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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Raman scattering measurements of vibrational and rotational distributions in expanding nitrogen

Vibrational and rotational population distributions in expanding nitrogen in the supersonic nozzle of a reflected shock tunnel were investigated using spontaneous Raman scattering spectroscopy. The experimental data are compared with two multitemperature nonequilibrium calculations, one based on the Landau-Teller model for vibrational relaxation, the other on the solution of the vibrational master equations. Good agreement was found between both the Landau-Teller and the master equation solutions for the vibrational energy mode, but the experimentally inferred rotational temperatures were found to be systematically low, due to collisional narrowing. The dramatic increase in vibrational relaxation rates for a cooling flowfield reported in most previous studies was not reproduced by the present experiments.

Gillespie, Walter D.↗
DOE OSTI2026

Pressure-dependent kinetics of cyclopentene consumption

Recent experiments have uncovered deficiencies in the ability of current kinetic models for cyclopentane combustion to predict species profiles as a function of O2 concentration. One likely source of these discrepancies flows from the limited availability of relevant kinetic data for key functionalized intermediates, requiring the use of distant analogies to estimate their rates. This work fills this gap for cyclopentene, the most prominent C5 intermediate in low-temperature cyclopentane combustion. Ab initio transition-state-theory based master equation methods are used to calculate pressure-dependent rate constants across four potential energy surfaces (C5H8 + OH, C5H8 + HO2, C5H7, and C5H7 + O2). Potential energy surfaces are characterized at the CCSD(T)-F12/cc-pVDZ-F12//revDSD-PBEP86-D3BJ/def2-TZVPP level of theory. Pressure-dependent rate constants and branching fractions are determined via 1D master equation calculations. The results are used to analyze the competition for radicals between cyclopentene and cyclopentane in the intermediate temperature region, and to identify the dominant pathways flowing from these initiation channels. On the OH initiation surface, we find good agreement with recently published experimental rate constants at high temperature, and we elucidate the complex temperature dependence below 800 K, where 𝜋𝜋 addition becomes prominent. On the HO2 initiation surface, we find an interesting alternative route to bicyclic ether formation via well-skipping over the HO2 adduct well. On the cyclopentenyl radical surface, the major product is cyclopentadiene plus H. On the cyclopentenyl + O2 surface, we find that resonance stabilization largely prevents the allylic radical from undergoing oxidation, whereas the alkylic radical has a somewhat elevated propensity for oxidation pathways relative to cyclopentyl.

ab initio calculations↗
DOE OSTI2024

Association Kinetics for Perfluorinated n -Alkyl Radicals

Radical-radical reaction channels are important in the pyrolysis and oxidation chemistry of perfluoroalkyl substances (PFAS). In particular, unimolecular dissociation reactions within unbranched n-perfluoroalkyl chains, and their corresponding reverse barrierless association reactions, are expected to be significant contributors to the gas-phase thermal decomposition of families of species such as perfluorinated carboxylic acids and perfluorinated sulfonic acids. Unfortunately, experimental data for these reactions are scarce and uncertain. Furthermore, obtaining reliable theoretical predictions for such reactions is a laborious and computationally intensive task. Here, in this work, the chemical kinetics of the various association/decomposition reactions producing/decomposing the C 2 -C 4 series of unbranched n-perfluoroalkanes (C 2 F 6 , C 3 F 8 , and C 4 F 10 ) are examined using state-of-the-art ab initio transition-state-theory-based master-equation calculations. The variable-reaction-coordinate transition-state theory (VRC-TST) formalism is employed in computing the microcanonical and canonical rates for the association reactions. Reaction thermochemistry is obtained via composite quantum chemistry calculations and the laddering of error-canceling reaction schemes via a connectivity-based hierarchy approach employing ANL1/ANL0-style reference energies. Lennard-Jones collision model parameters for the considered systems were estimated by a direct dynamics approach, and collisional energy transfer parameters were obtained from analogies to systems of similar size and heavy-atom connectivity. A one-dimensional master equation approach was used to convert the microcanonical rate coefficients from the VRC-TST analysis into temperature- and pressure-dependent rate constants for the association reactions and the reverse dissociation reactions. The data are reported in standardized formats for usage in comprehensive chemical kinetic models for PFAS thermal destruction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1996

Effect of Dust Coagulation Dynamics on the Geometry of Aggregates

Master equation gives a more fundamental description of stochastic coagulation processes rather than popular Smoluchowski's equation. In order to examine the effect of the dynamics on the geometry of resulting aggregates, we study Master equation with a rigorous Monte Carlo algorithm. It is found that Cluster-Cluster aggregation model is a good approximation of orderly growth and the aggregates have fluffy structures with a fractal dimension approx. 2. A scaling analysis of Smoluchowski's equation also supports this conclusion.

Nakamura, R.↗
NASA NTRS1996

Transient Sub-Poissonian Distribution for Single-Mode Lasers

In this paper, the transient photon statistics for single-mode lasers is investigated by making use of the theory of quantum electrodynamics. By taking into account of the transitive time l,we obtain the master equation for Jaynes-Cummings model. The relation between the Mandel factor and the time is obtained by directly solving the master equation. The result shows that a transient phenomenon from the transient super-Poissonian distribution to the transient sub-Poissonian distribution occurs for single-mode lasers. In addition, the influences of the thermal light field and the cavity loss on the transient sub-Poissonian distribution are also studied.

Zang, J. Y.↗
DOE OSTI2024

Implementation of new mixture rules has a substantial impact on combustion predictions for H 2 and NH 3

Complex-forming reactions comprise a substantial fraction of all important combustion reactions and are central to combustion behavior. Despite being often called “pressure-dependent” reactions, their rate constants depend on not only the pressure but also the composition. While modern combustion codes allow arbitrarily high accuracy in treating pressure dependence, recent work has consistently demonstrated dramatic failures of essentially all available treatments of mixture dependence. In situations where mixture dependence is treated at all, it is inevitably treated through specification of pressure-dependent rate constants for a set of pure bath gases, which are then combined to estimate the rate constant in a mixture via a “mixture rule.” While there had been a generally unquestioning confidence in these mixture rules, they had, in reality, been scarcely tested until the last decade, when comparisons against master equation calculations revealed order-of-magnitude errors for important pressure-dependent reactions. New mixture rules, based on the reduced pressure, have recently been proposed and shown to reproduce master equation calculations for broad classes of complex-forming reactions very accurately. Here, in this work, we present an implementation of one such new mixture rule (“LMR-R”) in Cantera and then use it to enable simulations that use new high-accuracy ab initio data for individual bath gases (for the first time, since codes previously could not accommodate the complex bath gas dependence). Demonstrations focus on combustion of H 2 and NH 3 , where (1) high-accuracy ab initio data are available and (2) the impact is expected to be large due to the high fractions of efficient colliders (e.g., H 2 O and NH 3 ) in the burned and unburned gases. Indeed, we find the impact of this treatment to be substantial and may explain previous modeling difficulties for these important carbon-free fuels, particularly for NH 3 , whose extraordinarily high third-body efficiency (~20) is often omitted from kinetic models.

Ammonia↗
DOE OSTI2026

Kinetic Model of HoxEFU reduction by NADH [SWR-26-087]

This repository is used to release code generated for manuscripts on the Photosynthetic Energy Transduction core program. This code simulates the reduction of HoxEFU by NADH. The electro transfer rate constants for the simulation are specified in the .csv files. The two .csv files correspond tot he two models described in Dawson et al. Cell. Rep. Phys. Sci. 2026. The code utilizes a chemical master equation, a set of differential equations, defining the time evolution of the oxidation and reduction kinetics of NAD+, NADH, a FMN flavin, and a set of iron sulfur clusters. The kinetics of HoxEFU reduction by NADH are evaluated by numerical integration of the chemical master equation using a variable-time-step Runge-Kutta algorithm.

Dahl, Peter [National Laboratory of the Rockies (N↗
NASA NTRS1965

Theory of Intramolecular Relaxation Processes

A master equation is derived to describe internal relaxation processes in molecular systems with a relatively small number of degrees of freedom. It is an inhomogeneous equation, taking into account nondiagonal elements of the coarse‐grained density matrix which prove to be the most relevant ones for the problem under consideration. Various relaxational time scales, inherent in a molecular system, can thus be shown to exist. Relaxation mechanisms and equilibrium states on these time scales can be determined. The general character and different types of solutions of the master equation are investigated. The theory is applied to internal vibrational relaxation and intramolecular rearrangement (isomerization) reactions.

Hofacker, G. Ludwig↗
DOE OSTI2024

Real-time dynamics of the Schwinger model as an open quantum system with Neural Density Operators

Ab-initio simulations of multiple heavy quarks propagating in a Quark-Gluon Plasma are computationally difficult to perform due to the large dimension of the space of density matrices. This work develops machine learning algorithms to overcome this difficulty by approximating exact quantum states with neural network parametrisations, specifically Neural Density Operators. As a proof of principle demonstration in a QCD-like theory, the approach is applied to solve the Lindblad master equation in the 1 + 1d lattice Schwinger Model as an open quantum system. Neural Density Operators enable the study of in-medium dynamics on large lattice volumes, where multiple-string interactions and their effects on string-breaking and recombination phenomena can be studied. Thermal properties of the system at equilibrium can also be probed with these methods by variationally constructing the steady state of the Lindblad master equation. Scaling of this approach with system size is studied, and numerical demonstrations on up to 32 spatial lattice sites and with up to 3 interacting strings are performed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2008

Non-Boltzmann Modeling for Air Shock-Layer Radiation at Lunar-Return Conditions

This paper investigates the non-Boltzmann modeling of the radiating atomic and molecular electronic states present in lunar-return shock-layers. The Master Equation is derived for a general atom or molecule while accounting for a variety of excitation and de-excitation mechanisms. A new set of electronic-impact excitation rates is compiled for N, O, and N2+, which are the main radiating species for most lunar-return shock-layers. Based on these new rates, a novel approach of curve-fitting the non-Boltzmann populations of the radiating atomic and molecular states is developed. This new approach provides a simple and accurate method for calculating the atomic and molecular non-Boltzmann populations while avoiding the matrix inversion procedure required for the detailed solution of the Master Equation. The radiative flux values predicted by the present detailed non-Boltzmann model and the approximate curve-fitting approach are shown to agree within 5% for the Fire 1634 s case.

Johnston, Christopher O.↗
NASA NTRS2007

Pressure and Temperature Dependence of the Reaction of Vinyl Radical with Ethylene

This work reports measurements of absolute rate coefficients and Rice-Ramsperger-Kassel-Marcus (RRKM) master equation simulations of the C2H3 + C2H4 reaction. Direct kinetic studies were performed over a temperature range of 300-700 K and pressures of 20 and 133 mbar. Vinyl radicals (H2C=CH) were generated by laser photolysis of vinyl iodide (C2H31) at 266 nm, and time-resolved absorption spectroscopy was used to probe vinyl radicals through absorption at 423.2 nm. Measurements at 20 mbar are in good agreement with previous determinations at higher temperature. A weighted three-parameter Arrhenius fit to the experimental rate constant at 133 mbar, with the temperature exponent fixed, gives k = (7 +/- 1) x 10(exp -l4) cu cm/molecule/s (T/298 K)(exp 2) exp[-(1430 +/- 70) K/T]. RRKM master equation simulations, based on G3 calculations of stationary points on the C4H7 potential energy surface, were carried out to predict rate coefficients and product branching fractions. The predicted branching to 1-methylallyl product is relatively small under the conditions of the present experiments but increases as the pressure is lowered. Analysis of end products of 248 nm photolysis of vinyl iodide/ethylene mixtures at total pressures between 27 and 933 mbar provides no direct evidence for participation of I -methylallyl.

Ismail, Huzeifa↗
DOE OSTI2024

Identifiability and characterization of transmon qutrits through Bayesian experimental design

Robust control of a quantum system is essential to utilize the current noisy quantum hardware to its full potential, such as quantum algorithms. To achieve such a goal, a systematic search for an optimal control for any given experiment is essential. The design of optimal control pulses requires accurate numerical models and, therefore, accurate characterization of the system parameters. We present an online Bayesian approach for quantum characterization of qutrit systems, which automatically and systematically identifies optimal experiments that provide maximum information on the system parameters, thereby greatly reducing the number of experiments that need to be performed on the quantum testbed. Unlike most characterization protocols that provide point-estimates of the parameters, the proposed approach is able to estimate their probability distribution. The applicability of the Bayesian experimental design technique was demonstrated on test problems, where each experiment was defined by a parameterized control pulse. In addition to this, we also present an approach for iterative pulse extension, which is robust under uncertainties in transition frequencies and coherence times, and shot noise, despite being initialized with wide uninformative priors. Furthermore, we provide a mathematical proof of the theoretical identifiability of the model parameters and present conditions on the quantum state under which the parameters are identifiable. The proof and conditions for identifiability are presented for both closed and open quantum systems using the Schrödinger equation and the Lindblad master equation, respectively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

JIMWLK on a quantum computer

We propose a method for solving the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution equation on quantum computers. Our approach exploits the reformulation of the JIMWLK equation as a Lindblad master equation governing the rapidity evolution of the hadronic density matrix, as established in prior work. To render the problem tractable for quantum simulation, we introduce several approximations: the two-dimensional transverse plane is reduced to a one-dimensional radial lattice by assuming azimuthal symmetry of the jump operators; the gauge group is restricted to SU(2); and the infinite Wilson lines of the JIMWLK equation are replaced by finite Wilson links along the light-cone direction. The resulting bosonic Hilbert space is truncated using the electric field basis familiar from Hamiltonian lattice gauge theory, with states restricted to angular momenta 𝑗 ≤ 𝑗 max . We derive the matrix elements of the JIMWLK Lindblad jump operators in this basis. As a benchmark, we demonstrate rapid convergence of the fundamental dipole expectation value with 𝑗 max for both pure and mixed Gaussian initial density matrices. For the simplest truncation, 𝑗 max =1/2, we implement the Lindblad evolution using a quantum simulation algorithm verified with the Qiskit statevector simulator by decomposing the non-unitary evolution operator into a linear combination of unitaries. This work establishes a concrete pathway toward quantum simulation of high-energy quantum chromodynamics evolution equations, with direct relevance to the physics program of the Electron-Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1990

A theoretical prediction of hydrogen molecule dissociation-recombination rates including an accurate treatment of internal state nonequilibrium effects

The dissociation and recombination of H2 over the temperature range 1000-5000 K are calculated in a nonempirical manner. The computation procedure involves the calculation of the state-to-state energy transfer rate coefficients, the solution of the 349 coupled equations which form the master equation, and the determination of the phenomenological rate coefficients. The nonempirical results presented here are in good agreement with experimental data at 1000 and 3000 K.

Schwenke, David W.↗
NASA NTRS1995

Wigner distribution function and entropy of the damped harmonic oscillator within the theory of the open quantum systems

The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.

Isar, Aurelian↗
NASA NTRS1985

Excitation of turbulence by density waves

A nonlinear system describes the microdynamical state of turbulence that is excited by density waves. It consists of an equation of propagation and a master equation. A group-scaling generates the scaled equations of many interacting groups of distribution functions. The two leading groups govern the transport processes of evolution and eddy diffusivity. The remaining sub-groups represent the relaxation for the approach of diffusivity to equilibrium. In strong turbulence, the sub-groups disperse themselves and the ensemble acts like a medium that offers an effective damping to close the hierarchy. The kinetic equation of turbulence is derived. It calculates the eddy viscosity and identifies the effective damping of the assumed medium self-consistently. It formulates the coupling mechanism for the intensification of the turbulent energy at the expense of the wave energy, and the transfer mechanism for the cascade. The spectra of velocity and density fluctuations find the power law k sup-2 and k sup-4, respectively.

Tichen, C. M.↗
NASA NTRS1986

Transport by negative eddy viscosity in soliton turbulence

The forced Schrodinger equation is used to describe the microhydrodynamical state of strong soliton turbulence. The Schrodinger equation is transformed into a master equation and is decomposed into a macrogroup, a microgroup, and a submicrogroup, representative of the three transport processes of spectral evolution, transport property, and relaxation. The kinetic equation for the macrodistribution is derived and reverted to the continuum by the method of moments in order to find the equation of spectral evolution. The spectral flow is found to be governed by three types of transport, which are discussed.

Tchen, C. M.↗