Search

This work investigates the equilibrium stage of the crack propagation of a fine-grained soil after several drying and wetting cycles (shrinkage and swelling hysteresis). This stage is found to be crucial in practical engineering since the soil continues to show its irreversible hydraulic settlement, which is a potential risk for some severe structural damages. The shrinkage area and the shrinkage crack area were determined by using the image processing method. For the cyclic experimental investigations, the shrinkage cracks were followed during six months of successive wetting and drying cycles for two samples (with two different initial water contents). These long-term tests were completed by some short term single drying path tests performed on samples prepared at different initial states. The results showed the existence of a unique equilibrium stage at the end of the wetting and drying cycles for the two studied samples. The equilibrated soil subsidence was separated into two parts: the reversible settlement of the equilibrium stage and the irreversible settlements cumulated during successive wetting and drying cycles. At the equilibrium stage, the reversible deformation was 5.9% and the irreversible deformation was 3.8%. A simplified theoretical approach was also used to predict the cracking equilibrium stage and its soil subsidence. The fitted parameters of the theoretical approach for each cycle were stabilized to confirm the existence of this equilibrium stage.

This study provides the complete liquid–liquid equilibrium (LLE) data including the solubility curves and tie-lines for heptane + thiophene + tetraethylene glycol and cyclohexane + thiophene + tetraethylene glycol ternary mixtures at 298.15–313.15 K under a pressure of 83.4 ± 1 kPa. The experimental data were obtained by the cloud point method. Type 1 phase behavior is observed for the systems. The observed behavior was interpreted based on the type and nature of the interactions between the components. The capability of tetraethylene glycol in extractive desulfurization of thiophene from liquid fuel is evaluated by determining the solute distribution coefficient and selectivity. The high values of the selectivity show that tetraethylene glycol is a good candidate for this purpose. The investigation of the effect of temperature on the area of the biphasic region and distribution ratios shows that the extraction process can be performed at room temperature. The experimental data were successfully correlated with the NRTL model. The reliability of the correlation results was checked by using a Graphical User Interface (GUI) for the representation of Gibbs energy of mixing (GM). The root mean square deviation (RMSD), a measure of the precision of the correlations, ranges from 0.0022 to 0.0040.

In "soft-soft nanocomposites " based on film formation of latexes with structured particles, the combination of particle structure and interparticle crosslinking leads to materials that behave as nonlinear viscoelastic fluids at small strains and as highly elastic networks at larger strains. Similarly, in studies of flow-induced crystallization in polymers, a two-phase model is often invoked in which a soft viscoelastic component is coupled with a rigid semi-crystalline phase providing stiffness. In the present work, we use the framework of non-equilibrium thermodynamics (NET) to develop stress-strain relationships for such two-phase systems characterized by a viscoelastic and an elastic component by making use of two conformation tensors: the first describes the microstructure of the viscoelastic phase while the second is related to the elastic Finger strain tensor quantifying the deformation of the elastic phase due to strain and is responsible for strain-hardening. The final transport equations are formulated in the context of the generalized bracket formalism of NET and can describe the rheological behavior and mechanical response of a large variety of soft materials ranging from rubbers to artificial tissues., Journal of Non-Equilibrium Thermodynamics, 48 (1), ISSN:0340-0204, ISSN:1437-4358

Industrial effluents have become an environmental issue harming the ecosystem, remediation of these effluents is critical in order to mitigate some of this issue. Three adsorbents, activated carbon from sugarcane bagasse (ASB), hydroxyapatite (HAP), and their composites (ncpA), were prepared for the adsorption of Cr (VI) and Fe (III) from wastewater in this work. The hydroxyapatite was synthesized using the wet precipitation method, and the activated carbon was derived from sugarcane bagasse, resulting in a composite with a hydroxyapatite to activated carbon ratio of 1:1. The adsorbents surface and chemical properties were determined by Fourier transform infrared spectroscopy (FT-IR), scanning electron microscopy (SEM), Brunauer-Emmett-Teller 2 2 -1 (BET), and X-ray diffraction (XRD). The BET surface areas were 1.34 ± 0.04 m2/g and 26.4 ± 0.4 m2g4 for HAP and ASB respectively. The influence of initial concentration of metal ions, adsorbent dosage, pH, contact time and temperature on the adsorption process were investigated. Two isotherm models and different kinetic models were used in fitting the experimental data. The adsorption of Cr (VI) and Fe (III) fitted well into the Langmuir isotherm model with maximum monolayer adsorption capacities of 19.92 mg/g, 16.69 mg/g and 10.33 mg/g respectively for Cr (VI) and 113.64 mg/g, 113.64 mg/g and 107.54 mg/g respectively for Fe (III) removal onto HAP, ASB and ncpA respectively. The pseudo-second-order model that best suited the kinetic data was chemisorption-controlled, and this is referred to as the mechanism of the adsorption. Sum of square 2 error (SSE) and non-linear chi-square (ꭓ2 ) were used to further validate the mechanism.

In this article, we address the problem of stochastic generalized Nash equilibrium (SGNE) seeking, where a group of noncooperative heterogeneous players aim at minimizing their expected cost under some unknown stochastic effects. Each player's strategy is constrained to a convex and compact set and should satisfy some global affine constraints. In order to decouple players' strategies under the global constraints, an extra player is introduced aiming at minimizing the violation of the coupling constraints, which transforms the original SGNE problems to extended stochastic Nash equilibrium problems. Due to the unknown stochastic effects in the objective, the gradient of the objective function is infeasible and only noisy objective values are observable. Instead of gradient-based methods, a semidecentralized zeroth-order method is developed to achieve the SGNE under a two-point gradient estimation. The convergence proof is provided for strongly monotone stochastic generalized games. We demonstrate the proposed algorithm through the Cournot model for resource allocation problems., IEEE Transactions on Automatic Control, 68 (2), ISSN:0018-9286, ISSN:1558-2523

We develop a Nash equilibrium problem representing a perfectly competitive market wherein all players are subject to the same source of uncertainty with an unknown probability distribution. Each player—depending on her individual access to and confidence over empirical data—builds an ambiguity set containing a family of potential probability distributions describing the uncertain event. The ambiguity set of different players is not necessarily identical, yielding a market with potentially heterogeneous ambiguity aversion. Built upon recent developments in the field of Wasserstein distributionally robust chance-constrained optimization, each ambiguity-averse player maximizes her own expected payoff under the worst-case probability distribution within her ambiguity set. Using an affine policy and a conditional value-at-risk approximation of chance constraints, we define a tractable Nash game. We prove that under certain conditions a unique Nash equilibrium point exists, which coincides with the solution of a single optimization problem. Numerical results indicate that players with comparatively lower consumption utility are highly exposed to rival ambiguity aversion.

The existence of simple uncoupled no-regret learning dynamics that converge to correlated equilibria in normal-form games is a celebrated result in the theory of multi-agent systems. Specifically, it has been known for more than 20 years that when all players seek to minimize their internal regret in a repeated normal-form game, the empirical frequency of play converges to a normal-form correlated equilibrium. Extensive-form games generalize normal-form games by modeling both sequential and simultaneous moves, as well as imperfect information. Because of the sequential nature and presence of private information in the game, correlation in extensive-form games possesses significantly different properties than its counterpart in normal-form games, many of which are still open research directions. Extensive-form correlated equilibrium (EFCE) has been proposed as the natural extensive-form counterpart to the classical notion of correlated equilibrium in normal-form games. Compared to the latter, the constraints that define the set of EFCEs are significantly more complex, as the correlation device must keep into account the evolution of beliefs of each player as they make observations throughout the game. Due to that significant added complexity, the existence of uncoupled learning dynamics leading to an EFCE has remained a challenging open research question for a long time. In this article, we settle that question by giving the first uncoupled no-regret dynamics that converge to the set of EFCEs in n-player general-sum extensive-form games with perfect recall. We show that each iterate can be computed in time polynomial in the size of the game tree, and that, when all players play repeatedly according to our learning dynamics, the empirical frequency of play is proven to be a O(T^-0.5)-approximate EFCE with high probability after T game repetitions, and an EFCE almost surely in the limit., Comment: Extended version of our NeurIPS 2020 paper. Compared to the conference version, this preprint gives finer, in-high-probability regret bounds. We also better connected our work to the phi-regret minimization framework

We formally assume that players in a game consider Nash Equilibrium (NE) the behavioral norm. In finite games of perfect information this leads to a refinement of NE: Faithful Nash Equilibrium (FNE). FNE is outcome equivalent to NE of the trimmed game, obtained by restricting the original tree to its NE paths. Thus, it always exists but it need not be unique. Iterating the norm ensures uniqueness of outcome. FNE may violate backward induction when subgame perfection requires play according to the SPE following a deviation from it. We thus provide an alternative view of tenable threats in equilibrium analysis.

Marine hydrates mainly occur in clayey silt sediments, and their occurrence environment has the characteristics of a high clay content and low permeability, which seriously inhibit an increase in the gas production rate. This study presents a new method, the high-pressure jet breaking and sand filling method, to transform the natural gas hydrate (NGH) reservoir near the production well, whereby a water jet is used to form an area of sediment with large particle diameters and high permeability. Based on indoor experiments, we report the characteristics of hydrate formation, decomposition, and phase equilibrium in the transition area formed by this method under different sand particle sizes and mass fractions. The addition of sand at a high mass fraction with a large particle diameter significantly shortened the time required for rapid hydrate formation, prolonged slow hydrate formation, and reduced the increase in temperature. With an increase in the mass fraction of large-diameter sand, the free water content of pores increased, which made it easier to form hydrates with large particles, thus delaying the hydrate decomposition rate. The phase equilibrium curves of hydrates in clayey silt sediments with sand added at mass fractions of 30% and 50% were close to that of bulk hydrate in pure water at lower temperatures. As the temperature increased, the phase equilibrium curves gradually approached those of hydrates in clayey silt sediments.

The object of research is the synthesis of methanol under medium pressure, and the subject of research is the calculation of the equilibrium composition. A method and an algorithm for calculating the equilibrium composition of products are proposed. Calculations have been carried out using two mechanisms of methanol synthesis. First of all, the first approach to the mechanism of methanol synthesis was applied, which provides for the formation of methanol from a mixture of carbon oxides and hydrogen by the simultaneous reaction of methanol synthesis from carbon monoxide (IV) and steam reforming of carbon monoxide (II). The poor convergence of the system of two equations on the basis of this interaction mechanism is established, which complicates the selection of initial approximations and the choice of a real solution. At the second stage, the mechanism of the formation of methanol from carbon monoxide (II) with the simultaneous flow of steam reforming of CO in the opposite direction is considered. The degree of the equation describing the dependence of the equilibrium constant on the partial pressures of the reactants decreases in comparison with the first approach and causes much better convergence when solving the system of two equations. The use of a coefficient that takes into account the effect of pressure on the value of the equilibrium constant is proposed, and its dependence on temperature is approximated. The developed algorithm is implemented in MathCAD, while the relative maximum deviation for methanol is 8.53%. The third approach is to use two coefficients that adjust the equilibrium constant depending on pressure. In this case, the relative maximum deviation of methanol is 16.25%. The program according to the proposed algorithm takes into account the multiplicity of the initial data, namely the possibility of varying the composition of the initial mixture, pressure and temperature. The calculation was carried out according to the initial data of industrial implementation of methanol synthesis. Comparison of the equilibrium concentration of methanol with the real one at the outlet of the synthesis column established the degree of equilibrium reaching 39.4%, which indicates the presence of a reserve of methanol synthesis and the possibility of increasing the practical yield of methanol.

This research article develops a dynamic framework for the Walrasian pure exchange economy and thus extends the static Walrasian general equilibrium theory into a dynamic one with price adjustments. An evolution equation for the price vector is derived from dynamic programming considerations. The economy tries to move from disequilibrium to general equilibrium by minimizing certain cost functional. The cost functional measures transactions costs and the total expenditure of agents when they optimize individually. Price determination is directly related to a gradient search. The general equilibrium is shown to be stable in the sense of Lyapunov if price adjustments can be large, when needed. The conditional stability could be one reason for volatility clustering in financial time series.

β-galactosidases are a class of enzyme widely used as biocatalysts in the food, dairy, and fermentation industries. However, due to their biological origin, enhancement of these enzymes is generally necessary. The effect of temperature upon enzymes is a mandatory stage in rational enzyme engineering. The present work was devoted to Rhynchophorus palmarum Linn. β-galactosidase (Rpbgal) as part of the investigation of insect-derived enzymes for biotechnological applications. The thermal behaviour of Rpbgal has been studied in the temperature range 303-353 K by measuring enzymatic activities in presence of oNPG as substrate. Equilibrium model which gives complete and quantitative description of the effect of temperature on enzyme activity has been used to analyze experimental data. A satisfactorily agreement between the calculated results and the experimental data was obtained. The thermodynamic parameters provided by this model were given. Results showed that Rpbgal is relatively stable and active at 323 K. Temperatures over 330 K produce a significant decrease in the enzyme activity. In the temperature range 331 - 339 K, Rpbgal showed the best thermal stability compared to a commercial β-galactosidase from Aspergillus oryzae.

A generalized game is a strategic situation in which agents’ behavior restricts their opponents’ available action choices, giving rise to interdependencies in terms of what strategy profiles remain mutually feasible. This paper proposes a novel example of a simple generalized game in which the well-known convexity, compactness, continuity, and concavity assumptions are satisfied, but no Nash equilibrium exists. This finding reinforces that certain additional conditions appearing in the literature (primarily, the lower hemicontinuity of feasibility correspondences) are indispensable for equilibrium existence and must be considered as supplemental desiderata beyond the usual regularity conditions. Implications for institutional design are discussed.

In this article, we study an energy-regulation trade-off that delineates the fundamental performance bound of a feedback control system over a noisy channel in an unreliable communication regime. The channel and process are modeled by an additive white Gaussian noise channel with fading and a partially observable Gauss-Markov process, respectively. Moreover, the feedback loop is constructed by designing an encoder with a scheduler and a decoder with a controller. Associated with this trade-off, we characterize an equilibrium at which neither the scheduler nor the controller has incentive to deviate from its policy. We argue that this equilibrium is a general one as it attains the global optimality in the presence of signaling (i.e., the process of exchanging implicit information through actions) and without any restriction on the information structure or policy structure.

We consider a queueing system which opens at a given point in time and serves a finite number of users according to the last-come first-served discipline with preemptive-resume (LCFS-PR). Each user must decide individually when to join the queue. We allow for general classes of user preferences and service time distributions and show existence and uniqueness of a symmetric Nash equilibrium. Furthermore, we show that no continuous asymmetric equilibrium exists, if the population consists of only two users, or if arrival strategies satisfy a mild regularity condition. For an illustrative example, we implement a numerical procedure for computing the symmetric equilibrium strategy based on our constructive existence proof for the symmetric equilibrium. We then compare its social efficiency to that obtained if users are instead served on a first-come first-served (FCFS) basis.

The advent of phases of matter which are inherently and explicitly quantum mechanical has made it possible to create devices with exciting capabilities that would otherwise be completely impossible. Recently, experimental advancements are beginning to make it feasible to not just create such quantum materials, but actually manipulate microscopic details in these systems to engineer their properties on demand. Furthermore, by externally interacting with quantum systems, it is possible to induce phases of matter (such as time crystals and materials exhibiting anomalous topological properties) that are forbidden for isolated systems in equilibrium. In this dissertation, we introduce a variety of new classes of physically realizable, non-equilibrium models with a focus on systems which are periodically driven or subjected to a periodic protocol of quantum measurements. We leverage this driving and these quantum measurements to induce non-trivial steady states and phases of matter with surprising and appealing novel properties. We first examine free fermionic lattice systems subject to quantum measurements (as well as other quantum operations such as particle injection). For example, we consider the effect of a measurement device (along with a variety of other kinds of disturbances) which is dragged through a Fermi sea. The device induces a wake pattern (in analogy with a boat moving through water) which is characterized by the speed at which the probe is moved through the system and its direction with respect to the lattice. Furthermore, stark contrasts emerge between the wake geometry of a quantum disturbance (such as a measurement) and classical disturbances (such as a potential). These effects are especially prominent at half-filling where the the density wake due to measurements disappears and the wake from a moving particle extractor is temperature invariant. We also introduce a model where lattice fermions are subjected to a periodic sequence of measurements which break the time reversal symmetry of the original free hopping evolution. We show that this protocol induces chiral edge transport in the system that is protected against perturbations and deformations of the boundary at high measurement rates. This model shows that it is possible to induce chiral edge modes in an analogous way to those in anomalous Floquet topological insulators via measurements alone. On the other hand, the measurement-induced model also exhibits novel, distinct features due to the non-unitary nature of the evolution. Finally, we turn to consider exotic non-equilibrium dynamics which may be induced via a combination of periodic driving and interactions, instead of through a protocol of measurements. Namely, we introduce a broad class of interacting Floquet models which exhibit special points in parameter space where the dynamics becomes exactly solvable. Additionally, at other interaction strengths and driving frequencies, we show that the system exhibits Hilbert space fragmentation with some subspaces corresponding to a (complex) permutation of number states while others may be non-integrable and thermalize. When disorder is added to the system, it is shown that this dynamics is stabilized within finite regions of parameters space (thereby corresponding to true dynamical phases of matter) instead of just at finely tuned parameter values. Importantly, the phases realizable in this fashion include many of the uniquely non-equilibrium materials which are currently the focus of active interest including, for example, time crystals and anomalous Floquet topological insulators. In this way, we show how our introduction and analysis of this broad class of interacting Floquet models allows for new insights into these non-equilibrium phases as well as provides a framework upon which to systematically search for and examine other completely novel non-equilibrium steady states.

Classical statistical mechanics is based on the notion of a particle (i.e. its x and p phase space) as is Newtonian mechanics which is based on x(t). Quantum mechanics, on the other hand, contains particle-wave duality and is linked to Newtonian mechanics (in that one considers bound state, motion etc), but is also considered to be statistical. In this note we consider the statistical features of quantum mechanics by examining a reflection/refraction of light problem with incident light moving along the positive x direction. If considered from the point of view of a particle (i.e. photon) (in accordance with Newtonian mechanics and classical statistical mechanics) there is no equilibrium. One may imagine one photon strike the medium at a time. This photon retains its energy, but has a certain probability “a” to reflect at x=0 and 1-a to refract. Thus energy and photon number are conserved, but “a” is unknown and the energy and particle number to the left and right of x are not the same, even if one considers a steady state stream. In other words, there is a discontinuity at x=0 because of the difference in energy and photon numbers, yet a steady state picture seems to imply a kind of equilibrium which is not present in the particle picture. In other words, there should be invariance along the x axis with continuity at x=0, but this cannot be achieved by only considering particles (i.e. photons). Nevertheless, photons are physical and whatever solution is found must be consistent with photon energy and number conservation. This seems to suggest a new physical property needed to establish the equilibrium which somehow coexists with the particle picture. We suggest this property is wavelength with a photon being described by exp(ipx) (the square root of flux) and that it is this scenario which allows one to see the reflection/refraction problem as an equilibrium one. In other words, one does not need a particle point of view to establish equilibrium, yet particle number/energy may still be conserved in this picture.

The precautionary principle (PP) is an influential principle for making decisions when facing uncertain, but potentially severe, harm. However, there is a persistent disagreement about what the principle entails, exactly. It exists in a multitude of formulations and has potentially conflicting ideas associated with it. Is there even such a thing as ‘the precautionary principle’? This paper analyses the debate between unificationists and pluralists about ‘the PP’, arguing that the debate is hindered by neglecting the question of justification. It introduces reflective equilibrium as a method of justification, and sketches how it could be applied to justify a PP.

This paper provides a sufficient condition for the existence of solutions for generalized Nash equilibrium problems in the infinite-dimensional setting and with a countable (possibly infinite) number of players. The result has been achieved as a consequence of a modified version of Michael’s selection theorem that works even when the range space is not metrizable and the set-valued map has not closed values.

Mega-events are often perceived as opportunities to foster regional development. To assist policymakers in deciding whether to host such events, Computable General Equilibrium are increasingly used. The literature has recently begun reviewing these studies and has shown that they are at risk of providing misleading policy recommendations if they do not pay more attention to the various specificities of mega-events. This paper identifies 13 modelling issues, examines their implications and discusses how they could be overcome. Fostering a discussion of these issues among scientists could be beneficial for the progress of policy modelling in this specific area.

Assuming the hypothesis of local thermal non-equilibrium, this work investigates the propagation of Rayleigh surface waves in a thermoelastic half-space, isotropic, homogeneous and structured with a triple level of porosity. Its surface is supposed to be stress-free, thermally insulated and characterized by null pressure boundary conditions. A class of wave solutions is highlighted for the differential system of the model, each solution satisfying suitable asymptotic conditions in the depth of the considered half-space. Then, the Rayleigh wave solution is sought as a linear combination of the elements of this class, and, moreover, by means of the selected boundary conditions, the associated secular equation is found. By solving the secular equation, the characteristics of the wave solution are determined: the propagation speed as well as the damping in time. With the purpose of clearly highlighting the characteristics of the model, the secular equation is solved numerically and significant graphical representations are provided, using the software packages Mathematica and MATLAB. This suggests an increase of the Rayleigh wave propagation speed, corroborated with the appearance of the damping in time of its amplitude.

The term “Dutch disease” is not new, but still remains one of the hot topics that reappear in Algeria each time the price of hydrocarbons decreases or increases. Our study starts from an assumption that the rise in the price of hydrocarbons will always have negative effects on the Algerian economy due to the deterioration of certain productive activities, in addition to the rise of the real exchange rate, the creation of a consumer society and the migration of labor to expanding sectors, all of which are synonymous with the Dutch disease. By using the calculable general equilibrium model, and the inclusion of oil rent as one of the production factors which is redistributed equally, and by building the model database via the social accounting matrix, we were able to simulate the increase in the price of hydrocarbons and to solve various non-linear equations with the Mat lab program; which leads to validating the hypothesis and concluding with a number of results and recommendations.

In this article, we investigate the distributed Nash equilibrium (NE) seeking problem for the multi-cluster game under switching communication topologies. Specifically, the communication topology switches between a group of jointly connected digraphs. First, a new distributed NE seeking algorithm for the multi-cluster games is designed by the consensus protocol and gradient play rule under the switching communication topologies. Furthermore, in order to make the algorithm still applicable when the agent only knows part of the decision information, the leader-following consensus protocol is used to generate the estimates for all agents action in the cluster under the assumption that the switching topology between clusters is directed and strongly connected. A more general NE seeking algorithm for the multi-cluster games is designed. For these two algorithms, the results of local convergence and non-local convergence are given, respectively. Two examples verify the validity of the theoretical results.

The learning of scientific concepts is one of the main research subjects in science education. Although little used, the theory of conceptual profiles allows the study of this knowledge, taking into account the presence of different ways of thinking about a certain concept in the same individual. This study aimed to build a conceptual profile for the concept of equilibrium and, based on this profile, relate it to the teaching and learning process of chemical equilibrium. Four zones were proposed to comprise the profile, called intuitive, static, kinetic and energetic. Subsequently, we analyzed the responses obtained in a questionnaire by students of Chemistry courses in order to group similar ways of speaking into categories related to the concept of equilibrium and the proposed zones for the conceptual profile. In the answers, we found some alternative conceptions already identified by the literature. Based on the results, the proposed zones for the conceptual profile of equilibrium indicate that establishing associations between the state of chemical equilibrium and the notion of equality can lead to conceptual errors and, therefore, it is suggested to give priority to the notion of stability. We also propose the use of studies on the History and Philosophy of Sciences applied to the teaching of chemical equilibrium to stimulate the emergence, dialogue and enrichment between the zones of conceptual profile in individuals.

This research proposes an updated evacuation model incorporating Bayesian Nash Equilibrium (BNE) within multi-agent systems. It augments the rationality of pedestrian decision-making processes and improves the evacuating behaviours of pedestrians. Recent research found that BNE pedestrians could evacuate more quickly by avoiding clogged areas, closely matching the pedestrian evacuating behaviours in reality. This paper extends this work by introducing a number of diamond- shaped barriers in the model to evaluate whether and how BNE affects the pedestrian evacuation process in more complex scenarios. It provides a detailed introduction of the updated simulation model and identifies several limitations and potential research directions.

Equilibrium problems provide a mathematical framework which includes optimization, variational inequalities, fixed point and saddle point problems, and noncooperative games as particular cases. In this paper sufficient conditions for the existence of solutions of an equilibrium problem are given by weakening the assumption of quasiconvexity of the involved equilibrium bifunction. The existence of solutions is established both in presence of compactness of the feasible set as well with a coercivity assumption. The results are obtained in an infinite dimensional setting, and they are based on the so called finite solvability property which is weaker than the recently introduced finite intersection property and in turn, weaker than most common cyclic and proper quasimonotonicity. Some examples are presented to illustrate the various cases in which other existence results for equilibrium problems do not apply. Finally, applications to the solution of quasiequilibrium problems, quasioptimization problems and generalized quasivariational inequalities are discussed.

In this study, a theoretical method is proposed to solve shock relations coupled with chemical equilibrium. Not only shock waves in dissociated flows but also detonation waves in combustive mixtures can be solved. The global iterative solving process is specially designed to mimic the physical and chemical process in reactive shock waves to ensure good stability and fast convergence in the proposed method. Within each global step, the single-variable equations of normal and oblique shock relations are derived and solved with the Newton iteration method to reduce the complexity of the problems, and the minimization of free energy method of NASA (National Aeronautics and Space Administration) is adopted to solve equilibrium compositions. It is demonstrated that the convergent process is stable and very close to the real chemical-kinetic process, and high accuracy is achieved in the solutions of normal and oblique reactive shock waves. Moreover, the proposed theoretical method has also been applied to many problems associated with reactive shocks, including the stability of oblique detonation wave, bow detonation over a sphere, and shock reflection in dissociated air. The great importance of using chemical equilibrium to theoretically predict the theoretical range of the wedge angle for a standing oblique detonation wave (the standing window of the oblique detonation wave), the stand-off distance of bow detonation wave and the transition criterion of shock reflection in dissociated air with high accuracy have been addressed.

We study a competitive partial equilibrium in markets where risk-averse agents solve multistage stochastic optimization problems formulated in scenario trees. The agents trade a commodity that is produced from an uncertain supply of resources. Both resources and the commodity can be stored for later consumption. Several examples of a multistage risked equilibrium are outlined, including aspects of battery and hydroelectric storage in electricity markets, distributed ownership of competing technologies relying on shared resources, and aspects of water control and pricing. The agents are assumed to have nested coherent risk measures based on one-step risk measures with polyhedral risk sets that have a nonempty intersection over agents. Agents can trade risk in a complete market of Arrow-Debreu securities. In this setting, we define a risk-trading competitive market equilibrium and establish two welfare theorems. Competitive equilibrium will yield a social optimum (with a suitably defined social risk measure) when agents have strictly monotone one-step risk measures. Conversely, a social optimum with an appropriately chosen risk measure will yield a risk-trading competitive market equilibrium when all agents have strictly monotone risk measures. The paper also demonstrates versions of these theorems when risk measures are not strictly monotone.

The stability property of the loss-aversion-based noncooperative switched systems with quadratic payoffs is investigated. In this system, each agent adopts the lower sensitivity parameter in the myopic pseudo-gradient dynamics for the case of losing utility than gaining utility, and both systems' dynamics and switching events (conditions) are depending on agents' payoff functions. Sufficient conditions under which agents' state converges towards the Nash equilibrium are derived in accordance with the location of the Nash equilibrium. In the analysis, the mode transition sequence and interesting phenomena which we call flash switching instants are characterized. Finally, we present several numerical examples to illustrate the properties of our results.

This paper considers the privacy-preserving distributed Nash equilibrium seeking strategy design for average aggregative games, in which the players' objective functions are considered to be sensitive information to be protected. In particular, we consider that the game is free of central node and the aggregate information is not directly available to the players. As there is no central authority to provide the aggregate information required by each player to update their actions, a dynamic average consensus protocol is employed to estimate it. To protect the players' privacy, we perturb the transmitted information among the players by independent random noises drawn from Laplace distributions. By synthesizing the perturbed average consensus protocol with a gradient algorithm, a distributed privacy-preserving Nash equilibrium seeking strategy is established for the aggregative games under both fixed and time-varying communication topologies. With explicit quantifications of the mean square errors, the convergence results of the proposed methods are presented. Moreover, it is analytically proven that the proposed algorithm is μ-differentially private. The presented results indicate that there is a tradeoff between the convergence accuracy and the privacy level. Lastly, a numerical example is provided for the verification of the proposed methods.

A non-equilibrium molecular flow through a carbon nanotube (CNT) serves as a key system for revealing molecular transport and establishing nanofluidics. It has been challenging to simulate a non-equilibrium flow of hydrogen molecules exhibiting strong nuclear quantumness. Taking advantage of the quantum molecular dynamics method that can calculate real-time trajectories of hydrogen molecules even under a non-equilibrium flow, we found that the non-equilibrium flow makes hydrogen molecules more condensed and accelerates their adsorption near a CNT surface, letting the molecules flow more smoothly by propagating velocity momenta more efficiently along the CNT axis and by suppressing transverse molecular dynamics on the CNT cross section. Such flow-induced autonomic ordering indicates the importance of monitoring and investigating dynamics and adsorption of hydrogen molecules under a non-equilibrium circumstance as well as in a quiet equilibrium state, opening a new strategy for efficient hydrogen liquefaction and storage.

The focus of this article is on the dynamics of a susceptible-infected model which consists of a susceptible group ( S ) and two different infectious groups ( I 1 and I 2 ). Once infected, an individual becomes a member of one of these infectious groups which have different clinical forms of infection. In addition, during the progress of the illness, an infected individual in group I 1 may pass to the infectious group I 2 which has a higher mortality rate. The infection is deadly and it has no cure. In this study, positiveness of the solutions for the model is proved. Stability analysis of species extinction, I 1 -free equilibrium and endemic equilibrium as well as disease-free equilibrium is studied, and it is shown that the disease-free equilibrium is stable whereas all other equilibrium points are asymptotically stable for parameter ranges determined by certain inequalities. In addition, relations between the basic reproduction number of the disease and the basic reproduction number of each infectious stage are examined. Furthermore, the case where all newborns from infected mothers are also infected is analysed. For this type of vertical transmission, endemic equilibrium is asymptotically stable for certain parameter ranges. Finally, a special case which refers to the disease without vital dynamics is investigated and its exact solution is obtained.

In this investigation, a comprehensive and accurate numerical analysis of the local thermal non-equilibrium effects on the natural convection characteristics in a horizontal elliptical porous annulus saturated with nanofluid has been carried out using finite volume technique. The internal surface is isothermally heated while the external one is fixed at uniform lower temperature. The nanofluid phase and the solid phase of the porous structure are hors local thermal equilibrium situation. The heat and the hydrodynamics equations in their dimensionless form under Darcy-Brinkman Forchheimer model were solved computationally by the finite volume technique using the standard SIMPLER algorithm. The results have been examined for various porous medium properties under the LTNE condition. The standard 0.05 significance level was used to identify the local thermal equilibrium within the system. According to the obtained results, the higher the Darcy number and the smaller the non-dimensional heat transfer coefficient for the solid/nanofluid interface, the modified thermal conductivity ratio and the media’s porosity, the higher are the LTNE effects. In addition, the spatial distribution contours of the LTNE sources within the porous annulus were schematized.

In this paper, the generalized Nash equilibrium problem over a fuzzy domain is considered. An existence result of the solution is given. Then, on the basis of the variational inequality approach, an algorithm is developed to solve the fuzzy Nash equilibrium problem. In addition, a stability analysis of the solution set is provided while the membership function is perturbed by a parameter. Finally, the fuzzy Nash equilibrium formulation is applied to the study of the conflicts faced by the fashion and textile industry: production and pollution.

In the analysis and design of a network system, one is often faced with the situation where the network structure is known but the node dynamics is almost unknown. Thus structural analysis problems, in which the prior knowledge is almost about the network structure, have received attention in science and engineering fields. Along this line of research, this paper addresses a structural design problem, that is, to find a sign pattern of the control input such that any constant input with the sign pattern drives the system to a desirable steady state in a qualitative sense. A solution is presented by reducing the problem into a design problem of the so-called sign-solvable equation, which is a linear equation whose qualitative solution can be determined from the prior knowledge of the sign pattern of the coefficients. Our framework is demonstrated by applying to a control problem of the biological network of apoptosis.

This paper analyzes the oligopolistic equilibrium of multiple price-maker agents in performance-based regulation (PBR) markets. In these markets, there are price-maker agents representing some frequency regulation (FR) providers and a number of independent price-taker FR providers. An equilibrium problem with equilibrium constraints (EPEC) model is employed in this paper to study the equilibria of a PBR market in the presence of price-maker agents and pricetaker FR providers. Due to the incorporation of the FR providers' dynamics, the proposed model is reformulated as a mixed-integer linear programming (MILP) problem over innovative mathematical techniques. An optimal equilibrium point is also selected for the market, where none of the agents is unique deviator and the dynamic performance of power system is improved simultaneously. The effectiveness of proposed optimal equilibrium point is evaluated in the numerical results section by comparing the outputs with conventional optimal dispatches of the FR providers.

We study a pure-exchange incomplete-market economy with heterogeneous agents. In each period, the agents choose how much to save (i.e., invest in a risk-free bond), how much to consume, and which bundle of goods to consume while their endowments are fluctuating. We focus on a competitive stationary equilibrium (CSE) in which the wealth distribution is invariant, the agents maximize their expected discounted utility, and both the prices of consumption goods and the interest rate are market-clearing. Our main contribution is to extend some general equilibrium results to an incomplete-market Bewley-type economy with many consumption goods. Under mild conditions on the agents' preferences, we show that the aggregate demand for goods depends only on their relative prices and that the aggregate demand for savings is homogeneous of degree in prices, and we prove the existence of a CSE. When the agents' preferences can be represented by a CES (constant elasticity of substitution) utility function with an elasticity of substitution that is higher than or equal to one, we prove that the CSE is unique. Under the same preferences, we show that a higher inequality of endowments does not change the equilibrium prices of goods, and decreases the equilibrium interest rate. Our results shed light on the impact of market incompleteness on the properties of general equilibrium models.

The phenomenon brake squeal has been an ongoing topic for decades, both in the automotive industry and in science. Although there is agreement on the excitation mechanism of brake squeal, namely self-excitation due to frictional forces between the disk and the pad, in the subject of squeal it is very complex to discover all relevant effects and to take them into account. Several of these problems are related to nonlinearities, for example, in the contact between pad and disk or drum or in the behavior of the brake pad material. One of these nonlinear effects, which has been almost completely neglected so far, is that the brake can engage, mainly due to the bushing and joint elements within the brake, different equilibrium positions. This in fact has serious influence on the noise behavior as shown in experimental studies. For example, it is observed in experiments that, despite identical operating parameters, squeal sometimes occurs and sometimes not. In initial experimental studies, this could be related to the engaged equilibrium position. Following these experimental studies, the present paper introduces a minimal model by extending the well-known minimal model by Hoffmann et al. by corresponding elements and nonlinearities allowing the system to engage different equilibrium positions. As will be presented, the stability behavior strongly depends on the engaged equilibrium position. Therefore, the minimal model represents the key experimentally observed issues. Additionally, a limit cycle behavior can also be observed.

Biocatalytic nucleoside (trans-)glycosylations catalyzed by nucleoside phosphorylases have graduated to a practical and convenient approach to the preparation of modified nucleosides, which are important pharmaceuticals for the treatment of various cancers and viral infections. However, the obtained yields in these reactions are generally determined exclusively by the innate thermodynamic properties of the nucleosides involved, hampering the biocatalytic access to many sought-after target nucleosides. We herein report an orthogonal dimension for reaction engineering of these systems. We show how apparent equilibrium shifts in phosphorolysis and glycosylation reactions can be effected through entropically driven, biased esterification of nucleosides with inorganic borate. Our multifaceted analysis further describes the kinetic implications of this in situ reactant esterification for a model phosphorylase. Our results suggest an unusual pseudo-non-competitive inhibitory mechanism where reversible binding of the borate ester of the nucleoside substrate yields a non-productive inhibitor-enzyme complex. This complex exhibits constricted molecular dynamics and exists in a rapid equilibrium with the productive enzyme-substrate complex via hydrolytic interconversion. Collectively, this report presents a partial departure from the stringent thermodynamic constraints of nucleoside phosphorolysis reactions and shines light on the molecular processes regulating the activity of nucleoside-binding enzymes in the presence of borate.

In this revision, it is possible to find different examples of publicly available MatLab Graphical User Interfaces (GUI’s) developed to help researchers and students that have to deal with the challenging problem phase equilibrium data correlation (e.g. LLE, LVE). These examples are: GMcal_TieLinesLL: http://hdl.handle.net/10045/51725 GMcal_TieLinesVL: http://hdl.handle.net/10045/122857 Boundaries_LL_NRTL: http://hdl.handle.net/10045/121471 ParamIni_LL_NRTL: http://hdl.handle.net/10045/130017

Atmospheric entry capsules shaped as spherically blunted, large apex-angle cones are widely used in space missions. In Part 1 of this study (Hornung, Martinez Schramm & Hannemann, J. Fluid Mech., vol. 871, 2019, pp. 1097–1116) we explored flows over the two elements of the capsule shape, the sphere and the sharp cone with detached shock, theoretically and computationally. Using a large number of inviscid, perfect-gas computations, analytical functions of two independent variables, the normal-shock density ratio $\varepsilon$ and a cone-angle parameter $\eta$ (which is a function of $\varepsilon$ and the cone half-angle $\theta$ ) were found for the dimensionless shock wave stand-off distance and the drag coefficient of a sharp cone. An analytical description was found for the shock stand-off distance in the transition from the 90 $^\circ$ cone (flat-faced cylinder) to the sphere. In Part 1, it was speculated that the perfect-gas results have relevance to non-equilibrium situations if the normal-shock density ratio is replaced by the density ratio based on the average density along the stagnation streamline. In Part 2, the investigation is extended to blunted-cone capsule shapes. High-precision force measurements and schlieren image analysis are performed in the High-Enthalpy Shock Tunnel Göttingen (HEG) of the German Aerospace Centre using air as the test gas, at conditions where vibrational non-equilibrium effects are significant. Accordingly, results are compared with viscous numerical predictions using different physico-chemical models. A theoretical model is constructed for the density profile along the stagnation streamline that is determined by the free stream conditions and gives the average density. Comparisons of the experimental and numerical results for the dimensionless shock stand-off distance and the drag coefficient, with the extension of the analytical functions of Part 1 to vibrationally relaxing flow, exhibit very good agreement in all of a range of geometries.

The term Anthropocene for the current geological era is a reflection of our known impacts on planetary systems. We, humans, desire balance and certainty, which unfortunately are two states that are highly ambitious–and difficult to attain. Achieving equilibrium in a static sense is unrealistic in an intrinsically non-equilibrium system. Full text available on Medium at https://medium.com/@asuglobalfuture/seeking-balance-in-an-uncertain-non-equilibrium-system-a6a7404e92fc.

Kernel mirror prox and RKHS gradient flow for mixed functional Nash equilibrium Pavel Dvurechensky , Jia-Jie Zhu Abstract The theoretical analysis of machine learning algorithms, such as deep generative modeling, motivates multiple recent works on the Mixed Nash Equilibrium (MNE) problem. Different from MNE, this paper formulates the Mixed Functional Nash Equilibrium (MFNE), which replaces one of the measure optimization problems with optimization over a class of dual functions, e.g., the reproducing kernel Hilbert space (RKHS) in the case of Mixed Kernel Nash Equilibrium (MKNE). We show that our MFNE and MKNE framework form the backbones that govern several existing machine learning algorithms, such as implicit generative models, distributionally robust optimization (DRO), and Wasserstein barycenters. To model the infinite-dimensional continuous- limit optimization dynamics, we propose the Interacting Wasserstein-Kernel Gradient Flow, which includes the RKHS flow that is much less common than the Wasserstein gradient flow but enjoys a much simpler convexity structure. Time-discretizing this gradient flow, we propose a primal-dual kernel mirror prox algorithm, which alternates between a dual step in the RKHS, and a primal step in the space of probability measures. We then provide the first unified convergence analysis of our algorithm for this class of MKNE problems, which establishes a convergence rate of O(1/N ) in the deterministic case and O(1/√N) in the stochastic case. As a case study, we apply our analysis to DRO, providing the first primal-dual convergence analysis for DRO with probability-metric constraints.

Publisher Summary This chapter develops a baseline analytical model of an economy, variations of which are used for almost all mainstream public sector analysis. A model must possess four attributes to be used as a framework for a normative theory of the public sector. First, it must be a general equilibrium model of the economy. All general equilibrium models describe the three fundamental elements of any economy: the preferences of every consumer, the production technologies, and market clearance for all goods and services and factors of production. Second, the model must be flexible enough to consider a broad spectrum of public sector problems—particularly those associated with externalities, decreasing cost production, asymmetric information, the distribution of income, and various issues in the theory of taxation. Third, the model must be designed to highlight the public interest in efficiency and equity, the two main objectives of normative public sector theory. Finally, the model must be compatible with a market economy because the Western public sector economics assumes that the government operates within the context of a market system. Furthermore, a general equilibrium model can be specified in terms of quantities or prices. The quantity model is the simpler one because it requires fewer assumptions.

Non-equilibrium property of turbulence modifies characteristics of turbulent transport. With the aid of response-function formalism, such non-equilibrium effects in turbulent transport can be represented by the temporal variation of the turbulent energy ($K$) and its dissipation rate ($\varepsilon$) along the mean stream through the advective derivatives of $K$ and $\varepsilon$. Applications of this effect to the turbulent convection with plumes are considered for the first time in this work. The non-equilibrium transport effects associated with plumes are addressed in two aspects. Firstly, the effect associated with a single plume is evaluated using data measured in the recent plume/jet experiments. The second argument is developed for the collective turbulent transport associated with multiple plumes mimicking the stellar convection zone. In this second case, for the purpose of capturing the plume motions into the advective derivatives, use has to be made of the time--space double averaging procedure, where the turbulent fluctuations are divided into the coherent or dispersion component (which represents plume motions) and incoherent or random component. With the aid of the transport equations of the coherent velocity stress and the incoherent counterpart, the interaction between the dispersion and random fluctuations are also discussed in the context of convective turbulent flows with plumes. It is shown from these analyses that the non-equilibrium effect associated with plume motions is of a great deal of relevance in the convective turbulence modelling., Comment: 22 pages, 6 figures, 2 tables, submitted to Atmosphere. Turbulence from Earth to Planets, Stars and Galaxies - Commemorative Issue Dedicated to the Memory of Jackson Rae Herring