Partial Equilibrium Conditions Research Articles

Hydrodynamics with parametric slowing down and fluctuations near the critical point

The search for the QCD critical point in heavy-ion collision experiments requires dynamical simulations of the bulk evolution of QCD matter as well as of fluctuations. We consider two essential ingredients of such a simulation: a generic extension of hydrodynamics by a_parametrically_ slow mode or modes ("Hydro+") and a description of fluctuations out of equilibrium. By combining the two ingredients we are able to describe the bulk evolution and the fluctutations within the same framework. Critical slowing down means that equilibration of fluctuations could be as slow as hydrodynamic evolution and thus fluctuations could significantly deviate from equilibrium near the critical point. We generalize hydrodynamics to partial-equilibrium conditions where the state of the system is characterized by the off-equilibrium magnitude of fluctuations in addition to the usual hydrodynamic variables -- conserved densities. We find that the key element of the new formalism -- the extended entropy taking into account the off-equilibrium fluctuations -- is remarkably similar to the 2PI action in quantum field theory. We show how the new Hydro+ formalism reproduces two major effects of critical fluctuations on the bulk evolution: the strong frequency dependence of the anomalously large bulk viscosity as well as the stiffening of the equation of state with increasing frequency or wave-number. While the agreement with known results confirms its validity, the fact that Hydro+ achieves this within a local and deterministic framework gives it significant advantages for dynamical simulations.

Temporal variations of electron density and temperature in Kr/Ne/H2 photoionized plasma induced by nanosecond pulses from extreme ultraviolet source

Spectral investigations of low-temperature photoionized plasmas created in a Kr/Ne/H2 gas mixture were performed. The low-temperature plasmas were generated by gas mixture irradiation using extreme ultraviolet pulses from a laser-plasma source. Emission spectra in the ultraviolet/visible range from the photoionized plasmas contained lines that mainly corresponded to neutral atoms and singly charged ions. Temporal variations in the plasma electron temperature and electron density were studied using different characteristic emission lines at various delay times. Results, based on Kr II lines, showed that the electron temperature decreased from 1.7 to 0.9 eV. The electron densities were estimated using different spectral lines at each delay time. In general, except for the Hβ line, in which the electron density decreased from 3.78 × 1016 cm−3 at 200 ns to 5.77 × 1015 cm−3 at 2000 ns, most of the electron density values measured from the different lines were of the order of 1015 cm−3 and decreased slightly while maintaining the same order when the delay time increased. The time dependences of the measured and simulated intensities of a spectral line of interest were also investigated. The validity of the partial or full local thermodynamic equilibrium (LTE) conditions in plasma was explained based on time-resolved electron density measurements. The partial LTE condition was satisfied for delay times in the 200 ns to 1500 ns range. The results are summarized, and the dominant basic atomic processes in the gas mixture photoionized plasma are discussed.

Effects of N/C Ratio on Solidification Behaviors of Novel Nb-Bearing Austenitic Heat-Resistant Cast Steels for Exhaust Components of Gasoline Engines

In order to comply with more stringent environmental and fuel consumption regulations, novel Nb-bearing austenitic heat-resistant cast steels that withstand exhaust temperatures as high as 1,323 K (1,050 °C) is urgently demanded from automotive industries. In the current research, the solidification behavior of these alloys with variations of N/C ratio is investigated. Directional solidification methods were carried out to examine the microstructural development in mushy zones. Computational thermodynamic calculations under partial equilibrium conditions were performed to predict the solidification sequence of different phases. Microstructural characterization of the mushy zones indicates that N/C ratio significantly influenced the stability of γ-austenite and the precipitation temperature of NbC/Nb(C,N), thereby altering the solidification path, as well as the morphology and distribution of NbC/Nb(C,N) and γ-ferrite. The solidification sequence of different phases predicted by thermodynamic software agreed well with the experimental results, except the specific precipitation temperatures. The generated data and fundamental understanding will be helpful for the application of computational thermodynamic methods to predict the as-cast microstructure of Nb-bearing austenitic heat-resistant steels.

Evaluation of the solute geothermometry of thermal springs and drilled wells of La Primavera (Cerritos Colorados) geothermal field, Mexico: A geochemometrics approach

A detailed study on the solute geothermometry of thermal water (18 springs and 8 drilled wells) of La Primavera geothermal field (LPGF) in Mexico has been carried out by employing a geochemical database compiled from the literature and by applying all the available solute geothermometers. The performance of these geothermometers in predicting the reservoir temperatures has been evaluated by applying a geochemometrics (geochemical and statistical) method. The springs of the LPGF are of bicarbonate type and the majority have attained partial-equilibrium chemical conditions and the remaining have shown non-equilibrium conditions. In the case of geothermal wells, water is dominantly of chloride-type and, among the studied eight geothermal wells, four have shown full-equilibrium chemical conditions and another four have indicated partial-equilibrium conditions. All springs of HCO3−​ type water have provided unreliable reservoir temperatures, whereas the only one available spring of SO42− type water has provided the reservoir temperature nearer to the average BHT of the wells. Contrary to the general expected behavior, spring water of non-equilibrium and geothermal well water of partial-equilibrium chemical conditions have indicated more reliable reservoir temperatures than those of partially-equilibrated and fully-equilibrated water, respectively. Among the chemical concentration data, Li and SiO2 of two springs, SO42− and Mg of four springs, and HCO3 and Na concentrations of two geothermal wells were identified as outliers and this has been reflected in very low reservoir temperatures predicted by the geothermometers associated with them (Li–Mg, Na–Li, Na–K–Mg, SiO2 etc.). Identification of the outlier data points may be useful in differentiating the chemical characteristics, lithology and the physico-chemical and geological processes at the sample locations of the study area.In general, the solute geothermometry of the spring waters of LPGF indicated a dominantly (94%) of underestimated deep reservoir temperatures, whereas in the case of the geothermal wells, many temperatures (54%) are underestimated, some are (43%) overestimated and a very small number (3%) are similar to an average bottom-hole temperatures (BHT) of the wells. 28 out of the total applied 29 geothermometers for spring waters have predicted the deep reservoir temperatures that are characterized by statistically significant large differences compared to the average BHTs of the geothermal wells. In the case of waters of the geothermal wells, 23 out of the total applied 28 geothermometers have predicted the reservoir temperatures similar (statistically no significant differences) to the BHTs of the corresponding geothermal wells.

Surplus Maximization and Optimality

Expected consumer's surplus rarely represents preferences over price lotteries. Still, I give sufficient conditions for policies which maximize aggregate expected surplus to be interim Pareto Optimal. Besides two standard partial equilibrium conditions, I assume that feasible prices satisfy a single-crossing property; and each consumer's indirect utility satisfies increasing differences in the price and income. I use the result to extend well-known welfare conclusions beyond the knife-edge quasilinear utility case. Since increasing differences puts no upper bound on risk aversion, the result is useful for applications in which risk aversion is important. (JEL D11, D24, D42, D81, D83, L42)

The Role of Stock and Currency Market Information in the Taylor Rule: Evidence from OECD Countries

The role of stock and currency market information in a forward-looking Taylor rule is analysed for monthly data from 13 OECD countries and the U.S. during the years 1988-2012. Based on a simple set of partial equilibrium conditions we fi nd that the stock market information in the form of dividend yield and the currency market information in the form of real exchange rate are especially relevant and actually instrumental in the GMM analysis of the Taylor rule or many of the countries examined in terms of obtaining a signi cant role for the traditional Taylor rule policy variables, that is, infl‡ation and real economic activity deviations. In many cases the rule also seems to be opportunistic, i.e., at least in the short term the infl‡ation target has been time-varying.

Hydrogeochemical comparison and effects of overlapping redox zones on groundwater arsenic near the Western (Bhagirathi sub-basin, India) and Eastern (Meghna sub-basin, Bangladesh) margins of the Bengal Basin

Although arsenic (As) contamination of groundwater in the Bengal Basin has received wide attention over the past decade, comparative studies of hydrogeochemistry in geologically different sub-basins within the basin have been lacking. Groundwater samples were collected from sub-basins in the western margin (River Bhagirathi sub-basin, Nadia, India; 90 samples) and eastern margin (River Meghna sub-basin; Brahmanbaria, Bangladesh; 35 samples) of the Bengal Basin. Groundwater in the western site (Nadia) has mostly Ca–HCO3 water while that in the eastern site (Brahmanbaria) is much more variable consisting of at least six different facies. The two sites show differences in major and minor solute trends indicating varying pathways of hydrogeochemical evolution However, both sites have similar reducing, postoxic environments (pe: +5 to −2) with high concentrations of dissolved organic carbon, indicating dominantly metal-reducing processes and similarity in As mobilization mechanism. The trends of various redox-sensitive solutes (e.g. As, CH4, Fe, Mn, NO3−, NH4+, SO42−) indicate overlapping redox zones, leading to partial redox equilibrium conditions where As, once liberated from source minerals, would tend to remain in solution because of the complex interplay among the electron acceptors.

PARTIAL EQUILIBRIUM AND MARKET COMPLETION

We consider financial markets with agents exposed to an external source of risk which cannot be hedged through investments on the capital market alone. The sources of risk we think of may be weather and climate. Therefore we face a typical example of an incomplete financial market. We design a model of a market on which the external risk becomes tradable. In a first step we complete the market by introducing an extra security which valuates the external risk through a process parameter describing its market price. If this parameter is fixed, risk has a price and every agent can maximize the expected exponential utility with individual risk aversion obtained from his risk exposure on the one hand and his investment into the financial market consisting of an exogenous set of stocks and the insurance asset on the other hand. In the second step, the market price of risk parameter has to be determined by a partial equilibrium condition which just expresses the fact that in equilibrium the market is cleared of the second security. This choice of market price of risk is performed in the framework of nonlinear backwards stochastic differential equations.

Transient phase of enzyme reactions.: Time course equations of the strict and the rapid equilibrium conditions and their computerized derivation

In this contribution, we present the derivation, from the strict transient phase equations of enzyme reactions, of the transient phase equations under the usual assumptions that one or more of the reversible steps involved in the mechanism of the enzyme reaction are assumed to be in rapid equilibrium. Moreover, we present the transient phase equations of all of the species in a general enzyme system model, valid for the partial or total rapid equilibrium conditions, as well as the particular case of the strict transient phase equations. In the case of the rapid equilibrium assumptions, the equations may be given either as functions of the individual rate constants in the reversible steps assumed in rapid equilibrium or as functions of the corresponding equilibrium constants. The steady state equations are easily obtained from the transient phase equations by setting the time →∞. We have implemented a computer program, easy to use and with a user-friendly format for the input of data and output of results, which allows the user to derive the symbolic strict transient phase equations and/or those corresponding to the assumption that one or more of the reversible reaction steps are in rapid equilibrium.

Eigenvector approximate dichotomic basis method for solving hyper- sensitive optimal control problems

The dichotomic basis method is further developed for solving completely hyper-sensitive Hamiltonian boundary value problems arising in optimal control. For this class of problems, the solution can be accurately approximated by concatenating an initial boundary-layer segment, an equilibrium segment, and a terminal boundary-layer segment. Constructing the solution in this composite manner alleviates the sensitivity. The method uses a dichotomic basis to decompose the Hamiltonian vector field into its stable and unstable components, thus allowing the missing initial conditions needed to specify the initial and terminal boundary-layer segments to be determined from partial equilibrium conditions. The dichotomic basis reveals the phase-space manifold structure in the neighbourhood of the optimal solution. The challenge is to determine a sufficiently accurate approximation to a dichotomic basis. In this paper we use an approximate dichotomic basis derived from local eigenvectors. An iterative scheme is proposed to handle the approximate nature of the basis. The method is illustrated on an example problem and its general applicability is assessed. Copyright © 1999 John Wiley & Sons, Ltd.

Comparing the welfare effects of income and excise taxes in the presence of the other taxation paradox

This paper implements numerically a general equilibrium model in which all private producers are price makers and the government utilizes tax revenues to provide a public good. After deriving the partial equilibrium condition for an excise tax to increase price by more than the tax (for a monopoly firm), numerical examples are given, demonstrating this phenomenon for both partial and general equilibrium. In the general equilibrium context, optimal excise taxation and optimal flat-rate income taxation are compared. In the excise tax regime, prices increase by more than the taxes. In the income tax regime, prices actually decline relative to the no-tax regime. In all of the examples given, flat-rate income taxation is superior to excise taxation in terms of welfare.

Mass transfer constraints on the chemical evolution of an active hydrothermal system, Valles caldera, New Mexico

Partial equilibrium conditions occur between fluids and secondary minerals in the Valles hydrothermal system, contained principally in the Tertiary rhyolitic Bandelier Tuff. The mass transfer processes are governed by reactive phase compositions, surface areas, water-rock ratios, reaction rates, and fluid residence times. Experimental dissolution of the vitric phase of the tuff was congruent with respect to Cl in the solid and produced reaction rates which obeyed a general Arrhenius release rate between 250 and 300°C. The 18O differences between reacted and unreacted rock and fluids, and mass balances calculations involving Cl in the glass phase, produced comparable water-rock ratios of unity, confirming the importance of irreversible reaction of the vitric tuff. A fluid residence time of approximately 2 × 10 3 years, determined from fluid reservoir volume and discharge rates, is less than 0.2% of the total age of the hydrothermal system and denotes a geochemically and isotopically open system. Mass transfer calculations generally replicated observed reservoir pH, P co2, and P O2 conditions, cation concentrations, and the secondary mineral assemblage between 250 and 300°C. The only extraneous component required to maintain observed calcite saturation and high P co2 pressures was carbon presumably derived from underlying Paleozoic limestones. Phase rule constraints indicate that Cl was the only incompatible aqueous component not controlled by mineral equilibrium. Concentrations of Cl in the reservoir directly reflect mass transport rates as evidenced by correlations between anomalously high Cl concentrations in the fluids and tuff in the Valles caldera relative to other hydrothermal systems in rhyolitic rocks.

Trade prices and supply in the UK economy

Current account imbalances are a major source of instability in the world monetary and trading system. Measures to correct these imbalances have largely involved adjustments to exchange rates. In the international trade literature, when the current account is in deficit, the Marshall-Lerner condition is sufficient for a successful devaluation. However, this partial equilibrium condition — apart from being based on the assumption that supply elasticities are infinite — abstracts from how the domestic economy responds to the change in relative prices. In this paper we develop a model of price and output determination in an open economy with imperpectly competitive markets, and draw a distinction between goods which are exported and those which are supplied to the domestic market. This means that we have to determine jointly both export prices and the domestic price of house sales. We show that as long as there is no money illusion in the labour market a fall in the nominal exchange rate raises domestic and export prices proportionally and leaves trade volumes unaffected. However, shifts in domestic absorption relative to overseas demand — by changing relative prices — cause shifts in the relative supply of exports and domestically sold goods and affect the trade balance. Thus fiscal and monetary measures directed towards reducing domestic absorption are more likely to be successful in correcting current account imbalances than exchange rate depreciation.

The chemical structure of premixed fuel-rich methane flames: the effect of hydrocarbon species in the secondary reaction zone

In a previous paper the analysis of a fuel-rich, ф =1.60, methane flame using a four-stage molecular beam inlet to a quadrupole mass spectrometer was described. The results were used to investigate the chemical structure of the primary reaction zone of the flame. In this paper, results from a richer flame, ф = 2.00, are presented and analysed. This premixed, laminar, flat flame had the following composition (all molar percentages) and conditions: 35.0% (CH 4 ), 35.0% (O 2 ), 30% (Ar); pressure = 8.00 kPa; cold-gas velocity at 293 K = 0.47 m s -1 . Mole fraction profiles through each flame were measured for a large number of stable and radical species, and those for the ф = 2.00 flame are presented in this paper and are compared with the results from the ф = 1.60 flame published earlier. Analysis and discussion in the present paper concentrates on the secondary reaction zone of both fuel-rich flames. Comparison of the profiles shows that hydrocarbon species survive the primary reaction zone in increasing concentrations as ф increases. It is shown that the reaction H + O 2 ⇌ OH + O (21, -21 ) does not achieve the partial equilibrium condition that is found in leaner flames, although the remaining bimolecular reactions of the H 2 -O 2 system do so. The competition between various species for the H, O and OH radicals is analysed using a convenient parameter which allows comparison of reaction rates and which has been called the 'characteristic reaction time’, r . It is concluded that the direct cause of the inability of (21, -21) to achieve partial equilibrium is the removal of O atoms from the available pool of H, O and OH radicals by reaction with hydrocarbon species, particularly C 2 H 2 . The rate of decrease of the H atom concentration in the secondary reaction zone is shown to be too fast to be the result of termolecular recombination reactions; it is suggested that the cause is the rapid response of the fast bimolecular reactions of the H 2 -O 2 system to the removal of O atoms via OH + H → O + H 2 , (-22) OH + OH → O + H 2 O (-23) thus reducing the concentrations of H and OH radicals. This mechanism explains the reduction in the excesses of the H, O and OH radicals above their thermodynamic equilibrium levels that is observed with increasing ф . It is concluded that it is possible to view a rich flame as consisting entirely of an extended primary reaction zone in which the concentrations of the H, O and OH radicals are controlled by bimolecular reactions throughout.

Redox‐controlled multiple‐species reactive chemical transport: 1. Model development

A redox‐controlled multiple‐species, multidimensional reactive chemical transport model, DYNAMIX, is developed. The model includes advection, diffusion‐dispersion, transport of oxygen, oxidation‐reduction and, as a consequence, acid‐base reactions, aqueous complexation, precipitation‐dissolution, and kinetic mineral dissolution. A partial equilibrium condition is incorporated into the model which accounts for both thermodynamic equilibrium and kinetic chemical interaction between aqueous and solid phases. The model solves for aqueous and mineral phase compositions as function of time and space. A correct mineral assemblage is automatically searched for based on the principle of minimized Gibbs free energy. The mass of chemicals is conserved in both aqueous and solid phases. A two‐step dynamic mixing algorithm is used to solve the coupled transport and reaction equations. At each time step, the transport equation is first solved by the explicit difference method. The chemical equilibrium submodel is then called to calculate the distribution of chemical species under thermodynamic partial equilibrium conditions. By splitting the transport and reaction equations, the two‐step method significantly reduces computational time and memory storage requirements, which allows DYNAMIX to efficiently handle two‐ or three‐dimensional problems.

Assessment of a partial-equilibrium/monte carlo model for turbulent syngas flames

Calculations and data for a turbulent jet flame of 40% CO, 30% H 2, and 30% N 2 in coflowing air are compared extensively. The calculations are based on a partial-equilibrium model for the oxyhydrogen radical pool including CO, and on a velocity-composition joint probability density function (pdf), which closes the turbulent flux and mean chemical source terms. The pdf is joint between the three velocity components and two thermochemical scalars needed to describe partial-equilibrium conditions. The equation is solved numerically by a Monte Carlo technique. The data used are major species concentrations and temperature from pulsed Raman scattering. Difficulties with Raman measurements at high temperatures and of measuring CO 2 directly are discussed. The Raman signals are taken from previous studies but here are corrected for high-temperature effects and CO 2 vibrational spectra. Temperatures are obtained from the instantaneous density of the major species rather than from the Stokes/anti-Stokes ratio, which is more affected by chemiluminescence. The level of agreement between the model and the data is more favorable to the partial-equilibrium model than previously thought. The relative simplicity of the partial-equilibrium model makes it a candidate for practical calculations.

Etude des eaux thermominérales carbogazeuses du Massif Central Français. I. Potentiel d'oxydo-réduction et comportement du fer

The thermomineral waters from Massif Central are iron rich waters of sodium bicarbonate type. The aim of this work is to provide more information about the geochemistry of iron, which is clearly related to the redox potential in this type of water. Thermodynamic calculations were used, and the distribution of iron was found to be controlled by the solubility of siderite. The oxidation potential that can be measured with calomel and platinum electrodes corresponds to an electrochemical equilibrium which involves a ferric hydroxide or oxyhydroxide. Finally E Pt values measured in the field are in good agreement with values predicted from the equilibrium between siderite and amorphous Fe(OH) 3, the association of which acts as a redox buffer. Dissolved oxygen is not in equilibrium with the ferrous-ferric couple and does not affect the measured potential. Even when of local theoretical significance as a thermodynamic variable, this redox potential represents only partial equilibrium conditions.

Analytical solution of leaf-shaped basin flow

ABSTRACT For a leaf-shaped basin geometry, the governing equations of flow are solved analytically by using the method of characteristics for prediction of the basin runoff. The flow model is based on kinematic wave theory and employs a diverging-converging model to represent the geometry of a leaf-shaped basin. Solutions are presented for both equilibrium and partial equilibrium conditions. In many solution domains explicit analytical solutions are obtained for constant rainfall excess. Considering two examples, the predictive potential of the proposed flow model is examined. The surface runoff hydrographs predicted by using the method of characteristics are compared with those of a finite difference method.

Water Routing on Diverging-Converging Watersheds

For a diverging-converging surface, the kinematic wave equations are solved using an implicit finite difference method. This diverging-converging representation is applicable to a natural watershed that has a leaf-shaped geometry. The results are compared with other idealistic representations. These are: plane surface, diverging surface, and converging surface. The diverging-converging model gives hydrograph values between those of converging and diverging models, depending on the geometric parameters. In general, the geometry of a watershed has important effects on the runoff hydrograph for both equilibrium and partial equilibrium conditions.

Transient oxygen atom yields in H2O2 ignition and the rate coefficient for O + H2 → OH + H

AbstractTime‐resolved measurements of the oxygen atom concentration during shock‐wave initiated combustion of low‐density (25 ≤ p ≤ 175 kPa) H2O2COCO2Ar mixtures have been made by monitoring CO + O → CO2 + hv (3 to 4 eV) emission intensity, calibrated against partial equilibrium conditions attained promptly at H2:O2 = 1. Significant transient excursions (“spikes”) of [O] above constant‐mole‐number partial‐equilibrium levels were found from 1400 to 2000°K for initial H2:O2 ratios of 16 and 10 and below ± 1780°K for H2:O2 = 6; they did not occur in this range for H2:O2 ± 4. Numerical treatment of the H2O2CO ignition mechanism for our conditions showed [O] to follow a steady‐state trajectory governed by large production and consumption rates from the reactions equation image with a pronounced maximum in the production term ka[H][O2]. The measured spike concentration data determine kb/ka = 3.6 ± 20%, independent of temperature over 1400 ≤ T ≤ 1900°K, which with well‐established ka data yields This result reinforces the higher of several recent combustion‐temperature determinations, and its correlation with results below 1000°K produces a distinctly concave upward Arrhenius plot which is closely matched by BEBO transition state calculations.