Mutual Equilibrium Research Articles

Absence of equilibrium among close-packed twisted flux tubest

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.

The sulfide capacities of CaO-SiO2 melts containing MgO, FeO, TiO2, and Al2O3

The sulfide capacities of CaO-SiO2 melts containing MgO, FeO, TiO2, and A12O3 have been measured by simultaneous equilibration within quartz capsules at 1776 K (1503 °C). The compositions of the melt samples and static gas phase within each capsule adjusted to establish a mutual equilibrium. The sulfide capacities, Cs, of all equilibrated samples must satisfy the following equation: $$C_{{\text{S(}}j{\text{)}}} = \frac{{{\text{pctS}}_j }}{{pctS_i }} \bullet C_{S(i)} $$ The inclusion of several reference slags for which values of Cs are known from previous measurements enabled the calculation of the sulfide capacities of unknown samples. The influences of basic oxide substitutions (FeO and MgO) for CaO and acidic oxide substitutions (TiO2 and A12O3) for SiO2 on the sulfide capacities of CaO-SiO2 melts have been measured. When a basic oxide/acidic oxide ratio of 1.21 is maintained, MgO additions decrease sulfide capacity, while FeO, TiO2 and A12O3 additions increase sulfide capacity. The results are compared with earlier measurements on the influences of CaF2 and B2O3, and the relative effects are discussed in terms of the activity of free oxide ions.

Summing Up On the Australian Case for Protection: Comment

In an article in this Journal Paul A. Samuelson [1981] supports my attempt to give belated recognition to Marion Samuelson's [1939] contribution to international trade theory. To avoid confusion, I suggest that the term, Australian Case for Protection (coined by Marion Samuelson), be replaced by the term SamuelsonSamuelson Theorem, since the argument expounded by her in that article had in fact little to do with that originally employed by the Australians. Paul Samuelson's revised evaluation of what is correct and incorrect in the original Australian argument is marred by his belief that only the Brigden Report of 1929 was embedded in pre-Ohlin orthodoxy, while Brigden's 1925 article and Copland's post-Report writings were inspired by some post-Ohlin insights. This attitude does less than justice to those who should be given credit where it is correctly due. Consider for a moment the significance of Ohlin's achievement. Ohlin [1933, p. 563] tells us that he was led to reexamine international economics from the mutual equilibrium (or market price) perspective because conventional theory was unable to explain currency price variations from purchasing parity during the immediate post-war period. The obvious explanation for this aberration, that exchange prices were determined by supply and demand factors, was logically inconsistent with classical theory, based as it was on the labor theory of value. The exchange problem in effect drove home the point that while the rest of economics had long ago abandoned labor value theory, international economics was still tied to it. Ohlin asked,

Love, the Couple, and the Group: A Psychoanalytic Frame

After a brief summary of previous work on the intrapsychic preconditions of love relations, this paper explores the built-in contradictions between the sexual couple and its social group, their mutual equilibrium, and the formation and dissolution of couples within the group. Clinical case material illustrates how three dimensions of love relations-namely, sexual experience, object relations, and superego integration-jointly determine a couple's stability within the social group. Finally, sexual psychopathology affecting the couple's interaction with its social group is explored in terms of some frequent pathological developments.

A photoacoustic study of the collisional deactivation of the first vibrational levels of CO 2 by N 2 and CO

The rate constant k′ 21 of the deactivation of the states (02 00, 10 00) I, (02 00, 10 00) II and (02 20), assumed in mutual equilibrium, towards (01 10) is measured between 170 and 300 K; the rate constant k′ bs which characterizes the deactivation of all symmetric-stretching and bending levels is measured from 170 to 370 K.

Determination of sulfide capacities of CaO-SiO2 slags containing CaF2 and B2O3 by an encapsulation method

The sulfide capacities of CaO-SiO2 melts containing CaF2 and B2O3 have been measured by simultaneous equilibration of samples within quartz capsules at 1503°C. In this method, the compositions of both the condensed phases and the static gas environment adjust to es-tablish a mutual equilibrium. Although the sulfurizing potential,PS2/PO2, is neither preset nor directly measured, the sulfide capacities,Cs, of all samples within the capsule are related by the following equation:CS(j)=(pct S)j/(pct S)i · CS(i)· Hence, the sulfide capacities of all samples may be calculated from the measurement of the final sulfur content of each sample and the inclusion of a “reference” slag sample for which CS is known from previous measurements. In the present study, quartz capsules containing as many as fifty slag samples including several reference samples have been equilibrated. With considerable difficulty the encapsulation-equilibration method atl503°C has been developed into an acceptable procedure. The influences of CaF2 and B2O3 on the sulfide capacities of several CaO-SiO2 melts have been measured. The results may be summarized as follows: 1) for melts of fixed CaO/SiO2 ratio, the addition of CaF2 increases sulfide capacity and the addition of B2O3 decreases sulfide capacity, 2) the substitution of CaF2 for CaO does not alter sulfide capacity significantly, and 3) the substitution of B2O3 for SiO2 increases sulfide capacity slightly. These results have been obtained for melts with CaO/SiO2 mass ratios ranging from 1.00 to 1.28 and with flux additions up to 10 wt pct.

Effect of small additions of a third component on the eutectic and peritectic temperatures of binary systems

The effect of additions of a third component on the temperature and composition of the eutectic or peritectic point of a binary system, at infinite dilution of this component, has been derived analytically. The depression of the eutectic temperature and the raising of the peritectic temperature are found to have an upper limit that no ternary element can exceed. The determination of the effect of a given solute on a eutectic or peritectic temperature hinges on the values of the activity coefficients of that solute at infinite dilution in the three phases in mutual equilibrium. In the absence of these data, various estimation methods can be used. Several of these methods have been illustrated in detail through the study of the effects of Sn, Zn and Au on the Ag-Cu eutectic temperature, and of the effects of Si on the peritectic and eutectoid temperatures of the Fe-C system. At least on a semiquantitative basis, the results are in very satisfactory agreement with data in the literature.

Rat-liver cell compartition as revealed by correlations between redox-quotient changes following alloxan treatment, starvation, carbohydrate- and fat-diet.

As reported elsewhere (FERAUDI, 1976a & b), we have studied the mathematical relations between metabolite concentrations in the rat liver at various redox states and expressed them algebraically. In the present work we have measured the liver-cell concentrations of lactate, pyruvate, glycerol 3-phosphate, dihydroxyacetone phosphate, malate, oxaloacetate, beta-hydroxybutyrate, acetoacetate, 2-oxoglutarate, ribulose 5-phosphate as pentose phosphates, gluconate 6-phosphate, isocitrate, aspartate in untreated and treated rats (alloxan-diabetic, insulin-treated alloxan-diabetic or starved rats as well as rats fed on carbohydrate- or fat diet). Through analysis of the algebraic correlation between metabolite concentrations, we arrived at the following statements: 1. Under certain physiological conditions the concentration of some metabolites in one compartment determines their total quantity in the cell; 2. NADP and NADPH are comparted within the cytosol; 3. Reduced cosubstrate/oxidized cosubstrate ratios of some enzymic reactions are under certain physiological conditions in mutual equilibrium; 4. Such relationships are first verified after treatment and therefore characterize the metabolite status.

Economic equilibrium in the Westland: An experimental analysis

The conditions prescribed in economic theory for “equilibrium” in an industry are “normal” earnings for those engaged. That best-known area of intensive horticulture, the Westland in South Holland, reached approximate economic equilibrium in 1971. Not all the constituent sectors of the industry were in mutual equilibrium, and to remain in overall equilibrium few additional resources will be permissible, although output must continue to increase relative to input. In the past such normal earnings are believed to have stimulated producers to further, unjustified expansion. Under current conditions Westland producers will be spared the consequences of unjustified response, because they will need to concentrate upon avoiding the trap of excess capacity. The purchasing power of their most important crop, tomatoes, being now seriously and progressively reduced, rationalization of production under glass is necessary and this is a difficult enough exercise in itself.

“Equilibrium” bubbles in the presence of applied stress and point-defect supersaturations

Spherical bubbles containing a fixed number of insoluble gas molecules n in an isothermal solid can come to equilibrium, provided the total applied stress σ t , is less than a critical tensile stress σ cr , and the relation (2γ ρ) + σ b(ρ) − σ t = 0 is satisfied. Here γ is the specific surface free energy, ρ is the bubble radius, and σ b is the negative of the gas pressure. For σ t < σ cr , the equilibrium values of ρ are among solutions to the above equation. If σ b ( ρ) has an inflection point in its σ b -gas density isotherm, then it is possible to have two equilibrium values of ρ for fixed n and temperature. The stress σ t is comprised of the applied mechanical stress σ H and a chemical stress σ chem that is induced and completely determined by vacancy supersaturations (undersaturations). When vacancies and interstitials are not in mutual equilibrium, a bubble may reach a size that is time invariant if the steady-state flux of vacancies to the bubble (causing expansion) is equal to the steady-state flux of interstitials to the bubble (causing contraction). Here an effective stress σ k- chem arises as a result of the opposite effects of vacancy and interstitial fluxes on the bubble size and replaces σ chem in the above equation.

Vibrational Relaxation of the Bending Mode of Shock-Heated CO2 by Laser-Absorption Measurements

The vibrational relaxation characteristics of shock-heated CO2 have been studied using a tuned CO2 laser absorption technique. Absorption-coefficient histories were obtained for a single rotational state in each of the 10°0 and 02°0 levels over the temperature range from 500 to 2000°K, and for 21 rotational states of the 10°0 level at 1000°K. These histories have been combined with translational-rotational temperature histories based on interferometer measurements to calculate vibrational relaxation times for the bending mode. The results verify the mutual equilibrium of the bending and symmetric-stretch modes due to Fermi resonance. The bending mode relaxation times are approximately 10% shorter than predicted from interferometer results using the ratio of specific heats. Furthermore, relaxation times based on measurements of different rotational states at 1000°K show a variation with quantum number J, indicating a possible rotational nonequilibrium during the vibration relaxation process.

Configurations d'équilibre pour l'orientation mutuelle d'un couple de molécules linéaires

A numerical study of the more stable mutual orientational equilibrium of a pair of linear molecules is deduced, based on a knowledge of the analytical expression for and the magnitude of the intermolecular potential. Numerical applications are presented for different pairs of molecules such as N 2, CO 2, rare gases and hydracids, and may be helpful in the interpretation of the shapes of the corresponding infrared spectra.

MUTUALSOLUBILITY AND EQUILIBRIUM DATA FOR TERNARY SYSTEMS

The mutual solubility and equilibrium data for the ternary liquid-liquid systems ; 1) ethanol-water-o-xylene ; II) ethanol-water-m-xylene ; III) ethanol-water-p-xylene ; IV) ethanolwater-o-chlorotoluene ; V) ethanol-water-m-chlorotoluene ; VI) ethanol-water-p-chlorotoluene, are determined at 25°C. The mutual solubility data are correlated by plotting XA/(1-XC)against log XC and the equilibrium data are correlated by the methods*of Bachman.Through these plots it becomes clear that the mutual solubility and equilibrium of ternary liquid-liquid systems are not affected by choice of ortho, meta or para isomers.

Vapour-liquid equilibrium and excess free energies for benzene + dioxan and carbon tetrachloride + dioxan systems

This paper deals with the isothermal total vapour pressure measurements on the systems benzene + dioxan and carbon tetrachloride + dioxan in the temperature range of 22–40°C and over the whole composition range. The activity coefficients and the excess Gibbs free energies are evaluated at 25, 30 and 40°C. For both the systems the excess entropies are negative, suggesting an ordering in the solution due to a solute-solvent specific interaction. The excess free energies of complexing are calculated on the basis of an ideal associated solution model with species A, B, AB and AB2 in mutual equilibrium and using for reference, the excess free energies of the system cyclohexane + dioxan. The calculated excess free energies agree with the observed results.

A Gas-Dynamic Model for Coupled Vibrational and Radiative Nonequilibrium in CO2—with Application to the Spectrophone

Macroscopic equations are formulated for the nonequilibrium interaction of vibrational and radiative rate processes in CO2. A model for CO2 is used that assumes that the energy levels of each vibrational mode are evenly spaced and that each mode can be assigned a vibrational temperature. The bending and symmetric-stretching modes are, however, taken to be in mutual equilibrium so that they have the same vibrational temperature. Collisional rate equations for the V—T and V—V processes are derived on a phenomenological basis. The resulting phenomenological coefficients are interpreted, with the help of basic knowledge of the microscopic physics, in terms of characteristic relaxation times and parameters measuring the relative amounts of energy exchanged by the various modes during V—V transitions. Radiative transfer equations are developed for the three strongest infrared bands, located in the spectrum at 15, 4.3, and 2.7 μ, by appropriately summing a previously derived microscopic transfer equation. It is found that the absorption coefficient is a function of the kinetic and the vibrational temperatures in a manner that depends on the band in question. The source function, which is also different for each band, depends strongly on the temperature of the vibrational modes involved in the transition and weakly on the kinetic temperature. The rate and transfer equations are then incorporated with the conservation equations of gas dynamics for application to linearized nonequilibrium flows of carbon dioxide gas. As a particularly simple example, a solution for the spectrophone is presented, including expressions for the phase lag in the pressure signal that results from radiative excitation via each of the bands individually. One of these expressions can be used in conjunction with experimental results from other sources to draw conclusions about predominant V—V transitions in CO2. The results of doing this using the 4.3-μ band have been reported previously. The utility of a spectrophone can also be extended by exploiting the possibility of selectively exciting CO2 through the different bands and making use of all the phase-lag expressions. All equations were derived without restriction to room temperature, allowing for possible use of spectrophones at higher temperatures. The approach used to derive the macroscopic rate equations can equally well be applied to other polyatomic molecules.

Electron Microscopic Evidence of Authigcnic Clay Minerals in the Gulf of Mexico

Authigenic mineral formation is one consequence of the geochemlcal model of a steady-state ocean-atmosphere. Many examples of authigenic clay minerals might be expected, however the distinction between authigenic and detritial clay minerals is not well defined. It is extremely difficult in most cases to distinguish between the two while running a standard mineraloglcal analysis. Consequently the formation or reconstitutlon of clay minerals in the world oceans has remained a matter of much consideration.Weaver points out that many of the clay minerals occuring in recent marine environments which are identified as being definitely authigenic are Fe-rich. These include glauconlte, nontronite, chamosite, montmorillonite and chlorite. The majority of these have been found in the Pacific Ocean with montmorillonite being the most abundant. Norin reported authigenic illitic mica in coarse-grained sediments from the Tyrrhenian Sea. Garrels has compiled a phase diagram which indicates that under the conditions normally found in seawater, kaolinite and K-mica can exist in mutual equilibrium growing from a solution derived from K-feldspar and quartz.

Concerning the so-called "isohydric point"

Evaluation of the formation function [Formula: see text] for a system of monomeric and polymeric (condensed) acids in mutual equilibrium can account for the appearance of a network of formation curves with a crossover point at a fixed value of the coordinates [Formula: see text], pH. The value of [Formula: see text] at this isohydric point is equal to 1 − z/n, where n is the degree of condensation and z the basicity of the condensed acid. A third formation curve is unlikely to pass through the same isohydric coordinates, so that the system is very probably restricted to two predominant species in equilibrium. These conclusions confirm the work of Carpéni and collaborators, but appear to have been derived in a different way.

On the relation between electrical conductivity and phase transition of non-stoichiometric cuprous selenides

The electrical conductivity of non-stoichiometric cuprous selenide samples having various compositions was examined. Measurements were performed over the temperature interval where the phase transformation appears. Conductivity variations are explained considering non-stoichiometric cuprous selenide as the binary system (Cu 2Se+ Se), in which alpha and beta phases in mutual equilibrium have different compositions, i.e. different concentrations of holes. The equations derived on the basis of an equilibrium process of phase transition describe the experimental curves with satisfactory agreement. Further consequences of such an approach to non-stoichiometric compounds are also discussed.

Modern Evaporite Deposition and Geochemistry of Coexisting Brines, the Sabkha, Trucial Coast, Arabian Gulf

ABSTRACT Near Abu Dhabi, Trucial Coast, diagenetic evaporite minerals are developed within an accumulation of detrital Pleistocene sands and Recent carbonate sediments which form a supratidal flat (sabkha) 8 miles wide. Field studies were carried out by the author and his co-workers of Imperial College in 1964. A further visit to the Trucial Coast was made by the author in 1967 under the auspices of the Dry Lands Research Institute, Riverside. A study of 260 interstitial brine samples showed that the distribution of the evaporite minerals, which include gypsum, anhydrite, dolomite, and balite, is largely controlled by the hydrology of the area. Interstitial brines within the sabkha sediments are replenished with sea water by abnormally high tides and storm surges. These surface waters, which soak down into the sediments, are concentrated both by solution of soluble salts and by evaporation. The subsequent equilibration between brines and host sediments leads to precipitation of aragonite, gypsum, and halite; alteration of gypsum to anhydrite, and dolomitization of carbonate sediment. A direct correlation exists between the frequency and extent of flooding, the mineral phases developed, and the chemical composition of interstitial brines. Flooding of a 2- to 3-mile wide belt roughly concentric to lagoon margins, occurs at monthly or longer intervals. In this belt, a surface gypsum crystal mush up to 12 inches thick is present which, landwards, is overlain and progressively replaced by anhydrite. Dolomitization is extensive toward the landward margin of this zone. From the lagoon laterally across the 2- to 3-mile wide belt to its landward margin, chlorinity increases from 44 to 155; sulfate concentration rises from 6 to 17 gm/kg and then falls to less than 3 gm/kg; the Mga2+/Ca2+ mole ratio increases from 5.3 to 35 and then decreases to about 4. Concentration of these components decreases with in reasing depth below the sediment surface. Gypsum is the stable calcium sulfate mineral in contact with brines of chlorinities less than 145 and anhydrite at chlorinities greater than 145. An additional 5-mile wide zone is flooded only at 4- to 5-year intervals. The original gypsum crystal mush in this zone is completely replaced by up to a 12-inch thick layer of chicken-wire mesh structure anhydrite, and the carbonates are highly dolomitized. Interstitial brines are Saturated with NaCl at chlorinity 160 and specific gravity 1.20. These brines contain less than 1 gm/kg sulfate and have Mg2+/Ca2+ mole ratios of about 4. In this zone, constant Mg2+/Ca2+ values with increasing magnesium concentration suggest that there has been an approach to mutual equilibrium between brines and evaporite-carbonate minerals. The remaining 1 to 2 miles at the landward margin of the sabkha are underlain by Pleistocene sands and are not flooded by marine waters. Ground waters in this zone are in part terrestrial in origin. Inland across this zone, chlorinity decreases from 160 to 107; the sulfate concentration is 2 gm/kg and the Mg2+/Ca2+ mole ratio averages 3.5. Locally, anhydrite is hydrated to gypsum where brine chlorinity is less than 145. Processes of gypsum precipitation and dolomitization are essentially restricted to the 2- to 3-mile wide belt close to the lagoon margin. In the mid-sabkha, equilibrium conditions probably prevail between brines, diagenetic minerals, and host sediments. Diagenesis at the landward margin of the sabkha is in part retrogressive. Both a progressive and a retrogressive diagenetic facies can be visualized as moving out with the progradation of the shore line. The similarity between the stratigraphy and mineralogy of some Ordovician, Silurian, Pennsylvanian, and Jurassic evaporite sequences and the sabkha on the Trucial Coast suggest that evaporites of supratidal origin may be more common in older evaporite rocks than previously realized.

Application of the Theory of Regular Solutions to Binary Phase Equilibria. I. Method of Application to Binary Liquid Equilibria

Abstract The same expression for the correlation of compositions in mutual equilibrium of two liquid phases as that which is immediately obtained from the empirical relations used by Cox and Herington was derived thermodynamically. The method has been given in such a manner as to represent the solubility curve for a binary liquid system symmetrically and to estimate the interchange energy from the mutual solubility data by applying the theory of regular solutions.