Equilibrium Behavior Research Articles

Revealing Solid–Liquid Equilibrium Behavior of 4-Fluorobenzoic Acid in 12 Pure Solvents from 283.15 to 323.15 K by Experiments and Molecular Simulations

Revealing Solid–Liquid Equilibrium Behavior of 4-Fluorobenzoic Acid in 12 Pure Solvents from 283.15 to 323.15 K by Experiments and Molecular Simulations

Pricing and low-carbon decisions in an uncertain supply chain with cap-and-trade regulation

This paper studies the pricing and low-carbon decision problems in a supply chain containing a manufacturer and a downstream retailer. The manufacturer produces a single product under the cap-and-trade scheme. We formulate the price and carbon-concerned demand function. To maximize their revenue, the manufacturer and the retailer determine their selling prices and carbon emission reduction rates separately. Due to the fast product updates speed, some parameters do not have enough historical data. For example, the sales cost of the retailer, the demand of consumers, and the total carbon emissions of manufacturers are far from frequency stability. This fact makes the distribution function obtained in practice usually deviate from the frequency. They are all uncertain variables whose distributions are estimated from the empirical data of experts or managers. In this paper, we give three decentralized game models to explore the equilibrium behaviors in the corresponding decision environment under an uncertain environment. Corresponding analytical solutions are offered under different game scenarios. Finally, numerical experiments are performed to illustrate the effectiveness of the established models and yield some remarkable insights.

Determination and correlation of LLE data for n-hexane, ethyl acetate and different extractants

In order to separate n-hexane/ethyl acetate (EA) produced in industrial production, the liquid–liquid extraction was used to separate the azeotropic system with sulfolane, 1,2-propanediol and dimethyl sulfoxide (DMSO) as extractants. The liquid–liquid equilibrium (LLE) data of the n-hexane + EA + sulfolane/1,2-propanediol/DMSO were measured at 303.15 K, 313.15 K and 323.15 K. The extraction capacity of the extractants were evaluated by the distribution coefficient (D) and separation factor (S). The LLE data were correlated using the NRTL and UNIQUAC thermodynamic models to obtain binary interaction parameters. The root mean square deviation (RMSD) were all less than 0.02 indicating that the two models were suitable for the phase equilibrium behavior. GUI-MATLAB software was used to test the reliability of the regressed binary interaction parameters. The Dmol3 module of the Materials Studio was used to analyze σ-profile of n-hexane, EA and extractants and to assess the interaction energy between the components. The results show that sulfolane is the best extractant for the separation of n-hexane + EA.

Pivoting and pandemics: A game-theoretic framework for agile personal protective equipment supply chains

Supply chain models frequently tackle manufacturing issues but must also account for the distinctive nature of the disease. Conversely, most epidemiological models solely concentrate on the disease’s spread but must address logistical challenges. The medical supply chain encounters numerous problems during a pandemic, requiring adaptation through pivoting strategies. For instance, when the COVID-19 outbreak began, several nations prohibited the export of medical supplies, including personal protective equipment (PPE). Consequently, in times of crisis, many countries adopt a localization strategy that encourages domestic companies to adapt their operations and produce medical items. Nevertheless, an interconnected system is essential to align suppliers with the actual demand for medical supplies. This study focuses on the design of a game model for the supply chain that considers manufacturers’ equilibrium behaviors in response to the real demand for medical items. We propose a game model that incorporates both the medical supply chain and the unique characteristics of pandemics. Various decisions are taken into account, such as production volume, actual demand for medical products, price, distribution of medical supplies, and investment costs in manufacturing technologies. To determine the Nash Equilibrium solutions for the proposed game model, the Variational Inequality (VI) theory is implemented.

Persistence in a dynamic moral hazard game

This paper explores how the persistence of past choices creates incentives in a continuous time stochastic game involving a large player (e.g., a firm) and a sequence of small players (e.g., customers). The large player faces moral hazard and her actions are distorted by a Brownian motion. Persistence refers to how actions impact a payoff‐relevant state variable (e.g., product quality depends on past investment). I characterize actions and payoffs in Markov perfect equilibria (MPE) for a fixed discount rate, show that the perfect public equilibrium (PPE) payoff set is the convex hull of the MPE payoff set, and derive sufficient conditions for a MPE to be the unique PPE. Persistence can serve as an effective channel for intertemporal incentives in a setting where traditional channels fail. Applications to persistent product quality and policy targeting demonstrate the impact of persistence on equilibrium behavior.

Passive fractionating mechanism for oil spill using shear-wettability modulation.

Oil spillage and organic solvent leakage have been a frequent occurrence in recent years, which pose a significant threat not only to the aquatic ecosystems but also result in substantial economic burdens. This has necessitated the search for materials capable of separating oil from water at enhanced efficiency with superior mechanical and thermal properties. In this study, we conduct a set of systematic molecular dynamics simulations to investigate the potential of two-dimensional graphene-like channels under extreme confinement to achieve efficient oil-water separation. Effective modulation of the wetting characteristics of graphene-like surfaces juxtaposed with unconventional flow behavior at the nanoscale unveils differential interaction of water and oil molecules towards the wall, thereby resulting in distinct separation zones for varying compositions of the oil-water mixture. Such separation zones have been observed to be highly correlated with mixture temperature, which provides effective separation pathways across diverse environmental conditions. Our study offers a paradigm shift in oil-water separation strategies, which not only provides deeper insights into the equilibrium and dynamic behavior of a two-phase mixture but also holds immense implications for the development of smart, wettability-based oil separation devices.

Asymmetric all‐pay auctions with spillovers

When opposing parties compete for a prize, the sunk effort players exert during the conflict can affect the value of the winner's reward. These spillovers can have substantial influence on the equilibrium behavior of participants in applications such as lobbying, warfare, labor tournaments, marketing, and R&D races. To understand this influence, we study a general class of asymmetric, two‐player all‐pay auctions where we allow for spillovers in each player's reward. The link between participants' efforts and rewards yields novel effects; in particular, players with higher costs and lower values than their opponents sometimes extract larger payoffs.

Characterization of Loading Rate of CO2 with Mono Ethanol Amine Continuous Reactor Experimentation & Titrimetric CO2 Loading Evaluation

This study delves into leveraging a continuous reactor experiment setup for CO2 Capture using Mono Ethanol Amine (MEA). A series of experiments were conducted utilizing various concentrations of MEA from 10% to 30% wt/wt under controlled conditions to determine their CO2 loading rates. The continuous reactor system offered insights into the kinetics and equilibrium behaviours of the MEA-CO2 interaction. The CO2 loading with MEA solvents is estimated using a titrimetric method, the UOP 829-821 which consumes less resources for research in a laboratory setup. This enabled repetitive and reciprocal loading rate assessments of CO2 loading rate analysis with MEA solvents. The CO2 content in the experimented amine samples ranged from 0.13 to 0.45 mol CO2 / mol MEA while varying the CO2 concentration between 10% to 20% and MEA Concentration from 10% to 30% for a range of absorption time periods. The CO2 loading performance showed only a marginal performance improvement was found between 20% and 30% MEA concentration. The results of this study can help pave pathways for more efficient MEA based CO2 Capture Technologies.

Shape anisotropy induced jamming of nanoparticles at liquid interfaces: a tensiometric study.

The intersection of nanotechnology and interfacial science has opened up new avenues for understanding complex phenomena occurring at liquid interfaces. The assembly of nanoparticles at liquid/liquid interfaces provides valuable insights into their interactions with fluid interfaces, essential for various applications, including drug delivery. In this study, we focus on the shape and concentration effects of nanoscale particles on interfacial affinity. Using pendant drop tensiometry, we monitor the real-time interfacial tension between an oil droplet and an aqueous solution containing nanoparticles. We measure two different types of nanoparticles: spherical gold nanoparticles (AuNPs) and anisotropic gold nanorods (AuNRs), each functionalized with surfactants to facilitate interaction at the interface. We observe that the interface equilibrium behaviour is mediated by kinetic processes, namely, diffusion, adsorption and rearrangement of particles. For anisotropic AuNRs, we observe shape-induced jamming of particles at the interface, as evidenced by their slower diffusivity and invariant rearrangement rate. In contrast, the adsorption of spherical AuNPs is dynamic and requires more time to reach equilibrium, indicating weaker interface affinity. By detailed analysis of the interfacial tension data and interaction energy calculations, we show that the anisotropic particle shape achieves stable equilibrium inter-particle separation compared to the isotropic particles. Our findings demonstrate that anisotropic particles are a better design choice for drug delivery applications as they provide better affinity for fluid interface attachment, a crucial requirement for efficient drug transport across cell membranes. Additionally, anisotropic shapes can stabilize interfaces at low particle concentrations compared to isotropic particles, thus minimizing side effects associated with biocompatibility and toxicity.

Numerical investigation of heterogeneous soft particle pairs in inertial microfluidics.

The formation of pairs of particles or cells of different types in microfluidic channels can be desired or detrimental in healthcare applications. It is still unclear what role softness heterogeneity plays in the formation of these particle pairs. We use an in-house lattice-Boltzmann-immersed-boundary-finite-element solver to simulate a pair of particles with different softness flowing through a straight channel with a rectangular cross-section under initial conditions representative of a dilute suspension. We find that softness heterogeneity significantly affects the pair dynamics, determining whether a pair will form or not, and determining the lateral and inter-particle equilibrium behaviour in the pair. We also observe close matches between the transient deformation of particles in a linear pair and single particles in isolation. These results further our understanding of pair behaviour, providing a foundation for understanding particle train formation, and open up the potential to develop reduced-order models for particle pair formation based upon the behaviour of single particles.

Decontamination of Congo red dye from aqueous solution using nanoclay/chitosan-graft-gelatin nanocomposite hydrogel

In this study, bentonite nanoclay (BNC) impregnated chitosan-g-gelatin (CS-g-GEL/BNC) nanocomposite hydrogels were prepared with multi-features including being cost-effective, high-performance, biodegradable, and easy to separate for Congo red (CR) dye adsorption. Various characterization techniques, including FTIR, XRD, SEM, TGA, and EDX, were used to verify the successful formulation of the prepared hydrogels. The results revealed that the thermal stability of CS-g-GEL/BNC nanocomposite hydrogel was improved compared to CS-g-GEL hydrogel. CR dye also reached its equilibrium adsorption quickly and effectively at 60 min. When bentonite clay nanoparticles content was increased to 10 %, the removal efficiency increased to 70.41 %, which was significantly greater than 43.20 % for CS-g-GEL hydrogel. The maximum removal and adsorption capacity of 93.85 % and 453.87 mg/g was achieved at the optimal conditions of the adsorption process (pH = 9, an adsorbent dosage of 2 g/L, a temperature of 25 °C for 60 min, and a CR concentration of 100 mg/L). The results in thermodynamics indicated spontaneous adsorption from negative Gibbs free energy (ΔG°). Also, the analysis of the thermodynamics of the adsorption process resulted in an adsorption enthalpy (ΔH°) of − 21.8699 kJ/mol, which shows its spontaneous and exothermic nature at temperatures ranging from 25 °C to 45 °C. An equilibrium behavior of adsorption was successfully described using the Langmuir isotherm model. Compared with the pseudo-second-order, intra-particle, and Elovich models, the pseudo-first-order model gave a better description of the adsorption kinetics. CS-g-GEL/BNC nanocomposite hydrogels demonstrated enhanced reusability over five successive cycles, indicating potential application in adsorptive removal from aquatic environments contaminated with anionic dyes.

Deep-sea Ordovician lingulide brachiopods and their associated burrows suggest an early colonization of proximal turbidite systems

Trace fossils from Ordovician deep-marine environments are typically produced by a shallow endobenthos adapted to live under conditions of food scarcity by means of specialized grazing, farming, and trapping strategies, preserved in low-energy intermediate to distal zones of turbidite systems. High-energy proximal zones have been considered essentially barren in the early Paleozoic. We report here the first trace and body fossils of lingulide brachiopods in deep-marine environments from an Upper Ordovician turbidite channel-overbank complex in Asturias, Spain. Body and trace fossils are directly associated, supporting the interpretation of a lingulide tracemaker. Ellipsoidal cross-section, cone-in-cone spreite, and spade morphologies suggest the specimens belong to Lingulichnus verticalis. The oblique orientation in both trace and body fossils is the result of tectonic deformation. The organisms were suspension feeders showing escape, dwelling, and equilibrium behaviours controlled by sedimentation rates associated with turbidite deposition. These trace fossils and their in situ producers represent the oldest evidence of widespread endobenthos colonization in high-energy, proximal areas of turbidite systems, expanding the bathymetric range of Lingulichnus and the variety of behaviours and feeding styles in early Paleozoic deep-marine environments.

Phase equilibrium behaviors of chiral threonine: Phase diagrams, solubility, and thermodynamic model correlations

Phase equilibrium behaviors of chiral racemic threonine, as well as D-Threonine and L-Threonine, have been systematically investigated. The PXRD patterns, DSC, and ternary phase diagram exhibited the typical characteristics of the conglomerate. As an essential basis for ternary phase diagrams, the solubility of D-Threonine, L-Threonine, and the racemic mixture was measured at a temperature range from 283.15 K to 308.15 K in both water/methanol and water/ethanol mixtures. The solubility of a single enantiomer was at a range from 1.08 to 2.23 (S, wt%) in water/methanol = 6/4 v/v and from 0.36 to 0.91 (S, wt%) in water/methanol = 4/6 v/v. The racemate exhibited a double solubility of the single enantiomer. Subsequently, the experimental solubility data showed promising correlations with five thermodynamic models: Jouyban-Acree equation, Machatha model, the modified Apelblat model, Wilson model, and NRTL model. The modified Apelblat model was the best-fit model when the temperature was primarily considered. Whereas Jouyban-Acree model demonstrated better alignment when the solvent composition was mainly regarded. Besides the above approaches for the determination of chiral drug systems, the results were analyzed in the different characteristics between the racemate and the single pure enantiomer. Selecting the appropriate model to correlate with solubility data can facilitate the exploration of the ternary phase diagram of chiral drugs under different conditions, thus favoring the subsequent enantiomeric separation and industrial production.

Measurements and modeling of liquid–liquid equilibrium for epichlorohydrin, water, and different extractants at 303.2 K

In order to remove epichlorohydrin from wastewater, liquid–liquid equilibrium behaviors in the systems {water + epichlorohydrin + solvents (1-hexanol/1-heptanol/2-octanol/1-nonanol)} were determined at 303.2 K under101.3 kPa. The partition coefficients and separation factors in each system were used to compare and discuss the effects of extraction. The σ-profiles were used to discuss the interactions of substances in this work. The experimental data were correlated with the NRTL and UNIQUAC models, to obtain the binary interaction parameters required for each system. The GMcal_TieLinesLL GUI tools were applied to verify the consistency of the binary interaction parameters.

Modeling of thermophysical properties and vapor-liquid equilibrium using Gaussian process regression

Thermophysical properties are essential in the numerical simulation of fluid flows and combustion in propulsion and power-generation systems. Existing property evaluation tools, such as NIST REFPROP, analytical methods based on cubic equations of state (EOSs), and deep neural network (DNN) models, tend to be inaccurate against experimental data in certain thermodynamic regions. The objective of this paper is to develop data-driven models based on Gaussian process regression (GPR), which correlates directly with experimental data in a statistical manner and can accurately predict thermodynamic and transport properties and vapor-liquid equilibrium (VLE) behavior across the entire range of thermodynamic regions. Different kernel functions in GPR training are examined for various data types. As specific examples, experimental property data of carbon dioxide and VLE behavior of four binary mixtures are collected extensively from literature for training and validation of GPR models. Besides, physical constraint is incorporated during the training process of VLE behavior via logit transformation. The results show that GPR with exponential kernel presents excellent performance for evaluation of density, constant-pressure specific heat, speed of sound, and viscosity, with prediction errors substantially lower than those of Peng-Robinson (PR) EOS, NIST REFPROP, and DNN models. GPR with Gaussian kernel shows minimal errors (less than 0.6%) for determination of saturation pressure and gas-phase composition against experimental counterparts for VLE of hydrocarbon/nitrogen binary mixtures. The developed GPR models can be programmed and incorporated into large-scale simulations to achieve more reliable calculations of practical fluid flows where real-gas effect is important.

When and how to introduce upstream competition in an innovation supply chain

Considering an innovation supply chain with a primary supplier involvement in the new product development of a downstream manufacturer who sells to consumers, we address when and how to introduce a secondary supplier by applying order commitment besides innovation quality-dependent contract and revenue-sharing contract. Our results show that the secondary supplier should be invited after the new product development is achieved. The innovation quality-dependent order commitment contract can improve the innovation quality of the supply chain. The innovation quality-dependent wholesale price contract warrants the supplier's innovation quality to keep the same level as the single-supplier supply chain and improves the primary supplier's profit. The incentive effect of a revenue-sharing contract on the supplier's innovation quality is more substantial when introducing a secondary supplier after new product development than before. Furthermore, the negative effect of the supplier's competition on innovation quality and profit of the manufacturer can be alleviated by wholesale price decision-making power consignment. We also provide rich managerial insights into supplier involvement in new product development practices by analyzing the equilibrium behaviors and numerically simulating significant decision variables concerning the demand sensitivity to innovation quality.

Optimal control of deterministic and stochastic Eco-epidemic food adulteration model

In this paper, we develop a deterministic and stochastic mathematical model to study the effect of contaminated foods on human health by spreading media awareness. A predator–prey SI model with media-induced response function is considered. In the deterministic case, the model has three equilibria: trivial, disease-free, and endemic. While the endemic equilibria exist for low media impact provided R0>1. Here, the trivial equilibrium is always unstable. However, the disease-free equilibrium exhibits local and global asymptotically stable behavior provided that R0<1. The conditions for the local behavior of endemic equilibrium are also determined along with the existence of Hopf bifurcation. Further, the impact of external interference is studied for the stochastic model. The stochastic model has a unique global positive solution which is ultimately bounded. The stochastic model also demonstrates asymptotic behavior around disease-free and endemic equilibria. Additionally, optimal control theory has been employed to explore deterministic and stochastic optimal control systems in depth. Finally, the analytical results are validated using some numerical simulations.

Abstract 18049: Mathematical Modeling Predicts Treatment Efficacy in Transthyretin Cardiac Amyloidosis

Introduction: Increased recognition of transthyretin cardiac amyloidosis (ATTR-CA) led to the development of treatments with different therapeutic targets. Optimal patient selection, treatment choice, timing and duration remain unclear. We evaluated the efficacy and timing of common and emerging ATTR-CA treatments with a mathematical model based on therapeutic mechanisms. Methods: We developed a system of ordinary differential equations describing transthyretin amyloid (ATTR) deposition and myocardial clearance by clusterin (Figure 1A,B). Published data and equilibrium analyses determined parameters for initial maximal ATTR density. Mechanisms of four therapies were modeled and simulated at varying levels of efficacy. Complete success of the mechanism defines 100% efficacy, i.e. full stabilization of tetramer. Expected clinical efficacy (ECE) is based on studies of clinical doses. Minimum effective clearance (MEC) is the theoretical efficacy required to reduce ATTR fibrils below the threshold for complete clearance. Results: All treatments reduced ATTR fibril density, correlating with efficacy (Fig 1C). At ECE, only NI006 demonstrated complete clearance of ATTR fibrils. With other current treatment strategies, amyloid density will be lowered but never cleared. The secondary mechanism of diflusinil did not change equilibrium behavior compared to tafamidis. MEC values and time to clearance at MEC were lowest for NI006 (14.7%; 65 days) and doxycycline (16.1%; 36 months). Tetramer stabilization required almost complete efficacy (99.3%) and about a decade (119 months) for tetramer clearance. Conclusion: This mathematical model predicts ATTR clearance by four distinct mechanisms of action. The novel anti-ATTR antibody NI006 is a promising treatment with predicted faster onset and higher effectiveness for clearance of ATTR fibrils from the myocardium. This model can evaluate future treatment strategies and therapeutic targets.

Spatiotemporal dynamics of a multi-delayed prey-predator system with variable carrying capacity.

This paper presents the temporal and spatiotemporal dynamics of a delayed prey-predator system with a variable carrying capacity. Prey and predator interact via a Holling type-II functional response. A detailed dynamical analysis, including well-posedness and the possibility of coexistence equilibria, has been performed for the temporal system. Local and global stability behavior of the co-existence equilibrium is discussed. Bistability behavior between two coexistence equilibria is demonstrated. The system undergoes a Hopf bifurcation with respect to the parameter β, which affects the carrying capacity of the prey species. The delayed system exhibits chaotic behavior. A maximal Lyapunov exponent and sensitivity analysis are done to confirm the chaotic dynamics. In the spatiotemporal system, the conditions for Turing instability are derived. Furthermore, we analyzed the Turing pattern formation for different diffusivity coefficients for a two-dimensional spatial domain. Moreover, we investigated the spatiotemporal dynamics incorporating two discrete delays. The effect of the delay parameters in the transition of the Turing patterns is depicted. Various Turing patterns, such as hot-spot, coldspot, patchy, and labyrinth, are obtained in the case of a two-dimensional spatial domain. This study shows that the parameter β and the delay parameters significantly instigate the intriguing system dynamics and provide new insights into population dynamics. Furthermore, extensive numerical simulations are carried out to validate the analytical findings. The findings in this article may help evaluate the biological revelations obtained from research on interactions between the species.

Hide-and-Seek Game with Capacitated Locations and Imperfect Detection

We consider a variant of the hide-and-seek game in which a seeker inspects multiple hiding locations to find multiple items hidden by a hider. Each hiding location has a maximum hiding capacity and a probability of detecting its hidden items when an inspection by the seeker takes place. The objective of the seeker (respectively, hider) is to minimize (respectively, maximize) the expected number of undetected items. This model is motivated by strategic inspection problems, where a security agency is tasked with coordinating multiple inspection resources to detect and seize illegal commodities hidden by a criminal organization. To solve this large-scale zero-sum game, we leverage its structure and show that its mixed-strategy Nash equilibria can be characterized using their unidimensional marginal distributions, which are pure equilibria of a lower dimensional continuous zero-sum game. This leads to a two-step approach for efficiently solving our hide-and-seek game: First, we analytically solve the continuous game and derive closed-form expressions of the equilibrium marginal distributions. Second, we design a combinatorial algorithm to coordinate the players’ resources and compute equilibrium mixed strategies that satisfy the marginal distributions. We show that this solution approach computes a Nash equilibrium of the hide-and-seek game in quadratic time with linear support. Our analysis reveals novel equilibrium behaviors driven by a complex interplay between the game parameters, captured by our closed-form solutions. Funding: This work was supported by the Georgia Tech Stewart Fellowship and the Georgia Tech New Faculty Start Up Grant. Supplemental Material: The online appendix is available at https://doi.org/10.1287/deca.2023.0012 .