Final Equilibrium Research Articles

LETTER FROM THE EDITOR

LETTER FROM THE EDITOR

Correlation functions and their universal connection during an extremely slow equilibration process.

We study the equilibration process of a one-dimensional lattice with transverse motions and external magnetic field. Starting from certain initial states, the system commonly reaches a metastable transient state shortly and then stays there for an extremely long time before it finally arrives in the ergodic equilibrium state. The relaxation time T_{eq} diverges even much more rapidly than exponential, which, compared with the widely reported power-law or even exponential divergence in many other systems, implies much higher stability of the transient state. Two correlation functions, the spatiotemporal correlation of the local energy and the autocorrelation of global heat current, are studied in both the metastable transient and the final equilibrium states. It is revealed that the correlations behave entirely differently in the two different states. In the former case they suggest normal heat diffusion and normal heat conduction; whereas in the latter one they indicate super heat diffusion and anomalous heat conduction. More importantly, we confirm that a general relation which connects the two correlations keeps valid not only in the equilibrium state but in the metastable transient state as well. The universality of the connection is, thus, extended.

Holographic topological defects in a ring: role of diverse boundary conditions

We investigate the formation of topological defects in the course of a dynamical phase transition with different boundary conditions in a ring from AdS/CFT correspondence. According to the Kibble-Zurek mechanism, quenching the system across the critical point to symmetry-breaking phase will result in topological defects — winding numbers — in a compact ring. By setting two different boundary conditions, i.e., Dirichlet and Neumann boundary conditions for the spatial component of the gauge fields in the AdS boundary, we achieve the holographic superfluid and holographic superconductor models, respectively. In the final equilibrium state, different configurations of the order parameter phases for these two models indicate a persistent superflow in the holographic superfluid, however, the holographic superconductor lacks this superflow due to the existence of local gauge fields. The two-point correlation functions of the order parameter also behave differently. In particular, for holographic superfluid the correlation function is a cosine function depending on the winding number. The correlation function for the holographic superconductor, however, decays rapidly at short distances and vanishes at long distance, due to the random localities of the gauge fields. These results are consistent with our theoretical analysis.

Geotechnical Issues in Decommissioning Surface Lignite Mines—The Case of Amyntaion Mine in Greece

Recent changes in the fossil-fuel energy sector require coal mining industries to plan for the future, including developing procedures for decommissioning and closure associated with mines. In surface coal mining, the geotechnical issues of decommissioning include the long-term stability of the pit slopes, particularly as the pit is gradually filled with water. This paper investigates such slope stability issues, with emphasis on the conditions prevailing in the Amyntaion surface lignite mine, in Western Macedonia, Greece. Analytical and numerical methods have been developed and used to estimate the temporal evolution of the overall safety factor, as the water level in the pit rises, creating a lake. It is shown that until the water level in the lake reaches a critical depth of approximately 15–35% of the final equilibrium condition, the safety factor against the overall slope instability decreases slightly (by about 3% in the case study, and up to 5–10% in other conditions) compared to its value at the end of exploitation. At higher lake levels, the safety factor increases significantly, as the beneficial effect of the lake water pressure acting on the slope overcomes the adverse effect of pore water pressure rise inside the slope. In typical mines, the critical water depth is achieved within a few years, since the surface area of the pit is smaller at deeper levels; thus, more favorable slope stability conditions are usually reinstated a few years after mine closure, while the small reduction in safety during the initial stages after closure is inconsequential. The paper investigates the parameters influencing the magnitude of the small reduction in the short-term safety factor and produces normalized graphs of the evolution of the safety factor as the lake water level rises. The results of the analyses can be used in preliminary closure studies of surface coal mines.

Henri-Michaelis-Menten kinetics of reversible enzymic reactions, and the determination of rate constants from kinetic constants.

The Michaelis constants derived for two reversible uni-reactant - uni-product reaction models, given originally by Haldane, are corrected. In the direction starting with the reactant having the lower binding constant, the steady state is one in which the enzyme-reactant intermediate has a concentration approximating the final equilibrium concentration., Consequently, the Haldane relationship is generally invalid, and kinetic analyses to validate the use of the kinetic constant ratio (kcat/Km) as a measure of specificity are also generally invalid. This correction of Michaelis constants is pertinent to attempts to back calculate rate constants from experimental values: the Michaelis constant used must be correct.

Experimental Study of Adsorption Characteristics and Deformation of Coal for Different Gases

Coal seam deformation due to gas adsorption affects the stability of the underground structure. Natural coal blocks of the Shanxi Formation were selected to study the dynamic adsorption characteristics of coal samples subjected to CO2, CH4, and N2 gas injections under coaxial pressure and confining pressure (7 MPa), as well as the displacement of CH4 with CO2 and N2 under the same conditions. The results show that, under the same conditions, the strain in the coal samples first increased, followed by a rapid increase along with the increase in pressure, with the transverse strain being always higher than the axial strain. The amount of gas adsorption varied from high to low as CO2 > CH4 > N2, and the final adsorption strains and equilibrium times were different for each gas. Based on the increase in gas pressure, the gas adsorption strain curve can be divided into two stages. The displacement of N2 only uses partial pressure to achieve the desorption of CH4 in the coal sample, leading to shrinkage deformation of the coal sample. In contrast, the displacement of CO2 has the dual effects of competitive adsorption and partial pressure reduction on CH4, leading to the swelling deformation of the coal sample.

The optimal green strategies for competitive ocean carriers under potential regulation

Uncertain green regulation and market competition are two major external environmental factors for ocean carriers to consider when making their decisions on business operations. The uncertainty of the green regulation arises from the probability of its occurrence. It is assumed that ocean carriers can adopt one of the two green strategies, i.e., the equipment upgrade strategy or the slow steaming strategy, to comply with the potential green regulation. This paper aims to examine the stable green strategies as well as the pricing decisions of competitive carriers in the shipping market considering the service differentiation and the upgrade risk. A two-period game model is formulated to seek the sub-game perfect Nash equilibrium under potential regulation. We obtain the final sub-game perfect Nash equilibrium, i.e., when the probability of enacting regulation is sufficiently high, there is always one carrier that will adopt the equipment upgrade strategy. However, because of the joint impact of market competition and uncertain regulation, the two carriers will never adopt the equipment upgrade strategy simultaneously. In addition, our results show that the potential regulation sometimes may help the two carriers achieve the optimal outcome. Nevertheless, the carriers may fall into a “sub-optimal outcome” in some situations.

AN OPTIMAL CONTROL OF SMUGGLING

Existing literature does not capture efficiency losses on the dynamic adjustment path of smuggling control market from initial to final equilibrium after a shock in order to formulate an optimal smuggling control policy. Furthermore, a number of public service units and smuggling control rate are major determinants of smuggling cases controlled in a society, and a policy without taking into consideration such vital determinants cannot ensure adjustment of a number of smuggling cases controlled as a result of cost movement in desired time, which may lead to extra efficiency losses than those envisaged during policy formulation for an optimal level of smuggling control in a society. This article designs a comprehensive optimal smuggling control policy mechanism by modeling a three-dimensional smuggling control system in society capturing the number of public service units, smuggling control rate, and cost, while taking into account efficiency losses during adjustment of smuggling control market, smuggling control rate and the number of public service units in addition to those which result due to movements from initial to final equilibriums.

Study on Final Equilibrium State and Process of CO2 Reacting with Fe–C Melt

Abstract To study the final equilibrium state and process of CO2 injecting into the Fe–C melt with different initial carbon contents, a model was established based on the method of minimization of Gibbs free energy and the corresponding experiments were carried out in a high-temperature tube furnace. When CO2 is continuously injected into the Fe–C melt at 1873 K, the final equilibrium state of the system is such that the carbon and oxygen contents in the melt are 0.1977 and 0.0115 wt pct, respectively, and the volume ratio of CO in the gas phase is 85.75 vol pct. When the initial a [O] × a [C] in the melt is greater than those in equilibrium with CO under 0.8575 atm, the CO2 gas removes carbon from the melt. On the contrary, the role of CO2 gas is to add carbon and oxygen to the melt. At the same time, the variation of carbon and oxygen with time obtained by experiments was different from the theoretical calculation at extremely low carbon content, which requires further study.

Study on the dissociation characteristics of methane hydrate in clayey silts

Most natural gas hydrate (NGH) resources worldwide are in clayey silt sediments. For the efficient production of NGH, a thorough understanding of the dissociation characteristics of NGH in clayey silt is essential. In this work, an experimental method for clayey silt NGH sample preparation and determination of the dissociation conditions has been established. The dissociation conditions of methane hydrate in clayey silt formed at different initial pressures and water contents have been measured, and the dissociation characteristics have been discussed. Methane hydrate is found to form in pores of different sizes in clayey silts. The filling status of the methane hydrate in the clayey silt pores might affect its dissociation characteristics. As the temperature increases, the hydrate in the smaller pores dissociates first, the hydrate in the larger pores dissociates later, and the final equilibrium conditions are consistent with the dissociation conditions of bulk hydrate. As the initial pressure increases or the water content decreases, the proportion of hydrate in the pores increases. When the clayey silt is saturated (water content 37%), hydrate rapidly forms on the surface, forming a mass transfer barrier and preventing further hydrate formation. The hydrate reforms when the hydrate in the small pores of surface sediments dissociates as the temperature increases. The methane hydrate in clayey silt exhibits multistage dissociation and complex reformation characteristics.

Ranked diffusion, delta Bose gas, and Burgers equation.

We study the diffusion of N particles in one dimension interacting via a drift proportional to their rank. In the attractive case (self-gravitating gas) a mapping to the Lieb-Liniger quantum model allows one to obtain stationary time correlations, return probabilities, and the decay rate to the stationary state. The rank field obeys a Burgers equation, which we analyze. It allows one to obtain the stationary density at large N in an external potential V(x) (in the repulsive case). In the attractive case the decay rate to the steady state is found to depend on the initial condition if its spatial decay is slow enough. Coulomb gas methods allow one to study the final equilibrium at large N.

Research on heavy metal release with suspended sediment in Taihu Lake under hydrodynamic condition.

Heavy metals are often stored in the sediment of lakes or reservoirs and are easily released to the overlying water in the case of strong wind, which greatly affects the water environment of lakes or reservoirs. The conventional investigation of heavy metals in lakes has been relatively extensive, but there is no numerical model for heavy metals released into overlying water with suspended sediment under hydrodynamic action. In this paper, laboratory experiments were carried out, and it is found that the concentration of heavy metals (Cr, Cu, Cd) often begins to stabilize after the concentration of total suspended solids (TSS) reaches a stable level. With the increase of flow velocity (3.2 to 14cm/s), the final equilibrium concentration of TSS, Cr, Cu, and Cd will also increase from 174 to 1102mg/L, 0.72 to 1.14μg/L, 2.34 to 10.45μg/L, and 0.13 to 0.35μg/L, respectively. Based on lattice Boltzmann method (LBM), a numerical model of heavy metal released into overlying water under hydrodynamic conditions is established. Compared the simulated data with measured data, the average [Formula: see text] of LBM model can be reached at 0.827, higher than 0.711 of traditional simulation model. The development of the numerical model is conducive to the prediction of lake or reservoir environment and also provides a theoretical basis for heavy metal treatment in reservoirs.

A Protein Corona Modulates Interactions of α-Synuclein with Nanoparticles and Alters the Rates of the Microscopic Steps of Amyloid Formation.

Nanoparticles (NPs) can modulate protein aggregation and fibril formation in the context of amyloid diseases. Understanding the mechanism of this action remains a critical next step in developing nanomedicines for the treatment or prevention of Parkinson's disease. α-Synuclein (α-Syn) can undergo interactions of different strength with nanoparticles, and these interactions can be prevented by the presence of a protein corona (PC) acquired during the exposure of NPs to serum proteins. Here, we develop a method to attach the PC irreversibly to the NPs, which enables us to study in detail the interaction of α-Syn and polyethylenimine-coated carboxyl-modified polystyrene NPs (PsNPs-PEI) and the role of the dynamics of the interactions. Analysis of the kinetics of fibril formation reveals that the NPs surface promotes the primary nucleation step of amyloid fibril formation without significantly affecting the elongation and fragmentation steps or the final equilibrium. Furthermore, the results show that even though α-Syn can access the surface of NPs that are precoated with a PC, due to the dynamic nature of the PC proteins, the PC nevertheless reduces the acceleratoring effect of the NPs. This effect is likely to be caused by reducing the overall amount of weakly interacting α-Syn molecules on the NP surface and the access of further α-Syn required for fibril elongation. Our experimental approach provides microscopic insight into how serum proteins can modulate the complex interplay between NPs and amyloid proteins.

Using Solid Catalysts in Disulfide-Based Dynamic Combinatorial Solution- and Mechanochemistry.

It was shown for the first time that solid amines can act as catalysts for disulfide-based dynamic combinatorial chemistry (DCC) by ball mill grinding. The mechanochemical equilibrium for the two disulfide reactions studied was reached within 1-3 h using ten different amine catalysts. This contrasts with the weeks to months to achieve solution equilibrium for most solid amine catalysts at 2 %mol mol-1 concentration in a 2 mMolar disulfide dynamic combinatorial library in a suitable solvent. The final mechanochemical equilibrium was independent of the catalyst used but varied with other ball mill grinding factors such as the presence of traces of solvent. The different efficiencies of the amines tested were discussed.

Composition-dependent mechanical property changes and damage recovery in He-ion-irradiated borosilicate glasses

This study explored the mechanical property changes in three kinds of pristine and Au3+ pre-irradiated Na2O-B2O3-SiO2 (labeled as NBS) glasses induced by 0.5-MeV He2+ ions over a broad fluence range. The glass samples were prepared with different R values = [Na2O]/[B2O3] (0.40, 0.75 and 1.34). After He-ion irradiation, the hardness diminished and finally reached saturation, the modulus showed a slight decrease for the NBS1 and NBS2 glasses, but the NBS3 glass exhibited no significant change. The mono He2+ ion irradiation scenario did not show the self-recovery effect of Au3+ ion irradiation scenario. The sequential He-ion irradiation can lead to damage recovery in the Au-ion pre-irradiated glasses. The final equilibrium state was affected by the composition of pristine glass, which can be attributed to lower thermal stability and the phase separation characteristic of NBS3 glass. Such results hold great significance for understanding the radiation damage caused by multiparticle irradiation in the glass matrix of nuclear wastes.

THE TRANSIENT EFFECTS OF FLOOD WATER ON A WARSHIP IN CALM WATER IMMEDIATELY FOLLOWING DAMAGE

The safety of a ship which is damaged below the waterline will depend on the way water floods into the internal compartments. The water will cause the ship to take on an angle of heel and trim which will further affect the flooding into the compartments. The ship’s equilibrium position in calm water can be predicted using hydrostatic theory, however at present it is difficult to predict the transient behaviour between the initial upright position of the ship and its final equilibrium. In some cases, the transient motion may cause a capsize prior to a possible equilibrium position being reached.
 This paper describes an investigation of this phenomenon using a model of a warship with simplified, typical internal geometry. With the model initially stationary, a rapid damage event was generated, and the global motions measured, along with the water levels in some of the internal compartments, as functions of time. Immediately after the damage occurred the model rolled to starboard (towards the damage). It then rolled to port (away from the damage) before eventually returning to starboard and settling at its equilibrium value. In all the tests conducted the equilibrium heel angle was less than that reached during the initial roll to starboard. This implies that the roll damping, and the way in which the water floods into the model immediately following the damage, could both have a very important influence on the likelihood of survival.

Effect of initial aluminium-oxygen concentration product on alumina-based inclusions in high carbon Al-killed steels during the ladle refining process

ABSTRACT The effect of different aluminium-oxygen concentration products at the start of deoxidation on the evolution of alumina-based inclusions in high carbon Al-killed steels during the ladle refining process was investigated. Results showed that the higher aluminium-oxygen concentration product at the start of deoxidation, the higher area fraction and the number density of large-sized inclusions before the slag melting, then clustered alumina-based inclusions gradually became ripening. Thermodynamic equilibrium results indicated that initial contents of the [O] were 100, 200, 300 and 400 ppm in the molten steel, then contents of the [O] at the final reaction equilibrium were 4.6, 4.9, 5.8 and 9.5 ppm, respectively. The relationship between oversaturation and size of Al2O3 inclusions showed that the larger the critical radius of nucleus, the lower the oversaturation. Meanwhile, the evolution mechanism of alumina-based inclusions during the LF refining process was also revealed.

Operational decisions and game analysis in the agricultural supply chain: invest or not?

PurposeWith the rapid growth of the economy, people have increasingly higher living standards, and although people simply pursued material wealth in the past, they now pay more attention to material quality and safety and environmental protection. This paper discusses the lack of motivation for investing in fresh-keeping technology for agricultural products by individual members of an agricultural supply chain composed of a supplier and a retailer by means of mathematical models and data simulations and discuss the optimal price-invest strategies under different sales models.Design/methodology/approachFirst, based on the model of no investment by both sides (NN), this paper considers three models: supplier only (MN), retailer only (NR) and cooperative investment (MR). Then, the authors analyze the influence of consumer price sensitivity and freshness sensitivity on the investment motivation of agricultural products under four models. Subsequently, the paper makes a sensitivity analysis of the optimal strategies under several models, and makes a game analysis of the suppliers and retailers of agricultural products. Finally, we conduct an empirical analysis through specific values.FindingsThe results show that (a) when the two sides cooperate, the amount of investment is largest, the freshness of the agricultural products is highest, and the sales volume is greatest; however, when both sides do not invest, the freshness of agricultural products and sales volume are lowest. (b) The price and freshness sensitivity of the consumer have an impact on investment decisions. Greater freshness sensitivity corresponds to a higher investment, higher agricultural product price, greater sales volume, and greater supply chain member income and overall income; however, greater price sensitivity corresponds to a lower investment, lower agricultural product price, lower sales volume, fewer supply chain members and lower overall income. (c) The investment game between the supplier and retailer is not only related to the sensitivity to price and freshness but also to the coordination coefficients of interest. At the same time, the market position of agricultural products should be considered when making decisions. The market share of agricultural products will affect the final game equilibrium and then affect the final benefit of the supply chain and individual members.Practical implicationsThese results provide managerial insights for enterprises preparing to invest in agricultural products preservation technology.Originality/valueAt present, the main problem is that member enterprises of agricultural supply chains operate based on their own benefits and are resistant to investing alone to improve the freshness of agricultural products. Instead, they would prefer that other members invest so that they may reap the benefits at no cost. Therefore, the enterprises in each node of the agricultural product supply chain are not motivated enough to invest, and competition and game states are observed among them, and such behavior is definitely not conducive to improving the freshness of agricultural products. However, the current research on agricultural products is more about price, quality and greenness, etc., and there are few studies on agricultural investment. Through the establishment of the model, this paper is expected to provide theoretical suggestions for the supply chain enterprises that plan to invest in agricultural products preservation technology.

Cinética de extracción acuosa de compuestos fenólicos a partir de hojas de yerba mate elaborada

In this study, the kinetics of aqueous extraction of phenolic compounds from the yerba mate leaves were analyzed. A temperature range between 40°C and 70°C and a ratio of 25 g of mate leaves in 200 mL of water were used. The extraction kinetic was studied adjustment of the kinetics models of first order, second order kinetic model and the second order diffusive model. The goodness of the fit was controlled by the magnitude of the coefficient of determination (R2), the percentage error (EP %) and the square root of the mean square error (RMSE).The second order kinetic models adequately described the extraction process, achieving the best fit with the second order diffusive model (EP%= 0,81 to 2,9; EP%= 11,24 to 14,99 and 4,72 and 6,92) that provided important information about the initial extraction process and the mechanism that occurs in the final extraction stage. The temperature influenced the kinetic parameters; however, the final equilibrium concentration of phenolic compounds was not affected by it. The results of this study allow us to obtain better overall knowledge of the times and temperatures for improved extraction rates and energy consumption for the industrialization of these compounds.

Wetting properties and morphological behavior of core-shell polymer-based nanoparticle coatings

The glass transition temperature (Tg) strongly affects the physicochemical properties of a polymer. In particular, coating a material with polymer nanocapsules with two or more Tg values can endow the material with variety of properties. We introduced polymer nanocapsules onto glass substrates and analyzed the effect of polymer Tg on the surface properties of the coating. Core-shell polymer (CSP) particles were prepared by a two-step emulsion polymerization procedure using poly(methyl methacrylate) (PMMA, Tg = 105 °C) and poly(butyl acrylate) (PBA, Tg = −54 °C) in different ratios as cores, and poly(nonafluorohexyl acrylate) (PNFHA, Tg = −6 °C) as shells. The microstructural and microbehavioral properties of the coating surface were found to depend on the Tgs of the synthesized CSP. Surface elemental distributions and chemical bonding were analyzed by XPS depth profiling to determine the behavior of the CSP nanoparticles. A core/shell nanoparticle with Tg = 55.81/−9.12 °C has a high probability of its core becoming located at the coating surface. On the other hand, a core/shell nanoparticle with Tg = −33.17.81/−28.6 °C has a high probability of its shell becoming located at the surface. Because the shell has a low surface energy, test solutions with a variety of surface tensions exhibited low wettabilities. These results allow the Tg values of the CSP to access the final thermodynamic equilibrium state, reveal that the Tg values affect the surface distribution of the functional groups of the coatings, which in turn determine its surface morphology and wetting properties.