Equilibrium of drops on inclined hydrophilic surfaces

Why does not gravity make drops slip down the inclined surfaces, e.g., plant leaves? The current explanation is based on the existence of surface inhomogeneities, which cause a sustaining force that pins the contact line. Following this theory, the drop remains in equilibrium until a critical value of the sustaining force is reached. We propose an alternative analysis, from the point of view of energy balance, for the particular case in which the drop leaves a liquid film behind. The critical angle of the inclined surface at which the drop slips down is predicted. This result does not depend explicitly on surface inhomogeneities, but only on the drop size and surface tensions. There is good agreement with experiments for contact angles below 90° where the formation of the film is expected, whereas for greater contact angles great discrepancies arise

Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly

We investigate the phase behavior of a single-component system in three dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an intermediate distance, and a hard-core repulsion at a short distance, similar to potentials used to describe liquid systems such as colloids, protein solutions, or liquid metals. We showed [Nature (London) 409, 692 (2001)] that, even with no evidence of the density anomaly, the phase diagram has two first-order fluid-fluid phase transitions, one ending in a gas¿low-density-liquid (LDL) critical point, and the other in a gas¿high-density-liquid (HDL) critical point, with a LDL-HDL phase transition at low temperatures. Here we use integral equation calculations to explore the three-parameter space of the soft-core potential and perform molecular dynamics simulations in the interesting region of parameters. For the equilibrium phase diagram, we analyze the structure of the crystal phase and find that, within the considered range of densities, the structure is independent of the density. Then, we analyze in detail the fluid metastable phases and, by explicit thermodynamic calculation in the supercooled phase, we show the absence of the density anomaly. We suggest that this absence is related to the presence of only one stable crystal structure.

Simultaneous determination of gross alpha, gross beta and Ra-226 in natural water by liquid scintillation counting.

The determination of gross alpha, gross beta and 226Ra activity in natural waters is useful in a wide range of environmental studies. Furthermore, gross alpha and gross beta parameters are included in international legislation on the quality of drinking water [Council Directive 98/83/EC].1 In this work, a low-background liquid scintillation counter (Wallac, Quantulus 1220) was used to simultaneously determine gross alpha, gross beta and 226Ra activity in natural water samples. Sample preparation involved evaporation to remove 222Rn and its short-lived decay daughters. The evaporation process concentrated the sample ten-fold. Afterwards, a sample aliquot of 8 mL was mixed with 12 mL of Ultima Gold AB scintillation cocktail in low-diffusion vials. In this study, a theoretical mathematical model based on secular equilibrium conditions between 226Ra and its short-lived decay daughters is presented. The proposed model makes it possible to determine 226Ra activity from two measurements. These measurements also allow determining gross alpha and gross beta simultaneously. To validate the proposed model, spiked samples with different activity levels for each parameter were analysed. Additionally, to evaluate the model's applicability in natural water, eight natural water samples from different parts of Spain were analysed. The eight natural water samples were also characterised by alpha spectrometry for the naturally occurring isotopes of uranium (234U, 235U and 238U), radium (224Ra and 226Ra), 210Po and 232Th. The results for gross alpha and 226Ra activity were compared with alpha spectrometry characterization, and an acceptable concordance was obtained.

Simultaneous determination of gross alpha, gross beta and Ra-226 in natural water by liquid scintillation counting.

The determination of gross alpha, gross beta and 226Ra activity in natural waters is useful in a wide range of environmental studies. Furthermore, gross alpha and gross beta parameters are included in international legislation on the quality of drinking water [Council Directive 98/83/EC].1 In this work, a low-background liquid scintillation counter (Wallac, Quantulus 1220) was used to simultaneously determine gross alpha, gross beta and 226Ra activity in natural water samples. Sample preparation involved evaporation to remove 222Rn and its short-lived decay daughters. The evaporation process concentrated the sample ten-fold. Afterwards, a sample aliquot of 8 mL was mixed with 12 mL of Ultima Gold AB scintillation cocktail in low-diffusion vials. In this study, a theoretical mathematical model based on secular equilibrium conditions between 226Ra and its short-lived decay daughters is presented. The proposed model makes it possible to determine 226Ra activity from two measurements. These measurements also allow determining gross alpha and gross beta simultaneously. To validate the proposed model, spiked samples with different activity levels for each parameter were analysed. Additionally, to evaluate the model's applicability in natural water, eight natural water samples from different parts of Spain were analysed. The eight natural water samples were also characterised by alpha spectrometry for the naturally occurring isotopes of uranium (234U, 235U and 238U), radium (224Ra and 226Ra), 210Po and 232Th. The results for gross alpha and 226Ra activity were compared with alpha spectrometry characterization, and an acceptable concordance was obtained.

The structural approach of a natrex model on equilibrium exchange rates

Following a general macroeconomic approach, this paper sets a closed micro-founded structural model to determine the long run real exchange rate of a developed economy. In particular, the analysis follows the structure of a Natrex model. The main contribution of this research paper is the development of a solid theoretical framework that analyse in depth the basis of the real exchange rate and the details of the equilibrium dynamics after any shock influencing the steady state. In our case, the intertemporal factors derived from the stock-flow relationship will be particularly determinant. The main results of the paper can be summarised as follows. In first place, a complete well-integrated structural model for long-run real exchange rate determination is developed from first principles. Moreover, within the concrete dynamics of the model, it is found that some convergence restrictions will be necessary. On one hand, for the medium run convergence the sensitivity of the trade balance to changes in real exchange rate should be higher that the correspondent one to the investment decisions. On the other hand, and regarding long-run convergence, it is also necessary both that there exists a negative relationship between investment and capital stock accumulation and that the global saving of the economy depends positively on net foreign debt accumulation. In addition, there are also interesting conclusions about the effects that certain shocks over the exogenous variables of the model have on real exchange rates.

The effect of candidate quality on electoral equilibrium: an experimental study

When two candidates of different quality compete in a one dimensional policy space, the equilibrium outcomes are asymmetric and do not correspond to the median. There are three main effects. First, the better candidate adopts more centrist policies than the worse candidate. Second, the equilibrium is statistical, in the sense that it predicts a probability distribution of outcomes rather than a single degenerate outcome. Third, the equilibrium varies systematically with the level of uncertainty about the location of the median voter. We test these three predictions using laboratory experiments, and find strong support for all three. We also observe some biases and show that they canbe explained by quantal response equilibrium.

General equilibrium with asymmetric information: a dual approach

We study markets where the characteristics or decisions of certain agents are relevant but not known to their trading partners. Assuming exclusive transactions, the environment is described as a continuum economy with indivisible commodities. We characterize incentive efficient allocations as solutions to linear programming problems and appeal to duality theory to demonstrate the generic existence of external effects in these markets. Because under certain conditions such effects may generate non-convexities, randomization emerges as a theoretic possibility. In characterizing market equilibria we show that, consistently with the personalized nature of transactions, prices are generally non-linear in the underlying consumption. On the other hand, external effects may have critical implications for market efficiency. With adverse selection, in fact, cross-subsidization across agents with different private information may be necessary for optimality, and so, the market need not even achieve an incentive efficient allocation. In contrast, for the case of a single commodity, we find that when informational asymmetries arise after the trading period (e.g. moral hazard; ex post hidden types) external effects are fully internalized at a market equilibrium.

Consumption externalities, habit formation, and equilibrium efficiency

We analyze the welfare properties of the competitive equilibrium in a capital accumulation model where individual preferences are subjected to both habit formation and consumption spillovers. We also discuss how consumption externalities and habits interact to generate an inefficient dynamic equilibrium. Finally, we characterize optimal tax policies aimed to restore efficient decentralized paths.

Real equilibrium exchange rates. A panel data approach for advanced and emerging economies.

Based on an behavioral equilibrium exchange rate model, this paper examines the determinants of the real effective exchange rate and evaluates the degree of misalignment of a group of currencies since 1980. Within a panel cointegration setting, we estimate the relationship between exchange rate and a set of economic fundamentals, such as traded-nontraded productivity differentials and the stock of foreign assets. Having ascertained the variables are integrated and cointegrated, the long-run equilibrium value of the fundamentals are estimated and used to derive equilibrium exchange rates and misalignments. Although there is statistical homogeneity, some structural differences were found to exist between advanced and emerging economies.

Equilibrium play and best response to (Stated) beliefs in constant sum games

We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our experiment coincided with the prediction of the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation effects and belief elicitation procedures may influence how subjects play in simple but non trivial games and explain the diferences we observe with respect to previous work.

A Computable general equilibrium approach to hypothetical extractions and missing links

Identifying key sectors or key locations in an interconnected economy is of paramount importance for improving policy planning and directing economic strategy. Hence the relevance of categorizing them and hence the corresponding need of evaluating their potential synergies in terms of their global economic thrust. We explain in this paper that standard measures based on gross outputs do not and cannot capture the relevant impact due to self- imposed modeling limitations. In fact, common gross output measures will be systematically downward biased. We argue that an economy wide Computable General Equilibrium (CGE) approach provides a modeling platform that overcomes these limitations since it provides (i) a more comprehensive measure of linkages and (ii) an alternate way of accounting for links' relevance that is in consonance with standard macromagnitudes in the National Income and Product Accounts.

Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach

Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equilibrium point with the discontinuity surface. Generically, these bifurcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible collision of a non-hyperbolic equilibrium with the boundary in a two-parameter framework and the nonlinear phenomena associated with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of such phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding bi-parametric bifurcation sets is developed.

Explaining High Economic Growth in Small Tourism Countries with a Dynamic General Equilibrium Model

This paper shows that tourism specialisation can help to explain the observed high growth rates of small countries. For this purpose, two models of growth and trade are constructed to represent the trade relations between two countries. One of the countries is large, rich, has an own source of sustained growth and produces a tradable capital good. The other is a small poor economy, which does not have an own engine of growth and produces tradable tourism services. The poor country exports tourism services to and imports capital goods from the rich economy. In one model tourism is a luxury good, while in the other the expenditure elasticity of tourism imports is unitary. Two main results are obtained. In the long run, the tourism country overcomes decreasing returns and permanently grows because its terms of trade continuously improve. Since the tourism sector is relatively less productive than the capital good sector, tourism services become relatively scarcer and hence more expensive than the capital good. Moreover, along the transition the growth rate of the tourism economy holds well above the one of the rich country for a long time. The growth rate differential between countries is particularly high when tourism is a luxury good. In this case, there is a faster increase in the tourism demand. As a result, investment of the small economy is boosted and its terms of trade highly improve.

Information Dispersion and Equilibrium Multiplicity

This paper studies the implications of correlation of private signals about the liquidation value of a risky asset in a variation of a standard noisy rational expectations model in which traders receive endowment shocks which are private information and have a common component. We …nd that a necessary condition to generate multiple linear partially revealing rational expectations equilibria is the existence of several sources of information dispersion. In this context equilibrium multiplicity tends to occur when information is more dispersed. A necessary condition to have strategic complementarity in information acquisition is to have mul- tiple equilibria. When the equilibrium is unique there is strategic substi- tutability in information acquisition, corroborating the result obtained in Grossman and Stiglitz (1980). JEL Classi…cation: D82, D83, G14 Keywords: Multiplicity of equilibria, strategic complementarity, asym- metric information.

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.