Necessary Conditions For Equilibrium Research Articles

A Conceptual Investigation of Transition to Self‐Driven Turbidity Currents From Along‐Shelf Current‐Supported Turbidity Currents

AbstractWave‐ and current‐supported turbidity currents (WCSTCs) are one of the sediment delivery mechanisms from the inner shelf to the shelf break. Therefore, they play a significant role in the global cycles of geo‐chemically important particulate matter. Recent observations suggest that WCSTCs can transform into self‐driven turbidity currents close to the continental margin. However, little is known regarding the critical conditions that grow self‐driven turbidity currents out of WCSTCs. This is in part due to the knowledge gaps in the dynamics of WCSTCs regarding the role of density stratification. Especially the effect of sediment entrainment on the amount of sediment suspension has been overlooked. To this end, this study revisits the existing theoretical framework for a simplified WCSTC, in which waves are absent, that is, along‐shelf current‐supported turbidity current. A depth‐integrated advection model is developed for suspended sediment concentration. The model results, which are verified by turbulence‐resolving simulations, indicate that the amount of suspended sediment load is regulated by the equilibrium among positive/negative feedback between entrainment and cross‐shelf gravity force/density stratification, and settling flux dissociated with density stratification. It is also found that critical density stratification is not a necessary condition for equilibrium. A quantitative relation is developed for the critical conditions for self‐driven turbidity currents, which is a function of bed shear stress, entrainment parameters, bed slope, and sediment settling velocity. In addition, the suspended sediment load is analytically estimated from the model developed.

Price salience in opinion polls and observed behavior: The case of Spanish cinema

In the market system, a necessary condition for equilibrium is that prices convey all relevant information. However, apparently biased responses about prices in survey polls may cast doubt on the way consumers understand prices. It has been argued that survey answers, based on salient aspects of products, are mostly driven by intuition and may be inaccurate. To investigate this, we take advantage of a VAT rise on cultural products that took place in Spain in 2012. Cinema prices were expected to increase substantially, but the tax was eventually absorbed by exhibitors, keeping average prices unchanged. Using the Spanish Survey on Cultural Habits and Practices (2010–2011 and 2014–2015), we find that, as price salience increased, declared concern with prices rose. However, average prices did not change and cinema attendance, which involves more deliberation, remained stable. Therefore, expenditure decisions, grounded on reflective thinking, rule out potentially biased elements of price perceptions.

A regular equilibrium solves the extended HJB system

Control problems not admitting the dynamic programming principle are known as time-inconsistent. The game-theoretic approach is to interpret such problems as intrapersonal dynamic games and look for subgame perfect Nash equilibria. A fundamental result of time-inconsistent stochastic control is a verification theorem saying that solving the extended HJB system is a sufficient condition for equilibrium. We show that solving the extended HJB system is a necessary condition for equilibrium, under regularity assumptions. The controlled process is a general Itô diffusion.

An experimental study of estimation and bidding in common-value auctions with public information

We study how subjects with identical public data first make estimates and then bid in common-value environments. The data presented rows of numbers and values associated with them by our (undisclosed) rule. Subjects were asked to estimate the missing value in the last row with only the numbers given, and then bid for that value in a second-price auction. There is no presumption of commonly-known distributions, yet we derive necessary conditions for equilibrium. The strong winner's curse that we observe in our data results from the dispersion of the value estimates and the poorly-chosen bid-strategies. We find that bidding is lower when bidders are more uncertain about the estimates they have made. Finally, the k-nearest-neighbor method does well in explaining the estimates of the (common) value.

A location model for boycotting with an application to kosher certification

We develop a one-sided location model to predict the ethical behavior of firms in a market with consumer boycotting. Consumers’ ethical level is distributed along a line segment and they purchase only at firms that conform to their ethical consciousness. Firms maximize profits by choosing their ethical level. To capture the boycotting phenomena we make two assumptions. First, that firms are driven by profits and not ethical considerations. Second, that if consumers deem a firm to be engaged in unethical activity, then they refuse to purchase from it even products that are not the result of this unethical behavior. We develop the profit-maximization necessary conditions for equilibrium and show that when consumers are uniformly distributed then the equilibrium – if it exists – is unique. We solve the model for the uniform distribution case and show that firms will distribute symmetrically – but not uniformly – around the center location. Additionally, we demonstrate how the effectiveness of boycotts diminishes as the number of firms increases. We apply the model to the issue of restaurant kosher certification in Israel. In our application, kosher-keeping customers are boycotting non-certified restaurants since they generally refuse to dine in these restaurants even menu items that are kosher. We derive the relationship between the percent of kosher-keeping consumers and the equilibrium number of certified restaurants. Using population and restaurant data from Israel’s eight largest cities we estimate the implied cost of certification and the relative purchasing power of kosher-keeping customers.

Stability analysis for multicomponent mixtures including capillary pressure

Despite the large potential of unconventional resources, many unknowns still exist regarding the physics controlling the extraction processes in these settings. These include accurate representation of phase equilibrium in tight formations and effective implementation of relevant models in simulation tools.When a fluid is confined in pore spaces of nanometer size, significant interfacial curvatures may occur that can result in large capillary pressures between the liquid and vapor phases: The pressure difference between the two phases will likely affect the vapor-liquid equilibrium state. Previous efforts have shown that this effect is negligible for conventional reservoirs (with pores in the micron range) and current commercial reservoir simulators commonly ignore the effect of capillary pressure in the VLE calculations. However, experimental and modeling efforts have shown that ignoring capillary pressure in the VLE calculations will not be a valid approximation for unconventional (tight) reservoirs.In this work, we analyze the numerical aspects of including capillarity phenomena in VLE calculations in an effort to arrive at robust and efficient algorithms for stability analysis that can be used in compositional modeling/simulation of unconventional reservoirs. While the equality of chemical potentials is a necessary condition for equilibrium, it is not a sufficient one. A sufficient condition for equilibrium is the minimization of Gibbs energy, and the latter can be tested using the tangent plane distance (TPD) criteria. We show that stability analysis based on the TPD criteria remains valid for systems with large capillary pressures and propose effective/robust algorithms for stability testing. The proposed algorithms are tested for multicomponent reservoir fluid systems over a range of relevant temperatures, pressures and pore radii.

Common tangent plane in mixed-gas adsorption

The minimisation of the distance function between the Gibbs energy of mixing and its common tangent plane (or line) is applied to adsorbed solutions. A specific algorithm to deal with the associated bilevel programming problem is presented and discussed. This approach is validated with experimental data and ideal adsorbed solution theory calculations for an ideal case and with experimental data for two non-ideal cases at low and high pressure. While the presently adopted non-ideal formulation provides solutions fulfilling only the necessary condition for equilibrium, the common tangent plane approach proposed in this paper enables the direct evaluation of the necessary and sufficient solution.

Equilibrium of Multi-Phase Systems in Gravitational Fields

Four necessary conditions for equilibrium of an isolated solid-liquid-vapor system in a gravitational field were derived by Ward and Sasges (1998) in a unified setting, by using an entropy maximization approach, and under the assumption that the liquid-vapor surface tension does not depend on elevation. These are thermal equilibrium, the Laplace and Young equations, and a condition on the chemical potentials of the components present in the system. Gibbs (1876) had obtained the Young equation in a derivation separate from the derivation of the other three conditions and by using an energy minimization approach. However, Gibbs had derived a more general form of the Laplace equation than Ward and Sasges's. Gibbs's equation contained a term expressing the contribution of the variation of surface tension with elevation. This equation has since been neglected by most of the scientific community. In the present paper, the same approach as Ward and Sasges's is used to derive, in an unified setting, the conditions for equilibrium of an isolated solid-liquid-vapor system in a gravitational field but under the assumption that the liquid-vapor surface tension may depend on elevation. The four well-known conditions for equilibrium are obtained, with Gibbs's generalized Laplace equation instead of the classical Laplace equation. The derivations in this paper were carried out for two different system geometries, namely, for a sessile drop and for a conical capillary tube, and similar conditions for equilibrium were obtained.

Actividad práctica de genética de poblaciones para alumnos de C.O.U.

Starting from two populations with identical genic frequencies, one of them being balanced and the other unbalanced, and being their genes represented by «pieces of paper)) that may be taken out at random from a box or bag, we sha!l obtain the same genotypic frequencies in both of them, coinciding with those of the balanced population. Students must deduce the necessary conditions for equilibrium in a population by comparing the different genic and genotypic frequencies of both original populations with the populations resulting from this experiment.

ON EQUILIBRIUM FOR OVERLAPPING GENERATIONS ORGANIZATIONS*

Necessary conditions for equilibrium are that beliefs about the behavior of other agents are rational and individuals maximize. We argue that in stationary OLG environments this implies that any future generation in the same situation as the initial generation must do as well as the initial generation did in that situation. We conclude that the existing equilibrium concepts in the literature do not satisfy this condition. We then propose an alternative equilibrium concept, organizational equilibrium that satisfies this condition. We show that equilibrium exists, it is unique, and it improves over autarky without achieving optimality. Moreover, the equilibrium can be readily found by solving a maximization program.

Effect of gravity on contact angle: An experimental investigation

A capillary system is considered that is exposed to a gravitational field and contains a single component fluid. A portion of the liquid is above and a portion below the vapor. A three-phase line is formed at both places. A previous thermodynamic analysis of such a system, based on the Gibbs model of the interphase and the resulting necessary conditions for equilibrium, has led to the prediction that the equilibrium contact angle at the upper three-phase line is necessarily smaller than that at the lower three-phase line, and to a method that can be used to predict the contact angle at the lower interface for a given value of the contact angle at the upper interface. Even in the absence of any line tension effects, this contact angle difference is predicted to exist for a solid surface that is both smooth and homogeneous. The experimental investigation reported herein supports this prediction and shows that if the system is displaced from this configuration that the system returns to the same configuration. This suggests that the configuration in which the contact angle is smaller at the upper three-phase line than at the lower three-phase line not only satisfies the necessary conditions for equilibrium, but that this configuration is the stable equilibrium configuration for the system.

Effect of gravity on contact angle: A theoretical investigation

Using the Gibbs description of an interphase, the necessary conditions for equilibrium of a closed, two-phase fluid system in the presence of gravity are the Laplace and Young equations and a condition on the chemical potentials. The last condition has been neglected in all previous examinations of contact angles in a gravitational field. After introducing explicit expressions for the chemical potentials, we find that the condition on the chemical potentials can be used to determine the pressure profile within the system. In a “two-interface” system in which a liquid phase is both above and below a vapor phase and the vapor phase forms a solid–vapor interphase in one region, the pressure profile in the liquid phases is the same as it would have been if the vapor phase were not there; thus in a gravitational field, the pressure is smaller in the liquid phase above the vapor phase than it is in the liquid phase below the vapor phase. This results in the contact angle at the upper three-phase line necessarily being smaller than that at the lower three-phase line. This difference in contact angles is conventionally referred to as contact angle hysteresis; however, we show that it is simply an equilibrium property of a capillary system in a gravitational field. The contact angle difference predicted to exist in the presence of gravity does not violate the Young equation, but the Young equation does impose a restriction on the equilibrium adsorption isotherms at the solid–vapor and solid–liquid interfaces.

Equilibrium and Local Redistribution in an Urban Economy when Households Differ in both Preferences and Incomes

This paper studies equilibrium and redistribution in a system of local jurisdictions when households differ by both preferences and income. Differences in preferences may be either idiosyncratic or associated with differing demographic characteristics. Households are free to move among communities that offer different tax-expenditure packages. Within communities, households vote on the tax-expenditure package the community provides. Heterogeneity of preferences, as well as incomes, gives rise to an allocation of households across communities in which stratification by income no longer holds. In most previous models, complete income stratification is a necessary condition for equilibrium. The partial, but not complete, sorting of households by income that arises in our model is in better accord with observed allocations of households across jurisdictions in U.S. metropolitan areas.

Ends against the middle: Determining public service provision when there are private alternatives

Public provision of a service coexists with private market provision. The quality of public provision is determined by majority vote. Preferences are not single peaked owing to the presence of private alternatives. We identify two cases. In one, majority voting equilibrium always exists and the median-income voter is pivotal. In the other, a necessary condition for equilibrium indentifies the pivotal voter who must have income below the median. When equilibrium exists, a coalition of middle-income households who consume the public alternative will be opposed by a coalition of rich and poor households, with the rich choosing private consumption.

An alternative method of finding bifurcation points in pseudo‐barotropes

AbstractStarting from the equations of hydrodynamics, which include both collisional and collisionless ideal fluids, the special case of pseudo‐arotropes with anisotropic pressure distribution along tangential or vertical direction (in respect to a “vertical” rotation axis) is considered. We find that vertical motions are equivalent to an imaginary rotation, and call “pseudo‐otation” the combination of rotation and real or imaginary peculiar circular motions. By use of a necessary condition for equilibrium, i.e. the coincidence of the boundary with an isopotential (gravitational + rotational centrifugal + real peculiar or imaginary peculiar centrifugal) surface, a new method of finding bifurcation points from axisymmetric to triaxial pseudo‐arotropic sequences – discussed in an earlier paper – is dealt with for the systems under discussion. A simple application to the special case where the isopycnic surfaces are spheroidal discloses that, on one hand, steadily pseudo‐otating, heterogeneous spheroids, cannot be equilibrium configurations and, on the other hand, the same results obtained by use of the virial technique hold when the current method can work. Then the coincidence of the boundary with an isopotential surface and the validity of the virial equations of the second order make two independent (necessary) conditions for equilibrium and both must be satisfied. Under the further assumptions of steady rotation and homeoidally or focaloidally striated distribution of matter, the configurations for which a bifurcation point must necessarily occurr, are determined. In the former alternative a connection is also established, between local (on the boundary) and global anisotropy of pressure distribution; in particular, it is found that local isotropy (on the boundary) involves global isotropy and vice versa. In both cases, the right amount of of anisotropy turns out to yield violation of a treshold for stability, ϵrot = −Erot/Epot ⩽ 0.14, conjectured by Ostriker and Peebles (1973). This result gives additional support to a conclusion established in an earlier paper: it seems more germane to speak about Ostriker‐eebles conjecture for stability in connection with visible bodies of galaxies, instead of Ostriker‐eebles criterion for stability in connection with self‐ravitating fluids.

Mathematical Model for Piping

In the technical note, a two-dimensional mathematical model for piping under a dam on a granular material is reported. No details of the calculation are given, but the results are communicated. The key feature of the model is the treatment of a piping channel, thus incorporating and unifying apparently conflicting hypotheses made in the past by Lane and Koshla. The result is a map of steady-state equilibrium situations that are possible for the length of the piping channel under the dam as a function of the water-level difference on both sides of the dam and the particle grain size. The latter parameter arises because of the necessary treatment of the stability of the channel walls. The results show that stable states are possible as long as the piping channel does not exceed half the length of the structure. A formula linking the relevant parameters to obtain a necessary condition for equilibrium is presented. Implications for model tests and centrifuge tests are discussed.

Marché classique et loi de Say

This paper aims at clarifying the relations between the caracteristics of the laws of value and the possibility of representing the market adjustment processes. It starts with a simplified model of a smithian economy which produces three commodities. We first look for the necessary conditions for equilibrium. We examine what happens when the agents' choices generate a variation of one of the parameters of the model. We show then that the market mechanisms cannot easily assure the return to an equilibrium position. Particularly, the caracteristics inherent to the smithian theory of value and revenues generate perturbations.

Equilibrium models for inter‐dependent Markov systems

A Markovian model of graded systems, like the educational system, ensures internal consistency between forecasts. Sometimes merely ensuring this consistency is not enough, for the stochastic system may be operating below desired planning levels. This is highlighted. The educational system is considered and necessary conditions for equilibrium between demand and supply of teachers at first level is given. Disequilibrium conditions are shown to exist when the resulting models are applied to an autonomous education zone.

A necessary condition for equilibrium in stellar systems with a continuous mass spectrum

view Abstract Citations (45) References (7) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A necessary condition for equilibrium in stellar systems with a continuous mass spectrum. Vishniac, E. T. Abstract Spitzer (1969) has derived the condition for the attainment of hydrostatic and thermal equilibrium in a two-component stellar system. The subsequent collapse of the self-gravitating system of heavy stars when this condition is not satisfied has been studied and verified numerically by Spitzer and Hart (1971). In the present paper, Spitzer's criterion is extended to cover a system with a continuous distribution of masses. The extended criterion makes it possible to apply Spitzer's results to real globular clusters. Publication: The Astrophysical Journal Pub Date: August 1978 DOI: 10.1086/156332 Bibcode: 1978ApJ...223..986V Keywords: Globular Clusters; Mass Spectra; Stellar Mass; Stellar Systems; Density Distribution; Equilibrium; Hydrostatics; Integral Equations; Star Distribution; Systems Stability; Astrophysics; Dynamics:Stellar Systems; Evolution:Globular Clusters full text sources ADS |

Insurer Optimizing Behavior and Capital Market Equilibrium

A financial model is developed of a non-life insurer selling in a monopolistically competitive market. The insurer is assumed to maximize profits in its pricing and claims' settlement policy. The optimal values of these decision variables are found simultaneously when profits are maximized. The necessary conditions for equilibrium and stability in the model and the sensitivity of the optimal decision variables to changes in parameters of the model also are analyzed. Finally, the implications of the model are assessed for capital market equilibrium and for the equilibrium market price per share of the insurer's stock. To date, an adequate comprehensive financial theory of the non-life insurance firm has not been developed. While some authors have dealt with parts of the general problem, the theory has proved sufficiently intractable such that a complete development has eluded researchers. The major problem seems to lie in the sheer complexity of insurer behavior. Each decision made by the insurer affects other decisions. When economists face these kinds of problems they generally begin by making simplifying assumptions which abstract from some of the complex details of the real world and try to focus on the major variables and relationships associated with the problem under consideration. Then they gradually relax the assumptions and move toward the original real-world context of the problem. The knowledge gained from their simple models, at a minimum, provides insights into the real-world problem and, at best, provides a solution to the problem. Without the simplifying assumptions, many of the insights would be lost in a bewildering complexity of detail. An attempt is made here to develop a simplified, but comprehensive,