Simultaneous Equilibria Research Articles

Towards Proof-of-Work Cryptocurrency Valuation: Mining Games, Network Effects and the Social Value of Blockchain

In this study, a mathematical model of proof-of-work cryptocurrency valuation is developed based on the concepts of simultaneous equilibria in two mining games, the purchasing power parity in the system of equations of exchange and the network effects of transaction cost optimisation in the economy where agents utilise both conventional and digital currencies to process payments. The model lays the foundation for rigorous long-term proof-of-work cryptocurrency valuation superior to existing approaches that are solely based on variations of Metcalfe’s law or costs of mining. Based on the model, the long-term Bitcoin equilibrium price conditional on current block size limit is $106, while if the block size limit is abandoned, the conditional equilibrium price is $6725. Network hashrate is consistent with the no-limit scenario, while the transaction fees are consistent with the status quo, revealing an important source of uncertainty on the market. The developed framework is also applied to the measure the net social value of proof-of-work cryptocurrencies, and Bitcoin long-term social value of equilibrium is shown to be positive at $126,200 per block. The comparison of equilibrium and optimal cases shows that external intervention is not necessary to guarantee socially beneficial outcomes.

A dual-indicator strategy for controlling the response of ionophore-based optical nanosensors

Optical nanosensors are used to detect a wide range of ions and molecules by changing their fluorescent properties in response to the local analyte concentration. Practical methods to adjust the sensor response characteristics of optical nanosensors are needed to match the sensor dynamic range with the expected analyte fluctuation for a given application. For ionophore-based optical sensors, the linear range is determined by three simultaneous equilibria, including the acid dissociation of a pH indicator. In this work, we add a second pH indicator to typical ionophore-based optical sensor formulations. We show that pH indicator acid-dissociation is fundamentally different when two indicators are loaded within the same nanoparticle, effectively coupling their equilibria, as opposed to being housed in separate sensor nanoparticles in a mixture that simultaneously interact with the sample. We demonstrate that these two methods of dual-indicator sensor design give control over the response range of ionophore-based optical sensors and can extend the linear range span over what is possible with a single-indicator nanosensor.

Heterogeneous reactive extraction for isopropyl alcohol liquid phase synthesis: Microkinetics and equilibria

The reaction kinetics for the liquid phase synthesis of isopropyl alcohol (IPA) from propene (P) and water (W) using a macroporous sulfonic acid ion exchange resin as catalyst were determined experimentally in a multiphase CSTR in the temperature range 398K to 433K at 8MPa. This high pressure is necessary to dissolve propene in the aqueous phase and to ensure a liquid or supercritical state of all components. At typical reaction conditions, the reactants form two immiscible phases; the reaction takes place in the water swollen gel phase of the catalysts microspheres. Due to the large excess of water in the gel phase the compositions in the gel phase, in the macropore fluid, and in the catalyst surrounding aqueous phase are assumed to be identical. For temperatures up to 413K the reaction kinetics for the used catalyst size are not influenced by mass transfer resistances within the catalyst matrix. Two reactions, the formation of IPA and the condensation reaction of two IPA molecules forming the by-product diisopropyl ether (DIPE), are investigated. The experimental results can be described sufficiently by pseudo-homogeneous rate expressions in aqueous phase activities. For the formation of IPA, the forward reaction is first-order in propene and water while the reverse reaction is first-order in IPA. The activation energy of the forward reaction was determined to 115.3kJ/mol. The formation of DIPE is second order with respect to the activity of IPA. The reverse reaction is first order with respect to the activities of DIPE and water. The activation energy was determined to 85.6kJ/mol. Simultaneous chemical and phase equilibria were investigated theoretically using the volume translated Peng-Robinson equation of state (VTPR-EoS) in combination with a gE-mixing rule. Parameters of the used gE-model were adjusted to experimental liquid-liquid equilibrium (LLE) data.

Approaching the geochemical complexity of As(V)-contaminated systems through thermodynamic modeling

Arsenate mobility in oxic environments is largely controlled by its adsorption to iron (hydr)oxides, but precipitation as heavy metal arsenates represents a potentially significant competing mechanism. Predicting As geochemical behavior in heterogeneous contaminated systems where various simultaneous equilibria are taking place may be achieved in a thermodynamically sound manner by coupling adsorption and solid-aqueous equilibria, provided that accurate equilibrium constants are employed; especially challenging is the surface complexation model segment.The influence of adsorption and precipitation processes on As(V) mobility was modeled in the presence of Pb(II) and goethite by varying the As/Fe and As/Pb ratios, the goethite particle size, pH, and the inclusion of chloride and sulfate ions. A bottom-up approach is adopted here to gradually approximate the geochemical complexity of real contaminated scenarios. A unified surface complexation model for goethites of different particle sizes was used, which accounts for differences in their reactivity, and was coupled with a thermodynamic speciation model for aqueous and solid-phase equilibria.The geochemical conditions found that favor As(V) precipitation as Pb(II) arsenates were high As/Fe, low As/Pb, goethites of small particle size, and especially the presence of chloride, and low sulfate concentrations (at low pH). The opposite conditions favor As(V) adsorption. Surprisingly, precipitation processes are more prevalent than expected and are favored from relatively low As/Fe in the presence of chloride, or with small particle-sized goethites.

Pairwise binding competition experiments for sorting hub-protein/effector interaction hierarchy and simultaneous equilibria.

NMR experiments on proteins in simultaneous equilibria with multiple binding partners can provide a tool to understand complex biological interaction networks. Competition among proteins for binding to signaling hubs is often at the basis of the information transmission across signaling networks in every organism. Changes in affinity towards one or more partners, as well as changes of the relative concentration of the competing partners, can determine pathways alterations that lead to pathological consequences. Overall, the knowledge of the interaction hierarchy of the multiple partners to a single signaling hub can lead to new therapeutic strategies. Smith and Ikura (Nat Chem Biol 10:223–230, 2014) have recently proposed pairwise competition NMR experiments to determine the binding hierarchy in network interactions. We have taken the moves from their approach to show how from pairwise competition NMR experiments the ratios between the equilibrium constants for multiple binding partners can be determined, and thus, given their concentration in solution, the concentrations of all the possible complexes can be obtained.

Chemical equilibrium in a heterogeneous fluid phase system: thermodynamic regularities and topology of phase diagrams

Singularities of the systems with simultaneous phase and chemical equilibria were examined. The thermodynamic regularities were revealed and topology of phase diagrams was presented for multicomponent heterogeneous systems including two or several equilibrium liquid phases (solution layering). The thermodynamic conditions for displacement of phase and chemical equilibrium are considered.

Human Capital and the Quality of Education in a Poverty Trap Model

This paper presents a model of a poverty trap that is caused by an unequal initial income and human capital distribution and differences in the quality of education between children from more and less advantaged social sectors. Under certain conditions, the economy converges to a situation with three stable and simultaneous equilibria, two of which constitute poverty traps, lowering the economy's current and steady-state aggregate output level as well as its growth rate. The model suggests that a policy oriented towards equalizing the quality of education would, in the long run, have the potential to reduce initial inequalities.

Heterogeneous reactive extraction for secondary butyl alcohol liquid phase synthesis: Microkinetics and equilibria

The reaction kinetics for the liquid phase synthesis of a racemic mixture of the secondary butyl alcohols (SBA) from linear butene isomers (1-butene (1B); cis-2-butene ( c2B); trans-2-butene ( t2B)) and water (W) using a macroporous sulfonic acid ion exchange resin as catalyst were determined experimentally in a multiphase CSTR in the temperature range 39–433 K at 6–8 MPa. This range of pressures is necessary to dissolve butenes in the aqueous phase and to ensure a liquid state of all components. For temperatures higher than 423 K the reaction kinetics for the used catalyst size are influenced by mass transfer resistances within the catalyst matrix. The reaction takes place in the water swollen gel phase of the catalysts microspheres. Due to the large excess of water in the gel phase the compositions in the gel phase, in the macropore fluid, and in the catalyst surrounding aqueous phase are assumed to be identical. According to the literature the reaction is rather catalyzed by hydrated acid protons ( specific catalysis) than by polymer-bonded-SO 3H groups ( general catalysis). The experimental results can therefore be described sufficiently by a pseudo-homogeneous 3-parameter rate expression in aqueous phase activities. The forward reaction is first-order in butene. The reverse reaction is first-order in secondary butyl alcohol. The activation energy was determined to be 108 kJ/mol. Practically no pressure dependence could be observed for pressures exceeding 6 MPa. The ever-present isomerization of the linear butenes on acid catalysts was found to be remarkably faster than the hydration of butenes to SBA. Therefore, the isomerization is considered to be always in equilibrium during the olefin hydration. The formation of the possible by-product di- sec-butyl ether (DSBE) was never observed to a measurable extent. Simultaneous chemical and phase equilibria were investigated theoretically using the volume translated Peng–Robinson equation of state (VTPR-EoS) in combination with a g E -mixing rule. Parameters of the used g E -model were adjusted to experimental ternary liquid–liquid equilibrium (LLE) data.

Hydration of Cellulose/Silica Hybrids Assessed by Sorption Isotherms

The hydration of cellulose/silica hybrids (CSH) containing 13, 35, and 46% (w/w) silica synthesized in situ by a mild sol-gel aqueous process was studied employing sorption isotherms and surface energy measurements. Water sorption is governed by two simultaneous equilibria at the silica-vapor and cellulose-vapor interfaces due to the presence of cellulose regions covered and uncovered with silica as confirmed by X-ray scattering analysis. The important contribution of a water impermeable cellulose-silica interface to the surface properties of CSH is highlighted. CSH exhibit type II isotherms in the temperature range 15-40 degrees C, more appropriately described by the Guggenheim-Anderson-de Boer (GAB) model than by the Brunauer-Emmett-Teller (BET) model. Specific surface areas calculated using both models (S(BET) and S(GAB)) increase linearly with the amount of silica influencing the higher moisture content of CSH for the same water activity. However, the presence of silica reduces the strength of interaction between monolayer water molecules and the CSH surface as revealed by the net isosteric heat of sorption (35 kJ/mol for cellulosic pulp and 26 kJ/mol for CSH with 35% silica). Silica confers a higher surface energy to CSH contributing to its polar component and surface wettability (contact angle with water) when compared to cellulosic pulp. The average diameter of cellulose microfibrils and the interfacial cellulose-silica areas are assessed on the basis of the analysis of sorption isotherms.

The complexation of aqueous metal ions relevant to biological applications: 2. Evaluation of simultaneous equilibria of poorly soluble zinc salts with select amino acids

Simultaneous equilibria calculations were completed for seven aqueous zinc-ligand systems: zinc citrate plus either glycine, alanine, or serine, and zinc succinate plus either glycine, alanine, or serine, and zinc oxalate plus glycine. Mixed-ligand complexes were predicted for all but the zinc citrate-glycine system, and the proportion tends to peak around 5 molar equivalents of amino acid. Potential bioavailability of zinc appears to be increased by the inclusion of amino acids in solution, roughly in parallel with the increase in solubility of the zinc salt. Therefore, measurement of the change in solubility caused by addition of amino acids to aqueous solution gives qualitative insight to the potential increase in bioavailability of the metal ion, and mixed-ligand complexes are a significant proportion of the complexes present in solution.

The complexation of aqueous metal ions relevant to biological applications. 2. Reactions of copper(II) citrate and copper(II) succinate with selected amino acids

Addition of amino acids, glycine, alanine, and serine, to poorly soluble copper(II) salts [copper(II) citrate and copper(II) succinate] all increase solubility of the copper(II) salts. Relative increases in solubility follow the polarity trend in the selected amino acids, with serine creating the greatest increase in solubility. Simultaneous equilibria calculations indicate the formation of mixed-ligand complexes in the copper(II) succinate–amino acid systems, the first time such mixed-ligand complexes have been observed. In contrast, mixed-ligand complexes are not predicted in the copper(II) citrate–amino acid systems. Potential bioavailability of copper(II) appears to be increased by the inclusion of amino acids in solution, roughly in parallel with the increase in solubility of the copper(II) salt. Therefore, measurement of the change in solubility caused by addition of amino acids to aqueous solution gives qualitative insight to the potential increase in bioavailability of the metal ion.

Drug–Excipient Complexation in Lipid Based Delivery Systems: An Investigation of the Tipranavir-1,3-Dioctanolyglycerol Complex

This report describes the solubility properties of a poorly soluble drug–excipient complex in a lipid based formulation. Tipranavir (TPV) was used as the model drug and 1,3-dioctanoylglycerol (DOG) as the excipient. The TPV–DOG complex was prepared by dissolving TPV and DOG in ethanol at 60°C followed by evaporation of ethanol. The formation of the complex with a 4:1 TPV-to-DOG molar ratio was confirmed by XRPD, DSC, and NMR. At 25°C, total solubility of TPV decreased with increasing DOG concentration. The solubility properties of the TPV–DOG complex can be described by two simultaneous equilibria: a liquid–solid phase equilibrium of the complex and a species equilibrium among the various species in the liquid phase. A model equation was derived accordingly with two parameters, the intrinsic solubility of the complex (So), and the solution complex constant (K41). The model was in good agreement with experimental results. The values of So and K41 are 0.0186±0.0025 (M) and 21.97±7.19 (1/M4), respectively. The equation can successfully predict the concentrations of total and free TPV as a function of DOG in the formulation. The approach developed provides a useful tool for rationale selection of excipients and their levels to avoid drug precipitation in lipid based formulations.

Soft‐modeling based spectrofluorimetric study of simultaneous equilibria

A two-way soft resolution method will fail when applied to a simultaneous equilibria system due to rank deficiency in its concentration profiles. Increasing the dimensionality of measurements from two-way to three-way data can be used to overcome this problem. Simultaneous dissociation of two weak acids is considered as a model for simultaneous equilibria. Three-way data obtained from excitation-emission spectrofluorimetric monitoring of a pH-metric titration is analyzed using a proper combination of well-known soft-modeling methods. Multivariate curve resolution-alternating least squares is used for calculating the excitation and emission spectral profiles of involved species and rank annihilation factor analysis for obtaining the contribution of each species in measured excitation-emission matrices at different pHs. The results of simulated and real simultaneous acids dissociation equilibria showed that the proposed combined method performs well even in situation when the equilibrium constants are close to each other. The applicability of method for study of an acidic dissociation is also shown.

Human Capital and the Quality of Education in a Poverty Trap Model

This paper presents a model of a poverty trap that is caused by an unequal initial income and human capital distribution, and differences in the quality of education between children from the more and less advantaged social sectors. Under certain conditions, the economy converges to a situation with three stable and simultaneous equilibria, two of which constitute poverty traps, lowering the economy’s current and steady-state aggregate output level as well as its growth rate. The model suggests that a policy oriented to equalizing the quality of education would, in the long run, have potential in reducing initial inequalities.

Modeling of the solubilities of NiO/NiAl2O4 and FeO/FeAl2O4 in cryolite melts at 1300 K

Experiments to measure the solubilities of NiO/NiAl2O4 and FeO/FeAl2O4 were performed, and the results confirmed existing literature values. The solubilities of NiAl2O4 and FeAl2O4 in Al2O3-saturated cryolite melts at 1300 K were modeled thermodynamically in terms of the Ni-containing complexes Na2NiF4 and Na4NiF6, and the Fe-containing solutes FeF2, Na2FeF4, and Na4FeF6. The experimental solubility data were fitted to multiple simultaneous equilibria. Equilibrium constants and ΔGf0 values for the formation reactions of the these solutes were thereby estimated. The solubilities of NiO/NiAl2O4 and FeO/FeAl2O4 and solute distributions in Al2O3-undersaturated cryolite melts were calculated for a number of melt compositions from the present model. The existence of several competitive solute species is inherent to highly buffered ionic cryolite solutions where the traditional log-log methodology had previously failed to identify dominant single solutes. In such solutions, individual solutes of oxides are not likely to dominate over a wide composition range so that a more global modeling is required. The principal solute species identified in the present study exhibit reasonable three-dimensional (3-D) anion geometries.

Origin of non-Nernstian anion response slopes of metalloporphyrin-based liquid/polymer membrane electrodes.

The origin of the non-Nernstian potentiometric anion response behavior exhibited by several metalloporphyrin-based liquid/polymeric membrane electrodes is examined. UV-visible spectrophotometry of organic-phase solutions and thin plasticized PVC films containing In(III) and Ga(III) octaethylporphyrins suggests that, in the absence of preferred axial coordination anions, the metalloporphyrins form hydroxide ion bridged dimers within the organic phases, as indicated by a significant blue shift of the Soret band in the visible spectrum. As increasing levels of the preferred anions are added, the degree of dimerization decreases and the intensity of the Soret band corresponding to the monomer species increases. Observation of Nernstian responses with membranes doped with picket fence-type In(III) and Ga(III) porphyrins not capable of forming hydroxide bridged structures (as determined by UV-visible spectroscopy) confirms that dimerization is likely responsible for the super-Nernstian slopes of membrane electrodes formulated with the non-picket fence species. A phase boundary model based on simultaneous binding equilibria of hydroxide ions with two metalloporphyrins to form the dimeric species, while the target anions bind with metalloporphyrins to form neutral 1:1 complexes, is shown to fully predict the observed non-Nernstian behavior. The prospect of utilizing this anion-dependent dimer-monomer metalloporphyrin equilibrium to fabricate anion-selective optical sensors using thin films of metalloporphyrin-doped polymers is also discussed.

Simultaneous Chemical and Phase Equilibria for Mixtures of Acetic Acid, Amyl Alcohol, Amyl Acetate, and Water

Phase compositions of simultaneous chemical and phase equilibria are measured with a static apparatus for the multicomponent system of acetic acid, amyl alcohol, amyl acetate, and water at temperatures from 373.15 to 393.15 K. Various molar ratios of acetic acid to amyl alcohol of feed, ranging from 1:3 to 3:1, are employed in the experiments. An acidic cation-exchange resin, Amberlyst 39, is used to promote the esterification. In addition, vapor−liquid equilibrium data are also determined for the binary mixtures of acetic acid + amyl alcohol at 333.15 K and acetic acid + amyl acetate at 353.15−393.15 K. These new binary data are applied to determine the binary parameters of the NRTL model for the corresponding systems that are needed for prediction of the multicomponent systems. By accounting the dimerization of acetic acid in the vapor phase, the reliability of the binary parameters obtained from different types of equilibrium data is evaluated by comparing the results of equilibrium calculations with the experimental phase compositions of the esterification system.

Substituent effects on the thioamide group in thiobenzanilides: simultaneous conformational and acid-base equilibria

Substituent effects on the thioamide group in thiobenzanilides: simultaneous conformational and acid-base equilibria

Endogenous timing and the choice of quality in a vertically differentiated duopoly

The endogenous choice of timing is discussed in a vertically differentiated duopoly where quality improvement requires a fixed convex cost. The timing decision concerns the quality stage. Using an extended game with observable delay, it is shown that only simultaneous equilibria can arise. This puts into question the ability of Stackelberg games to describe the entry process.

The reactivity of chlorine atoms in aqueous solution Part II.The equilibrium SO4-+Cl-ClNsbd+SO42-

A study of the two simultaneous equilibria, reactions (1) and (2), has been performed by pulse radiolysis in Ar-saturated aqueous solution at 25°C. The forward and reverse rate constants of equilibrium (2) were determined at 0.3 mol dm-3 ionic strength to be k2=(6.1±0.2)×108 and k-2=(2.1±0.1)×108 d mol-1 s-1. These yield the equilibrium constant K2=k2/k-2=(2.9±0.2) at 0.3 mol dm-3 ionic strength, or 1.2 corrected to zero ionic strength. As part of the study, the reactions of SO4- with S2O82-, t-BuOH and water were found to be <1.5×103, (7.8±0.2)×105 d mol-1 s-1 and (690±120) s-1, respectively. The relevance of these results to cloud chemistry is discussed.