Equilibrium Behavior Research Articles

Blockchain Operations in the Presence of Security Concerns

Problem definition: A blockchain payment system, such as Bitcoin or Ethereum, validates electronic transactions and stores them in a chain of blocks without a central authority. Miners with computing power compete for the rights to create blocks according to a preset protocol, referred to as hashing or mining, and, in return, earn fees paid by users who submit transactions. Because of security concerns caused by decentralization, a transaction is confirmed after a number of additional blocks are subsequently extended to the block containing it. This confirmation latency introduces an intricate interplay between miners and users. This paper provides approximate system equilibria and studies optimal designs of a blockchain. Methodology/results: The hashing process is essentially a single-server queue with batch services based on a fee-based priority discipline, and confirmation latency adds complexity to the equilibrium behavior and optimal design. We analyze how miners’ participation decisions interact with users’ participation and fee decisions and identify optimal designs when the goal is to maximize the throughput or social welfare. We validate our model and conduct numerical studies using data from Bitcoin. Managerial implications: By incorporating security issues, we uncover the interdependence of the decisions between users and miners and the driver for nonzero entrance fees in practice. We show that miners and users may end up in either a vicious or virtuous cycle, depending on the initial system state. By allowing the entrance fee to be a design parameter, we are able to establish that it is optimal to simply run a blockchain system at its full capacity and a block size as small as possible. Funding: This work was supported by the Hong Kong Research Grants Council [Grants 16200019, 16200617, 16200821, 16208120, and 16214121]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/msom.2023.1197 .

The Effect of Sulfate Electrolytes on the Liquid–Liquid Equilibrium of 2-MTHF/Water/5-HMF: Experimental Study and Thermodynamic Modeling

We investigate the influence of sulfate salts and sulfuric acid on the equilibrium behavior of 2-methyltetrahydrofuran (2-MTHF)/H2O/5-hydroxymethylfurfural (5-HMF). Liquid–liquid equilibrium measurements are performed at atmospheric pressure and in a temperature range of T = (293–333) K. The compositions of the aqueous and organic phases, together with the dissociation state of the sulfate species, are determined with infrared spectroscopy and Indirect Hard Modeling. We show that the addition of the salts Na2SO4 and Li2SO4 results in salting out of 2-MTHF and 5-HMF from the aqueous phase. With increasing temperature, this effect gets less pronounced. In contrast, the addition of H2SO4 does not result in any salting-out behavior. The investigation of the dissociation states shows that H2SO4 dissociates to HSO4– while Na2SO4 and Li2SO4 dissociate completely to SO42–. Parameter regression is performed to model the liquid–liquid equilibrium with the electrolyte perturbed-chain statistical associating fluid theory (ePC-SAFT) equation of state. For the analyzed salts, Na2SO4 and Li2SO4, the performed parameter regression accurately predicts the measurement results. Still, we observe slight deviations between measured values and modeling when predicting the liquid–liquid equilibrium and the liquid density in the presence of sulfuric acid.

A method for evaluating resource potential and oil mobility in liquid-rich shale plays—An example from upper Devonian Duvernay formation of the Western Canada Sedimentary Basin

This paper discusses methods of assessing oil and gas resources and evaluating their mobility in shale reservoirs using programed pyrolysis data in conjunction with reservoir engineering parameters derived from production data. The hydrocarbon resource is calculated from the measured free hydrocarbon by programed pyrolysis with correction of evaporative loss that occurred during coring, storage and sample preparation. The correction takes account of the loss of light hydrocarbon fluids as a result of phase change during core retrieval to the surface and evaporative loss related to storage and sample preparation. Based on their response to ramping temperature during sample pyrolysis and thermal equilibrium behavior of distinct petroleum products at different thermal maturities, the estimated oil and gas resources are divided into three categories: non-movable, restricted, and movable to characterize the mobility of the petroleum fluids. The mobility classification is compared with oil compositional grouping based on evaporative kinetics of petroleum products in rock samples to examine their affinity. Pyrolysis analysis results from naturally matured samples and production data from different fluid zones in the Duvernay Shale resource play in Western Canada Sedimentary Basin (WCSB) were used to demonstrate the application of the proposed method. While the mobility of petroleum fluids increases with thermal maturation in general, the total movable resource reaches its maximum at the end of oil generation window, then declines as a result of massive loss due to hydrocarbon expulsion towards to gas window where liquids are thermally cracked to gaseous hydrocarbons. Compositional grouping based on evaporative kinetics does not show a complete accordance with mobility grouping, suggesting composition is only one of many factors affecting hydrocarbon fluid flow in shale reservoir. More studies are required to better understand the fundamentals of oil mobility in shale reservoir.

Liquid–Liquid Equilibrium for Ternary Systems 2,2,2-Trifluoroethanol + Water + (Ethyl Acetate/Isopropyl Acetate/Isobutyl Acetate) at 308.15 K under 101.3 kPa

2,2,2-Trifluoroethanol (C2H3F3O, TFE) is a useful fluorine-containing alcohol. During the synthesis and application of TFE, TFE, and water can form an azeotropic mixture. To recover TFE from the mixture of TFE and water by liquid–liquid extraction (LLET), in the current work, three organic solvents, isobutyl acetate (C6H12O2), isopropyl acetate (C5H10O2), and ethyl acetate (C4H8O2), were chosen as the extractants. The liquid–liquid equilibrium (LLE) behavior for the three mixtures (water + TFE + ethyl acetate/isopropyl acetate/isobutyl acetate) was investigated at 101.3 kPa and 308.15 K. Selectivity (S) and distribution constant (D) were calculated as indexes to evaluate the extraction capacity of the three extractants. The results indicated that isobutyl acetate has better extraction ability in extracting TFE from its aqueous solution of TFE compared to the esters. The NRTL model was used to regress the determined tie-line data. The coherence of the fitted parameters of the NRTL model with the experimental data was checked by topological analysis.

Simultaneous Predictions of Chemical and Phase Equilibria in Systems with an Esterification Reaction Using PC-SAFT

The study of chemical reactions in multiple liquid phase systems is becoming more and more relevant in industry and academia. The ability to predict combined chemical and phase equilibria is interesting from a scientific point of view but is also crucial to design innovative separation processes. In this work, an algorithm to perform the combined chemical and liquid-liquid phase equilibrium calculation was implemented in the PC-SAFT framework in order to predict the thermodynamic equilibrium behavior of two multicomponent esterification systems. Esterification reactions involve hydrophobic reacting agents and water, which might cause liquid-liquid phase separation along the reaction coordinate, especially if long-chain alcoholic reactants are used. As test systems, the two quaternary esterification systems starting from the reactants acetic acid + 1-pentanol and from the reactants acetic acid + 1-hexanol were chosen. It is known that both quaternary systems exhibit composition regions of overlapped chemical and liquid-liquid equilibrium. To the best of our knowledge, this is the first time that PC-SAFT was used to calculate simultaneous chemical and liquid-liquid equilibria. All the binary subsystems were studied prior to evaluating the predictive capability of PC-SAFT toward the simultaneous chemical equilibria and phase equilibria. Overall, PC-SAFT proved its excellent capabilities toward predicting chemical equilibrium composition in the homogeneous composition range of the investigated systems as well as liquid-liquid phase behavior. This study highlights the potential of a physical sound model to perform thermodynamic-based modeling of chemical reacting systems undergoing liquid-liquid phase separation.

Unveiling the thermodynamic and molecular mechanisms for the separation of diethoxymethane and ethanol azeotrope by deep eutectic solvents

The selection of efficient and environmental extractants is essential for the sustainable development of extraction processes. Based on the conductor-like screening model for the segment activity coefficient (COSMO-SAC), three deep eutectic solvents (DESs) were screened from 1000 DESs for the separation of diethoxymethane (DEM) and ethanol (EA). Subsequently, the liquid–liquid equilibrium behavior of the DEM + EA + DES system at different temperatures was measured. The results show that benzyltrimethylammonium chloride/glycerol (BTACl/GLY) has the highest selectivity and benzyltrimethylammonium chloride/ethylene glycol (BTACl/EG) and tetraethylammonium chloride/ethylene glycol (TEACl/EG) have similar extraction performance. More importantly, the extraction performance of DESs reported in this work is stronger than that of the solvents already reported. Additionally, analysis of the separation mechanism by various quantum chemical methods revealed that the purification of DEM and EA mixtures is mainly ascribed to the difference in electrostatic forces between the solvent and DEM/EA. The result confirmed that solvents with small molecular structures and strong nucleophilic sites are more competitive in separating the mixtures.

The Dynamics of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate

In this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey-predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcation by using normal form theory and center manifold theorem are identified. Additionally, using numerical simulations and a hypothetical dataset, various dynamic characteristics are discovered, including stability switches, chaos, and Hopf bifurcation scenarios.

Coarse-grained intrinsically disordered protein simulations with explicit ions parameterized by salting-out constants.

Implicit solvent coarse-grained models have emerged as an effective method for simulating intrinsically disordered proteins (IDPs) due to the long length and time-scale need to effectively simulate their equilibrium behavior. These coarse-grained methods typically rely on Debye-Hückel theory to explain the effects of salt in the simulations. However, Debye-Hückel electrostatics are only accurate over a limited range of ionic strengths and are also unable to capture ion-type specific effects, typically called Hofmeister effects that arise at higher salt concentrations. To address this, we developed an explicit ion model of potassium chloride that can interface with the otherwise implicit solvent hydrophobicity scale model for intrinsically disordered protein. Parameters for the explicit ion model were determined by matching the salting-out constants of several small peptide-like molecules. Salting-out constants were determined in the simulation by creating a system with an ion concentration gradient via an external potential and performing umbrella sampling along the concentration gradient. The remaining amino acids for which there is no data for the salting-out constant are determined using a scaled Kapcha-Rosky hydrophobicity scale determined from the umbrella sampling simulations. The parameters are validated against a set FRET data from a diverse set of linker peptides at several salt concentrations. This explicit ion model is able to capture the changes in protein expansion as a function of salt concentration at concentration above 0.5 M where Debye-Hückel screened electrostatics predict no change in protein expansion.

Vaccination dilemma in the thermodynamic limit.

The vaccination game is a social dilemma that refers to the conundrum individuals face (to get immunized or not) when the population is exposed to an infectious disease. The model has recently gained much traction due to the COVID-19 pandemic since the public perception of vaccines plays a significant role in disease dynamics. This paper studies the vaccination game in the thermodynamic limit with an analytical method derived from the 1D Ising model called Nash equilibrium mapping. The individual dilemma regarding vaccination comes from an internal conflict wherein one tries to balance the perceived advantages of immunizing with the apparent risks associated with vaccination, which they hear through different news media. We compare the results of Nash equilibrium (NE) mapping from other 1D Ising-based models, namely, Darwinian evolution (DE) and agent-based simulation. This study aims to analyze the behavior of an infinite population regarding what fraction of people choose to vaccinate or not vaccinate. While Nash equilibrium mapping and agent-based simulation agree mostly, DE strays far from the two models. DE fails to predict the equilibrium behavior of players in the population reasonably. We apply the results of our study to analyze the AstraZeneca (AZ) COVID-19 vaccine risk vs disease deaths debate, both via NE mapping and the agent-based method. Both predict nearly 100% AZ vaccine coverage for people aged above 40, notwithstanding the risk. At the same time, younger people show a slight reluctance. We predict that while government intervention via vaccination mandates and/or advertisement campaigns are unnecessary for the older population, for the younger population (ages: 20-39), some encouragement from the government via media campaigns and/or vaccine mandates may be necessary.

Optimal large population Tullock contests

Abstract We consider Tullock contests where contestants can be divided into a finite set of types according to their strategy cost function. Solving such contests is intractable if the number of players is finite but large and there are nonlinearities and asymmetries present. But by approximating the finite player contest with a large population model that can be solved in closed form, we can approximate equilibrium behavior in the finite player model. We then characterize the optimal bias parameters of the large population contest and interpret them as approximations of optimal bias parameters in finite player contests. We also identify conditions under which those parameters are increasing or decreasing according to the cost parameters. The parameters are biased in favor of high-cost agents if the cost functions are strictly convex and the likelihood of success is sufficiently responsive to strategy.

Modelling of PFAS-surface interactions: Effect of surface charge and solution ions

Per-and poly-fluoroalkyl substances (PFAS) are a class of substances of increasing concern as environmental contaminants. The interactions between PFAS and surfaces play an important role in PFAS transport and remediation. Previous studies have found PFAS adsorption to be dependent upon properties including pH, organic matter and particle size, along with PFAS functional group and carbon chain length. It is hypothesised that a theoretical examination of PFAS-surface interactions, via Monte Carlo molecular simulation, would show differences resulting from changes in surface charge, H+, OH−, Ca2+ concentrations and PFAS carbon chain length. Monte Carlo molecular simulations of perfluorooctane and perfluorobutane sulfonic acids interacting with a graphite surface in an aqueous medium were performed. Variations in surface charge, H+, OH− and Ca2+ concentrations were made. The distance-dependent density of molecules from the surface was analysed as a proxy for PFAS adsorption to the surface. Simulation results showed differences in surface behaviour that depended on surface charge, H+, OH− and Ca2+ concentrations, along with carbon chain length, with surface charge playing the most prominent role in controlling PFAS adsorption. For negatively charged surfaces, adsorption due to divalent cation bridging was observed in Ca2+ solutions. Modelling, such as in this study, of the thermodynamic equilibrium behaviour of low concentrations of molecules, in scenarios where both adsorption and mobility of PFAS occur, can aid in the design and testing of sorptive surfaces for amendment-based PFAS remediation.

Critical net-baryon fluctuations in an expanding system

In this work we study the consequences of a longitudinal Bjorken expansion and a Hubble-like temperature cooling scenario on a $1+1$ dimensional nonlinear model of the diffusive dynamics of fluctuations in the net-baryon density. The equilibrium behavior of the fluctuations is fully encoded in the temperature dependence of the susceptibilities on the crossover side both in the vicinity of the assumed location of the critical point and at vanishing baryochemical potential in line with lattice quantum chromodynamics calculations. We demonstrate the great sensitivity of the fluctuation observables on the dynamics, in particular on the diffusion length and the freeze-out conditions. While the critical signals are visible and the critical region is broadened by the expansion, a too small diffusion length can strongly reduce the amplitude of the signals. We propose to search for significant anticorrelations of baryons at intermediate rapidity experimentally and to map out the rapidity dependence of the fourth-order cumulant, which, in the presence of a critical point (and only in its presence), has a pronounced minimum at intermediate rapidities.

Phase Equilibrium of Methane Hydrate in Sediments: Experimental and Theoretical Characterization

A series of phase equilibrium tests were performed to explore the influence of various experimental conditions, including initial water content, dry density, and salt content, on the phase equilibrium behavior of methane hydrate in fine- and coarse-grained sediments. The results indicate that the phase equilibrium condition of pore hydrate is significantly influenced by the adopted experimental conditions and the sediment types. It is shown that in equilibrium, a unique relationship (the soil hydration characteristic curve (SHCC)) exists among the temperature shift, the unhydrated water, and the amount of dissolved salt. Under salt-free conditions, the SHCC is independent of dry density for coarse-grained specimens, whereas it is slightly influenced by the dry density for fine-grained specimens. A recently developed phase equilibrium model of pore hydrate, which can account for osmotic, capillary, and adsorptive effects, is introduced to interpret the experimental results. It is shown that the SHCC of the coarse-grained specimens can be very well described by the model; for fine-grained specimens, however, the effect of salt content on matric suction has to be taken into account in the model prediction.

Strategic behavior in queues with arrival rate uncertainty

This paper shows how to account for arrival rate uncertainty in the analysis of queueing models with strategic customer behavior. We consider a general queueing model with a Poisson arrival process whose rate is random, and realized once for the entire process. We show that the distribution of the arrival rate at arrival instants is the size-biased counterpart of the original distribution. In particular, the ASTA (arrivals see time averages) property does not hold but rather a rate-biased version of it which we define and coin by the term RASTA (Rate-biased ASTA). We show that the RASTA phenomenon plays a crucial role in the analysis of strategic behavior of customers who evaluate the consequences of the actions they take upon arrival. By studying such a system with a single server and strategic customers who decide whether to join or balk without observing the queue, we exemplify the importance of RASTA in deriving the equilibrium behavior.

Phase separation and dynamical arrest of protein solutions dominated by short-range attractions.

The interplay of liquid-liquid phase separation (LLPS) and dynamical arrest can lead to the formation of gels and glasses, which is relevant for such diverse fields as condensed matter physics, materials science, food engineering, and the pharmaceutical industry. In this context, protein solutions exhibit remarkable equilibrium and non-equilibrium behaviors. In the regime where attractive and repulsive forces compete, it has been demonstrated, for example, that the location of the dynamical arrest line seems to be independent of ionic strength, so that the arrest lines at different ionic screening lengths overlap, in contrast to the LLPS coexistence curves, which strongly depend on the salt concentration. In this work, we show that the same phenomenology can also be observed when the electrostatic repulsions are largely screened, and the range and strength of the attractions are varied. In particular, using lysozyme in brine as a model system, the metastable gas-liquid binodal and the dynamical arrest line as well as the second virial coefficient have been determined for various solution conditions by cloud-point measurements, optical microscopy, centrifugation experiments, and light scattering. With the aim of understanding this new experimental phenomenology, we apply the non-equilibrium self-consistent generalized Langevin equation theory to a simple model system with only excluded volume plus short-range attractions, to study the dependence of the predicted arrest lines on the range of the attractive interaction. The theoretical predictions find a good qualitative agreement with experiments when the range of the attraction is not too small compared with the size of the protein.

Anion Effects on the Liquid-Liquid Equilibrium Behavior of Pluronic L64 + Water + Sodium Salts at Different pH: Determination of Thermodynamic Parameters

Two-phase aqueous systems have replaced and simplified steps in extraction and purification processes, especially for biocompounds. Thus, this study evaluated the liquid-liquid equilibrium behavior of Pluronic L64 + water + sodium salts at pH 5.0, 7.5, and 10.0. Sodium sulfate demonstrated the greatest phase separation, followed by sodium citrate and sodium tartrate. Higher pH values resulted in larger biphasic regions. The polymer distribution coefficients increased with the addition of salt. As pH increased, there was a tendency for Pluronic L64 to migrate to the polymer-rich phase. The Gibbs energy of micellization between −11,000 and −25,000 kJ mol−1 indicated the spontaneity of the process micellization for all systems, showing lower values for the systems with sodium sulfate. This parameter was related to the anion speciation at each pH. Besides, the effects of water structuring around ions and ion-polymer interaction influenced the phase separation.

The underlying coherent behavior in intraday dynamic market equilibrium

PurposeThis paper applies a volume-price probability wave differential equation to propose a conceptual theory and has innovative behavioral interpretations of intraday dynamic market equilibrium price, in which traders' momentum, reversal and interactive behaviors play roles.Design/methodology/approachThe authors select intraday cumulative trading volume distribution over price as revealed preferences. An equilibrium price is a price at which the corresponding cumulative trading volume achieves the maximum value. Based on the existence of the equilibrium in social finance, the authors propose a testable interacting traders' preference hypothesis without imposing the invariance criterion of rational choices. Interactively coherent preferences signify the choices subject to interactive invariance over price.FindingsThe authors find that interactive trading choices generate a constant frequency over price and intraday dynamic market equilibrium in a tug-of-war between momentum and reversal traders. The authors explain the market equilibrium through interactive, momentum and reversal traders. The intelligent interactive trading preferences are coherent and account for local dynamic market equilibrium, holistic dynamic market disequilibrium and the nonlinear and non-monotone V-shaped probability of selling over profit (BH curves).Research limitations/implicationsThe authors will understand investors' behaviors and dynamic markets through more empirical execution in the future, suggesting a unified theory available in social finance.Practical implicationsThe authors can apply the subjects' intelligent behaviors to artificial intelligence (AI), deep learning and financial technology.Social implicationsUnderstanding the behavior of interacting individuals or units will help social risk management beyond the frontiers of the financial market, such as governance in an organization, social violence in a country and COVID-19 pandemics worldwide.Originality/valueIt uncovers subjects' intelligent interactively trading behaviors.

Solubility and Data Correlation of 2-Bromo-5-hydroxypyrazine in Four Cosolvent Mixtures and Ten Mono-Solvents from 278.15 to 323.15 K

The experimental solubility of 2-bromo-5-hydroxypyrazine dissolved in 10 mono-solvents (methanol, ethanol, isopropanol, N,N-dimethylformamide (DMF), n-propanol, acetonitrile, acetone, ethylene glycol (EG), propylene glycol (PG), water) and cosolvent mixtures of methanol + water, ethanol + water, isopropanol + water, and DMF + water was determined by the isothermal saturation method between 278.15 and 323.15 K at 101.2 kPa. The largest solubility was observed in DMF + 2-bromo-5-hydroxypyrazine for mono-solvent systems and in DMF + water for mixed solvent systems. The Jouyban–Acree model (J–A), van’t Hoff–Jouyban–Acree model (V–J–A), and Apelblat–Jouyban–Acree model (A–J–A) were utilized to correlate the 2-bromo-5-hydroxypyrazine solubility in mixtures, and the Apelblat model, van’t Hoff model, λh model, and Jouyban model were used to correlate the 2-bromo-5-hydroxypyrazine solubility in 10 mono-solvents. The preferential solvation of 2-bromo-5-hydroxypyrazine in mixed solvents was researched by calculation of δx1,3. This study presents insights into modulating the 2-bromo-5-hydroxypyrazine crystallization process and in understanding equilibrium behaviors in different solvents.

Reputation, Competition, and Lies in Labor Market Recommendations

We examine strategic communication in labor market recommendations. Our formal model features two-sided asymmetric information: An adviser has private information about his own preference bias for a focal candidate and a signal of the quality of this candidate, whereas the hiring firm has private information about the quality of an alternative candidate. The adviser can choose whether to recommend his focal candidate to the firm. If he recommends and the firm hires the candidate, then the adviser pays a reputational cost (receives a reputation boost) if the firm later learns that the hire has low quality (high quality). Our main results describe how the equilibrium behavior of advisers (lying choices) and firms (hiring choices) depend on the intricate interplay between preference biases, reputation, lying costs, and the hiring firm’s labor market strength (access to alternative candidates with higher quality). We show that the equilibrium features assortative matching: advisers with a higher (lower) reputation choose to lie less (more), and consequently, their candidates are more likely to be hired by firms with strong (weak) access to high-skilled outside candidates. Two equilibrium forces create a “rich get richer” effect. First, advisers choose to lie less to hiring firms with access to better top candidates, further benefiting those firms. Second, advisers with a higher (lower) reputation choose to lie less (more), which increases (decreases) their future reputation, creating a “reputation trap.” We discuss the implications of our model for hiring strategy, referral systems, and the ability to accrue and sustain human capital-based competitive advantages. This paper was accepted by Alfonso Gambardella, business strategy.

Analysis of a heterogeneous SEIRS patch model with asymmetric mobility kernel.

In this paper, we establish a spatial heterogeneous SEIRS patch model with asymmetric mobility kernel. The basic reproduction ratio $ \mathcal{R}_{0} $ is defined, and threshold-type results on global dynamics are investigated in terms of $ \mathcal{R}_{0} $. In certain cases, the monotonicity of $ \mathcal{R}_{0} $ with respect to the heterogeneous diffusion coefficients is established, but this is not true in all cases. Finally, when the diffusion rate of susceptible individuals approaches zero, the long-term behavior of the endemic equilibrium is explored. In contrast to most prior studies, which focused primarily on the mobility of susceptible and symptomatic infected individuals, our findings indicate the significance of the mobility of exposed and recovered persons in disease dynamics.