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At least 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Approximate explicit analytic solution of the Elenbaas-Heller equation

The Elenbaas-Heller equation describing the temperature field of a cylindrically symmetrical non-radiative electric arc has been solved, and approximate explicit analytic solutions are obtained. The radial distributions of the heat-flux potential and the electrical conductivity have been figured out briefly by using some special simplification techniques. The relations between both the core heat-flux potential and the electric field with the total arc current have also been given in several easy explicit formulas. Besides, the special voltage-ampere characteristic of electric arcs is explained intuitionally by a simple expression involving the Lambert W-function. The analyses also provide a preliminary estimation of the Joule heating per unit length, which has been verified in previous investigations. Helium arc is used to examine the theories, and the results agree well with the numerical computations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Analytic gradients for the single-reference driven similarity renormalization group second-order perturbation theory

Herein we derive and implement analytic energy gradients for the single-reference driven similarity renormalization group second-order perturbation theory (DSRG-PT2). The resulting equations possess an asymptotic scaling that is identical to that of the second-order Møller–Plesset perturbation theory (MP2), indicating that the exponential regularizer in the DSRG equations does not introduce formal difficulties in the gradient theory. We apply the DSRG-PT2 method to optimizing the geometries of 15 small molecules. The equilibrium bond lengths computed with DSRG-PT2 are found similar to those of MP2, yielding a mean absolute error of 0.0033 Å and a standard deviation of 0.0045 Å when compared with coupled cluster with singles, doubles, and perturbative triples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Direct diabatization and analytic representation of coupled potential energy surfaces and couplings for the reactive quenching of the excited 2 Σ + state of OH by molecular hydrogen

In this work, we have employed extended multiconfiguration quasidegenerate perturbation theory, fourfold-way diabatic molecular orbitals, and configurational uniformity to develop a global three-state diabatic representation of the potential energy surfaces and their couplings for the electronically nonadiabatic reaction OH* + H 2 → H 2 O + H, where * denotes electronic excitation to the A 2 Σ + state. To achieve sign consistency of the computed diabatic couplings, we developed a graphics processing unit-accelerated algorithm called the cluster-growing algorithm. Having obtained consistent signs of the diabatic couplings, we fit the diabatic matrix elements (which consist of the diabatic potentials and the diabatic couplings) to analytic representations. Adiabatic potential energy surfaces are generated by diagonalizing the 3 × 3 diabatic potential energy matrix. The comparisons between the fitted and computed diabatic matrix elements and between the originally computed adiabatic potential energy surfaces and those generated from the fits indicate that the current fit is accurate enough for dynamical studies, and it may be used for quantal or semiclassical dynamics calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Analytical gradients for molecular-orbital-based machine learning

We report molecular-orbital-based machine learning (MOB-ML) enables the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. Here, we present the derivation, implementation, and numerical demonstration of MOB-ML analytical nuclear gradients, which are formulated in a general Lagrangian framework to enforce orthogonality, localization, and Brillouin constraints on the molecular orbitals. The MOB-ML gradient framework is general with respect to the regression technique (e.g., Gaussian process regression or neural networks) and the MOB feature design. We show that MOB-ML gradients are highly accurate compared to other ML methods on the ISO17 dataset while only being trained on energies for hundreds of molecules compared to energies and gradients for hundreds of thousands of molecules for the other ML methods. The MOB-ML gradients are also shown to yield accurate optimized structures at a computational cost for the gradient evaluation that is comparable to a density-corrected density functional theory calculation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Analytic and numerical vibronic spectra from quasi-classical trajectory ensembles

The truncated Wigner approximation to quantum dynamics in phase space is explored in the context of computing vibronic line shapes for monomer linear optical spectra. We consider multiple model potential forms including a shifted harmonic oscillator with both equal and unequal frequencies on the ground and excited state potentials as well as a shifted Morse potential model. For the equal-frequency shifted harmonic oscillator model, we derive an analytic expression for the exact vibronic line shape that emphasizes the importance of using a quantum mechanical distribution of phase space initial conditions. For the unequal-frequency shifted harmonic oscillator model, we are no longer able to obtain an exact expression for the vibronic line shape in terms of independent deterministic classical trajectories. We show how one can rigorously account for corrections to the truncated Wigner approximation through nonlinear responses of the line shape function to momentum fluctuations along a classical trajectory and demonstrate the qualitative improvement in the resulting spectrum when the leading-order quantum correction is included. Finally, we numerically simulate absorption spectra of a highly anharmonic shifted Morse potential model. We find that, while finite quantization and the dissociation limit are captured with reasonable accuracy, there is a qualitative breakdown of the quasi-classical trajectory ensemble’s ability to describe the vibronic line shape when the relative shift in Morse potentials becomes large. The work presented here provides clarity on the origin of unphysical negative features known to contaminate absorption spectra computed with quasi-classical trajectory ensembles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Molten Salt vs. Liquid Sodium Receiver Selection Using the Analytic Hierarchy Process

An international team led by NREL analyzed the favorability of two alternative liquid receiver designs for a 700+ degrees C receiver under the Gen3 CSP Liquid Pathway project. The competing liquid heat transfer fluids were a ternary chloride salt and liquid-metal sodium. The team applied a facilitated analytic hierarchy process (AHP) to arrive at a recommended alternative and set a path forward for the project. The AHP criteria were formulated, weighted, and scored by the project leadership team and technical advisory committee consisting of energy industry and CSP experts. The six- month process culminated with a two-day workshop where the sodium alternative was deemed to have both a significantly higher benefit (19.3%) and a lower LCOE (11.4%), with only a slightly higher risk (~3%) than the salt alternative. Consequently, a sodium-receiver design was selected for the Liquid Pathway project, where it will be used to charge a two- tank chloride salt thermal energy storage system.

analytic hierarchy process↗
DOE OSTI2022

Comparing correlation components and approximations in Hartree–Fock and Kohn–Sham theories via an analytical test case study

The asymmetric Hubbard dimer is a model that allows for explicit expressions of the Hartree–Fock (HF) and Kohn–Sham (KS) states as analytical functions of the external potential, Δv, and of the interaction strength, U. We use this unique circumstance to establish a rigorous comparison between the individual contributions to the correlation energies stemming from the two theories in the {U, Δv} parameter space. Within this analysis of the Hubbard dimer, we observe a change in the sign of the HF kinetic correlation energy, compare the indirect repulsion energies, and derive an expression for the “traditional” correlation energy, i.e., the one that corrects the HF estimate, in a pure site-occupation function theory spirit [Eq. (45)]. Next, we test the performances of the Liu–Burke and the Seidl–Perdew–Levy functionals, which model the correlation energy based on its weak- and strong-interaction limit expansions and can be used for both the traditional and the KS correlation energies. Further, our results show that, in the Hubbard dimer setting, they typically work better for the HF reference, despite having been originally devised for KS. These conclusions are somewhat in line with prior assessments of these functionals on various chemical datasets. However, the Hubbard dimer model allows us to show the extent of the error that may occur in using the strong-interaction ingredient for the KS reference in place of the one for the HF reference, as has been carried out in most of the prior assessments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Analytical nonadiabatic coupling and state-specific energy gradient for the crystal field Hamiltonian describing lanthanide single-ion magnets

Paramagnetic molecules with a metal ion as an electron spin center are promising building blocks for molecular qubits and high-density memory arrays. However, fast spin relaxation and decoherence in these molecules lead to a rapid loss of magnetization and quantum information. Nonadiabatic coupling (NAC), closely related to spin-vibrational coupling, is the main source of spin relaxation and decoherence in paramagnetic molecules at higher temperatures. Predicting these couplings using numerical differentiation requires a large number of computationally intensive ab initio or crystal field electronic structure calculations. To reduce computational cost and improve accuracy, we derive and implement analytical NAC and state-specific energy gradient for the ab initio parametrized crystal field Hamiltonian describing single-ion molecular magnets. Our implementation requires only a single crystal field calculation. In addition, the accurate NACs and state-specific energy gradients can be used to model spin relaxation using sophisticated nonadiabatic molecular dynamics, which avoids the harmonic approximation for molecular vibrations. To test our implementation, we calculate the NAC values for three lanthanide complexes. Finally, the predicted values support the relaxation mechanisms reported in previous studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Fast methods for multisite charge transfer. Processes II. Analytic nuclear gradients and nonadiabatic dynamics for cCASSCF(1,n) and cCASSCF(2n-1,n) wavefunctions

In this work we derive and implement analytic nuclear gradients and derivative couplings for a constrained complete active space self-consistent field with a small active space designed to model electron or hole transfer. Using a Lagrangian formalism, we are able to differentiate both the CASSCF energy and the constraint (which is required for smooth surfaces over a wide range of parameter space), and the resulting efficient algorithm can be immediately applied to nonadiabatic dynamics simulations of charge transfer processes. Here, we run initial surface-hopping simulations of a proton coupled electron transfer event for a phenoxyl–phenol system.

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

Analytical description of attosecond pulse generation on a plasma surface irradiated by high-intense laser pulses

We study theoretically the process of turning a laser pulse into a train of attosecond or even zeptosecond pulses due to high harmonic generation (HHG) upon backreflection of intense laser radiation from a plasma surface. It is shown that under appropriate conditions these attosecond pulses may have an amplitude that is several orders of magnitude larger than that of the laser pulse. We study this process in detail, especially the nanobunching of the plasma electron density. We derive the analytical expression that describes the electron density profile and obtain a good agreement with particle-in-cell simulations. We investigate the most efficient case of HHG at a moderate laser intensity (normalised vector potential α{sub 0} = 10) on the overdense plasma slab with an exponential pre-plasma profile. Subsequently we calculate the spectra of single attosecond pulses from back radiation using our expression for density shape in combination with the equation for spectrum of nanobunch radiation. (extreme laser radiation: physics and fundamental applications)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

Convergence of multipoint Pade approximants of piecewise analytic functions

The behaviour as n{yields}{infinity} of multipoint Pade approximants to a function which is (piecewise) holomorphic on a union of finitely many continua is investigated. The convergence of multipoint Pade approximants is proved for a function which extends holomorphically from these continua to a union of domains whose boundaries have a certain symmetry property. An analogue of Stahl's theorem is established for two-point Pade approximants to a pair of functions, either of which is a multivalued analytic function with finitely many branch points. Bibliography: 11 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials

New inequalities are established for analytic functions satisfying Meiman's majorization conditions. Estimates for values of and differential inequalities involving rational trigonometric functions with an integer majorant on an interval of length less than the period and with prescribed poles which are symmetrically positioned relative to the real axis, as well as differential inequalities for trigonometric polynomials in some classes, are given as applications. These results improve several theorems due to Meiman, Genchev, Smirnov and Rusak. Bibliography: 27 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Analytic gradients for compressed multistate pair-density functional theory

Photochemical reactions often involve states that are closely coupled due to near degeneracies, for example by proximity to conical intersections. Therefore, a multistate method is used to accurately describe these states; for example, ordinary perturbation theory is replaced by quasidegenerate perturbation theory. Multiconfiguration pair-density functional theory (MC-PDFT) provides an efficient way to approximate the full dynamical correlation energy of strongly correlated systems, and we recently proposed compressed multistate pair-density functional theory (CMS-PDFT) to treat closely coupled states. In the present paper, we report the implementation of analytic gradients for CMS-PDFT in both OpenMolcas and PySCF, and here we illustrate the use of these gradients by applying the method to the excited states of formaldehyde and phenol.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2013

ANALYTIC MODEL OF THE IBEX RIBBON WITH NEUTRAL SOLAR WIND BASED ION PICKUP BEYOND THE HELIOPAUSE

Energetic neutral atom (ENA) full sky maps obtained with the Interstellar Boundary Explorer revealed a surprising narrow band of increased intensity, the Ribbon, which has been attributed to the ordering effect of the interstellar magnetic field immediately outside the heliosphere. Among models to explain the enhanced ENA Ribbon intensity, Heerikhuisen et al. base theirs on neutral solar wind origin. It reflects the Ribbon angular and energy distribution correctly, but experiences inherent challenges from the long-term stability of the pickup ion (PUI) ring in velocity space, required for the observed ENA fluxes, and from time variations observed after less than one year due to the long integration length. We provide a simplified analytic model of the neutral solar wind, PUI production beyond the heliopause, and subsequent ENA production. We include convection of the PUIs with the interstellar flow toward the heliopause perpendicular to the interstellar magnetic field, thus far not in any model, extinction of the outward propagating neutral solar wind, and of the PUIs and ENAs on their way inward. Based on hybrid simulations of PUI driven instabilities, with injection rates from this model, scattering and isotropization of the PUIs is noticeably weaker than previously thought, yet too fast for ENA production. Assuming a narrow PUI velocity ring, we find a strong concentration of the ENA origin just outside the heliopause and Ribbon intensities comparable with the observations. Conversely, an isotropic PUI distribution produces ENA fluxes factor of ten too low, thus reemphasizing the need of very slow scattering.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

ANALYTIC SOLUTION FOR SELF-REGULATED COLLECTIVE ESCAPE OF COSMIC RAYS FROM THEIR ACCELERATION SITES

Supernova remnants (SNRs), as the major contributors to the galactic cosmic rays (CRs), are believed to maintain an average CR spectrum by diffusive shock acceleration regardless of the way they release CRs into the interstellar medium (ISM). However, the interaction of the CRs with nearby gas clouds crucially depends on the release mechanism. We call into question two aspects of a popular paradigm of the CR injection into the ISM, according to which they passively and isotropically diffuse in the prescribed magnetic fluctuations as test particles. First, we treat the escaping CR and the Alfven waves excited by them on an equal footing. Second, we adopt field-aligned CR escape outside the source, where the waves become weak. An exact analytic self-similar solution for a CR ''cloud'' released by a dimmed accelerator strongly deviates from the test-particle result. The normalized CR partial pressure may be approximated as P(p,z,t)=2[|z|{sup 5/3}+z{sub dif}{sup 5/3}(p,t)]{sup -3/5} exp[-z{sup 2}/4D{sub ISM}(p)t], where p is the momentum of CR particle, and z is directed along the field. The core of the cloud expands as z{sub dif}{proportional_to}{radical}(D{sub NL}(p)t) and decays in time as p{proportional_to}2z{sup -1}{sub dif}(t). The diffusion coefficient D{sub NL} is strongly suppressed compared to its background ISM value D{sub ISM}: D{sub NL} {approx} D{sub ISM}exp (- {Pi}) << D{sub ISM} for sufficiently high field-line-integrated CR partial pressure, {Pi}. When {Pi} >> 1, the CRs drive Alfven waves efficiently enough to build a transport barrier (p Almost-Equal-To 2/ Divides z Divides -{sup p}edestal{sup )} that strongly reduces the leakage. The solution has a spectral break at p = p{sub br}, where p{sub br} satisfies the equation D{sub NL}(p{sub br}) {approx_equal} z {sup 2}/t.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

DYNAMICS OF ASTROPHYSICAL BUBBLES AND BUBBLE-DRIVEN SHOCKS: BASIC THEORY, ANALYTICAL SOLUTIONS, AND OBSERVATIONAL SIGNATURES

Bubbles in the interstellar medium are produced by astrophysical sources, which continuously or explosively deposit large amounts of energy into the ambient medium. These expanding bubbles can drive shocks in front of them, the dynamics of which is markedly different from the widely used Sedov-von Neumann-Taylor blast wave solution. Here, we present the theory of a bubble-driven shock and show how its properties and evolution are determined by the temporal history of the source energy output, generally referred to as the source luminosity law, L(t). In particular, we find the analytical solutions for a driven shock in two cases: the self-similar scaling law, L{proportional_to}(t/t{sub s} ) {sup p} (with p and t{sub s} being constants) and the finite activity time case, L{proportional_to}(1 - t/t{sub s} ){sup -p}. The latter with p > 0 describes a finite-time-singular behavior, which is relevant to a wide variety of systems with explosive-type energy release. For both luminosity laws, we derived the conditions needed for the driven shock to exist and predict the shock observational signatures. Our results can be relevant to stellar systems with strong winds, merging neutron star/magnetar/black hole systems, and massive stars evolving to supernovae explosions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

SIMPLE ANALYTICAL FORMS OF THE PERPENDICULAR DIFFUSION COEFFICIENT FOR TWO-COMPONENT TURBULENCE. I. MAGNETOSTATIC TURBULENCE

We explore perpendicular diffusion based on the unified nonlinear transport theory. We derive simple analytical forms for the perpendicular mean free path and investigate the influence of different model spectra. We show that for cases where the field line random walk is normal diffusive, the perpendicular diffusion coefficient consists of only two transport regimes. Details of the spectral shape are less important, especially those of the inertial range. Only the macroscopic properties of the turbulence spectrum control the perpendicular diffusion coefficient. Simple formulae for the perpendicular diffusion coefficient are derived which can easily be implemented in solar modulation or shock acceleration codes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

ANALYTICAL FORMULAE OF MOLECULAR ION ABUNDANCES AND THE N{sub 2}H{sup +} RING IN PROTOPLANETARY DISKS

We investigate the chemistry of ion molecules in protoplanetary disks, motivated by the detection of the N{sub 2}H{sup +} ring around TW Hya. While the ring inner radius coincides with the CO snow line, it is not apparent why N{sub 2}H{sup +} is abundant outside the CO snow line in spite of the similar sublimation temperatures of CO and N{sub 2}. Using the full gas-grain network model, we reproduced the N{sub 2}H{sup +} ring in a disk model with millimeter grains. The chemical conversion of CO and N{sub 2} to less volatile species (sink effect hereinafter) is found to affect the N{sub 2}H{sup +} distribution. Since the efficiency of the sink depends on various parameters such as activation barriers of grain-surface reactions, which are not well constrained, we also constructed the no-sink model; the total (gas and ice) CO and N{sub 2} abundances are set constant, and their gaseous abundances are given by the balance between adsorption and desorption. Abundances of molecular ions in the no-sink model are calculated by analytical formulae, which are derived by analyzing the full-network model. The N{sub 2}H{sup +} ring is reproduced by the no-sink model, as well. The 2D (R-Z) distribution of N{sub 2}H{sup +}, however, is different among the full-network model and no-sink model. The column density of N{sub 2}H{sup +} in the no-sink model depends sensitively on the desorption rate of CO and N{sub 2} and the cosmic-ray flux. We also found that N{sub 2}H{sup +} abundance can peak at the temperature slightly below the CO sublimation, even if the desorption energies of CO and N{sub 2} are the same.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗