Initial Equilibrium Research Articles

Understanding of thermal-hydraulic instabilities and the mutual interactions at supercritical pressure

In the present work, a steady state and a simple transient models are integrated to simulate various thermal-hydraulic (TH) static and dynamic instabilities in a single vertical channel, subjected to time independent power, for supercritical fluid (SCF). The scheme of U.S. supercritical water reactor (SCWR) design is analyzed for different TH instabilities and the mutual interactions of such instabilities. An in-house steady state TH model, which solves a set of nonlinear coupled mass, momentum and energy conservation equations accounting for the pressure and enthalpy dependent thermodynamic equation of state, is implemented to find the solution at the initial equilibrium condition. The steady state model is then validated against the recently available experimental results. Next, the simple transient model is integrated with the steady state model to simulate Ledinegg excursion, pressure drop oscillations (PDOs), density wave oscillations (DWOs), and the mutual interactions of each other in presence as well as in absence of a surge tank at the upstream of the heated section. A number of simulations are carried out considering various typical pump (external) characteristic curves. Results provide the understanding what are the different operational criteria on which the Ledinegg excursion, PDOs and DWOs, or the interactions of the aforementioned TH instabilities will depend.

Measurement and modeling of temperature evolution during methane desorption in coal

The decrease of coal temperature has been confirmed by many tests during methane desorption in coal, including coal and gas outburst, but the thermal-dynamic process for methane desorption has not been quantitatively studied. Therefore, firstly, the coal temperature and gas pressure are measured by temperature and pressure sensors in the process of methane desorption. Secondly, isosteric heats of adsorption are calculated according to the adsorption isotherm. Finally, heat transfer model is established and simulate the temperature evolution during methane desorption in coal under different conditions (initial temperature and gas pressure). The real tests and simulation results show that a lot of heat will be absorbed from coal as methane desorbing, which causes the coal temperature will go down by 5.5 K, and methane desorption is no longer isothermal process. In the initial stage of methane desorption in coal, the coal temperature will decrease sharply to an extremely low value, then slowly rise to the previous ambient temperature. And at the same ambient temperature, the higher the initial methane equilibrium pressure is, the larger the temperature at the coal body center drops in the process of methane desorption. In the coal body, the farther away from the wall of the coal sample canister, the more significant the decrease of the coal body temperature is, and the longer the time is to reach extremely low value, which is mainly due to the different heat transfer coefficients at different positions in the coal body. The total specific power, which is a key index in heat transfer model to simulate the change of coal temperature, sharply decreases during methane desorption, because the methane desorption quantity in unit time decreases gradually. This study has an important practical significance to reveal the evolution mechanism of coal and gas outburst, and predict outburst with temperature change as an index.

Biosorption mechanisms of cationic and anionic dyes in a low-cost residue from brewer’s spent grain

ABSTRACT The brewer's spent grain (BSG) is a byproduct of the brewing industry produced in large quantities and with few ecological disposal options. The use of this low-cost residue was investigated for the removal of methylene blue (MB) and tartrazine yellow (TY) dyes. The BSG has been extensively characterized to obtain its physicochemical characteristics. Batch experiments were conducted to investigate the effects of biosorption parameters: initial pH, kinetics, equilibrium isotherms and adsorption thermodynamics. The characterization showed high carbon content and heterogeneous morphology with the presence of meso and macropores. The best experimental conditions were obtained as pH 11 for MB and pH 2 for TY. Kinetics resulted in an equilibrium time of 240 min for MB and 300 min for TY and was best represented by the pseudo-second order model. Different interaction mechanisms were suggested, such as electrostatic interactions, electron donors and electron acceptors, hydrogen bonds, π–π dispersion interactions and the dye molecules aggregation. Equilibrium data were better represented by Langmuir isotherm. The maximum adsorbed amount of MB and TY was 284.75 and 26.18 mg/g, respectively, in each better experimental condition. Through the thermodynamic analysis, it was observed that the adsorption of the dyes was spontaneous and favourable. MB is preferentially retained through chemisorption, whereas TY followed a physical process. Considering the characteristics and results found compared to the recent literature, it was verified that BSG can be used as an effective and innovative biosorbent for removal purposes of dyeing effluent.

Introduction and Validation of the APEC Code for the Simulation of Plasma Equilibrium and Evolution in the Presence of 3-D Passive Structures

Recently, a novel code for the simulation of the plasma equilibrium and its evolution has been developed and fully implemented in ANSYS. We named it ANSYS Plasma Equilibrium and Evolution Code (APEC). It is based on the solution of the Grad–Shafranov equation and exploits the finite-element method using the magnetic potential vector formulation. In this article, we present a further development on the coupling of the axisymmetric plasma equilibrium equations, describing the plasma behavior, with the full 3-D eddy current equations, defining the surrounding 3-D structures. One test case, related to the International Thermonuclear Experimental Reactor (ITER) tokamak, has been fully analyzed and benchmarked with a validated code showing the validity of the proposed approach. In particular, the benchmark has concerned the comparison of the initial equilibrium and plasma evolution.

Wealth distribution models with regulations: Dynamics and equilibria

Simple agent based exchange models are a commonplace in the study of wealth distribution in an artificial economy. Generally, in a system that is composed of many agents characterized by their wealth and risk-aversion factor, two agents are selected sequentially and randomly to exchange wealth, allowing its redistribution. Here we analyze how the effect of social protection policies, which favor agents of lower wealth during the exchange, influences the stability and some relevant economic indicators of the system. On the other hand, we study how periods of interruption of these policies produce, in the short and long term, changes in the system. In all cases, a steady state is reached, but with varying relaxation times. We conclude that regulations may improve economic mobility and reduce inequality. Moreover, our results indicate that the removal of social protection entails a high cost associated with the hysteresis of the distribution of wealth. Economic inequalities increase during the period without social protection and decrease when they are restored. But recovery to the initial equilibrium may take longer than it took to disturb it. In some extreme cases, inequality is irreversible.

Stability of a Sandwich Cylindrical Shell with Core Subject to External Pressure and Pressure in the Inner Cylinder*

A generalized design model is proposed to study the stability and initial post-buckling equilibrium trajectory of sandwich cylindrical shells with elastic core that resists only transverse tension–compression. The model includes nonlinear equilibrium mixed-form equations, asymptotic equations obtained by the Koiter–Budiansky method, and the analytical solution of a homogeneous eigenvalue problem and inhomogeneous problem to find the values of the unknown functions at the critical point. The numerical results obtained indicate that the internal pressure strongly influences the critical load and initial post-buckling behavior of the shells.

On the possibility of successive approximation towards an equilibrium in a coalition game with reiterating collective action

The study investigates the possibility for the participants of collective action of avoiding a Nash equilibrium trap resulting from a non-coalition game, and of achieving a Pareto-preferable outcome. It is assumed that individual efforts invested by all members of a collective create revenue of which each member is entitled to a certain share. Each agent’s efforts have a positive effect on the value of marginal revenue per effort of any other agent. Each agent aims to maximize their own individual gain. It is further assumed that the lack of trust prevents members of the collective to coordinate their efforts in such a way that allows them to break out of the initial Nash-ineffective equilibrium which occurs in a non-coalition game setting. A small group (coalition) in which agents are united by mutual trust deploys a coalition strategy aimed at maximizing coalitional gains. As a result, not only do gains increase for each member of the larger collective, but also their marginal revenue per effort. The corresponding shift of the individual gain maximum point per each non-cooperated agent towards increasing the volume of effort invested thereby creates the prerequisites for the successive increase of effort invested in a reiterating game not only by coalition members, but also by non-cooperated agents. It is shown that the outcome in each consecutive game dominates over Pareto in the preceding game. Limit of an infinite sequence of outcomes corresponds with a Nash-balanced outcome of a coalition game, where non-cooperated agents assume that all coalition members will necessarily adhere to the coalition strategy.

Diffusional Electrochemical Catalytic (EC’) Mechanism Featuring Chemical Reversibility of Regenerative Reaction-Theoretical Analysis in Cyclic Voltammetry

We consider theoretically a specific electrochemical-catalytic mechanism associated with reversible regenerative chemical reaction, under conditions of cyclic staircase voltammetry (CSV). We suppose scenario in which two electrochemically inactive substrates “S” and “Y”, together with initial electrochemically active reactant Ox are present in voltammetric cell from the beginning of the experiment. Substrate “S” selectively reacts with initial electroactive reactant Ox and creates electroactive “product” Red (+ Y) in a reversible chemical fashion. The initial chemical equilibrium determines the amounts of Ox and Red available for electrode transformation at the beginning of the electrochemical experiment. Under conditions of applied potential, the electrode reaction Ox(aq) + ne– ⇋ Red(aq) occurs, producing flow of electric current. Under such circumstances, the chemical reaction coupled to the electrochemical step causes a regeneration of initial electroactive species during the time-frame of current-measuring segment in CSV. The features of cyclic voltammograms get significantly affected by the kinetics and thermodynamics of reversible regenerative reaction. We elaborate several aspects of this specific electrode mechanism, and we focus on the role of parameters related to chemical step to the features of calculated voltammograms. While we provide a specific set of results of this particular mechanism, we propose methods to get access to relevant kinetic and thermodynamic parameters relevant to regenerative chemical reaction. The results elaborated in this work can be valuable in evaluating kinetics of many drug-drug interactions, but they can be relevant to study interactions of many enzyme-substrate systems, as well.

Developments in the resolution of systemic problems

Producers and products as part of 'problem solving' drive the change from an initial equilibrium to a final state forming the operations in the natural, living, artificial and social words. This paper discusses the application, through modelling, of these concepts to these operations. Current approaches to 'systems thinking' are inadequate and design methods are fragmented which is improved by the proposed 'new science of systems' representing the systemic or structural view of the world. The notions of 'ambition' and 'achievement' lead to a 'problem solving scheme'. 'Market', 'requirements' and 'specifications' enable a product or 'achievement' to resolve a 'problematic issue' by achieving a new equilibrium state to satisfy the expectations of a user/consumer. This activity needs discussion and design thinking is accomplished by 'linguistic modelling'. Abstract properties and interactions of agents are interpreted to achieve operational description. The method outlined satisfies the criteria for a symbolism to be testable.

Evolution of Critical Correlations at the QCD Phase Transition

We investigate the evolution of the density-density correlations in the isoscalar critical condensate formed at the QCD critical point. The initial equilibrium state of the system is characterized by a fractal measure determining the distribution of isoscalar particles (sigmas) in configuration space. Non-equilibrium dynamics is induced through a sudden symmetry breaking leading gradually to the deformation of the initial fractal geometry. After constructing an ensemble of configurations describing the initial state of the isoscalar field we solve the equations of motion and show that remnants of the critical state and the associated fractal geometry survive for time scales larger than the time needed for the mass of the isoscalar particles to reach the two-pion threshold. This result is more transparent in an event-by-event analysis of the phenomenon. Thus, we conclude that the initial fractal properties can eventually be transferred to the observable pion-sector through the decay of the sigmas even in the case of a quench.

Stability of a rock mass using the key block theory: a case study

In underground mines, excavating disturb the initial equilibrium state of the rock mass, and therefore require selection of a support in order to control the movement of rocks, avoid landslide and work safely. Thus, the progress of mining operations in the ST2 mineralization, in the eastern zone of the Bouazzer mine, is disrupted because of stability problems. On the basis of field observations and analyzes of core drill, the geological and structural study, carried out in this area, has shown the existence of three types of facies: altered and cracked diorite, cobaltiferous mineralization which is in contact with serpentinites. In fact, the empirical methods such as Barton, Bieniawski and the recommendations of the AFTES have qualified the rock mass as poor, furthermore they proposed as kind of supports: steel arches, shotcrete and rock-bolts. Numerical simulation by the finite element method proved to be very complex due to existence of several types of discontinuities (faults, shistosities and joints).These discontinuities are natural fractures that delimit various shapes and sizes of wedges, which can become detached from the roof or siding of the excavation and collapse under their own weight. Although the empirical methods cited above provide supports for each facies, however, this support is expensive and difficult to implement in practice because it must cover the entire surface of the excavation and thus not allowing to detect stable blocks that do not require a support. For this it was essential to carry out an analysis of wedges to better locate unstable blocks. The treatment of fracturing data has highlighted the presence of five sets of discontinuities of which three sets are principals and the other two are minor joints. Then, while taking into account the geometrical, mechanical data of the discontinuities as well as the geometrical data of the excavation, we were able to detect the shape and the size of the unstable blocks and the sets of discontinuities delimiting them and which favor their sliding and tilting. Thus, we calculated the number of anchor bolts needed to stabilize these blocks in order to ensure an acceptable safety factor. This study shows clearly how a wedge analysis of the rock mass can guide and optimize the support work.

Reflective model of the stock market

The paper presents a new conceptual approach to analyzing processes in the stock market. The elementary mathematical model of the market is based on the mutually agreed dynamic description of the queue of buyers and sellers and the main actual parameters of the market — the price and executed volumes of transactions. The principal feature of the model is the description of the participants of supply and demand based on two parametric gamma distributions. The parameters of the distribution are the integral behavioral characteristics of bidders, called conditionally — "fear" and "greed". It is shown that the values of fear and greed, formalized with the help of gamma distribution, can be estimated quantitatively. A reflexive mechanism of transactions is proposed to display the interaction of bidders. This mechanism has two-way feedback. Current values of fear and greed of buyers and sellers determine the price change and the volume of transactions. In turn, price changes and fulfilled volumes lead to changes in fear and greed for supply and demand. The results of numerical simulation of the simplest market fluctuation caused by external influence are presented. Two main stages of this process are considered: 1) external influence leads the market from the state of initial equilibrium to the excited non-equilibrium state, 2) after the end of the influence, the market returns to equilibrium at a new price level. It is suggested that the proposed method can be used not only to describe the securities market, but also for other financial markets, as well as for modeling various social interactions.

Soap Film of Tensioned Fabric Structure in the Form of Handkerchief Surface

Form-finding has to be carried out for tensioned fabric structure in order to determine the initial equilibrium shape under prescribed support condition and pre-stress pattern. Tensioned fabric structures are normally designed to be in the form of equal tensioned surface. Tensioned fabric structure is highly suited to be used for realizing the surfaces of complex or new forms. However, the research study on a new form as a tensioned fabric structure has not attracted much attention. Alternative source of inspiration of minimal surface which could be adopted as form for tensioned fabric structure is very crucial. The aim of this study is to investigate initial equilibrium shape of tensioned fabric structures in the form of Handkerchief surface, u=v=0.2 and u=v=1.2. Experimental form-finding using soap film model is frequently used to develop the possible form of uniformly stressed surfaces. Apart from that, soap film model also provides a means for checking the accuracy of computational form-finding results. In this study, soap film model is used to investigate surface form corresponding to boundary shape defined by mathematical equation for minimal surface. Computational form-finding using nonlinear analysis method has been used in this study. The study proposes an alternative architectural surface for architect and structural engineer to consider Handkerchief surface, u=v=0.2 and u=v=1.2 applied in tensioned fabric structure. The results on factors affecting initial equilibrium shape can serve as a reference for proper selection of surface parameter for achieving a structurally viable surface. Such in-sight will lead the improvement of rural basic infrastructure, economic gains, sustainability of built environment and green technology initiative.

Characterization of Tagaran natural clay and its efficiency for removal of cadmium (II) from Sulaymaniyah industrial zone sewage.

The fine fraction of the Tagaran natural clay (TC) from the Kurdistan region of Iraq-Sulaimani was characterized and used to remove Cd ions from industrial swage. Using XRF, XRD, SEM, and FTIR, the dominant clay mineral of the Tagaran clay mineral was identified as saponite, with minor amounts of chlorite. The clay was examined for its efficiency to adsorb and remove (Cd2+) in the presence of other heavy metal contaminants from Sulaimani industrial zone sewage by a batch method. The effect of initial pH, equilibrium time, temperature, clay dosage, and Cd2+ concentration was studied. Results were evaluated using Langmuir, Freundlich, Temkin, and Redlich-Peterson isotherms. The kinetics could be best fitted to pseudo-second-order reaction kinetic model. In addition, the activation energy and the amount of calculated and experimentally determined heavy metal loads were consistent. The thermodynamic studies showed spontaneous endothermic adsorption. The trioctahedral smectite (saponite) showed a good efficiency for the adsorption of Cd2+ from the real sample (up to 100%) which at least partly can be explained by cation exchange. Tagaran clay is a candidate material for the production of an adsorber material for removing Cd2+ from aqueous solutions.

P.347 Alterations in key elements of the immune system in suicide victims

The paper concerns flexural buckling and initial post-buckling of axially compressed columns made of aluminium alloy described by the Ramberg-Osgood relationship. The non-linear differential equation of the problem is derived using the stationary total energy principle and the assumptions of classical beam theory within a finite range. The approximate analytical solution of the equation leading to the buckling loads and initial post-buckling equilibrium path is determined by means of the perturbation approach. Numerical examples dealing with simply supported and clamped I-columns are presented, the effect of the material non-linearity on the critical loads and initial post-buckling behaviour in comparison to linear one is discussed too. The analytical results are compared with the FEM solutions to present a good agreement.

Stability analysis and motion control of spinning electrodynamic tether system during transition into spin

Spinning electrodynamic tether systems are considered one of the most promising potential applications of tethered satellite systems, which require little fuel and avoid the equilibrium limit of conventional vertical electrodynamic tether systems. Therefore, spinning electrodynamic tether systems have good prospects in debris removal, orbit reboost, payload transportation, and so on. It has been found that, if not carefully controlled, tethers easily become slack or sagging during the transition process from equilibrium state into spin. In this regard, this paper mainly focuses on the transition process of spinning electrodynamic tether systems from the initial equilibrium state into the final spinning state with expected angular velocities. Conditions of dynamic equilibrium position and minimum current for acceleration (critical current) are firstly derived in this paper, which provide references for future space tether experiments. The motion of spinning electrodynamic tether systems is described by the Lagrangian model, which takes orbital motion into consideration. By considering power limits of electrodynamic tether systems, this paper proposes two open-loop control methods for the safe transition into spinning state as nominal control algorithms with different mission objectives. The first method (direct transition) provides a near time-minimum solution, and the second method (swinging transition) provides a minimum current-energy solution for acceleration into spin. Considering perturbations in space, including inhomogeneous distribution of magnetic induction, varying mass distribution of the system and so on, an adaptive sliding mode controller is proposed to regulate the system and to track nominal trajectories of acceleration. The effectiveness of the proposed control methods is validated by numerical results.

Stochastic thermodynamics of a harmonically trapped colloid in linear mixed flow.

In this paper, motivated by a general interest in the stochastic thermodynamics of small systems, we derive an exact expression-via path integrals-for the conditional probability density of a two-dimensional harmonically confined Brownian particle acted on by linear mixed flow. This expression is a generalization of the expression derived earlier by Foister and Van De Ven [J. Fluid Mech. 96, 105 (1980)10.1017/S0022112080002042] for the case of the corresponding free Brownian particle, and reduces to it in the appropriate unconfined limit. By considering the long-time limit of our calculated probability density function, we show that the flow-driven Brownian oscillator attains a well-defined steady state. We also show that, during the course of a transition from an initial flow-free thermal equilibrium state to the flow-driven steady state, the integral fluctuation theorem, the Jarzynski equality, and the Bochkov-Kuzovlev relation are all rigorously satisfied. Additionally, for the special cases of pure rotational flow we derive an exact expression for the distribution of the heat dissipated by the particle into the medium, and for the special case of pure elongational flow we derive an exact expression for the distribution of the total entropy change. Finally, by examining the system's stochastic thermodynamics along a reverse trajectory, we also demonstrate that in elongational flow the total entropy change satisfies a detailed fluctuation theorem.

Peace keeping in a model of conflict with foreign investments

PurposeThis paper aims to examine the role of outside peacekeepers in a bilateral conflict.Design/methodology/approachThe authors build upon a trade theoretic framework by incorporating disruptions due to war, which could affect directly the return to investment, both domestic and foreign, and by introducing explicitly peacekeeping forces into the model. Two countries are engaged in a war, with the purpose of capturing capital. A third country plays a dual role: it is the source of investments in the warring countries, and it deploys soldiers on ground for peacekeeping purposes. The authors consider the cases where the levels of foreign investments are exogenous and when they are endogenously determined by free mobility conditions. In the worst case, they find that foreign investment reduces conflict. In the case of endogenous foreign investments, they examine the effect of multilateral agreements where the two warring countries reduce their number of soldiers and the third increases the number of peacekeepers.FindingsThe authors find that the reform benefits all three countries and increases the level of foreign investments. They consider the cases of exogenous and endogenous foreign direct investment (FDI). In the first case, the authors examine the effect of an exogenous increase in FDI on the war equilibrium and find that it reduces the employment of soldiers in the warring countries and increases the size of the peacekeeping force. They also find that the first-best level of peacekeeping is larger than the equilibrium level. When FDI is endogenous, starting from the initial war equilibrium, they also examine the effect of a multilateral agreement in which the size of the peacekeeping force is increased by the third country and the two warring countries agree to reduce their war efforts. The authors find that the reform makes all three countries better off and increases the level of FDI.Originality/valueThe paper uses a theoretical model with third-party interventions in a bilateral war. It intends to shed light on some of the missing economic implications of peacekeeping. The paper introduces explicitly peacekeeping forces into the analysis and introduces a factor that represents a disruption to return on investment in both warring countries. The third country has a dual role; it provides investments in the warring countries and deploys soldiers for peacekeeping. Peacekeeping reduces the disruption mentioned above and affects the employment of soldiers by the warring countries. The authors find that a multilateral agreement in which the two warring countries reduce their war efforts and the third party increases its peacekeeping force can increase welfare in all three countries.

Dynamics of economic efficiency in tariff and trade

AbstractWhen the efficiency losses or gains as a result of an ad valorem import tariff are accounted for, the exisiting literature compares the equilibrium states before and after the tariff. However, after the imposition of an ad valorem tariff, the cost of the foreign producer to sell in the domestic market jumps upwards by the extent of the ad valorem tariff. This affects the quantity of imports, and the market is no longer in the initial equilibrium. The market then adjusts and after some efficiency loss, a new equilibrium state is arrived at. The mechanism of price adjustment has a basis of lack of coordination among buyers and sellers at the exisiting prices. The economic efficiency loss when the market is out of equilibrium is not taken into consideration in the literature, while deriving an optimal ad valorem tariff rate. In this article, an optimal ad valorem tariff schedule has been derived. From optimality, it should be construed that the economic efficiency losses get minimised when the market is adjusting and also during the equilibrium. A revenue constraint has to be met in addition.

The behavior of Fe and S isotopes in porphyry copper systems: Constraints from the Tongshankou Cu-Mo deposit, Eastern China

Iron isotopes have been widely applied to trace mineralization processes of magmatic-hydrothermal ore systems, yet the application of Fe isotopes in porphyry Cu deposits (PCDs) is still restricted by the lack of understanding of its behaviors during hydrothermal alteration and ore formation processes. In this study, Fe isotope systematics in whole-rocks and Fe-bearing minerals coupled with S isotope compositions of Fe-sulfides are investigated for the early Cretaceous Tongshankou porphyry Cu-Mo deposit from Eastern China. The results show that altered ore-hosting granodiorite porphyries display a small δ56Fe variation (0.04‰ to 0.17‰) with an average of 0.10 ± 0.08‰ (2SD, n = 10), indistinguishable from the values for global igneous rocks. The δ56Fe of magnetite (0.22‰) and biotite (-0.08‰ to 0.12‰) from the altered porphyries are also within the δ56Fe ranges of those from global igneous rocks. These results indicate that hydrothermal fluids have negligible effect on Fe isotope compositions of the porphyry host rocks, likely due to the insignificant contributions of fluid-derived iron relative to the total Fe budget of the host rocks.The Fe-sulfides in the porphyry system record geochemical and iron isotopic characteristics of the ore-forming fluids. Specifically, chalcopyrites show large Fe isotope variations with δ56Fe ranging from −0.60‰ to 0.61‰. The calculated Fe isotope compositions of ore-forming fluids based on the chalcopyrite δ56Fe are thus not uniform and fall in the range from −0.69 ± 0.18‰ to 0.52 ± 0.18‰ (2SD). On the other hand, pyrites exhibit a δ56Fe variation between −0.48‰ and 0.40‰ and show distinct Fe isotopic characteristics for disseminated and vein-type pyrite. The δ56Fe for disseminated pyrites are consistently higher than whole-rock values, ranging from 0.14‰ to 0.40‰, likely reflecting equilibrium Fe isotopic exchange between pyrite and dissolved Fe in fluid. By contrast, δ56Fe for pyrites in veins are highly variable (−0.48‰ to 0.34‰) and show an inverse correlation with the chalcopyrite δ56Fe. These observations, in concert with S isotope data, have been interpreted to reflect pyrite formation through the FeS pathway, whereas the wide range in δ56Fe for pyrite may record isotopic change from initial FeS-fluid equilibrium towards pyrite-fluid equilibrium due to different extent of reaction upon precipitation. Additionally, when compared to sulfides formed by non-magmatic, low-temperature processes, the sulfides in our study exhibit a relatively narrow range of δ56Fe and δ34S, implying a high-temperature magmatic origin for both elements. Overall, our study demonstrates that the coupling of Fe and S isotopes could be a useful tool for tracking the processes of sulfide mineralization in porphyry-related deposits.