ = 3) are particularly probable. Finally, the total internal partition function sum (TIPS) of CH was computed over a broad temperature range (10–30,000 K) based on our high-accuracy ab initio results.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Complex eigenvalue instantons and the Fredholm determinant expansion in the Gross-Witten-Wadia model

We study the leading nonperturbative corrections to the strong-coupling (ungapped) phase of the Gross-Witten-Wadia (GWW) integral over unitary matrices, to one-loop order. We compute these corrections directly in terms of eigenvalue tunneling in a holomorphic presentation of the integral over eigenvalues. The leading nonperturbative contribution to the partition function comes from a pair of complex eigenvalue instantons. We show that these are in fact “ghost instantons”, which are extrema of the one-eigenvalue effective potential on the “unphysical sheet” of the spectral curve and have been discussed in detail recently by Mariño, Schiappa, and Schwick. Further, we discuss the relationship of these instantons to the Fredholm determinant expansion of the unitary matrix integral, which has recently become an object of interest in the computations of BPS indices of supersymmetric gauge theories and black holes. We find that, after taking the ’t Hooft limit, the first correction given by the Fredholm determinant expansion of the GWW integral agrees precisely with the leading nonperturbative correction, to one-loop order.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Self-duality under gauging a non-invertible symmetry

Abstract We discuss two-dimensional conformal field theories (CFTs) which are invariant under gauging a non-invertible global symmetry. At every point on the orbifold branch ofc= 1 CFTs, it is known that the theory is self-dual under gauging a ℤ 2 × ℤ 2 symmetry, and has Rep(H 8 ) and Rep(D 8 ) fusion category symmetries as a result. We find that gauging the entire Rep(H 8 ) fusion category symmetry maps the orbifold theory at radiusRto that at radius 2/R. AtR=$$ \sqrt{2} $$ 2 , which corresponds to two decoupled Ising CFTs (Ising 2 in short), the theory is self-dual under gauging the Rep(H 8 ) symmetry. This implies the existence of a topological defect line in the Ising 2 CFT obtained from half-space gauging of the Rep(H 8 ) symmetry, which commutes with thec= 1 Virasoro algebra but does not preserve the fully extended chiral algebra. We bootstrap its action on thec= 1 Virasoro primary operators, and find that there are no relevant or marginal operators preserving it. Mathematically, the new topological line combines with the Rep(H 8 ) symmetry to form a bigger fusion category which is a ℤ 2 -extension of Rep(H 8 ). We solve the pentagon equations including the additional topological line and find 8 solutions, where two of them are realized in the Ising 2 CFT. Finally, we show that the torus partition functions of the Monster 2 CFT and Ising×Monster CFT are also invariant under gauging the Rep(H 8 ) symmetry.

Physics↗
DOE OSTI2020

$$ T\overline{T},J\overline{T},T\overline{J} $$ partition sums from string theory

We calculate the torus partition sum of a general CFT 2 with left and right moving conserved currents J and $ \overline{J} $ J ¯ , perturbed by a combination of the irrelevant operators $ T\overline{T},J\overline{T} $ T T ¯ , J T ¯ and $ T\overline{J} $ T J ¯ . We use string theory techniques to write it as an integral transform of the partition sum of the unperturbed CFT with chemical potentials for the left and right moving conserved charges. The resulting expression transforms in the right way under the modular group, and reproduces the known spectrum of these models. We also derive a formula for the partition function of deformed CFT 2 with non-vanishing chemical potentials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Bootstrapping boundaries and branes

The study of conformal boundary conditions for two-dimensional conformal field theories (CFTs) has a long history, ranging from the description of impurities in one-dimensional quantum chains to the formulation of D-branes in string theory. Nevertheless, the landscape of conformal boundaries is largely unknown, including in rational CFTs, where the local operator data is completely determined. We initiate a systematic bootstrap study of conformal boundaries in 2d CFTs by investigating the bootstrap equation that arises from the open-closed consistency condition of the annulus partition function with identical boundaries. We find that this deceivingly simple bootstrap equation, when combined with unitarity, leads to surprisingly strong constraints on admissible boundary states. In particular, we derive universal bounds on the tension (boundary entropy) of stable boundary conditions, which provide a rigorous diagnostic for potential D-brane decays. We also find unique solutions to the bootstrap problem of stable branes in a number of rational CFTs. Along the way, we observe a curious connection between the annulus bootstrap and the sphere packing problem, which is a natural extension of previous work on the modular bootstrap. We also derive bounds on the boundary entropy at large central charge. These potentially have implications for end-of-the-world branes in pure gravity on AdS 3 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Hilbert series, the Higgs mechanism, and HEFT

We expand Hilbert series technologies in effective field theory for the inclusion of massive particles, enabling, among other things, the enumeration of operator bases for non-linearly realized gauge theories. We find that the Higgs mechanism is manifest at the level of the Hilbert series, as expected for the partition function of an S-matrix that is subject to the Goldstone equivalence theorem. In addition to massive vectors, we detail how other massive, spinning particles can be studied with Hilbert series; in particular, we spell out the ingredients for massive gravity in general spacetime dimensions. Further methodology is introduced to enable Hilbert series to capture the effect of spurion fields acquiring vevs. We apply the techniques to the Higgs Effective Field Theory (HEFT), providing a systematic enumeration of its operator basis. This is achieved both from a direct and a custodial symmetry spurion-based approach; we compare and contrast the two approaches, and our results to those appearing in previous literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

The geometry of the modular bootstrap

Abstract We explore the geometry behind the modular bootstrap and its image in the space of Taylor coefficients of the torus partition function. In the first part, we identify the geometry as an intersection of planes with the convex hull of moment curves onR + ⊗ℤ, with boundaries characterized by the total positivity of generalized Hankel matrices. We phrase the Hankel constraints as a semi-definite program, which has several advantages, such as the validity of bounds irrespective of spin truncation. We derive bounds on the gap, twist-gap, and the space of Taylor coefficients themselves. We find that if the gap is above$$ {\Delta }_{\textrm{gap}}^{\ast } $$ ∆ gap ∗ , where$$ \frac{c-1}{12}<{\Delta}_{\textrm{gap}}^{\ast }<\frac{c}{12} $$ c − 1 12 < Δ gap ∗ < c 12 , all coefficients become bounded on both sides and kinks develop in the space. In the second part, we propose an analytic method of imposing the integrality condition for the degeneracy number in the spinless bootstrap, which leads to a non-convex geometry. We find that even at very low derivative order this condition rules out regions otherwise allowed by bootstraps at high derivative order.

Physics↗
DOE OSTI2026

Coarse-grained fixed-point tensor networks and holographic reflected entropy in 3D gravity

We use the framework of fixed-point BCFT tensor networks to present a microscopic CFT derivation of the correspondence between reflected entropy (RE) and entanglement wedge cross section (EW) in AdS 3 /CFT 2 , for both bipartite and multipartite settings. These fixed-point tensor networks, obtained by triangulating Euclidean CFT path integrals, allow us to explicitly construct the canonical purification via cutting-and-gluing CFT path integrals. Employing modular flow in the large-c limit, we demonstrate that these intrinsic CFT manipulations reproduce bulk geometric prescriptions, without assuming the AdS/CFT dictionary. The emergence of bulk geometry is traced to coarse-graining over heavy states in the large-c limit. Universal coarse-grained BCFT data for compact 2D CFTs, through the relation to Liouville theory with ZZ boundary conditions, yields hyperbolic geometry on the Cauchy slice. The corresponding averaged replica partition functions reproduce all candidate EWs, arising from different averaging patterns, with the dominant one providing the correct RE and EW. In this way, many heuristic tensor-network intuitions in toy models are made precise and established directly from intrinsic CFT data.

AdS-CFT correspondence↗
DOE OSTI2020

Diagrammatic state sums for 2D pin-minus TQFTs

The two dimensional state sum models of Barrett and Tavares are extended to unoriented spacetimes. The input to the construction is an algebraic structure dubbed half twist algebras, a class of examples of which is real separable superalgebras with a continuous parameter. The construction generates pin-minus TQFTs, including the root invertible theory with partition function the Arf-Brown-Kervaire invariant. Decomposability, the stacking law, and Morita invariance of the construction are discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Rotating black hole entropy from M5-branes

We compute the superconformal index of 3d N = 2 superconformal field theories obtained from N M5-branes wrapped on a hyperbolic 3-manifold. Exploiting the 3d-3d correspondence, we use perturbative invariants of SL(N, C) Chern-Simons theory to determine the superconformal index in the large N limit, including corrections logarithmic in N. The leading order partition function provides a microscopic foundation for the entropy function of the dual rotating asymptotically AdS 4 black holes. We also verify that the supergravity one-loop contribution to the log N term coincides with the field theoretic result. We propose a 3d-3d formulation for the refined topologically twisted index, and provide strong evidence in support of its vanishing — which agrees with the fact that the expected dual rotating magnetically-charged black hole does not exist. This provides an interesting link between gravity and a tantalizing mathematical result.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Holographic duality for Ising CFT with boundary

We extend the holographic duality between 3d pure gravity and 2d Ising CFT proposed in ref. [1] to CFTs with boundaries. Besides the usual asymptotic boundary, the dual bulk spacetime now has a real cutoff, on which live branes with finite tension, giving Neumann boundary condition on the metric tensor. The strongly coupled bulk theory requires that we dress the well-known semiclassical AdS/BCFT answer with boundary gravitons, turning the partition function into the form of Virasoro characters. Using this duality, we relate the brane tensions to the modular S-matrix elements of the dual BCFT and derive the transformation between gravitational solutions with different brane tensions under modular S action.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗