Mixed duopolies with advance production

Production to order and production in advance has been compared in many frameworks. In this paper we investigate a mixed production in advance version of the capacity-constrained Bertrand-Edgeworth duopoly game and determine the solution of the respective timing game. We show that a pure-strategy (subgame-perfect) Nash-equilibrium point exists for all possible orderings of moves. It is pointed out that unlike the production-to-order case, the equilibrium of the timing game lies at simultaneous moves. An analysis of the public firm's impact on social welfare is also carried out. All the results are compared to those of the production-to order version of the respective game.

Equilibrium distributions of microsatellite repeat length resulting from a balance between slippage events and point mutations

We describe and test a Markov chain model of microsatellite evolution that can explain the different distributions of microsatellite lengths across different organisms and repeat motifs. Two key features of this model are the dependence of mutation rates on microsatellite length and a mutation process that includes both strand slippage and point mutation events. We compute the stationary distribution of allele lengths under this model and use it to fit DNA data for di-, tri-, and tetranucleotide repeats in humans, mice, fruit flies, and yeast. The best fit results lead to slippage rate estimates that are highest in mice, followed by humans, then yeast, and then fruit flies. Within each organism, the estimates are highest in di-, then tri-, and then tetranucleotide repeats. Our estimates are consistent with experimentally determined mutation rates from other studies. The results suggest that the different length distributions among organisms and repeat motifs can be explained by a simple difference in slippage rates and that selective constraints on length need not be imposed.

Equilibrium and column studies of iron exchange with strong acid cation resin

The exchange of iron species from iron (III) chloride solutions with a strong acid cation resin has been investigated in relation to a variety of water and wastewater applications. A detailed equilibrium isotherm analysis was conducted wherein models such as Langmuir Vageler, Competitive Langmuir, Freundlich, Temkin, Dubinin Astakhov, Sips and Brouers-Sotolongo were applied to the experimental data. An important conclusion was that both the bottle-point method and solution normality used to generate the ion exchange equilibrium information influenced which sorption model fitted the isotherm profiles optimally. Invariably, the calculated value for the maximum loading of iron on strong acid cation resin was substantially higher than the value of 47.1 g/kg of resin which would occur if one Fe3+ ion exchanged for three “H+” sites on the resin surface. Consequently, it was suggested that above pH 1, various iron complexes sorbed to the resin in a manner which required less than 3 sites per iron moiety. Column trials suggested that the iron loading was 86.6 g/kg of resin when 1342 mg/L Fe (III) ions in water were flowed at 31.7 bed volumes per hour. Regeneration with 5 to 10 % HCl solutions reclaimed approximately 90 % of exchange sites.

An examination of isotherm generation : impact of bottle-point method upon potassium ion exchange with strong acid cation resin

This paper relates to the importance of impact of the chosen bottle-point method when conducting ion exchange equilibria experiments. As an illustration, potassium ion exchange with strong acid cation resin was investigated due to its relevance to the treatment of various industrial effluents and groundwater. The “constant mass” bottle-point method was shown to be problematic in that depending upon the resin mass used the equilibrium isotherm profiles were different. Indeed, application of common equilibrium isotherm models revealed that the optimal fit could be with either the Freundlich or Temkin equations, depending upon the conditions employed. It could be inferred that the resin surface was heterogeneous in character, but precise conclusions regarding the variation in the heat of sorption were not possible. Estimation of the maximum potassium loading was also inconsistent when employing the “constant mass” method. The “constant concentration” bottle-point method illustrated that the Freundlich model was a good representation of the exchange process. The isotherms recorded were relatively consistent when compared to the “constant mass” approach. Unification of all the equilibrium isotherm data acquired was achieved by use of the Langmuir Vageler expression. The maximum loading of potassium ions was predicted to be at least 116.5 g/kg resin.

The Cougar Point tuff: Implications for thermochemical zonation and longevity of high-temperature, large-volume silicic magmas of the Miocene Yellowstone hotspot

The 12.7-10.5 Ma Cougar Point Tuff in southern Idaho, USA, consists of 10 large-volume (>10²-10³ km³ each), high-temperature (800-1000 °C), rhyolitic ash-flow tuffs erupted from the Bruneau-Jarbidge volcanic center of the Yellowstone hotspot. These tuffs provide evidence for compositional and thermal zonation in pre-eruptive rhyolite magma, and suggest the presence of a long-lived reservoir that was tapped by numerous large explosive eruptions. Pyroxene compositions exhibit discrete compositional modes with respect to Fe and Mg that define a linear spectrum punctuated by conspicuous gaps. Airfall glass compositions also cluster into modes, and the presence of multiple modes indicates tapping of different magma volumes during early phases of eruption. Equilibrium assemblages of pigeonite and augite are used to reconstruct compositional and thermal gradients in the pre-eruptive reservoir. The recurrence of identical compositional modes and of mineral pairs equilibrated at high temperatures in successive eruptive units is consistent with the persistence of their respective liquids in the magma reservoir. Recurrence intervals of identical modes range from 0.3 to 0.9 Myr and suggest possible magma residence times of similar duration. Eruption ages, magma temperatures, Nd isotopes, and pyroxene and glass compositions are consistent with a long-lived, dynamically evolving magma reservoir that was chemically and thermally zoned and composed of multiple discrete magma volumes.

Equilibrium studies of ammonium exchange with Australian natural zeolites

This paper is concerned with the study of the equilibrium exchange of ammonium ions with two natural zeolite samples sourced in Australia from Castle Mountain Zeolites and Zeolite Australia. A range of sorption models including Langmuir Vageler, Competitive Langmuir, Freundlich, Temkin, Dubinin Astakhov and Brouers–Sotolongo were applied in order to gain an insight as to the exchange process. In contrast to most previous studies, non-linear regression was used in all instances to determine the best fit of the experimental data. Castle Mountain natural zeolite was found to exhibit higher ammonium capacity than Zeolite Australia material when in the freshly received state, and this behavior was related to the greater amount of sodium ions present relative to calcium ions on the zeolite exchange sites. The zeolite capacity for ammonium ions was also found to be dependent on the solution normality, with 35–60% increase inuptake noted when increasing the ammonium concentration from 250 to 1000 mg/L. The optimal fit ofthe equilibrium data was achieved by the Freundlich expression as confirmed by use of Akaikes Information Criteria. It was emphasized that the bottle-point method chosen influenced the isotherm profile in several ways, and could lead to misleading interpretation of experiments, especially if the constant zeolite mass approach was followed. Pre-treatment of natural zeolite with acid and subsequently sodium hydroxide promoted the uptake of ammonium species by at least 90%. This paper highlighted the factors which should be taken into account when investigating ammonium ion exchange with natural zeolites.

Re-examination of one-point methods of liquid limit determination

This Paper deals with the analysis of liquid limit of soils, an inferential parameter of universal acceptance. It has been undertaken primarily to re-examine one-point methods of determination of liquid limit water contents. It has been shown by basic characteristics of soils and associated physico-chemical factors that critical shear strengths at liquid limit water contents arise out of force field equilibrium and are independent of soil type. This leads to the formation of a scientific base for liquid limit determination by one-point methods, which hitherto was formulated purely on statistical analysis of data. Available methods (Norman, 1959; Karlsson, 1961; Clayton & Jukes, 1978) of one-point liquid limit determination have been critically re-examined. A simple one-point cone penetrometer method of computing liquid limit has been suggested and compared with other methods. Experimental data of Sherwood & Ryley (1970) have been employed for comparison of different cone penetration methods. Results indicate that, apart from mere statistical considerations, one-point methods have a strong scientific base on the uniqueness of modified flow line irrespective of soil type. Normalized flow line is obtained by normalization of water contents by liquid limit values thereby nullifying the effects of surface areas and associated physico-chemical factors that are otherwise reflected in different responses at macrolevel.Cet article traite de l'analyse de la limite de liquidité des sols, paramètre déductif universellement accepté. Cette analyse a été entreprise en premier lieu pour ré-examiner les méthodes à un point destinées à la détermination de la teneur en eau à la limite de liquidité. Il a été démontré par les caractéristiques fondamentales de sols et par des facteurs physico-chimiques associés que les résistances critiques à la rupture au cisaillement pour des teneurs en eau à la limite de liquidité résultent de l'équilibre des champs de forces et sont indépendantes du type de sol concerné. On peut donc constituer une base scientifique pour la détermination de la limite de liquidité par des méthodes à un point lesquelles, jusqu'alors, n'avaient été formulées que sur la base d'une analyse statistique des données. Les méthodes dont on dispose (Norman, 1959; Karlsson, 1961; Clayton & Jukes, 1978) pour la détermination de la limite de liquidité à un point font l'objet d'un ré-examen critique. Une simple méthode d'analyse à un point à l'aide d'un pénétromètre à cône pour le calcul de la limite de liquidité a été suggérée et comparée à d'autres méthodes. Les données expérimentales de Sherwood & Ryley (1970) ont été utilisées en vue de comparer différentes méthodes de pénétration par cône. En plus de considérations d'ordre purement statistque, les résultats montrent que les méthodes de détermination à un point constituent une base scientifique solide en raison du caractère unique de la ligne de courant modifiée, quel que soit le type de sol La ligne de courant normalisée est obtenue par la normalisation de la teneur en eau en faisant appel à des valeurs de limite de liquidité pour, de cette manière, annuler les effets des surfaces et des facteurs physico-chimiques associés qui sans cela se manifesteraient dans les différentes réponses au niveau macro.

Critical point phenomena in the electrical resistivity of binary liquid systems: Cs2 + CH3CN and CS2 + CH3NO2

Electrical resistance measurements are reported on the binary liquid mixtures CS2 + CH3CN and CS2 + CH3NO2 with special reference to the critical region. Impurity conduction seems to be the dominant mechanism for charge transport. For the liquid mixture filled at the critical composition, the resistance of the system aboveT c follows the relationR=R c−A(T−T c) b withb=0·6±0·1. BelowT c the conductivities of the two phases obey a relation σ2−σ1=B(T c−T)β with β=0·34±0·02, the exponent of the transport coefficient being the same as the exponent of the order parameter, an equilibrium property.

A one point shock capturing kinetic scheme for hyperbolic conservation laws

We have presented a new low dissipative kinetic scheme based on a modified Courant Splitting of the molecular velocity through a parameter φ. Conditions for the split fluxes derived based on equilibrium determine φ for a one point shock. It turns out that φ is a function of the Left and Right states to the shock and that these states should satisfy the Rankine-Hugoniot Jump condition. Hence φ is utilized in regions where the gradients are sufficiently high, and is switched to unity in smooth regions. Numerical results confirm a discrete shock structure with a single interior point when the shock is aligned with the grid.

Temperature dependent free energy surface of polymer folding from equilibrium and quench studies

Langevin dynamics simulation studies have been employed to calculate the temperature dependent free energy surface and folding characteristics of a 500 monomer long linear alkane (polyethylene) chain with a realistic interaction potential. Both equilibrium and temperature quench simulation studies have been carried out. Using the shape anisotropy parameter (S) of the folded molecule as the order parameter, we find a weakly first order phase transition between the high-temperature molten globule and low-temperature rodlike crystalline states separated by a small barrier of the order of k(B)T. Near the melting temperature (580 K), we observe an intriguing intermittent fluctuation with pronounced ``1/f noise characteristics'' between these two states with large difference in shape and structure. We have also studied the possibilities of different pathways of folding to states much below the melting point. At 300 K starting from the all-trans linear configuration, the chain folds stepwise into a very regular fourfold crystallite with very high shape anisotropy. Whereas, when quenched from a high temperature (900 K) random coil regime, we identify a two step transition from the random coiled state to a molten globulelike state and, further, to a anisotropic rodlike state. The trajectory reveals an interesting coupling between the two order parameters, namely, radius of gyration (R-g) and the shape anisotropy parameter (S). The rodlike final state of the quench trajectory is characterized by lower shape anisotropy parameter and significantly larger number of gauche defects as compared to the final state obtained through equilibrium simulation starting from all-trans linear chain. The quench study shows indication of a nucleationlike pathway from the molten globule to the rodlike state involving an underlying rugged energy landscape. (C) 2010 American Institute of Physics. doi:10.1063/1.3509398]

Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics

This paper attempts to unravel any relations that may exist between turbulent shear flows and statistical mechanics through a detailed numerical investigation in the simplest case where both can be well defined. The flow considered for the purpose is the two-dimensional (2D) temporal free shear layer with a velocity difference Delta U across it, statistically homogeneous in the streamwise direction (x) and evolving from a plane vortex sheet in the direction normal to it (y) in a periodic-in-x domain L x +/-infinity. Extensive computer simulations of the flow are carried out through appropriate initial-value problems for a ``vortex gas'' comprising N point vortices of the same strength (gamma = L Delta U/N) and sign. Such a vortex gas is known to provide weak solutions of the Euler equation. More than ten different initial-condition classes are investigated using simulations involving up to 32 000 vortices, with ensemble averages evaluated over up to 10(3) realizations and integration over 10(4)L/Delta U. The temporal evolution of such a system is found to exhibit three distinct regimes. In Regime I the evolution is strongly influenced by the initial condition, sometimes lasting a significant fraction of L/Delta U. Regime III is a long-time domain-dependent evolution towards a statistically stationary state, via ``violent'' and ``slow'' relaxations P.-H. Chavanis, Physica A 391, 3657 (2012)], over flow time scales of order 10(2) and 10(4)L/Delta U, respectively (for N = 400). The final state involves a single structure that stochastically samples the domain, possibly constituting a ``relative equilibrium.'' The vortex distribution within the structure follows a nonisotropic truncated form of the Lundgren-Pointin (L-P) equilibrium distribution (with negatively high temperatures; L-P parameter lambda close to -1). The central finding is that, in the intermediate Regime II, the spreading rate of the layer is universal over the wide range of cases considered here. The value (in terms of momentum thickness) is 0.0166 +/- 0.0002 times Delta U. Regime II, extensively studied in the turbulent shear flow literature as a self-similar ``equilibrium'' state, is, however, a part of the rapid nonequilibrium evolution of the vortex-gas system, which we term ``explosive'' as it lasts less than one L/Delta U. Regime II also exhibits significant values of N-independent two-vortex correlations, indicating that current kinetic theories that neglect correlations or consider them as O(1/N) cannot describe this regime. The evolution of the layer thickness in present simulations in Regimes I and II agree with the experimental observations of spatially evolving (3D Navier-Stokes) shear layers. Further, the vorticity-stream-function relations in Regime III are close to those computed in 2D Navier-Stokes temporal shear layers J. Sommeria, C. Staquet, and R. Robert, J. Fluid Mech. 233, 661 (1991)]. These findings suggest the dominance of what may be called the Kelvin-Biot-Savart mechanism in determining the growth of the free shear layer through large-scale momentum and vorticity dispersal.

Equilibrium phases in the multiferroic BiFeO3-PbTiO3 system - a revisit

The(1-x) BiFeO3-(x) PbTiO3 solid solution exhibiting a Morphotropic Phase Boundary (MPB) has attracted considerable attention recently because of its unique features such as multiferroic, high Curie point (T-C similar to 700 degrees C) and giant tetragonality (c/a -1 similar to 0.19). Different research groups have reported different composition range of MPB for this system. In this work we have conclusively proved that the wide composition range of MPB reported in the literature is due to kinetic arrest of the metastable rhombohedral phase and that if sufficient temperature and time is allowed the metastable phase disappears. The genuine MPB was found to be x=0.27 for which the tetragonal and the rhombohedral phases are in thermodynamic equilibrium. In-situ high temperature structural study of x=0.27 revealed the sluggish kinetics associated with the temperature induced structural transformation. Neutron powder diffraction study revealed that themagnetic ordering at room temperature occurs in the rhombohedral phase. The magnetic structure was found to be commensurate G-type antiferromagnetic with magnetic moments parallel to the c-direction (of the hexagonal cell). The present study suggests that the equilibrium properties in this solid solution series should be sought for x=0.27.

Essays on Correlated Equilibrium and Voter Turnout

This thesis consists of three essays in the areas of political economy and game theory, unified by their focus on the effects of pre-play communication on equilibrium outcomes.

Communication is fundamental to elections. Chapter 2 extends canonical voter turnout models, where citizens, divided into two competing parties, choose between costly voting and abstaining, to include any form of communication, and characterizes the resulting set of Aumann's correlated equilibria. In contrast to previous research, high-turnout equilibria exist in large electorates and uncertain environments. This difference arises because communication can coordinate behavior in such a way that citizens find it incentive compatible to follow their correlated signals to vote more. The equilibria have expected turnout of at least twice the size of the minority for a wide range of positive voting costs.

In Chapter 3 I introduce a new equilibrium concept, called subcorrelated equilibrium, which fills the gap between Nash and correlated equilibrium, extending the latter to multiple mediators. Subcommunication equilibrium similarly extends communication equilibrium for incomplete information games. I explore the properties of these solutions and establish an equivalence between a subset of subcommunication equilibria and Myerson's quasi-principals' equilibria. I characterize an upper bound on expected turnout supported by subcorrelated equilibrium in the turnout game.

Chapter 4, co-authored with Thomas Palfrey, reports a new study of the effect of communication on voter turnout using a laboratory experiment. Before voting occurs, subjects may engage in various kinds of pre-play communication through computers. We study three communication treatments: No Communication, a control; Public Communication, where voters exchange public messages with all other voters, and Party Communication, where messages are exchanged only within one's own party. Our results point to a strong interaction effect between the form of communication and the voting cost. With a low voting cost, party communication increases turnout, while public communication decreases turnout. The data are consistent with correlated equilibrium play. With a high voting cost, public communication increases turnout. With communication, we find essentially no support for the standard Nash equilibrium turnout predictions.

Analysis of steric mass-action model for protein adsorption equilibrium onto porous anion-exchange adsorbent

The ion-exchange equilibrium of bovine serum albumin (BSA) to an anion exchanger, DEAE Spherodex M, has been studied by batch adsorption experiments at pH values ranging from 5.26 to 7.6 and ionic strengths from 10 to 117.1 mmol/l. Using the unadjustable adsorption equilibrium parameters obtained from batch experiments, the applicability of the steric mass-action (SMA) model was analyzed for describing protein ion-exchange equilibrium in different buffer systems. The parametric sensitivity analysis was performed by perturbing each of the model parameters, while holding the rest constant. The simulation results showed that, at high salt concentrations or low pHs close to the isoelectric point of the protein, the precision of the model prediction decreased. Parametric sensitivity analysis showed that the characteristic charge and protein steric factor had the largest effects on ion-exchange equilibrium, while the effect of equilibrium constant was about 70%-95% smaller than those of characteristic charge and steric factor under all conditions investigated. The SMA model with the relationship between the adjusted characteristic charge and the salt concentration can well predict the protein adsorption isotherms in a wide pH range from 5.84 to 7.6. It is considered that the SMA model could be further improved by taking into account the effect of salt concentration on the intermolecular interactions of proteins. (c) 2006 Elsevier Ltd. All rights reserved.