Engineering Papers⌕ Search

SEARCH · Engineering Papers

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 109 records · Page 6

Nonequilibrium hypersonic aerothermodynamics

Nonequilibrium phenomena in hypersonic flows are examined on the basis of theoretical models and selected experimental data, in an introduction intended for second-year graduate students of aerospace engineering. Chapters are devoted to the physical nature of gas atoms and molecules, transitions of internal states, the formulation of the master equation of aerothermodynamics, the conservation equations, chemical reactions in CFD, the behavior of air flows in nonequilibrium, experimental aspects of nonequilibrium flow, a review of experimental results, and gas-solid interaction. Diagrams, graphs, and tables of numerical data are provided.

Park, Chul↗

Vibration-dissociation coupling in nonequilibrium flows

The purpose of the study is to evaluate all important physical phenomena contributing to the vibration-dissociation problem by developing a numerical technique for the simulation of the vibrational relaxation and dissociation/recombination of N(2) in an isothermal box. A set of coupled master equations representing each vibrational level of N(2) is solved, and both V-V and V-T exchanges between molecules and atoms are included, along with the effects of dissociation and recombustion from/to each level. It is observed that the inverse range parameter has a strong impact on the vibrational exchange rates and relaxation. In a heating case, the lower vibrational levels relax through a series of equilibrium distributions, while in a cooling case, a population inversion is formed in the upper levels. Other cases of heating and cooling will be simulated, and together with this work, used to develop a matrix of nonequilibrium relaxation runs.

Landrum, D. Brian↗

Density measurements in an expanding flow using holographic interferometry

A nonequilibrium expansion of nitrogen through a 2-dimensional nozzle of a reflected shock tunnel is investigated with laser holography, time resolved pressure measurements and emission spectroscopy to characterize the flow field for vibrational relaxation measurements. A 2D computation is used to simulate the nozzle flow field. Synthetic holograms are generated using the computed density profiles and are compared with the experimental holograms. Also, using a quasi 1-D approximation, populations for each vibrational level are computed by (1) solving the master equations and (2) using the Landau-Teller formulation. Computational accuracy of both models is assessed against the experimental data.

Sharma, Surendra P.↗

State-to-state rotational energy-transfer measurements in the nu(2) = 1 state of ammonia by infrared-infrared double resonance

The state-resolved rotational (R-R, R-T) energy transfer in (N-14)H3 (for NH3-NH3 and NH3-Ar collisions) was studied using an IR double-resonance laser spectroscopic technique. Measurements of both the total rate of depopulation by collisions, and the rates of transfer into specific final rovibrational states (v,J,K) were performed using time-resolved tunable diode laser absorption spectroscopy. A kinetic master-equation analysis of time-resolved level populatons was carried out, yielding state-to-state rate constants and propensity rules for NH3-NH3 and NH3-Ar collisions.

Abel, Bernd↗

Rotational relaxation of molecular H2 at moderate temperatures

A coupled rotation-vibration-dissociation model is used to compute the rotational relaxation times for molecular hydrogen as a function of final temperatures (500-5000 K) in a hypothetical scenario of sudden compression. The theoretical model is based on a master equation solver. The bound-bound and bound-free transition rates have been computed using a quasi-classical trajectory method. A review of the available experimental data on the rotational relaxation of hydrogen is presented, with a critical overview of the method of measurements and data reduction, including the sources of errors. The experimental data are compared with the computed results.

Sharma, S. P.↗

Nonequilibrium vibrational population measurements in an expanding flow using spontaneous Raman scattering

Vibrational relaxation of nitrogen in a 2D nozzle flow is studied using spontaneous Raman scattering. An electric arc driven shock tube operating as a reflected shock tunnel produces stagnation conditions of 5600 K and 100 atm. A 248 nm KrF laser pulse is focused into the nozzle to produce spatially resolved spontaneous Raman spectra. Vibrational population distributions are derived from the spectra for the states v = 0 to v = 8. The experimental results are compared with two theoretical models: the Landau-Teller relaxation model and a numerical solution of the master equations using transition rates derived from SSH theory. The Landau-Teller correction factor has been measured at 1.0 - 1.5.

Sharma, Surendra P.↗

Quantum harmonic oscillator in a thermal bath

The influence functional path-integral treatment of quantum Brownian motion is briefly reviewed. A newly derived exact master equation of a quantum harmonic oscillator coupled to a general environment at arbitrary temperature is discussed. It is applied to the problem of loss of quantum coherence.

Zhang, Yuhong↗

Statistical modeling of capture, association, and exit-channel dynamics in the CH3(+)/CH3CN system

The ion-molecule CH3(+) + CH3CN reaction is presently modeled by means of a master equation treatment incorporating weak collisions. The parameter required for the Rice-Ramsberger-Kassel-Markus (RRKM) treatment is derived from an ab initio investigation of the energy surface in question, and a means of including the capture rate coefficients in the RRKM approach is developed in which only the hindered dipole rotation is coupled in the reaction coordinate at large separations. Unimolecular rate coefficients for the (CH3CNCH3+)-activated complex are calculated for all product channels in the 300-600 K temperature range.

Smith, S. C.↗

Amplitude and Transverse Quadrature Component Squeezing of Coherent Light in High Q Cavity by Injection of Atoms of Two-Photon Transition

The amplitude and transverse quadrature component squeezing of coherent light in high Q cavity by injection of atoms of two-photon transition are studied. The Golubev-Sokolov master equation and generating function approach are utilized to derive the exact variances of photon number and of transverse quadrature component as function of t. The correlation functions and power spectrums of photon number noise and of output photon current noise are also investigated.

Cao, Chang-Qi↗

The FLUKA code for space applications: recent developments

The FLUKA Monte Carlo transport code is widely used for fundamental research, radioprotection and dosimetry, hybrid nuclear energy system and cosmic ray calculations. The validity of its physical models has been benchmarked against a variety of experimental data over a wide range of energies, ranging from accelerator data to cosmic ray showers in the earth atmosphere. The code is presently undergoing several developments in order to better fit the needs of space applications. The generation of particle spectra according to up-to-date cosmic ray data as well as the effect of the solar and geomagnetic modulation have been implemented and already successfully applied to a variety of problems. The implementation of suitable models for heavy ion nuclear interactions has reached an operational stage. At medium/high energy FLUKA is using the DPMJET model. The major task of incorporating heavy ion interactions from a few GeV/n down to the threshold for inelastic collisions is also progressing and promising results have been obtained using a modified version of the RQMD-2.4 code. This interim solution is now fully operational, while waiting for the development of new models based on the FLUKA hadron-nucleus interaction code, a newly developed QMD code, and the implementation of the Boltzmann master equation theory for low energy ion interactions. c2004 COSPAR. Published by Elsevier Ltd. All rights reserved.

Non-NASA Center↗

Computational Role of Tunneling in a Programmable Quantum Annealer

Quantum tunneling is a phenomenon in which a quantum state tunnels through energy barriers above the energy of the state itself. Tunneling has been hypothesized as an advantageous physical resource for optimization. Here we present the first experimental evidence of a computational role of multiqubit quantum tunneling in the evolution of a programmable quantum annealer. We developed a theoretical model based on a NIBA Quantum Master Equation to describe the multi-qubit dissipative cotunneling effects under the complex noise characteristics of such quantum devices.We start by considering a computational primitive, the simplest non-convex optimization problem consisting of just one global and one local minimum. The quantum evolutions enable tunneling to the global minimum while the corresponding classical paths are trapped in a false minimum. In our study the non-convex potentials are realized by frustrated networks of qubit clusters with strong intra-cluster coupling. We show that the collective effect of the quantum environment is suppressed in the critical phase during the evolution where quantum tunneling decides the right path to solution. In a later stage dissipation facilitates the multiqubit cotunneling leading to the solution state. The predictions of the model accurately describe the experimental data from the D-WaveII quantum annealer at NASA Ames. In our computational primitive the temperature dependence of the probability of success in the quantum model is opposite to that of the classical paths with thermal hopping. Specially, we provide an analysis of an optimization problem with sixteen qubits,demonstrating eight qubit cotunneling that increases success probabilities. Furthermore, we report results for larger problems with up to 200 qubits that contain the primitive as subproblems.

hard problems↗

Desorption Kinetics of O and CO from Graphitic Carbon Surfaces

The desorption of O/CO from graphitic carbon surfaces is investigated using a one-dimensional model describing the adsorbate interactions with the surface phonon bath. The kinetics of desorption are described through the solution of a master equation for the time-dependent population of the adsorbate in an oscillator state, which is modified through thermal fluctuations at the surface. The interaction of the adsorbate with the surface phonons is explicitly captured by using the computed phonon density Of states (PDOS) of the surface. The coupling of the adsorbate with the phonon bath results in the transition of the adsorbate up and down a vibrational ladder. The adsorbate-surface interaction is represented in the model using a Morse potential, which allows for the desorption process to be directly modeled as a transition from bound to free (continuum) state. The PDOS is a property of the material and the lattice; and is highly sensitive to the presence of defects. The effect of etch pits along with random surface defects on the PDOS is considered in the present work. The presence of defects causes a redshift and broadening of the PDOS, which in turn changes the phonon frequency modes available for adsorbate coupling at the surface. Using the realistic PDOS distributions, the phonon-induced desorption (PID) model was used to compute the transition and desorption rates for both pristine and defective systems. Mathissen’s rule is used to compute the phonon relaxation time for pristine and defective systems based on the phonon scattering times for each of the different scattering processes. First, the desorption rates of the pristine system is fitted against the experimental values to obtain the Morse potential parameters for each of the observed adatoms. These Morse potential parameters are used along with the defective PDOS and phonon relaxation time to compute the desorption rates for the defective system. The defective system rates (both transition and desorption) were consistently lower in comparison with the pristine system. The difference between the transition rates is more significant at lower initial states due to higher energy spacing between the levels. In the case of the desorption rates, the difference between the defective and pristine system is more significant at higher temperatures. The desorption rates for each of the system shows an order of magnitude decrease with the strongly bound systems exhibiting the greatest reduction in the desorption rates.

Swaminathan-Gopalan, Krishnan↗

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↗

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↗

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↗

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↗

Quantum speed limit for the out-of-time-ordered correlator from an open-system perspective

Scrambling, the delocalization of initially localized quantum information, is commonly characterized by the out-of-time-ordered correlator (OTOC). Employing the OTOC–Renyi-2 entropy theorem, we derive a quantum speed limit for the OTOC, which sets a lower bound for the rate with which information can be scrambled. This bound becomes particularly tractable by describing the scrambling of information in a closed quantum system as an effective decoherence process of an open system interacting with an environment. We prove that decay of the OTOC can be bounded by the strength of the system-environment coupling and two-point environmental correlation functions. We validate our analytic bound numerically using the nonintegrable transverse field Ising model. Furthermore, our results provide a universal and model-agnostic quantitative framework for understanding the dynamical limits of information spreading across quantum many-body physics, condensed matter systems, and engineered quantum platforms.

Fermions↗

Time-Resolved Stochastic Dynamics of Quantum Thermal Machines

Steady-state quantum thermal machines are typically characterized by a continuous flow of heat between different reservoirs. However, at the level of discrete stochastic realizations, heat flow is unraveled as a series of abrupt quantum jumps, each representing an exchange of finite quanta with the environment. Here, in this work, we present a framework that resolves the dynamics of quantum thermal machines into cycles classified as enginelike, coolinglike, or idle. We analyze the statistics of individual cycle types and their durations, enabling us to determine both the fraction of cycles useful for thermodynamic tasks and the average waiting time between cycles of a given type. Central to our analysis is the notion of intermittency, which captures the operational consistency of the machine by assessing the frequency and distribution of idle cycles. Our framework offers a novel approach to characterizing thermal machines, with significant relevance to experiments involving mesoscopic transport through quantum dots.

full counting statistics↗