Equilibrium Behavior Research Articles

Long-Run Behavior and Convergence of Dynamic Mean Field Equilibria

AbstractWe study the behavior of dynamic equilibria in mean field games with large time horizons in a dynamic consumer choice model. We show that if the stationary equilibrium in the associated infinite horizon game is unique, the dynamic equilibria of the finite horizon games converge to the stationary equilibrium of the infinite horizon game as the time horizon tends to infinity. If the stationary equilibrium is not unique, however, the situation becomes more involved. In this case, we show that in addition to convergence to the stationary equilibria, in the long run, the dynamic equilibria circle around randomized stationary equilibria for certain choices of boundary data.

Influence of micromorphology and water content on the rheological properties and performance evaluation model of loess mudflow

Evaluation of the rheological characteristics of loess mudflow is of great significance to ecological environment protection (by loess, we mean a wind-blown Quaternary silt deposit), and geological disaster assessment in the Loess Plateau of China. Rheological characteristics of rheology for loess mudflow are highly variable due to heterogeneity in particle micromorphology and water content, and current rheological models struggle to reconcile the structural dynamics with the equilibrium behavior of soil at different concentrations and microstructures. A rheological study of loess mudflow for five regions on the Loess Plateau was carried out in this investigation, and the results showed that loess transformed from a solid-like stage to a liquid-like stage under steady loads and exhibited significant shear thinning characteristics and shear rate dependence, in which the shear rate less than 2 s−1 was the main region of loess strength attenuation and the maximum yield stress is about 1411 Pa. A smaller water content and more complex particle micromorphology led to a higher yield stress, but there was no significant correlation between flow index and particle shape and water content. Additional structural dynamics and particle fractal theory were then introduced, providing an improved model that could reconcile the structural dynamics and particle micromorphology of loess with its equilibrium behavior at different water contents and shear stresses. All the test data were distributed around a dimensionless master curve. Considering the difficulty of obtaining rheological parameters, an evaluation criterion containing three levels (clay-rich, silt-rich, and sand-rich) for the evaluation of the rheological properties of loess mudflow was proposed, which can reconcile the test results and models under different working conditions. Such an evaluation criterion can also be applied to soils of other textures, providing a straightforward manner to determine the relevant rheological parameters. The research results provide a theoretical basis for ecological environmental protection and geological disaster assessment in the Loess Plateau region based on rheological characteristics.

Recent development on neem (azadirachta indica) biomass absorbent: surface modifications and its applications in water remediation

This review paper discusses the latest advances in transfiguring Azadirachta indica (neem) biomass into an adsorbent and how it can be used to clean the environment. As an economical and environmentally favorable adsorbent material, neem biomass has become increasingly popular due to its bioactive properties and abundance. The review breaks down modification techniques into chemical and physical processes. Important physical changes covered include preactivation, carbonization, and using fluidized bed technologies and rotary kilns. It has been shown that these methods greatly improve the surface properties of neem biomass, which makes it better at absorbing things and holding more. The changes that were made also have an effect on the adsorption kinetics and isotherms, which helps us understand the adsorption rates and equilibrium behaviors of the changed adsorbents better. Neem biomass adsorbents are illustrated through their versatility and efficacy in the removal of organic pollutants, dyes, and heavy metals from effluent. This is illustrated through specific applications. Additionally, computational studies and artificial intelligence are looked into to see if they can help us understand how adsorption works at the molecular level, improve the efficiency of modification processes, and guess how adsorption will behave. The review also talks about the research gaps and suggests areas for future research. The review emphasizes the crucial importance of integrating experimental and computational methods to enhance the performance of the modified neem biomass and increase its environmental cleaning potential.

An overlapping-generations model with data-driven equilibrium behavior

We propose a class of overlapping generations models that can serve as a workhorse for policy analysis. Recent literature identifies several features of key observable economic variables in Europe and the U.S.: the life-cycle path of earnings is hump-shaped, while the aggregate variables — per-capita consumption and labor hours — exhibit a clear time trend. Our class generates non-monotonic life-cycle behavior of labor supply and the desired aggregate trends in all its balanced-growth equilibria (BGE). There is a finite number of these equilibria and at least one of them exists provided a single-generation consumer problem has a solution. The model has a constant-returns-to-scale production, non-trivial depreciation of capital, exogenous labor-saving growth and an arbitrary individual life-cycle productivity. The necessary restrictions imposed on preferences are consistent with those generating the aggregate trends in a representative-agent economy, while ruling out popular specifications such as Cobb–Douglas or CES. We characterize BGE with MaCurdy preferences and solve a parametrized model that yields at least two stationary equilibria with reasonable interest rates. The hump-shaped life-cycle consumption profile can be generated with an additional parameter interpreted as reflecting family structure or a desire for immediate gratification that peaks at mid-life.

Kinetics of Adsorption-Induced Deformation of Microporous Carbons.

Equilibrium and kinetic behavior of adsorption-induced deformation have attracted a lot of attention in the last few decades. The theoretical and experimental works cover activated carbons, coals, zeolites, glasses, etc. However, most of the theoretical works describe only the equilibrium part of the deformation process or focus on the time evolution of the adsorption process. The present paper aims to cover the existing gap using the thermodynamic framework combined with the diffusion-based description of adsorbate time evolution inside an adsorbent. We obtained self-consistent equations describing equilibrium and out-of-equilibrium adsorption, as well as deformation processes. Further, the obtained equations were verified on the experimental data of carbon dioxide and methane on activated carbons. The model is capable of describing both equilibrium and kinetic adsorption and adsorption-induced deformation data. Additionally, we studied the possible influence of slow relaxation processes in the adsorbent on the adsorption process. The current work helps to interpret experimental data for time-dependent adsorption-induced deformation.

Screening deep eutectic solvents as green solvents for efficient extraction of carbazole from model crude anthracene oil

Carbazole is a high value-added component of crude anthracene. Highly efficient and sustainable extraction solvents are extremely significant for carbazole separation. Deep eutectic solvents (DESs), as a new class of green solvents, have gained extensive attention from researchers in the field of separation. However, a large number of DESs are generated due to the enormous combinations of hydrogen bond acceptors (HBAs) and hydrogen bond donors (HBDs), which makes it challenging to identify the most suitable DES for specific separation process. Therefore, a reliable and effective method for DESs screening was highly desirable. In this work, a DESs screening method was proposed for the separation of carbazole. Initially, the COSMO-RS model was employed to calculate thermodynamic properties at infinite dilution. Subsequently, the liquid–liquid phase equilibrium behavior of prescreened DESs was further predicted by COSMO-RS to eliminate those that were miscible with toluene. Finally, the practical extraction performance of the top DES candidates was evaluated through experimental investigation. The results well validated the reliability of the screening method, identifying tetraethylammonium chloride/propionic acid (1:2) as the most promising DES for carbazole separation. Furthermore, the extraction mechanism was explored using FT-IR analysis and quantum chemical calculations.

Development of fuel depletion code for molten salt reactor with very deep burnup

A liquid-fueled molten salt reactor (MSR) can reach a deep burnup based on online reprocessing and continuously refueling, which requires significantly different burnup calculation methods for MSRs compared with those for the traditional reactors. To address the unique burnup features and consider the fidelity of isotopic evolution in an MSR, a fuel depletion code ThorMCB is developed based on the OpenMC coupled with a specific depletion code, MODEC. Furthermore, to lower the computational cost of acquiring the equilibrium state through the time evolution step by step for an MSR, an equilibrium burnup calculation code ThorMCB-eq based on the OpenMC and MODEC is developed, which can obtain the equilibrium burnup efficiently. A single fuel lattice of MSR and an a Molten Salt Fast Reactor (MSFR) benchmark are applied for verifying the correctness of the ThorMCB and ThorMCB-eq codes. Compared with a neutron transport calculation code KENO-VI coupled with MODEC, the maximum deviation of the dominant heavy nuclides (HNs) at equilibrium state by ThorMCB is less than 10%, and that of the total mass of fission products (FPs) is less than 3%. For the MSFR benchmark, the neutronic parameters including temperature reactivity coefficient, the mass evolution of main HNs and FPs and breeding ratio (BR) from ThorMCB agree with the references. The equilibrium behavior can be quickly obtained with ThorMCB-eq, and the relative mass deviations of most nuclides keep around 2% in comparison with the results of step-by-step burnup evolution with ThorMCB. Furthermore, the same fuel contents and micro one-group cross sections at equilibrium are obtained with two different types of start-up fuels and a constant power density and fuel reprocessing scheme. In conclusion, the verified results indicate that ThorMCB and ThorMCB-eq can both provide reliable simulation for depletion evolution and equilibrium burnup for MSR fuel cycle.

Extraction of mandelic acid with tri-octyl-phosphine oxide (TOPO) in different solvents: Equilibrium and neural network analysis

Mandelic acid is an important carboxylic acid used in pharmaceutical industries. It is also important to use it as a purified form. In this study, selective extraction of mandelic acid was done by tri-octyl-phosphine oxide (TOPO) diluted in different solvents such as methyl isobutyl ketone, 1-octanol, octyl acetate, dimethyl phthalate, 2-octanone, cyclohexane and toluene. The high selectivity of mandelic acid from aqueous solution was supported by thermodynamic parameters (loading factor, distribution coefficient, and extraction efficiency). The obtained values for each solvent were applied to the Neural Network Analysis to predict phase equilibrium behaviour in ternary systems. The results showed the highest mandelic acid extraction efficiency (93.65 %) and distribution coefficient (14.74) were attained with the organic phase mixture prepared with MIBK and TOPO. Also, it was found that extraction efficiencies increased with increasing TOPO amount in the medium for all studied solvents.

Liquid-Liquid equilibrium Behavior and intermolecular interactions of Levulinic acid and water with isopropyl ether and methyl Tert-Butyl ether

Levulinic acid (LA) is a crucial bio-based chemical with extensive industrial applications. Due to its significant share in the cost of production, the development of efficient techniques for the separation of LA is essential. Traditional separation using sulphuric acid raises environmental and cost concerns, making liquid–liquid extraction a more sustainable and cost-effective alternative. liquid–liquid equilibrium (LLE) investigation was carried out for two ternary mixtures of water + LA + isopropyl ether / methyl tert-butyl ether (MTBE) at two temperatures and 101.3 kPa. The results indicated that the solvent MTBE, as an extractant, showed a higher partition coefficient and selectivity for LA than isopropyl ether, demonstrating its superior effectiveness in recovering LA. The interaction insights between LA and the extractants were explored using quantum chemistry calculations, which aligned well with the collected results. The ascertained LLE data was modeled using the NRTL equation, achieving the RMSD values below 0.01, demonstrating a good concordance between the collected data and computed values. The fitted NRTL model parameters are conducive to the designing and optimizing the LA separation process.

A sequentially variant Blotto game with one-sided and incomplete information

We develop a sequentially variant Blotto game with one-sided and incomplete information to investigate strategic interactions between a defender and an attacker whose target site values are unknown. The defender first allocates defensive resources before the attacker decides a probability distribution over which site to attack between the target sites. The attacker perfectly observes the defender’s resource allocations. The attacker’s type is continuous, following the attacker’s private values of victoriously attacking each site. We find the game’s essentially unique subgame perfect equilibrium. In equilibrium, the site the attacker attacks with a higher probability is the site with a lower expected loss for the defender when the defender defends both sites. We present numerical examples to examine (1) the impacts of the informational uncertainty concerning the attacker’s site values, (2) the impacts of the site values of the defender, (3) the impacts of the site values of the attacker, and (4) the impacts of the defender’s defense efficiency on the equilibrium behavior.

Phase Behavior of System Carbon Dioxide + Hydrogen Sulfide

The global phase equilibrium behavior of the CO2+H2S system is discussed in this work for temperatures ranging from 160 K up to the critical region. Solid phases of CO2 and H2S and corresponding equilibria have been modeled by considering either a 4th-order equation of state (also used for the fluid phases) or a solid fugacity model for the pure components combined with an activity coefficient model (both coupled with a reference equation of state for the fluid phases).Phase equilibrium calculations have been performed by the minimization of the Gibbs Free Energy of mixing and compared to existing literature data.The types of pressure-mole fraction phase diagrams that can be encountered in the low-temperature thermodynamic region have been described. The temperature and pressure ranges where the phase behavior of the system changes have been identified and a representative phase diagram is presented for each range.

Polyvinylpyrrolidone mediated electrospun ZnO-ZnFe2O4 composite nanofibers for removing malachite green from water

This study explores the application of ZnO-ZnFe2O4 composite nanofibers for the adsorption of Malachite Green (MG) dye from water. The composite nanofibers were fabricated using simple polyvinylpyrrolidone (PVP) mediated electrospinning method by changing zinc and iron precursor weight ratio named as Zn–Fe (1-1), Zn–Fe (2–1) and Zn–Fe (1–2). The diameter of 1D nanofibers was found to be 40–60 nm. The formation of hexagonal wurtzite structure of ZnO and cubic spinel structure of ZnFe2O4 was confirmed by XRD and HRTEM analysis. The effects of various parameters such as pH, contact time and initial concentration on the adsorption process were investigated. The Zn–Fe (1-1) nanofibers showed higher adsorption efficiency than other two. The adsorption results demonstrated excellent adsorption performance, with a maximum adsorption capacity of 146.77 mg/g at pH = 7 for Zn–Fe (1-1). Furthermore, the adsorption kinetics and isotherms were analyzed to understand the adsorption mechanism and equilibrium behaviour. It was found that the nanofibers material can be recycled and reused up to five cycles.

Critical dimension for hydrodynamic turbulence.

Hydrodynamic turbulence exhibits nonequilibrium behavior with k^{-5/3} energy spectrum, and equilibrium behavior with k^{d-1} energy spectrum and zero viscosity, where d is the space dimension. Using recursive renormalization group in Craya-Herring basis, we show that the nonequilibrium solution is valid only for d<6, whereas equilibrium solution with zero viscosity is the only solution for d>6. Thus, d=6 is the critical dimension for hydrodynamic turbulence. In addition, we show that the energy flux changes sign from positive to negative near d=2.15. We also compute the energy flux and Kolmogorov's constants for various d's, and observe that our results are in good agreement with past numerical results.

Low-Temperature Water Electrolysis Under a Sustained pH-Gradient for Electrochemically-Induced Decarbonation of Limestone into Hydrated Lime

Lime holds considerable potential in diverse environmental applications. However, its current production remains highly carbon-intensive, emitting more than one ton of CO2 per ton of lime. To address this issue, recent studies have explored the concept of electrifying the decarbonation of limestone to produce hydrated lime. In this work, a two-compartment electrolysis cell capable of producing Ca(OH)2 has been tested at different currents. Precise pH and Ca2+ concentration measurements demonstrate that the electrolysis setup is able to dissolve CaCO3 and precipitate Ca(OH)2 with near-perfect efficiencies. Notably, it highlights that Faraday’s law and the concept of transport number can be applied to predict both the equilibrium and kinetic behavior of each step of the process in each of the two cell compartments. Moreover, the use of controlled batch additions of CaCO3 in the system, as opposed to one-time excess addition, was assessed to mitigate the fouling of the cationic exchange membrane used to separate the compartments. Finally, based on the experimental findings, key guidelines are proposed to achieve a perfect reaction stoichiometry for each step. These findings pave the way for a more sustainable and environmentally friendly approach to lime production.

Everybody’s talkin’ at me: levels of majority language acquisition by minority language speakers

AbstractImmigrants in economies with a dominant native language exhibit substantial heterogeneities in language acquisition of the majority language. We model partial language acquisition as an equilibrium phenomenon. We consider an environment where heterogeneous agents from various minority groups choose whether to acquire a majority language fully, partially, or not at all, with varying communicative benefits and costs. We provide an equilibrium characterization of language acquisition and demonstrate that partial acquisition can arise as an equilibrium behavior. We also show that a language equilibrium may exhibit insufficient learning relative to the social optimum. Finally, we formulate a deterministic language learning dynamic process and find that our language equilibrium arises in the long run under suitable conditions.

Enhanced methylene blue adsorption using single-walled carbon nanotubes/chitosan-graft-gelatin nanocomposite hydrogels

In the present study, single-walled carbon nanotubes (SWCNTs) incorporating chitosan-graft-gelatin (CS-g-GEL/SWCNTs) hydrogels were fabricated with multiple advantages, including cost-effectiveness, high efficiency, biodegradability, and ease of separation for methylene blue (MB) dye from aqueous solution. To verify the successful formulation of the prepared hydrogels, various characterization methods such as NMR, FTIR, XRD, FE-SEM, TGA, BET, and EDX were employed. The removal efficiency of CS-g-GEL/SWCNTs nanocomposite hydrogel increased significantly to 98.87% when the SWCNTs percentage was increased to 20%. The highest adsorption was observed for pH = 9, an adsorbent dose = 1.5 g L−1, a temperature = 25 °C, a contact time = 60 min, and a contaminant concentration = 20 mg L−1. Based on the thermodynamic results, spontaneous adsorption occurred from a negative Gibbs free energy (ΔG°). In addition, the thermodynamic analysis of the adsorption process revealed an average enthalpy of − 21.869 kJ mol−1 for the adsorption process at a temperature range of 25–45 °C, which indicates its spontaneous and exothermic behavior. The Langmuir isotherm model was successfully used to describe the equilibrium behavior of adsorption. The pseudo-first-order model better described adsorption kinetics compared to the pseudo-second-order, intra-particle, and Elovich models. CS-g-GEL/SWCNTs hydrogels have improved reusability for five consecutive cycles, suggesting that they may be effective for removing anionic dyes from aquatic environments.

Cross-linked chitosan-adipic/zirconia (ZrO2) nanocomposite for removal of eosin y dye: insight into physicochemical properties, adsorption modelling, isotherms, and kinetics

ABSTRACT A nanocomposite adsorbent of cross-linked chitosan-adipic/zirconia nanoparticles (CHI-ADI/ZNPs) was successfully formed through the modifying of a naturally occurring polymer (CHI) with a nanoscale material (zirconia, ZrO2), which was subsequently subjected to an ionic cross-linking technique facilitated by adipic (ADI). The physicochemical properties of this innovative nanocomposite have been thoroughly investigated utilising a variety of techniques, such as CHN, XRD, FTIR, FESEM-EDX, and BET. Using response surface methodology, the capacity of CHI-ADI/ZNPs to remove organic dye (Eosin Y, EY) from an aqueous system was thoroughly investigated, with adsorption-influencing parameters including CHI-ADI/ZNPs dosage (0.02–0.08 g), removal time (10–90 min), and pH solution (4–10). Using the Langmuir and Temkin isotherm, the equilibrium behaviour of EY as determined by CHI-ADI/ZNPs is well illustrated. The adsorption kinetics data of EY by CHI-ADI/ZNPs were aptly characterised by a model of the pseudo-first-order. At 199.84 mg/g, CHI-ADI/ZNPs exhibit a remarkably adsorption capacity. The efficient adsorption of EY onto the CHI-ADI/ZNPs is likely assigned to H-bond interactions, n-π stacking, and the positively charged CHI-ADI/ZNPs and EY anions. The findings of this research illustrate the exceptional adsorption capabilities of CHI-ADI/ZNPs in the context of eliminating synthetic anionic dyes from wastewater.

Mixed-Mode Adsorption of l-Tryptophan on D301 Resin through Hydrophobic Interaction/Ion Exchange/Ion Exclusion: Equilibrium and Kinetics Study.

The adsorption of l-tryptophan (l-Trp) was studied based on the hydrophobic interaction/ion exchange/ion exclusion mixed-mode adsorption resin D301. Firstly, the interaction mode between l-Trp and resin was analyzed by studying the influence of pH variation on the adsorption capability and the dissociation state of l-Trp. Secondly, the adsorption mechanism was illuminated by studying the adsorption equilibrium and kinetic behaviors. The adsorption equilibrium and a kinetics model were constructed. The augmentation of pH gradually elicited an enhancement in the adsorption capacity of l-Trp. l-Trp existing in varied dissociation states could be adsorbed by the resin, and the interaction mode relied upon the pH of the solution. An integrated adsorption equilibrium model with the coadsorption of different dissociation states of l-Trp was developed and could predict the adsorption isotherms at various pH levels satisfactorily. Both external mass transfer and intra-particle diffusion collectively imposed constraints on the mass transfer process of l-Trp onto the resin. An improved liquid film linear driving force model (ILM) was constructed, and the model provided a satisfactory fit for the adsorption kinetics curves of l-Trp at various pH levels. l-Trp molecules had a high mass transfer rate at a relatively low solution pH.

Electrospun polyacrylonitrile reinforced greenly synthesized iron oxide nanocomposite fibers sheet for remediation of azithromycin from water

The contamination of water bodies by pharmaceuticals, such as azithromycin (AZM), poses significant environmental concerns. In this study, electrospun polyacrylonitrile (PAN) reinforced with greenly synthesized iron oxide nanocomposite (PAN@Fe2O3) fibers sheet was prepared for the removal of azithromycin from water. The Fe2O3 nanopowder was synthesized via a facile and eco-friendly method using natural extracts as reducing and stabilizing agents. Then synthesized nanoparticles powder was incorporated in PAN surface by using simple electrospinning method. The morphology, structure, and composition of the nanocomposite fibers were characterized using XRD, FTIR, BET, FESEM and HRTEM analytical techniques. Utilising a molecular dynamics (MD) method, the mechanical characteristics of the PAN@Fe2O3 nanocomposite were theoretically examined. Batch adsorption experiments were conducted to evaluate the adsorption capacity of the nanocomposite fibers for AZM removal from aqueous solutions. The effects of various parameters such as dose, pH, contact time and initial AZM concentration on the adsorption process were investigated. The results demonstrated excellent adsorption performance, with a maximum adsorption capacity of 73.49 mg/g at pH=7. Furthermore, the adsorption kinetics and isotherms were analysed to understand the adsorption mechanism and equilibrium behaviour. Furthermore, for a minimum of four adsorption-desorption cycles, the adsorbent may be cycled and regenerate in succession.

Menadione sodium bisulfite as an efficient anti-corrosion additive for mild steel in acid corrosion: Electrochemical, surface morphological and theoretical studies

The corrosion inhibition behavior of Menadione Sodium Bisulfite (MSB) in 1.0 M HCl medium was evaluated using weight loss, electrochemical techniques (Tafel polarisation and Electrochemical impedance spectra), surface analysis (SEM and EDX), Density Functional Theory (DFT), Noncovalent interaction- Reduced Density Gradient (NCI-RDG) and Monte Carlo (MC) simulation techniques. Weight loss measurement showed that as inhibitor concentration increased, the corrosion rate decreased which means that a protective film formed on the metal surface. At 300 ppm, the inhibitor showed a maximum inhibition efficiency of 89.7 %. Tafel polarisation studies indicate that the inhibitor is mixed-type in nature. The inhibitor adsorption on the mild steel is the best fit for the Langmuir isotherm model. As the weak interaction of sodium and oxygen in the inhibitor molecules, the inhibitor exhibits two distinct equilibrium behaviors. (i) inhibitor with sodium (solid-state) and inhibitor without sodium (in liquid-state). These two behaviors were theoretically investigated using DFT and MD simulation studies. The inhibitor and metal interaction is further supported using these theoretical studies. The electron population of the inhibitor was analyzed using molecular electrostatic potential, NCI-RDG, Fukui function, and natural bond orbital analysis. These studies further give an understating of the inhibitor and metal interactions.