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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Equilibrium expectations for non-Gaussian fluctuations near a QCD critical point

With the highly anticipated results from the Beam Energy Scan II program at RHIC being recently revealed, an understanding of particle-number fluctuations and their significance as a potential signature of a possible QCD critical point is crucial. Early works that embarked on this endeavor sought to estimate the fluctuations due to the presence of a critical point assuming they stay in equilibrium. From these results came the proposal to focus efforts on higher, non-Gaussian, moments of the event-by-event distributions, in particular of the number of protons. These non-Gaussian moments are especially sensitive to critical fluctuations, as their magnitudes are proportional to high powers of the critical correlation length. As the equation of state provides key input for hydrodynamical simulations of heavy-ion collisions, we estimate equilibrium fluctuations from the BEST equation of state (EoS) that includes critical features from the 3D Ising Model. In particular, the proton factorial cumulants and their dependence on non-universal mapping parameters is investigated within the BEST EoS. Furthermore, the correlation length, as a central quantity for the assessment of fluctuations in the vicinity of a critical point, is also calculated in a consistent manner with the scaling equation of state. An understanding of the equilibrium estimates of proton factorial cumulants will be useful for further comparison to estimates of out-of-equilibrium fluctuations in order to determine the magnitude of the observable fluctuations to be expected in heavyion collision experiments, in which the time spent near a critical point is short.

Karthein, Jamie M. [Massachusetts Institute of Tec↗
DOE OSTI2024

Non-equilibrium rate theory for polariton relaxation dynamics

We derive an analytic expression of the non-equilibrium Fermi’s golden rule (NE-FGR) expression for a Holstein–Tavis–Cumming Hamiltonian, a universal model for many molecules collectively coupled to the optical cavity. These NE-FGR expressions capture the full-time-dependent behavior of the rate constant for transitions from polariton states to dark states. The rate is shown to be reduced to the well-known frequency domain-based equilibrium Fermi’s golden rule (E-FGR) expression in the equilibrium and collective limit and is shown to retain the same scaling with the number of sites in non-equilibrium and non-collective cases. We use these NE-FGR to perform population dynamics with a time-non-local and time-local quantum master equation and obtain accurate population dynamics from the initially occupied upper or lower polariton states. Furthermore, NE-FGR significantly improves the accuracy of the population dynamics when starting from the lower polariton compared to the E-FGR theory, highlighting the importance of the non-Markovian behavior and the short-time transient behavior in the transition rate constant.

Chemical dynamics↗
NASA NTRS1972

Surface roughness effects on equilibrium temperature.

An analysis is presented for evaluation of equilibrium temperature distribution on radiatively adiabatic, adjoint planes which are uniformly irradiated by a collimated solar flux. The analysis employs a semigrey spectral model. Radiation properties for surface emitted radiation are obtained from the expressions of electromagnetic theory for smooth surfaces. Rough surface properties for solar radiation are given by the Beckmann bidirectional reflectance model. Numerical solutions to the governing equations yield equilibrium temperature distributions for a range of the influencing parameters. Surface roughness has little influence on equilibrium temperature for materials with high values for solar absorptance. However, for low or intermediate values of solar absorptance, roughness effects on the spatial distribution of reflected solar radiation can significantly alter equilibrium temperature particularly at surface elements where radiant interaction is small.

Houchens, A. F.↗
NASA NTRS1974

Radiative-dynamical equilibrium states for Jupiter

In order to obtain accurate estimates of the radiative heating that drives motions in Jupiter's atmosphere, previous radiative equilibrium calculations are improved by including the NH3 opacities and updated results for the pressure-induced opacities. These additions increase the radiative lapse rate near the top of the statically unstable region and lead to a fairly constant radiative lapse rate below the tropopause. The radiative-convective equilibrium temperature structure consistent with these changes is calculated, but it differs only slightly from earlier calculations. The radiative equilibrium calculations are used to calculate whether equilibrium states can occur on Jupiter which are similar to the baroclinic instability regimes on the earth and Mars. The results show that Jupiter's dynamical regime cannot be of this kind, except possibly at very high latitudes, and that its regime must be a basically less stable one than this kind.

Trafton, L. M.↗
NASA NTRS1974

Ionization equilibrium in soft X-ray-emitting solar flares

Studies of the 1.9-A line produced by highly ionized iron during a solar flare indicate that this emission occurs under conditions approaching a steady-state ionization equilibrium. Time-dependent and steady-state ionization equilibrium values are used for calculation of 1.9 A line fluxes per unit flare emission. The results are compared with those obtained by observations of some four solar flares, showing that the calculations from time-dependent equilibrium values approximate the observed line flux values with the same accuracy as the calculations from steady-state equilibrium values only when the electron densities are equal to or greater than 10 billion per cu cm.

Phillips, K. J. H.↗
NASA NTRS1977

Thermodynamic properties of gaseous fluorocarbons and isentropic equilibrium expansions of two binary mixtures of fluorocarbons and argon

Equations and computer code are given for the thermodynamic properties of gaseous fluorocarbons in chemical equilibrium. In addition, isentropic equilibrium expansions of two binary mixtures of fluorocarbons and argon are included. The computer code calculates the equilibrium thermodynamic properties and, in some cases, the transport properties for the following fluorocarbons: CCl2F, CCl2F2, CBrF3, CF4, CHCl2F, CHF3, CCL2F-CCl2F, CCLF2-CClF2, CF3-CF3, and C4F8. Equilibrium thermodynamic properties are tabulated for six of the fluorocarbons(CCl3F, CCL2F2, CBrF3, CF4, CF3-CF3, and C4F8) and pressure-enthalpy diagrams are presented for CBrF3.

Talcott, N. A., Jr.↗
NASA NTRS1977

CO2 and humidity removal system for extended Shuttle missions - CO2, H2O, and trace contaminant equilibrium testing

The equilibrium relationships for the co-adsorption of CO2 and H2O on an amine coated acrylic ester are presented. The equilibrium data collection and reduction techniques are discussed. Based on the equilibrium relationship, other modes of operation of systems containing HS-C are discussed and specific space applications for HS-C are presented. Equilibrium data for 10 compounds which are found as trace contaminants in closed environments are also presented.

Davis, S. H.↗
NASA NTRS1980

Collapse and equilibrium of rotating, adiabatic clouds

A numerical hydrodynamics computer code analysis of the collapse and establishment of equilibrium of adiabatic gas clouds restricted to axial symmetry found that the clouds are originally uniform in density and rotation. The method can compare the dynamic collapse and approach to equilibrium with the data on incompressible uniformly rotating equilibrium clouds and on equilibrium structures of differentially rotating polytropes. It is concluded that the stellar formation theory indicates that the low alpha fragments produced at the termination of the dynamic isothermal collapse phase of interstellar clouds may undergo significant dynamic collapse in an adiabatic regime leading to transitory ring formation and additional fragmentation on a smaller scale.

Boss, A. P.↗
NASA NTRS1982

Magnetohydrodynamic equilibrium. III - Helically symmetric fields. IV - Nonequilibrium of nonsymmetric hydrodynamic topologies

It is pointed out that plasma confinement in stable equilibrium states constitutes a fundamental and still unresolved question in plasma astrophysics and thermonuclear fusion research. The problem has two parts related to the equilibrium states themselves and their mechanical stability. The question of the existence of general solutions of the field and fluid equations for the steady dynamical interaction of inviscid compressible fluids of high electrical conductivity with magnetic and gravity fields is considered. In the absence of fluid motions, the presented equations become the familiar equations of magnetostatics supplemented by an equation of state. Starting from this simplest case of magnetostatic equilibrium, the investigation proceeds to the more complex case of magnetohydrodynamic equilibrium. Examples of helically symmetric fields are presented to illustrate the use of the formulation for treating the dynamics of helically symmetric hydromagnetic flows.

Tsinganos, K. C.↗
NASA NTRS1983

Absence of equilibrium among close-packed twisted flux tubes

The lack of equilibrium in twisted, close-packed flux tubes is demonstrated in terms of a topology of the transverse field and the necessity of defining restricted solutions for an arbitrary function in the equilibrium equation. It is shown that nearly all combinations of flux connections and functional forms have no mutual equilibrium and that the flux connections in nature are formed by footprint convection at an origin. The most close-packed twisted flux tubes are subject to dynamical nonequilibrium, with the transverse flux connections being reduced through neutral point rapid reconnection. The precise solutions which can be obtained through functional forms in the equilibrium equation do not have an analog in the real world.

Parker, E. N.↗
NASA NTRS1986

General equilibrium characteristics of a dual-lift helicopter system

The equilibrium characteristics of a dual-lift helicopter system are examined. The system consists of the cargo attached by cables to the endpoints of a spreader bar which is suspended by cables below two helicopters. Results are given for the orientation angles of the suspension system and its internal forces, and for the helicopter thrust vector requirements under general circumstances, including nonidentical helicopters, any accelerating or static equilibrium reference flight condition, any system heading relative to the flight direction, and any distribution of the load to the two helicopters. Optimum tether angles which minimize the sum of the required thrust magnitudes are also determined. The analysis does not consider the attitude degrees of freedom of the load and helicopters in detail, but assumes that these bodies are stable, and that their aerodynamic forces in equilibrium flight can be determined independently as functions of the reference trajectory. The ranges of these forces for sample helicopters and loads are examined and their effects on the equilibrium characteristics are given parametrically in the results.

Cicolani, L. S.↗
NASA NTRS1989

Determining Equilibrium Position For Acoustical Levitation

Equilibrium position and orientation of acoustically-levitated weightless object determined by calibration technique on Earth. From calibration data, possible to calculate equilibrium position and orientation in presence of Earth gravitation. Sample not levitated acoustically during calibration. Technique relies on Boltzmann-Ehrenfest adiabatic-invariance principle. One converts resonant-frequency-shift data into data on normalized acoustical potential energy. Minimum of energy occurs at equilibrium point. From gradients of acoustical potential energy, one calculates acoustical restoring force or torque on objects as function of deviation from equilibrium position or orientation.

Barmatz, M. B.↗
NASA NTRS1989

Siphon flows in isolated magnetic flux tubes. 3: The equilibrium path of the flux tube arch

The arched equilibrium path of a thin magnetic flux tube in a plane-stratified, nonmagnetic atmosphere is calculated for cases in which the flux tube contains a steady siphon flow. The large scale mechanical equilibrium of the flux tube involves a balance among the magnetic buoyancy force, the net magnetic tension force due to the curvature of the flux tube axis, and the inertial (centrifugal) force due to the siphon flow along curved streamlines. The ends of the flux tube are assumed to be pinned down by some other external force. Both isothermal and adiabatic siphon flows are considered for flux tubes in an isothermal external atmosphere. For the isothermal case, in the absence of a siphon flow the equilibrium path reduces to the static arch calculated by Parker (1975, 1979). The presence of a siphon flow causes the flux tube arch to bend more sharply, so that magnetic tension can overcome the additional straightening effect of the inertial force, and reduces the maximum width of the arch. The curvature of the arch increases as the siphon flow speed increases. For a critical siphon flow, with supercritical flow in the downstream leg, the arch is asymmetric, with greater curvature in the downstream leg of the arch. Adiabatic flow have qualitatively similar effects, except that adiabatic cooling reduces the buoyancy of the flux tube and thus leads to significantly wider arches. In some cases the cooling is strong enough to create negative buoyancy along sections of the flux tube, requiring upward curvature of the flux tube path along these sections and sometimes leading to unusual equilibrium paths of periodic, sinusoidal form.

Thomas, John H.↗
NASA NTRS1992

Structural design using equilibrium programming

Multiple nonlinear programming methods are combined in the method of equilibrium programming. Equilibrium programming theory has been appied to problems in operations research, and in the present study it is investigated as a framework to solve structural design problems. Several existing formal methods for structural optimization are shown to actually be equilibrium programming methods. Additionally, the equilibrium programming framework is utilized to develop a new structural design method. Selected computational results are presented to demonstrate the methods.

Scotti, Stephen J.↗
NASA NTRS1992

Monte Carlo computer simulations of Venus equilibrium and global resurfacing models

Two models have been proposed for the resurfacing history of Venus: (1) equilibrium resurfacing and (2) global resurfacing. The equilibrium model consists of two cases: in case 1, areas less than or equal to 0.03 percent of the planet are spatially randomly resurfaced at intervals of less than or greater than 150,000 yr to produce the observed spatially random distribution of impact craters and average surface age of about 500 m.y.; and in case 2, areas greater than or equal to 10 percent of the planet are resurfaced at intervals of greater than or equal to 50 m.y. The global resurfacing model proposes that the entire planet was resurfaced about 500 m.y. ago, destroying the preexisting crater population and followed by significantly reduced volcanism and tectonism. The present crater population has accumulated since then with only 4 percent of the observed craters having been embayed by more recent lavas. To test the equilibrium resurfacing model we have run several Monte Carlo computer simulations for the two proposed cases. It is shown that the equilibrium resurfacing model is not a valid model for an explanation of the observed crater population characteristics or Venus' resurfacing history. The global resurfacing model is the most likely explanation for the characteristics of Venus' cratering record. The amount of resurfacing since that event, some 500 m.y. ago, can be estimated by a different type of Monte Carolo simulation. To date, our initial simulation has only considered the easiest case to implement. In this case, the volcanic events are randomly distributed across the entire planet and, therefore, contrary to observation, the flooded craters are also randomly distributed across the planet.

Dawson, D. D.↗
NASA NTRS1993

Loss of equilibrium and reconnection in tearing of two-dimensional equilibria

Two-dimensional tearinglike behavior is studied in reduced resistive magnetohydrodynamics (MHD) with flux conserving boundary conditions on a rectangular box. The tearinglike perturbations do not destroy the symmetries of the initial state, either discrete or continuous. In such cases, in which the perturbation does not break a symmetry of the equilibrium, linear instability is typically not directly observed. However, there can be a loss of equilibrium associated with the existence of a tearing unstable state. These ideas are illustrated with three examples: a very elongated tokamak, a tokamak with pinching coils to elongate its flux surfaces, and a model for the magnetotail or for solar arcades. The loss of equilibrium is demonstrated by means of a nonlinear energy functional. The importance of the fact that the dynamics shows a loss of equilibrium is that a large amount of free energy can be released, in the form of reconnection, and that there is a possibility of hysteresis.

Finn, John M.↗
NASA NTRS1993

Confirmation of saturation equilibrium conditions in crater populations

We have continued work on realistic numerical models of cratered surfaces, as first reported at last year's LPSC. We confirm the saturation equilibrium level with a new, independent test. One of us has developed a realistic computer simulation of a cratered surface. The model starts with a smooth surface or fractal topography, and adds primary craters according to the cumulative power law with exponent -1.83, as observed on lunar maria and Martian plains. Each crater has an ejecta blanket with the volume of the crater, feathering out to a distance of 4 crater radii. We use the model to test the levels of saturation equilibrium reached in naturally occurring systems, by increasing crater density and observing its dependence on various parameters. In particular, we have tested to see if these artificial systems reach the level found by Hartmann on heavily cratered planetary surfaces, hypothesized to be the natural saturation equilibrium level. This year's work gives the first results of a crater population that includes secondaries. Our model 'Gaskell-4' (September, 1992) includes primaries as described above, but also includes a secondary population, defined by exponent -4. We allowed the largest secondary from each primary to be 0.10 times the size of the primary. These parameters will be changed to test their effects in future models. The model gives realistic images of a cratered surface although it appears richer in secondaries than real surfaces are. The effect of running the model toward saturation gives interesting results for the diameter distribution. Our most heavily cratered surface had the input number of primary craters reach about 0.65 times the hypothesized saturation equilibrium, but the input number rises to more than 100 times that level for secondaries below 1.4 km in size.

Hartmann, William K.↗
NASA NTRS1994

Computer program for calculation of complex chemical equilibrium compositions and applications. Part 1: Analysis

This report presents the latest in a number of versions of chemical equilibrium and applications programs developed at the NASA Lewis Research Center over more than 40 years. These programs have changed over the years to include additional features and improved calculation techniques and to take advantage of constantly improving computer capabilities. The minimization-of-free-energy approach to chemical equilibrium calculations has been used in all versions of the program since 1967. The two principal purposes of this report are presented in two parts. The first purpose, which is accomplished here in part 1, is to present in detail a number of topics of general interest in complex equilibrium calculations. These topics include mathematical analyses and techniques for obtaining chemical equilibrium; formulas for obtaining thermodynamic and transport mixture properties and thermodynamic derivatives; criteria for inclusion of condensed phases; calculations at a triple point; inclusion of ionized species; and various applications, such as constant-pressure or constant-volume combustion, rocket performance based on either a finite- or infinite-chamber-area model, shock wave calculations, and Chapman-Jouguet detonations. The second purpose of this report, to facilitate the use of the computer code, is accomplished in part 2, entitled 'Users Manual and Program Description'. Various aspects of the computer code are discussed, and a number of examples are given to illustrate its versatility.

Gordon, Sanford↗