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At least 307 records · Page 17

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DOE OSTI2017

Arrhenius Rate: constant volume burn

A constant volume burn occurs for an idealized initial state in which a large volume of reactants at rest is suddenly raised to a high temperature and begins to burn. Due to the uniform spatial state, there is no fluid motion and no heat conduction. This reduces the time evolu tion to an ODE for the reaction progress variable. With an Arrhenius reaction rate, two characteristics of thermal ignition are illustrated: induction time and thermal runaway. The Frank-Kamenetskii approximation then leads to a simple expression for the adiabatic induction time. For a first order reaction, the analytic solution is derived and used to illustrate the effect of varying the activation temperature; in particular, on the induction time. In general, the ODE can be solved numerically. This is used to illustrate the effect of varying the reaction order. We note that for a first order reaction, the time evolution of the reaction progress variable has an exponential tail. In contrast, for a reaction order less than one, the reaction completes in a nite time. The reaction order also affects the induction time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1977

Adiabatic particle motion in a nearly drift-free magnetic field: Application to the geomagnetic tail

The guiding center motion of particles in a nearly drift free magnetic field is analyzed in order to investigate the dependence of mean drift velocity on equatorial pitch angle, the variation of local drift velocity along the trajectory, and other properties. The mean drift for adiabatic particles is expressed by means of elliptic integrals. Approximations to the twice-averaged Hamiltonian W near z = O are derived, permitting simple representation of drift paths if an electric potential also exists. In addition, the use of W or of expressions for the longitudinal invariant allows the derivation of the twice averaged Liouville equation and of the corresponding Vlasov equation. Bounce times are calculated (using the drift-free approximation), as are instantaneous guiding center drift velocities, which are then used to provide a numerical check on the formulas for the mean drift.

Stern, D. P.↗

NASA NTRS1982

The dynamics of the Venus ionosphere. II - The effects of the time scale of the solar wind dynamic pressure variations

The effects on the upper dayside Venus ionosphere of a slow increase in solar wind dynamic pressure are simulated numerically with a one-dimensional (spherically symmetric) Lagrangian hydrodynamical code. The simulation is started with an extended ionosphere in pressure equilibrium with the solar wind at the ionopause. The pressure at the ionopause is gradually increased to five times the initial pressure with rise times of 5, 15, and 30 min. It is found that, for rise times greater than about 10 min, the compression of the ionopause is nearly adiabatic, with the ionopause moving downward at velocities of approximately 1-2 km/sec until it reaches a maximally compressed state, at which time the motion reverses. For short rise times the compression produces a shock wave similar to that occurring in the case of a sudden increase in pressure. The global implications of these processes are discussed within the context of Pioneer Venus observations and future theoretical work on this problem is outlined.

Stein, R. F.↗

NASA NTRS1994

Hybird state of the tail mangetic configuration during steady convection events

Previous observations have shown that during periods of steady magnetospheric convection (SMC) a large amount of magnetic flux crosses the plasma sheet (corresponding to approximately 10 deg wide auroral oval at the nightside) and that the magnetic configuration in the midtail is relaxed (the curent sheet is thick and contains enhanced B(sub Z). These signatures are typical for the substorm recovery phase. Using near-geostationary magnetic field data, magnetic field modeling and a noval diagostic technique (isotropic boundary algorithm), we show that in the near-Earth tail the magnetic confirguration is very stretched during the SMC events. This stretching is caused by an intense, thin westward current. Because of the srongly depressed B(sub Z), there is a large radial gradient in the near-tail magetic field. These signatures have been peviously associated only with the substorm growth phase. Our results indicate that during the SMC periods the magnetic configuration is very peculiar, with co-existing thin near-Earth current sheet and thick midtail plasma sheet. The deep local minimum of the equatorial B(sub Z) that devleops at R approximately 12 R(sub E) is consistent with steady, adiabatic, Earthward convection in the midtail. These results impose contraints on the existing substorm theories, and call for an explanation of how such a stressed configuration can persist for such a long time without tail current disruptions that occur at the end of a substorm growth phase.

Sergeev, V. A.↗

DOE OSTI2022

Initial Design and Experimental Results of a Novel Near-Isothermal Compressor for Heat Pump Applications

In efforts to increase the efficiency of residential and commercial air conditioners and heat pumps, it is found that the compressor has the highest electrical energy usage of the system. Therefore, it is appropriate to try to increase the efficiency of this component to reduce its energy usage. Another challenge with heat pump design is that some compressor types have drawbacks that make modulation difficult. To answer these challenges, we are developing an isothermal liquid compressor. The compressor uses propylene glycol to compress carbon dioxide. In the compression chamber the propylene glycol can enter either from the bottom to create a liquid piston for compression or it can enter through a spray nozzle at the top of the chamber. In the latter case, heat transfer from the gas to be compressed to the liquid droplets is high. This allows near isothermal operation of the compressor, which increases the efficiency by 17% to 30%, compared to adiabatic compression. In addition, the isothermal liquid compressor enables very efficient and simple part load modulation.Experimental results demonstrating the operation of the liquid compressor are presented. Initial data demonstrated a temperature rise of 7 K at pressure ratios of almost 4. For comparison at the same initial pressure, temperature, and pressure ratio, adiabatic compression would result in a temperature increase of approximately 70 K. Plotting data on a P-h diagram demonstrates that the compression started at superheated state and ended in supercritical state. Testing was later performed with repeated compressions in the superheated region of the P-h diagram at liquid flow rates of 2 x 10-3 m3/min and 2 x 10-3 m3/min to understand the limitations of the prototype for use with an actual heat pump system. This work demonstrated a novel cycle on a T-s diagram. Results from this work will be used to develop a second-generation prototype where more rapid cycling is possible.

Kowalski, Steve↗

DOE OSTI2011

Laser cooling of a trapped particle with increased Rabi frequencies

This paper analyzes the cooling of a single particle in a harmonic trap with red-detuned laser light with fewer approximations than previously done in the literature. We avoid the adiabatic elimination of the excited atomic state but are still interested in Lamb-Dicke parameters {eta}<<1. Our results show that the Rabi frequency of the cooling laser can be chosen higher than previously assumed, thereby increasing the effective cooling rate but not affecting the final outcome of the cooling process. Since laser cooling is already a well-established experimental technique, the main aim of this paper is to present a model which can be extended to more complex scenarios, like cavity-mediated laser cooling.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2013

Benchmark tests and spin adaptation for the particle-particle random phase approximation

The particle-particle random phase approximation (pp-RPA) provides an approximation to the correlation energy in density functional theory via the adiabatic connection [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)]. It has virtually no delocalization error nor static correlation error for single-bond systems. However, with its formal O(N{sup 6}) scaling, the pp-RPA is computationally expensive. In this paper, we implement a spin-separated and spin-adapted pp-RPA algorithm, which reduces the computational cost by a substantial factor. We then perform benchmark tests on the G2/97 enthalpies of formation database, DBH24 reaction barrier database, and four test sets for non-bonded interactions (HB6/04, CT7/04, DI6/04, and WI9/04). For the G2/97 database, the pp-RPA gives a significantly smaller mean absolute error (8.3 kcal/mol) than the direct particle-hole RPA (ph-RPA) (22.7 kcal/mol). Furthermore, the error in the pp-RPA is nearly constant with the number of atoms in a molecule, while the error in the ph-RPA increases. For chemical reactions involving typical organic closed-shell molecules, pp- and ph-RPA both give accurate reaction energies. Similarly, both RPAs perform well for reaction barriers and nonbonded interactions. These results suggest that the pp-RPA gives reliable energies in chemical applications. The adiabatic connection formalism based on pairing matrix fluctuation is therefore expected to lead to widely applicable and accurate density functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Quantum and anharmonic effects in non-adiabatic transition state theory

Quantitative descriptions of non-adiabatic transition rates at intermediate temperatures are challenging due to the simultaneous importance of quantum and anharmonic effects. Here, in this paper, the interplay between quantum effects—for motion across or along the seam of crossing—and anharmonicity in the seam potential is considered within the weak coupling limit. The well-known expression for quantized 1-D motion across the seam (i.e., tunneling) in the linear terms approximation is derived in the thermal domain using the Lagrangian formalism, which is then applied to the case when tunneling is distributed along the seam of crossing (treating motion along the seam classically). For high-frequency quantum modes, a vibrationally adiabatic (VA) approach is developed that introduces to the non-adiabatic rate constant a factor associated with high-frequency wavefunction overlap; this approach treats the high-frequency motion along the seam quantum mechanically. To test these methodologies, the reaction N 2 O ↔ N 2 + O( 3 P) was chosen. CCSD(T)-F12b/cc-pVTZ-F12 explorations of the 3 A'- 1 A' seam of N 2 O revealed that seam anharmonicity has a strong effect on the rate constant (a factor of ~20 at 2000 K). Several quantum effects were found to be significant at intermediate/lower temperatures, including the quantum N–N vibration that was coupled with seam anharmonicity using the VA approach. Finally, a 1-D approximation to non-adiabatic instanton theory is presented to estimate the validity limit of the linear terms model at low temperatures (⁠~ 250 K for N 2 O). We recommend that the assumptions built into many statistical theories for non-adiabatic reactions—harmonic behavior, classical motion, linear terms, and weak coupling—should be verified on a case-by-case basis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

A tutorial introduction to the statistical theory of turbulent plasmas, a half-century after Kadomtsev’s Plasma Turbulence and the resonance-broadening theory of Dupree and Weinstock

In honour of the 50th anniversary of the influential review/monograph on plasma turbulence by B. B. Kadomtsev as well as the seminal works of T. H. Dupree and J. Weinstock on resonance-broadening theory, an introductory tutorial is given about some highlights of the statistical–dynamical description of turbulent plasmas and fluids, including the ideas of nonlinear incoherent noise, coherent damping, and self-consistent dielectric response. The statistical closure problem is introduced. Incoherent noise and coherent damping are illustrated with a solvable model of passive advection. Self-consistency introduces turbulent polarization effects that are described by the dielectric function ${\mathcal{D}}$ . Dupree’s method of using ${\mathcal{D}}$ to estimate the saturation level of turbulence is described; then it is explained why a more complete theory that includes nonlinear noise is required. The general theory is best formulated in terms of Dyson equations for the covariance $C$ and an infinitesimal response function $R$ , which subsumes ${\mathcal{D}}$ . An important example is the direct-interaction approximation (DIA). It is shown how to use Novikov’s theorem to develop an $\boldsymbol{x}$ -space approach to the DIA that is complementary to the original $\boldsymbol{k}$ -space approach of Kraichnan. A dielectric function is defined for arbitrary quadratically nonlinear systems, including the Navier–Stokes equation, and an algorithm for determining the form of ${\mathcal{D}}$ in the DIA is sketched. The independent insights of Kadomtsev and Kraichnan about the problem of the DIA with random Galilean invariance are described. The mixing-length formula for drift-wave saturation is discussed in the context of closures that include nonlinear noise (shielded by ${\mathcal{D}}$ ). The role of $R$ in the calculation of the symmetry-breaking (zonostrophic) instability of homogeneous turbulence to the generation of inhomogeneous mean flows is addressed. The second-order cumulant expansion and the stochastic structural stability theory are also discussed in that context. In conclusion, various historical research threads are mentioned and representative entry points to the literature are given. In addition, some outstanding conceptual issues are enumerated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Efficiently embedding QUBO problems on adiabatic quantum computers

Adiabatic quantum computers like the D-Wave 2000Q can approximately solve the QUBO problem, which is an NP-hard problem, and have been shown to outperform classical computers on several instances. Solving the QUBO problem literally means solving virtually any NP-hard problem like the traveling salesman problem, airline scheduling problem, protein folding problem, genotype imputation problem, thereby enabling significant scientific progress, and potentially saving millions/billions of dollars in logistics, airlines, healthcare and many other industries. Yet, before QUBO problems are solved on quantum computers, they must be embedded (or compiled) onto the hardware of quantum computers, which in itself is a very hard problem. Here, we propose an efficient embedding algorithm, that lets us embed QUBO problems fast, uses less qubits and gets the objective function value close to the global minimum value. We then compare the performance of our embedding algorithm to that of D-Wave’s embedding algorithm, which is the current state of the art, and show that our embedding algorithm convincingly outperforms D-Wave’s embedding algorithm. Our embedding approach works with perfect Chimera graphs, i.e., Chimera graphs with no missing qubits.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

A POLYTROPIC MODEL FOR SPACE AND LABORATORY PLASMAS DESCRIBED BY BI-MAXWELLIAN ELECTRON DISTRIBUTIONS

Non-local electron energy probability functions (EEPFs) are shown to have an important effect on the thermodynamic behavior of plasmas in the context of solar wind and laboratory plasmas. A conservation relation is held for electron enthalpy and plasma potential during the electron transport. For an adiabatic system governed by non-local electron dynamics, the correlation between electron temperature and density can be approximated by a polytropic relation, with different indexes demonstrated using three cases of bi-Maxwellian EEPFs. This scenario differs from a local thermodynamic equilibrium having a single polytropic index of 5/3 for adiabaticity.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Ponderomotive Forces On Waves In Modulated Media

Nonlinear interactions of waves via instantaneous cross-phase modulation can be cast in the same way as ponderomotive wave-particle interactions in high-frequency electromagnetic fi eld. The ponderomotive effect arises when rays of a probe wave scatter off perturbations of the underlying medium produced by a second, modulation wave, much like charged particles scatter off a quasiperiodic field. Parallels with the point-particle dynamics, which itself is generalized by this theory, lead to new methods of wave manipulation, including asymmetric barriers for light.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1979

Post-shock temperatures in minerals

An experimental technique was developed for measuring post-shock temperatures in a wide variety of materials, including those of geophysical interest such as silicates. The technique uses an infrared radiation detector to determine the brightness temperature of samples shocked to pressures in the range 5 to approximately 30 GPa; in these experiments measurements were made in two wavelength ranges (4.5 to 5.75 microns and 7 to 14 microns). Reproducible results, with the temperatures in the two wavelength bands generally in excellent agreement, were obtained for aluminum-2024 (10.5 to 33 GPa, 125 to 260 C), stainless steel-304 (11.5 to 50 GPa, 80 to 350 C), crystalline quartz (5.0 to 21.5 GPa, 80 to 250 C), forsterite (7.5 to 28.0 GPa, approximately 30 to 160 C) and Bamble bronzite (6.0 to 26.0 GPa, approximately 30 to 225 C). It is concluded that release adiabat data should be used, wherever available, for calculations of residual temperature, and that adequate descriptions of the shock and release processes in minerals are more complex than generally assumed.

Raikes, S. A.↗

DOE OSTI2019

A Polytropic Approximation of Compressible Flow in Pipes With Friction

This paper demonstrates the usefulness of treating subsonic Fanno flow (adiabatic flow, with friction, of a perfect gas in a constant-area pipe) as a polytropic process. It is shown that the polytropic model allows an explicit equation for mass flow rate to be developed. The concept of the energy transfer ratio is used to develop a close approximation to the polytropic index. Explicit equations for mass flow rate and net expansion factor in terms of upstream properties and pressure ratio are developed for Fanno and isothermal flows. An approximation for choked flow is also presented. Here, the deviation of the results of this polytropic approximation from the values obtained from a traditional gas dynamics analysis of subsonic Fanno flow is quantified and discussed, and a typical design engineering problem is analyzed using the new method.

42 ENGINEERING↗

NASA NTRS1978

Derivation and evaluation of an approximate analysis for three-dimensional viscous subsonic flow with large secondary velocities

An approximate analysis is presented for calculating three-dimensional, low Mach number, laminar viscous flows in curved passages with large secondary flows and corner boundary layers. The analysis is based on the decomposition of the overall velocity field into inviscid and viscous components with the overall velocity being determined from superposition. An incompressible vorticity transport equation is used to estimate inviscid secondary flow velocities to be used as corrections to the potential flow velocity field. A parabolized streamwise momentum equation coupled to an adiabatic energy equation and global continuity equation is used to obtain an approximate viscous correction to the pressure and longitudinal velocity fields. A collateral flow assumption is invoked to estimate the viscous correction to the transverse velocity fields. The approximate analysis is solved numerically using an implicit ADI solution for the viscous pressure and velocity fields. An iterative ADI procedure is used to solve for the inviscid secondary vorticity and velocity fields. This method was applied to computing the flow within a turbine vane passage with inlet flow conditions of M = 0.1 and M = 0.25, Re = 1000 and adiabatic walls, and for a constant radius curved rectangular duct with R/D = 12 and 14 and with inlet flow conditions of M = 0.1, Re = 1000, and adiabatic walls.

Anderson, O. L.↗

NASA NTRS1991

Diskoseismology: Probing accretion disks. I - Trapped adiabatic oscillations

The normal modes of acoustic oscillations within thin accretion disks which are terminated by an innermost stable orbit around a slowly rotating black hole or weakly magnetized compact neutron star are analyzed. The dominant relativistic effects which allow modes to be trapped within the inner region of the disk are approximated via a modified Newtonian potential. A general formalism is developed for investigating the adiabatic oscillations of arbitrary unperturbed disk models. The generic behavior is explored by way of an expansion of the Lagrangian displacement about the plane of symmetry and by assuming separable solutions with the same radial wavelength for the horizontal and vertical perturbations. The lowest eigenfrequencies and eigenfunctions of a particular set of radial and quadrupole modes which have minimum motion normal for the plane are obtained. These modes correspond to the standard dispersion relation of disk theory.

Nowak, Michael A.↗

DOE OSTI2020

hi_class background evolution, initial conditions and approximation schemes

Cosmological datasets have great potential to elucidate the nature of dark energy and test gravity on the largest scales available to observation. Theoretical predictions can be computed with hi_class (www.hiclass-code.net), an accurate, fast and flexible code for linear cosmology, incorporating a wide range of dark energy theories and modifications to general relativity. We introduce three new functionalities into hi_class: (1) Support for models based on covariant Lagrangians, including a constraint-preserving integration scheme for the background evolution and a series of worked-out examples: Galileon, nKGB, quintessence (monomial, tracker) and Brans-Dicke. (2) Consistent initial conditions for the scalar-field perturbations in the deep radiation era, identifying the conditions under which modified-gravity isocurvature perturbations may grow faster than adiabatic modes leading to a loss of predictivity. (3) An automated quasistatic approximation scheme allowing order-of-magnitude improvement in computing performance without sacrificing accuracy for wide classes of models. These enhancements bring the treatment of dark energy and modified gravity models to the level of detail comparable to software tools restricted to standard $\Lambda$CDM cosmologies. Finally, the hi_class code is publicly available (https://github.com/miguelzuma/hi_class_public), ready to explore current data and prepare for next-generation experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1982

Extended adiabatic blast waves and a model of the soft X-ray background

The suggestion has been made that much of the soft X-ray background observed in X-ray astronomy might arise from being inside a very large supernova blast wave propagating in the hot, low-density component of the interstellar (ISM) medium. An investigation is conducted to study this possibility. An analytic approximation is presented for the nonsimilar time evolution of the dynamic structure of an adiabatic blast wave generated by a point explosion in a homogeneous ambient medium. A scheme is provided for evaluating the electron-temperature distribution for the evolving structure, and a procedure is presented for following the state of a given fluid element through the evolving dynamical and thermal structures. The results of the investigation show that, if the solar system were located within a blast wave, the Wisconsin soft X-ray rocket payload would measure the B and C band count rates that it does measure, provided conditions correspond to the values calculated in the investigation.

Cox, D. P.↗