Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5<α<10. At α=2.5 and α=10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α<4. However, downscale energy flux in the EDQNM self-similar inertial range for α>2.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum.

Pulsating equilibria: stability through migration

This paper is to present a model of spatial equilibrium using a nonlinear generalization of Markov-chain type model, and to show the dynamic stability of a unique equilibrium. Even at an equilibrium, people continue to migrate among regions as well as among agent-types, and yet their overall distribution remain unchanged. The model is also adapted to suggest a theory of traffic distribution in a city.

Phase equilibria study of systems composed of refined babassu oil, lauric acid, ethanol, and water at 303.2 K

Deacidification of vegetable oils can be performed using liquid-liquid extraction as an alternative method to the classical chemical and physical refining processes. This paper reports experimental data for systems containing refined babassu oil, lauric acid, ethanol, and water at 303.2 K with different water mass fractions in the alcoholic solvent (0, 0.0557, 0.1045, 0.2029, and 0.2972). The dilution of solvent with water reduced the distribution coefficient values, which indicates a reduction in the loss of neutral oil. The experimental data were used to adjust the NRTL equation parameters. The global deviation between the observed and the estimated compositions was 0.0085, indicating that the model can accurately predict the behavior of the compounds at different levels of solvent hydration. (C) 2011 Elsevier Ltd. All rights reserved.

Liquid-liquid equilibria for systems composed of refined soybean oil, free fatty acids, ethanol, and water at different temperatures

Soybean oil can be deacidified by liquid-liquid extraction with ethanol. In the present paper, the liquid-liquid equilibria of systems composed of refined soybean oil, commercial linoleic acid, ethanol and water were investigated at 298.2 K. The experimental data set obtained from the present study (at 298.2 K) and the results of Mohsen-Nia et al. [1] (at 303.2 K) and Rodrigues et al. [2] (at 323.2 K) were correlated by applying the non-random two liquid (NRTL) model. The results of the present study indicated that the mutual solubility of the compounds decreased with an increase in the water content of the solvent and a decrease in the temperature of the solution. Among variables, the water content of the solvent had the strongest effect on the solubility of the components. The maximum deviation and average variance between the experimental and calculated compositions were 1.60% and 0.89%, indicating that the model could accurately predict the behavior of the compounds at different temperatures and degrees of hydration. (C) 2010 Elsevier B.V. All rights reserved.

Polymethine cyanine dyes in beta-cyclodextrin solution: multiple equilibria and chemical oxidation

Absorption and fluorescence spectroscopy, electrochemical techniques, and semiempirical calculations were employed to characterize the multiple complexation equilibria between two polymethine cyanine dyes (IR-786 and Indocyanine green-ICG, 5) and beta-cyclodextrin (beta-CD, L), as well as the chemical reactivity of the complexed and uncomplexed species against the oxidizing agents hypochlorite (HC) and hydrogen peroxide (HP). IR-786 dimerization is favored with the increase in beta-CD concentration in the form of (SL)(2) complexes. In the case of ICG, free dimers (D) and SL complexes are favored. Both IR-786 and ICG react and discolor in the presence of HC and HP. For IR-786, the reaction with HP and HC proceeds with observed rate constants of 10(-3) and 0.28 s(-1) and second-order rate constants (k(2)) of similar to 10(-3) and 10(4) M(-1) s(-1), respectively. The intermediate species observed in the bleaching reactions of IR-786 and ICG were shown, by cyclic voltammetry and VIS absorption, to result from one electron oxidation. IR-786 complexed with beta-CD is protected against bleaching in the presence of HP and HC by factors of 20 and 4, respectively. This protection was not observed in ICG complexes. Superdelocalizability profile of both dyes and frontier orbital analysis indicates that beta-CD does not protect ICG from oxidation by HP or HC, whereas the 2:2 IR-786/beta-Cd complex is able to avoid the oxidation of IR-786. We concluded that the decrease in the chemical reactivity of the dyes against oxidant agents in the presence of beta-CD is due to the formation of (SL)(2) complexes. Copyright (C) 2010 John Wiley & Sons, Ltd.

Equilibria in security markets with a continuum of agents

We prove the existence of a competitive equilibrium for exchange economies with a measure space of agents and for which the commodity space is ` p, 1 < p < +∞. A vector x = (xn) in ` p may be interpreted as a security which promises to deliver xn units of numeraire at state (or date) n. Under assumptions imposing uniform bounds on marginal rates of substitution, positive results on core-Walras equivalence were established in Rustichini–Yannelis [21] and Podczeck [20]. In this paper we prove that under similar assumptions on marginal rates of substitution, the set of competitive equilibria (and thus the core) is non-empty.

First-price auction symmetric equilibria with a general distribution

In this paper I obtain the mixed strategy symmetric equilibria of the first-price auction for any distribution. The equilibrium is unique. The solution turns out to be a combination of absolutely continuous distributions case and the discrete distributions case.

Pure strategy equilibria of multidimensional and non-monotonic auctions

We give necessary and sufficient conditions for the existence of symmetric equilibrium without ties in interdependent values auctions, with multidimensional independent types and no monotonic assumptions. In this case, non-monotonic equilibria might happen. When the necessary and sufficient conditions are not satisfied, there are ties with positive probability. In such case, we are still able to prove the existence of pure strategy equilibrium with an all-pay auction tie-breaking rule. As a direct implication of these results, we obtain a generalization of the Revenue Equivalence Theorem. From the robustness of equilibrium existence for all-pay auctions in multidimensional setting, an interpretation of our results can give a new justification to the use of tournaments in practice.

The set of equilibria of first-price auctions

In this note I specify the class of functions that are equilibria of symmetric first-price auctions.

Competitive equilibria in infinite-horizon collateralized economies with default penalties

Araújo, Páscoa and Torres-Martinez (2002) have shown that, without imposing either debt constraints or transversality conditions, Ponzi schemes are ruled out in infinite horizon economies with default when collateral is the only mechanism that partially secures loans. Páscoa and Seghir (2008) subsequently show that Ponzi schemes may reappear if, additionally to the seizure of the collateral, there are sufficiently harsh default penalties assessed (directly in terms of utility) against the defaulters. They also claim that if default penalties are moderate then Ponzi schemes are ruled out and existence of a competitive equilibrium is ensured. The objective of this paper is two fold. First, contrary to what is claimed by Páscoa and Seghir (2008), we show that moderate default penalties do not always prevent agents to run a Ponzi scheme. Second, we provide an alternative condition on default penalties that is sufficient to rule out Ponzi schemes and ensure the existence of a competitive equilibrium.

Bertrand, Cournot and monopolistically competitive equilibria

Using an example, we study the analogs, for the differentiated product case, of the Cournot and Bertrand equilibria. These equilibria can be shown to exist and be uni que if we impose a sim pie and natural restriction on the elasticities of the demand functions for the differentiated products. Our characterizations of these equilibria make it possible to compare them and to determine how they are affected by the size of the market and the number of firms. We are also able to prove the existence of Cournot free-entry equilibria in which the number of firms is determined endogenously. In addition, we are able to prove that, in a large market, the Cournot free-entry equilibria approximate the Dixit-Stiglitz monopolistically competitive equilibria. The free-entry equilibrium concept we study is an analog of the one studied by Novshek for the case of firms selling products that are perfect substitutes. Our results are extensions of Novshek's. While we were unable to establish a general existence result for Bertrand free-entry equilibria, we were able to prove that, when these equilibria exist, they are unique and that in large markets they also approximate the Dixit-Stiglitz equilibria.

Multiple equilibria and protectionism

In a nonnative approach, I analyze trade policies when the industrial sector genentes positive extemalities in production, and there are adjustments costs to changing production from one sector to the other. Protectionist trade policy can make workers intemalize the benetits from moving into the industrial sector, but it is a second best policy as it also causes consumption distortions. I show that if the govemment is able to fully commit to its tariff schedule for the future, the welfare maximizing policy is to maintain a positive tariff forever, even after all adjustment has already taken place . However, if the govemment is not able to commit at all, the only time consistent policy is zero tariff at any point in time. The time inconsistency of the full commitment policy is derived from the fact that in the model only production needs interference, and the production distortion is lagged one period with respect to the tariff wbile the consumption distortion is simultaneous to the tariff. In the intermediary case, i.e., when the government can commit for a limited period of time, the time consistent optimal tariff will be positive but lower than the "full commitment" tariff. This result indicates that some institutions that have always been considered pure sources of inefficiency, such as protectionist lobbying, may in fact be welfare improving in some cases!

Equilibria in exchange economies with financial constraints : beyond the Cass trick

We consider an exchange economy under incomplete financiaI markets with purely financiaI securities and finitely many agents. When portfolios are not constrained, Cass [4], Duffie [7] and Florenzano-Gourdel [12] proved that arbitrage-free security prices fully characterize equilibrium security prices. This result is based on a trick initiated by Cass [4] in which one unconstrained agent behaves as if he were in complete markets. This approach is unsatisfactory since it is asymmetric and no more valid when every agent is subject to frictions. We propose a new and symmetric approach to prove that arbitrage-free security prices still fully characterize equilibrium security prices in the more realistic situation where the financiaI market is constrained by convex restrictions, provided that financiaI markets are collectively frictionless.