Search NASA⌕ Search

SEARCH · Search NASA

Results for “Master equation”

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 181 records · Page 10

Thermalization at low temperatures via weakly damped multisite baths

We study the thermalization properties of one-dimensional open quantum systems coupled to baths at their boundary. The baths are driven to their thermal states via Lindblad operators, while the system undergoes Hamiltonian dynamics. We specifically consider multisite baths and investigate the extent to which the late-time steady state resembles a Gibbs state at some controllable temperature set by the baths. We study three models: a noninteracting fermion model accessible via free-fermion technology, and two interacting models, the XZ model and the chiral clock model, which are accessible via tensor network methods. We show that, by tuning towards the weak coupling and slow relaxation limits, one can engineer low temperatures in the bulk of the system provided the bath size is big enough. Here, we use this capability to study energy transport in the XZ model at lower temperatures than previously reported. Our work paves the way for future studies of interacting open quantum systems at low temperatures.

1-dimensional spin chains↗

Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation

The theory of open quantum systems lays the foundation for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of simulating open quantum systems calls for the development of strategies to approximate their dynamics. In this Letter, we present an approach for tackling open quantum system dynamics. Using an exact probabilistic formulation of quantum physics based on positive operator-valued measure, we compactly represent quantum states with autoregressive neural networks; such networks bring significant algorithmic flexibility due to efficient exact sampling and tractable density. We further introduce the concept of string states to partially restore the symmetry of the autoregressive neural network and improve the description of local correlations. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator using a forward-backward trapezoid method and find the steady state via a variational formulation. Our approach is benchmarked on prototypical one-dimensional and two-dimensional systems, finding results which closely track the exact solution and achieve higher accuracy than alternative approaches based on using Markov chain Monte Carlo method to sample restricted Boltzmann machines. Our Letter provides general methods for understanding quantum dynamics in various contexts, as well as techniques for solving high-dimensional probabilistic differential equations in classical setups.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Formation of phenanthrene via H–assisted isomerization of 2–ethynylbiphenyl produced in the reaction of phenyl with phenylacetylene

Model chemistry G3(MP2,CC)//B3LYP/6–311G(d,p) calculations of the potential energy surface for the reaction of phenyl radical (C 6 H 5 ) with phenylacetylene (C 8 H 6 ) have been carried out and combined with Rice–Ramsperger–Kassel–Marcus/Master Equation calculations of temperature– and pressure–dependent rate constants. The results showed that the reaction can serve as a viable source for the formation of phenanthrene via an indirect route involving a primary reaction of phenyl addition to the ortho carbon in the ring of phenylacetylene and H elimination producing 2–ethynylbiphenyl followed by secondary H–assisted isomerization of 2–ethynylbiphenyl to phenanthrene. In the secondary reaction, the H atom adds to the α carbon of the ethynyl side chain, then a six–member ring closure takes place followed by aromatization via an H loss. The channel of H addition to the side chain of 2–ethynylbiphenyl appears to be much faster than H addition to the ortho carbon in the ethynyl–substituted ring leading back to the initial C 6 H 5 + C 8 H 6 reactants. Rate constants for the primary C 6 H 5 + C 8 H 6 ⇌2–ethynylbiphenyl (p1) + H and secondary p1 + H⇌phenanthrene (p2) + H reactions have been computed in the temperature range of 500–2500 K at pressures of 30 Torr, 1, 10, and 100 atm and fitted to modified Arrhenius expressions. Here, the suggested kinetic scheme and rate constants are proposed as a prototype for the modeling of the growth of polycyclic aromatic hydrocarbons via the phenyl addition–dehydrocyclization (PAC) mechanism involving an addition of a PAH radical to an ethynyl–substituted PAH molecule.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Correlated particle transport enables biological free energy transduction

Studies of biological transport frequently neglect the explicit statistical correlations among particle site occupancies (i.e., they use a mean-field approximation). Neglecting correlations sometimes captures biological function, even for out-of-equilibrium and interacting systems. Here, we show that neglecting correlations fails to describe free energy transduction, mistakenly predicting an abundance of slippage and energy dissipation, even for networks that are near reversible and lack interactions among particle sites. Interestingly, linear charge transport chains are well described without including correlations, even for networks that are driven and include site-site interactions typical of biological electron transfer chains. We examine three specific bioenergetic networks: a linear electron transfer chain (as found in bacterial nanowires), a near-reversible electron bifurcation network (as in complex III of respiration and other recently discovered structures), and a redox-coupled proton pump (as in complex IV of respiration).

bacterial nanowires↗

Effects of non-thermal termolecular reactions on detonation development in hydrogen (H 2 )/methane (CH 4 ) - air mixtures

The binary fuel blend of H 2 /CH 4 is one of the most promising hydrogen-enriched hydrocarbon fuels in spark-ignition (SI) engines. Yet, the undesirable phenomenon of super-knock, which can severely and in-stantaneously damage an SI engine, limits its widespread adoption. Moreover, there is still a lack of con-sensus on the precise mechanism by which this phenomenon occurs i.e. via flame acceleration or spon-taneous ignition, despite numerous previous investigations. At the same time, recent studies [M. P. Burke, S. J. Klippenstein, Nat. Chem. 9 (2017) 1078 -1082, Y. Tao, A. W. Jasper, Y. Georgievskii, S. J. Klippenstein, R. Sivaramakrishnan, Proc. Combust. Inst. 38 (2021) 515-522] have demonstrated a high probability of occurrence of non-thermal reactions in premixed flames of such H 2 /CH 4 fuel blends with air due to the presence of non-trivial amounts of highly reactive radicals including H, O and OH apart from O 2 . The present study focuses on the evolution of an initial deflagration front to a detonation wave in H 2 /CH 4 - air mixtures under SI engine relevant conditions through fully resolved, constant volume 1D simulations with and without non-thermal reactivity. Non-thermal reactions were included in the macroscopic kinetics model as chemically termolecular reactions facilitated by the H + CH 3 and H + OH radical-radical recombination and the H + O 2 radical-molecule association reactions. Further, the nonthermal reactions result in a corresponding decrease in the reaction fluxes of the incipient recombination/association reactions. Therefore, an additional set of simulations were performed by applying corrections to the respective incipient recombination/association rate constants using the methodology demonstrated by Tao et al. [Y. Tao, A. W. Jasper, Y. Georgievskii, S. J. Klippenstein, R. Sivaramakrishnan, Proc. Combust. Inst. 38 (2021) 515-522]. Compared to the baseline case, the onset of spontaneous ignition in the end-gas region was observed to be delayed in the presence of non-thermal termolecular reactions. Concurrently, the developing detonation was observed to be significantly stronger. In contrast, applying corrections to the recombi-nation/association rate constants resulted in a completely different behavior. Specifically, detonation was observed to occur due to self acceleration of the primary flame in the absence of spontaneous ignition in the end-gas region. Sensitivity analysis was performed to quantify the effects of non-thermal reactions on the duration of heat release rate and thereby the mechanism of detonation formation. In addition, chemical explosive mode analysis (CEMA) was performed to identify the dominant species/reactions re-sponsible for the observed results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Automated identification and calculation of prompt effects in kinetic mechanisms using statistical models

The kinetics of prompt dissociation involves rovibrationally excited species (generally formed by exothermic reactions) which may dissociate or isomerize prior to thermalization via collisions with the bath gas. Treating such rovibrationally excited species (so-called "hot" species) with standard kinetic phenomenology may result in incorrect macroscopic representation of their reactivity. Here this work presents the first fully automated methodology for the calculation of prompt effects of a chosen species in a kinetic mechanism, including (i) reaction selection; (ii) theoretical calculation of rate constants and prompt branching fractions; and (iii) final rate constant fitting. The energy partition between hot fragments is estimated using a variety of statistical models, including a new physically sound microcanonical statistical model based on the rovibrational density of states of the fragments. The methodology is validated against literature data for the prompt dissociations of HCO and C 3 H 7 radicals. The microcanonical statistical model is in better agreement with trajectory simulations for larger species and is thus applicable for practical systems that typically involve large molecules, for which direct dynamics calculations are impractical. The automated workflow is applied to the evaluation of the effects of prompt dissociation for two isomeric radicals C 4 H 7 1-3 (1-methylallyl) and C 4 H 7 1-4 (3-buten-1-yl). Twelve H-atom abstraction reactions are selected and the corresponding rate constants are computed with first principles theory. The microcanonical statistical model predicts that prompt dissociations of C 4 H 7 1-3 and C 4 H 7 1-4 are already significant at 1000K, resulting in differences of up to an order of magnitude at 2000K with respect to the phenomenological thermal rate constants. To illustrate the effects of prompt dissociation on simulations of experimental data, the calculated prompt rate constants are implemented in both CRECK and C3MechV3.3 kinetic mechanisms. Simulations of experimental flame data illustrate the noticeable impact of prompt dissociation kinetics on the high-temperature combustion reactivity of C 4 H 8 -1 and C 4 H 8 -2.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The role of energy transfer and competing bimolecular reactions in characterizing the unimolecular dissociations of allylic radicals

Resonantly stabilized radicals (RSR's) such as allylic radicals typically have bond energies exceeding 45 kcal/mol and are therefore reasonably long-lived up to quite high temperatures. Consequently, kinetics of the unimolecular dissociations and bimolecular reactions of these long-lived RSR's assume significance in high temperature chemically reacting systems such as in flames. Our recent analyses (J. Cho et al., Proc. Comb. Inst., 2022) of the uncertainty propagated by the energy transfer parameters for 1-methylallyl (1MA) dissociation to the laminar flame speed, indicates an intricate coupling between the kinetics of 1MA dissociation (chain propagation) and its reaction with H-atoms (chain-termination). Here, this work extends such analyses to other C 3 – C 5 allylic radicals: allyl, 2-methylallyl, 1,1-dimethylallyl, 1,2-dimethylallyl, and 1,3-dimethylallyl. Theoretical kinetics for the C 3 – C 4 allylic radicals were taken from prior literature studies (J.A. Miller et al., J. Phys. Chem., 2008; J. Cho et al., Proc. Comb. Inst., 2022; R.S. Tranter et al., Proc. Comb. Inst., 2017). Potential energy surfaces were newly computed for the dissociations of the larger C5 allylic radicals and the reactions of these radicals with H-atoms. These PES's were then used to calculate rate constants for the relevant unimolecular and bimolecular reactions. Energy transfer has a crucial role to play in these pressure-dependent reactions and therefore the present kinetics calculations relied on a-priori predictions of collisional energy transfer parameters to best characterize the branching between chain propagating unimolecular dissociations of these allylic radicals and chain terminating bimolecular reactions of these RSR's with H-atoms. Prompt dissociations are now established to be a universal feature of free radical dissociations. Here we have also characterized the propensity for prompt dissociations in these more-stable allylic RSR's and their role in combustion simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A workflow for automatic generation and efficient refinement of individual pressure-dependent networks

Manual chemical kinetic model construction often requires modelists to at least implicitly guess all possible decay pathways and their relative fluxes for all important species. We present a workflow and associated tool for automatic generation and re finement of pressure-dependent networks that should enable modelists to efficiently and comprehensively identify decay pathways and estimate respective parameters for chemical species. This tool combines the capabilities of the Reaction Mechanism Generator (RMG) software to generate possible reaction paths, determine thermochemistry, approximate rate coefficients and estimate frequencies with the capabilities of the Arkane software to use quantum chemical parameters to compute thermochemistry and pressure dependent rates. A flux-based algorithm is used to decide which isomers to add to the network. Isomers added to the network are reacted to form other channels. When enough of the flux is accounted for by the isomers and bimolecular product channels, the generation process terminates to yield a comprehensive network. Network sensitivity analysis is applied to the network to identify the most important wells and barriers that can be refined using quantum chemistry calculations. Iterative refinement can then be used to achieve accuracy. The comprehensive network can be easily reduced using energy and flux-based algorithms to the most important channels and isomers in the network.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Theoretically Informed Kinetics (ThInK): Establishing a modern C 0 -C 3 mechanism for combustion modeling

In contrast to the adage “Models are to be used, not believed”, combustion kinetics models have been intended to be predictive in nature. Theoretical chemical kinetics is now understood to provide a firm foundation for the reaction parameters, thereby facilitating predictive simulations of chemical reactivity, even in regimes that are poorly characterized by chemical kinetic and/or combustion experiments. In this study, we describe a theory-informed kinetics model (ThInK) for small molecule combustion chemistry (H 2 and C 1 – C 3 species) that is based on the prodigious use of theoretical predictions for reaction rate coefficients, thermochemistry, and transport parameters. The distinct features of this kinetics model, which was developed over the course of several decades, are illustrated through simulations of flame propagation and auto-ignition.

Energy transfer↗

Combustion chemistry in the twenty-first century: Developing theory-informed chemical kinetics models

Over the past 20 to 25 years theoretical chemistry (particularly theoretical chemical kinetics) has played an increasingly important role in developing chemical kinetics models for combustion. Theoretical methods of obtaining rate parameters are now competitive in accuracy with experiment, particularly for small molecules. Moreover, theoretical methods can deal with conditions that experiments frequently cannot. In addition to increased accuracy, theory has rejuvenated methods and discovered phenomena that were completely unappreciated, or at least underappreciated, in the 20th century. Our primary interest here is in molecular-level issues, i.e. in calculating rate and transport parameters. However, dealing with kinetics models that involve thousands of reactions and hundreds of species is important for practical applications and is relatively new to the 21st century. Theory, in a general sense, and theoretical methods development have a role to play here too. We discuss in this review all these topics in some detail with an emphasis on issues and methods that have emerged in the last 20 years or so. Even so, our review is selective, rather than comprehensive, out of necessity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Resolving Discrepancies Between Theory and Experiment for the NCN + H Reaction

Flame modeling studies have highlighted the role of branching in the kinetics for the prompt NO switch reaction, NCN + H. In this reaction, there is strong competition between the CH + N2 (R1) and HCN + N (R2) product channels. Increased branching towards reaction R2 promotes the subsequent formation of Fenimore or Prompt NO. Recent direct shock tube studies on this complex reaction conclude that branching to reaction R2 is much more favorable than the predicted branching from theoretical studies. The experimentally predicted prompt NO switch temperature (TS), i.e., the temperature at which k2/(k1+k2) = 0.5, is at 1670 K, in contrast to theory that predicts Ts > 3200 K. The present theory/modeling work was initiated to highlight potential causes for this significant discrepancy between experiment and theory. Our analysis of the simulations reported in the experimental studies indicate that including a fall-off representation for C2H5 radical dissociation (with C2H5 produced from C2H5I dissociation and acting as an H-atom source) has a noticeable influence on the simulations for NCN decay and HCN formation in the shock tube studies. With the inclusion of a theory-based pressure fall-off representation for C2H5 dissociation, we show that this radical persists for much longer timescales even at the high-temperatures in the shock tube studies. This persistence then facilitates the rapid conversion of reactive H-atoms to CH3 radicals at the shock tube conditions via the H + C2H5 → CH3 + CH3 reaction. An updated theoretical analysis for this classic addition-elimination reaction is also provided in this work. The rapid formation of CH3 radicals necessitates the inclusion of additional reactions to adequately simulate the NCN and HCN data. Our simulations conclude that, with the inclusion of these additional reactions, the NCN and HCN profiles can be reasonably well simulated by the most recent theoretical predictions.

Ethyl Radicals↗

ab initio Sub-Mechanism Development for Cyclopentene Oxidation

To accurately predict low-temperature oxidation behavior, chemical kinetics mechanisms must contain complete reaction networks that include detailed consumption reactions of intermediates produced directly from hydroperoxyalkyl radicals, Q̇OOH, which undergo competing unimolecular reactions and bimolecular reactions with O2. Rates of chain-branching are governed by the flux between the two competing pathways, and inherently depend on temperature, pressure, and oxygen concentration. Neglect of consumption pathways for major oxidation intermediates leads to mechanism truncation error that is ameliorated by expanding the level of detail included in sub-mechanisms and employing ab initio methods for computing rates of elementary reactions and thermochemical properties of species involved. In the present work, an ab initio-derived sub-mechanism is developed using AutoMech to model the chemical kinetics of cyclopentene, a major product of cyclopentane oxidation. The ab initio sub-mechanism builds on a detailed mechanism developed using Reaction Mechanism Generator (RMG) for the specific purpose of determining the extent to which replacing cyclopentene-specific reactions and species with quantum chemical computations reduces model inaccuracies resulting from mechanism truncation error. In an effort to minimize interference from other reactions present during the formation of cyclopentene from cyclopentyl + O2, providing a narrower experimental scope, the model is compared against speciation measurements from jet-stirred reactor (JSR) experiments on cyclopentene oxidation. The experiments utilize vacuum ultraviolet-absorption spectroscopy and mass spectrometry for isomer-resolved speciation of intermediates at 835 Torr from 700 – 950 K. [O2]-dependent experiments were also conducted from 0.057 – 2.01 · 1018 molecules cm–3 at 825 K to examine the influence of oxygen on species profiles. Model predictions using the ab initio-revised mechanism yielded significant improvements in species profiles for both the temperature- and [O2]-dependent measurements, owing in part to increased rates of HOȮ and H2O2 production, which underscores the influence of theoretical calculations of reaction rates involving species produced from Ṙ + O2 such as cyclopentene.

AutoMech↗

Thermal Shape Stability of fcc Metal Nanocrystals Synthesized with Faceted Nonequilibrium Shapes

Highly refined capabilities of the shape-controlled solution-phase synthesis of metal nanocrystals (NCs) allow the generation of NCs with faceted nonequilibrium shapes, which optimize properties for target applications such as catalysis and plasmonics. Often, for such applications and also for TEM analysis, the NCs are removed from the solution-phase environment. We explore the postsynthesis evolution of these metastable NCs in a high-vacuum TEM environment. Specifically, here we analyze their reshaping toward the equilibrium Wulff shapes mediated by surface diffusion, where such reshaping degrades the above-mentioned optimized properties. Typical sizes for these NCs range from 5 to 30 nm or 10 3 –10 6 atoms, and reshaping often occurs on the time scale of minutes for temperatures around, say, 400 °C. We discuss the development of predictive stochastic atomistic-level models for NC evolution with a realistic description of surface diffusion. These models, in contrast to Molecular Dynamics, can naturally address the relevant time and length scales for these systems. KMC simulation results for the stochastic models are described, focusing on the reshaping of slightly elongated nanorods and of mildly truncated octahedra and nanocubes. In addition, we review appropriate theoretical formulations for reshaping, which involves the nucleation and growth on 2D islands or layers on outer facets of the NC. We note the limitations of classical nucleation theory in some scenarios and demonstrate the successes of a more fundamental and general master equation-based analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Unraveling spin entanglement using quantum gates with scanning tunneling microscopy-driven electron spin resonance

Quantum entanglement is a fundamental resource for quantum information processing, and its controlled generation and detection remain key challenges in scalable quantum architectures. Here, we numerically demonstrate the deterministic generation of entangled spin states in a solid-state platform by implementing quantum gates via electron spin resonance combined with scanning tunneling microscopy (ESR-STM). Using two titanium atoms on a MgO/Ag(100) substrate as a model, we construct a two-qubit system whose dynamics are coherently manipulated through tailored microwave pulse sequences. We generate Bell states by implementing a Hadamard gate followed by a controlled-NOT gate, and evaluate its fidelity and concurrence using the quantum-master equation-based code TimeESR. Our results demonstrate that ESR-STM can create entangled states with significant fidelity. This study paves the way for the realization of atom-based quantum circuits and highlights ESR-STM as a powerful tool for probing and engineering entangled states on surfaces.

Switzer, Eric D. [Donostia International Physics C↗

A Stochastic Transport Model for the Cumulative Number of Fissions and Deposited Fission Energy

The stochastic theory of neutron transport is extended to describe the cumulative distribution of fission numbers and deposited fission energy in a multiplying assembly. Solutions for the probability distributions are obtained using analytical approximations and Monte Carlo simulation in lumped geometry and in symmetric homogeneous and heterogeneous spheres. The results show the development of a power-law tail in the steady state fission number and deposited energy distributions when the medium is critical, independent of the fission neutron multiplicity distribution and domain heterogeneity. In contrast, the asymptotic decay is faster than exponential in subcritical media due to rapid chain extinction and in supercritical media due to the increasing probability of chain divergence. Here, a formal asymptotic analysis of the problem in lumped geometry with an arbitrary fission neutron multiplicity confirms the existence of power-law tails at critical.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Long-time memory effects in a localizable central spin problem

We study the properties of the Nakajima–Zwanzig memory kernel for a qubit immersed in a many-body localized (i.e. disordered and interacting) bath. We argue that the memory kernel decays as a power law in both the localized and ergodic regimes, and show how this can be leveraged to extract t → ∞ populations for the qubit from finite time (Jt ≤ 10 2 ) data in the thermalizing phase. This allows us to quantify how the long-time values of the populations approach the expected thermalized state as the bath approaches the thermodynamic limit. This approach should provide a good complement to state-of-the-art numerical methods, for which the long-time dynamics with large baths are impossible to simulate in this phase. Additionally, our numerics on finite baths reveal the possibility for unbounded exponential growth in the memory kernel, a phenomenon rooted in the appearance of exceptional points in the projected Liouvillian governing the reduced dynamics. In small systems amenable to exact numerics, we find that these pathologies may have some correlation with delocalization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Engineering long-lived entanglement through dissipation in quantum hybrid solid-state platforms

Spin squeezing, a form of many-body entanglement, is a crucial resource in quantum metrology and information processing. While experimentally viable protocols for generating stable spin squeezing have been proposed in quantum optics setups, there is growing interest in quantum hybrid solid-state systems as alternative platforms for both engineering and exploring many-body quantum phenomena. In this work, we propose a scheme to generate long-lived spin squeezing in an ensemble of solid-state qubits interacting with electromagnetic noise emitted by a squeezed solid-state bath. We identify the conditions under which quantum correlations within the bath can be transferred to the qubit array, driving it into an entangled state independently of its initial configuration. To assess the experimental feasibility of our approach, we analyze the dynamics of an array of solid-state spin defects coupled to a common ferromagnetic bath, which is driven into a non-equilibrium squeezed state through its interaction with a surface acoustic wave mode. Our results demonstrate that the ensemble can exhibit steady-state spin squeezing under suitable conditions, opening new pathways for the generation of robust many-body entanglement in solid-state spin ensembles.

NV centers↗

Bayesian filtering for model predictive control of stochastic gene expression in single cells

This study describes a method for controlling the production of protein in individual cells using stochastic models of gene expression. By combining modern microscopy platforms with optogenetic gene expression, experimentalists are able to accurately apply light to individual cells, which can induce protein production. Here we use a finite state projection based stochastic model of gene expression, along with Bayesian state estimation to control protein copy numbers within individual cells. We compare this method to previous methods that use population based approaches. We also demonstrate the ability of this control strategy to ameliorate discrepancies between the predictions of a deterministic model and stochastic switching system.

59 BASIC BIOLOGICAL SCIENCES↗